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

http://forum.swarthmore.edu/epigone/geometry-research/khulstaymerm/3.0.3.32.19980120205333.03196da0@mail.teleport.com

 

 

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