The author's writing style and overuse of parentheses is excruciating. True parenthetic material is rare, good technical writers use them sparely.
Category Theory Illustrated – Orders
51–60 of 72 posts
Re: Category Theory Illustrated – Orders
#52The author's writing style and overuse of parentheses is excruciating. True parenthetic material is rare, good technical writers use them sparely.
I can read a person’s ADHD level by their parentheses usage. Unless they are lisp programmers.
Re: Category Theory Illustrated – Orders
#53Earlier quoted context omitted.
You say pretty obvious, but it took me 2 years during my PhD to be consciously aware of this. And once I did, I immediately knew I wanted to leave my field as soon as I would finish.
I'm just curious. Do you play computer games?
I have played quite a lot of video games in the past yes. But not much anymore.
Re: Category Theory Illustrated – Orders
#54Re: Category Theory Illustrated – Orders
#55I think it is pretty obvious that at the challenge with all abstract mathematics in general and the category theory in particular isnt the fact that people dont understand what a "linear order" is, but the fact it is so distant from daily routine that it seems completely pointless. It's like pouring water over pefectly smooth glass
Is there a "mind-blowing fact" about category theory? Like the first time I've heard that one can prove there is no analytical solution for a polynomial equation with a degree > 5 with group theory , it was mind-blowing. What's the counterpart of category theory?
well, this is more applied and less straightforwardly categorical, but thinking along the lines of solely looking at compositional structure rather than all the properties of functions we usually take as semantic bedrock in functional programming (namely referential transparency) is how you start doing neat arrowized tricks like tracking state in the middle of a big hitherto-functional pipeline (for instance automata, functions which return a new state/function alongside a value, can be neatly woven into pipelines composed via arrow composition in a way they can't be in a pipeline composed via function composition)
Re: Category Theory Illustrated – Orders
#56I once saw a man with a notebook and pencil drawing these kinds of diagrams, at the time I saw them as graph theory. I wasn't in an extrovert moment and missed my chance to ask. He seemed to be working recreationally on them. I'm wondering about puzzles that could be easily created using these theories / maths. You, practitioners, any suggestions?
Re: Category Theory Illustrated – Orders
#57Earlier quoted context omitted.
> an untyped closure-based programming language with a similar array and sort api to JS Ah! You're talking about Racket or Scheme! ``` > (sort '(3 1 2) (lambda (a b) ( '(1,2,3) ``` I suppose you ought to go and tell the r6rs standardisation team that a HN user vehemently disagrees with their api: https://www.r6rs.org/document/lib-html-5.96/r6rs-lib-Z-H-5.h... To address your actual pedantry, clearly you have some imp…
The syntax in the article is not scheme, you can clearly see it in my comment you're responding to. As for your 'light introduction' comment: even ignoring the code, these are not pedantic complaints but basic mathematical and factual errors. For example, the statement of Birkhoff’s Representation Theorem is wrong. The article says: > Each distributive lattice is isomorphic to an inclusion order of its join-irreducib…
> That is simply not the theorem.
> The article is plain wrong.
> This does not excuse the article from reversing the meaning of the theorem.
What's with this hyperbole? Even the best math books have loads of errors (typographical, factual, missing conditions, insufficient reasoning, incorrect reasoning, ...). Just look at any errata list published by any university for their set books! Nobody does this kind of hyperbole for errors in math books. Only on HN do you see this kind of takedown, which is frankly very annoying. In universities, professors and students just publish errata and focus on understanding the material, not tearing it down with such dismissive tone. It's totally unnecessary.
I don't know if you've got an axe to grind here or if you're generally this dismissive but calling it "simply not the theorem" or "plain wrong" is a very annoying kind of exaggeration that misses all nuance and human fallibility.
Yes, the precise statement of Birkhoff's representation theorem involves down-sets of the poset of join-irreducibles. Yes, the article omits that. I agree that it is imprecise.
But it's not "reversing the meaning". It still correctly points to reconstructing the lattice via an inclusion order built from join-irreducibles. What's missing is a condition. It is sloppy wording but not a fundamental error like you so want us to believe.
Feels like the productive move here is just to suggest the missing wording to the author. I'm sure they'll appreciate it. I don't really get the impulse to frame it as a takedown and be so dismissive when it's a small fix.
Re: Category Theory Illustrated – Orders
#58I once saw a man with a notebook and pencil drawing these kinds of diagrams, at the time I saw them as graph theory. I wasn't in an extrovert moment and missed my chance to ask. He seemed to be working recreationally on them. I'm wondering about puzzles that could be easily created using these theories / maths. You, practitioners, any suggestions?
> I once saw a man with a notebook and pencil drawing these kinds of diagrams, at the time I saw them as graph theory.
I have been engaged in some work on s-arc transitive graphs in algebraic graph theory. You'd be surprised how rarely I have to draw an actual graph. Most of the time my work involves reasoning about group actions, automorphisms, arc-stabilisers, etc.
For anyone curious what this looks like in practice, I have some brief notes here: https://susam.net/26c.html#algebraic-graph-theory>. They do not cover the specific results on s-arc-transitivity I have been working on but they give a flavour of the area. A large part of graph theory proceeds without ever needing to draw specific graphs.
Re: Category Theory Illustrated – Orders
#59Earlier quoted context omitted.
Is there a "mind-blowing fact" about category theory? Like the first time I've heard that one can prove there is no analytical solution for a polynomial equation with a degree > 5 with group theory , it was mind-blowing. What's the counterpart of category theory?
Just Yoneda Lemma. In fact it feels like the theory just restates Yoneda Lemma over and over in different ways.
How is this useful?