The mascot of New College, in Florida, was the empty set. Technically the Null Set. But New College was considered "woke" - so a board of trustees dominated by conservatives appointed by Gov. Ron DeSantis voted to replace the Null Set with a new mascot: a tree. www.nullsets.org/nullsethistory
If the universities become too corrupt, maybe we'll return to the roots from which universities emerged: individual scholars advertising their willingness to take on students for a fee! Over time these scholars got more organized and formed universities.... en.wikipedia.org/wiki/Medieva...
![Characteristics
Initially medieval universities did not have physical facilities such as the campus of a modern university. Classes were taught wherever space was available, such as churches and homes. A university was not a physical space but a collection of individuals banded together as a universitas. Soon, however, universities began to rent, buy or construct buildings specifically for the purposes of teaching.[27]
Universities were generally structured along three types, depending on who paid the teachers. The first type was in Bologna, where students hired and paid for the teachers. The second type was in Paris, where teachers were paid by the church. Oxford and Cambridge were predominantly supported by the crown and the state, which helped them survive the Dissolution of the Monasteries in 1538 and the subsequent removal of all principal Catholic institutions in England. These structural differences created other characteristics. At the Bologna university the students ran everything—a fact that often put teachers under great pressure and disadvantage. In Paris, teachers ran the school; thus Paris became the premiere spot for teachers from all over Europe. Also, in Paris the main subject matter was theology, so control of the qualifications awarded was in the hands of an external authority – the chancellor of the diocese. In Bologna, where students chose more secular studies, the main subject was law.
It was also characteristic of teachers and scholars to move around. Universities often competed to secure the best and most popular teachers, leading to the marketisation of teaching. Universities published their list of scholars to entice students to study at their institution. Students of Peter Abelard followed him to Melun, Corbeil, and Paris,[28] showing that popular teachers brought students with them.
From https://en.wikipedia.org/wiki/Medieval_university#Establishment](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:fb5fjz7jxmbf3alhwh44ookd/bafkreiblwmiv4bbl6a4z5f7uddqcpyooodganmq5ayhvdixrztsf7tdaxy)
Arula Ratnakar@arula-ratnakar.bsky.social · 3d agoMaybe in the age of LLMs instead of becoming a professor I’ll one day start some cult like thing trying to preserve the pencil and paper methodology of developing theories. And I’d take on apprentices who want to learn the art.
Archaeologists believe this stone circle was built before the island it was on lost its vegetation.
Edinburgh! There's a brand new shop a few blocks away, full of spices and other goods, many unknown to me.
Newly found art from 40,000 BC! Tiny ivory figurines of birds, found 1.5 meters apart in a cave called Hohle Fels in Germany. From the Aurignacian culture - Cro-Magnons. The glaciers had receded: the area was a steppe-tundra with permafrost, supporting mammoth, reindeer, horse, and bison.
Now I can say I put off paying my taxes because I'm a piezophile.
Quanta Magazine@quantamagazine.org · last wk.In 2017, the bacterium 𝘊𝘰𝘭𝘸𝘦𝘭𝘭𝘪𝘢 𝘮𝘢𝘳𝘪𝘯𝘪𝘮𝘢𝘯𝘪𝘢𝘦 was found growing on a decaying crustacean in the Mariana Trench. This piezophile (pressure lover) grows best at 120 megapascals of pressure — or nearly 1,200 atmospheres. www.quantamagazine.org/the-organism...
I'd go into biology if I could write a paper with a title like "Dynamic instability of Asgard archaeal tubulins". So intense! Asgard is the dwelling of the gods in Norse mythology. Archaea are an important group of organisms, going back to the early hot Earth. (1/n)
Eukaryotic-like microtubules and dynamic instability of Asgard archaeal tubulins
Asgard archaeal mini microtubules suggest an archaeal origin of eukaryotic microtubules.
science.org
A really good mathematician told me Anthropic is paying people like him $250/hour to improve Fable by throwing hard math problems at it. They also get a separate account where they can use Fable for their own purposes. They can do it for 5 months maximum.
