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James R

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Easy answer:How in practice do we know that our space is 3-dimensional?

We seem to be able to specify the location of any particular object in our universe with 3 numbers.

More complicated answer:

Our space

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I actually think that's a really good question. It's probably because we generally assume space is homogeneous and isotropic, and since we've always been able to describe the positions of everything with three numbers we assume it works everywhere in the universe. There is no reason to believe there are more than three macroscopic spacial dimensions, so there's no reason to have a physical model that uses any number of macroscopic spacial dimensions than three. The assumption that space is homogeneous and isotropic dates back to Galileo, and so far it's proven to be a valuable postulate.asdf60 said:

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perhaps we can create an other way to describe the universe with extra demension.

(M-theory describes the universe with 11 demension???)

this is what I THINK.

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reilly

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Regards,

Reilly Atkinson

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HallsofIvy

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"well, almost always"!! I have a recently published map that has an entirereilly said:

Regards,

Reilly Atkinson

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"P. Ehrenfest, Proc. Amsterdam Acad. 20, 200 (1917).

P. Ehrenfest, Ann. Physik 61, 440 (1920)."

are the references, taken from the references of Max Tegmark's paper "On the dimensionality of spacetime" http://arxiv.org/abs/gr-qc/9702052 , which I haven't read.

For more references, you might try scholar-googling

"dimensionality of spacetime"

"dimensionality of space"

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You might want to take a look at this threadasdf60 said:

https://www.physicsforums.com/showthread.php?t=41627&highlight=dimension

especially the last post by Mathwonk. Come to think of it, it's short, so I'll just quote it.

There are other approaches - my personal favorite approach is the "Lebesque covering dimension". This allows one to derive the notion of dimension from the notion of "neiborhood". See the previous thread for more details.esources: "dimension theory" by hurewicz and wallman, "why space has 3 dimensions" by poincare.

poincare's essay is for the general public on the notion of dimension. he says basically that he calls a finite set zero dimensional for starters. then a set is 1 dimensional if it can be separated by removing a zero dimensional set. e.g. as matt grime pointed out, R^1 is disconnected by the removal of any one point, hence is one dimensional.

R^2 is not disconnected by removing one point, but is disconnected by removing a copy of R^1 hence R^2 is two dimensional. etc etc..

So ultimately our notion of distance is what defines the dimensionality of space, because our notion of distance is what defines the "neighborhood" of a point, and we can determine the dimension of a space given only it's characterization as a topological space (the notion of "neihborhood").

Note that if we include time in our notion of "distance", we get a 4-d space-time, rather than a 3-d space.

There aren't any obvious candidates to extend the notion of dimensionality beyond 4. It is possible that there could be more dimensions that are "rolled up", so that they are so small they do not affect distances very much on a macroscopic scale.

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