Science & Technology

# The Hairy Ball Theorem Says There's Always a Storm Brewing Somewhere

The hair on your head doesn't all grow in the same direction — most of us have a cowlick or two. The same goes for wind on Earth. In fact, there's a bizarrely named theorem that says it's impossible for wind (or hair!) to all move in the same direction on a sphere like the Earth. It's called the hairy ball theorem.

## Come Again?

You heard us — the hairy ball theorem. It comes from a field of mathematics called topology, which deals with the properties an object that can't be changed by deforming them. Thus the old joke about how a topologist is someone who can't tell the difference between a coffee mug and a donut: if they were both made of rubber, you could turn one into the other without changing their essential properties.

That's important, because it means the hairy ball theorem doesn't just apply to spheres. Instead, it applies to any shape that's topologically equivalent to a two-dimensional sphere (not an oxymoron!). That includes shaggy throw pillows, furry coconuts, and fuzzy kiwis. Hell, if you had a banana that grew hair, it would apply to that too. For any shape that can be morphed into a sphere, the theorem goes, if that shape is fully covered in hair (or has a "continuous vector field"), there will always be one point where the hair stands straight up (or there's a "zero vector").

## You Spin Me Right Round

This doesn't actually apply to the hair on your head, because it has a stopping place. The Fonz could easily comb all of his hair in the same direction. But the Earth's atmosphere covers every bit of its surface, so the hairy ball theorem definitely applies there. In atmospheric terms, the point where the hair stands straight up would be a point with no wind. That means there's always one point on Earth where the wind isn't blowing.

Don't believe us? Let's try a few examples. Say all of the wind all over the globe is blowing East to West. There would still be two points with no wind: the North Pole and the South Pole. Same goes for wind blowing North to South; two spots on the equator would be still as death. In fact, you can have any number of points where the wind is still, but you can't have zero. You can see this beautifully illustrated in real time on the earth.nullschool.net Earth Wind Map.

But this headline says there's always a storm brewing somewhere, not that it's always still somewhere. What gives? Well, the two go hand in hand. Any point where the wind isn't blowing must have wind blowing around it, and in physical terms, that's found in the eye of a tropical cyclone. A tropical cyclone is the umbrella term for a hurricane, typhoon, cyclone, tropical storm, or tropical depression. Think of a tropical cyclone as an atmospheric cowlick — just with more serious effects than a rotten picture day.

For a riveting take on the history of Geometry, try Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace by Leonard Mlodinow. It's free with a 30-day trial of Audible. We handpick reading recommendations we think you may like. If you choose to make a purchase through that link, Curiosity will get a share of the sale.

– MinutePhysics

### Key Facts In This Video

1. If you tried to comb the hair on a hairy sphere flat, you would fail—some hair will need to stand up. 00:01

2. The Hair Ball Theorem proves that hair on a sphere can never be laid completely flat. 00:16

3. The Hair Ball Theorem implies that there is always a place on Earth where the wind is not blowing. 00:45

Ashley Hamer