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Note:These pages make extensive use of the latest XHTML and CSS Standards. They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in Mozilla. My best suggestion (and you will thank me when surfing an ever-increasing number of sites on the web which have been crafted to use the new standards) is to upgrade to the latest version of your browser. If that's not possible, consider moving to the Standards-compliant and open-source Mozilla browser.

August 27, 2018

Exceptional Quantum Geometry and Particle Physics

Posted by John Baez

It would be great if we could make sense of the Standard Model: the 3 generations of quarks and leptons, the 3 colors of quarks vs. colorless leptons, the way only the weak force notices the difference between left and right, the curious gauge group SU(3)×SU(2)×U(1)\mathrm{SU}(3) \times \mathrm{SU}(2)\times \mathrm{U}(1), the role of the Higgs boson, and so on. I can’t help but hope that all these facts are clues that we have not yet managed to interpret.

These papers may not be on the right track, but I feel a duty to explain them:

After all, the math is probably right. And they use the exceptional Jordan algebra, which I’ve already wasted a lot of time thinking about — so I’m in a better position than most to summarize what they’ve done.

Don’t get me wrong: I’m not claiming this paper is important for physics! I really have no idea. But it’s making progress on a quirky, quixotic line of thought that has fascinated me for years.

Here’s the main result. The exceptional Jordan algebra contains a lot of copies of 4-dimensional Minkowski spacetime. The symmetries of the exceptional Jordan algebra that preserve any one of these copies form a group…. which happens to be exactly the gauge group of the Standard Model!

Posted at 5:26 AM UTC | Permalink | Followups (24)

August 24, 2018

Compositionality: Now Open For Submissions

Posted by John Baez

Our new journal Compositionality is now open for submissions!

It’s an open-access journal for research using compositional ideas, most notably of a category-theoretic origin, in any discipline. Topics may concern foundational structures, an organizing principle, or a powerful tool. Example areas include but are not limited to: computation, logic, physics, chemistry, engineering, linguistics, and cognition.

Compositionality is free of cost for both readers and authors.

Posted at 3:35 PM UTC | Permalink | Followups (1)

August 22, 2018


Posted by John Baez

Jake Bian works on the topology and geometry of neural networks. But now he’s created a new add-on—okay, let’s say it, an extension—for Firefox, designed to make nLab entries look more like textbook chapters:

Posted at 11:42 AM UTC | Permalink | Post a Comment

August 10, 2018

The Philosophy and Physics of Noether’s Theorems

Posted by David Corfield

Nicholas Teh tells me that there is to be a conference held in London, UK, on October 5-6, 2018, celebrating the centenary of Emmy Noether’s work in mathematical physics.

2018 brings with it the centenary of a major milestone in mathematical physics: the publication of Amalie (“Emmy”) Noether’s theorems relating symmetry and physical quantities, which continue to be a font of inspiration for “symmetry arguments” in physics, and for the interpretation of symmetry within philosophy.

In order to celebrate Noether’s legacy, the University of Notre Dame and the LSE Centre for Philosophy of Natural and Social Sciences are co-organizing a conference that will bring together leading mathematicians, physicists, and philosophers of physics in order to discuss the enduring impact of Noether’s work.

Speakers include our very own John Baez.

Posted at 10:05 AM UTC | Permalink | Followups (5)