John Carlos Baez

I'm a mathematical physicist who likes explaining stuff. Sometimes I work at the Topos Institute. Check out my blog! I'm also a member of the n-Category Café, a group blog on math with an emphasis on category theory. I also have a YouTube channel, full of talks about math, physics and the future.

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Last Notes

2025-04-19 05:36:09

Some have been shouting it from the rooftops for months, but now even Ezra Klein is saying it: the emergency is here.
By refusing to bring back Kilmar Ábrego García from the prisons of El Salvador, even when the Supreme Court says to do it, Trump is saying: "hey, you in the USA. I can lock you up, outside the reach of reach of the law, and nobody can stop me". He's publicly said that he wants to be able to do this to US citizens. This is meant to terrify us into submission.
Klein calls this an emergency. But he doesn't offer a solution, or even a suggestion of what we might do. Mild-mannered conservative columnist David Brooks gives a try. He's calling for a "comprehensive national civic uprising" - see next page.
https://www.youtube.com/watch?v=JN1oBfg0fwI

2025-04-12 18:22:27

How are international conferences dealing with the fact that some people are now afraid or unwilling to enter the US? Are they holding conferences elsewhere, encouraging remote participation, ignoring the issue, or what?
If you're helping run an international conference (like me), or even just going to one, I'd like to know what you're seeing.
https://www.science.org/content/article/international-scientists-rethink-us-conference-attendance

2025-04-06 18:10:06

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@nprofile…e5g0 - I'm curious about why Bluetooth is so bad. I have a couple devices at home that I connect to using Bluetooth. Lots of different problems: 1) setup is unable to remember which stereo is which, 2) sometimes it takes a few tries to connect, 3) sometimes it fails completely and I have to delete the devices and reinstall them.

2025-04-06 01:48:47

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I'm glad people are standing up for the CDC.
https://media.mathstodon.xyz/media_attachments/files/114/288/497/652/009/625/original/51d0bf04fa890bdc.jpg

2025-04-06 01:46:18

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https://media.mathstodon.xyz/media_attachments/files/114/288/490/663/668/478/original/2673fcd27fdd6d7b.jpg

2025-04-06 01:41:11

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NO TYRANTS
https://media.mathstodon.xyz/media_attachments/files/114/288/469/509/476/409/original/d787fdbf6e88799a.jpg

2025-04-06 01:39:44

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First time I saw a pro-IRS sign.

2025-04-06 01:38:57

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https://media.mathstodon.xyz/media_attachments/files/114/288/461/672/994/749/original/f964ebfb52f043f2.jpg

2025-04-06 01:38:15

The protest here in Riverside... live!
https://media.mathstodon.xyz/media_attachments/files/114/288/458/453/185/234/original/463598a5849c1705.jpg

2025-04-03 01:57:26

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@nprofile…0kak @nprofile…m2ru - yes, and I wouldn't have used the phrase "resonance invariance", which means nothing and thus reeks of crackpot. Instead I would have referred to Pierre Cartier's paper on the "cosmic Galois group", in which he writes:
"From the physics point of view, the work of Connes and Kreimer about renormalization in quantum field theory has been deepened. The so-called “forest formula” of Zimmermann was translated into the language of Hopf algebras by Kreimer, and Connes introduced the efficient tool of Birkhoff factorization. Inspired by the theory of algebraic groups, I reformulated everything in terms of exponential of triangular matrices. Together with my student Marcus Berg, we made it a practical tool for calculation of counter-terms in renormalized field theories. At a deeper level, I was more prophetic than I had thought, and there are many reasons to believe in a “cosmic Galois group” acting on the fundamental constants of the physical theories. This group should be closely related to the group GRT₁ and might eventually help understanding of the numerical value of the fine structure constant, a long-standing puzzle."
http://www.ams.org/bull/2001-38-04/S0273-0979-01-00913-2/S0273-0979-01-00913-2.pdf
I don't understand his optimism regarding the fine structure constant, but at least he's a certified math genius so referring to him would add cred.

2025-04-03 01:35:51

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@nprofile…m2ru - btw I didn't write this myself, I really got it in my email.

2025-03-31 20:56:22

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@nprofile…vgna - I'm not really doing enough, but thanks. I feel like I'm a bad movie where a bunch of sleepwalkers are walking off a cliff.

2025-03-31 20:36:11

How does "president for life" sound?
Since his second term is going so well, Trump is starting to talk about a third term. It's against the constitution, but don't count on that stopping him.
Asked by NBC News about a scenario involving Vice President Vance, Trump said "that's one" method. A 1999 Minnesota Law Review article called "The Twice and Future President" explains that a twice-elected president could become vice president and then — if the current president were to be removed from office, resign or die — return as commander in chief. Another equally sleazy possibility is for Trump to serve as speaker of the House and then become president through Presidential Succession Act of 1947.
We've got to stop this and all the other ways Trump is trying to destroy democracy in the US. I urge all US citizens to check out the BLOP - the Big List of Protests - and go to a protest near you!
https://theblop.org/

2025-03-19 17:45:19

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@nprofile…uxsy - you mean the appalling list of people on the organizing commitee, I guess.
If the publicly available stories about what happened aren't actually useful (and I admit I just looked at one), then someone really should write a fuller story.

2025-03-16 21:27:32

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@nprofile…uxsy - @nprofile…yu7x showed how to embed the McGee graph into a genus 2 surface here:
https://mathoverflow.net/questions/215211/what-algebraic-structures-are-related-to-the-mcgee-graph

2025-03-15 16:55:33

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@nprofile…l9jz @nprofile…yu7x - okay, I read that this paper shows the semidirect product of ℤ/n and its multiplicative group has an outer automorphism that preserves conjugacy classes whenever n is divisible by 8:
G. E. Wall, Finite groups with class-preserving outer automorphisms, J. London Math. Soc. 22 (1947), 315–320.
I read it here:
Peter A. Brooksbank and Matthew S. Mizuhara, On groups with a class-preserving outer automorphism, https://msp.org/involve/2014/7-2/involve-v7-n2-p04-p.pdf

2025-03-15 16:36:15

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@nprofile…l9jz @nprofile…yu7x - Here are a bunch of examples of finite groups with outer automorphisms that preserve conjugacy classes"
https://www.sciencedirect.com/science/article/pii/S0021869301987605
The first examples were found by Burnside in 1913, in his paper "On the outer automorphisms of a group"! But I'm not seeing our friend with 32 elements.

2025-03-15 15:58:29

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@nprofile…l9jz @nprofile…yu7x - SmallGroup(32,43) is indeed the group we're talking about here:
https://groupprops.subwiki.org/wiki/Holomorph_of_Z8
It's called the "holomorph" of ℤ/8 because it's the semidirect product of ℤ/8 and its automorphism group (which as Greg checked is the multiplicative group of ℤ/8).

2025-03-15 15:49:03

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@nprofile…l9jz @nprofile…yu7x - I'm afraid this is one of those nasty puzzles where I don't know the answer. Worst case: the guy who confidently told me SmallGroup(32,43) has this surprising property was wrong, or it's not the group of affine transformations we think it is.
It's true that in a semidirect product A ⋉ B with both A and B abelian, conjugation by any element leaves the first component in (a,b) ∈ A ⋉ B unchanged. (Another fun example: the rotation/translation group of the plane.)
The only way out I see is what @nprofile…l9jz suggests: there's an automorphism f that multiplies b by 3,5,or 7 in a manner that depends nontrivially on a:
f(a,b) = (a, n(a)b)
where n(a) = 3,5, or 7.
Thanks for tackling this!

