Suppose you have a ball covered entirely with hair and you're trying to comb the hair
假设你试图抚平一个长满了毛的球体
so that it lies flat everywhere along the surface.
使毛都顺滑的贴在表面上
If the ball were a donut, or it existed in two dimensions,
如果是长毛的甜甜圈 或者二维空间的球
this would be easy!
就能轻松做到
But in three dimensions?
但是如果在三维空间
Well, you're going to run into trouble.
你就摊上事了
A lot of trouble. A big hairy ball of trouble.
你摊上一大团毛球的事了
That's because of a theorem in algebraic topology called the "Hairy Ball Theorem"
因为拓扑学中的"毛球定理"
(and yes, that's it's real name)
是的 你没有听错
which unequivocally proves that at some point, the hair must stick up.
指出毛球上必然会有某点的毛理不顺
Now don't go wasting your time playing around with a hairy ball
所以别浪费时间
trying to prove the theorem wrong -
去尝试证伪它
this is math we're talking about.
这是数学家的事
It's proven - done - QED!
而且这个定理已经被证明了
Technically speaking, what the Hairy Ball theorem says
确切的说 毛球定理表述的是
is that a continuous vector field tangent to a sphere
在一个与球面相切的连续向量场中
must have at least one point where the vector is zero.
至少存在一点向量模为零
So what does this have to do with reality apart from uncombable hairy balls?
所以这个定理有什么实际应用吗
Well, the velocity of wind along the surface of the earth is a vector field,
实际上 地球表面的风就是一个矢量场
so the Hairy Ball Theorem guarantees that
所以毛球定理证明
there's always at least one point on earth where the wind isn't blowing.
地球表面至少有一点的风速为零
=And it doesn't really matter that the object in question is ball-shaped.
而且这和物体是不是个球没啥关系
As long as it can be smoothly deformed into a ball without cutting or sewing edges together,
对于一个拥有光滑表面但不经修建的不规则物体
the theorem still holds.
定理同样适用
So the next time a mathematician gives you trouble,
所以下次你的数学老师给你出难题
ask them if they can comb a hairy banana.
让他给香蕉理毛去吧