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A Rebuttal

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Posted by Paul R. Martin on December 7, 2001 17:27:04 UTC

Hi Yanniru,

You have overlooked the implications of the possibility that our 3D space is a 3D manifold in 4D (or higher) space, as has Alex and everyone else on this forum who has commented on my exasperating exhortations to consider that possibility.

I suspect that the reason is that you did not take the requisite undergraduate course in topology that the cited site claims is common knowledge.

Some of the implications that I think are important are:

1) The extra dimensions (as Alex correctly observed) would be qualitatively different from the ordinary three, just as the surfaces of the oceans and the continents are qualitatively different from magma, air and outer space.

2) The qualitative differences can account for the maintenance of inverse square laws in the manifold, thus answering your problems 1 and 3.

3) Being a manifold imbedded in higher space places no restrictions on whether or not our 3D space is flat or curved, Euclidean or non-Euclidean, or singly or multiply connected. To the contrary, it provides for some of those possibilities. If our 3D space is *not* a manifold, then being curved, non-Euclidean, or multiply connected are not possible.

Warm regards,

Paul

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