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Do Points
Have Area? Volumetric Points Subject: Re: Reply to Do Points Have Area? Author: Kirby Urner <pdx4d@teleport.com> Date: Tue, 20 Jan 1998 20:53:33 -0800 >points. Mutiplying 0 by infinity still equals 0. As far as I can see, >this remains an unresolved problem for Euclid's Axiom One (definition >of point), and I believe that ascribing area to points is the only way >around it. > At the risk of being redundant, I'd prefer to ascribe volume to points, since your pancake points, if as flat as the ghostly "2D plane" won't stack to create volume, any more than ghostly "0D points" you criticize would make a line. So I'd go with centers floating in an isotropic matrix or lattice, ala the centers of fcc spheres -- thinking of an ideal gas (Avogadro) with this being a snap shot of atoms in their "averaged home position" (of course in reality everything is moving like crazy). The stuff you say about a reference frame being bracketed by frequency limits sounds fine to me. I'm also willing to have a zerovolume in my philosophy -- but it's conceptually a tetrahedron, because is in the event of four planes approaching one another and passing on through (an "inside outing" operation wherein a tetrahedron is instantaneously zerovolume). This is a departure from the axiomatic Euclidean concept of point I suppose, but still supports Euclidean-style geometry ala the many constructions in The Elements. Kirby
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