John C. Baez

@johncarlosbaez

Mathematical physicist

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John C. Baez@johncarlosbaez· 21d

This paper argues that tubulins in the Asgard archaea are unstable and can change to tubulins like those in plants and animals. More evidence that eukaryotes came from Archaea. Someday we may ditch the domain Eukarya. There will just be two: Archaea and Bacteria. All hail Odin! (3/n, n = 3)

Eukaryotic-like microtubules and dynamic instability of Asgard archaeal tubulins

Jan Löwe https://orcid.org/0000-0002-5218-6615,
Andriko von Kügelgen https://orcid.org/0000-0002-0017-2414, Vicente J. Planelles-Herrero https://orcid.org/0000-0002-1665-184X, Martin B. L. McAndrew https://orcid.org/0000-0001-7338-3119, María A. Oliva https://orcid.org/0000-0002-2215-4639, Julian Vosseberg https://orcid.org/0000-0002-3105-9414, Stephan Köstlbacher https://orcid.org/0000-0001-6710-7572, Jennah E. Dharamshi https://orcid.org/0000-0003-4563-3939, Kathryn E. Appler https://orcid.org/0000-0002-1219-1786, [...] , and Thijs J. G. Ettema https://orcid.org/0000-0002-6898-6377+8 authors Authors Info & Affiliations
Science Advances

Abstract
Eukaryotic cells change their shapes, actively segregate their DNA, and contain membrane networks, facilitated by a complex cytoskeleton containing actin filaments, microtubules made from tubulin, and other components. These filaments have ancient evolutionary origins because actin- and tubulin-like proteins form prokaryotic cytoskeletons in archaea and bacteria. Bona fide eukaryotic F-actin can be traced back to crenarchaea and Asgard archaea, which are the closest known relatives of eukaryotes. A possible Asgard archaeal origin of microtubules was suggested recently with the discovery of a lokiarchaeon containing AtubAB mini microtubules that share architectural features with their eukaryotic counterparts. Using phylogenetic analyses of metagenomic data, here we report the broad occurrence of tubulins in Asgard archaea. Biochemical and structural analyses showed that one of our previously unidentified heimdallarchaeial AtubAB tubulin pairs forms four-protofilament mini microtubules that show dynamic instability and are inhibited by the tubulin drug maytansine. Our work raises the possibility that microtubule architecture and dynamics evolved in Asgard archaea prior to eukaryogenesis.

John C. Baez@johncarlosbaez· 21d

The perils of being a role model. They will imprint on you.

Ducklings following their mother across a road.

John C. Baez@johncarlosbaez· 25d

What's a non-mathematical conceptual model? A bunch of verbal explanations about how things work? That seems like a prerequisite for building a mathematical model. Then we want to generate some numerical predictions that we can test, if possible.

John C. Baez@johncarlosbaez· 28d

Yes! Sometimes math runs out of simple numbers and goes for a more complicated one!

John C. Baez@johncarlosbaez· 28d

Why do paths through the Sierpiński triangle correspond to allowed sequences of moves in the Tower of Hanoi? Suppose we have 3 discs. Say (3,2,3) means "biggest disc on post 3, second biggest on post 2, third biggest on post 3". Suppose edges are allowed moves. We get this picture! (4/n)

If we draw all allowed states of the n-disc Tower of Hanoi puzzle, connected by edges representing allowed moves, we get a finite approximation of the Sierpinski triangle. This is the picture for n = 3, taken from here:

https://www.cut-the-knot.org/triangle/Hanoi.shtml

John C. Baez@johncarlosbaez· 28d

Wow! If the side length of this "Sierpiński triangle" is 1, the average distance between its points is 466/885. Double wow! The average number of moves in a shortest path between two random states in the n-disc Tower of Hanoi puzzle is asymptotically (466/885)·2ⁿ as n → ∞. (1/n)

$A Sierpiński triangle. Take an equilateral triangle, divided it into 4 smaller equilateral triangles, removed the middle one... and then repeat this procedure on the remaining 3, and repeat forever. What's left is a fractal with measure zero. Picture created by Marco Polo and placed on Wikicommons under a Creative Commons Attribution-Share Alike 3.0 Unported license, here: https://commons.wikimedia.org/wiki/File:Sierpinski_triangle.svg$

John C. Baez@johncarlosbaez· Jul 14

The math has been around for decades - but nobody noticed it gives a new framework for quantum mechanics from which the Standard Model gauge group and its representation on one generation of quarks and leptons falls out pretty naturally. arxiv.org/abs/2607.10833

John C. Baez@johncarlosbaez· Jul 11

From the Eₙ lattice there's a standard way to get the Eₙ group. Putting everything together: if you take ℂℙ², blow up 3 points in general position, use the resulting surface to build the E₃ lattice, and form the corresponding group, it's the gauge group of the Standard Model! 😵‍💫 (7/n, n = 7)

Black-and-white drawing of a sinister man leaning back and saying BWAHAHAHAHAHA.

