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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)

#421

Post by GoblinSlayer »

voidspark wrote: post #416
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.

That may be true to some extent, but I think you are missing the point. Quarks are physical in nature, and code is logical in nature. Programs themselves are formal systems. Code isn’t just modelled by mathematics, it is defined by mathematics. In the case of code, we can argue that the map is the territory.

Code is logical if you define logic as reasoning in general, broader than mathematics, and since it runs in physical environment, it now interacts with a messy world. Code is defined by business requirements, and there's no mathematics for that.

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

#422

Post by voidspark »

GoblinSlayer wrote: post #421
voidspark wrote: post #416

Earlier quoted context omitted.

That may be true to some extent, but I think you are missing the point. Quarks are physical in nature, and code is logical in nature. Programs themselves are formal systems. Code isn’t just modelled by mathematics, it is defined by mathematics. In the case of code, we can argue that the map is the territory.

Code is logical if you define logic as reasoning in general, broader than mathematics, and since it runs in physical environment, it now interacts with a messy world. Code is defined by business requirements, and there's no mathematics for that.

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.

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

#423

Post by godelski »

GoblinSlayer wrote: post #415
voidspark wrote: post #338

Earlier quoted context omitted.

That is a narrow perspective of mathematics and computer science. Assigning a variable is a mathematical operation. It is a logical state transition. This is formalized in Programming Language Theory. We are not talking about quarks. We are talking about lines of code which are objectively mathematical statements, no matter how non-mathematical they seem to you subjectively. You start with a practical problem to solv…

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 description of reality highly leverages the language of math, as that language was developed to enforce rules of consistency. Much the same way we design our programming languages, which is why programming language people study so much more math than your typical CS person.

If you're going to accuse someone of confusing the map with the territory, you really should make sure you aren't making the same error.

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

#424

Post by GoblinSlayer »

TheOtherHobbes wrote: post #377
mmaunder wrote: post #356

Earlier quoted context omitted.

> These more abstract skills—not basic arithmetic—are essential for understanding recursion, type inference, or algorithm design. No they're not. Academia has spent decades trying to formalize many aspects of programming and continues to be confused by the lack of correlation between comp sci grads and innovative programmers. Why is it that the drop-outs are succeeding so wildly? Recursion, for example, is learned by…

The drop-outs are "succeeding wildly" because people like Turing, Church, and Hilbert invented the sand pit they're playing in. Knuth created LaTeX. Pandoc is written in Haskell, famous for being a completely useless academic language with no real purpose beyond torturing undergraduates (it says here.) Efficient search and data compression algorithms aren't hacked together in late night hobby coding sessions. Cryptog…

>mathematical inventions

Like Rijndael?

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

#425

Post by godelski »

seba_dos1 wrote: post #404
seadan83 wrote: post #393

Earlier quoted context omitted.

You point out the "is a" relationship, not the "is" relationship, they are different. [0] Find examples with two singular nouns and just the word 'is'. The phrase in question: 'Math is language' is an example, or something like 'food is love' is too. I concede you could interpret those last few sentences with poetic license to be read more like: "A is a form of B", or "A is a B" - though that is not what was written…

> 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 in bad faith and using an intentional misinterpretation of my words in order to fit them to their conclusion. I'm not going to entertain them more because I won't play such a pointless game. The ambiguity of written and spoken language always allows for such abuse. So either they are a bad faith actor "having fun" (trolling) finding intentional misinterpretations to frustrate those who wish to act in good faith or they are dumb. Personally, I don't think they're dumb.

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

#426

Post by GoblinSlayer »

godelski wrote: post #290
ghurtado wrote: post #279

Earlier quoted context omitted.

> Not "coding uses math", I mean it is math > I mean equivalent in the way mathematicians do That sounds like you're backing off from your original claim, probably because it is impossible to defend. That you can use mathematics to describe code doesn't seem very different from using math to describe gravity, or the projected winner in an election, or how sound waves propagate. Isn't the primary purpose of math to de…

> Isn't the primary purpose of math to describe the world around us? No, that's Physics[0]. I joke that "Physics is the subset of mathematics that reflects the observable world." This is also a jab at String Theorists[1]. Physicists use math, but that doesn't mean it is math. It's not the only language at their disposal nor do they use all of math. > software engineering has nothing to do with mathematical abstractio…

>Even if all observable consequences could be explained through this theory it would still be indistinguishable from any other alternative theory which could do so.

That's not unique, all quantitative theories allow small modifications. Then you select parsimonious theory.