2025-02-27 17:24:04

Mathematicians number our theorems because... well, we can buy numbers for cheap from the wholesaler, so we have a lot of them lying around, and we use them for everything. But it's very rare for the number of a theorem to become famous. The only exception that leaps to my mind is Hilbert's Theorem 90. Do you know any others?
If you ask a number theorist about Hilbert's Theorem 87, they'll look at you like you're nuts. But if you ask about Theorem 90 they'll know it, or at least be embarrassed for forgetting the exact statement. Try it!
It was the the 90th theorem in Hilbert's paper "Theory of algebraic number fields", and for some reason it became more famous than most. So what does it say?
Here's an easy special case. The real numbers ℝ sit inside the complex numbers ℂ, and the complex numbers have exactly two symmetries that leave every real number unchanged. Complex conjugation is the interesting one, and the other is the identity. If we take a complex number z, apply each of these symmetries, and multiply the results, we get
zz*
Hilbert's Theorem 90 says that if zz* = 1, then z = a*/a for some nonzero complex number a.
But his theorem is a lot more general! It applies whenever you've got a field F sitting in a larger field K, and the symmetries of K that leave all elements of F unchanged form a finite group generated by some symmetry σ.
Here's what it says. Take an element z of K, apply all these symmetries to it, and multiply the results. If you get 1, then we must have z = σ(a)/a for some nonzero a in F.
But what's really going on here???
(1/2)

2025-02-16 02:03:30

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@nprofile…vgna - we can treat gravity as a force "perturbatively", i.e. for metrics that are very close to the Minkowski metric. When we linearize Einstein's field equations around the Minkowski metric, they reduce to a linear wave equation, and when we quantize this equation we get the quantum field theory of massless spin-2 particles. These are called gravitons.
When we go beyond the linear approximation things get hard, and we are probably being punished for a somewhat stupid idea! But some of the results from this approach are probably okay. I sketched a bit of this here:
https://mathstodon.xyz/@johncarlosbaez/113750000394097420

2025-02-11 21:29:17

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@nprofile…vgna - that is surprising! While a field theory approach to vision or brain will only be an approximation, it still might be very useful.

2025-02-07 06:05:20

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@nprofile…m2ru - I said I'm getting a job that will give me "the right to remain". This means that if I work for 5 years and stay in the UK at least half the years, I'll get the right to stay there. But first I have to get a visa so I can actually go there and work!

2025-01-11 17:43:46

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@nprofile…guz4 - I left a comment on your blog. I agree with you!

2025-01-03 07:12:53

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@nprofile…hn0f - Be careful: if you slip up, you'll be a millennium off.
https://media.mathstodon.xyz/media_attachments/files/113/763/179/705/233/205/original/44636a0e74a8bb87.jpg

2024-12-31 18:04:41

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One reason for the Great Stagnation was physicists' near-obsessive desire to find a theory of quantum gravity that's 'renormalizable'. This led them to focus huge amounts of energy on theories with no obvious connection to the real world, like supergravity and superstrings. Ironically, none of these theories were ever proved to be renormalizable, and the obsession slowly died away. Nobody claims M-theory is renormalizable. But we're stuck living in the ruins of a dream.
It's understandable how we got into this mess. In the early days, like the 1940s, everyone was scared of the infinities that quantum field theory gives if you let particles interact by exchanging virtual particles with arbitrarily high energies. They desperately sought to avoid those infinities - and they discovered how to do it for 'renormalizable' theories.
The idea is roughly this. You start by saying no virtual particle can have energy² - momentum² bigger than some chosen number called the 'cutoff'. This makes all the infinities go away. The question becomes: what happens as you change the cutoff?
A quantum field theory is renormalizable if you can let the cutoff approach infinity, while simultaneously rejiggering the parameters in your theory, in such a way that answers to questions about physics at low energies actually converge!
But what about theories that aren't renormalizable, like the simplest theory of quantum gravity? What actually happens with these, as you let the cutoff approach infinity? It's surprisingly hard to get a straight answer! You'd think this would be settled by now. But experts are still arguing about it!
(5/n)
https://media.mathstodon.xyz/media_attachments/files/113/748/748/596/747/863/original/dd03dc878251046f.jpg

2024-12-31 06:17:57

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@nprofile…vgna - I don't know anything about Schwinger's source theory, but the article says the famous physicist Weinberg used it to "set the underpinnings of effective field theory", and effective field theory is crucial to the modern understanding of renormalization. In fact my very sketchy description of Wilson's approach to QFT in part 3 of this post touches on effective field theory, but I was trying to minimize technical details. You can read a bit more here:
https://en.wikipedia.org/wiki/Effective_field_theory
and since effective field theory is fundamental to understanding problems in quantum gravity I may have to say more in my series!
@nprofile…e5g0

2024-12-29 18:15:55

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@nprofile…e5g0 @nprofile…vgna - I'm going to say a lot more about this. The nonrenormalizability of quantum gravity is less of a problem than the old conventional wisdom has it: we now know you can work out quantum corrections to the inverse square force law (below), etc:
https://arxiv.org/abs/1209.3511
Renormalization is a way to get a theory that works to indefinitely small distance scales. We don't know that we *need* a theory that works to indefinitely small distance scales, and the traditional criteria for renormalizability neglect the existence of nontrivial ultraviolet fixed points. The study of "asymptotically safe gravity" explores this:
https://arxiv.org/abs/2003.00044
I believe the obsessive quest for a renormalizable theory of quantum gravity led people down a lot of wrong paths.
https://media.mathstodon.xyz/media_attachments/files/113/737/431/349/081/331/original/81299b2daceabaf9.jpg

2024-12-28 16:40:34

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@nprofile…m2ru - thanks! Weirdly, people have become a lot more eager to talk about stuff with me here in the last week. It could be a holiday effect - I'll see if it goes away - or it could be that some attempts to tweak my style to be more inviting have paid off. I'm (belatedly) guessing that just explaining things clearly is not a good way to start a conversation.
For example, admitting that I'm confused about the magnetic and electric limits of Maxwell's equations seems to have brought out people who know about them, or at least want to talk about them.

2024-12-28 16:29:07

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@nprofile…cnse @nprofile…mqrg - yes, this claim is on Wikipedia, and it puzzled me:
"Cassini believed that a planet orbiting around another body traveled on one of these ovals, with the body it orbited around at one focus of the oval.[2]"
where [2] is
Cohen, I. Bernard (1962). "Leibniz on elliptical orbits: as seen in his correspondence with the Académie Royale des Sciences in 1700". Journal of the History of Medicine and Allied Sciences. 17 (1): 72–82. doi:10.1093/jhmas/xvii.1.72.
and now I'm going to read it here:
https://www.jstor.org/stable/24620858
It's about a guy named Fontenelle telling Leibniz that Cassini has abandoned Kepler's ellipses. I don't see anything about *why* Cassini did this. It mentions that Leibniz might have liked this because it could invalidate Newton's mechanics, but it doesn't provide any evidence that Leibniz actually *did*. So, fairly mysterious.

