5 ms·

It pleases me to see the classic "high votes, no comments" on this post, as people upvote it since they can tell its smart, but have literally no clue what the

It pleases me to see the classic "high votes, no comments" on this post, as people upvote it since they can tell its smart, but have literally no clue what the words mean. Neither do I for that matter, he might as well be speaking an alien language.

scarmig 4y ago
For something more accessible of his, check out his Real Analysis textbook! Most people can understand it without difficulty; he starts by teaching you how to count and add the natural numbers. It's far more readable than other introductory analysis texts (e.g. Rudin) without sacrificing rigor.
082349872349872 4y ago
Are you familiar with the idea that to prove a loop correct only takes two things: A/ proving (o->o), that it makes progress with each iteration, and B/ proving (->o), that it terminates? If so, he's speaking a bunch of different alien languages, showing how the same basic pattern (prove something for an infinite number of things by looking at their structure and proving something for the finite number of ways each of those things can be put together) works in each of the alien languages. Or at least that's what I got from the few of those languages which I speak — all the rest are, as they say, greek to me.
- deleted 4y ago
  [deleted]
- mrmuagi 4y ago
  Induction proofs are indeed useful, the strongest argument for learning these sort of formal tricks, is you can convince another human that your algorithm correct with pure math. It's one thing to say, look, my program's test suite (that I wrote) passes, or it passes a few criteria, it is another thing entirely to prove without a shadow of a doubt the algorithm is logically sound and correct. Induction proofs are useful with loops, but there are a lot of tricks useful for programmers.
hardware2win 4y ago
Ah, good old mathematics (business model: uber for abstract concepts)
deleted 4y ago
[deleted]
bryanrasmussen 4y ago
I often upvote things that I don't have time to say anything about, not that I've upvoted this, but there can be lots of reasons to upvote something and not comment on it.
- Workaccount2 4y ago
  We all know this post is going over 95% of our heads.
- dj_mc_merlin 4y ago
  Sure.. but you've been around this site for at least as long as I have, so you must've seen that you can directly tell how technical a discussion is by the points/comments ratio. The ranking goes like this: 1. Political/current events stories have a million comments -- sometimes more comments than points if the OP is a controversial opinion 2. Software engineering opinion pieces have the 2nd most comments (everyone has an opinion), followed by 3. Software engineering technical pieces. These usually have a few comments by some smartypants that has worked with the software, and a few other people hallucinating technical challenges around them for some reason. 4. The least commented on are these kinds of pieces that require at least a master's in some other non-SWE field. Mathematics gets quite popular since most of HN was "good at maths", and thus will upvote it, even though the most maths they have understood in the last decade was when they copied some formulas from a random paper.
  - stocknoob 4y ago
    It’s great. The infamous HN “well actually” contrarian is left speechless.
    - sdwr 4y ago
      Well, being contrary on HN is actually the majority viewpoint. Piggybacking on other people's thoughts and poking holes in them is the easiest way to maintain a healthy defensive wall of superiority while communicating.
  - johnfn 4y ago
AlexSW 4y ago
You may not be as far as you think. If you've done 'proof by induction', that's listed there (beginning of post 6), and should hopefully give you some grounding. Several of these are not as complicated as they may look. Though some of them I certainly have no ideas on at all.
- dj_mc_merlin 4y ago
  For fun then, let's see just how far I am: > Reflection symmetry -> suffices to test odd and even functions separately. Maybe reflection means flipping a function? Or when it goes above or below an axis? > Translation invariance -> suffices to test individual plane waves (i.e., to inspect the Fourier multiplier symbol). Fourier transform has something to do with frequencies. A plane wave sounds like part of a DnD spell. > Dilation invariance [if unitary] -> suffices to test homogeneous functions. If this didn't have "functions" in it I would think it's biology. > Rotation invariance -> suffices to test the case of spherical harmonic behavior in angular variable (separation of variables). Good thing the spherical harmonic behaviour sufficies, I do not know I would test the cubic dissonant one. > Invariance under linear combinations / convex combinations / algebraic operations -> suffices to check basis elements / extreme elements / generators Combinations has something to do with choosing things? Generators.. no, I give up. > Invariance under tensor products -> suffices to check one-dimensional/irreducible case Aha! Tensors! Like TensorFlow! I know one-dimensional too! This is the closest I've gotten to having a smart thought. > Invariance under limits -> suffices to check a dense subclass "Dense subclass" is exactly how I'm feeling right now. > Multiplicative structure (in analytic number theory) -> suffices to check prime powers ¯\_(ツ)_/¯ > [Principle of induction] Preserved by successor -> suffices to test base case and/or limiting cases I do know this one, but I actually wouldn't have figured it out if he hadn't pointed out this is induction. I'm tired of showing how dumb I am for now, but you get me. I am as far as I think.
  - AlexSW 4y ago
    I think you're getting at the point with this though: > I actually wouldn't have figured it out if he hadn't pointed out this is induction. A lot of these other ones are not that complicated either, it's just hard to parse and sometimes requires a small bit of math knowledge, which I think is within reach if you're familiar with induction and would only take e.g. a minute for you to understand if someone explained it (ideally with a blackboard than in text). Some of those are definitely nonsense to me. But, to put my money where my mouth is and to give some examples (as you spent the time to type that out), 'invariance under linear combinations' just means that, if something holds for f(x), then it holds for 2f(x), f(x) + 10, etc. (these are all linear combinations). So then saying 'suffices to check basis elements' means 'just check f(x), and the others all fall out for free'. As another example, convex combinations: Google 'convex hull' for images, but basically this one is just saying just check the 'extreme elements', i.e. the 'corners' at the boundary, and everything in the middle falls out for free because we have 'invariance under convex combinations'. A convex combination here is just a some point in the middle of these extremes. While these may not be immediately obvious when reading them, the pictures or ideas are actually sometimes quite simple. I hope that helps.
jordigh 4y ago
He's talking about the general principle that if something only depends on composable atoms, then in order to know how that thing changes, you only need to know how those composable atoms change. Probably a simple example is a rotation in the plane about the origin. If you know it's a rotation, then in order to know how any point in the plane is moved by this rotation, you only need to know how one point is moved.
antman 4y ago
I upvoted because the sentences look beautiful and it is pretty sure they are right. I could not not upvote.
commandlinefan 4y ago
I came to the comments to see if anybody did understand it. (I know I didn't).

