Riemann space

[Monte Davis]

>Is there a simple or even simplistic, but nonetheless 
> digestible way 
> to explain it using some easily perceptible images?

Just a start:

Before Gauss at the earliest, mathematicians and mathematical scientists
treated Euclidean geometry as not only mathematical representation, but
physical fact: three orthogonal (at right angles to each other) coordinates
suffice to identify any imaginable point in space, so the world is 3-D. end
of story. There didn't seem to be any <ahem> point in thinking about what
was so obviously an inescapable given of thought as well as experience.

Then, starting in Gauss and flowering in Lobachevsky and Bolyai, it became
clear that there were alternative geometries that were as
logico-mathematically consistent as Euclid's, at first explored for their
purely mathematical interest.

Riemann stands at the next cusp -- systematizing and extending what G, L and
B had done, and spreading the word that (1) some physical phenomena might be
better understood via non-Euclidean geometries, and (2) -- much more
far-reaching and scary -- that we might *live* in a non-E. g. Just as an ant
on a large beach ball might never apprehend its curvature, our orthogonal
3-space might have a curvature too gentle and large-scale for us to have
noticed. Maybe Euclid's parallel lines that never meet are a parochial
fiction; maybe they cross or diverge at cosmic distances, because our
3-space is curved through one or more additional dimensions.

While Riemann provided or inspired much of the toolkit for general
relativity, what AtD plays with is the Manick Speculation that followed: all
sorts of people who didn't bother to get anything out of the math beyond
"maybe there are MORE DIMENSIONS!" used them as escape routes from the
seemingly tight "box" of mainstream science a la Euclid->Newton->Maxwell,
Gibbs & Boltzmann. All you needed was the fact that mathematicians and
scientists were *talking about it* to legtimize a claim that extra
dimensions are the playground of the (real or desired) mysteries of time,
spirit, life force, or any other ghosties and goblins you like.