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Think in Math, Write in Code

justinmeiners.github.io

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Re: Think in Math, Write in Code

#11

Post by rowanG077 »

LandR wrote: post #9
warent wrote: post #8

There's an unpopular and somewhat seemingly contradictory opinion that I have regarding this, because this isn't the first time I've seen this topic brought up. Mathematics and programming are not really all that related to each other and I think there's an overemphasis on the importance of math in programming for 99% of applications. Sure, mathematical thinking can be useful, but it's only one type of logical thinki…

> Is this really a common thing? How can you try to implement something without first having had thought of the solution? Unfortunately, it's incredibly common. The result is always almost a mess. Functions that are never called, parameters that are never used, as they discovered their mistake as they were coding but then never went and cleaned up the stuff they don't use anymore. Broken logic, poor performance. Func…

Really? I think the best way to solve a problem is to code it. I can never see all the corner cases and logical inconsistencies before I start typing. I have tried to formally model software before I start writing it and in the end it was largely a waste of time because real understanding of the problem comes with coding the solution.

Of course when doing it like this you write a lot of code which later is unused or bad. But I think that will always happen and it's just a matter of having the discipline to continuously clean up after yourself.

Re: Think in Math, Write in Code

#12

Post by _v7gu »

codr7 wrote: post #7

It's not math, though. It's abstract reasoning, as is math. And that's about as deep as the similarities go. Math can't deal with imperfect input and/or side effects without turning into something else. And code without real world side effects is useless, as is real world perfection.

Well, you have Maybe for imperfect inputs and monads for side effects.

Re: Think in Math, Write in Code

#13

Post by braythwayt »

rowanG077 wrote: post #11
LandR wrote: post #9

Earlier quoted context omitted.

> Is this really a common thing? How can you try to implement something without first having had thought of the solution? Unfortunately, it's incredibly common. The result is always almost a mess. Functions that are never called, parameters that are never used, as they discovered their mistake as they were coding but then never went and cleaned up the stuff they don't use anymore. Broken logic, poor performance. Func…

Really? I think the best way to solve a problem is to code it. I can never see all the corner cases and logical inconsistencies before I start typing. I have tried to formally model software before I start writing it and in the end it was largely a waste of time because real understanding of the problem comes with coding the solution. Of course when doing it like this you write a lot of code which later is unused or…

Writing a lot of code you later discard because it isn’t part of the final solution is like throwing clay on the table and then carving away the bits that don’t fit.

Nobody criticizes the sculptor for the clay that ends up on the floor, and clay is heavy. We carve away bits, they have no mass and don’t need to be swept up, all we have to do is cut them away, revealing the final program.

Re: Think in Math, Write in Code

#14

Post by onion2k »

skohan wrote: post #10
onion2k wrote: post #5

Earlier quoted context omitted.

I do that. Then people hate me because all my variable names are single letters... Then you're thinking in math and also writing in math, so you're getting the second bit wrong. You need to write in code, and code should be optimized for readability.

I think single letter variable names are fine within the scope of a single function. Especially if I'm doing something with a lot of math, like a lighting calculation, the computations are often more readable with short variable names. I'll also usually give a detailed description of what the variable is in comments for clarity.

I think single letter variable names are fine within the scope of a single function.

I don't. One of the things I like most about eslint is the id-length rule - https://eslint.org/docs/rules/id-length

Re: Think in Math, Write in Code

#15

Post by smallnamespace »

warent wrote: post #8

There's an unpopular and somewhat seemingly contradictory opinion that I have regarding this, because this isn't the first time I've seen this topic brought up. Mathematics and programming are not really all that related to each other and I think there's an overemphasis on the importance of math in programming for 99% of applications. Sure, mathematical thinking can be useful, but it's only one type of logical thinki…

> It's all just flashes of algorithms, data structures, potential modifications, moving pieces, how they all affect each other and what happens to the entire entangled web when you alter something.

That's what doing math is like too - just substitute axioms, mathematical objects (whether numbers, sets, rings, or whatever is under discussion), potential lemmas and approaches, what bag of mathematical tools (theorems) you can use, and how much closer to a solution when you shift terms in your formulae around.

Then you write it all down (if you haven't already), simplify it, and clean it up before showing it to others, just like you would code.

Also, you can map programs to proofs and vice versa: https://en.wikipedia.org/wiki/Curry–Howard_correspondence

Re: Think in Math, Write in Code

#16

Post by mannykannot »

rowanG077 wrote: post #11
LandR wrote: post #9

Earlier quoted context omitted.