John C. Baez@johncarlosbaez· Jul 11

But here's part of the story that remains entirely magical to me: you can get the Eₙ series from del Pezzo surfaces! This is a story from algebraic geometry, so these surfaces are really smooth 2d complex varieties, hence compact oriented 4-manifolds. But a real slice might look like this: (3/n)

A real slice of a simple sort of Fano surface, called the Clebsch cubic surface. Picture by Greg Egan. For more see this: https://blogs.ams.org/visualinsight/2016/02/15/27-lines-on-a-cubic-surface/

John C. Baez@johncarlosbaez· Jul 11

The exceptional groups E₈, E₇ and E₆ are famous - but we can define Eₙ groups for smaller n too. E₃ is the gauge group of the Standard Model! Some larger ones are gauge groups of famous grand unified theories. I'm starting to understand what's really going on here. (1/n)

The E8 root polytope projected from 8 dimensions down to 3. A bunch of points connected to edges in an almost chaotic-looking but actually symmetrical pattern.

John C. Baez@johncarlosbaez· Jul 10

Here in the UK, a stainless steel trash can may be our hope for the future.

John C. Baez@johncarlosbaez· Jul 8

A rainbow is a portion of a circle centered on the point directly opposite the sun. This circle always has an angular radius of 42 degrees: that's how raindrops work. A full moon is directly opposite the sun. So if the moon is in a rainbow, it's close to 42° degrees away from being full. (2/2)

$Refraction and reflection in a raindrop, producing a rainbow. White light separates into different colours (wavelengths) on entering the raindrop, as red light is refracted by a lesser angle than blue light. It reflects against the back of the raindrop and gets refracted again as it leave the front. On leaving the raindrop, the red rays have turned through a smaller angle than the blue rays, producing a rainbow. However, all the reflected light comes out at angle of roughly 42 degrees from the line at which it came in. From https://commons.wikimedia.org/wiki/File:Rainbow1.svg$

John C. Baez@johncarlosbaez· Jul 8

Mark Ham wowed the world with this picture. But then someone wowed me even more by pointing out that the moon always has the same phase when it's in a rainbow! (1/2)

A closeup of a rainbow with the Moon in it. The Moon is not full, it is gibbous. This photo was taken by Mark Ham. In this photo you can work out exactly where the sun is—behind him over his left shoulder—from both the position of the rainbow and from the phase of the moon.

John C. Baez@johncarlosbaez· Jul 6

Realizing more and more how modern-day AI taps into some very old urges. So many would like "unsurpassed mastery without any effort", and would gladly summon a demon to get it.

Passage from Magic in the Middle Ages, 2nd edition, by Richard Kieckhefer:

Necromancy in the clerical underworld

The uses of necromancy were legion. One conjuration in the Munich handbook, for example, is intended to summon a demon who will impart unsurpassed mastery of all the arts and sciences without any effort on the part of the necromancer. Evidently the author was an ambitious but not particularly diligent scholar. In general, however, the aims of this magic

John C. Baez@johncarlosbaez· Jul 5

No selfie, but I went to Oxford and took some nice walks by the Thames. Lots of houseboats!

John C. Baez@johncarlosbaez· Jul 4

Nice! One of those shapes is based on the famous "lune of Hippocrates", which tantalized early Greeks attempting to square the circle: en.wikipedia.org/wiki/Lune_of... The two shaded regions here have the same area; the crescent is called the lune of Hippocrates.

A right triangle inscribed in a semicircle, and a smaller semicircle centered at the midpoint of its hypotenuse, with the region in the larger semicircle removed, leaving a crescent or "lune".

John C. Baez@johncarlosbaez· Jul 3

I love it! The idea of "traveling to Andalusia and stealing a tome of secret knowledge" is a wonderfully distorted pop version of what Sylvester II actually did: read books in Catalan monasteries and use what he learned to introduce the abacus, armillary sphere and decimal system to the West. (4/n)

Model of Gerbert of Aurillac's (= Pope Sylvester the Second's) abacus showing how he might have added 908 and 95 (labeled with modern numerals, not Gerbert's). From JRGomà, placed on Wikicommons under a Creative Commons Attribution-Share Alike 3.0 Unported license: https://commons.wikimedia.org/wiki/File:%C3%80bac_de_Gerbert.png

John C. Baez@johncarlosbaez· Jul 2

If you write an 878-page treatise revolutionizing all aspects of natural science, from grammar and logic to mathematics, physics, and philosophy, you get a grubby little lane in Oxford.

