Question: Why can't you extend the complex numbers to 3D space?

Answer: Because the hairy ball theorem says so.

Yes, that's right. There really is a theorem called "the hairy ball 
theorem". Isn't that wonderful? :-D

Perhaps even more satisfyingly, what this theorem /says/ isn't some 
obscure exotic thing that only a mathematician could understand. 
Actually, it just says you can't comb the hair on a ball flat. You 
always end up with at least one tufty bit. (You /can/ comb the hair flat 
on a flat plane, a torus, or a number of other 3D shapes. Just not a 
sphere.)

Post a reply to this message