[Dimensio]

>The simplest case is the celebrated hypersphere, which is finite yet with no boundary.

My brain hurts.

It's not hard to understand. The notion is that space is curved, kind of like the outer edge of a ring. The outer edge of a ring is finite, but you can go along it forever and never hit a boundary -- you just eventually end up right back where you started. Thus you have a finite spance with no boundaries, and from a two dimensional perspective it could be seen as infinite, because it can be traversed indefinitely.

Expand that to a three-dimensional curve, wheren you can start at one point in the universe, travel and after some indeterminable time you end up right back where you started. That's also what would create the illusion of a massive universe -- you keep looking and you keep seeing more "stuff" but as you go further you're really just looking at the same thing over and over again.

Now just try to picture it in your head. I'll try it...

...okay, now my brain hurts.

[Dead Corpse]

So that means that with a powerful enough telescope my wife can answer the Question:"Does my butt* look big in these?" without my input. ;-)

*It doesn't. She has a very nice derriere.