scarmig 4y ago

For something more accessible of his, check out his Real Analysis textbook! Most people can understand it without difficulty; he starts by teaching you how to count and add the natural numbers. It's far more readable than other introductory analysis texts (e.g. Rudin) without sacrificing rigor.

082349872349872 4y ago

Are you familiar with the idea that to prove a loop correct only takes two things: A/ proving (o->o), that it makes progress with each iteration, and B/ proving (->o), that it terminates? If so, he's speaking a bunch of different alien languages, showing how the same basic pattern (prove something for an infinite number of things by looking at their structure and proving something for the finite number of ways each of those things can be put together) works in each of the alien languages. Or at least that's what I got from the few of those languages which I speak — all the rest are, as they say, greek to me.

deleted 4y ago
[deleted]
mrmuagi 4y ago
Induction proofs are indeed useful, the strongest argument for learning these sort of formal tricks, is you can convince another human that your algorithm correct with pure math. It's one thing to say, look, my program's test suite (that I wrote) passes, or it passes a few criteria, it is another thing entirely to prove without a shadow of a doubt the algorithm is logically sound and correct. Induction proofs are useful with loops, but there are a lot of tricks useful for programmers.

hardware2win 4y ago

Ah, good old mathematics (business model: uber for abstract concepts)

deleted 4y ago

[deleted]

bryanrasmussen 4y ago

I often upvote things that I don't have time to say anything about, not that I've upvoted this, but there can be lots of reasons to upvote something and not comment on it.

