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The language brain matters more for programming than the math brain? (2020)

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Re: The language brain matters more for programming than the math brain? (2020)

#431

Post by [deleted] »

GoblinSlayer wrote: post #430
voidspark wrote: post #422

Earlier quoted context omitted.

Now you’re talking about the human activity of writing code, not the code itself. Those business requirements are inputs to the process of writing the code. Once the code is actually written, that exists as a formal logical system, defined by mathematics, not business requirements.

The discussion started about whether human needs math skills to write code. That's what I mean when I say programming isn't mathematics. Meaning of code is defined by human, how do you intend code to be defined by mathematics? The human first imagines mathematical formulas, then by some unknown process they become code? I don't think anybody does it like that. You start with requirements, intuitively guess architectu…

[deleted]

Re: The language brain matters more for programming than the math brain? (2020)

#432

Post by Nevermark »

godelski wrote: post #254
Nevermark wrote: post #188

Earlier quoted context omitted.

> I mean is it any surprise kids get bored in math? Indeed. Kids did not evolve to learn things because they would be useful years down the road. But they did evolve to inhale knowledge at very high rates wherever it extends their capabilities in the moment. My take on this is that math should be tied to kids crafting, experimenting, and learned directly in the context of its fun and creative uses. Geometry screams o…

In general I agree but > Indeed. Kids did not evolve to learn things because they would be useful years down the road. But they did evolve to inhale knowledge at very high rates wherever it extends their capabilities in the moment. I strongly disagree with this. Children play. Most animals play. It is not hard to see how the skills learned through play lead to future utility despite potentially none at the time. We i…

> I strongly disagree with this. Children play. Most animals play.

I am not arguing against this. On the contrary, I agree with this completely.

Pairing the opportunity to learn and use highly general long term knowledge, toward progression in their own intrinsic interests (crafting, whatever) is the point I am making.

The alternative, a long line of math for math's sake, which neglects to harness and support each child's need and motivation to continually advance their own natural interests in all kinds of idiosyncratic directions.

Re: The language brain matters more for programming than the math brain? (2020)

#433

Post by voidspark »

GoblinSlayer wrote: post #430
voidspark wrote: post #422

Earlier quoted context omitted.

Now you’re talking about the human activity of writing code, not the code itself. Those business requirements are inputs to the process of writing the code. Once the code is actually written, that exists as a formal logical system, defined by mathematics, not business requirements.

The discussion started about whether human needs math skills to write code. That's what I mean when I say programming isn't mathematics. Meaning of code is defined by human, how do you intend code to be defined by mathematics? The human first imagines mathematical formulas, then by some unknown process they become code? I don't think anybody does it like that. You start with requirements, intuitively guess architectu…

> The discussion started about whether human needs math skills to write code.

Writing code IS a math skill. When writing code you are writing logic in a formal system. Logic is mathematics.

You may be thinking that mathematics is just like doing arithmetic or solving equations. It is way deeper and broader than that.

> I still think that's not code, but your favourite model of code

Code is not just modelled through mathematics, it is actually defined by mathematics. It is fundamentally a mathematical construct, grounded in formal semantics.

https://en.wikipedia.org/wiki/Semantics_(computer_science)

Re: The language brain matters more for programming than the math brain? (2020)

#434

Post by GoblinSlayer »

godelski wrote: post #423
GoblinSlayer wrote: post #415

Earlier quoted context omitted.

You confuse map with the territory. By the same logic you can say quarks are mathematics, because they are modeled by a theory that has some mathematics in it.

Our mathematical models of reality (i.e. Physics) is not the same as reality. So yes, by the same logic "quarks" are mathematics, but only in the same way that a "cup" is English. The quark was a great example, considering we can't observe it and purely rely on mathematical models, but the same argument would still hold true for a bowling ball. Physics is our description of reality, not reality itself. Our descriptio…

How math helps with programming languages? What math says about zero based indexes? How do you prevent off by one errors? How do you prevent buffer overflows? It's ergonomics problems.

Re: The language brain matters more for programming than the math brain? (2020)

#435

Post by seba_dos1 »

godelski wrote: post #425
seba_dos1 wrote: post #404

Earlier quoted context omitted.

