To whom is this book addressed? Ideally, of course, to readers
very like the author" to scientifically inclined philosophers and
philosophically inclined scientists who have read and pondered the
literature on Einstein's theory of relativity with a mixture of awe
and puzzlement. This theory, it is clear, effects a profound transfor-
mation in both our understanding of nature and our conception of
that understanding itself, that is, our conception of what a scientific
understanding of nature is. In particular, the theory casts an entirely
new light on the role of geometry and geometrical structure in our
physical world picture. The problem is that very different, if not
incompatible conceptions of geometrical structure emerge. On the
one hand, the development of relativity appears to lead to what one
might call a physicalization of geometrical structure" to the view that
the geometrical structure of space or space-time is an object of
empirical investigation in just the same way as are atoms, molecules,
and the electromagnetic field. As such, geometry describes the
furniture of the universe. Indeed, on some extremely ambitious
developments of Einstein's ideas it describes the entire furniture of
the universe, for everything else is to be constructed from geometry.
Yet, on the other hand, relativity is often taken to embody what one
might call an idealization of geometrical structure" a view on which
geometry is conventionally imposed on the physical universe as a
device for conveniently describing the concrete distribution of
matter, which alone really exists.