
Planet Hopf - ThomPete
https://www.math.toronto.edu/drorbn/Gallery/KnottedObjects/PlanetHopf/index2.html
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ryanmercer
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](http://podcasts.joerogan.net/podcasts/eric-weinstein-2)

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headShrinker
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...](https://en.m.wikipedia.org/wiki/Hopf_bifurcation#/media/File%3AHopf-
bif.gif)

Gauge theory
[https://en.m.wikipedia.org/wiki/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](http://cds.cern.ch/record/551093/files/0205114.pdf)

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risto1
I found this really nice explanation of hopf fibrations:

[https://www.youtube.com/watch?v=QXDQsmL-8Us](https://www.youtube.com/watch?v=QXDQsmL-8Us)

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kkylin
More on the Hopf fibration:

[https://en.wikipedia.org/wiki/Hopf_fibration](https://en.wikipedia.org/wiki/Hopf_fibration)

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

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Saltybear13
[https://youtu.be/AKotMPGFJYk](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.

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nerdponx
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...](https://web.archive.org/web/20160304022738/http://biology.clc.uc.edu/fankhauser/cheese/cheese_5_gallons/cheese_5gal_00.htm)

