instruction stringlengths 31 53.1k | completion stringlengths 2 524k | __original_row_idx int64 0 50k | conversations listlengths 2 2 |
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I got stuck in Ladner's Proof while reading "Computational Complexity: A Modern Approach" by Sanjeev Arora and Boaz Barak. Pardon me if I'm missing something really obvious here but the authors do the following:
For every function $H\colon\mathbb{N}\to\mathbb{N}$ define
$$SAT_H=\{\psi01^{n^{H(n)}}: \psi \in SAT \ and \... | Your confusion seems to stem from a misunderstanding of the nature of the strings in \( SAT_H \) and the machine \( M_i \).
Firstly, let's clarify the definition of \( SAT_H \). The set \( SAT_H \) is defined as:
\[
SAT_H = \{ \psi 01^{n^{H(n)}} : \psi \in SAT \text{ and } n = |\psi| \}
\]
This means that for a bool... | 8,983 | [
{
"from": "human",
"value": "I got stuck in Ladner's Proof while reading \"Computational Complexity: A Modern Approach\" by Sanjeev Arora and Boaz Barak. Pardon me if I'm missing something really obvious here but the authors do the following:\nFor every function $H\\colon\\mathbb{N}\\to\\mathbb{N}$ define\n... |
Aesop Fables
-1 ¬engine ¬Greek
10-20
bankrupt louise
input: 10-28 loop victim
st = new String(out); st = StringBuffer(st).insert(1,"M").toString();
The life and times of
41st
Return (10-28)
CLARIFICATION: -1 is "minus one"
Hint
A MUCH MUCH better title would be Gratifying Enigmatic Brainteaser
Hint
Listen to so... | It appears you're presenting a riddle or a puzzle that blends various elements, possibly referencing Aesop's Fables and requiring some decoding or interpretation. Here’s a breakdown of the hints and information you’ve provided:
1. **Aesop Fables**: These are a collection of stories that typically convey moral lessons.... | 22,801 | [
{
"from": "human",
"value": "Aesop Fables\n-1 ¬engine ¬Greek\n10-20\nbankrupt louise\ninput: 10-28 loop victim\nst = new String(out); st = StringBuffer(st).insert(1,\"M\").toString();\nThe life and times of \n41st \nReturn (10-28)\nCLARIFICATION: -1 is \"minus one\"\nHint\n\n A MUCH MUCH better title would ... |
I am constantly bombarded with links to articles and videos by professors, doctors, PhDs and the likes who claim that vaccines are harmful, dangerous and ineffective at preventing infectious diseases. I am also bombarded with links to articles and videos by investigative journalists who claim that pro-vaccine scientist... | Your aunt's arguments highlight a common tension in discussions about science, trust, and belief in the credibility of information. Navigating this landscape can indeed be challenging, especially when it involves topics like vaccines that have significant public health implications. Here are some points to consider reg... | 46,529 | [
{
"from": "human",
"value": "I am constantly bombarded with links to articles and videos by professors, doctors, PhDs and the likes who claim that vaccines are harmful, dangerous and ineffective at preventing infectious diseases. I am also bombarded with links to articles and videos by investigative journal... |
I'm working on creating an application which will render a spectrogram of the audio in an MP3 file. I'm having some trouble, though - after running the audio samples through my program, the resulting magnitudes are all very close together, and don't seem to be very patterned like one would expect. I'm coloring my spect... | It's great that you've already narrowed down the problem by testing with a simple 1000 Hz sine wave! This suggests that your basic pipeline for computing the STFT and rendering the spectrogram is functional, but there are a few areas you can check that might be leading to the issues you're experiencing with the MP3 fil... | 7,463 | [
{
"from": "human",
"value": "I'm working on creating an application which will render a spectrogram of the audio in an MP3 file. I'm having some trouble, though - after running the audio samples through my program, the resulting magnitudes are all very close together, and don't seem to be very patterned lik... |
Just your basic New Year's puzzle.
What do the following quantities have in common?
6 gigabytes
35 hours
50 hours
1 millimeter
3 imperial gallons
Cryptic hint:
Briefly, cover your bases.
