IT PREDICTS THE EXISTENCE OF DEAD SPOTS ON THE LAKE. Alex at Marginal Revolution notes the death of mathematician Shizuo Kakutani, whose fixed-point theorem is a foundation of much work in theoretical economics. The tribute introduces three of the classical, if counterintuitive, fixed point arguments.
Let me offer a corollary to the coffee-stirring problem: at any time, there is a spot on Earth at which the wind is not blowing. The mean and nasty application: just about any Saturday morning, when I was learning to sail my M-Scow, I found ALL such spots on the surface of Lake Geneva. (The theorem is an existence proof, it says nothing about uniqueness!) On the other hand, my local knowledge got good enough that when I started learning to sail my Laser, my efforts were good enough for two seconds and a third in the season series.
SECOND SECTION: Oh, hey, look at this!