The time is back to nanosecond accuracy at the National Institute of Standards and Technology! groups.google.com/a/list.nist....

Ever wonder about the math hiding in music? There's a lot of it, and it's really fun! Here's a first take on some of it. (When you're done, you'll know why musicians have special names for the numbers 81/80 and 128/125.) johncarlosbaez.wordpress.com/2025/12/26/t...

New result: you can build a universal computer using a single billiard ball on a carefully crafted table! More precisely: you can create a computer that can run any program, using just a single point moving frictionlessly in a region of the plane and bouncing off the walls elastically. (1/n)

The atomic clocks in Boulder are back in service. But they could be as much as 5 microseconds off! That's no big deal for transmitting time on the internet, where millisecond irregularities are common. But it'd be 5000 times the usual nanosecond errors! groups.google.com/a/list.nist....

There's something satisfying about finding that two words you know are part of a doublet - like "regal" and "royal", the first coming directly from Latin and the second taking a detour through French. Now in Spanish: "Siesta" vs "sixta". Oh! "Siesta" happens at the 6th hour after dawn! 😀

Ouch! The most accurate standard of time in the USA may have gone down! Yup, a bunch of atomic clocks at the National Institute of Standards and Technology (NIST) in Boulder, Colorado seem to have lost power. (1/n)

Another installment! This time I explain spin-1/2 particles, the Stern-Gerlach experiment that convinced people they exist, and why a quantum state of a spin-1/2 particle is the same as a vector of length 1/2 saying which way the spin points. youtu.be/sZgjh_lqelY

When Lee and Yang suggested there's a fundamental difference between left and right, Pauli wrote: "Ich glaube aber nicht, daß der Herrgott ein schwacher Linkshänder ist." (I do not believe that the Lord is a weak left-hander.) 2 days later, Wu's experiment showed that Lee and Yang were correct!

Huge good news! They saw a "fisher" in a park in Cleveland Ohio! This is the is the first sighting of a fisher in Cuyahoga County since the 1800s. The sighting was recorded on a trail camera: www.instagram.com/p/DSM9EpzjtR... (The photo here is from Massachusetts.) (1/n)

In 1973, Penrose conjectured a lower bound on the mass M of a black hole as a function of its area A: M ≥ sqrt(A/16π) Now someone claims to have a proof - 449 pages long. Do any experts have opinions on this? arxiv.org/abs/2512.04137

Is anyone taking bets on when the Kessler syndrome starts? That's when a chain reaction of colliding satellites destroys many of them. All the experts say it's coming our way. www.theverge.com/news/844502/...

This chart shows all objects in the Universe, arranged by mass (vertical) and radius (horizontal). Let me explain it a bit... • C. H. Lineweaver and V. M. Patel, “All objects and some questions”, American Journal of Physics 91 (2023), 819-825. www.researchgate.net/publication/... (1/n)

"I've never met any child prodigies, but I did meet many of their parents." - Daniel Baremboim

At 17:00 UTC today I'm going to give a talk at the Topos Institute. You can watch it here! youtube.com/watch?v=GzBV... (1/n)

Wow! Now the arXiv is demanding that all papers have a full English-language version, either as the original language or as an included translation. It looks like this is pushing some French scientists to use HAL instead. blog.arxiv.org/2025/11/21/u...

Aquinas texted while driving. Those who fail to learn from history are doomed to repeat it.

Here's a speculative physics talk, in which I explain this weird fact: The Standard Model gauge group is the group of symmetries of an octonionic quitrit that are also symmetries of an octonionic qubit and a complex qutrit. I'm still thinking about this. youtu.be/OH9e9C0xvUg

Yum! Frogs can eat murder hornets and don't seem to mind the venom... even if they're left with a big stinger stuck in their throat. This could be good because these hornets, technically Asian giant hornets, are invasive in America. More here: doi.org/10.1002/ecs2...

Just when you thought you had 'em figured out.

My series of posts below was very confused! Business Insider *did* write this - but it's another company, Harmonic, that claims to have solved "multiple open Erdős math problems": the two I discussed, and a third as well. (1/2)

This startup, Axiom Math, seems to be trying to automate the "puzzle solving" aspect of math. I'll be glad if they transfer some money from investors to mathematicians. But I've got a bit to say about this. (1/n) www.businessinsider.com/axiom-math-s...

I've decided to spend some time on a quest that's likely to fail. I'm trying to start with the Standard Model of particle physics, ponder its patterns, and figure out *why* it's that way. www.youtube.com/watch?v=6zrp...

Lie groups and Noether's theorem are the tools that let 20th-century physicists wield *symmetry* as a powerful tool to study crystals, molecules, atoms, and elementary particles. (1/n)

The Linear Pottery Culture ended around 5000 BC... with grim signs of something like a genocide: mass graves, with fractured skulls and beheaded skeletons. Nobody knows why, though there are theories. Details here: archive.is/v4HYp

The main rule of quantum mechanics answers: if a system is in one state, what's the probability that it's in some different state? Shockingly, it's not zero! I explain this with minimum jargon, and fear not: I say what all the funky symbols here mean: ∈, ℂᵈ, etc. www.youtube.com/watch?v=Y0a8...