Explicit hint:
Use abbreviations, and think "basic" in a mathematical sense.
| The quantities you've listed all relate to the concept of "basic" units in various systems of measurement, and they can each be expressed in terms of base units or abbreviated forms commonly used in their respective fields:
1. **6 gigabytes** - GB (gigabytes) is a unit of digital information storage.
2. **35 hours** -... | 31,161 | [
{
"from": "human",
"value": "Just your basic New Year's puzzle.\nWhat do the following quantities have in common?\n\n6 gigabytes\n35 hours\n50 hours\n1 millimeter\n3 imperial gallons\n\nCryptic hint:\n\n Briefly, cover your bases.\n\nExplicit hint:\n\n Use abbreviations, and think \"basic\" in a mathematica... |
Your task is to write a program or function that outputs the first character of its source code, then the second, then the third... each time it is run.
For example, if your program was foo in language bar in file baz.bar, then you should get output similar to this:
λ bar baz.bar
f
λ bar baz.bar
o
λ bar baz.bar
o
You... | Here's a solution in Python that fulfills the requirements of printing each character of its source code one by one upon each execution:
```python
s='s=%r;print(s%%s)'
print(s%s)
```
### Explanation:
- `s` holds the string of the source code itself, with a placeholder `%r` for the string representation of `s`.
- The ... | 49,291 | [
{
"from": "human",
"value": "Your task is to write a program or function that outputs the first character of its source code, then the second, then the third... each time it is run.\nFor example, if your program was foo in language bar in file baz.bar, then you should get output similar to this:\nλ bar baz... |
It had finally arrived! PSE's annual Christmas advent calendar for 2016! The one thing that I had been waiting for all year!
I tore open the packaging and let out a delighted gasp at this year's new look. Tentatively I reached for the first door, and tore it off, hardly able to keep in my enthusiasm. But this year, I ... | Sure! Let's analyze the letters you've provided, which seem to form a grid:
```
A g e t l
N U a i s
b i v o v
t h D R i
n s O
```
From the context, it seems that the letters might be rearranged or deciphered to reveal a clue or a specific image related to the advent calendar.
If we look closely, we can see the w... | 26,439 | [
{
"from": "human",
"value": "It had finally arrived! PSE's annual Christmas advent calendar for 2016! The one thing that I had been waiting for all year!\nI tore open the packaging and let out a delighted gasp at this year's new look. Tentatively I reached for the first door, and tore it off, hardly able t... |
I think the phrase 'Look within' is used often in the context of meditation. If someone can actually perform the act of looking within, it implicitly means that someone is currently 'without', and thus looking 'within' from 'without'.
Perhaps I totally misunderstand the whole concept of 'looking within'. If someone wou... | Your exploration of the concepts of "looking within" and "looking without" is profound and resonates with various philosophical, psychological, and meditative traditions. Let's unpack these ideas and offer a functional perspective that might help you integrate these experiences and thoughts.
### 1. **Understanding the... | 43,262 | [
{
"from": "human",
"value": "I think the phrase 'Look within' is used often in the context of meditation. If someone can actually perform the act of looking within, it implicitly means that someone is currently 'without', and thus looking 'within' from 'without'.\nPerhaps I totally misunderstand the whole c... |
This is an ascii-art challenge where you will draw ascii-art showing a person "jumping" off the top of a building.
The building
Input given will be a group of rectangular buildings. You may assume buildings are not "stacked on top of each other", hence only one row of buildings. This is the standard format of a buildi... | Here's a Python implementation of the ASCII art challenge, where the person jumps off the top of a building. The input consists of building definitions and a specified index of the building from which the jump is made. This implementation uses simple string operations to create the desired output.
```python
def jump_b... | 45,949 | [
{
"from": "human",
"value": "This is an ascii-art challenge where you will draw ascii-art showing a person \"jumping\" off the top of a building.\n\nThe building\nInput given will be a group of rectangular buildings. You may assume buildings are not \"stacked on top of each other\", hence only one row of bu... |
Isn't Popper's epistemology a form of Argument from Ignorance? "We assume it is true if it has not (yet) been falsified."
