```X-Message-Number: 19167
From:  var s1 = "Ettinger"; var s2 = "aol.com"; var s3 = s1 + "@" + s2; document.write("<a href='mailto:" + s3 + "'>" + s3 + "</a>");
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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