A Wineskin For Aliens

A 3D representation of a 4D Klein bottle.

What is that? A bottle that pours back into itself? A bottle with a long, twisted snout?

Take a strip of paper. Give it half a twist. Tape it together. And you have what’s known as a Möbius strip, a one-sided, one-edged surface. In the 19th century, Felix Klein, a mathematician, wondered what it’d mean to join two such bands together.

He created a bizarre bottle that would pass through itself, without making a hole in it. Such an object, which I liken to an alien wineskin, can only be made in a 4D environment, and can’t be represented correctly in 3D.



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