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I love these. Imagine a giant Mobius strip. Cut a hole in it and install a doorway. When you walk through that doorway where do you go? Not to the other side because THERE IS NO OTHER SIDE!

Personally I think you enter an alternate universe. Just thinking about it makes my brain dribble out of my ears.

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Interesting question, absurd conclusion. You exit at a different coordinate on the same side. That coordinate is x/2 meters along the surface, where x is the repeat length of the surface.

It doesn't make sense to make a hole in a two-dimensional room. That hole exists in the 3rd dimension. It would be as if you imagined a hole through the fourth dimension, you stick your hand in and you simply reach whatever is Euclidically speaking close in space.

take a big piece of paper, make a Mobius strip, cut a hole in it as you describe, hold it up by your ear, stick your finger through the hole in such a way that it would be expected to enter your ear if there was another 'side' to the hole.

Did your finger enter your ear?

Tried that but when I tried to hold it up by my ear my arms sort of faded out and disappeared. Weird.

>Personally I think you enter an alternate universe.

wat

Seriously though, have you tried to experiment with a paper strip yourself?

Why not use sphere instead? It has no "sides" at all by your definition of "side".

A sphere has two sIdes: an internal side, and an external side. This is why there are theories of “hollow earth”!

huh? that would not be a sphere. A sphere has no internal sides it's solid all the way through

For what it’s worth, mathematically a “sphere” is the set of all points which are equidistant from its centre — it’s hollow all the way through. The solid version is called a “ball”.

That's an interesting way of putting it. On the other hand though it feels like a sphere has an inside and an outside...

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