I tend to miss out on links in the logical chain.Helio Post #31.
My emphasis.
As I have been posting over a long period, the balloon analogy has some good aspects.
Helio, are you fully allowing for the fact that we are looking at the surface (two dimensions, as you correctly state) and, in this case, the balloon surface does not have a centre, although the three dimensional "balloon" does? I cannot quite see whether or not your quote is clear on this. If we are taking the Universe as the surface, what then does the three dimensional sphere represent? I have suggrsted that it involves a higher dimendional view of the same Universe than is currently available to our sensory mechanisms, but that still makes it not understandable to us. See also my recent comments on "multiverse".
Cat
Addition: here is one example:
The analogy drops a dimension. If we put the dimension back then we have a hypersphere.
A Hypersphere has a 3-dimensional surface (check with Wikipedia or similar math site
Although we are (i suggest) part of a Hypersphere the part that is our universe is only the surface. The Center then is not in our universe.
In addition, our universe is expanding and suggests that if you diagrammatically express this you would (at its simplest), draw a circle and a radius. Label the radius "time" and the circumference "The universe now". 'Now' is important, it is no longer part of the universe.
So yes, each dimension set is embedded in a more numerous dimension set.
Re multiverse, where should I look - must have overlooked , sorry