Riemann space

[Ya Sam]

What a great start it is! I'm subscribing to the course.

So Riemann had the idea of the curved space before Einstein?
Did he have concrete geometrical figures in mind as images to describe his 
notion of space?


>From: "Monte Davis" <monte.davis at verizon.net>
>Reply-To: <monte.davis at verizon.net>
>To: <pynchon-l at waste.org>
>Subject: RE: Riemann space
>Date: Tue, 28 Nov 2006 13:07:44 -0500
>
> >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.
>
>

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