2024-12-27 02:22:33

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@nprofile…m2ru - there's no point in whining, so I usually don't, but after most of my Twitter math pals came here and then left, I've mainly been hanging on due to sheer stubbornness and my love of talking... but I quit talking about serious math because there's little point.
Then they went to Bluesky and tried to get me to go there.

2024-12-27 00:50:47

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@nprofile…u4rg - you're right. Another thing: a bunch of good mathematicians came to Mathstodon shortly after Musk took over Twitter. For a while it was lively. I was happy. Then most of them left, finding this place to be too quiet compared to Twitter. At that point, posting advance math stuff here started seeming pointless. Now I spend about an hour a day discussing math on the Category Theory Community server, a Zulip. I wish it weren't so focused on category theory, but there are a lot of people who enjoy sustained conversations about advanced math.
Over here, I get the most satisfying reactions when I post something explaining math or science in way that educated nonscientists can easily understand. People also seem to like the history of these subjects.
I keep tweaking my style, hoping to figure out things that are enjoyable for me and lots of other people.
@nprofile…p7tf
@nprofile…wlc0

2024-12-26 22:01:34

Hardcore math post:
After my spectacularly popular post on Alfvén waves, there's nothing to do but write a much less popular post on the math behind them. People say magnetic field lines in a plasma can act like stretched rubber bands: if they're bent, they try to straighten out. There's a Wikipedia article on this idea, which is called 'magnetic tension':
https://en.wikipedia.org/wiki/Magnetic_tension#Mathematical_statement
and I'd like to understand it.
They start with the equations of 'ideal magnetohydrodynamics' where you have a plasma with velocity vector field 𝐯, pressure p, density ρ and electric current vector field 𝐉 in a magnetic field 𝐁. It's called 'ideal' because we're assuming the plasma conducts electricity so well that the electric field is zero.
One of these equations, called the 'Cauchy momentum equation', says the plasma accelerates due to two forces:
the gradient of pressure, or more precisely −∇p, and
the force caused by the magnetic field, which is 𝐉 × 𝐁 as usual - this is called the Lorentz force.
They then do some fun vector calculus manipulations. Assuming |𝐁| is constant everywhere, they find a term in the force whose magnitude is the curvature κ of the magnetic field line, which points to the center of curvature of the magnetic field - where you approximate the magnetic field locally as going around a circle of radius 1/κ. See the picture to understand what the hell I just said.
I think I follow the calculation, but this is a force on the plasma, right? Not the magnetic field line per se! So why do they interpret it as the field line wanting to straighten out? If we knew 𝐯 is proportional to 𝐁 that would make sense, but they don't say anything about that.
https://media.mathstodon.xyz/media_attachments/files/113/721/349/151/384/313/original/e3ad8806d7d78792.png

2024-12-24 17:37:22

Today the Parker Solar Probe will get 7 times closer to the Sun than anything spacecraft ever has, going faster than any spacecraft ever has - 690,000 kilometers per hour. WHEEEEEE!!!!!!!
But the really cool part is what the newspapers are barely talking about: what it's like down there. The Sun doesn't have a surface like the Earth does, since it's all just hot gas. But it has an "Alfvén surface" - and the probe has penetrated that.
What's the Alfvén surface? In simple terms, it's where the solar wind - the hot gas emitted by the Sun - breaks free of the Sun and shoots out into space. But to understand how cool it is, we need to dig a bit deeper.
After all, how can we say where the solar wind "breaks free of the Sun"?
Hot gas shoots up from the Sun, faster and faster due to its pressure, even though it's pulled down by gravity. At some point it goes faster than the speed of sound! This is the Alfvén surface. Above this surface, the solar wind becomes supersonic, so no disturbances in its flow can affect the Sun below.
But it's even cooler than that, because "sound" in the solar wind is very different from sound on Earth. Here we have air. The Sun has ions - atoms of gas so hot that electrons have been ripped off - interacting with powerful magnetic fields. You can visualize these fields as tight rubber bands, with the ions stuck to them. They vibrate back and forth together!
You could call these vibrations "sound", but the technical term is "Alfvén waves". Alfvén was the one who figured out how fast these waves move. Parker studied the surface where the solar wind's speed exceeds the speed of the Alfvén waves.
And now we've gone deep below that surface!
(1/n)
https://media.mathstodon.xyz/media_attachments/files/113/708/838/045/816/269/original/56bcd57bc6216c76.jpg

2024-12-18 00:25:44

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@nprofile…j7pr - if you don't read Woit's blog you don't get the intelligent skeptic's careful eye on what's up with string theory. I recommend starting around 2000 and working your way forward. 🙃

2024-12-08 19:36:29

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@nprofile…c4xk - Sure! The final, clearest story came much later, thanks to calculations by @nprofile…yu7x. I summarized them in words here:
https://johncarlosbaez.wordpress.com/2024/11/30/black-hole-puzzle/#comment-186085

2024-12-01 17:25:04

If fundamental physics were making big progress, I'd be all over it - that's what I wanted to do ever since I was a kid. But it's stagnant: the action is elsewhere, like using category theory to design radical new kinds of software. So these days I get some of my physics fix by studying the *history* of physics.
After studying the hell out of particle physics and general relativity, I went back and dug into the history of electromagnetism, which is really just as fascinating. Now I'm going back to medieval physics - because the idea that everyone was an idiot until Galileo is just plain wrong.
"Natural philosophers" in the 1200s and 1300s developed key concepts, utterly necessary for modern physics, but almost invisible now because we're so used to them - except for students, who find physics really hard because we don't bother to CLEARLY EXPLAIN those concepts: we act like children are born knowing them.
I'm talking about concepts like "the speed of an object at a moment of time". What the hell does that even mean? How can you figure out how fast something is going in one instant of time, when doesn't have time to go anywhere?
Well, that was clarified by calculus, and we credit it to Newton and Leibniz. But they had to have the idea already, in order to clarify it! And the idea of "instantaneous velocity" was developed around 1340 by the Oxford Calculators, a school of thinkers like Heytesbury and Swineshead - geniuses we never hear about.
Now I'm going back further. Did you know that back in 420 AD Martianus Capella had a theory where Mercury and Venus revolved around the Sun? And this was known to thinkers in Charlemagne's day... and also Copernicus! Wow!
https://media.mathstodon.xyz/media_attachments/files/113/578/696/013/956/853/original/ac0cf3f472c321a3.jpeg

2024-12-01 01:44:17

101 starship captains, bored with life in the Federation, decide to arrange their starships in a line, equally spaced, and let them fall straight into an enormous spherically symmetrical black hole — one right after the other.
As the 50th captain, say Bob, falls into the black hole, he sees 49 starships in front of him and 49 behind him. This is true at all times: *before* he crosses the horizon, *when* he crosses it, and *after* he crosses it.
Captain Bob never sees any starship cross the horizon until he crosses it. At the moment he crosses the horizon, he sees all 49 starships ahead of him also crossing it — but not the 49 behind him.
However, when any of the starships behind him crosses the horizon, the captain of *that* starship will see Bob also crossing the horizon!
Captain Bob never sees any starship hit the singularity — not even the 49 starships in front of him. The singularity is always in his future, until he hits it.
Thus, as Captain Bob falls into the black hole, he sees his partner, Captain Alice, in front of him for the rest of his short life. But how much is she redshifted?
Greg Egan made some assumptions and graphed the result. This shows frequency of light Bob sees divided by the frequency of light Alice emitted, as a function of time as ticked off by Bob’s watch.
Thus, “1” means no redshift at all, and smaller numbers means Alice looks *more* redshifted to Bob!
So: Alice as seen by Bob becomes more and more redshifted as time goes by. She becomes infinitely redshifted at the exact instant Bob hits the singularity!
More details here:
https://johncarlosbaez.wordpress.com/2024/11/30/black-hole-puzzle/
https://media.mathstodon.xyz/media_attachments/files/113/574/988/780/071/309/original/08c543b358e727e4.png

