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.
3b1b Talent
I foreshadowed this in the last post, but this year I’m launching a new thing this year, which I’m thinking of as a kind of virtual career fair. If you’re looking for a job and want a team that values mathematical and technical curiosity, check out 3b1b.co/talent.
What I love about the hairy ball theorem is that it shows how geometry enforces limits without dynamics. No matter how carefully you try to smooth things out locally, the global structure has the final word.
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?