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julesh

@julesh.mathstodon.xyz.ap.brid.gy
305 followers 0 following 1.8K posts

Applied Compositional Thinking 🌉 bridged from ⁂ mathstodon.xyz/@julesh, follow @ap.brid.gy to interact

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julesh @julesh.mathstodon.xyz.ap.brid.gy · 23h
My understanding of the new law in the uk is that it remains legal to marry your first cousin, but if you ever made a sex tape together, even for your own private enjoyment, you would get 5 years
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 16/10/2026
@at Oh huh, makes me wonder how to write weird things like continuation and selection monads as infinitary lawvere theories, that isn't obvious how to do it
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 16/10/2026
I intuitively feel like polynomial monads should be equivalent to infinitary Lawvere theories, ie. intermediate between finitary monads (which correspond to ordinary Lawvere theories) and general monads. But the nLab pages don't mention any such thing. Am I right or am I confused?
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 15/10/2026
I'm on a train that stops in Ware, which in the hands of a couple of people with the timing to do the Who's On First routine might be the actual winner of funniest place name in English
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 13/10/2026
I just saw a diplomatic convoy from St Lucia in Dalston in London, for sure they were visiting the amazing St Lucian bakery at Dalston Junction
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 11/10/2026
"Is Material Girl a Marxist song", the greatest thread in the history of forums, locked by a moderator after etc etc etc
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 11/10/2026
Sunset through the palm house at Kew
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 11/10/2026
Pagoda? I 'ardly know 'er
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 08/10/2026
Like many people I am very worried for the near future of my field. I'm not a problem solver and I think the problem solving half of the field is toxic and they are deserving of literally everything that has happened to them. But the dialectic between problem solving and theory building has […]
mathstodon.xyz
Original post on mathstodon.xyz
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 06/10/2026
@dimpase Something like 25 years ago I knew a similar chord on windows ME (?) specifically to type the é in Pokémon
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 06/10/2026
@dimpase ė Well that's intuitive
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 06/10/2026
Here is an extremely neat definition of dependent lenses I've never seen before, as kleisli morphisms of the extension (ie. the equivalence of categories from containers to polynomial functors) considered as some exotic kind of generalised monad
  record Cont where
    constructor MkCont
    base : Type
    fib : base -> Type
  
  record Ext (c : Cont) (y : Type) where
    constructor MkExt
    value : c.base
    continuation : c.fib value -> y

  unit : (x : c.base) -> Ext c (c.fib x)
  unit x = MkExt {
    value = x,
    continuation = id
  }

  extend : ((x : c.base) -> Ext d (c.fib x)) -> Ext c y -> Ext d y
  extend f x = MkExt {
    value = (f x.value).value,
    continuation = x.continuation . (f x.value).continuation
  }

  Lens : Cont -> Cont -> Type
  Lens c d = (x : c.base) -> Ext d (c.fib x)