2024-11-30 18:08:33

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@nprofile…e5g0 -
"Ok but I still don't get why he should "see her at a close distance"?"
"Because he sees her in front of the horizon, and he's nearing the horizon himself. So her image is in between."
You're still not reckoning with the fact that the horizon is not a location in space: it's a lightlike surface and it contains very long light rays, like the light ray going from you now back to the Andromeda Galaxy. You can see lots of things between you and Andromeda, and they're all on the same light ray, but you don't say that therefore you see them at a close distance. Nor do you say this for things that are *almost* on this light ray - that's what's analogous to "nearing the horizon".
@nprofile…su6u @nprofile…yu7x

2024-11-25 19:52:20

A hundred starship captains, bored with life in the Federation, decide to form a line of ships and plunge straight into an enormous spherically symmetrical black hole - one right after the other.
The black hole is so large that the tidal forces don't destroy them as they cross the horizon. What does the 50th captain see, the moment their starship crosses the horizon?
(1/n)

2024-11-22 05:16:59

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@nprofile…j7pr @nprofile…e5g0 - right, as you approach the horizon it looks dark except perhaps for Einstein rings.
From a distance:
https://media.mathstodon.xyz/media_attachments/files/113/524/904/054/037/448/original/65841f4666e67bdd.mp4

2024-11-19 03:51:40

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And that's how it goes. Read the whole story here:
https://pluralistic.net/2024/11/02/ulysses-pact/#tie-yourself-to-a-federated-mast
So I'd rather not hop onto the next sinking ship, even though lots of my friends are there, and I hear the buffet and entertainment are great... for now.
(15/n, n = 15)

2024-11-17 17:29:53

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@nprofile…wlc0 - actually I think people would accept other systems that made it easy for them to find interesting people. It's quite hard here, and I dislike that, but I stick around because I'm tired of social media run by corporations.
@nprofile…ccu8

2024-11-17 17:24:59

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@nprofile…wlc0 - You asked "Why do people need followpacks?" and I answered. Perhaps your intent was to persuade people to be different (by insulting them, calling them "sheep").
@nprofile…ccu8

2024-11-17 17:19:32

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@nprofile…wlc0 - people
are hungering for these followpacks because they come to Mastodon and find it to be dead as a graveyard until they slowly, laboriously stumble across interesting people. They are primarily interested in people, not hashtags.
@nprofile…ccu8

2024-11-16 23:58:28

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@nprofile…hszg - I never fully grew up: when I was a kid I wanted to learn names of dinosaurs and now I want to learn about Lie groups, cataclysmic variable stars, elementary particles, etc.
Quoting a story:
Robert Wilson worked in the Manhattan Project and later helped set up the particle accelerator Fermilab. On April 19, 1969, Wilson was among a number of scientists who testified in Washington, DC before the Joint Committee on Atomic Energy concerning this multimillion-dollar project to be built in Batavia, Illinois. Despite the key role physicists played in ending World War II, some members of Congress were skeptical of paying a hefty price tag for a machine that did not seem to directly benefit the U.S. national interest.
During Wilson’s testimony, then-senator John Pastore bluntly asked, "Is there anything connected with the hopes of this accelerator that in any way involves the security of the country?"
"No, sir, I don’t believe so," Wilson replied.
"It has no value in that respect?"
"It has only to do with the respect with which we regard one another, the dignity of man, our love of culture. It has to do with: Are we good painters, good sculptors, great poets? I mean all the things we really venerate in our country and are patriotic about. It has nothing to do directly with defending our country except to make it worth defending."

2024-11-16 18:59:51

I don't really know why people study astronomy in such great detail - except that it's fun. I think it's important to understand how the universe as we know it began about 14 billion years ago, and understand how the Earth was formed about 4.5 billion years ago, and how evolution brought us here. My life fits into this frame. But is important to know the various dramatic ways that stars can die?
I don't think so... but it's sure fun!
Here's a tiny white dwarf star called a 'polar' sucking hot gas from its much larger companion. What makes it a 'polar' is its intense magnetic field - so strong that the gas falling in is forced to move along the field lines, rather than forming the usual pancake-shaped 'accretion disk'.
This means the ionized gas falling onto this white dwarf lands only on its north and south magnetic poles. It's like how ions from the Sun hit our Earth near its poles, producing auroras there. But it's vastly more intense! The magnetic field of a 'polar' is about 100 million times stronger than the Earth's magnetic field. And a lot more stuff is falling in. Now and then a *huge* amount.
So, polars are considered 'cataclysmic variable stars': now and then they blast out huge amounts of radiation, as a clump of infalling gas hits their surface. There are different kinds of cataclysmic variable stars. This is just one!
Now, why is it so fun to think about this... instead of, say, politics? I guess the question answers itself.
https://en.wikipedia.org/wiki/Polar_(star)
https://media.mathstodon.xyz/media_attachments/files/113/494/097/803/935/705/original/7a053bc1210da5b4.jpg

2024-11-16 01:14:10

This is not the math I know! 😡
https://media.mathstodon.xyz/media_attachments/files/113/489/976/374/200/725/original/b0d26b0e82069ded.jpg

2024-11-09 00:57:40

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@npub13g2…m4y3 - I agree with most of those tactical remarks. I wouldn't quite say the Cheney family stuff "totally failed" - it may have helped - but I'd say it's way too little for just a couple of Republicans to speak out. Nikki Haley made a great case against Trump and won plenty of votes in the primary, even in states where she wasn't running! But then she knuckled under and kissed the ring. Mitt Romney spoke out for a while but then became quiet.
There's a reason: death threats.
https://www.vox.com/23899688/2024-election-republican-primary-death-threats-trump

2024-11-08 20:21:50

21% of the total US population voted for Trump - not really more than when he lost in 2020. But fewer people voted against him this time, so our crappy system put him in charge.
We can't expect he surrounds himself with people who will restrain him. The Senate and probably the House will be controlled by people under his thumb. The Supreme Court, three of whose members he appointed, has already announced he'll have wide powers to act without being legally liable. He's lining up a cabinet full of billionaires.
My worries are not for my family. We planned ahead and are ready to move to Scotland. My worries are for the US, Ukraine, democracy worldwide, and the biosphere.
We need to organize to resist Trump's bad ideas and criminality. Unfortunately I am not good at politics. So, just a couple of thoughts:
The Democratic Party needs to figure out what it's doing wrong. Many Americans are desperate. 50% live paycheck to paycheck all the time. 25% have negative net worth: they owe more than they own. If Democrats don't take this seriously, people will keep voting for demagogues.
I wish there were a serious constituency for constitutional change: abolishing the electoral college, introducing ranked choice voting, limiting or banning campaign contributions and other forms of pay-to-play politics, increasing taxes on the super-rich, etc. I don't see how these changes have a chance in the current environment. How can we improve the overall framework when politics devolves to a culture war, a battle between two dominant parties, a plutocracy - or actually all of the above? How could a new party devoted to true reform gain power? Time for me to study more history.

