@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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I've never seen a perspective on elementary game theory that emphasises tensor algebra, but I've been recently thinking it's a useful perspective. The closest standard perspective that if an individual player of a bimatrix game has payoff matrix U, and the 2 players have mixed strategies given by stochastic column vectors x,y then player 1's expected utility is xUyᵀ

I think it would be useful to say that a bimatrix game is a rank-3 tensor Gᵢⱼₖ , then the expected utility of both players is given by (in Einstein notation) Uₖ = Gᵢⱼₖxⁱyʲ

julesh,
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@johncarlosbaez I teach game theory as part of a masters degree in AI, so they definitely know a bit of tensor algebra, and they probably call it "einsum notation”

christianp, to random
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I'm pretty disappointed to see that mathstodon.xyz is pretty low down this ranking of instances by percentage of images with alt text. https://mastodon.social/@AltTextHealthCheck/111994660926898501

Pals! We can do better! It doesn't take long and it's not hard to add alt text to any images or videos you post.

julesh,
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@christianp Being in the top 50 seems pretty good to me. Learning that we're even eligible by active user count suddenly makes the network feel much smaller than I thought it was

julesh, to random
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It's only a quite small exaggeration to say all the smartest people I know are leaving academia

julesh, to random
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Apparently MS Word now uses AI to add alt text to images, so an extensive form game in my exam model solutions is now labelled "a diagram of a train"

julesh,
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I added another one and it immediately outdid itself with the glorious "A diagram of a diagram"

BartoszMilewski, to random
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At long last our paper from the 2019 Applied Category School in Oxford was published. Congratulations to the whole team!
https://compositionality-journal.org/papers/compositionality-6-1/

julesh,
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@BartoszMilewski @johncarlosbaez Some of it was me finding out the hard way that I'm not cut out to be a journal editor :(

julesh, to random
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julesh's algebraic axiom tier list:

S: associativity (if you don't have it you have nothing)
A: unitality (you can get by without it in a pinch but it's unpleasant)
B: commutativity (it makes your life easier, but it makes you over-reliant and you often don't actually need it)
C: invertibility (it has such nice consequences that mathematicians assume it by default, but it's pretty rare in real examples)
D: idempotency (lattices and projectors are cool, but niche)
F: invertibility except for zero (the world if fields were algebraic...)

julesh, to random
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It's not a coincidence that (1) my PhD thesis had 2 different major mathematical errors that I would have caught if I'd written my proofs more carefully and which took multiple person-years to fix, and (2) it founded an entire field that is still going from strength to strength

Writing proofs just weighs you down. I see no need whatsoever to prove something that I already know is true.

julesh,
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@boarders Testing!!! That's why I write code at all, so I can run it. Every time we add a new feature we validate it against some models we solve by hand or with analytic solutions or simulations taken from papers or books

At the moment the testing is super disorganised, it's on the todo list to have a proper CI test suite that validates every push to main against a whole battery of pre-solved models coming from various domains

julesh, to random
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Seems like there's a major gap in the market for someone to make a federated social network on top of ActivityPub that’s, like, good

julesh, to random
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I'm not sure how to feel about the fact that the UK has a worse recent success rate than North Korea at testing nuclear missiles

christianp, to random
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Lisp: what if everything was a function?

Smalltalk: what if everything was an object?

Ruby on Rails: what if everything was defined somewhere else?

julesh,
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@christianp Ah yes, I remember when nonlocality-oriented programming was the hype new thing that was going to solve everyone's problems

shriramk, to random
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A British man in this airport is telling a Moroccan waiter that he's never before been to Morocco despite having a house "in Gibraltar". The Moroccan has trouble understanding so he repeats, "Gibraltar, in Spain".

I may have just witnessed the birth of an international incident.

julesh,
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@dimpase @christianp @johncarlosbaez @ccppurcell @shriramk Since we sometimes call them "these islands", if you are not located here it would make grammatical sense to call them "those islands"

christianp, to random
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The 3-year-old 🧒: "Is it later now?"

The answer is either "yes, by definition" or "no, by definition", but I'm not sure which.

julesh,
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@christianp There's a version for distance too
"Are we there yet?"
"No, the place we're going is 1 mile away"
Later: "Are we 1 mile away yet?"

julesh, to random
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The funny thing about English history is that for each of its many civil wars you can look up which side the Sandwiches were on

julesh, to random
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I vaguely wonder, if you have a language like C that has a way to refer to functions by variables and call them, but doesn't have lambda, can you emulate lambda by some like CPS stuff or something

BartoszMilewski, to random
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I derived a van Laarhoven representation for a parametric lens (used in neural networks). Is this a known thing?

julesh,
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@BartoszMilewski I don't consider this a “true” vL representation. I would like something like this to be possible, but so far I didn't figure out a way to do it:

class (Functor f) => Foo p dp f where
-- ?????

type ParaLens a da p dp s ds = forall f. (Foo p dp f) => (a -> f da) -> (s -> f ds)

julesh,
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@BartoszMilewski Right.... there's a parallel version of this conversation happening on monoidal cafe that reached the same idea, this is also something I realised a few months back but then forgot again. It's definitely tricky, but I also can't help thinking it could be possible with some complicated subtyping shenanigans

julesh, to random
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The category of finite dimensional vector spaces is traced for its tensor product, which amounts to the ordinary matrix trace

Is it also traced for the direct product? If so, what does it do? My gut feeling is something to do with eigenvectors...??

christianp, to random
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When your son starts saying seemingly random numbers and you wonder if he's a numbers station sleeper cell

julesh,
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@christianp he'll grow up to be a Numberwang champion

julesh, to random
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Closed borders are inherently communist, right? It's completely about disrupting the free market for labour which would otherwise find the most efficient assignment of people to jobs

julesh, to random
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von Neumann & Morgenstern's observation that moves of nature can always be floated up to the top of an extensive form game tree using information sets is definitely a distributive law wearing a false moustache

julesh, to random
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Haskell hot take: Prelude should make Float and Double non-instances of Eq, and then provide functions unsafeFloatEq and unsafeDoubleEq for those cases when you really do want to compare them for equality

julesh, to random
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Thing that just came up in teaching: Num used to be a subclass of Eq in the 2010 Haskell Prelude, but isn't any more

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