Bartosz Milewski

Physicist, programmer (Haskell, C++), mathematician, category terrorist, I mean tourist, I mean theorist. Author of Category Theory for Programmers.

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Last Notes

2024-09-24 04:37:25

I love the light effects, reflections, and distortions. Downtown Seattle view from Charlotte restaurant. Puget Sound and Olympic Mountains in the background.
https://media.mathstodon.xyz/media_attachments/files/113/190/674/837/939/002/original/bdba6f98527c58a8.jpg

2024-09-24 03:19:54

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@npub16hx…u6hc Good question. In Polish the two sides are called "orzeł"- eagle; and "reszka"- which apparently originates from the Russian word for sieve or lattice. Strangely enough, the eagle side is usually translated to English as "heads". Go figure!
https://media.mathstodon.xyz/media_attachments/files/113/190/368/589/485/075/original/12c695b9bbf27ed7.png

2024-09-24 00:41:15

I have just mailed my voting ballot. Even if WA is not a swing state, it will count in the popular vote.

2024-09-15 21:11:27

I'm trying to come up with an interesting example of a coequalizer in Haskell. The problem is that coequalizers are usually sets, and representing sets in programming is non-trivial. Essentially, a set is defined as a quotient over lists.

2024-09-15 00:53:53

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@npub13tk…6h9s
I think what the AI has shown us is that 99% of human intelligence is just sentence completion.

2024-09-14 20:08:34

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@npub1nad…2adz You are correct.

2024-09-14 19:58:30

I can imagine some extraterrestrials discussing human intelligence. "Human brains have nothing to do with intelligence, it's just a bunch of neurons adjusting their synaptic weights."

2024-09-14 06:05:31

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@npub18f5…30zn
The thing is that in a collider we are throwing matter at matter, and if dark matter doesn't interact with matter, then we can't produce it in matter collisions. So there won't be missing energy.

2024-09-14 02:03:22

Dark matter just got darker.
https://www.youtube.com/watch?v=_P6WIRnweRo

2024-09-11 19:50:33

I was surprised that in Seattle many establishments don't accept digital wallet payments. Apparently because of fraud. "Nearly a quarter of merchants say that Google Wallet and Apple Pay are top vehicles for fraudsters using stolen credit card details."

2024-09-10 22:26:04

We got it all wrong! Life on Earth is all about bacteria. Multicellular life started with bacteria herding up some protozoans to form a protective barrier around their colonies. 3 billion years later and we are still serving as vehicles for bacteria. We even evolved intelligence to better protect our gut biome and let it spread everywhere on Earth, and reach the Space.

2024-09-08 23:38:20

Today I visited the Almannagjá Gorge in Þingvellir National Park. This is the rift between the North American and Eurasian continental plates. Europe is slowly moving away from America (about one inch per year).
https://media.mathstodon.xyz/media_attachments/files/113/104/530/465/420/265/original/1bb9ff9f392b6908.jpeg

2024-09-08 21:11:57

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@npub16hx…u6hc Maybe it's not exactly what you mean, but I'm kinda partial to Morlocks

2024-09-07 19:39:57

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@npub1rcd…w0na You mean only diagrams that are part of the exercise/answer?

2024-09-07 19:22:57

Has anybody figured out how to format exercises together with answers in LaTeX, so that (properly numbered) answers appear at the end of the textbook? I tried the "solution" package but ran into weird compilation problems.

2024-09-07 16:54:16

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@npub178r…33zt I know, but it was a surprise for me.

2024-09-07 14:37:36

I ran into Thorsten Altenkirch and Tarmo Uustalu in Reykjavik. Small world!

2024-09-07 10:51:00

It looks like a major blow to Loop Quantum Gravity.
https://www.youtube.com/watch?v=krifXJLTfQk

2024-09-06 10:00:30

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@npub1qg4…an2g The problem is that these two notations switch the meaning of super- and sub-scripts.

2024-09-06 09:44:24

I'm trying to use consistent notation in my book. Should I follow the nLab, which says "presheaf represented by c as \(h_c\)," or the Wikipedia with \( h_A = Hom (A, -)\), which is a co-presheaf? In physics, a subscript index is used for covariant tensors, so that would favor the nLab convention.

2024-09-05 12:27:10

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@npub16hx…u6hc My favorite group, Pink Floyd, went dark in the 70s: The Dark Side of the Moon and The Wall.
Contrast this with 1967 Sgt. Pepper's Lonely Hearts Club Band.

