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> Bullshit. Your claim that there is no abstraction error in linear algebra (when run on computers - we're in subdiscussion related to programming) is false. T

> Bullshit. Your claim that there is no abstraction error in linear algebra (when run on computers - we're in subdiscussion related to programming) is false. The fact that you had to change my statement to add computers to it already makes it clear that you know my statement is correct. Don't put words into my mouth to prove statements that I have never made false. You also failed to realize that the tweaked statement you put in to my mouth is still correct! You fail to realise that we can prove theorems about linear algebra using computers without actually using floating point numbers. Linear algebra can be infinite dimensional and not just be defined on the complex field, and this doesn't introduce any errors in to the abstraction or theorems being proved, with or without computers. Your assumption that linear algebra on computers is exclusively about floating point number crunching tells me that you don't understand what abstraction linear algebra represents. Linear algebra is the study of linear maps. This is a good book for you to get started [1] You also failed to address the gazillions of abstractions that don't have errors, some of which I have listed along with linear algebra. For those familiar with proofs, Just one counter example can prove your sweeping statement "all abstractions have errors" false. We are discussing math, not physics. And if you want to restrict yourself to computable functions- modulo arithmetic with groups, rings and fields suffices as a counter example. It isn't even clear what you mean by abstraction at all. > We're talking about learning as it relates to abstraction. The OP was not discussing learning at all. Your segue into machine learning concepts is completely unrelated to the topic being discussed. So is game theory. I am familiar with virtually all the topics you are discussing, so you can skip the citations. I find no coherence to any of your segues. > You're just ignoring that these things when implemented in computers actually do have error, because you find it convenient. You are completely out of touch [2][3] [1] https://linear.axler.net/LinearAbridged.pdf https://linear.axler.net/LinearAbridged.pdf [2] https://en.wikipedia.org/wiki/Univalent_foundations https://en.wikipedia.org/wiki/Univalent_foundations [3] Mathematician Kevin Buzzard https://www.microsoft.com/en-us/research/video/the-future-of-mathematics/ https://www.microsoft.com/en-us/research/video/the-future-of...

