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.
Wow, this is great! I had no idea the hairy ball theorem had so many applications. I used to not really care about such things but now that I'm teaching time I can see that they serve a pedagogical purpose.
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.
I'm gonna write something stupid about this in like three months
Wow, this is great! I had no idea the hairy ball theorem had so many applications. I used to not really care about such things but now that I'm teaching time I can see that they serve a pedagogical purpose.
do you think allowing self intersections makes it easy???
Gold 😆