We were listening to Roger Penrose being interviewed on The Life Scientific
http://www.bbc.co.uk/programmes/b082ymnx and he mentioned the hairy ball theorem. I first came across it in the Sixth Form when we asked our maths teacher Dr Fernandez what he researched for his PhD. He told us that it was about combing hairy tennis balls and whether or not you could comb it all flat by combing in one dimension. We had a go at the weekend. You can on a hairy flat surface but in 3-dimensions on a ball you can't. You can on a torus - a donut shape, And he said he'd been working on it in any number of dimensions. We thought he was winding us up but here it is
https://en.wikipedia.org/wiki/Hairy_ball_theorem And even better, watch this one minute long animation
https://www.youtube.com/watch?v=B4UGZEjG02s If the winds on Earth correspond to the hairs on the sphere, you will get at least one spike. This will be a place with wind speed zero, so you have to get cyclonic behaviour. I'm working on how it relates to Penrose's work on space-time. In particular, I want to find out if the spikes are places where the vector function is actually discontinuous and therefore undifferentiable. When I was reading his book two years ago, there were points like this on Riemann surfaces that he then cut away to allow the surfaces to be patched. Are those places like the hairy spikes or have I misunderstood?
