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BartoszMilewski

@BartoszMilewski@mathstodon.xyz

Physicist, programmer (Haskell, C++), mathematician, category theorist. Author of Category Theory for Programmers and The Dao of Programming

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BartoszMilewski, to random
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Is this what the US Congress is devolving into?

BartoszMilewski, to random
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Remove "ask" from Haskell and you get Hell.

julesh, to random
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Obviously not everything can be understood with just category theory, although I'm starting to kinda suspect that everything can be understood with a mixture of category theory and statistical physics

BartoszMilewski,
@BartoszMilewski@mathstodon.xyz avatar

@julesh I think category theory defines what can be understood because "understanding" is the ability to decompose.

I also believe that not everything can be understood (in fact, things that can be understood have measure zero).

BartoszMilewski, to random
@BartoszMilewski@mathstodon.xyz avatar

Shocking! According to NYT, "17 percent of voters in the top six battleground states believed, incorrectly, that Mr. Biden, not Mr. Trump, was responsible for ending the constitutional right to abortion."

johncarlosbaez, to random
@johncarlosbaez@mathstodon.xyz avatar

Chemistry is like physics where the particles have personalities - and chemists love talking about the really nasty ones. It makes for fun reading, like Derek Lowe's column "Things I Won't Work With". For example, bromine compounds:

"Most any working chemist will immediately recognize bromine because we don't commonly encounter too many opaque red liquids with a fog of corrosive orange fumes above them in the container. Which is good."

And that's just plain bromine. Then we get compounds like bromine fluorine dioxide.

"You have now prepared the colorless solid bromine fluorine dioxide. What to do with it? Well, what you don't do is let it warm up too far past +10C, because it's almost certainly going to explode. Keep that phrase in mind, it's going to come in handy in this sort of work. Prof. Seppelt, as the first person with a reliable supply of the pure stuff, set forth to react it with a whole list of things and has produced a whole string of weird compounds with brow-furrowing crystal structures. I don't even know what to call these beasts."

https://www.science.org/content/blog-post/higher-states-bromine

BartoszMilewski,
@BartoszMilewski@mathstodon.xyz avatar

@johncarlosbaez In physics particles have personalities too. Some quarks have charm, others beauty.

BartoszMilewski, to random
@BartoszMilewski@mathstodon.xyz avatar

Putin is going on a visit to China in a few days. We'll see if Xi is willing to grant him asylum.

dpiponi, to random
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Watched The Descent for the second time. Just as good as the first time. To me it's the perfect little horror movie.

BartoszMilewski,
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@dpiponi I just watched Moana-- also the upbeat American version with a happy ending. Wander what the original ending was. 🤔

dpiponi, to random
@dpiponi@mathstodon.xyz avatar

I love the waves of leg motion on this critter that was walking across our driveway.

Very dark red segmented worm like creature with maybe 100 legs that move in waves starting at the back and moving forward.

BartoszMilewski,
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@dpiponi It looks like it's lost part of one of its antennae, and yet it's able to somehow compensate for it.

BartoszMilewski, to random
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I'm struggling with the definition of the category of elements--the direction of morphisms. Grothendieck worked with presheaves (C^{op} \to \mathbf{Set}), with a morphism ((a, x) \to (b, y)) being an an arrow (a \to b) in (C). The question is, what is it for co-presheaves? Is it (b \to a)? nLab defines it as (a \to b) and doesn't talk about presheaves. Emily Riehl defines both as (a \to b), which makes one wonder what it is for (𝐶ᵒᵖ)ᵒᵖ→𝐒𝐞𝐭 , not to mention (C^{op}\times C \to \mathbf{Set}).

BartoszMilewski,
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I posted this question to MathOverflow. https://mathoverflow.net/questions/470999/morphisms-in-the-category-of-elements

BartoszMilewski,
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@johncarlosbaez It's actually a serious problem. How do I define the category of elements for a profunctor: both arrows in the same direction, or twisted?

