3 ms·

Planet Hopf

34 points by ThomPete 8y ago

ryanmercer 8y ago
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
Saltybear13 8y ago
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.
headShrinker 8y ago
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%3AHopf-bif.gif https://en.m.wikipedia.org/wiki/Hopf_bifurcation#/media/File... 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
kkylin 8y ago
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).
nerdponx 8y ago
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.clc.uc.edu/fankhauser/cheese/cheese_5_gallons/cheese_5gal_00.htm https://web.archive.org/web/20160304022738/http://biology.cl...
chucktesting12 8y ago
JRE - iship420.com
T3RMINATED 8y ago
biggest garbage post ever, ever! Take it off the internet now, shoot it behind a barn or something.
risto1 8y ago
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

34 points by ThomPete 8y ago

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

Saltybear13 8y ago

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.

headShrinker 8y ago

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

kkylin 8y ago

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).

nerdponx 8y ago

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.clc.uc.edu/fankhauser/cheese/cheese_5_gallons/cheese_5gal_00.htm https://web.archive.org/web/20160304022738/http://biology.cl...

chucktesting12 8y ago

JRE - iship420.com

T3RMINATED 8y ago

biggest garbage post ever, ever! Take it off the internet now, shoot it behind a barn or something.

risto1 8y ago

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