The Golden Ratio and the Entropy of Braids — Azimuth

Here’s a cute connection between topological entropy, braids, and the golden ratio. I learned about it in this paper: • Jean-Luc Thiffeault and Matthew D. Finn, Topology, braids, and mixing in fluids. Topological entropy I’ve talked a lot about entropy on this blog, but not much about topological entropy. This is a way to define […] […]

A Kind Of Magic — CQG+

The road from Dunsink to the exceptional symmetries of M-theory By Leron Borsten and Alessio Marrani Our journey starts in the fall of 1843 at the Dunsink Observatory[1], presiding from its hill-top vantage over the westerly reaches of Dublin City, seat to the then Astronomer Royal Sir William Rowan Hamilton. In the preceding months Hamilton […]

Thoughts on Polchinski’s Memoir — 4 gravitons

I didn’t get a chance to meet Joseph Polchinski when I was visiting Santa Barbara last spring. At the time, I heard his health was a bit better, but he still wasn’t feeling well enough to come in to campus. Now that I’ve read his memoir, I almost feel like I have met him. There’s […] […]