julesh

Thinking as a Service

@mudri Oh gods, I sincerely hope it's not NP-hard otherwise I'm going to totally lose my mind. My gut feeling is that it can be done recursively, it might be that some specific feature of my situation makes it easier than what you were doing, or it might be that there's another complication that […]

A diagram expressing a result in higher category theory, stating that there is a biadjoint biequivalence between ddBicat_s-Cat and BrMonCat. One of the functors, U, is explicit, the theorem is stated that U is a pointwise biequivalence. The corollary is that there exists the functor in the other direction, following "from U being a pointwise biequivalence and [Gurski]".

From @alexcorner
I both love and respect this result ... but so much meme potential.

"...and [Gurski]".

@mudri Thanks!

@mudri After a couple more days of thought I'm going with your idea, since switching from codebruijn to debruijn broke everything I know about typechecking. This design is quite a challenge for my scopechecker though, I don't suppose you've trodden the same path as me so exactly that you've ever […]

Building a 21st century equivalent to emacs used to be mainly just a fun idea, but apparently Cursor has provided a serious use case for having an editor built on top of a language with a very fine grained effect system. I don't want to use it unless I can specify edit permissions not just at […]

RE: https://mastoxiv.page/@arXiv_mathLO_bot/116169874137501492

That's what you think Kaiba! I just drew my grandfather's proof that the Halting Problem is actually decidable! Using my grandfather's proof, my Dark Magician is able to compute an optimal play to break through your defenses and […]

Starmer is for sure no Churchill, but then again, Trump is also no Hitler

@mudri It sounds plausible... in fact it sounds plausible that it's the only possible thing that could work. But it feels a bit janky, I wonder if there's some theoretical justification for it

I've been having a gut feeling that some of the additives want to be debruijn so I've been wondering […]

@julesh A system I've considered before for other purposes is one where ⊤-introduction (and, dually, 0-elimination) mentions explicitly all the variables it wants to use. Would that, or that way of thinking, help at all?

@mudri In the meantime I'm currently switched back to debruijn, but for quite a complicated reason: I'm working in a polarised system L where positive inputs are linear and negative inputs are cartesian, and we have a hypothesis that positive inputs should be synth and negative inputs should be […]

@mudri It sounds plausible... in fact it sounds plausible that it's the only possible thing that could work. But it feels a bit janky, I wonder if there's some theoretical justification for it

I've been having a gut feeling that some of the additives want to be debruijn so I've been wondering […]

@mudri Units!!

I have finally come to the conclusion that I have no idea conceptually how do to co de Bruijn scoped additives in linear logic

"The golden goose does not own the farm"
-- @zanzi apparently inventing a new saying that really ought to be 100 years old

Hold the phone, I *might* know how to get static array bounds safety without using dependent types or whatever crazy System Fω stuff that haskell uses to do it

This is an exaggeration of course, Anthropic are nowhere near big enough to qualify as a megacorporation, although I expect one of the others to grab them as soon as they fall on hard times

It's funny that the leadership of Microsoft, who apparently think that all other forms of software are […]

Let's see what level of cyberpunk dystopia we've got up to. Ah yes, level "the fascist government's department of war are feuding with the megacorporation run by the eugenics cult worshipping a machine god that they are trying to create"

I want to start an online anarchist research university. Fuck signalling and degrees and publication count, I want to host a place where people come to collaborate on building knowledge and to learn and teach things. Not so you can "improve your resume" or "get a job" or create connections to […]

@christianp My theory is that since youtube turned 20 years old some people have been watching very old videos and it's causing them to get algorithm'd

(Draw in Rust with a CPU graphics buffer)

Square

One conclusion of the success of transformers I think is underappreciated is that finite support probability is all you need. Gaussians in absolute shambles.

Let me do a quick run down of what I consider to be the major divisions of applied category theory and what they are up to now

- Categorical quantum mechanics (aka the theory of tensor products of vector spaces): huge success, ZX calculus is in widespread commercial use

- Graphical linear […]

It happens that unification is a prerequisite for instantiation, so there is an option to say "we or somebody else will do it later, pinky promise". I was part of the chorus saying that when the field officially got named in 2018. I was one of a very small number who were actually telling the […]

I could say it like this. If you want to do metascience you have one task, which is to unify. If you want to do actual science that merely looks like metascience you have two tasks: unify, and then instantiate in useful ways. Both of these are incredibly difficult, but I would say that applied […]

It's one of the explicit reasons for doing applied category theory at all that it's good at systematising and unifying, which is classic metascience. If that's the main thing it actually achieves, I would consider it metascience. I hope that it will instead be a nice side effect

The biggest […]

There's a slightly subtle distinction between metascience proper, and just umbrella fields. For example, I don't think thermodynamics counts as metascience despite kinda resembling it, because it can be instantiated in different ways to do practical things like modelling the cooling requirements […]

RE: https://mathstodon.xyz/@jonmsterling/116142506010242587

I have virtually a small blog post worth of thoughts about this twoot and the thread below it. tl;dr I broadly agree and this is a better phrasing than I ever managed of why I mostly lost interest in the field of applied category […]

Although. The biggest Pokémon cryptid of my childhood was not Mew or Ho-oh or anything from Fossil like Aerodactyl, it was Jungle Pidgeot: a disturbing monster pictured in flight seen from below, flying in the direction of the arrow, with a gaping open mouth and its top row of teeth circled