Thursday November 14th 2013 Tim
I'd prefer to think of geometry as being
about how to describe space. And you can read some interesting
things about space. For example "The vase is a contained space."
Yet, tell a potter they are engaged in geometry and you'll probably
never reach the end of the conversation, because potters do not think of
themselves as being engaged in geometry. "The contained space" is
nothing to do with geometry, instead they might suggest, space is a function of their expression
The idea of the universe as being described by geometry works for me.
Oh certainly, you have your Euclid's, you have your spatial relationships,
you have your angles and your circumferences all of them prettified by the
language of arithmetic and fearfully useful. You have the endlessness of pi,
incidentally an irrational
number. You have the rules, your well written regulations and your
politics that contain space. Which could make the "Vase" a mathematics,
rather than a geometry, because geometry is the act of imagination that
precedes the language of math. So it's well worth thinking of geometry
as being about how to describe space before knocking on the dull door of
theory and practice.