[true_blue_texican]

Geometry is a product of rational thought. Euclidean geometry is "real" as is Reimann (sp?). A sphere exists in Euclidean space just as a sphere can exist in Reimann or in a negatively curved space (it may "look" different but it satisfies a definition of a sphere in that space). BUT, "space" here does not mean space like the cosmos when we look up at it. Space is a very specificly defined mathematical term. I think that the problem is that the term is confused with space as in the cosmos. To think of the cosmos as possessing a certain geometry doesn't make much sense to me. To use geometry as a metaphor to make calculations about gravitational attraction is useful where it can make accurate predictions. But there are places where GR doesn't appear to predict things that actually exist so kludges keep being stuck onto the metaphor.

[RightWhale]

There is a great confusion of terms. In a monograph such as Sein und Zeit it is possible to be more or less consistent and to introduce new terms when existing words don't make enough distinction. It might be interesting to note that the Hubble telescope, wonderful as it is, cannot quite see to the edge of the universe. But, it might also be noted that according to the big Bang model as it is now, the entire universe, including the Hubble volume, is 25 billion times larger in radius than the Hubble volume; seeing beyond the visible universe is impossible since the objects are receding faster than the speed of light and have been since the main inflation phase. It might be compared to looking at a grain of sand and imagining that it is the entire earth.