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

#427

Post by godelski »

seadan83 wrote: post #307
godelski wrote: post #267

Earlier quoted context omitted.

> Math major here Forgive me if I doubt, but your comment would strongly suggest otherwise, along with this one[0]. The reason for doubt is a failure in fairly basic logic. Your claim is: ¬(A ↦ B) ⟹ ¬(B ↦ A) I'd expect anyone willing to claim the title of "math major" is aware of structures other than bijections and isomorphisms. The mapping operator doesn't form an abelian group. [0] https://news.ycombinator.com/ite…

The word "is", typically refers to the logical equals operator (written as "="). Let A = Math, and let B = Language, the phrase "Math is Language" is therefore "A = B". My claim is that "B != A", which implies "A != B" because "!=" is reflexive. "A != B" then contradicts the claim "A = B". In words: because "language is not math", therefore it cannot be true that "math is language". This is not number theory, not set…

As I said elsewhere (here for others), I'm not going to play this game of *willful misinterpretation.* Your very words do not hold up to the same bar your are attempting to hold mine to. I know you are upset you got caught in a lie, but fuck around and find out. ¯\_(ツ)_/¯ Domain experts can recognize other domain experts pretty easily

  > No, my counter claim is simply that because "B != A" therefore "A != B"
We all know that this is not always true. It may be true in certain cases, in certain fields (pun intended), but you know that this is such a basic logical fallacy that it is taught to children.

Here's a counterexample so we can lay this to rest.

  Let "A" be "a square"
  Let "B" be "a rectangle"

  B != A -> "A rectangle is not a square" (True)
  A != B -> "A square is not a rectangle" (False)
Stop cosplaying, stop trolling, stop acting in bad faith.

Did you even look at my name? There's 2 people that should come to mind. Certainly any logician would notice.

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

#428

Post by GoblinSlayer »

godelski wrote: post #289
dayvigo wrote: post #228

Earlier quoted context omitted.

Sure, lambda calculus is math. To call assembly or typical imperative C math, at least in the same sense, is a bit of a stretch.

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 instances—an immaterial source and explanation; that which we call reality arises in the last analysis from the posing of yes–no questions and the registering of equipment-evoked responses; in short, that all things physical are information-theoretic in origin and that this is a participatory universe.

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

#429

Post by ndriscoll »

seadan83 wrote: post #410
voidspark wrote: post #325

Earlier quoted context omitted.

CREATE, READ, UPDATE, DELETE are fundamentally mathematical in nature. In a typical implementation these are database operations. That involves relational algebra operations, state transitions, boolean logic. The READ part can be a very complex SQL query (composed of many algebraic operations) but even the simplest query (SELECT * from t where ID = 1) is filtering a set based on a predicate. That is mathematics. No o…

It's almost the argument of programming vs computer science coming out here. This is math: {x | x.id = 1} OTOH, a SQL query is a SQL query. This thread is hilarious though. It's like - Cashier: here is your change. - Customer: you did math! - Cashier, no, I gave you change. - Customer: that IS math! - Cashier: You mean, I used math to give you change? - Customer: No, giving change doesn't use math, it IS math!!!!" [2…

The problem you're running into is that people who have some "mathematical maturity" don't get bogged down in notation, so it's difficult for them to see the distinction you're trying to draw between e.g. `{ x∈S | x.id = 1}` and `select x from S where x.id = 1`[0]. You say "a SQL query is a SQL query" and they just think "yes, which is also obviously a mathematical expression".

Computer programs are proofs[1]. This is intuitively and also formally true. You would agree writing proofs is doing math, yeah? Then obviously writing a computer program is also doing math.

Like I have a degree in math and have been a software engineer for over a decade. I do not know what distinction people are trying to get at. 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.

[0] Modulo details like NULLs and multi-set semantics, but surely that's not the distinction?

[1] Up to isomorphism

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

#430

Post by GoblinSlayer »

voidspark wrote: post #422
GoblinSlayer wrote: post #421

Earlier quoted context omitted.

Code is logical if you define logic as reasoning in general, broader than mathematics, and since it runs in physical environment, it now interacts with a messy world. Code is defined by business requirements, and there's no mathematics for that.

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 architecture, then decompose it, it works more like Cauchy problem (but less numeric, more conceptual, you have an owl, now draw it), but I don't think anybody models it like that.

>Once the code is actually written, that exists as a formal logical system, defined by mathematics

I still think that's not code, but your favorite model of code. For spellchecker language is defined by mathematics too: it splits text into words by whitespace, then for each word not found in dictionary it selects best matches and sorts them by relevance. Oh and characters are stored as numbers.

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