Re: Riemann geometry, chicken or the egg?
- From: "Jan Bielawski" <filmart@xxxxxxxxx>
- Date: 25 Oct 2006 12:43:24 -0700
bootlace wrote:
Many mathematical representations are borne from observation. For
example base 10 likely developed logically from counting fingers on
the human hand. Early astronomical observations inspired the math to
build the pyramids etc etc.
During the mid 1800's when Riemann was evolving his theories,
Euclidean geometry was completely adequate to describe the
observations of Newtonian physics.
Only since the turn of the century has modern physics turned to
Riemann geometry to represent and describe observations. How is it
that the math theory developed first before the observations?
Mathematicians were interested in quantifying curvature. It's easy to
do this with curves and the investigation into extending this idea to
higher dimensions was only natural. Later Einstein's principle of
equivalence makes it possible to interpret the changes in space and
time measurements due to gravity as changes in spacetime metric (rather
than "just" a tensor field on the Minkowski spacetime).
--
Jan Bielawski
.
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- Riemann geometry, chicken or the egg?
- From: bootlace
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