JoshCole 4y ago
> I am familiar with virtually all the topics you are discussing, so you can skip the citations. I really can't, because other people might believe you if I don't; I don't hate them. I want them to know the truth. So I'll oppose you strongly, for their sake, so they can discriminate between my counterintuitive truth and your rejection of the truth on that basis of confusion. Go read page 173 of Artificial Intelligence: A Modern Approach. I'll quote Norvig here. "Because calculating optimal decisions in complex games is intractable, all algorithms must make some assumptions and approximations." Now go to page 172. I'll quote Norvig again. "One way to deal with this huge number is with abstraction: i.e. by treating similar hands as identical. For example, it is very important which aces and kings are in a hand, but whether hand has a 4 or a 5 is not as important, and can be abstracted away." But, the discerning might ask, what of the talk of the infinite? Why does Josh speak of such an absurd thing? Isn't it irrelevant? It is not. Go to page 611, "Non-Cooperative Game Theory". I'll quote him again for you, "With this observation in mind, the minimax trees can be thought of as having infinitely many mixed strategies the first player can choose." The thing to notice in this quote is that we have a simple game - very simple. Yet Norvig just explained that in this simple game we have the quality of a tree of infinite size. This growth to infinite is actually very normal - mixed strategies are continuous and we have proofs that mixed strategies are the solution for a variety of different games involving imperfect information.
JoshCole 4y ago
> You fail to realise that we can prove theorems about linear algebra Obviously I realize we can prove theorems. If I didn't realize it was possible to prove things I wouldn't claim things were provable. This is false by contradiction with my previous statements. Your worldview of me isn't consistent. > You also failed to address the gazillions of abstractions that don't have errors, some of which I have listed along with linear algebra. Why should I have to prove that abstractions without error don't exist? They do. I never claimed they didn't. My point was that abstractions with error reduce computational complexity. This gives them room to outcompete perfect abstraction for sufficiently complex problems. It honestly seems insane to me to not believe what I'm saying is true, because it is true. I can't fathom how the concept would be impossible to grasp. Showing that we regularly use error filled abstractions is more important than demonstrating something I don't intend to show. > The OP was not discussing learning at all. I literally quoted him saying there was never a reason to teach bad abstractions. Teaching is related to learning. Abstractions are related to abstractions. So abstraction and learning were a topic of discussion. Even the original post we're under is about teaching programming technique. Which is about learning, because of the relationship between teaching and learning. It is also about abstraction, because problem modeling is very related to abstraction. > "all abstractions have errors" Ctrl + F shows no instance of this except for you saying it. What do you think I'm claiming? I'm really confused? You seem to think I'm saying something I'm definitely not saying. Notice how when I said it I put parantheses and explained my reasoning as to why I felt your claim was your claim? You meanwhile misquote me. Strict quotes imply actual attribution, but I never said what you claimed I said. I don't want to talk to you anymore. I very much don't appreciate your comparison to someone who just makes stuff up. I found that very rude and insulting. A kind person would help correct me if my reasoning was wrong and I would appreciate it, but you haven't done that. When you quoted me, it wasn't even something I said or tried to argue. If you were trying to make someone have a worse day, congratulations, you did.
- random314 4y ago
  >>>> One abstraction that is very useful is linear algebra which is an abstraction without errors. >>> Bullshit. Your claim that there is no abstraction error in linear algebra (when run on computers - we're in subdiscussion related to programming) is false >> You fail to realise that we can prove theorems about linear algebra USING COMPUTERS > Obviously I realize we can prove theorems. If I didn't realize it was possible to prove things You have been arguing in bad faith by either putting words in my mouth (when run on computers) or deleting key phrases from my reply (USING COMPUTERS - reinserted by me) These 2 statements by you contradict each other "Bullshit, Your claim that there is no abstraction error in linear algebra (when run on computers - we're in subdiscussion related to programming) is false " " Obviously I realize we can prove theorems" -----> USING COMPUTERS It is clear that you thought of computers as IEEE floating point number crunching machines, with implicit floating point errors. All of your arguments rested on this irrelevant point. You even condescended to teach me about floating points using citations not needed by anyone who has attended CS101. You failed to realize that finite sized representations of computable real numbers exist, by definition[1]. One such representation could be a finite sum on surd basis, instead of using a binary basis eg sqrt(2) instead of 1.414.... and the most general form is a theorem prover like Lean. All of these misunderstandings in your head because you failed to realize the gist of the Church Turing thesis ' - Everything that you do with your brain and paper can be duplicated on a computer. In any case, I am glad you learned something today. Computers don't relate to math via IEEE floating pointing numbers, the connection is a lot deeper[1]. You won't acknowledge this, but frankly speaking, I can't really stand out- jargoning pretending to be an honest discussion. I did give an opportunity to you to correct yourself with my first comment. But you only doubled down - more jargon, bad paraphrasing of diagonalization, putting words in my mouth, followed by removing key phrases from my replies amongst other bad faith arguments. [1] https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis To establish that a function is computable by Turing machine, it is usually considered sufficient to give an informal English description of how the function can be effectively computed, and then conclude "by the Church–Turing thesis" that the function is Turing computable
JoshCole 4y ago
> The OP was not discussing learning at all Yes they were. They were discussing teaching, which is related to learning. Moreover, the person they were responding to - they also were talking about learning. They talked about how it was good to learn an abstraction that wasn't perfect. Even the article is about whether we should teach one abstraction or another. > You are completely out of touch Gaslighting is abusive. Stop abusing me. > I am familiar with virtually all the topics you are discussing, so you can skip the citations. I find no coherence to any of your segues. This is an argument from authority. It is a fallacious argument. If my segue is incorrect, you need to show it from the structure of the argument, not by appealing to your authority, which is irrelevant; you might be great - I'm not saying your not. You are great; I'm not saying you're not. I'm sure you're intelligent and smart and witty and cool. But who we are - it doesn't matter. We're irrelevant. The ideas are all that matters. If I'm wrong - why isn't chess solved? Why do we approximate solutions? Meanwhile, why is checkers solved? Why do games with simpler graphs get solved perfectly but more complex games with more complex graphs not get solved perfectly? Please back up the ideas you would be advancing were it the case you actually disagreed with what I claim is provable. If you actually understood my point, than you should know that the opposite of my point isn't that perfect abstractions exist - it is that the run time of specific learning algorithms aren't correlated with their input size. Your trying to get me to defend conclusions I didn't make, treating me like I'm stupid and comparing me to people who are rambling. You are being abusive. Lying. Gaslighting. Attacking me as a person rather than my ideas. Appealing to authority. I'm sorry that I thought you were referring to linear algebra when used as abstraction in the way I meant it - I'm talking about computational abstractions; stuff with many dimensions, compressed to be in fewer dimensions. That happens when we do linear algebra on computers in practice. I thought it was reasonable to point this out, because my claim is closer to "abstractions with errors in them can be useful" than it is to "abstractions without error don't exist". But I feel like you do understand me in this - because you seem desperate not to admit this. To pretend we can represent all things in finite space, when we can't, because the infinite things can't all be represented in finite space. And it seems to me the only reason you would be so desperate not to admit this - to try and throw up so much confusion about this idea - is that you do understand me. And you understand that if you surrender on that point, you admit I'm right. So I think you already know I'm right. And you're just being mean intentionally. I think I probably offended you. It best explains the inconsistency in your reasoning. So I'm sorry about that - and I assume it was sometime in the past, because my first replies didn't deserve your malice.
JoshCole 4y ago
> It isn't even clear what you mean by abstraction at all. I'm using abstraction in the sense of 'blueprint abstraction' from game theory. This is basically compression of the input to your learning algorithm. There exists lossless compression - perfect one to one abstraction. There is also lossy compression - given one compressed form it could be any number of uncompressed forms. Abstraction with error is then compression with error. What I was trying to prove and what I still believe to have proved is that some algorithms when given an input of unbounded size have the property of not terminating. What I then tried to show was that abstraction breaks the proof of non-termination, because it breaks the core assumption of diagnolization - that there is a one to one mapping. So the proof of non-termination doesn't hold. > I am familiar with virtually all the topics you are discussing, so you can skip the citations. I literally linked to a paper that used abstractions in the way I meant it. So maybe you should not skip citations? Clearly you don't know the fields as well as you think you do. > I find no coherence to any of your segues. It isn't a segue; it is what you asked for. I gave you a proof that unabstracted learning problems can terminate where abstracted problems terminate. > You are completely out of touch [2][3] This is such an ironic statement; here we were discussing what abstraction techniques we should teach when teaching computer programming and you're trying to complain that I'm the one who is out of touch when I say computers use abstractions. They definitely do. In fact, they use abstractions with error.

