relativity

A broader issue, however, is that
relativity is a purely local theory [!]. It predicts the curvature
of each small volume of space — its geometry — based on the matter
and energy it contains. Neither relativity nor standard cosmological
observations say anything about how those volumes fit together to
give the universe its overall shape — its topology.

Jean-Pierre Luminet, Glenn D. Starkman, & Jeffrey R. Weeks, “Is
Space Finite?” /Scientific American/, April 1999, pp.90-92.

[A Deuteronomy of Kant’s Geometry](http://www.friesian.com/space-1.htm)

So what happens with Einstein? General Relativity eliminates the idea of
the “force” of gravity by substituting a geometry of /curvature/, a
Riemannian geometry of positively curved space, which allows the paths
of free falling bodies to /look like/ they are responding to a
gravitation force. But it is actually the curvature of space. Since all
these non-Euclidean geodesics intersect (like the Meridians of
Longitude), gravity brings all things together. This is an elegant and
brilliant idea, and it accomplishes the beautiful union of physics and
geometry, as Descartes <http://www.friesian.com/hist-2.htm#descartes&gt;
had accomplished the union of algebra and geometry in Analytic Geometry,
or Galileo the union of physics and mathematics — for which he expected
to be rebuked.

[A Deuteronomy of Kant’s Geometry](http://www.friesian.com/space-1.htm)

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