2024-09-04 21:42:55

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@npub1czz…5kz5
I don't think anything terrible happened in the 70s. It's just that we picked most of the low-hanging fruit in the 60s.

2024-09-04 19:44:51

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@npub1c9m…9xjd Is it related to fanging?
https://starwars.fandom.com/wiki/Fanging

2024-09-04 17:31:25

Around the 1960s humanity reached the peak of optimism.
1968 was when "2001: A Space Odyssey" was released. 1969 was the Moon landing and Woodstock.
Compare this with 1979 hoplessness of "Alien." It's been downhill since then. We lost hope in the future.

2024-09-03 21:26:10

It's easy to come up with an elegant theory, but when you try to apply it to reality, you are forced to add epicycles upon epicycles. This is the story of the superstring theory in a nutshell.

2024-08-29 19:45:16

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@npub1c9m…9xjd Is this a covid home remedy?

2024-08-24 21:34:35

I feel like I'm missing something. In developing categorical topology, coverage is defined using a collection of families of morphisms, which works just fine. But in classical topology a coverage is defined using a union of sets. In the poset of open sets (with inclusions as morphisms) the union is a categorical coproduct (it's actually a union, not a discriminated union). So why can't we define coverage using a coproduct? What's the advantage of defining it the hard way?

2024-08-20 14:41:16

The Bear was like Whiplash, but about cooking. The problem is that a film about percussion can let you sample the music; but with food, you can only show, never taste.

2024-08-18 10:56:42

Continuing the series on topology and category theory. https://bartoszmilewski.com/2024/08/18/sheaves-and-topology/

2024-08-17 17:16:12

There's talk in Russian media about Ukrainians planning attacks on nuclear power stations (Kurchatov near Kursk and Zaporizhzhia in Ukraine) and dirty bombs. It could be Putin's usual threats, or he might be planning a false flag operation (as with the Kakhovka Dam). He must be aware that, if the order is given, a mutiny and the demise of his regime could follow.

2024-08-14 16:39:41

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@npub1knz…c73p There has to be a catch there, because just looking at the objects, there must be at least \(\mathbb N ^{\mathbb N}\) such functors. What am I not seeing?

2024-08-13 20:16:00

The emotional-state monad with its lonely unit and the hollow echo chamber of multiplication...

2024-08-08 13:29:39

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@npub1q79…ltcs
https://en.wikipedia.org/wiki/Scottish_Caf%C3%A9

2024-08-07 10:16:09

A second post on the categorical approach to topology.
https://bartoszmilewski.com/2024/08/07/presheaves-and-topology/

2024-08-05 20:12:59

Predictive model of music appreciation:
After hearing the first few bars, we develop a pretty good idea what will follow. If this expectation is easily satisfied, we get bored. It's monotony. We lose interest.
The more musically savvy we get, the stronger the predictive model, and the harder it is to get surprised. But too much unpredictability also feels monotonous.
The best music strikes the balance between predictability and novelty. We love structure, and we hate it.

2024-08-04 21:45:27

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I just realized that I had a similar thought some time ago:
"This is how our consciousness works. Most of the time our brain is on autopilot, and our train of thought is totally automatic and unconscious. It's like driving a car. What we perceive as consciousness is the discrepancy between what we're supposed to think and what we actually think."

2024-08-04 16:09:28

The holistic car mechanic:
Oil change comes from within.

2024-08-04 15:33:35

An interesting problem with immortality is that it would be very difficult to remain conscious forever. Like driving the car, everything would eventually become automatic, and you'd gradually zone out and go on autopilot. Nothing is unexpected if you live long enough.

2024-08-03 12:22:26

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@npub1knz…c73p
What we know for sure is that phishing hasn't started until about 530 mln year ago, during the Cambrian explosion.

2024-08-03 10:38:27

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@npub1knz…c73p This is really surprising: "cellular life was already involved in an arms race with viruses at the time of LUCA"

2024-07-29 14:26:11

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@npub1knz…c73p I would reduce it to the problem of tiling a torus.

2024-07-26 22:49:12

Essential Paris
https://media.mathstodon.xyz/media_attachments/files/112/855/227/641/201/044/original/7ce78e2cd6108900.jpeg

2024-07-25 18:07:21

Currently enjoying: The Four Seasonings by Antonio Mortadelli

2024-07-24 13:34:04

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@npub1knz…c73p BTW, I'm not arguing that the Copenhage interpretation is any better than Everett's interpretation. They both seem very ad-hoc.