> You point out the "is a" relationship, not the "is" relationship, they are different. Well, what you reacted to was, let me copy'n'paste, "Math is a language". It was you who insisted that "is" in this sentence maps to "equals" relation, so thanks for agreeing that you were wrong.

Honestly I don't think his point even stands. We were using English to communicate and English doesn't have the strict rules of mathematics. That's literally why we created math (which I'll gladly call "a class of languages"). He's right, "is" maps to "equivalent" but he's also wrong because "is" also maps to "subset" and several other things. "Is" is a surjection. The problem here all comes down to seadan83 acting i…

It's such an absurd thing to argue about that I just assumed that some massive brainfart happened there. It happens to everyone, not everyone doubles down on it though.

Re: The language brain matters more for programming than the math brain? (2020)

#436

Post by sebastialonso »

vidarh wrote: post #401
sebastialonso wrote: post #392

Earlier quoted context omitted.

Is it possible your mental model of what CS is more aligned with software engineering rather than actual CS? Could you share some examples of what you consider to be CS but lacks any mathematical relation? I agree is not a useful grouping in practice. I'm just interested in what makes you think like you do.

I did categorically not claim, nor even suggest, that any CS "lacks any mathematical relation". What I claimed was that in computer science we often discuss things in terms that would not be the natural way of dealing with it in maths. We do that because our focus is different, and our abstractions are different. It doesn't mean it's not math. It means it's not useful to insist that it isn't a different field, and it…

Got it, thanks for the reply

Re: The language brain matters more for programming than the math brain? (2020)

#437

Post by sebastialonso »

GoblinSlayer wrote: post #412
sebastialonso wrote: post #394

Earlier quoted context omitted.

A lot of people in this type of threads always makes the same mistake: confusing what math is with branches of math, or rather, ways in which math is used. The way the education system is built certainly contributes to this. I've always found the car metaphor to work very good to understand this: A car is a machine that can transport itself to point A to B (some other rules apply). There are different types of cars,…

Declarative construct is made of relations, but imperative execution isn't, rather it's a process in time, but time is not a thing in math.

Another misconception I'd say.

"Time is not a thing in math" is not understanding what math is. Time is another ideal object following certain rules under a given domain. Programming is coming up with objects of different size, with different characteristics, with interact at different points in time, i.e. following certain rules.

Re: The language brain matters more for programming than the math brain? (2020)

#438

Post by godelski »

GoblinSlayer wrote: post #428
godelski wrote: post #289

Earlier quoted context omitted.

Working with different objects doesn't make it any less of math. Just because you can derive calculus from set theory (analogous to assembly or even binary here) doesn't make calculus "not math". Math is about abstractions and relations. See the Poincare quote again. Plus, the Programming Languages people would like to have a word with you. Two actually: Category Theory. But really, if you get them started they won't…

Wheeler: It from bit. Otherwise put, every it—every particle, every field of force, even the space-time continuum itself—derives its function, its meaning, its very existence entirely—even if in some contexts indirectly—from the apparatus-elicited answers to yes-or-no questions, binary choices, bits. It from bit symbolizes the idea that every item of the physical world has at bottom—at a very deep bottom, in most ins…

That is not in contention with what I said, now is it?

Wheeler is arguing that if a tree falls in the forest, and there is nobody to hear it, that it still makes a sound because there are things that interact with the sound. But if the tree fell in a forest and there was nothing else in the universe then there is no sound because there is no observation.

It helps to read the whole thing[0] and to understand the context of the discussion. This is meta-physics and a deep discussion into what the nature of reality is. Ian Hacker has a good introduction to the subject but I find develop grave misunderstandings when they also do not have the strong math and physics background necessary to parse the words. Even people who understand the silliness of "The Secret" and that an observer need not be human often believe that this necessitates a multi-verse. A wildly convoluted solution to the problem of entropy not being invertible. Or closer to computer terms, a solution that insists that P = NP. There is information lost.

If you wanna argue that there's no difference between the word cup and a cup itself because there is no word without the observer who has the language, then yeah.

[0] https://historyofinformation.com/detail.php?id=5041

Re: The language brain matters more for programming than the math brain? (2020)

#439

Post by godelski »

GoblinSlayer wrote: post #434
godelski wrote: post #423

Earlier quoted context omitted.

