X-Message-Number: 19203
From: 
Date: Tue, 4 Jun 2002 10:53:01 EDT
Subject: dimensions again

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Yvan Bozzonetti wrote that "curvature" in a space of N dimensions does not 
require an extra dimension to support the curvature. As I think I wrote 
previously, it seems to be a language problem, or perhaps a perspective 
problem.

Again, if a hypothetical being that only perceives one dimension could live 
on the perimeter of a circle, he would say what Yvan said. His universe (like 
Einstein's) is "finite but unbounded," and his single-coordinate system, 
whether expressed as an angle or as a displacement from an origin, is cyclic. 
From our point of view the circle necessarily exists in two dimensions, and 
his "dimension" is curved in visible reality and not just as an inference 
from cyclicality.

Yvan does, however, appear to agree that there are problems with the confused 
use of terms such as dimensions, coordinates, and degrees of freedom.

Robert Ettinger

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