JoshCole 4y ago

> I am familiar with virtually all the topics you are discussing, so you can skip the citations. I really can't, because other people might believe you if I don't; I don't hate them. I want them to know the truth. So I'll oppose you strongly, for their sake, so they can discriminate between my counterintuitive truth and your rejection of the truth on that basis of confusion. Go read page 173 of Artificial Intelligence: A Modern Approach. I'll quote Norvig here. "Because calculating optimal decisions in complex games is intractable, all algorithms must make some assumptions and approximations." Now go to page 172. I'll quote Norvig again. "One way to deal with this huge number is with abstraction: i.e. by treating similar hands as identical. For example, it is very important which aces and kings are in a hand, but whether hand has a 4 or a 5 is not as important, and can be abstracted away." But, the discerning might ask, what of the talk of the infinite? Why does Josh speak of such an absurd thing? Isn't it irrelevant? It is not. Go to page 611, "Non-Cooperative Game Theory". I'll quote him again for you, "With this observation in mind, the minimax trees can be thought of as having infinitely many mixed strategies the first player can choose." The thing to notice in this quote is that we have a simple game - very simple. Yet Norvig just explained that in this simple game we have the quality of a tree of infinite size. This growth to infinite is actually very normal - mixed strategies are continuous and we have proofs that mixed strategies are the solution for a variety of different games involving imperfect information.