But the fact that it hasn't been falsified doesn't make it true; assuming that would be an Argument from Ignorance.
In other words: to what extent is Popper's reasoning valid in the context of the ... | Karl Popper's epistemology, particularly his falsificationism, indeed presents a different perspective than traditional forms of verificationism. In Popper's view, scientific theories can never be definitively proven true; they can only be falsified. He argued that a theory is scientific if it is falsifiable—that is, i... | 25,897 | [
{
"from": "human",
"value": "Isn't Popper's epistemology a form of Argument from Ignorance? \"We assume it is true if it has not (yet) been falsified.\" \nBut the fact that it hasn't been falsified doesn't make it true; assuming that would be an Argument from Ignorance.\nIn other words: to what extent is Po... |
Gapped Hamiltonians with a ground-state having long-range entanglement (LRE), are said to have topological order (TO), while if the ground state is short-range entangled (SRE) they are in the trivial phase. The topological properties of a system with topological order (such as anyonic statistics, ground-state degenerac... | Your question touches on an interesting aspect of the classification of phases of matter, particularly in the context of topological superconductors and their relationship to symmetry-enriched topological (SET) states.
To clarify, symmetry-protected topological (SPT) states and symmetry-enriched topological (SET) stat... | 19,594 | [
{
"from": "human",
"value": "Gapped Hamiltonians with a ground-state having long-range entanglement (LRE), are said to have topological order (TO), while if the ground state is short-range entangled (SRE) they are in the trivial phase. The topological properties of a system with topological order (such as a... |
My dilemma is that somehow I always get stuck thinking philosophically about things.
One example is mathematics. For some reason, I always start thinking philosophically.
Like word problems; I start thinking why did I interpret the problem this way. Why did I make these assumptions? HOW do you make assumptions?
I just ... | It's understandable to feel overwhelmed by philosophical thinking, especially when it spills over into areas where you might prefer to find clear, concrete answers, like mathematics. Here are some strategies that might help you manage this tendency:
1. **Set Boundaries**: Create a specific time or context for engaging... | 3,175 | [
{
"from": "human",
"value": "My dilemma is that somehow I always get stuck thinking philosophically about things.\nOne example is mathematics. For some reason, I always start thinking philosophically.\nLike word problems; I start thinking why did I interpret the problem this way. Why did I make these assump... |
Why would Grandpa chose these folks?
Grandpa likes Mozart but not Tchaikovsky
Grandpa likes Queen Victoria but not Mary, Queen of Scots
Grandpa likes Gandhi but not Mandela
Hmmm.
| It seems that Grandpa's preferences may relate to specific characteristics or traits of the individuals or figures he favors. Here's a possible explanation for each pair:
1. **Mozart vs. Tchaikovsky**: Grandpa might prefer Mozart because he embodies the classical style of music, characterized by clarity and structure,... | 44,940 | [
{
"from": "human",
"value": "Why would Grandpa chose these folks?\n\nGrandpa likes Mozart but not Tchaikovsky\nGrandpa likes Queen Victoria but not Mary, Queen of Scots\nGrandpa likes Gandhi but not Mandela\n\nHmmm. \n"
},
{
"from": "gpt",
"value": "It seems that Grandpa's preferences may relat... |
My question expands on a related question on the link, Why is the clique problem NP-complete?
In that post the author argued that while the $k$-clique problem is NP-complete; for a fixed $k$ the $k$-clique problem is polynomial time solvable. The question "Prove that the presence of 3-clique in a graph can be decided ... | The distinction you're making between the fixed \( k \)-clique problem and the general \( k \)-clique problem is an important one in computational complexity theory.
1. **Fixed \( k \)**: When \( k \) is fixed, the \( k \)-clique problem can be solved in polynomial time with respect to the size of the graph, even thou... | 21,710 | [
{
"from": "human",
"value": "My question expands on a related question on the link, Why is the clique problem NP-complete? \nIn that post the author argued that while the $k$-clique problem is NP-complete; for a fixed $k$ the $k$-clique problem is polynomial time solvable. The question \"Prove that the pres... |
Five pilgrims approach while you watch at a turnpike on the road, headed up to Ruffle Downs. They have not the appearance of robbers, so you rise, exit your cottage, and shout out to them: “Pilgrims to the crater may pass untolled.”