The largest fundamental science agency in Europe will save €1.4 million annually by breaking free from Clavariate Analytics' huge databases of references and citations. "We have worked for free to lock ourselves collectively into a paid system", one head of the CNRS explains - but no more! 🎉

Saying you do math is a bad conversation starter. So when a mathematician friend of mine went on a hitchhiking trip, he told each ride that his profession was that of the *last* ride he'd gotten! He learned how to ask lots of good questions so he could simulate different professions. But... (1/2)

Arabian oryxes. Beautiful! But what do they eat out here? Basically any vegetation at all. They can detect rainfall from far away, and move towards it. They have huge ranges: one herd in Oman roams over 3,000 square kilometers! Hunted to near-extinction, now they're back.

A mathematician friend of mine went on a long hitchhiking trip and told each ride that his profession was that of the *last* ride he'd gotten! He learned how to ask lots of good questions so he could simulate different professions. But then he said "architect" and his new ride was an architect.

There are about 10 billion tons of bacteria floating around in the ocean. That's about 10³⁰ bacteria — a nonillion of them. They're called 'bacterioplankton'. But about 40% of these bacteria are infected by viruses! (1/n)

Some places have too many tourists, but one of the places I love the most - the Navajo Nation, which stretches across Arizona, New Mexico and Utah - is begging for them. www.nytimes.com/2025/11/26/t... Free version here: archive.is/QTt63

My series explaining the Standard Model of particle physics has 3 parts so far: 1) Particles 2) The Big Ideas 3) Qubits Next: 4) Quantum Physics 5) Spinors Then isospin, pions and more particle physics! Alas, I've been slowed down by our kitchen remodeling. I want to pick up the pace.

Want to know what climate change will look like? The drought in Tehran has gotten so bad that people are seriously talking about evacuating this city of 15 million. "Day zero" is expected in a few weeks. That means NO WATER. peterfrankopan.substack.com/p/makran-or-...

Sometimes gauge transformations have a physical effect. (The connection to railway tracks is no coincidence: Weyl first introduced the term "gauge invariance", or really "Eichinvarianz", in a theory where lengths could only be compared locally.)

Tirelessly toiling, I added two of these Clifford algebra isomorphisms to Wikipedia: Cl(q+2,p) ≅ Cl(p,q) ⊗ Cl(2,0) Cl(q,p+2) ≅ Cl(p,q) ⊗ Cl(0,2) Cl(p+1,q+1) ≅ Cl(p,q) ⊗ Cl(1,1) but without the obscenely large tensor product symbols. en.wikipedia.org/wiki/Classif...

Two new pieces by the teenage Bach just dropped! They were preserved in only one source. www.youtube.com/watch?v=0X1x... (1/2)

If you ever want to make an scientist really happy, cite a paper of theirs that nobody paid attention to for decades, and call it "pioneering". Great new global existence results for classical Yang-Mills theory by Nicolas and Taujanskas: arxiv.org/abs/2507.16750

The International Association of Cryptologic Research cancelled the results of its annual leadership election after an official lost an encryption key needed to get access to the results. 😆 www.nytimes.com/2025/11/21/w... Free here: archive.is/NOnfx

Had a great conversation with Tymoczko about groupoids in music theory yesterday - I'm the guy introducing him here. But at this Higgs Centre Colloquium, he preferred to talk in terms of things physicists know and love: gauge theory and orbifolds! media.ed.ac.uk/media/Beyond...

Coming up in less than 45 minutes: a great talk on groupoids in music theory! You can join us online. mathstodon.xyz/@johncarlosb...

If you wrote the first article in a volume in a Springer Nature journal, congratulations - you won the lottery! You're getting credit for citations to all the papers in that volume! 🤪 arxiv.org/abs/2511.01675

Wow. I knew Lawrence Krauss was a sex pest and a creep. But I didn't know who he ran to for advice when he got caught. Jeffrey Epstein! All the details are here: www.youtube.com/watch?v=VNLd...

After a huge fire in Oregon, streams were choked with ash — but the water downstream of these beaver dams was crystal clear — and trout were thriving! The dams were acting as a water treatment plant. www.scientificamerican.com/article/beav...

A moody evening sky in Edinburgh, viewed from my apartment October 11, 2025.

Lynx, formerly exterminated in Germany, France and Switzerland, have been brought back to these countries. There's now a campaign to reintroduce them in Scotland! The Greens plan to bring this to a vote. (1/n)

All US news media, all the time: men are really in trouble!!! They need more help!!! 40% of young US women: umm, excuse me, can I leave now? news.gallup.com/poll/697382/...

As a happy new resident of Scotland, I just signed a petition to to demand the UK Government tax the super rich to rebuild our NHS, schools, and other public services. Will you sign too? you.38degrees.org.uk/petitions/ta...

The most beautiful spaces are the irreducible compact Riemannian symmetric spaces! There are the infinite series: the Lie group SO(n), SU(n), Sp(n) and the 6 series listed below. And then there are the exceptions.... (1/3)

This is the closest you'll ever see to the color called "olo". To see "olo" you need a mad scientist to map your retina, individually identify each cone cell as one of 3 kinds - and then use lasers to deliver light exclusively to your "M" cones. Done recently: mathstodon.xyz/@johncarlosb...