JoshCole 4y ago

> You fail to realise that we can prove theorems about linear algebra Obviously I realize we can prove theorems. If I didn't realize it was possible to prove things I wouldn't claim things were provable. This is false by contradiction with my previous statements. Your worldview of me isn't consistent. > You also failed to address the gazillions of abstractions that don't have errors, some of which I have listed along with linear algebra. Why should I have to prove that abstractions without error don't exist? They do. I never claimed they didn't. My point was that abstractions with error reduce computational complexity. This gives them room to outcompete perfect abstraction for sufficiently complex problems. It honestly seems insane to me to not believe what I'm saying is true, because it is true. I can't fathom how the concept would be impossible to grasp. Showing that we regularly use error filled abstractions is more important than demonstrating something I don't intend to show. > The OP was not discussing learning at all. I literally quoted him saying there was never a reason to teach bad abstractions. Teaching is related to learning. Abstractions are related to abstractions. So abstraction and learning were a topic of discussion. Even the original post we're under is about teaching programming technique. Which is about learning, because of the relationship between teaching and learning. It is also about abstraction, because problem modeling is very related to abstraction. > "all abstractions have errors" Ctrl + F shows no instance of this except for you saying it. What do you think I'm claiming? I'm really confused? You seem to think I'm saying something I'm definitely not saying. Notice how when I said it I put parantheses and explained my reasoning as to why I felt your claim was your claim? You meanwhile misquote me. Strict quotes imply actual attribution, but I never said what you claimed I said. I don't want to talk to you anymore. I very much don't appreciate your comparison to someone who just makes stuff up. I found that very rude and insulting. A kind person would help correct me if my reasoning was wrong and I would appreciate it, but you haven't done that. When you quoted me, it wasn't even something I said or tried to argue. If you were trying to make someone have a worse day, congratulations, you did.

random314 4y ago
>>>> One abstraction that is very useful is linear algebra which is an abstraction without errors. >>> Bullshit. Your claim that there is no abstraction error in linear algebra (when run on computers - we're in subdiscussion related to programming) is false >> You fail to realise that we can prove theorems about linear algebra USING COMPUTERS > Obviously I realize we can prove theorems. If I didn't realize it was possible to prove things You have been arguing in bad faith by either putting words in my mouth (when run on computers) or deleting key phrases from my reply (USING COMPUTERS - reinserted by me) These 2 statements by you contradict each other "Bullshit, Your claim that there is no abstraction error in linear algebra (when run on computers - we're in subdiscussion related to programming) is false " " Obviously I realize we can prove theorems" -----> USING COMPUTERS It is clear that you thought of computers as IEEE floating point number crunching machines, with implicit floating point errors. All of your arguments rested on this irrelevant point. You even condescended to teach me about floating points using citations not needed by anyone who has attended CS101. You failed to realize that finite sized representations of computable real numbers exist, by definition[1]. One such representation could be a finite sum on surd basis, instead of using a binary basis eg sqrt(2) instead of 1.414.... and the most general form is a theorem prover like Lean. All of these misunderstandings in your head because you failed to realize the gist of the Church Turing thesis ' - Everything that you do with your brain and paper can be duplicated on a computer. In any case, I am glad you learned something today. Computers don't relate to math via IEEE floating pointing numbers, the connection is a lot deeper[1]. You won't acknowledge this, but frankly speaking, I can't really stand out- jargoning pretending to be an honest discussion. I did give an opportunity to you to correct yourself with my first comment. But you only doubled down - more jargon, bad paraphrasing of diagonalization, putting words in my mouth, followed by removing key phrases from my replies amongst other bad faith arguments. [1] https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis To establish that a function is computable by Turing machine, it is usually considered sufficient to give an informal English description of how the function can be effectively computed, and then conclude "by the Church–Turing thesis" that the function is Turing computable