Alpöge's counterexample to the Jacobian conjecture has consequences for quantum mechanics in 3 dimensions! You can find operators obeying the usual position–momentum commutation relations that generate a smaller algebra than the usual ones do. Some observables become unreachable. (1/9)
The Gaussian Moments Conjecture is a pretty conjecture connected to probability and quantum field theory. Two days ago we suddenly learned it's false! - since it implies the Jacobian conjecture. Let me explain this conjecture - it's pretty simple as these things go. (1/n)
The Gaussian Moments Conjecture and the Jacobian Conjecture
We first propose what we call the Gaussian Moments Conjecture. We then show that the Jacobian Conjecture follows from the Gaussian Moments Conjecture. We also give a counter-example to a more general ...
arxiv.org
Mathematician Levent Alpöge found a counterexample to the Jacobi conjecture using Claude Fable! This conjecture claims that if F: ℂⁿ→ℂⁿ is a polynomial map whose Jacobian is invertible at each point, F has a polynomial inverse. Open since 1939. But no more! (1/n)
Jacobian conjecture - Wikipedia
en.wikipedia.org
When they find out I'm interested in quaternions and octonions, some folks ask about the next algebra on this list: the sedenions. I always say there's only one interesting thing known about those. Now there are more! Not enough to be profoundly exciting. But you gotta start somewhere.
The geometry of sedenion zero divisors
The sedenion algebra $\mathbb S$ is a non-commutative, non-associative, $16$-dimensional real algebra with zero divisors. It is obtained from the octonions through the Cayley-Dickson construction. The...
arxiv.org
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 remarkable summary. I especially like the warnings in part 10. It's amazing how some parts of the Standard Model fall out from the Jordan pair approach to quantum theory - like the gauge group, and one generation of fermions. But so far, that's all. Back to work.
Nereide@drnereide.bsky.social · 3w ago1/12 John Baez et al. have just published a paper linking decades-old #mathematics to a new way of thinking about quantum mechanics. 🔭🧪⚛️ The result? The Standard Model (SM) of particles seems to emerge naturally from certain mathematical structures. Here’s a simple explanation, I hope. #physics
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
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 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)
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)
Coming from the States I've always struggled to understand UK politics. Apparently Farage has resigned from office in order to be elected to that office - but nobody will run against him except a talking trash can. And the BBC is actually interviewing the trash can.
paulusthewoodgnome@paulusthewoodgnome.bsky.social · 4w agoTruly, we are blessed. 😊 "My job is to demonstrate that British democracy is wonderful and unique in the entire Cosmos" 'Count Binface told BBC Breakfast why he plans to stand against Nigel Farage in the Clacton by-election.' via x.com/i/status/207...
He's back. And you can see he's not taking any more of this shit.
Retraction Watch@retractionwatch.com · 4w agoAfter days of scrutiny, Springer Nature has restored two papers by Planck, who won the Nobel for Physics in 1918, reversing a 2011 decision to retract the articles for “copyright violations.”
Amazing flyby: Japan's Hayabusa2 just made a high-precision flyby of previously unexplored asteroid Torifune. The probe was traveling at 3 miles per second, and skimmed just about half a mile from the asteroid! First images coming in now. 🧪🔭 www.jaxa.jp/press/2026/0...
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.
The sun has this annoying habit of shining much brighter in the day - so bright they're now giving away free electric power for 3 hours a day in large parts of Australia! The power companies want to raise prices at other times to make up for this. Fight back: buy a battery.
Australia produces so much solar power that they’re giving three hours of it away each day for free
Three hours of free power.
good.is
In each diagram, the green area and blue area are equal
Ireland's oldest pub, established in 1198, is called The Brazen Head. And I just learned it's named after an early dream of AI! In stories going back to the Middle Ages, a "brazen head" was a brass head that could correctly answer any question put to it - or sometimes just yes/no questions. (1/n)
Irelands Oldest Pub - The Brazen Head
The Brazen Head, Irelands oldest pub, Est. 1198. Enjoy traditional Irish music, Irish food and a traditional Irish bar in the heart of Dublin city.
brazenhead.com
I had a grad student in what some call the purest of pure mathematics: category theory. But he did *applied* category theory. Now he's applying category theory to robotics. He has an engineering postdoc at Caltech. And he just finished building a robot! I feel so proud. Like a grandfather.
Joe@lgyraoptuhneonvdie.bsky.social · last mo.We did the test today. This is a better perspective for the size.
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.
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.
Typical brown dwarfs have clouds with a range of molecules from carbon monoxide and methane to more interesting minerals like magnesium silicates and liquid iron. The colder the brown dwarf, the more cloud layers and the more diverse the cloud species. Y dwarfs sit between T dwarfs and Jupiter.
The publisher Springer claims it can only discuss why it retracted Planck's paper with... Planck! But until they hold a seance, they are happy to sell you a completely redacted version: a blank page for $39.95.
Thiago Carvalho@cyrilpedia.bsky.social · last mo.This is what makes it art: '(...) the publisher posted a blank white page with the cryptic phrase, “This article has been withdrawn due to article violation.” Springer Nature is nevertheless still selling the empty PDF for $39.95.' www.science.org/content/arti...