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October 29, 2020

Octonions and the Standard Model (Part 5)

Posted by John Baez

Last time I stated a couple of theorems connecting the gauge group of the Standard Model to the exceptional Jordan algebra. To prove them, it helps to become pretty comfortable with the exceptional Jordan algebra and its symmetries. And instead of trying to get the job done quickly, I’d prefer to proceed slowly and gently.

One reason is that while the exceptional Jordan algebra consists of 3×33 \times 3 self-adjoint matrices of octonions, we can think of the space of 2×22 \times 2 self-adjoint matrices of octonions as 10-dimensional Minkowski spacetime. So, to understand the exceptional Jordan algebra we can use facts about spinors and vectors in 10d spacetime! This is worth thinking about in its own right.

Posted at 12:50 PM UTC | Permalink | Followups (2)

October 21, 2020

Epidemiological Modeling With Structured Cospans

Posted by John Baez

This is a wonderful development! Micah Halter and Evan Patterson have taken my work on structured cospans with Kenny Courser and open Petri nets with Jade Master, together with Joachim Kock’s whole-grain Petri nets, and turned them into a practical software tool!

Then they used that to build a tool for ‘compositional’ modeling of the spread of infectious disease. By ‘compositional’, I mean that they make it easy to build more complex models by sticking together smaller, simpler models.

Even better, they’ve illustrated the use of this tool by rebuilding part of the model that the UK has been using to make policy decisions about COVID19.

All this software was written in the programming language Julia.

Posted at 9:14 PM UTC | Permalink | Followups (4)

October 20, 2020

No New Normed Division Algebra Found!

Posted by John Baez

Good news! The paper mentioned in my last article here, Eight-dimensional octonion-like but associative normed division algebra, has been retracted:

Posted at 3:28 AM UTC | Permalink