JoshCole 4y ago

> The OP was not discussing learning at all Yes they were. They were discussing teaching, which is related to learning. Moreover, the person they were responding to - they also were talking about learning. They talked about how it was good to learn an abstraction that wasn't perfect. Even the article is about whether we should teach one abstraction or another. > You are completely out of touch Gaslighting is abusive. Stop abusing me. > I am familiar with virtually all the topics you are discussing, so you can skip the citations. I find no coherence to any of your segues. This is an argument from authority. It is a fallacious argument. If my segue is incorrect, you need to show it from the structure of the argument, not by appealing to your authority, which is irrelevant; you might be great - I'm not saying your not. You are great; I'm not saying you're not. I'm sure you're intelligent and smart and witty and cool. But who we are - it doesn't matter. We're irrelevant. The ideas are all that matters. If I'm wrong - why isn't chess solved? Why do we approximate solutions? Meanwhile, why is checkers solved? Why do games with simpler graphs get solved perfectly but more complex games with more complex graphs not get solved perfectly? Please back up the ideas you would be advancing were it the case you actually disagreed with what I claim is provable. If you actually understood my point, than you should know that the opposite of my point isn't that perfect abstractions exist - it is that the run time of specific learning algorithms aren't correlated with their input size. Your trying to get me to defend conclusions I didn't make, treating me like I'm stupid and comparing me to people who are rambling. You are being abusive. Lying. Gaslighting. Attacking me as a person rather than my ideas. Appealing to authority. I'm sorry that I thought you were referring to linear algebra when used as abstraction in the way I meant it - I'm talking about computational abstractions; stuff with many dimensions, compressed to be in fewer dimensions. That happens when we do linear algebra on computers in practice. I thought it was reasonable to point this out, because my claim is closer to "abstractions with errors in them can be useful" than it is to "abstractions without error don't exist". But I feel like you do understand me in this - because you seem desperate not to admit this. To pretend we can represent all things in finite space, when we can't, because the infinite things can't all be represented in finite space. And it seems to me the only reason you would be so desperate not to admit this - to try and throw up so much confusion about this idea - is that you do understand me. And you understand that if you surrender on that point, you admit I'm right. So I think you already know I'm right. And you're just being mean intentionally. I think I probably offended you. It best explains the inconsistency in your reasoning. So I'm sorry about that - and I assume it was sometime in the past, because my first replies didn't deserve your malice.

JoshCole 4y ago

> It isn't even clear what you mean by abstraction at all. I'm using abstraction in the sense of 'blueprint abstraction' from game theory. This is basically compression of the input to your learning algorithm. There exists lossless compression - perfect one to one abstraction. There is also lossy compression - given one compressed form it could be any number of uncompressed forms. Abstraction with error is then compression with error. What I was trying to prove and what I still believe to have proved is that some algorithms when given an input of unbounded size have the property of not terminating. What I then tried to show was that abstraction breaks the proof of non-termination, because it breaks the core assumption of diagnolization - that there is a one to one mapping. So the proof of non-termination doesn't hold. > I am familiar with virtually all the topics you are discussing, so you can skip the citations. I literally linked to a paper that used abstractions in the way I meant it. So maybe you should not skip citations? Clearly you don't know the fields as well as you think you do. > I find no coherence to any of your segues. It isn't a segue; it is what you asked for. I gave you a proof that unabstracted learning problems can terminate where abstracted problems terminate. > You are completely out of touch [2][3] This is such an ironic statement; here we were discussing what abstraction techniques we should teach when teaching computer programming and you're trying to complain that I'm the one who is out of touch when I say computers use abstractions. They definitely do. In fact, they use abstractions with error.