> Is this really a common thing? How can you try to implement something without first having had thought of the solution? Unfortunately, it's incredibly common. The result is always almost a mess. Functions that are never called, parameters that are never used, as they discovered their mistake as they were coding but then never went and cleaned up the stuff they don't use anymore. Broken logic, poor performance. Func…

Really? I think the best way to solve a problem is to code it. I can never see all the corner cases and logical inconsistencies before I start typing. I have tried to formally model software before I start writing it and in the end it was largely a waste of time because real understanding of the problem comes with coding the solution. Of course when doing it like this you write a lot of code which later is unused or…

Really? yes, it is very common.

The problem of this approach is that it does not scale to large systems. If you don't spend much time on thinking in the abstract about how it will work and what might go wrong, then, by the time you have written enough code to find that out, you may have gone a long way down the wrong path, and not all architectural-level mistakes and oversights can be patched over.

No-one does this perfectly -- even people using formal methods will overlook things -- but, on a big project, if you don't put much effort into thinking ahead about how it should work, and try to identify the problems before you have coded them, you are likely to end up where, in fact, many projects do find themselves: with something that is nominally close to completion but very far from working. Those that are not canceled end up looking like legacy code even when brand new.

Re: Think in Math, Write in Code

#17

Post by mpweiher »

hannofcart wrote: post #6

I think that the total programming man hours spent on writing pure math computation would be dwarfed by the much larger number (I think) spent on doing menial computation: fetching data, transforming it and sending it forward/rendering some output. I suppose this article is targeted at that privileged former group.

"One of the miseries of life is that everyone names everything a litte bit wrong, and so it makes everything a little harder to understand in the world than it would be if it were named differently. A computer does not primarily compute in the sense of doing arithmetic. Strange. Although they call them computers, that's not what they primarily do. They primarily are filing systems. People in the computer business say they're not really computers, they are "data handlers". All right. That's nice. Data handlers would have been a better name because it gives a better idea of the idea of a filing system."

Richard Feynman

https://youtu.be/EKWGGDXe5MA?t=278

Re: Think in Math, Write in Code

#18

Post by higherkinded »

warent wrote: post #8

There's an unpopular and somewhat seemingly contradictory opinion that I have regarding this, because this isn't the first time I've seen this topic brought up. Mathematics and programming are not really all that related to each other and I think there's an overemphasis on the importance of math in programming for 99% of applications. Sure, mathematical thinking can be useful, but it's only one type of logical thinki…

Logic is part of math, not the other way around. Basically the same goes for your "how it affects the web" since that becomes about directed graphs. On algorithms and data structures: do you actually evaluate their complexity if that's not about math? Math is everywhere.

Re: Think in Math, Write in Code

#19

Post by kd5bjo »

warent wrote: post #8

There's an unpopular and somewhat seemingly contradictory opinion that I have regarding this, because this isn't the first time I've seen this topic brought up. Mathematics and programming are not really all that related to each other and I think there's an overemphasis on the importance of math in programming for 99% of applications. Sure, mathematical thinking can be useful, but it's only one type of logical thinki…

> Is this really a common thing? How can you try to implement something without first having had thought of the solution?

There appears to be two distinct kinds of programmers that are about equally effective: ones that think through the problem first and then write down the solution on the one hand, and ones that start with something close and then iteratively refine it into the desired result on the other hand.

When you’re doing things like writing documentation, this is important to remember as the two kinds of programmer will approach the documentation differently — important information needs to be put where both approaches will find it: http://sigdoc.acm.org/wp-content/uploads/2019/01/CDQ18002_Me...

Re: Think in Math, Write in Code

#20

Post by diffeomorphism »

warent wrote: post #8

There's an unpopular and somewhat seemingly contradictory opinion that I have regarding this, because this isn't the first time I've seen this topic brought up. Mathematics and programming are not really all that related to each other and I think there's an overemphasis on the importance of math in programming for 99% of applications. Sure, mathematical thinking can be useful, but it's only one type of logical thinki…

> but it's only one type of logical thinking among many types which can be applied to programming.

Could you elaborate on this? Mathematics is abstract/meta enough that I would consider any type of logical thinking as part of math.

> It's all just flashes of algorithms, data structures, potential modifications, moving pieces, how they all affect each other and what happens to the entire entangled web when you alter something.

That for example sounds very much like "think in math" to me.

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