The Hairy Ball Theorem
A few surprising applications of one of the most absurdly named theorems in topology, together with a beautiful proof for why it is true.
New video! This one was a joy to animate.
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For black holes, we have the “no hair theorem,” but a quasar and the radiation emitted from an accretion disk eerily match the poles of the hairy ball theorem for a sphere rotating in one direction. Stars before they collapse into a black hole have spin angular momentum. Neutron stars are electrically neutral before the black hole forms. Where does the rest of the stars' information, the entropy, go?
Does it go out of the poles due to the hairy ball theorem?
Love how the topology angle connects to such tangible examples. The wether pattern application is mindblowing bc it makes such an abstract theorem suddenly feel almost obvious once you see it. I spent way too long trying to mentally 'solve' the hairy ball before accepting its impossibility, which probly means the visualiztion worked perfectly.