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Planet Hopf (toronto.edu)
34 points by ThomPete on Nov 17, 2018 | hide | past | web | favorite | 6 comments



Someone listened to Rogan today ;P

Since the site gives virtually no context, this site was discussed when talking about gauge theory by Eric Weinstein (mathematician, economist, managing director of Thiel Capital) and Joe Rogan on this episode http://podcasts.joerogan.net/podcasts/eric-weinstein-2


I watched the program with Eric Weinstein and Joe Rogan and I have a superbasic understanding of quantum mechanics. I will try to understand and explain this by using phrases and words that I don’t understand. It is extremely complicated.

The image you see here is created using Hopf algebra. Hopf algebra seems to be the visualization of differential equations at a moment when local symmetry is created. The moment of creation is called bifurcation?... Hopf math is required to explain symmetry in gauge theory.

“Gauge theories are important as the successful field theories explaining the dynamics of elementary particles.” —Wikipedia

Just assume everything I said here is wrong...

Hopf bifurcation https://en.m.wikipedia.org/wiki/Hopf_bifurcation#/media/File...

Gauge theory https://en.m.wikipedia.org/wiki/Gauge_theory

Hopf symmetry breaking and confinement in (2+1) dimensional Gauge Theory http://cds.cern.ch/record/551093/files/0205114.pdf


I found this really nice explanation of hopf fibrations:

https://www.youtube.com/watch?v=QXDQsmL-8Us


More on the Hopf fibration:

https://en.wikipedia.org/wiki/Hopf_fibration

Note this is due to Heinz Hopf, different from Eberhard (known for the Hopf bifurcation).


https://youtu.be/AKotMPGFJYk Each fiber is linked with each other fiber exactly once. This is the property that first attracted attention to the Hopf fibration, and a pair of circles in this configuration is called a Hopf link. The collection of fibers over a circle in S2 is a torus (doughnut shape), S1×S1, and each such pair of tori are linked exactly once. The collection of fibers over an arc form an annulus whose boundary circles are linked. This is known as a Hopf band; it is a Seifert surface for the Hopf link.


Probably off-topic, but there's a great cheese-making web page linked down at the bottom: https://web.archive.org/web/20160304022738/http://biology.cl...




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