2024-10-31 16:57:32

We can be kind to nature. We don't always have to exploit it.
Since 1860, Britain has lost 85% of its salt marshes. A decade ago, this region was torn up by bulldozers and excavators. But on Sept. 8, 2014, the tide was allowed to come in. Water flowed through a new gap, about 220 yards wide. This was the start of an experiment that continues to this day.
Now Steart Marsh acts as a bulwark against flooding, absorbing and slowing tides. Even last winter — the wettest anyone in the area could remember — the village at one edge of the peninsula did not flood.
The area is also a haven for wildlife. The birds include godwits, plovers, oystercatchers, egrets, herons, and a growing population of avocets — black-and-white wading birds with distinctive curling beaks.
There's a lot more to this story, though.
For more, read this:
https://archive.is/tna5m
https://media.mathstodon.xyz/media_attachments/files/113/403/026/081/487/942/original/7c448dee31b7101e.png

2024-10-25 16:55:59

If you cut out the yellow shape here, you can fold it up along the red lines, and all 11 sharp tips will meet at one point! You'll get a polyhedron with 12 corners, tiled by equilateral triangles. 5 triangles meet at each corner. There are also places where 6 triangles meet: these places are flat. Some triangles get folded along the red lines.
This may seem like a curiosity. But it shows up in a paper by the great mathematician William Thurston, which I'm writing an article about, and there's a lot more to it.
Notice how he got this. He drew a lattice of equilateral triangles on the plane. Then he drew an 11-sided polygon whose corners are lattice points. Along each edge of this polygon, he drew a green equilateral triangle pointing inward. If you cut out these green triangles, you're left with the yellow shape, which you can fold up.
There are lots of ways you can draw such an 11-sided polygon; the picture shows just one. Each way gives a way of triangulating the sphere where the number of triangles meeting at a vertex is always either 5 or 6. In fact - and this is not obvious - you can get *all* such triangulations using this trick.
Is anyone out there willing to draw such an 11-sided polygon and then draw the polyhedron you get when you cut out the green triangles and fold up the left-over yellow shape? A super-genius could write a program where the user could choose 11 points that define a valid polygon, and then the program would show what happens when you fold up the yellow shape. But I'd be thrilled to see just one example.
(1/2)
https://media.mathstodon.xyz/media_attachments/files/113/368/928/892/084/817/original/f07aa3b844823767.jpg

2024-10-18 04:34:48

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@npub1305…k70l - super-cool!
This statue of a Buddha was found in a Viking's grave in Sweden. It dates from about the 6th century AD and was probably made in Kashmir.
http://irisharchaeology.ie/2013/12/the-helgo-treasure-a-viking-age-buddha/
https://media.mathstodon.xyz/media_attachments/files/113/326/560/541/148/109/original/62d67fa9e7f6d296.webp

2024-10-17 00:21:42

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@npub1eu3…d529 - whoops! I'll kill that post and try again.

2024-10-17 00:21:00

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@npub1ky2…ghvc @npub1c9m…9xjd - the Bayesian interpretation of probability is a way to think about probabilities of one-time events, like "what's the probability that Donald Trump will win the 2024 election?"
"QFT, the best theory of the micro-world we currently have, can only answer a very narrow selection of questions. It lets us calculate the S-matrix: a transition function between asymptotically free states."
Now you're changing the subject and making some unrelated claim, which happens to be false. QFT lets us compute many things other than S-matrices. I invite people here to list four.

2024-10-16 17:48:40

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@npub1c9m…9xjd @npub1ky2…ghvc -
Second,, I talked to an early-universe cosmologist, John Peacock, about this because I wanted to be sure that the standard theory *does* say that the inhomogeneities in the early Universe arise as quantum fluctuations, rather than being put in "by hand". He said that it does. I pressed him on it, and in the end I felt a bit dumb because it turns out to be textbook stuff. He wrote:
"Many textbooks treat inflationary generation of fluctuations at various levels of detail. You can have an entire (excellent) book dedicated to the subject:
https://www.amazon.co.uk/Primordial-Density-Perturbation-Cosmology-Inflation/dp/052182849X
Or for a briefer tour of the key elements you could look at Section 6.5 of my cosmology notes:
https://www.roe.ac.uk/japwww/teaching/cos5_1213/cos5_full.pdf
The basic idea is to say that the inflaton field must experience quantum fluctuations (since it’s just a harmonic oscillator in the ground state). These fluctuations can be computed on small scales using standard flat-space QFT. Now follow a given field mode in comoving terms, so that the mode becomes stretches beyond the inflationary de Sitter horizon, transforming the inflaton fluctuation into a classical perturbation to the energy density."
Of course this being the standard theory doesn't mean it's true. But I'm greatly relieved that the fluctuations aren't stuck in by hand: the initial conditions are translation and rotation invariant; all inhomogeneities result from spontaneous symmetry breaking, i.e. the total wavefunction retains its symmetry but it's a superposition of inhomogeneous states.
(2/2)

2024-10-16 17:46:06

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@npub1c9m…9xjd @npub1ky2…ghvc
no, your doubts are not legiimate.
First, if "there is only one Universe" was a legitimate argument against using probability and statistics in cosmology, it would also be a legiimate argument against using probability and statistics when playing poker. "There is only one Universe, and in this Universe you either have a royal flush or you don't. It makes no sense to say you have one with probability 0.005%." "But we could repeat this experiment many times!" "But not in this room on Wednesday October 16th at 2 pm!"
I believe you are stuck in a frequentist interpretation of probability theory which is just not up to the job for cosmology. Maybe try taking a more Bayesian stance.
(1/2)

2024-10-15 16:10:45

The Europa Clipper finally took off! It'll reach this icy, water-filled moon of Jupiter in 2030. But it won't orbit that moon. Instead, it will fly by Europa 44 times, tracing out these wonderful tracks.
Why not orbit Europa? There's too much radiation that close to Jupiter, and the Clipper can collect data much faster than it can transmit it to Earth. If it orbited Europa it would fry before it could tell us very much!
Thus, the Clipper will spend most of its time farther from Jupiter, transmitting data to Earth. Using gravity assists from 2 other moons, it will occasionally swoop down, zip past Europa, and make more measurements.
In its 3.5 year life, it will get 2.8 megarads of radiation from Jupiter. This is about 280 times the amount that would kill you! Jupiter is pretty, but don't try to live nearby.
(1/n)
https://media.mathstodon.xyz/media_attachments/files/113/312/253/329/856/740/original/3031a2f4b7e17066.jpg

2024-10-15 15:52:01

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@npub1c9m…9xjd - I think people like you are just quieter than people who love or hate LLM. It's hard to YELL a balanced opinion.

2024-10-15 15:36:10

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@npub1ulf…sjfm - there is one, but they've never gotten around to publishing it.

2024-10-15 05:21:58

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@npub1jdy…zw04 - that's what I want to know, now! I had thought there was none, but I don't really know.

