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The Mathematical Hacker (2012)

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Re: The Mathematical Hacker (2012)

#121

Post by mindcrime »

agalunar wrote: post #116
mindcrime wrote: post #102

I basically hate math discussions on HN. Why? Because it seems like there's two (at least) "camps" in terms of how they interpret what "math" even means. And the various camps constantly talk around each other, with neither camp seeming to realize that they're arguing about completely different things. So they keep arguing, nobody gets anywhere, and the whole thing is largely a cluster-fuck. So what do I mean by "cam…

This is not the divide I see, but it's the divide I hear many people say they see, and so I've always wondered if the majority of people actually fall into these two camps. From where I happen to stand, I see four camps or so: 1 · those who see mathematics as a particular subject area, body of knowledge, or set of topics, with limited applicability to programming (which, given that definition of mathematics, I think…

From where I happen to stand, I see four camps or so:

I have no doubt that there are more ways to segment people in terms of how they view math, then the simple model I mentioned. That just happens to be the divide that I feel like I see most commonly and that often leads to fruitless discussions.

they replied that anybody who does mathematics is a mathematician.

The problem with that is the definition of "doing mathematics". And that's where I see the divide I mentioned above. Some people would consider "finding the derivative of f(x) = x/x^2 to be "doing math" whereas other people say that's "mere computation" and think of math only as things like "proving why the derivative of f(x)=x/x^2 is $WHATEVER".

I suppose one might say the former is "using math" where the latter is "doing math", but in popular usage it seems like people freely intermix those notions, and people who feel strongly about it one way or the other get their knickers all wadded up over it and hilarity ensues.

Re: The Mathematical Hacker (2012)

#122

Post by harshreality »

Project Euler's higher-numbered problems often require a combination of analytic solutions to vastly simplify some parts of the search space, and brute force for the rest. Without math or lucky guesses—where you've googled a partial solution you don't understand, or you've naively found a function which seems to get the right answer for test cases, but you can't be sure it generalizes—you're left with brute force methods that won't finish in a reasonable amount of time, possibly not even before the Sun turns into a red giant.

Those kinds of problems are not relevant to most everyday software engineering, but in the few cases when you need math, you really need it or you have to scrap the entire feature for being too slow or impractical.

Also, designing neural nets...

Re: The Mathematical Hacker (2012)

#123

Post by [deleted] »

dysoco wrote: post #53
bmitc wrote: post #9

In Steve Yegge’s linked post: > Math is a lot easier to pick up after you know how to program. In fact, if you're a halfway decent programmer, you'll find it's almost a snap. This couldn’t be more wrong. Mathematics is the hardest thing I have ever done. I’m sorry, but mathematics is orders of magnitude more intensive and difficult than most programming. A simple fact that shows this is the amount of programmers who…

> mathematics is orders of magnitude more intensive and difficult than most programming But what level of programming and mathematics are you comparing here though? because college-level algebra and calculus is really not that hard imho (once it "clicks" for you, but it's the same for programming), and if we are comparing math as in what you see in a BSc/Msc of Mathematics (or research-level) then I agree it's hard b…

[deleted]

Re: The Mathematical Hacker (2012)

#124

Post by kovac »

dysoco wrote: post #53
bmitc wrote: post #9

In Steve Yegge’s linked post: > Math is a lot easier to pick up after you know how to program. In fact, if you're a halfway decent programmer, you'll find it's almost a snap. This couldn’t be more wrong. Mathematics is the hardest thing I have ever done. I’m sorry, but mathematics is orders of magnitude more intensive and difficult than most programming. A simple fact that shows this is the amount of programmers who…

> mathematics is orders of magnitude more intensive and difficult than most programming But what level of programming and mathematics are you comparing here though? because college-level algebra and calculus is really not that hard imho (once it "clicks" for you, but it's the same for programming), and if we are comparing math as in what you see in a BSc/Msc of Mathematics (or research-level) then I agree it's hard b…

College-level means undergraduate-level? If so, how is algebra/calculus not that hard? Abstract algebra is one of the hardest stuff I've come across. Calculus? Do you think it's not that hard to prove convergence/bounds/limits of random series and sequences... I agree though that calculus is not that hard, compared to the rest.

