Re: Riemann geometry, chicken or the egg?

On Fri, 27 Oct 2006 00:03:29 GMT, Gerry Myerson
<gerry@xxxxxxxxxxxxxxxxxxxxxxxxx> wrote:

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.

Clearly Reimann visualized more than three dimensions

"In a famous lecture he gave 10 June 1854, entitled On the Hypothesis
That Lie at the Foundations of Geometry, Riemann emphasized that the
truth about space is to be discovered not from perusal of the
2000-year-old books of Euclid but from physical experience. He pointed
out that space could be highly irregular at very small distances and
yet appear smooth at everyday distances."

[Snip]
.

Relevant Pages
Quantcast