2024-10-13 16:13:27

Hey, they did it! People have known for a long time that in 4 dimensions you can pack equal-sized balls so that each touches 24 others. In 2008 someone showed that's the best you can do. But in April this year, three mathematicians showed there's essentially just 𝑜𝑛𝑒 𝑤𝑎𝑦 you can accomplish this!
This way is easy to describe. Take the points whose coordinates are all integers, together with those whose coordinates are all integers plus 1/2. Use each of these points as the center of a ball of radius 1/2. Then each ball touches 24 others. This pattern is called the 𝗗𝟰 𝗹𝗮𝘁𝘁𝗶𝗰𝗲.
The new result shows that if you pack equal-sized balls in 4 dimensions so that each touches 24 others, you're 𝑓𝑜𝑟𝑐𝑒𝑑 to create a version of the D4 lattice - possibly rotated, translated and/or rescaled.
This sort of thing is hard to show: it took a lot of fancy math and two weeks of calculation on a standard desktop computer. I believe only other dimensions where we know a result like this are 1, 2, 8 and 24. In dimension 3 it's just false: you can pack equal-sized balls so that each touches 12 others, and this is the best you can do, but there are uncountably many different ways to do it!
https://arxiv.org/abs/2404.18794

2024-10-13 13:56:24

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@npub1mtx…y3ul - I've never even 𝘩𝑒𝑎𝑟𝑑 𝑜𝑓 the Suite Italienne, so thanks - this is gonna be interesting!
I definitely need music as a mood-lifter; what lifts my mood can be pretty weird sometimes, but I don't look down my nose on sheer pep, like Vivaldi's Four Seasons.

2024-10-11 04:54:17

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@npub1g7v…scf3 - a bunch of people were wondering about such things on the Zulip.

2024-10-09 15:34:09

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@npub1jzg…hc3a - a lot of people don't like AI and they think machine learning researchers have essentially managed to steal the physics Nobel.

2024-10-09 02:35:47

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@npub1hv3…rjmk - I wrote this:
https://mathstodon.xyz/@johncarlosbaez/113272834785880929

2024-10-09 01:06:31

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@npub10l8…ath2 - I don't really care much who wins Nobel prizes, but yes a lot of my favorite physicists never won Nobels. Heck, Einstein didn't win one for special relativity, and he didn't win one for general relativity - just one for understanding photons, which is fine as far as it goes.
Btw, actually the point of LIGO was not to test our theory of gravitational waves: that would be a lot of money to check something we all believed in. The real point was to revolutionize astronomy by creating a new kind of telescope: we've seen a lot of unexpected things, like lots of black holes of masses 30-60 times the Sun, and we don't know where they came from.

2024-10-08 23:36:43

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@npub10l8…ath2 - You mean like LIGO's detection of gravitational waves? The physics was worked out long before, and we all knew gravitational waves existed - Hulse and Taylor had already won the Nobel for that - so one could argue that all LIGO did was an (magnificent, awesome) application of physics. But apparently the Nobel committee thought that was fine.
Or how about the 1912 physics prize, to Gustaf Dalén, for "for his invention of automatic valves designed to be used in combination with gas accumulators in lighthouses and buoys"? 😆

2024-10-08 22:52:57

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@npub10l8…ath2 - but I didn't say "neural networks research is physics". I say "it all started with physics", and gave evidence for how Hopfield and Hinton were using ideas from statistical mechanics. Yes, neural network research has grown beyond this now - it's now its own subject. I don't think anyone is claiming otherwise.
Wikipedia on Hopfield networks:
"The Sherrington–Kirkpatrick model of spin glass, published in 1975, is the Hopfield network with random initialization. Sherrington and Kirkpatrick found that it is highly likely for the energy function of the SK model to have many local minima. In the 1982 paper, Hopfield applied this recently developed theory to study the Hopfield network with binary activation functions. In a 1984 paper he extended this to continuous activation functions. It became a standard model for the study of neural networks through statistical mechanics."
Wikipedia on Boltzmann machines:
"They are named after the Boltzmann distribution in statistical mechanics, which is used in their sampling function. They were heavily popularized and promoted by Geoffrey Hinton, Terry Sejnowski and Yann LeCun in cognitive sciences communities, particularly in machine learning, as part of "energy-based models" (EBM), because Hamiltonians of spin glasses as energy are used as a starting point to define the learning task."

2024-10-08 16:51:32

Yay! John Hopfield and Geoffrey Hinton won the physics Nobel for their work on neural networks... work that ultimately led to modern-day machine learning.
Some of you are wondering why this counts as physics.
In the 1980s, Hopfield invented the 'Hopfield network' based on how atomic spins interact in a chunk of solid matter. Each atom's spin makes it into a tiny magnet. Depending on the material, these spins may tend to line up, or point opposite to their neighbors, or interact in even more complicated ways. No matter what they do, at very low temperatures they tend to minimize energy.
A Hopfield network is a simulation of such a system that's been cleverly set up so that the spins store data, like images. When the Hopfield network is fed a distorted or incomplete image, it keeps updating the spins so that the energy decreases... and works its way toward the saved image that's most like the imperfect one it was fed with.
Later, Geoffrey Hinton and others generalized Hopfield's ideas and developed 'Boltzmann machines'. These exploit a discovery by the famous physicist Boltzmann!
Boltzmann realized that the probability that a chunk of matter in equilibrium has energy E is proportional to
exp(-E/kT)
where E is its energy, T is its temperature and k is a number now called Boltzmann's constant. When the temperature is low, this makes it overwhelmingly probable that the stuff will have low energy. But at higher temperatures this is less true. By exploiting this formula and cleverly adjusting the temperature, we can make neural networks do very useful things.
There's been a vast amount of work since then, refining these ideas. But it started with physics.
https://arstechnica.com/ai/2024/10/in-stunning-nobel-win-ai-researchers-hopfield-and-hinton-take-2024-physics-prize/

2024-10-05 16:30:07

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@npub1ky2…ghvc - back when I was working on loop quantum gravity I thought it was dumb to claim it predicted violations of Lorentz invariance, because arguments for such violations were hand-wavy in the extreme: we didn't - and still don't - know enough about loop quantum gravity to make any such claims. We don't even know that loop quantum gravity predicts anything like the spacetime we see around us. Everyone who works on the subject should know that. But some people wanted to claim loop quantum gravity makes some testable predictions, so they stuck their neck out and made this 'prediction".
it's a lot like how some string theorists claimed it 'predicts' superpartners of mass accessible at the LHC. That's not a prediction of string theory. It's a personal decision that string theory 'should' predict that.

2024-10-05 16:18:12

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@npub1t76…4l63 - what's the idea of 'tidal squeeze' and 'tidal stretch'? I guess these are forces that appear when we have a central gravitational field and we're working in a rotating coordinate system, maybe with its origin at a point that's rotating in a circular orbit around the center?

2024-10-05 15:37:26

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@npub1ky2…ghvc - you'd damn well better use the canonical ones, unless your goal is to do something weird.

