Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Applied Compositional Thinking for Engineers

applied-compositional-thinking.engineering

Post reply on HN
Print view View original

11–20 of 33 posts

Re: Applied Compositional Thinking for Engineers

#11

Post by neonological »

spekcular wrote: post #6

I always groan when I see posts on HN with grandiose claims about category theory, like this one. I think it is actively harmful to propagate pseudo-mathematical claims like the those, for example, found in the slides of Guest Lecture 1: >>> It’s touched or greatly influenced all corners of mathematics. >>> It’s become a gateway to learning mathematics. And from the audio of the lecture (paraphrasing): >>> Category t…

>>> Category theory is the stem cell that differentiates into and lies at the root of all pure mathematics. ["All forms of pure math" is also written on the slides.]

I would say this statement is not false. It does seem to lie at the root and is an alternative to set theory which means that mathematics can be perceived with category theory as it's foundation. Whether an actual written CT reformalization has been executed within all the pure mathematical sub fields or whether doing an actual formalization from the perspective of CT will be a benefit at all is another topic all together.

I agree that category theory is not popular. However I feel software engineers should have interest in it as Category theory looks to intersect with an area of software engineering that is currently done ad-hoc style with just gut feelings.

If you squint, Category theory looks to be a formalized theory for the design and complexity of modules. Fully understanding Category theory and how it applies to software could lead to a future where design and architecture is "calculated" rather then "designed."

Re: Applied Compositional Thinking for Engineers

#12

Post by Koshkin »

bcheung wrote: post #7
gugagore wrote: post #5

I had (maybe unreasonably) hoped that this course would provide a glimpse into how CT can be applied to organizing and processing data in the sense of keywords like "knowledge graphs", "graph databases", "ontologies", "model-based engineering".... And on top of that, representing operations to do meaningful (semantic) version control on these representations (e.g. [1, 2]), and bidirectional transformations [3] betwee…

CT is universal in the sense that if you understand how it is applied in one domain you can easily apply it to others. The problem with CT education IMO is that it cannot be taught at the abstraction level only -- there are too many floating abstractions that people can't anchor to any existing knowledge. This means CT can only REALLY be understood once you apply it to a domain. The problem is that not many people ou…

In CT terms, "CT has a universal property..."

Re: Applied Compositional Thinking for Engineers

#13

Post by spekcular »

Koshkin wrote: post #9
spekcular wrote: post #6

I always groan when I see posts on HN with grandiose claims about category theory, like this one. I think it is actively harmful to propagate pseudo-mathematical claims like the those, for example, found in the slides of Guest Lecture 1: >>> It’s touched or greatly influenced all corners of mathematics. >>> It’s become a gateway to learning mathematics. And from the audio of the lecture (paraphrasing): >>> Category t…

Personally, I wouldn't be that skeptical. By its very nature CT as a foundational theory and is relevant to, and has at least in that sense indeed touched, all corners of mathematics. (Mathematicians had the same skepticism about Set Theory when it first appeared.) Especially the "theoretical" (pure) math. So, sure, "you can read the entire thing without it, with no real loss", but this only says something about the…

Can you please explain to me how learning category theory is relevant to, or would enhance the work of, a research mathematician who works on, say, harmonic analysis or probability theory?

What is the actual loss to these mathematicians?

Also, your claim that category theory is a foundational theory (in the sense that set theory is) is just mistaken. Homotopy type theory claims to be such a theory, but homotopy type theory should not be identified with category theory more broadly.

Re: Applied Compositional Thinking for Engineers

#14

Post by nine_k »

spekcular wrote: post #6

I always groan when I see posts on HN with grandiose claims about category theory, like this one. I think it is actively harmful to propagate pseudo-mathematical claims like the those, for example, found in the slides of Guest Lecture 1: >>> It’s touched or greatly influenced all corners of mathematics. >>> It’s become a gateway to learning mathematics. And from the audio of the lecture (paraphrasing): >>> Category t…

I suspect such claims might grow from the idea that you can replace set-theoretic constructs with category-theoretic constructs in certain places, and see what happens. It must be pretty fundamental, in the sense that dependence on a set theory lies in the foundation of many branches of mathematics. I can't say how universally such an approach can be applied; likely not very much.

