that it lies flat everywhere along the surface. If the ball were a donut, or it existed in

它沿著表面到處都是平的。如果球是一個甜甜圈，或者它存在於

two dimensions, this would be easy! But in three dimensions? Well, you're going to run

二維空間，這很容易！但在三維空間裡呢？那麼，你將會運行

into trouble. A lot of trouble. A big hairy ball of trouble.

陷入了麻煩。很多麻煩。一個大毛球的麻煩。

That's because of a theorem in algebraic topology called the "Hairy Ball Theorem" (and yes,

那是因為代數拓撲學中的一個定理，叫做"毛球定理"（沒錯。

that's it's real name) which unequivocally proves that at some point, the hair must stick

那是它的真名），這明確地證明，在某些時候，頭髮必須堅持。

up. Now don't go wasting your time playing around with a hairy ball trying to prove the

了。現在，不要去浪費你的時間玩周圍的毛球試圖證明的毛球

theorem wrong - this is math we're talking about. It's proven - done - QED!

定理錯了--這是我們正在談論的數學。它'的證明--完成--QED!

Technically speaking, what the Hairy Ball theorem says is that a continuous vector field

從技術上講，毛球定理說的是，一個連續的向量場的

tangent to a sphere must have at least one point where the vector is zero.

與球體相切，至少有一點矢量為零。

So what does this have to do with reality apart from uncombable hairy balls? Well, the

那麼，除了無法梳理的毛球，這和現實有什麼關係呢？嗯，這個

velocity of wind along the surface of the earth is a vector field, so the Hairy Ball

風沿地球表面的速度是一個矢量場，所以毛球的

Theorem guarantees that there's always at least one point on earth where the wind isn't

該定理保證了地球上總有至少一個點的風不是'的。

blowing.

吹。

And it doesn't really matter that the object in question is ball-shaped. As long as it

而且它並不'有關物體是球狀的，這並不重要。只要它

can be smoothly deformed into a ball without cutting or sewing edges together, the theorem

可以順利地變形為一個球，而不需要切割或縫合邊緣，定理為

still holds. So the next time a mathematician gives you trouble, ask them if they can comb

仍然成立。所以，下次有數學家給你添麻煩的時候，問問他們能不能梳理一下。

a hairy banana.

一根毛茸茸的香蕉。