2024-10-04 05:22:59

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@npub12n4…5dmn - to compute the de Rham cohomology of SO(n) we should probably use the fact that these cohomology groups form a graded-commutative algebra (as de Rham cohomology groups of any manifold always do). Moreover, for SO(n) I believe we get the exterior algebra on generators of degree 4k-1 where 4k-1 goes 3, 7, ... all the way up to the largest number less than the dimension of SO(n), which I guess is n(n-1)/2.
But the proof of this fact, assuming I've got it right, is not trivial! It's part of a general theory of the de Rham cohomology of compact Lie groups. Looking around, I see people pointing toward this:
Mark Reeder, On the cohomology of compact Lie groups, L'Enseignement Math 41 (1995), 181-200.
though the basic ideas are a lot older.
(2/n)

2024-10-04 04:46:41

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@npub12n4…5dmn - interesting puzzle! To me the obvious approach is to start with some low 𝑛.
Let's compare SO(3) to S² × SO(2). Since π₁(SO(3)) ≅ ℤ/2 while π₁(S² × SO(2)) ≅ ℤ, they're not homeomorphic. By the way, SO(3) ≅ ℝP² since it's SU(2)/±1 and SU(2) is a 3-sphere.
Next let's compare SO(4) to S³ × SO(3). Since π₁(SO(n)) ≅ ℤ/2 for all n ≥ 3 now both these spaces have π₁ ≅ ℤ/2 so the above fundamental group argument no longer works, and we see it will never work to distinguish SO(n+1) from Sⁿ × SO(n) for n ≥ 3: they both have π₁ ≅ ℤ/2.
So we need a deeper idea.
(1/n)

2024-10-03 17:17:44

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"“The Neptunian Ridge stands tall above the Desert and Savanna. It provides us with a key to understanding the physical mechanisms shaping the Desert,” points out Vincent Bourrier. Most Neptunes may be distributed over the Savanna and Desert early in their life by migrating within the disk in which they formed. The existence of the Ridge suggests that some Neptune-size planets are brought to this region by a type of migration called high-eccentricity migration, which occurs later in their life and allow them to survive erosion from the stars.
These migration processes, coupled with photoevaporation, likely shape the distinct features observed in the Neptunian landscape. The similarities between the Neptunian Ridge and another feature in the exoplanet distribution, the hot Jupiter pileup, suggests that similar evolutionary processes may influence both groups of planets."
(2/2)
https://astrobiology.com/2024/09/hidden-exoplanets-between-the-neptunian-desert-and-savanna.html

2024-10-03 17:14:10

𝗧𝗛𝗘 𝗡𝗘𝗣𝗧𝗨𝗡𝗜𝗔𝗡 𝗗𝗘𝗦𝗘𝗥𝗧
Once we knew just one solar system. Now we can see 𝘩𝘶𝘯𝘥𝘳𝘦𝘥𝘴 of solar systems and learn how they work on average! We are learning amazing things, like this:
Here's a chart showing planets whose year is 25 Earth days long or less. These planets are very close to their suns. There's a big blob of planets with mass 10-20 times the Earth's mass, whose year is just 1-10 days long! These are called 𝗵𝗼𝘁 𝗡𝗲𝗽𝘁𝘂𝗻𝗲𝘀.
But there's an interesting shortage of slightly less massive planets that are quite close to their sun. This is called the 𝗡𝗲𝗽𝘁𝘂𝗻𝗶𝗮𝗻 𝗱𝗲𝘀𝗲𝗿𝘁. And there's another less dramatic shortage of planets in the 𝗡𝗲𝗽𝘁𝘂𝗻𝗶𝗮𝗻 𝘀𝗮𝘃𝗮𝗻𝗻𝗮. Both these need to be explained.
Now we have a new clue. This September astronomers discovered that the desert and savanna are separated by a region with more planets, which they call the 𝗡𝗲𝗽𝘁𝘂𝗻𝗶𝗮𝗻 𝗿𝗶𝗱𝗴𝗲.
What does it all mean? There are lots of theories, but it will take a while to figure it out.
Here's the new paper:
• A. Castro-González, V. Bourrier, J. Lillo-Box, J.-B. Delisle, D. J. Armstrong, D. Barrado and A. C. M. Correia, Mapping the exo-Neptunian landscape: a ridge between the desert and savanna, https://arxiv.org/abs/2409.10517.
With all this work we need to think about 'selection bias': some planets are easier to see than others, so what we see is not the same as the real situation! So, a lot of this paper is about compensating for selection bias.
For a link to a gentler, less technical article, read on.
(1/2)
https://media.mathstodon.xyz/media_attachments/files/113/244/496/342/306/359/original/8a986be8fc9391fa.jpg

2024-10-02 16:58:27

My wife Lisa Raphals got a Leverhulme Visiting Professorship in the classics department at the University of Edinburgh! It will last for 2 years. This is great because we'll already be there for my math job.
She compares classical Greek and classical Chinese philosophy. I'm very happy that her office is full of books in two languages I can't read, just as she can't read my math books.
Lately she's been comparing Western 'dualistic' views of the self, where it was split into mind and body, to the views in early China. But this project became so big that her latest book, 𝘈 𝘛𝘳𝘪𝘱𝘢𝘳𝘵𝘪𝘵𝘦 𝘚𝘦𝘭𝘧: 𝘔𝘪𝘯𝘥, 𝘉𝘰𝘥𝘺, 𝘢𝘯𝘥 𝘚𝘱𝘪𝘳𝘪𝘵 𝘪𝘯 𝘌𝘢𝘳𝘭𝘺 𝘊𝘩𝘪𝘯𝘢, only covers the Chinese side.
A lot of people say Chinese philosophy was 'monistic' or 'holistic', treating the mind and body as one. But she argues that if you actually read the early texts, including medical texts, you get a different and more interesting picture, which involves body, mind and a third entity: 'spirit', or
𝘴𝘩𝘦́𝘯.
The word 𝘴𝘩𝘦́𝘯 originally referred to external 'spirits', external entities like the spirits of rivers and mountains, or spirits of dead ancestors. But in the late 4th or early 3rd century BCE, some thinkers started discussing practices that could enhance your internal 'spirit', using the same word 𝘴𝘩𝘦́𝘯.
Later thinkers developed this idea along two lines. In one, mind and spirit are closely aligned, and rule the body as a ruler rules a state. In the other, the person is tripartite, with mind and spirit as independent entities.
I think it's really cool how our understanding of personhood has evolved over time.
https://media.mathstodon.xyz/media_attachments/files/113/238/877/124/358/401/original/c7efaad2922e4119.jpg

2024-10-02 05:36:34

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@npub1g7f…25j2 - meaning?