Programming is child's play compared to undergraduate mathematics taught in math departments. It's important that you take a module from the math department, not from a physical science or engineering department if you want to experience what it is like.

Re: The Mathematical Hacker (2012)

#125

Post by kaashif »

BeetleB wrote: post #58
tombert wrote: post #22

Earlier quoted context omitted.

I think Yegge is actually completely correct. I started to learn to program when I was 14, and once I understood the concept of functions, I found it much easier to do my calculus and physics work. Fundamentally I understood how to break things down into computable steps. Granted, I think get the impression we might be overloading the term "mathematics".

For most mathematicians, calculus as is often taught in typical undergrads is not "true" mathematics. It's just a tool for computation. For them, calculus is analysis (theorems/proofs that are used to build up calculus). So my question is: Did you study analysis and would you credit programming in helping you get good at it?

I don't understand this comment. Calculus as taught to mathematics undergrads is analysis, right?

Where is calculus "often taught" without "theorems/proofs that are used to build up calculus"?

Re: The Mathematical Hacker (2012)

#126

Post by kaashif »

constantcrying wrote: post #95
epgui wrote: post #90

Earlier quoted context omitted.

>> What I did say is that writing down mathematics is equivalent to writing software. > It is not. That is plainly false. Whether the two look the same or not, maths and computer programs are in fact fundamentally isomorphic. [1] [1] https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspon...

>isomorphic Certainly not every computation is a proof. What statement does: void f(){ printf("?"); } prove?

The fact that you have found a function of type () -> () is a proof that true implies true. This is the Curry-Howard isomorphism.

Not a particularly interesting proof.

Re: The Mathematical Hacker (2012)

#127

Post by sillysaurusx »

geysersam wrote: post #114
nickelpro wrote: post #69

Earlier quoted context omitted.

I would hard disagree that undergrad level Analysis or even just the trickier corners of vector calculus are within the bounds of what programmers can easily pick up without dedicated and guided study. Everybody's gangster until they have to parameterize some bullshit helical structure in R3. Comparable levels of programming, what we expect of CS juniors, are regularly picked up by "the guy who is good with Excel" in…

I think you're hitting the nail on the head here. Something about the learning process makes programming much easier to pick up. What if we had something similar for mathematics? Rapid feedback, error messages, maybe even linters and highlighting for the "mathematical syntax". I've though about this before and I think tools like this could unlock math for a lot of people, and also increase the effectiveness of profes…

What a creative, delightful solution. I encourage you to pursue this!

Re: The Mathematical Hacker (2012)

#129

Post by kthielen »

geysersam wrote: post #114
nickelpro wrote: post #69

Earlier quoted context omitted.

I would hard disagree that undergrad level Analysis or even just the trickier corners of vector calculus are within the bounds of what programmers can easily pick up without dedicated and guided study. Everybody's gangster until they have to parameterize some bullshit helical structure in R3. Comparable levels of programming, what we expect of CS juniors, are regularly picked up by "the guy who is good with Excel" in…

I think you're hitting the nail on the head here. Something about the learning process makes programming much easier to pick up. What if we had something similar for mathematics? Rapid feedback, error messages, maybe even linters and highlighting for the "mathematical syntax". I've though about this before and I think tools like this could unlock math for a lot of people, and also increase the effectiveness of profes…

I think this is the goal of proof assistants based on the Curry-Howard isomorphism, which the original author thought to denigrate for some reason.

Re: The Mathematical Hacker (2012)

#130

Post by [deleted] »

kaashif wrote: post #125
BeetleB wrote: post #58

Earlier quoted context omitted.

For most mathematicians, calculus as is often taught in typical undergrads is not "true" mathematics. It's just a tool for computation. For them, calculus is analysis (theorems/proofs that are used to build up calculus). So my question is: Did you study analysis and would you credit programming in helping you get good at it?

I don't understand this comment. Calculus as taught to mathematics undergrads is analysis, right? Where is calculus "often taught" without "theorems/proofs that are used to build up calculus"?

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