Why I am learning category theory • Hacker News Board

Re: Why I am learning category theory

#181

Post by larve » Thu, Dec 01, 2022, 4:44 AM UTC

q7xvh97o2pDhNrh wrote: post #180

rssoconnor wrote: post #78

Earlier quoted context omitted.

I agree with you. CT seems mostly useful as a way of devising entirely new abstractions, but once those abstractions are developed, you don't need CT to use them. For example if it were 2008 and you want to be inventor Applicative functors for use in Haskell, then knowing lax monoidal functors from CT might be helpful. But if you want to just use Applicative functors, you don't need to learn lax monoidal functors fir…

Do you have any recommended reading for learning CT from the perspective of an engineer who does want to make their own abstractions? Your description is the single best sales pitch for learning it that I've ever heard. I'm legitimately interested now — in a way that I simply wasn't before your comment. Everyone else who tries to hype up CT is always like, "Whoa, bro, don't you know that addition is actually a monoid…

(author here) I found the corecursive podcast episode about "portal abstractions" with sam ritchie quite inspiring. It's about monoids from the algebraic point of view, but the mindset is very similar, I think.

https://corecursive.com/050-sam-ritchie-portal-abstractions-...

I think I might have linked it in the article.

Re: Why I am learning category theory

#182

Post by charcircuit » Thu, Dec 01, 2022, 4:48 AM UTC

ukj wrote: post #176

charcircuit wrote: post #173

Earlier quoted context omitted.

>You don’t have to reinvent 70+ years of Mathematics What do those 70 years of mathematics do for me as a software engineer? >or teach your language to other people before you can have a meaningful design discussion. It's the other way around. Most engineers will have no clue what you are saying.

>What do those 70 years of mathematics do for me as a software engineer? You mean other than inventing the entire industry in which you work? It's a weird question that I have no idea how to answer for you. What is 70+ years of computer science doing for you as a software engineer? Are you standing on the shoulder of giants; or are you inventing/re-discovering everything by yourself from first principles? >It's the o…

>What is 70+ years of computer science doing for you as a software engineer?

No, what does category theory unlock from mathematics that I can not get without it.

Re: Why I am learning category theory

#183

Post by trenchgun » Thu, Dec 01, 2022, 5:02 AM UTC

edgyquant wrote: post #34

I’ve become increasingly obsessed with set theory. I think we can derive set theory from Turing machines and basically “solve” incompleteness.

Uh... how?

Re: Why I am learning category theory

#184

Post by charcircuit » Thu, Dec 01, 2022, 5:07 AM UTC

larve wrote: post #177

charcircuit wrote: post #173

Earlier quoted context omitted.

>You don’t have to reinvent 70+ years of Mathematics What do those 70 years of mathematics do for me as a software engineer? >or teach your language to other people before you can have a meaningful design discussion. It's the other way around. Most engineers will have no clue what you are saying.

I'm not sure if this is supposed to be sarcastic, but taking it at face value, mathematics are the underpinning of both computer hardware and computer science. Since we are talking about more abstract mathematics, it is what gave us the lambda calculus, complexity analysis of algorithms, type theory, relational algebra, distributed systems. more pragmatically, libraries like redux, react are heavily influenced by con…

>redux, react are heavily influenced by concepts from functional programming

Functional programming concepts don't require learning category theory

>rust has novel concepts from type theory

Type theory isn't category theory. Rust's borrow checker was not inspired by affine types.

https://smallcultfollowing.com/babysteps//blog/2012/02/15/re...

>data engineering in the cloud age leverages a lot of algebraic concepts to achieve massive data throughput

This doesn't requite category theory and those are basic concepts from algebra that you can learn outside of the context of algebra.

>We have parser combinators, lambdas, stronger typing, map and flatmap

These don't require category theory either.

Re: Why I am learning category theory

#185

Post by routerl » Thu, Dec 01, 2022, 5:13 AM UTC

adamddev1 wrote: post #2

Bartosz Milewski's series of lectures on YouTube is a really engaging and enjoyable introduction to category theory. These are really helping me get it. https://www.youtube.com/playlist?list=PLbgaMIhjbmEnaH_LTkxLI...

Bartosz's teaching/explanation style does not work for me.

I have no formal critique of him, or even concrete things to point at to say why it doesn't work for me, but I wanted to add my comment in case someone else was also feeling discouraged by not taking much away from the writings/lectures of an often and highly recommended person.

I generally learn very well from lectures/essays, but that hasn't been true for me re: his work.

Re: Why I am learning category theory

#186

Post by ukj » Thu, Dec 01, 2022, 5:21 AM UTC

charcircuit wrote: post #182

ukj wrote: post #176

Earlier quoted context omitted.

