- #71
No-where-man
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bapowell said:I did address your previous post. Let me be more clear (also, keep in mind that this discussion assumes from the outset that the universe is globally positively curved...it might not be.) Here:Because the region you are proposing does not have spherical topology. A positively curved 3D universe has the shape of a 3-sphere, with the 3D universe corresponding to the surface of the sphere. The 4-space is indeed mathematically superfluous, but it helps us visualize. Here's an example: a torus is readily visualized as the 2D surface of a donut. We can easily visualize the torus by picturing a donut in everyday 3D space. But we don't need the 3rd dimension -- we can define a torus using only 2 dimensions by starting with a 2D surface and assigning rules for how the edges are to be connected (think of the Asteroids Atari game -- that is an example of bona fide toroidal topology, and it is perfectly defined on just your 2D screen.) So, getting back to the universe. Supposing that the universe is positively curved and has 3 spatial dimensions, then we are dealing with a 3D volume that has spherical topology. Geometrically, this is the surface of a 3-sphere. Now, we don't need the 4th dimension to fully define the topology or geometry (just as we didn't need the 3rd for the torus), but it helps us visualize -- especially since the 4D space becomes the 3D ambient space when we consider the balloon analogy.
Every time I look at every model, I always ask what's outside that model, because even model as well as the universe has its size and diameter, and if something like the universe with size can exist in nothing (since there is absolutely nothing outside the universe)-which means no space-zero size, than it's not science.
You cannot have anything that has size (and requires space) to exist in something (which is actually absolute nothing/nothingness) that has no space and no size, this is absolutely impossible.