Ultrafinitists wanted to organize a conference but the only place that still had rooms available was the Hilbert Hotel
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Bartosz Milewski
@BartoszMilewski@mathstodon.xyz
mastodon 4.7.2Physicist, programmer (Haskell, C++), mathematician, category theorist. Author of Category Theory for Programmers and The Dao of Functional Programming
5287 Followers
12 Following
49 Posts
Joined April 27, 2022
Replying to
@johncarlosbaez@mathstodon.xyz
Our worm-like ancestors were cyclops. When they decided to start swimming, the central eye squeezed out two side eyes and was itself reduced to the pineal gland that to this day regulates our circadian cycle.
https://theconversation.com/our-modern-vision-evolved-from-an-ancient-one-eyed-worm-creature-278120
I just realized that Chekhov's Gun is an example of linear logic. It's a premise that has to be consumed at some point in the plot.
Democracy is like health: You don't appreciate it until you lose it.
In the future, body shaming will be the AI making fun of people who have bodies
Filling my whiteboard with string diagrams. Comma objects and Kan extensions in a double category
Programmers might be able to compete with the AI after all. As long as human intellectual labor is cheaper.
https://www.aol.com/finance/microsoft-ceo-sends-shocking-message-163700210.html
Finishing a blog post on profunctor equipments.
Unit and counit of the adjunction between companions and conjoints in a double category.
Homeopathy in computer science: Take a random sequence and sort it ten times. How much of the original sequence can you recover?
A new post in the series on double categories and profunctor equipment.
https://bartoszmilewski.com/2026/05/18/bending-yanking-and-cartesian-squares-in-double-categories/
Replying to
@dpiponi@mathstodon.xyz
With an obvious sequel: They movie you're pitching wins and Oscar, which is then used to highjack a metro train in Berlin.
Another installment in the series on Double Categories and Profunctor Equipments.
https://bartoszmilewski.com/2026/05/23/tabulation-tribulations/
I decided to popularize double categories using profunctor equipment as a model.
https://bartoszmilewski.com/2026/04/24/profunctor-equipment/
Haskell implementation of 2-cells in profunctor equipment
Replying to
@dpiponi@mathstodon.xyz
The goal, though, is noble: Using Banach-Tarski, produce two Earths, one red, one blue.
Another blog post in the series on profunctor equipment
https://bartoszmilewski.com/2026/05/16/profunctor-equipment-in-haskell/
Replying to
@johncarlosbaez@mathstodon.xyz
That reminds me of the lemur aye-aye that also has very long fingers.
@sjoerd_visscher@types.pl
I decided to write a post about my toy implementation of profunctor equipments. Here's the preview.
https://bartoszmilewski.com/?p=14290&preview=1&_ppp=770ff31cfc
TIL that Haskell module names cannot start with a number. I have a bunch of Haskell files for my book, whose names start with chapter numbers. I can compile them, but when I tried to add them to a cabal file, I was thwarted. What could be the reason for such a restriction, one wonders.
@sjoerd_visscher@types.pl
I worked out the right adjoints to profunctor composition. Do you already have it in your library?
https://v15.next.forgejo.org/BartoszMilewski/Categories/src/branch/main/src/ProfClosed.hs
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@h0gh@mastodon.social @drmakimber@mathstodon.xyz
I bet they blame it on Dedekind cuts
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@johncarlosbaez@mathstodon.xyz
The US has a huge infrastructure debt. All those overhead power lines that snap every time the wind starts blowing. Not to mention the esthetic nightmare of tangles of sky-obscuring wires in every residential area. Most Americans don't even notice it.
Replying to
@vnikolov@ieji.de
Joking aside, ultrafinitists actually had a conference. Not at any math department, but at a philosophy department, where they are tolerated. I even recognize some names.
https://philosophy.columbia.edu/events/ultrafinitism-physics-mathematics-and-philosophy
Replying to
@sjoerd_visscher@types.pl
Have you seen this paper? It shows that Tambara modules form a proarrow equipment.
https://arxiv.org/abs/2210.13443
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@johncarlosbaez@mathstodon.xyz @gregeganSF@mathstodon.xyz
In the modern world you need a PhD to realize how insignificant the chances of you advancing science really are.
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@GoodAaron@mastodon.social
And of course "Dune" -- the strugles against colonialism and theocracy
Replying to
@sjoerd_visscher@types.pl
Half of category theory is struggling with conventions. I decided to use the convention where the direction of the profunctor arrow agrees with the direction of morphisms in the hom-functor.