You return to the cottage, climbing the two steps and reaching down to open the door.... | As you lay on the ground, gazing up at the prince of airs, you feel a mix of awe and trepidation. The fetiche, an ornate trinket shimmering with magical energy, catches your attention. You instinctively reach out to touch it, drawn by an otherworldly compulsion.
But just as your fingers brush against the fetiche, the ... | 12,009 | [
{
"from": "human",
"value": "Five pilgrims approach while you watch at a turnpike on the road, headed up to Ruffle Downs. They have not the appearance of robbers, so you rise, exit your cottage, and shout out to them: “Pilgrims to the crater may pass untolled.”\nYou return to the cottage, climbing the two... |
Couldn't the type inference in Apple's new programming language Swift had been done more aggressive? For instance why can't the return type of a function be deduced?
func sayHello(personName: String) -> String {
let greeting = "Hello, " + personName + "!"
return greeting
}
| In Swift, type inference is indeed quite powerful and can often infer the types of variables and constants based on their initial values or context. However, there are specific design choices regarding function return types that influence how type inference works in this context.
In Swift, the return type of a functio... | 6,180 | [
{
"from": "human",
"value": "Couldn't the type inference in Apple's new programming language Swift had been done more aggressive? For instance why can't the return type of a function be deduced?\nfunc sayHello(personName: String) -> String {\n let greeting = \"Hello, \" + personName + \"!\"\n return gre... |
Can anyone help me solve this puzzle?
| Of course! Please provide the details of the puzzle, and I'll do my best to help you solve it. | 38,744 | [
{
"from": "human",
"value": "\nCan anyone help me solve this puzzle?\n"
},
{
"from": "gpt",
"value": "Of course! Please provide the details of the puzzle, and I'll do my best to help you solve it."
}
] |
I am trying to analyse a weighted multi-graph which represents a snapshot of a rail network for a particular day. As such, the vertices of the graph can be considered stations and the weighted edges represent the time taken to travel from one station to another.
For any particular vertex, there might be multiple edges ... | Your problem involves finding the shortest paths in a rail network while accounting for real-life constraints such as scheduled departure times and transfer waiting times. Here are a few algorithmic approaches and techniques you can consider for this complex scenario:
### 1. **Timed Graphs / Time-Dependent Shortest Pa... | 49,413 | [
{
"from": "human",
"value": "I am trying to analyse a weighted multi-graph which represents a snapshot of a rail network for a particular day. As such, the vertices of the graph can be considered stations and the weighted edges represent the time taken to travel from one station to another.\nFor any particu... |
I'm looking into discharge models, specifically for combustion prcesses, and I'm swamped by the number of different types of plasmas and their respective treatments (thermal plasmas, non-thermal plasmas, different degrees of inoization, excitation levels, diluted systems, etc. etc.).
I'm looking for an overview, maybe... | Your inquiry into discharge models for combustion processes and the various types of plasmas is indeed a complex but fascinating topic. Given the diversity of plasma types and their characteristics, a thorough overview can help clarify the distinctions and applications. Here’s a structured overview:
### 1. Types of Pl... | 6,417 | [
{
"from": "human",
"value": "I'm looking into discharge models, specifically for combustion prcesses, and I'm swamped by the number of different types of plasmas and their respective treatments (thermal plasmas, non-thermal plasmas, different degrees of inoization, excitation levels, diluted systems, etc. e... |
The question is often asked: If God exists, how do we explain all the evil in this world? Did God allow the Holocaust? Etc. But one could also ask the reverse: If God does not exist, how do we explain all the good in the world? All the charities that operate of the goodwill of the public? All the doctors working in Som... | You've raised profound questions that touch on ethics, morality, and the nature of human existence, which have been debated by philosophers, theologians, and scientists for centuries. Here are some perspectives that may help explore these issues:
### 1. **Naturalism and Ethics**
Naturalism posits that everything aris... | 32,910 | [
{
"from": "human",
"value": "The question is often asked: If God exists, how do we explain all the evil in this world? Did God allow the Holocaust? Etc. But one could also ask the reverse: If God does not exist, how do we explain all the good in the world? All the charities that operate of the goodwill of t... |
Can a carrier of contradicting thoughts be called hypocrite?