2024-07-24 08:16:56

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@npub1knz…c73p
p. 92 The formula for S in the box should have lambda cubed.

2024-07-23 11:38:01

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@npub1knz…c73p Erratum: p 47: Indeed, the when people tried to apply the equipartition theorem

2024-07-22 22:28:47

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@npub1knz…c73p Also page 40: "Inevitably, this can make the entropy if c is small enough." missing "negative".

2024-07-21 18:58:55

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@npub1klq…c7yj Buying a lottery ticket lowers your Shannon entropy.

2024-07-21 18:55:42

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@npub1klq…c7yj It says nothing about experiences, just the probabilities of predicted outcomes.

2024-07-21 18:55:42

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@npub1klq…c7yj It says nothing about experiences, just the probabilities of predicted outcomes.

2024-07-21 18:50:02

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Shannon entropy is the average shock value you are likely to experience. It should be called boredom, because it peaks when any outcome is as likely as any other.

2024-07-21 13:11:43

I postulate that our brains have a shock-detector. The shock value of a sure thing is zero, so it doesn't even register. The shock value of an impossible thing is infinite. To accommodate a wide range of shocks, the response of the shock detector is logarithmic. So for an event of probability \(p\) we register the shock value of \(sh = log (1/p)\).

2024-07-19 14:05:06

The best defense against cyberattacs is to disable your computer.

2024-07-16 08:12:37

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@npub1v6a…h5rz Indexed algebras are a thing. https://bartoszmilewski.com/2015/07/13/from-lenses-to-yoneda-embedding/

2024-07-12 20:12:51

New blog post. https://bartoszmilewski.com/2024/07/12/topology-as-a-dietary-choice/

2024-07-12 10:13:47

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@npub1knz…c73p Another option could be repeating the title multiple times, making it progressively fuzzier.

2024-07-11 21:15:12

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@npub1c9m…9xjd This is the proposal for C++26, so at least 2 more years.

2024-07-11 20:06:38

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@npub1c9m…9xjd Or you could wait a few years until C++ supports reflection. https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2023/p2996r0.html

2024-07-08 17:24:16

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@npub1knz…c73p
And for this you need those meta-stable states which you can pump up.

2024-07-08 15:14:03

In classical logic, if you don't have a T-shirt you have to wear an F-shirt

2024-07-06 11:26:54

3,000 newtons -- the force needed to tip one cow. Sounds like a definition of an imperial unit.

2024-07-04 20:48:19

I don't see many reaction videos on YouTube to category theory talks

2024-07-04 20:16:23

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What I meant is that, by choosing a safe path, we often miss the opportunity to spread our wings and soar.

2024-07-04 15:58:47

Given a choice, most birds would rather walk than fly.

2024-07-04 12:12:39

A brilliant chemical pun: A fluorescent map of Europe in euro bills is made by doping with Europium (Eu)

2024-07-03 17:11:19

Scientists uncover a 50,000 years old Rorschach test. https://www.bbc.com/news/articles/c0vewjq4dxwo

2024-07-03 13:59:38

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@npub1uzg…ychd Don't take it literally. It's a figure of speech.

2024-07-03 10:38:03

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@npub1knz…c73p Congratulations! I insist that you visit Paris one of these days.

2024-07-03 08:48:09

It's funny how deluded Americans are. Everybody thinks that one day they will become a billionaire, so they vote to lower taxes for the rich. Everybody thinks they will never become old, so they are not worried about social security going bankrupt.

2024-07-03 08:48:09

2024-07-02 08:46:45

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@npub1knz…c73p Reminds me of Yes, especially Jon Anderson's voice.

2024-07-01 13:44:50

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@npub19ly…y4lk
I'm using uBlock origin to block ads. But I'm paying a ransom to Facebook.

2024-06-30 21:12:47

Is there a sense in which filters are dual to sieves? After all, filters a upward closed and sieves are downward closed.

2024-06-30 13:55:12

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@npub10ts…wved Notice, in particular, the use of hook arrows in this nLab entry:
https://ncatlab.org/nlab/show/subobject+classifier

2024-06-30 13:50:34

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@npub10ts…wved This distinction (injections vs inclusions) makes sense in sets, but does it make sense in category theory?

2024-06-30 13:07:54

Is it standard to use \(a \hookrightarrow b\) for monomorphisms and
\(a \twoheadrightarrow b\) for epimorphisms?