BartoszMilewski,
@BartoszMilewski@mathstodon.xyz avatar

@johncarlosbaez I thought that once you define a thing called the "category of elements" for (C \to Set), then it should work the same if I replace (C) with (C^{op}) or with (C \times C) or (C^{op} \times C) and so on. All other definition in nLab (or in math, in general) worked this way.

BartoszMilewski,
@BartoszMilewski@mathstodon.xyz avatar

@madnight My knowledge of string theory is totally disjoint from my knowledge of category theory, both being rather shallow at this point. Maybe @johncarlosbaez can help.

BartoszMilewski,
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@madnight @johncarlosbaez Google search shows this paper: https://arxiv.org/abs/0908.2469

BartoszMilewski, to random
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Appeal to "real life" fallacy in programming: Justifying programming constructs, like mutation, by invoking examples from real life.

BartoszMilewski, to random
@BartoszMilewski@mathstodon.xyz avatar

Recursion is human, tail recursion is canine.

dpiponi, to random
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I kept saying to myself "he's gotta be an alien", "surely he's not human", but in my heart of hearts I didn't really believe it...until...well I'm not giving you any spoilers...

BartoszMilewski,
@BartoszMilewski@mathstodon.xyz avatar

@dpiponi Same here. I knew it. There were so many hints.

BartoszMilewski,
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@dpiponi The biggest giveway was: We don't expect humans to be that compassionate.

JimPropp, to random

Is there a video that provides intuition about why countable subsets of R (even dense ones) have outer measure zero, by zooming in on a cover of such a set by a union of countably many intervals?

BartoszMilewski,
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@dpiponi @johncarlosbaez @JimPropp Isn't it a fractal thing? If you consider rationals with denominators less than some n, you can cover them with open intervals small enough to leave big gaps between them. Then zoom on one such gap. If you see there rationals with denominators less than n+1, cover them with smaller open intervals, again leaving gaps, and so on. You can always make gaps larger than the current cover. I think this works, doesn't it?

dpiponi, to random
@dpiponi@mathstodon.xyz avatar

I don't know if I hallucinated this but maybe someone recognises it:

I'm sure I once (~20 years ago) saw an arbitrary precision real number library for C or C++ that worked by picking some fixed precision and worked until it produced a result at the required precision, or, if it convinced itself it couldn't achieve that precision, did some kind of backtracking so it could redo the computation at a higher fixed precision. Somewhat analogously to how transactional memory works - and I think under the hood there may have been some unusual memory model.

Sound familiar to anyone?

BartoszMilewski,
@BartoszMilewski@mathstodon.xyz avatar

@dpiponi On a multicore computer, it might make sense to start multiple fixed-point computations in parallel, and then kill them as they fail or as soon as one of them produces a result.

dpiponi, to random
@dpiponi@mathstodon.xyz avatar

I'd love something like algebraic effects in C++. So I could write code like (and this is just a sketch, not a realistic proposal for syntax):

handle (new -> MyOwnMemoryAllocator)
{
int* x = new int[n];
...
}

or

handle(out -> Log)
{
out << "debugging stuff" << endl;
}

BartoszMilewski,
@BartoszMilewski@mathstodon.xyz avatar

@dpiponi It reminds me of DOS interrupt 21h. The latest iteration on this theme is the hypervisors used to implement virtual machines and the Blue Pill rootkit. https://en.wikipedia.org/wiki/Blue_Pill_(software)

paolop, to random
@paolop@mathstodon.xyz avatar

"What do you mean, naturality? It's not like arrows grow on trees!"
Codiaeum variegatum:

BartoszMilewski,
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@paolop I want to use it as an illustration of the Yoneda lemma.

BartoszMilewski, to random
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A little village called Saussignac in the Bordeaux wine region.

BartoszMilewski, to random
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Organic wine tasting in the Bordeaux region

BartoszMilewski, to random
@BartoszMilewski@mathstodon.xyz avatar

We'll know we have reached the singularity when the AI is able to sort our garbage into recycling bins. Everything else is just hype.

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