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From what I understand, one thing scientists are proposing is that at nearly every point in space there is a tiny rolled up dimension. So what I do not understand: if one dimension is rolled up, then isn't the space it contains two-dimensional? Does the "extra" dimension just become something like a brane? Also, does the very act of rolling-up change the dimensions of the rolled-up dimension? I am so confused! Enlightenment would be appreciated.

how does that make any more sense? eek

A good analogy to sibeliusgroupie's question is to think of a very thin pole or branch along which an ant is walking. If you look at the very thin pole so that you can see it's circular side then all you see is a dot, but if you look at it sideways then you see a very long line. Say an ant is walking along the pole, and say you were limited to see only along the long line, that is you perceived two dimensions not three. Then at times, you'd see the ant dissapear, this is because the ant has made use of the extra dimension and gone 'around' the pole (using the third dimension) and thus dissapeared from the view with which you were watching her. It would seem almost magical, the manifestation of the third dimensions from your limited two dimensional view, and yet, it's very very small (since the circumference of the pole is very small).

The one reason I never understood this analogy (from Dr. Michio Kaku's Hyperspace) is that the third dimension isn't rolled up but stretches on forever, it is just that the pole is defined in the third dimension with very small 'dimensions', oh god how easy it is to play on words. Perhaps the pole is like spacetime and in the scenario it's hyperdimension manifestations are like the hyperdimension manifestation of the pole, with a curled up front view.

Not sure if you're talking about string theory...
which would mean, depending on the loop/open loop, it is a different dimesion.

Just as depending on the arrangement of quarks, a proton or neutron is formed, and the formation of protons and neutrons form different atoms, and...
so on and so forth.

i just woke up. someone correct me if I'm .. you know, talking like an idiot.

It's hard for most people to think of topologies as instrinsic, rather than extrinsic properties of surfaces. Think of a space shaped like a circle. You're probably thinking of the space in some higher two-dimensional space, e.g., a cirle in a plane. That's extrinsic. Get rid of the plne but keep the circle. That's intrinsic.

Imagine yourself in a straight corridor with two doors at the ends. As you approach door 1 and open it, the door behind you opens. As you step through, you find yourself in the exact same corridor at the other end, looking at your own back. The corridor loops around on itself, but there is no space "in between the loop", so to speak--it has a circular topology (inerior of a torus, actually). From the point of view of anything inside the corridor, it's not even curved.


Sometimes it is convenient in string theory to refer to "the bulk", a space in which the branes are embedded in. But this does not mean that the space can't be compact ('rolled up') without any external space whatsoever. That happens in GTR a lot--every closed universe model is compact, curving around on itself, but there is nothing outside the universe.


I have trouble imagining what that even might mean, much less how it would work. Maybe something like a sequence of compact surfaces in a higher-dimensional space, but then each surface would not be a "dimension" in any proper sense. (Come to think of it, part of the difficulty may be from conflating "dimension" in the properly mathematical sense and "dimension" in the sci-fi "alternate dimension" sense.)


Well, yes; Calabi-Yau manifolds are quite a bit more messy than circles. Using a circle, however, makes it more intuitive for someone who has trouble understanding that topology can be an intrinsic property of spaces rather than something they inherit from higher-dimensional ones.