X-Message-Number: 19167
Date: Tue, 28 May 2002 20:02:13 EDT
Subject: coiled dimensions again

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A couple of kind people tried to straighten me out on coiled dimensions, but 
here is just a bit more to make my problem clearer:

The early universe may have been small, but that is not the same as saying 
that dimensions themselves were small then. Yes, they say space itself 
expanded, but I don't agree that is the same as saying that "dimensions" 
became bigger. 

"Length" is a dimension--or one way of describing one of the rectangular 
coordinates--but "length" doesn't have length. It is just a way of describing 
direction and size. (For that matter, some of the avante garde speculate that 
space does not even exist.)

If you use spherical coordinates you can talk about azimuth, altitude, and 
radius, and at least the first two are limited or cyclical, but that only 
emphasizes the traps inherent in equating coordinates with dimensions.

One can claim that space is curved in the same sense that the surface of the 
earth is curved, or the circumference of a circle; and one can claim that the 
circumferential size of a given circle is limited, but that does not seem to 
me the same as saying that a "dimension" is curved or has size. 

"Curvature" itself implies at least one extra dimension, or else it implies 
that your "dimension" is illusory. If you are limited to the circumference of 
a circle, you can locate yourself with a single coordinate and you may 
perceive only one dimension, but the "dimension" you perceive is only a point 
of view and not a true dimension.

Naturally I recognize that the statements I have criticized were made by 
people much more knowledgeable than I, but I am unconvinced. 


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