I'm too dumb to be an atheist

[Alex K]

Omg that nasa page is wrong! Flat geometry does not imply noncompact topology(ie infinite spatial extent)! I'll write them, maybe they'll answer then I post it

Really? Damn.

In layman's terms, could you explain it a little? I'm interested in science, but I don't have the extensive learning background, so I usually just go with what the pHD's say.

So, intuitively one thinks that flat means it cant fold back onto itself, because as the word implies, space would have to be bent like a piece of paper to close on itself. However, this intuition is not correct: the curvature which is relevant in general relativity, the ricci curvature, vanishes e.g. for the torus. This is easiest to see if you understand that a torus is basically a flat square with opposing borders identified as being truly the same. You end up with a space which has finite volume, but no curvature and no boundary anymore - a twodimensional torus. There are like a dozen or so mathematical spaces in 3D with this property, and in nature one of them could be realized as the global geometry of our universe.