81–90 of 224 posts
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I think the best way to become a better React developer is to learn Elm, and then build your React apps the same way Elm would have forced you to.
… and Redux was born!
https://redux.js.org/understanding/history-and-design/prior-...
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Honestly I'm pretty weak in both, but they seem to reflect my intuitions, if that makes sense? I'm nowhere near a working mathematician, and proofs usually bore me. I prefer writing code.
If you're looking for an alternate perspective, I would suggest taking an advanced undergraduate analysis book and working through it, proofs and all. It'll teach you the same kinds of stuff that you're getting out of CT but will give you "working" (lol) knowledge of how to apply it. A lot of mathematical work is about creating math objects and relations and proving properties of these objects through their relations…
In parallel I developed this very "visual" way of thinking about structure that makes me really resonate with CT. In a way I'm less interested in learning new maths, more so than learning more about how people approach (complex) structures I already know with these very rudimentary concepts, and seeing how their formalizations match my "folk mathematics".
I'm having a lot of fun!
edit: thanks for the book recommendation! that looks like my kind of maths book
As a former category theorist: don't learn category theory unless you're already rich or want to do it for fun. It will be a lot less rewarding than you expect RE: your engineering ability/understanding.
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Morphisms are not a concept that is specific to category theory. Are there any lemmas or theorems of category theory that are useful in software development?
that's interestingly enough not something I'm interested in (formally deriving things and doing "proper" maths as part of my software work). I care much more about developing new intuitions, and seeing the category theoretical definition of monoid https://en.wikipedia.org/wiki/Monoid_(category_theory) inspired me a lot. In fact I think that one of the great things about software is that you can not care about being v…
What applicable insight did you gain over the normal algebraic definition (https://en.wikipedia.org/wiki/Monoid)?
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> As a programmer and hobbyist math reader, I found category theory to be very unrewarding (and I gave up on it) because of the lack of interesting theorems and lemmas. My takeaway was that there's Yoneda lemma and really nothing interesting before you reach that One of the most interesting things in CT are adjoints. They happen literally everywhere. For example, static analysis via abstract interpretation is an exam…
Sure, but what does the knowledge of something being an adjoint give you?
as with every abstraction, its value is in the value it brings you. That sounds a bit tautological, but I think that's the crux of the matter. If you like abstraction, and abstractions help you think, you are going to find value in them. If you feel they bring you nothing, then there is no need for you to use them.
Mathematics is the mathematics of abstraction. That's all you're doing in math, from the beginning to the end. What's the same between "I have two sheep in this pen and five in that one" and "I have two apples in this basket and five in that one"? Hmm, you can abstract out 2+5=7, since it works the same in both contexts.
Everything in math is creating and exploring abstractions. The good ones tend to stick around, the bad ones tend to be forgotten.
Category theory is the mathematics of composition. How much knowledge can you throw away and create reusable patterns of composition? How many interesting things can you find by adding back the smallest bits of additional structure on top of that minimum? How well do those things compose together, anyway?
I would be willing to drink the kool-aid if I saw it being used in a practical way. I always feel these posts are filled with category theory jargon without ever explaining why any of the jargon is relevant or useful. I’ve even watched some applied category theory courses online and have yet to feel I’ve gained anything substantive from them. However, as I started off with, I’m always willing to try something out or…
A good example is LINQ, they use monads and functors. They just gave them other names.
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Honestly I'm pretty weak in both, but they seem to reflect my intuitions, if that makes sense? I'm nowhere near a working mathematician, and proofs usually bore me. I prefer writing code.
If you're looking for an alternate perspective, I would suggest taking an advanced undergraduate analysis book and working through it, proofs and all. It'll teach you the same kinds of stuff that you're getting out of CT but will give you "working" (lol) knowledge of how to apply it. A lot of mathematical work is about creating math objects and relations and proving properties of these objects through their relations…
I also like the focus on quotient groups and galois fields, as well as using graphs as recurring examples, which have been the only times I really put the pedal to the maths metal in my programming (for some crypto and error correction stuff).
Cool, I am also spending a little time on this. I bought a CT book by Emily Riehl but I am finding it rough going. I find her YouTube talks and lectures to be easier to follow.
Try Eugenia Chang’s new book, The Joy of Abstraction . Riehl’s book is very technical.