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[Comments] (4) Extra Spatial Dimensions: I have a question about these little buggers. Kris couldn't answer it, so you know it's tough. Whenever I heard an explanation of string theory or any other theory that predicts more spatial dimensions, they always said the extra dimensions were "rolled up very small". That doesn't make sense. Rolled up very small through what dimensions?

Then I think I figured it out with a Flatland analogy. Suppose Flatland exists in a 3D universe, but one in which nothing is more than a Planck distance tall. The Flatlanders extend in three dimensions, but they only perceive two. They would say that the third dimension was "rolled up very small", even though that doesn't make sense.

Wikipedia seems to back me up on this one, ladies, so the first question is, am I right? Does the analogy hold? Second question is, what is with the "rolled up" nonsense? Are they trying to convey that the structure of space makes it impossible for something to be large in that dimension ("the universe measured along these additional dimensions is subatomic in size")?


Comments:

Posted by Ian Bicking at Wed Jun 21 2006 01:31

If it wasn't rolled up, and it was small, then wouldn't it have boundaries? I think that's what the metaphor is for. Like the flatworld put onto a sphere or globe, it is finite but has no start or end.

Or maybe it would be like a 2 dimensional world on a very long, skinny cylinder. It would seem 1 dimensional, because everything would nearly always collide on the when it went up and down the cylinder. But there would actually be this other very constrained dimension. It wouldn't have a start or end or height, but it would be rolled up.

So there is an extra dimension, in that we find that extra dimension convenient to create metaphors about the topology.

At least, that's the metaphor I'm pulling out of my ass tonight.

Posted by Tim May at Wed Jun 21 2006 06:32

The "long, skinny cylinder" analogy is the one I remember from, oh, some popular work on the subject, probably Michio Kaku's Hyperspace. Certainly it's the only way "rolled up" has made any sense to me.


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