Re: Applied Compositional Thinking for Engineers

#15

Post by Koshkin »

spekcular wrote: post #13
Koshkin wrote: post #9

Earlier quoted context omitted.

Personally, I wouldn't be that skeptical. By its very nature CT as a foundational theory and is relevant to, and has at least in that sense indeed touched, all corners of mathematics. (Mathematicians had the same skepticism about Set Theory when it first appeared.) Especially the "theoretical" (pure) math. So, sure, "you can read the entire thing without it, with no real loss", but this only says something about the…

Can you please explain to me how learning category theory is relevant to, or would enhance the work of, a research mathematician who works on, say, harmonic analysis or probability theory? What is the actual loss to these mathematicians? Also, your claim that category theory is a foundational theory (in the sense that set theory is) is just mistaken. Homotopy type theory claims to be such a theory, but homotopy type…

I wouldn't try, but Helemskii's Lectures And Exercises on Functional Analysis show all this in exquisite detail.

The Convenient Setting of Global Analysis (freely available as a PDF) makes extensive use of the categorical notions and methods.

Re: Applied Compositional Thinking for Engineers

#16

Post by spekcular »

Koshkin wrote: post #15
spekcular wrote: post #13

Earlier quoted context omitted.

Can you please explain to me how learning category theory is relevant to, or would enhance the work of, a research mathematician who works on, say, harmonic analysis or probability theory? What is the actual loss to these mathematicians? Also, your claim that category theory is a foundational theory (in the sense that set theory is) is just mistaken. Homotopy type theory claims to be such a theory, but homotopy type…

I wouldn't try, but Helemskii's Lectures And Exercises on Functional Analysis show all this in exquisite detail. The Convenient Setting of Global Analysis (freely available as a PDF) makes extensive use of the categorical notions and methods.

This does not answer my question. The material in the first book is all well-known. A standard reference is Reed and Simon's Methods of Modern Mathematical Physics. Categories don't gain you anything there, and in any case it's tangentially relevant to most work in harmonic analysis and probabiility. The second book is not relevant at all.

Just because you can produce books on analysis where someone uses the word "category," does not mean a working mathematician ought to care.

Re: Applied Compositional Thinking for Engineers

#18

Post by motohagiography »

The way that CT is explained to engineers here is what tech architects do every day, and with the rigour of formalisms that would help clarify a lot of the muddled thinking some architects suffer from. Arguably, an architect is someone who uses categories and relationships between them to solve and optimize for aggregate behaviour and outcomes.

I watched the first guest lecture, which was very good. I'm not a mathematician, engineer, or a category theorist, but I can apply the formalisms to system architecture instantly.

Re: Applied Compositional Thinking for Engineers

#19

Post by Koshkin »

spekcular wrote: post #16
Koshkin wrote: post #15

Earlier quoted context omitted.

I wouldn't try, but Helemskii's Lectures And Exercises on Functional Analysis show all this in exquisite detail. The Convenient Setting of Global Analysis (freely available as a PDF) makes extensive use of the categorical notions and methods.

This does not answer my question. The material in the first book is all well-known. A standard reference is Reed and Simon's Methods of Modern Mathematical Physics . Categories don't gain you anything there, and in any case it's tangentially relevant to most work in harmonic analysis and probabiility. The second book is not relevant at all. Just because you can produce books on analysis where someone uses the word "c…

(Funny that you mentioned "a working mathematician.")

Anyway, wouldn't it be nice to really understand, on some (higher, admittedly) level, what it is that you are actually doing? Functors and all...

Re: Applied Compositional Thinking for Engineers

#20

Post by skybrian »

motohagiography wrote: post #18

The way that CT is explained to engineers here is what tech architects do every day, and with the rigour of formalisms that would help clarify a lot of the muddled thinking some architects suffer from. Arguably, an architect is someone who uses categories and relationships between them to solve and optimize for aggregate behaviour and outcomes. I watched the first guest lecture, which was very good. I'm not a mathema…

I guess, but I'm reminded of the promises made for UML, where in the end it just introduced some standard conventions for whiteboard diagrams.

Abstract, domain-independent formalisms can make ideas harder to understand than domain-specific, concrete examples. With category theory, I'm not seeing examples of the formalism paying off that would justify the endeavor.

Post reply on HN