Our mathematical models of reality (i.e. Physics) is not the same as reality. So yes, by the same logic "quarks" are mathematics, but only in the same way that a "cup" is English. The quark was a great example, considering we can't observe it and purely rely on mathematical models, but the same argument would still hold true for a bowling ball. Physics is our description of reality, not reality itself. Our descriptio…

How math helps with programming languages? What math says about zero based indexes? How do you prevent off by one errors? How do you prevent buffer overflows? It's ergonomics problems.

It is hard to answer because of exactly what ndriscoll said[0]

  > It's like trying to argue about the distinction between U(1), the complex numbers with magnitude 1, and the unit circle, and getting upset when the mathematicians say "those are 3 names for the same thing". Or saying that writing C is programming but writing in a functional language like Scala or Haskell (or Lean) is not.
As ndriscoll suggests, it is tautological. I mean look at what I said. I really need you to hear it. I said that coding is math. So what I hear is "How programming languages helps with programming languages?" Why are you expecting me to hear anything different?

  > What math says about zero based indexes?
Start at 0? Start at 1? Who cares, it is the same thing. The natural numbers, non-negative integers, integers, even integers, who cares? They're the same thing. And who cares about indexing at 0 or 1 in programming? That's always been a silly argument that's inconsequential.

  > How do you prevent off by one errors?
By not being off by one? What's the question? Like being confused about if you start at 0 or start at 1 and how to get the right bound? It is a shift from one to the other, but they are isomorphic. We can perfectly map. But I really don't get the question. You can formalize these relationships with equations you know. I know it isn't "cool" but you can grab a pen and paper (or a whiteboard) and write down your program structure if you are often falling for these mistakes. This seems more about the difficulties of keeping track of a lot of things in your head all at once.

  > How do you prevent buffer overflows?
By not going over your bounds? I'm so confused. I mean you are asking something like "if f(x) = inf when x > 10, how does math help you prevent the output of the function from being infinite?"

Maybe what will help is seeing what some of the Programming Languages people do and why they like Haskell[1].

Or maybe check out Bartosz Milewski[2,3]. His blog[2], is titled "Bartosz Milewski's Programming Cafe: Category Theory, Haskell, Concurrency, C++". It may look very mathy, and you'd be right(!), but it is all about programming! Go check out his Category Theory Course[3], it is _for programmers_.

Don't trust me, go look at papers published in programming language conferences [4]. You'll find plenty of papers that are VERY mathy as well as plenty that are not. It really depends on the topic and what is the best language for the problems they're solving. But you'll certainly find some of the answers you're looking for.

Seriously, don't trust me, verify these things yourself. Google them. Ask an LLM. I don't know what to tell you because these are verifiable things (i.e. my claims are falsifiable!). The only thing you need to do is look.

[0] https://news.ycombinator.com/item?id=43882197

[1] https://excessivelyadequate.com/posts/isomorphisms.html

[2] https://bartoszmilewski.com/

[3] https://www.youtube.com/watch?v=I8LbkfSSR58&list=PLbgaMIhjbm...

[4] https://www.sigplan.org/Conferences/

Re: The language brain matters more for programming than the math brain? (2020)

#440

Post by godelski »

seba_dos1 wrote: post #435
godelski wrote: post #425

Earlier quoted context omitted.

Honestly I don't think his point even stands. We were using English to communicate and English doesn't have the strict rules of mathematics. That's literally why we created math (which I'll gladly call "a class of languages"). He's right, "is" maps to "equivalent" but he's also wrong because "is" also maps to "subset" and several other things. "Is" is a surjection. The problem here all comes down to seadan83 acting i…

It's such an absurd thing to argue about that I just assumed that some massive brainfart happened there. It happens to everyone, not everyone doubles down on it though.

Oh, they did it much more than twice: https://news.ycombinator.com/item?id=43873381

But then again, isn't a good portion of this thread non-mathematicians arguing about what math is? I really thought ndriscoll put it succinctly[0]

  > It's like trying to argue about the distinction between U(1), the complex numbers with magnitude 1, and the unit circle, and getting upset when the mathematicians say "those are 3 names for the same thing".
I fear the day some of these people learn about Topology.

[0] https://news.ycombinator.com/item?id=43882197

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