Replying to
@6d03@mathstodon.xyz
For me they're horizontal lines, although they connect two areas that are on top of each other, so I see your point. I've been following the conventions of David Jaz Myers.
https://arxiv.org/abs/1612.02762
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Replying to
@julesh@mathstodon.xyz The main problem is that the exponentials diverge, so the rich are getting richer, while the poor are getting relatively poorer. A quarter of American household have zero or negative net worth, so they are getting poorer with time.
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@johncarlosbaez@mathstodon.xyz @alisonkiddle@mathstodon.xyz
I whould divide the two numbers and see if the result is less than one. The advantage is that you can cancel the factor of 2⁴
Replying to
@sjoerd_visscher@types.pl
My experience was that any optics I could put my hands on has a Tambara representation and that this is related to Tannakian reconstruction. So I'm looking for a grand unified theory of optics, and double categories look promising in this respect. At the very least they unify regular optics with enriched optics.
Replying to
@sjoerd_visscher@types.pl
This is some very impressive library. Are you planning on writing more detailed documentation for it? Translating from category theory to Haskell involves a lot of implementation decisions, so some kind of roadmap would be very useful.
Replying to
@julesh I guess it satisfies the first definition. But notice that it's subjective. A "hallucination" doesn't meet our expectations. But whose fault is it?
- an unattractive or unsatisfactory feature, especially in a piece of work or in a person's character.
- responsibility for an accident or misfortune.
Replying to
@julesh But how is this a fault? The LLM provides the most plausible sounding answer to your question. It's painting a picture or writing a novel for you. You might not like it because you have a particular esthetic in mind. A novel is not wrong because it cites a non-existing paper to move forward the plot.
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@regehr@mastodon.social
There's also the option of installing an electrical outlet in the shower...
Though, on second thought...☠️
Replying to
@regehr@mastodon.social
Has anyone tried using an iPhone in the shower? They are supposed to be water resistant and there is a ToDo applet on them.
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@colincornaby
Ever since people realized that you can sear a steak on a GPU running LLM, the Nvidia stock is skyrocketing
Replying to
@sjoerd_visscher@types.pl @6d03@mathstodon.xyz
It seems to me like you're defining a subcategory of Hask by imposing a Constraint on objects. So a Tabulator would be a class that takes two categories and a profunctor between them. It would have two projections giving objects in these two categories, and a projection that gives the element of the type given by the profunctor on these two objects. Does it make sense?
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@sjoerd_visscher@types.pl @6d03@mathstodon.xyz
A morphism is built from two pairs of objects (a, b) and (a', b') and a pair of arrows (u: a -> a', v: b -> b'). They have to satisfy a commuting square that uses lmap and rmap.
Replying to
@6d03@mathstodon.xyz
No, they are horizontal, but I use string diagrams. For instance, this is vertical composition of 2-cells:
Replying to
@sjoerd_visscher@types.pl @6d03@mathstodon.xyz
Well, I'm afraid my code is really a toy example based on endofunctors. What I really need is categories and functors between them. What definition of a category did you use?
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@sjoerd_visscher@types.pl @6d03@mathstodon.xyz
Next I want to test the definition of tabulation in Prof
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@sjoerd_visscher@types.pl @6d03@mathstodon.xyz
This is also known as a Bool-enriched profunctor
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@EUCommission@ec.social-network.europa.eu
I'm using uBlock origin to block ads. But I'm paying a ransom to Facebook.
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@sjoerd_visscher@types.pl @6d03@mathstodon.xyz
Yes, trying to do dependent types in Haskell is a challenge. How would you encode the simplest category of elements of a functor. An object is a type a and a value x :: f a. A morphism from (a, x) to (b, y) is a function u: a->b such that fmap u x = y. If you can encode this, then tabulation should be relatively easy.
Replying to
@bjacobs
Why is Europe so far behind the US and China? There must be some deep systemic issues that work against European innovation. Why isn't there a European Microsoft or Apple and, more recently, an AI company on a par with the Americans? It's definitely not for want of intellectual power in Europe.
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@sjoerd_visscher@types.pl @6d03@mathstodon.xyz
Yes, I also used (Co-)Star as my Conjoint/Companion.
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@varkor@mathstodon.xyz
Thanks, I'll correct this. It was the result of my perusing Grandis & Pare, where they say "the (strict) double category Dbl consisting of weak double categories, lax double functors (as horizontal arrows) and colax double functors (as vertical arrows), with suitable cells." So this works for pseudo or weak double categories.