2024-10-01 21:47:35

This undergraduate thesis by Jan Strehmel deserves a prize:
𝐀𝐛𝐬𝐭𝐫𝐚𝐜𝐭. One of the most fundamental unanswered questions that has been bothering mankind during the Anthropocene is whether the use of swearwords in open source code is positively or negatively correlated with source code quality. To investigate this profound matter we crawled and analysed over 3800 C open source code containing English swearwords and over 7600 C open source code not containing swearwords from GitHub. Subsequently, we quantified the adherence of these two distinct sets of source code to coding standards, which we deploy as a proxy for source code quality via the SoftWipe tool developed in our group. We find that open source code containing swearwords exhibit significantly better code quality than those not containing swearwords under several statistical tests. We hypothesise that the use of swearwords constitutes an indicator of a profound emotional involvement of the programmer with the code and its inherent complexities, thus yielding better code based on a thorough, critical, and dialectic code analysis process.
https://cme.h-its.org/exelixis/pubs/JanThesis.pdf
It cites some previous research:
• Yehuda Baruch et al. Swearing at work: the mixed outcomes of profanity,
Journal of Managerial Psychology 32 (Jan. 2017),149–162, https://doi.org/10.1108/JMP-04-2016-010
𝐀𝐛𝐬𝐭𝐫𝐚𝐜𝐭. In contrast to much of the incivility and social norms literatures, the authors find that male and female business executives, lawyers and doctors of all ages admit to swearing. Further, swearing can lead to positive outcomes at the individual, interpersonal and group levels, including stress-relief, communication-enrichment and socialization-enhancement
https://media.mathstodon.xyz/media_attachments/files/113/234/356/291/079/488/original/2543f3662e0ff1e1.jpg

2024-10-01 05:32:37

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@npub1rf7…zwfx - this is cool, but the subtitle "This is very unexpected" is an exaggeration: the issue has been around for a long time:
https://en.wikipedia.org/wiki/Cuspy_halo_problem

2024-09-30 16:34:21

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@npub1z4e…aasw - yes, I hope you read the image description.

2024-09-29 16:02:08

𝗤𝗨𝗜𝗖𝗞! 𝗙𝗘𝗘𝗗 𝗧𝗛𝗘 𝗕𝗘𝗔𝗦𝗧!
Academic publisher Taylor & Francis recently sold many of its authors’ works to Microsoft for $10 million, without asking or paying the authors — to train Microsoft’s large language models!
Taylor & Francis asked their journal "Learning, Media and Technology" to cut peer review time to 15 days — absurdly little time — to crank out more content.
And Taylor & Francis's subsidiary Routledge told staff that it was “extra important” to meet publishing targets for 2024. It moved some book deadlines from 2025 to 2024. Why? To meet its deadline with Microsoft.
Another academic publisher, Wiley, made a $44 million deal to feed academic books to LLMs — with no way for authors to opt out. They say “it is in the public interest for these emerging technologies to be trained on high-quality, reliable information.”
When you publish with one of the big academic publishers, they try to make you sign a contract saying they can do whatever they want with your work. That means anything.
Hat-tip to @npub1yt3…wmv6 for pointing this out.
These articles have links to original sources:
https://pivot-to-ai.com/2024/08/04/more-academic-publishers-are-doing-ai-deals/
https://pivot-to-ai.com/2024/09/28/routledge-nags-academics-to-finish-books-asap-to-feed-microsofts-ai/
https://media.mathstodon.xyz/media_attachments/files/113/221/626/482/836/881/original/b380b5ccede93fcd.jpg

2024-09-28 21:22:47

In 1596, Kepler claimed that the planetary orbits would only follow "God's design" if there were two more planets: one between Mars and Jupiter and one between Mercury and Venus. Later folks came up with the Titius-Bode rule. This says there should be a planet whose orbital radius is
0.4 + 0.3 × 2ⁿ
times the distance between the Earth and Sun.
• For n = 0 we get Venus.
• For n = 1 we get Earth.
• For n = 2 we get Mars.
• For n = 3 we get... NOTHING???
• For n = 4 we get Jupiter.
• For n = 5 we get Saturn.
• For n = 6, this rule correctly predicted the location of another planet: Uranus.
So, 24 astronomers called the "celestial police" looked between Mars and Jupiter. And in 1801 one of them found a small object in the right place! Later people found other asteroids in a belt between Mars and Jupiter, but the first was the biggest: Ceres.
In 2015 we sent a probe called Dawn to investigate Ceres. It found something wonderful.
The surface of Ceres is a mix of ice and hydrated minerals like carbonates and CLAY! It probably doesn't have an internal ocean of liquid water like Jupiter's moon Europa. But it seems that brine still flows through its outer mantle and reaches the surface!
A new paper argues that Ceres contains a 𝑙𝑜𝑡 of ice, and was once an ocean-covered world:
"We think that there's lots of water-ice near Ceres surface.... People used to think that if Ceres was very icy, the craters would deform quickly over time, like glaciers flowing on Earth, or like gooey flowing honey. However, we've shown through our simulations that ice can be much stronger in conditions on Ceres than previously predicted if you mix in just a little bit of solid rock.""
https://phys.org/news/2024-09-asteroid-ceres-ocean-world-slowly.html

2024-09-27 22:28:44

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@npub19eg…ma58 @npub1kqz…8s5l - I don't primarily post interesting things for other people: fundamentally I post for myself. I explain things so I understand them. But people seem to like it.
I don't follow anyone who posts stupid memes or political rage bait, so I don't see that, though I'm sure it's there.
And so, I'm happy.

2024-09-26 21:06:31

Professor emeritus blues:
You know you've been retired a while when the department staff accidentally puts some new lecturer's photo up with your name on it, because they don't remember who you are.
https://media.mathstodon.xyz/media_attachments/files/113/205/883/520/123/142/original/0547f399b930ed86.jpg

2024-09-24 05:35:29

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@npub1l40…nm43 - our ancestors probably killed them off, and they may have passed down tales about how in the old days there were a lot more dangerous predators but the game was more plentiful.

2024-09-20 18:59:17

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@npub1uhn…2f8t - are you talking about the paper or the video? I didn't even watch the video yet.

2024-09-20 06:12:47

What would happen if the Moon broke into seven pieces? It would not be good. Check out this simulation, including a video.
https://jasmcole.com/2017/09/20/the-moon-blew-up-without-warning-and-for-no-apparent-reason/

2024-09-18 00:09:11

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@npub1d8z…zgls - "no" to the first question, in the math department at U. C. Riverside.

2024-09-17 20:23:56

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@npub12nw…uegw - I used the "explosion" feature in Irfanview, setting it to different levels in different patches of the picture.

2024-09-17 16:46:23

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@npub18vx…zvkl - if it's easy, why do you have to steel youself for it? 😈

2024-09-16 15:24:32

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@npub1el0…j0zm - they've been marching for decades, since the 1980s, and seem no closer today.

2024-09-16 15:19:49

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@npub1sqt…hmh2 - beautiful!

2024-09-15 20:36:51

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@npub1ld9…04d0 - No problem! Btw, if the size of a rainbow depended on the droplet size, rainbows would probably look 'fuzzed-out', since different drops often have different sizes.

2024-09-14 17:03:46

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@npub1vt8…yzq0 - I guess you know about the new "Beat" tour:
https://www.youtube.com/watch?v=QIgxRK914WI

2024-09-13 23:38:25

This feature in Hudson Bay is probably 𝑛𝑜𝑡 a large meteor crater. It's called the Nastapoka Arc. While the dark red part of the circle really is the coastline, the rest of the circle is not anything real.
Details:
https://en.wikipedia.org/wiki/Nastapoka_arc
https://media.mathstodon.xyz/media_attachments/files/113/132/859/294/301/181/original/abfcc15cc37dda23.png

2024-09-13 21:53:21

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@npub1wnd…8kcm - they should repeat it with people who aren't Dutch. 🙃

2024-09-13 16:08:36

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@npub17q0…je6u - if you block the email address and/or journal/conference name for each one, does it help at all? Or are they mostly new instances?

2024-09-13 01:43:08

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@npub1cd3…paq7 - you meant to say rig.