  compose : Lens c1 c2 -> Lens c2 c3 -> Lens c1 c3
  compose l m x = extend m (l x)
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 06/10/2026
> apt install texlive-full *goes away to do some other stuff for a while*
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 05/10/2026
New profile picture who dis (not sure I'll keep it yet)
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 05/10/2026
It occurs to me that if actually working AI was developed 70 years earlier, as many of the earliest pioneers of the field apparently expected, it would definitely have been immediately taken over by hyper-capitalism back then too
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 05/10/2026
When your brain is smooth so all the thoughts just run off it, that's called a thoughterfall
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 04/10/2026
Reason number whatever that I already hate linux + kde coming from a mac: keyboard shortcuts for diacritics are just shit. After a ridiculous amount of trial an error I have managed to type ëẽéêèẹȩ, but as far as I can tell it is straight up impossible to type ė (a diacritic used in Lithuanian) […]
mathstodon.xyz
Original post on mathstodon.xyz
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 03/10/2026
🚄 : Durham → London
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 02/10/2026
Just stopped in Morpeth, notably the only UK station that is named after a Dark Lord
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 02/10/2026
🚄 : Glasgow → Edinburgh → Durham
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 02/10/2026
Very proud that I successfully did my nails on a moving train without any major mishaps
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 01/10/2026
Haii
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 01/10/2026
Going to the AI shop, anyone need anything?
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 01/10/2026
Doing machine learning (parametric anamorphisms)
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 01/10/2026
RE: wandering.shop/@xgranade/1173609604… Several of these are historical and/or scams, but it's a constant source of confusion that the term AI now refers to at least 3 very different technologies that Actually Work: - LLMs and similar generative models - deep reinforcement […]
mathstodon.xyz
Original post on mathstodon.xyz
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 30/09/2026
I noticed a small sign on a platform in Glasgow central station saying cctv footage is used to train AI models I guess you can opt out of it by walking to London
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 28/09/2026
Rug discovery (visiting small carpet shops in cities like Tehran looking for undocumented designs)
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 24/09/2026
In the very early days of applied category theory around 2018, I twote something to the effect that the next layer up from applied category theory will be design patterns In the last several weeks at Glaive I feel like we have finally reached the design patterns layer
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 24/09/2026
@eigil Here's a fun thing: the version I wrote there was the simply type case, it is easy to construct essentially the same monad on the category of containers and dependent lenses, but to get the corresponding adjunction you need to make dependent adaptors
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 24/09/2026
Here is the extremely tl;dr version of what's happening. The embedding of Set x Setᵒᵖ into lenses admits a left adjoint, and kleisli categories of the induced monad on lenses basically capture the essence of what open games are. And the crazy thing is that I totally knew about this adjunction in […]
mathstodon.xyz
Original post on mathstodon.xyz
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 24/09/2026
Open games are evolving! Preview of a blog post I'm about to write
pd : (PDMove * PDMove) -> Bool
pd = extract $ CalcWith $
  |~  ((PDMove * PDMove) :- Bool)
  <~  (PDMove :- Bool) // (PDMove :- Bool)
  ... and
  <~  Game (PDMove :- Nat) // Game (PDMove :- Nat)
  ... select {c = PDMove :- Nat} (argmax [C, D]) ~//~ select {c = PDMove :- Nat} (argmax [C, D])
  <~  Game ((PDMove :- Nat) // (PDMove :- Nat))
  ... nash {c = PDMove :- Nat, d = PDMove :- Nat}
  <~  Game End
  ... mapGame {c = (PDMove :- Nat) // (PDMove :- Nat)} (costate pdPayoffs)
  <~  End
  ... runGame
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 24/09/2026
Train internet creating a very 21st century Cthulhu cult chant
Jules Hedges: Oh gods emailJules Hedges: Oh gods emailJules Hedges: Oh gods emailJules Hedges: Oh gods email
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 24/09/2026
🚄 : London → Glasgow
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 23/09/2026
Flashback to the one blog post I wrote so far about dependent optics: julesh.com/posts/2025-10-16-depende… I really need to continue this series. Unlike most blog posts I write this is not something I can do easily, this stuff is really complicated and I am a bit out of […]
mathstodon.xyz
Original post on mathstodon.xyz
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 20/09/2026
We had a very close encounter with a very inquisitive fops
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Reposted by julesh
theHigherGeometer @highergeometer.mathstodon.xyz.ap.brid.gy · 20/09/2026
@julesh Gödel was reviewer 2 on Hilbert's program, supplying a counterexample to the main claim
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 20/09/2026
Last week I went to 2 different events. Most of the time I was surrounded by mostly pure mathematicians at an event about AI, and on the whole everybody seemed to be extremely depressed and/or shellshocked about recent events. Then one evening I went to the new London Haskell meetup and it was […]
mathstodon.xyz
Original post on mathstodon.xyz
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 20/09/2026
Hilbert was reviewer 2 to Euclid, finding all the mistakes 2500 years later
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 19/09/2026
> "The agent escaped its sandbox" > looks inside > It's just evaling untrusted code again
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Reposted by julesh
theHigherGeometer @highergeometer.mathstodon.xyz.ap.brid.gy · 19/09/2026
Here's a question that occurred to me: suppose I have a symmetric monoidal category with diagonals and *one* projection (say \\(\mathrm{pr}_1 \colon A \otimes B \to A\\) (so diagonals and this projection is natural. is the monoidal structure necessarily cartesian?
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 19/09/2026
RE: mathstodon.xyz/@mc/1172975366592084… It's lenses again
mathstodon.xyz
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 18/09/2026
It's not a magic box, it's a sufficiently advanced technology box
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 18/09/2026
Bro, just ask Claude whether the Turing machine halts or not
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 18/09/2026
One of the spots in London that can pass for Amsterdam
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Reposted by julesh
raganwald.com @raganwald.functional.cafe.ap.brid.gy · 16/09/2026
“Selection functions and lenses,” from @julesh julesh.com/posts/2021-03-30-selecti…
julesh.com
Jules Hedges - Selection functions and lenses
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 16/09/2026
Flashback to this very short blog post I wrote 5 years ago: Selection functions and lenses julesh.com/posts/2021-03-30-selecti…
julesh.com
Jules Hedges - Selection functions and lenses
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 16/09/2026
Part 5 in the increasingly inaccurately named European Trilogy
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 15/09/2026
I guess we formalised "make no mistakes"
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 14/09/2026
Only you can prevent entropy
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julesh @julesh.mathstodon.xyz.ap.brid.gy · 14/09/2026
One simple practical way to fight against corporations and some of the other bad people is to randomly interleave sexual content with serious work. For slightly complicated historical reasons most of them are puritan (the same ones we expelled from Europe back in the day) so I suspect it sort of […]
mathstodon.xyz
Original post on mathstodon.xyz
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