Riemann space

[Ya Sam]

Thanks for this attempt! Have to confess it is still kinda foggy to me.

So the laws of Euclidian space will work locally and not globally?

I've read that some Euclid's notions do not hold in Riemann space, like 
there are no parallel lines there...



>From: the Robot Vegetable <veg at dvandva.org>
>To: Ya Sam <takoitov at hotmail.com>
>CC: pynchon-l at waste.org
>Subject: Re: Riemann space Date: Tue, 28 Nov 2006 09:50:20 -0800 (PST)
>
>
>Ok, I'll try.  I studied this a billion years ago, my brain's
>gone soft, and this is simplistic.
>
>I need to assume some things, basically the idea of the cartesian
>plane.  An plane, points described by X and Y coordinates, where
>certain propeties hold.  They're basically what makes sense in
>our world, and the most important things is that there are no
>shortcuts. (and things like isf two points are distinct, then
>the distance between them is nonzero)
>
>If you have 3 points, and they do not lie in a line, then the distance
>between any two points is shorter than if you went through the
>third point first.   This is (sort of) the triangle inequality.
>
>The cartesian plane is a metric space is a Riemann Space.
>
>A manifold is just a fancy name for some space, like the plane.  You
>got your spheres, and saddle shapes, and potato shapes and whatever.
>As long as you can lay a coordinate system on in, and the points
>described adhere to metric space properties, then it's a Riemann
>Space.
>
>Really, the idea itself is very easy, it's a generalization of
>space, where you'll plopped down a set of rules so as to do some
>calculation.
>
>This is very sloppy, I have a math degree, but all I do day to
>day is arithmetic...
>

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