@julesh@mathstodon.xyz
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julesh

@julesh@mathstodon.xyz

Applied category theorist
Games, learning, control, complex systems, diagrams, syntax
Affiliations: MSP Group / 20squares / CyberCat Institute

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julesh, to random
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A style I very rarely hear about in Haskell is using the module system to implement quotient types, which as far as I know is quite common in ML land. For example if you want to implement finite sets you can implement them as boxed lists, in a module that only exports operations that are well-defined on sets, ie. invariant under commutativity and idempotency of lists

BartoszMilewski, to random
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Today's NYT crossword puzzle used an abelian comonoid without a counit. They call it a "letter bank". It's like an anagram where you can duplicate letters, but you can't delete them.

julesh,
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@BartoszMilewski I'd call it a "cosemigroup", but crap terminology doesn't need any more encouragement

julesh, to random
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I don't understand why more blockchain people aren't on mastodon. Obviously the grifters want to be where the suckers are, but I'm talking about the serious people. The network is literally decentralised, what more do they want?

julesh,
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@jennwrites Oh yeah, I think this is probably the biggest reason... This protocol isn't trustless, but building a trustless social network is solving a problem that pretty much doesn't exist in return for a heap of downsides, and federation mostly solves the same problem but better

julesh, to random
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Any given year could be the year that the gulf stream goes away and northern Europe returns to its natural temperature, but given everything this year I'm more concerned than most...

julesh, to random
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Category theory fact: cocoa is just a

julesh, to random
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🚄 : London -> Paris

julesh, to random
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How in the world did people do international travel before the internet?

Like... you can't even look up hotels in the phone book, unless you happen to have a phone book for the country you're going to...

julesh, to random
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I don't remember who recommended me https://followgraph.vercel.app/ but it's the most amazing thing for finding new people to follow, it's outdone twitter even in its heyday

julesh, to random
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"No, the Yoneda lemma doesn't solve the problem of qualia" by @mc
https://matteocapucci.wordpress.com/2023/07/15/no-the-yoneda-lemma-doesnt-solve-the-problem-of-qualia/

julesh,
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@johncarlosbaez It sounds very brutal to actually write down

johncarlosbaez, (edited ) to random
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I can tell I'm no longer in the USA, land of large cars.

I just heard that the very nice 90-year-old French lady who owns this car is the mother of two members of the band Ministry. Are there really two brothers in that band? Or were there? It seems to have a changing cast of members.

julesh,
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@johncarlosbaez Are you doing seminars again when the next semester starts?

I wonder if I can invent some plausible excuse to visit you sooner than then...

julesh,
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@johncarlosbaez Officially we finished seminars for the summer, unofficially it's totally fine if you want to show up and do a talk. Some people will be away on holiday at each time, but not all at the same time

julesh, to random
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I reckon I could unhook myself from caffeine if I was determined, at the expense of a few weeks of withdrawal - If I don't have coffee by around midday I feel like my head is in an underwater vice and I get in an extremely bad mood and can't think about anything except how to get coffee

But, I like coffee. Also I probably need some stimulant to function effectively, and caffeine is probably the mildest and safest and by far the easiest to obtain

julesh, to random
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Street advertising is just legal tagging

julesh, to random
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julesh, to random
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Given a linear function there's an easy way to determine whether it's invertible, namely its determinant. Is there a comparable way to determine whether a term in linear λ-calculus is invertible?

julesh, to random
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Bringing a product to market is an extemely leaky way of measuring usefulness, but it has the advantage of being unambiguous

From applications of category theory I exclude industrial functional programming (Facebook, Jane Street etc) because that's kind of its own thing. I also exclude corporations that have dabbled with category theory but not (yet?) brought it to market (eg. Uber, Siemens).

That leaves us with...

  • ZX calculus (Quantinuum, IBM etc)
  • Functorial database theory (Connexus)
  • Compositional game theory (20squares)
    ... and that's all I can think of right now
julesh, to random
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Yeah Boii

Joemoeller, to random
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If your base of enrichment is a Markov category, you should say the category is “probably enriched”.

julesh,
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@Joemoeller Enriching in a Markov category is kind of gnarly, I can't think of anything that could be useful for...

julesh,
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@Joemoeller A category enriched in Markov kernels could itself have morphisms that are entirely deterministic or are not functions at all, but composition is a stochastic process. Given morphisms f : X -> Y, g : Y -> Z and h : X -> Z, you can never say that h = fg, only talk about the probability P[h = fg]

julesh, to random
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Simon Burton (@simonburton) - Categorified path calculus
https://arxiv.org/abs/2307.03075

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julesh,
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These diagrams are apparently equivalent to sheet diagrams (https://arxiv.org/abs/2010.13361) but make different tradeoffs. We required all objects to be in disjunctive normal form, which makes our diagrams much simpler but our composition law much more complicated

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julesh, to random
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Little functional programming exercise that I repeatedly find myself solving and find surprisingly tricky but maybe there's a trick that I missed:

Given 2 types with finitely many values enumerated by lists xs and ys, produce the list of all possible functions x -> y, whose length is (length ys)^(length xs)

julesh,
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@BartoszMilewski This is the version that looks like my coding style (I like to use sequence a lot), then the list of pairs can be turned into a function using lookup, as in https://recurse.social/@rntz/110672161748619552

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