Re: Re: Re: Re: Infinite vs finite universe/existence
Flatworm said:
It means that space could have 'positive curvature'- like the surface of a sphere.
Let me explain it a bit more in detail.
Perhaps you have heard that the world is a fourdimensional 'spacetime'. Perhaps you have heard that new theories demand 11 dimensions. But for pedagogical reasons, imagine our universe having only two space dimensions (and one dimension for time).
Now what shapes could our universe have? It could be an infinite flat plane: infinite, euclidean, no boundaries.
It could be the surface of a ball (a sphere): finite, but still no boundaries: you can go round and round a sphere without finding any boundaries (remember, our universe and its inhabitants are only two-dimensional, so they can't dig the sphere or leave it into space).
Another possibility: the universe is the interiour of a circle, the circle the boundary of the universe. Such a universe would be finite and would have boundaries.
Another possibility: the universe is an inifnite flat plane with a hole in it. Such a universe would be infinite, but it would also have a boundary (the edge of the hole).
So you see, a two-dimensional universe can be infinite without boundaries, finite without boundaries, finite with boundaries, or infinite with boundaries.
You may imagine other possible shapes, like the surface of a torus, a projective plane, a hyperbolic plane, and so on.
Now the same holds if you imagine not a two-dimensional, but a three-dimensional universe. The universe could be an euclidean space (infinite, no boundary), the three-dimensional 'surface' of a four-dimensional hyperball (finite, no boundary), the interiour of a ball (finite, boundary) or an infinite space with holes (infinte, boundary).