2024-06-29 12:11:41

Categorical doodles
https://media.mathstodon.xyz/media_attachments/files/112/699/840/044/638/727/original/99d090cc37cf01fd.jpeg

2024-06-29 08:29:33

Spotted Tambara modules in the wild.
https://arxiv.org/abs/2210.13443

2024-06-28 23:46:56

Wonderful! Wise just informed me that the bank they worked with was hacked. I guess "Trust" was meant ironically.
"The information that we shared with Evolve Bank & Trust to provide USD account details included name, address, date of birth, contact details, SSN for US customers"

2024-06-28 23:46:56

2024-06-28 18:08:27

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@npub1c9m…9xjd Let's just hope that Trump cannot dismantle democracy in four years.

2024-06-28 12:25:43

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@npub1c9m…9xjd Can we postpone the elections by a year to find more suitable candidates?

2024-06-28 08:16:48

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@npub1c9m…9xjd I'm watching it right now and my heart is sinking.

2024-06-27 21:54:44

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@npub1c9m…9xjd Same thing in Russian, you hear Dostoyeffski.
https://www.howtopronounce.com/russian/dostoyevsky

2024-06-27 18:45:36

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@npub1c9m…9xjd When I'm in the States, I use the americanized pronunciation of my name. In Europe, though, I fall back on the Polish pronunciation, Mileffski. https://www.howtopronounce.com/bartosz-milewski

2024-06-26 20:05:56

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@npub1knz…c73p My experience with LaTeX is to search the internet for answers and copy them--with minor modifications. If that doesn't work, I ask chat GPT.

2024-06-26 17:23:42

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@npub1knz…c73p May I suggest small caps, like \(\textsc{Five Kinds of Entropy}\) (latex \textsc{})? All caps are harder to read.

2024-06-26 13:26:39

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@npub1hez…qkaa Yeah, this general cluster of ideas.

2024-06-26 12:25:09

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@npub16g7…wuy4
Correct.

2024-06-26 12:06:01

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@npub19et…jx5h
"oxygen distribution is not random".
Are coin tosses random?

2024-06-25 21:32:09

I started watching The Old Man with Jeff Bridges in the title role. I'm used to highly stylized Hollywood fight scenes, where people exchange dozens of choreographed punches without breaking a sweat. This serial's fight scenes are brutally realistic.

2024-06-24 09:15:02

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@npub1c9m…9xjd We are circling around the sink-ularity.

2024-06-22 19:51:46

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@npub1knz…c73p
I assume you've listened to Mohini Dey.

2024-06-22 19:47:15

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@npub16hx…u6hc (Complex) probability amplitudes in QM are sort of like this. Plus you get interference.

2024-06-20 22:44:51

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@npub1c9m…9xjd You should be able to make a Klein bottle (Euler characteristic 0) out of hexagons, I think.

2024-06-18 22:09:36

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@npub1knz…c73p I was thinking more of electric pianos or synthesizers.

2024-06-18 19:02:24

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@npub1knz…c73p My prediction is that we'll combine pianos with AI and it will adjust the tuning witnin every chord on the fly. If a barbershop quartet can do it, the AI should have no problem with it.

2024-06-12 15:07:44

https://www.youtube.com/watch?v=Ri_oC2gf-aY

2024-06-10 19:07:06

Macron is calling the French people's bluff: You want to be governed by fascists? Go ahead, make my day. Will it work?
https://media.mathstodon.xyz/media_attachments/files/112/593/890/123/675/680/original/c60e2b657f7dcb4f.jpeg

2024-06-09 12:54:48

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@npub16hx…u6hc I consider all of mathematics as Applied Compositional Thinking

2024-06-08 20:48:17

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@npub1czy…wyvm
Our civilization started in the Fertile Crescent. Most of it is now a desert.

2024-06-08 19:38:00

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@npub1p4u…l2nd No soil on Mars. Also, no humans on Mars. Coincidence?

2024-06-08 19:05:44

We don't think of soil as a finite resource. But it can take 500 to 1,000 years for one inch of topsoil to form. Up to 40 percent of all soils worldwide are moderately or severely degraded--a figure that could rise to 90 percent by 2050.

2023-09-23 17:25:14

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@npub1knz…c73p I'm not sure what you mean by this: "Since T is the union of three fundamental domains for SL(2,Z)..." It's not obvious how you combine the six domains into three.