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Think in Math, Write in Code

justinmeiners.github.io

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Re: Think in Math, Write in Code

#191

Post by _zachs »

justinmeiners wrote: post #148
_zachs wrote: post #134

I disagree with the author’s points that you can’t represent a graph with a single interface. Write an interface with the methods you need, i.e., `findNeighbors()`, `getAllFriends()`, `retrieveDogPhotos()`, and implement it for the specific underlying data structure/implementation of Graph you choose later. A graph is a graph, the interface doesn’t care if you’re using an adjacency matrix or a node. I don’t see how w…

Can you represent Facebook's graph of friends as an interface? Do you think they also do a lot of graph theory about it?

`getFriends(userId)`, how's that? :D

Re: Think in Math, Write in Code

#192

Post by naturlich »

FiberBundle wrote: post #120
pgcj_poster wrote: post #67

I was surprised to learn that I really enjoy coding, whereas I rather dislike math. I feel like this article might resonate with some people, but not with me. > Programming languages are implementation tools, not thinking tools. They are strict formal languages invented to instruct machines in a human-friendly way. In contrast, thoughts are best expressed through a medium which is free and flexible. I don't find math…

> When I write code, the computer forces me to be 100% precise and will spit errors at me as soon as I do something wrong. This is similar to math though, with the exception that you don't have something or someone telling you that you made a mistake, but you have to seriously question every step in your proof by applying the rules of logic and your knowledge. At a certain point you develop sufficient intuition to sp…

Indeed, I'd recommend the "interesting proof" vignettes by 3Blue1Brown: https://www.youtube.com/watch?v=OkmNXy7er84&list=PLZHQObOWTQ...

These are my favorite videos of his

Re: Think in Math, Write in Code

#193

Post by slx26 »

rowanG077 wrote: post #84
mannykannot wrote: post #50

Earlier quoted context omitted.

> Big projects should be cut into smaller pieces where each piece can be relatively easy rewritten. To come up with the right smaller pieces, you have to think about how they will work together to achieve the big picture. That means interfaces and their contracts, and if you get them wrong, you end up with pieces that don't fit together, and do not, collectively, get the job done. Big problems cannot be effectively s…

That's my point you CANNOT possibly come up with the right smaller pieces until you have a solution that you have verified works. What do you think other engineering principles do? They create a proof of concept. Verify it works and then create the real thing. That is why "real" engineering companies have hundreds of tools to test stuff. I really don't understand why people want software to be different. You write so…

in my opinion the big difference and problem is that space and resources are virtually unlimited, and a "product" can keep changing indefinitely too. and if something fails, in most cases it will fail very differently than in other engineering disciplines. I agree it would be great to write more prototypes and all that, but hey, capitalism: good_enough/shitty makes money, so that's where we are (also, CS is rather new, we are still figuring out a lot of things, still getting deep in the mess)

Re: Think in Math, Write in Code

#194

Post by [deleted] »

agentultra wrote: post #164
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…

> Mathematics and programming are not really all that related to each other I may be wrong but I believe the Curry-Howard correspondence disproves your claim. One can translate between the two and find that they are equivalent. The difficulty is that some programming languages are hard to model mathematically due to the way they were designed and implemented. Some, like Idris or Agda, make it easy to see the correspo…

[deleted]

Re: Think in Math, Write in Code

#195

Post by makz »

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…

I agree with you. There's a popular book they recommend around here for learning linear algebra, which they say its very related to coding.

I found it to be not the case. Upon reading the first chapters I started wondering how could this be useful for coding. So I jumped to one of the last chapters where they show you practical applications. Upon reading those I thought: "I can do all this in code just fine without using linear algebra".

I never touched that book again.

About two years ago or so I started to make little games for the pico-8 fantasy console. There's some math involved there but almost always you don't use the math formulas as you would in a text book, for example, for something simple like drawing a straight line or a circle, finding paths, collisions... there are very specific algorithms for that, they don't look anything like a math formula, even if they are derived from those.

Just my point of view.

Re: Think in Math, Write in Code

#196

Post by Sharlin »

smallnamespace wrote: post #15
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)…

Yeah. It is easy to people with no university-level math background to think math is a deterministic, conscious effort to execute what are basically algorithms, like long division with pen and paper.

Whereas actually ”mathematical thinking”, like coming up with a proof, is an incredibly intuition-guided process, a parallel heuristic search in the solution space, a fundamentally creative endeavour. And as your intuition comes up with promising paths through the search space, you write them down, formalize them, probably discover some corner cases you have to handle, and either continue down that path or realize that it is a dead end and you have to backtrack.

At least to me, this process is incredibly similar to programming effort. You come up with subsolutions, formalize them, fix issues revealed by the formalization, carry on with the next subsolution or realize that approach can’t work after all, and come up with something else.

Re: Think in Math, Write in Code

#198

Post by thfuran »

makz wrote: post #195
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…

I agree with you. There's a popular book they recommend around here for learning linear algebra, which they say its very related to coding. I found it to be not the case. Upon reading the first chapters I started wondering how could this be useful for coding. So I jumped to one of the last chapters where they show you practical applications. Upon reading those I thought: "I can do all this in code just fine without u…

> there are very specific algorithms for that, they don't look anything like a math formula

I'm not sure what you mean by that. I'd describe making a 3D game (engine) with rendering, collision detection, etc as probably one of the math-heaviest areas of programming outside of scientific computing or algorithm R&D.

Re: Think in Math, Write in Code

#199

Post by lonelappde »

dkarl wrote: post #171
misterdoubt wrote: post #136

Earlier quoted context omitted.

Ah, well, you just described the relative value of math in much the way I'd describe the relative value of... well, just about any intellectual pursuit. Same in philosophy. Or in law. Or in physics. A lot of people with particular interest in one area -- say, mathematics -- don't realize that much of what is important is much more generally applicable. It's not that these things are distinctly important for math. It'…

That's true to a certain extent, but math and programming share the property of being built up from logical building blocks that are combined in strict logical ways. Law and philosophy are built on language and culture; physics is closer but is empirical. Math and programs are built from logic, and this gives them more of a common aesthetic sense. For example, in law or philosophy, repeating the same argument multipl…

Modern computing is empirical. That's why MIT switched their intro to CS class from Scheme theory of computation to Python robot controllers.

Re: Think in Math, Write in Code

#200

Post by lonelappde »

thfuran wrote: post #198
makz wrote: post #195

Earlier quoted context omitted.

I agree with you. There's a popular book they recommend around here for learning linear algebra, which they say its very related to coding. I found it to be not the case. Upon reading the first chapters I started wondering how could this be useful for coding. So I jumped to one of the last chapters where they show you practical applications. Upon reading those I thought: "I can do all this in code just fine without u…

> there are very specific algorithms for that, they don't look anything like a math formula I'm not sure what you mean by that. I'd describe making a 3D game (engine) with rendering, collision detection, etc as probably one of the math-heaviest areas of programming outside of scientific computing or algorithm R&D.

Numerical solutions in computer programs look very different from the closed form symbolic theorems in math books.
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