Can you theoretically create a universe that will have the same dimensions but will look different? For example, a paper that has a limit, or another similar dimension can it be different?
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Just 3D but "look different"? Sure, see e.g. the eight Thirston geometries, and those are just the most symmetric ones. The Poincaré Dodecahedral Space and the Mystery of the Missing Fluctuations by Weeks explains what will look different for one of them. But how is this about philosophy? – Conifold May 20 at 17:49
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What do you mean by "look different"? I don't understand the second part about the paper. – Jishin Noben May 20 at 20:14
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I mean, can the third dimension look any different than the one with the viewers? Are there any other combinations of our dimensions – Walter W May 21 at 12:28
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Conifold That's more or less what I mean. – Walter W May 21 at 12:35
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If by this you mean for example a universe with two spatial dimensions and one of time, the answer is yes- at least in the world of physics.
Physicists often try to formulate their theories in spaces simpler than (three space, one time) when it isn't known yet how to do it in (3+1) space. Then they look for clues in (for example) two-space, one time universes to guide the search for solutions that exist in the (3+1) spacetime that we inhabit.
These simpler worlds are called "toy universes" by practitioners of the art. They are mathematical abstractions and in no sense do they represent "real" universes because they would not support life as we know it.
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I mean, can our spatial dimension look any different? Can it have other combinations? – Walter W May 21 at 12:30
