文档介绍：Chapter 1 1
Introduction
What is the essential nature of physical space? This is a physical question but the
answer sought is a mathematical one -- a mathematical description faithful to reality.
The classical geometry of the ancient Greeks is at least such an excellent
approximation that it surely must contain something of the answer to this question.
But what about it is central and universal and what is inessential and particular?
How can the physically appropriate generalization be identified?
Generalization
The discovery, during the Renaissance, that geometry could be modeled in algebraic
terms gave rise to analytic geometry. This provided the basis on which Riemann
developed a differential generalization of geometry. But analytic geometry
introduces artifacts which pertain to the model and are extraneous to the geometry
itself. It is, as a result, characteristically difficult, in this form of geometry, to
separate out the essential from the extraneous. The question then arises as to the
nature of the Riemannian generalization. Is it purely a generalization of the geometry
 
or is it, at least in part, a generalization of inessential aspects of the particular
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model? Is it inadvertently specialized in an essential way (at least for use as a
description of physical space) by the peculiarities of the algebraic model or its
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