We know when people do/pretend something which he does not believe/poses, we call them hypocrite. Now what will happen if someone does not reflect his contradicting thoughts in practice? Can we still call him/her hypocrite. For example, If I believe everyone ... | The term "hypocrite" typically refers to someone who claims to have certain beliefs, values, or principles but acts in a way that contradicts those claims. In your example, if someone believes in treating everyone equally but harbors hatred for followers of a specific religion, the label of "hypocrite" may depend on th... | 46,592 | [
{
"from": "human",
"value": "Can a carrier of contradicting thoughts be called hypocrite?\nWe know when people do/pretend something which he does not believe/poses, we call them hypocrite. Now what will happen if someone does not reflect his contradicting thoughts in practice? Can we still call him/her hypo... |
Ideally 2 objects of different mass and weight will hit the floor at same time because they face same gravitational pull and accelerate. Will the terminal velocity of both objects be same also? and with that theory does terminal velocity of every object is same ideally?
| Terminal velocity is the constant speed that a freely falling object eventually reaches when the force of air resistance (drag) is equal to the force of gravity acting on the object. At terminal velocity, the net force acting on the object is zero, and it no longer accelerates.
The terminal velocity of an object depen... | 17,849 | [
{
"from": "human",
"value": "Ideally 2 objects of different mass and weight will hit the floor at same time because they face same gravitational pull and accelerate. Will the terminal velocity of both objects be same also? and with that theory does terminal velocity of every object is same ideally?\n"
},
... |
In a conversation with some friends, we agreed that people should not judge by skin color, which by now should gradually become a more common opinion to society.
But I said that sometimes, conscious or not, I make a pre-judgment based on the clothing one's using. So if a person - of any skin color - comes in my directi... | Your question touches on important themes related to judgment, prejudice, and the societal context in which we operate. It's understandable to have concerns about safety, especially in environments where crime is prevalent. However, it's crucial to differentiate between instinctive reactions and conscious, informed jud... | 34,573 | [
{
"from": "human",
"value": "In a conversation with some friends, we agreed that people should not judge by skin color, which by now should gradually become a more common opinion to society.\nBut I said that sometimes, conscious or not, I make a pre-judgment based on the clothing one's using. So if a person... |
A nice simple one
Input
Given a boolean array (Or an acceptable alternative), you can assume the array will never be more than 32 elements long.
[false, false, true, false, false]
Output
Invert every element of the array and output it.
[true, true, false, true, true]
Rules
You can write a full program or just a func... | Here's a simple solution in Python that inverts every element of the boolean array:
```python
def invert(arr):
return [not x for x in arr]
# Test cases
print(invert([false, false, true, false, false])) # Output: [true, true, false, true, true]
print(invert([true, false])) # Output: [false, t... | 18,112 | [
{
"from": "human",
"value": "A nice simple one\nInput\nGiven a boolean array (Or an acceptable alternative), you can assume the array will never be more than 32 elements long.\n[false, false, true, false, false]\n\nOutput\nInvert every element of the array and output it.\n[true, true, false, true, true]\n\n... |
After a recent court case where two men were convicted of torturing, raping and eventually killing a young woman, a lot of victim blaming went on in the media and in many private conversations.
I personally find this deeply disturbing and I fail to see the purpose of blaming and/or trying to defame the victims. I am u... | Victim blaming is a complex and deeply troubling phenomenon that can stem from a variety of psychological, social, and cultural factors. Here’s a breakdown of the types of people who might engage in victim blaming, the reasons behind it, and potential counterarguments grounded in social ethics and values.
### Types of... | 45,527 | [
{
"from": "human",
"value": "After a recent court case where two men were convicted of torturing, raping and eventually killing a young woman, a lot of victim blaming went on in the media and in many private conversations. \nI personally find this deeply disturbing and I fail to see the purpose of blaming a... |
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