Can a Sphere Be Creased in UIUC's Optiverse Exploration?

[HeavyMetal]

I caught a video online released by UIUC entitled "The Optiverse." Very cool video! Anyways, the idea is that a sphere can be turned inside-out under the premises that 1.) you cannot tear, puncture, or crease the edges, and 2.) that the sphere can pass through itself.

While I understand that you cannot tear or puncture the sphere -- that would defeat the point -- and that the sphere must be able to pass through itself, I do not understand why you cannot crease it. I would also imagine that creasing would fall under the list of things that would "defeat the point," but I'm just wondering if there is something unique about the crease.

 

[lavinia]

I think that creasing is non differentiable.

Allowing creases also makes the theorem trivial Just push the sphere through itself along a great circle. This creates a loop which ties itself off.

 

[HeavyMetal]

That makes sense to me! Yes, it can't be differentiable if an increasingly tight loop ends up becoming a point. And obviously, points aren't differentiable. Thanks!