A wall, red brick on bottom and yellow brick on top, separated by a band of concrete, with a sign on it saying ROGER BACON LANE. Photograph by John Baez, July 2026.

John C. Baez@johncarlosbaez· Jun 30

Solar power on a houseboat on the Thames, near Oxford where this river is still small. Just part of the peaceful walk to Topos UK, where I'm helping David Jaz Myers with his book on category theory for the design of open systems.

John C. Baez@johncarlosbaez· Jun 26

While France roasted and England sweltered, Scotland had some fine sunny days - a rarety. Tonight, however, a cold fog rolled into Edinburgh.

View down a foggy road in Edinburgh in the evening, with traffic lights gleaming and rows of flats.

John C. Baez@johncarlosbaez· Jun 24

First, derived geometry shows up whenever you have a classical mechanical system (or field theory) with constraints that carve out a non-smooth subvariety of the configuration space or phase space, e.g. 𝑦³=𝑥². Stacky geometry shows up whenever you have to mod out by gauge symmetries. (1/2)

John C. Baez@johncarlosbaez· Jun 23

Is topos theory scary? Yes, but only like gorillas are scary.

Steve Vickers on topos theory:

As a parable, I think of toposes as gorillas.... At first they look very fierce and hostile, and the locker-room boasting is all tales of how you overpower the creature and take it back to a zoo to live in a cage — if it’s lucky enough not to have been shot first. When it dies you stuff it, mount it in a threatening pose with its teeth bared and display it in a museum to frighten the children. But get to know them in the wild, and gain their trust, then you begin to appreciate their gentleness and can play with them.

The gorilla in the cage is the topos in the classical world.

For more, go here: https://golem.ph.utexas.edu/category/2008/03/learning_to_love_topos_theory.html

John C. Baez@johncarlosbaez· Jun 20

This whole picture is a photo! It's the sky as viewed through a 6-meter-wide hole at the top of James Turrell's huge new installation The Dome. The light inside this dome keeps changing - and so does the color of the sky, as the day goes by. People like to lie in the dome and stare up.

A dark blue-gray disk on a magenta background. Inside the disk are two birds, flying. The disk is the sky. Photo by Mathias Eis for The New York Times:

https://www.nytimes.com/2026/06/19/arts/james-turrell-aros-aarhus.html

John C. Baez@johncarlosbaez· Jun 19

When I worked in Singapore at the Centre of Quantum Technologies I went to Cambodia and visited Ta Prohm, an old temple near Angkor Wat. You may have seen it in "Tomb Raider". As nature regains control, it beautifies what it ruins.

The outer wall of the temple of Ta Prohm, with a giant tree root growing down it, and at left the statue of a busty dancer in bas-relief, built into the wall. Photograph by John Baez, February 20, 2011.

John C. Baez@johncarlosbaez· Jun 17

Yes, the n point function is an nth moment. You my try making yourself a little dictionary and keep adding to it. Here's a start:

John C. Baez@johncarlosbaez· Jun 15

I think a great way to start is this paper by two students at Harvard: • Chao Li and Charmaine Sia, Knots and Primes, www.math.columbia.edu/~chaoli/tuto... The chart on page 3 show the amazing analogy between knots and primes!

John C. Baez@johncarlosbaez· Jun 14

Great deal from the local charity shop: a massive two-volume treatise on the steam engine for just 12 pounds. Almost a pound per pound.

Two orange volumesJohn Farey's "A Treatise on the Steam Engine: Historical, Practical and Descriptive", 1827.

John C. Baez@johncarlosbaez· Jun 13

The JUNO detector, a huge sphere full of 20,000 tonnes of transparent organic goop, is detecting antineutrinos produced by two nuclear reactors each located the same distance away. After just 2 months, it measured some things about neutrino masses better than ever before! Let's dig in. (1/13)

A schematic of the JUNO detector: a huge blue ball surrounded by detectors.

John C. Baez@johncarlosbaez· Jun 10

I've been fascinated by those mysterious Roman dodecahedra for a while. My friend Alexandre Popoff also showed me pictures of medieval Islamic weights, like these: