X: Yes, that's true.
Y: What's the big deal? Just poke a hole in it and pull it through.
X: Sure, but the point is to do it without making a hole.
Y: But then it seems impossible!
X: You're right, you cannot do it with an ordinary sphere like a basketball. You have to understand the rules of the game: this sphere is made of an abstract elastic material that can stretch and bend and pass through itself. [MW]
But you cannot rip or puncture this material without destroying it, and you cannot crease it or bend it sharply. [MW]
Y: If the surface can pass through itself, what's the problem?
X: Do you think allowing self-intersections makes it easy? Try it.
Y: I'll push the two halves right through each other.
X: Be careful. What about that ring around the equator? Remember, you mustn't tear or crease it.
Y: Argh---let me try again.
X: That's no good either---you're pinching it infinitely tight.
Y: But then there's no way! It's impossible! You have to crease or pinch it to turn it inside out.
X: It is surprising. But watch this:
Y: ... Is this it? Is this a sphere turning inside out?
X: You bet!
Created: May 8, 1995 --- Last modified: Mon Jun 17 13:53:37 1996
Copyright © 1995-1996 by The Geometry Center All rights reserved.