Workaccount2 4y ago
We all know this post is going over 95% of our heads.
dj_mc_merlin 4y ago
Sure.. but you've been around this site for at least as long as I have, so you must've seen that you can directly tell how technical a discussion is by the points/comments ratio. The ranking goes like this: 1. Political/current events stories have a million comments -- sometimes more comments than points if the OP is a controversial opinion 2. Software engineering opinion pieces have the 2nd most comments (everyone has an opinion), followed by 3. Software engineering technical pieces. These usually have a few comments by some smartypants that has worked with the software, and a few other people hallucinating technical challenges around them for some reason. 4. The least commented on are these kinds of pieces that require at least a master's in some other non-SWE field. Mathematics gets quite popular since most of HN was "good at maths", and thus will upvote it, even though the most maths they have understood in the last decade was when they copied some formulas from a random paper.
- stocknoob 4y ago
  It’s great. The infamous HN “well actually” contrarian is left speechless.
  - sdwr 4y ago
    Well, being contrary on HN is actually the majority viewpoint. Piggybacking on other people's thoughts and poking holes in them is the easiest way to maintain a healthy defensive wall of superiority while communicating.
- johnfn 4y ago

AlexSW 4y ago

You may not be as far as you think. If you've done 'proof by induction', that's listed there (beginning of post 6), and should hopefully give you some grounding. Several of these are not as complicated as they may look. Though some of them I certainly have no ideas on at all.

dj_mc_merlin 4y ago
For fun then, let's see just how far I am: > Reflection symmetry -> suffices to test odd and even functions separately. Maybe reflection means flipping a function? Or when it goes above or below an axis? > Translation invariance -> suffices to test individual plane waves (i.e., to inspect the Fourier multiplier symbol). Fourier transform has something to do with frequencies. A plane wave sounds like part of a DnD spell. > Dilation invariance [if unitary] -> suffices to test homogeneous functions. If this didn't have "functions" in it I would think it's biology. > Rotation invariance -> suffices to test the case of spherical harmonic behavior in angular variable (separation of variables). Good thing the spherical harmonic behaviour sufficies, I do not know I would test the cubic dissonant one. > Invariance under linear combinations / convex combinations / algebraic operations -> suffices to check basis elements / extreme elements / generators Combinations has something to do with choosing things? Generators.. no, I give up. > Invariance under tensor products -> suffices to check one-dimensional/irreducible case Aha! Tensors! Like TensorFlow! I know one-dimensional too! This is the closest I've gotten to having a smart thought. > Invariance under limits -> suffices to check a dense subclass "Dense subclass" is exactly how I'm feeling right now. > Multiplicative structure (in analytic number theory) -> suffices to check prime powers ¯\_(ツ)_/¯ > [Principle of induction] Preserved by successor -> suffices to test base case and/or limiting cases I do know this one, but I actually wouldn't have figured it out if he hadn't pointed out this is induction. I'm tired of showing how dumb I am for now, but you get me. I am as far as I think.
- AlexSW 4y ago
  I think you're getting at the point with this though: > I actually wouldn't have figured it out if he hadn't pointed out this is induction. A lot of these other ones are not that complicated either, it's just hard to parse and sometimes requires a small bit of math knowledge, which I think is within reach if you're familiar with induction and would only take e.g. a minute for you to understand if someone explained it (ideally with a blackboard than in text). Some of those are definitely nonsense to me. But, to put my money where my mouth is and to give some examples (as you spent the time to type that out), 'invariance under linear combinations' just means that, if something holds for f(x), then it holds for 2f(x), f(x) + 10, etc. (these are all linear combinations). So then saying 'suffices to check basis elements' means 'just check f(x), and the others all fall out for free'. As another example, convex combinations: Google 'convex hull' for images, but basically this one is just saying just check the 'extreme elements', i.e. the 'corners' at the boundary, and everything in the middle falls out for free because we have 'invariance under convex combinations'. A convex combination here is just a some point in the middle of these extremes. While these may not be immediately obvious when reading them, the pictures or ideas are actually sometimes quite simple. I hope that helps.

jordigh 4y ago

He's talking about the general principle that if something only depends on composable atoms, then in order to know how that thing changes, you only need to know how those composable atoms change. Probably a simple example is a rotation in the plane about the origin. If you know it's a rotation, then in order to know how any point in the plane is moved by this rotation, you only need to know how one point is moved.

antman 4y ago

I upvoted because the sentences look beautiful and it is pretty sure they are right. I could not not upvote.

commandlinefan 4y ago

I came to the comments to see if anybody did understand it. (I know I didn't).