This Escher-looking structure is the Klein Bottle. It exists only in four dimensions, has only one surface, and contains itself. See what happens when the Möbius Strip turns to drink.

Many people have made a Möbius Strip in an early science class. Take a long strip of paper and hold it in a loop with the ends just barely not touching. Give one end a twist – flipping it over so the edge that once faced the floor now faces the ceiling and the ‘back' of the paper is now the ‘front' – and then put the ends together and tape them to secure the loop. You have now created a Möbius Strip, with one edge and one side, out of a flat plane. In theory, you could do the same with a three dimensional object. It's called a Klein Bottle.

To make a Klein Bottle, you would have to make a long paper cylinder, and treat it a little like a proto-Möbius Strip. Invert the bottom edge. Give the cylinder a half-twist. Now pull the ends together and link them up.

Can't do it, can you? That's okay. The Klein Bottle is only possible in four dimensions, since for it to be one long, one-sided object the top part of the cylinder will have to pierce through a side of the cylinder to link up with the inverted bottom edge. If it were possible, the Klein Bottle would literally contain itself. And since many people theorize that the universe has many different dimensions, of which humans can only perceive a few, it's possible we're all inside a Klein Bottle right now. Which means we're also outside a Klein Bottle right now.

Trippy.

Via Klein Bottle and Math World.

## DISCUSSION

If it has to pass through itself, doesn't it have more than one surface? I kind of feel like you're saying it would be really cool if this could work, but it can't.