Would a 3-D spatial universe and a 4-D spatial universe have a different geometry?

Yes. It would be similar to the difference between Euclidian geometry and Newtonian. (2D vs. 3D)

There is a book called "Flatland" that does a real good job of explaining 1,2,3&4D space. Try here. It is a very interesting read.

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Thanks alot, I am going to check that link out

Do you think we could keep this in one thread? This is the third one you've started about this.

cyrek reply

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Would a 3-D spatial universe and a 4-D spatial universe have a different geometry?

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IMHO, I would say no. Both spaces would be 3D, but 4D would add motion with the introduction of time. Time would be a 'variable point' added to the 3D dimentions.

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aka Michael Cyrek

I meant spatial dimensions

I would think that they would be different

Gravity would reduce by the cube of the distance instead of the square of the distance.

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There are 10 kinds of people. Those who understand binary, and those who do not.

But the problem with the whole inverse cube law thing is that they got the inverse cube law just by adding an additional dimension but applying the same geometry as before, wouldnt you have to do more than that? because 3D geometry and 4D geometry are different from each other

life not being possible in 4D+ universe is just a sad sad thought

Like a 2D piece of paper can exist in a 3D universe so, I would have thought could a 3D frame work exist within a 4D universe.

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But a 2D piece of paper is not really a 2D universe with laws and such, the 2D paper with 3D laws, I dont think there could be a 2D universe

A piece of paper is a valid representation of a 2-D universe (ignore the thickness). Take a pencil and try drawing a line ABOVE the paper.
Try a balloon for a closed universe.

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Does earth plug a hole in Heaven or Heaven plug a hole in Earth? -Peter Gabriel

Then there certainly could not be any orbits in a 2-D universe

But the 3D frame work would certainly be upgraded

What would happen if you took out one spatial dimension of our universe, expect there to be radical, massive changes

if you took out one of the 'rolled up' ones that they keep going on about, perhaps you wouldn't notices any difference.

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Probably but there will be effects (if they do exist), but taking out a large macroscopic spatial dimension will result in a completely different universe.

Historical quote about 4-D space:

“When we either apply such fancies as these, or others not less inconsistent with our innate conceptions, to space relations, we are naturally led to a geometry unlike that dealt with by common-sense geometricians. We may call the geometry to which we are thus led non-Euclidean, and it may please the fanciful to find in the cumbrous term something suggestive of scientific profundity. If we called these imaginary relations “dream -geometry,” we should be somewhat nearer the truth, for it is only in dreams that men can fancy things are and are not, at one and the same time.” Richard Proctor, 1884