Wind and hairy balls

Hairy Ball Theorem is serious business and it has had plenty of smart folk scratching their heads over it. Henri Poincaré first suggested the idea in the late 19th century.

Basically, it goes like this:

If you try to comb a hairy ball so all the hair lays flat, there will always be at least one tufty bit of hair at some point on the ball.

Think of the hairs like the direction of an arrow and you’re starting to understand the underlying importance of Hairy Ball Theorem. These arrows are vectors pointing in, say, the direction of the wind on the surface of the Earth. The theorem therefore states that there must be at least one place on the Earth where the net velocity of the wind must be zero.

So next time your chimney pot is howling and the trees are bending you can be know that no matter how strongly it blows, somewhere on Earth there is no wind at all.