Re: Riemann geometry, chicken or the egg?

In article <7tj1k2h3iemc5m7iqnq8gn4lch1uft1gjk@xxxxxxx>,
bootlace <anonymous@xxxxxxxxxx> wrote:

On Thu, 26 Oct 2006 03:30:00 GMT, Gerry Myerson
<gerry@xxxxxxxxxxxxxxxxxxxxxxxxx> wrote:


For example you might find a function that will produce the hex base
digits of pi to infintity. You could calculate more hex digits of pi
than are needed to describe anything in the physical universe. Is
this example the same as developing a geometry that describes more
htan 3 physical dimensions?

Yes. No. I don't know. What do you mean?

You can calculate pi to more digits than any physicist will ever need.
You can develop a geometry of four, five, or infinitely many
dimensions. Physicists use these all the time - Hilbert spaces are
(I'm told) hugely important in some parts of physics. Although I
suppose those extra dimensions aren't "physical" dimensions. What
do you mean by asking whether these two examples are the same?

In any event, neither Riemann geometry, nor chickens & eggs,
presuppose more than three dimensions.

I believe that doing geometry without an eye to physics goes back
to ancient Greece. Conic sections were studied pretty much for
their own sake.

The motion of planets and asteroids were available to the greeks and
it seems logical they might have wondered how you could describe an
ellipse.

The Greeks had no idea that the planets moved in ellipses.
It even took Kepler a long time to come to that conclusion.
At one point he wrote in his notes that if only the planets
moved in ellipses, his work would be so much easier, because
then he could use all the stuff Apollonius had done on conic
sections - but at that point, Kepler thought his data showed
the orbits were *not* ellipses.

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
.

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