### The hairy ball theorem and why there is no wind (somewhere) on Earth

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What if I told you that

In less rigorous contexts, one can phrase the Hairy Ball Theorem as such:

In this particular image, the hair is pointing up both on the top and on the bottom.

More formally, the Hairy Ball Theorem can be formulated like so:

From this theorem it is actually quite easy to establish our interesting fact!

If we think of the wind at the Earth's surface as a continuous vector field, the Hairy Ball Theorem says that there must be a point where the wind isn't blowing to the sides!

Now all tha…

*right now*there is a place on Earth where there is no wind blowing to the sides? None at all! How can I know that? All we need is what is usually called the Hairy Ball Theorem.In less rigorous contexts, one can phrase the Hairy Ball Theorem as such:

**Theorem (Hairy Ball I):**if you have a hairy ball, regardless of the way you comb its hair there will always be a spot where the hair points right up.In this particular image, the hair is pointing up both on the top and on the bottom.

More formally, the Hairy Ball Theorem can be formulated like so:

**Theorem (Hairy Ball II):**every continuous vector field over $S^2$ has at least a point where the tangential component is $0$.From this theorem it is actually quite easy to establish our interesting fact!

If we think of the wind at the Earth's surface as a continuous vector field, the Hairy Ball Theorem says that there must be a point where the wind isn't blowing to the sides!

Now all tha…