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Posted by Harvey on July 18, 2001 22:21:54 UTC

Alex,

I think your question should be, 'have you ever studied mathematics'? since you are presenting a mathematical argument that there is no mathematical difference between various geometries. If that is what you believe, then my question to you is 'have you ever studied mathematics?' All kidding aside, there is a great deal of difference between Euclidean and non-Euclidean geometries. A Euclidean geometry is based on the five postulates whereas all non-Euclidean geometries deny to some degree the fifth postulate. From the denial of the fifth postulate other deriviations of spatial geometries are possible. Here is a summary of the developments of non-Euclidean geometry in case anyone is interested:

http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Non-Euclidean_geometry.html

When you say that the space is all the same in terms of being bent positively or negatively by the motion and presence of energy-mass, you are not discussing mathematics but physics (hence your question regarding physics). However, this is not your premise. Your premise is that our physics has originated in pure mathematical logic, and this means that you must justify why mathematical logic only produces a space stateable in Einsteinian spacetime geometry at macroscales (and Hilbert space geometries at QM scales). There are other geometries studied in mathematics that have little physical signifance for the properties of space (either macro space or micro space) such as Lobachevskii geometry. If Lobachevskii geometry is the same as Euclidean geometry, then why did it take so long for mathematicians to 'discover' geometries that deny the fifth postulate?

>>>Or do you call DIFFERENT math, say, the difference between sin and tan functions? So, that one universe only has sin(x) in it but no tan (x), yet another - only tan(x) but no sin(x)? Or one universe "has" only positive numbers, and another- only negative?

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