>What do those 70 years of mathematics do for me as a software engineer? You mean other than inventing the entire industry in which you work? It's a weird question that I have no idea how to answer for you. What is 70+ years of computer science doing for you as a software engineer? Are you standing on the shoulder of giants; or are you inventing/re-discovering everything by yourself from first principles? >It's the o…

>What is 70+ years of computer science doing for you as a software engineer? No, what does category theory unlock from mathematics that I can not get without it.

Nothing. You can re-invent and re-discover everything. By yourself. From first principles.

You can re-discover and re-invent all of computation, Mathematics and physics.

Heck, you don’t even need computers if you have pen and paper.

You can do absolutely everything all by yourself. All you need is infinite time.

Re: Why I am learning category theory

#187

Post by larve » Thu, Dec 01, 2022, 5:26 AM UTC

charcircuit wrote: post #184

larve wrote: post #177

Earlier quoted context omitted.

I'm not sure if this is supposed to be sarcastic, but taking it at face value, mathematics are the underpinning of both computer hardware and computer science. Since we are talking about more abstract mathematics, it is what gave us the lambda calculus, complexity analysis of algorithms, type theory, relational algebra, distributed systems. more pragmatically, libraries like redux, react are heavily influenced by con…

>redux, react are heavily influenced by concepts from functional programming Functional programming concepts don't require learning category theory >rust has novel concepts from type theory Type theory isn't category theory. Rust's borrow checker was not inspired by affine types. https://smallcultfollowing.com/babysteps//blog/2012/02/15/re... >data engineering in the cloud age leverages a lot of algebraic concepts to…

Oh, I thought your point was that mathematics wasn't bringing anything to computers. As far as I understand it, category theory is more about finding commonalities across mathematical fields (or indeed, scientific / engineering fields), more so than solving more concrete problems.

What does that give you? For me, I think it gives me an easier way to see common abstractions across different problems I work on.

I am at the beginning of my CT journey itself, but a layman's understanding of monads, functors and applicatives gets me really far writing pretty much the same code when i do bare-metal embedded or frontend javascript. The point is not that I couldn't write bare-metal code or frontend code without, is that I am much quicker seeing "my javascript promises are like a monad" and "my coroutines are like a monad" and being able to shrink my cognitive load.

Re: Why I am learning category theory

#188

Post by larve » Thu, Dec 01, 2022, 5:29 AM UTC

routerl wrote: post #185

adamddev1 wrote: post #2

Bartosz Milewski's series of lectures on YouTube is a really engaging and enjoyable introduction to category theory. These are really helping me get it. https://www.youtube.com/playlist?list=PLbgaMIhjbmEnaH_LTkxLI...

Bartosz's teaching/explanation style does not work for me. I have no formal critique of him, or even concrete things to point at to say why it doesn't work for me, but I wanted to add my comment in case someone else was also feeling discouraged by not taking much away from the writings/lectures of an often and highly recommended person. I generally learn very well from lectures/essays, but that hasn't been true for m…

I really like the "Programming with categories" lecture because you basically get 3 teaching styles for the same material. Brendan Fong is very straightforward "definition lemma definition lemma", Spivak is slightly more example-oriented, and then Bartosz is... bartosz. The juxtaposition helps to unstick me. I do use Eugenia Cheng's Catsters video to complement as well. If I had to chose one personal favourite, it would be her for sure.

Re: Why I am learning category theory

#189

Post by [deleted] » Thu, Dec 01, 2022, 5:32 AM UTC

charcircuit wrote: post #182

ukj wrote: post #176

Earlier quoted context omitted.

>What do those 70 years of mathematics do for me as a software engineer? You mean other than inventing the entire industry in which you work? It's a weird question that I have no idea how to answer for you. What is 70+ years of computer science doing for you as a software engineer? Are you standing on the shoulder of giants; or are you inventing/re-discovering everything by yourself from first principles? >It's the o…

>What is 70+ years of computer science doing for you as a software engineer? No, what does category theory unlock from mathematics that I can not get without it.

[deleted]

Re: Why I am learning category theory

#190

Post by routerl » Thu, Dec 01, 2022, 5:51 AM UTC

larve wrote: post #188

routerl wrote: post #185

Earlier quoted context omitted.

Bartosz's teaching/explanation style does not work for me. I have no formal critique of him, or even concrete things to point at to say why it doesn't work for me, but I wanted to add my comment in case someone else was also feeling discouraged by not taking much away from the writings/lectures of an often and highly recommended person. I generally learn very well from lectures/essays, but that hasn't been true for m…

I really like the "Programming with categories" lecture because you basically get 3 teaching styles for the same material. Brendan Fong is very straightforward "definition lemma definition lemma", Spivak is slightly more example-oriented, and then Bartosz is... bartosz. The juxtaposition helps to unstick me. I do use Eugenia Cheng's Catsters video to complement as well. If I had to chose one personal favourite, it wo…

I've gotten a lot more out Spivak than Bartosz.

It might just be a stylistic thing. I can't quite pinpoint it.

Edit: Eugenia Cheng also makes more sense to me than Bartosz.