`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