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Posted by Harvey on July 20, 2004 15:31:51 UTC

If I understand you correctly, you wish to apply your 'axioms' to what we observe about space. That is, 'space' has these attributes. Is that right?

If so, then I still think you are far too premature in your assessment of space. Sure, right now we see these attributes, but in the case of GR, we didn't know space had curvature prior to the 20th century. Perhaps space has new attributes that we are not aware of at this time. For example, maybe what we currently conceive as space will eventually turn out to be 'quantum foam'. That is, perhaps space has an Heisenberg uncertainty about it that destroys the whole notion of 'space points'. I'm not saying this is or isn't the case, but as our theories of space continue to develop so will our understanding of what space is will also develop. The axioms that you use today, might not be the axioms someone a century from now would utilize.

Think of how Decartes might have axiomized space. He certainly wouldn't have mentioned anything about a curvature, or expansion of space, or twisting of space, etc. Similarly, there are attributes which we certainly may not be able to imagine. Perhaps new words from mathematics will appear that mathematicians of the future will understand, but we have no clue to their meaning. Suppose future mathematicians/physicists find that space can be thought of in terms of 'levels'. We certainly wouldn't put 'levels' in our notion of space, but who the heck says that isn't possible?

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