Smale's Paradox

Just stumbled across a nice demonstration of this eversion on youtube:

Part 1  |  Part 2

One of the members of Smale's group, Bernard Morin, is notable for being an accomplished topologist in spite of being blind since the age of six.  He was also the first person to parametrize Boy's Surface, an immersion of the real projective plane in 3-space.  Here's a model of Boy's surface at a mathematical research institute in Oberwolfach, Germany:

Morin, who is still alive, was shown this model one day.  Being blind, he had to touch the surface to determine what it was.  After a minute or two of feeling around, he shook his head and said, "This is not Boy's Surface.  This is a mirror image of Boy's Surface."  Morin was, apparently, the first person to point this out.

So with that, think of all the new perspectives you might get if you blindfolded yourself for a month. Vision being a crutch for your spatial imagination and all that.

Story source: the guy who taught me Algebraic Topology.