CB Willis (cbwillis@adore.lightlink.com) wrote:
>Homer Wilson Smith (homer@lightlink.com) wrote:
>>    A line needs one dimension.

>A point is 0 dimensions?  because it's a postulate or because it has no 
>extension?  Duh?!  I will get this...

     Point     is 0 dimensions
     Line      is 1 dimension
     Square    is 2 dimensions
     Cube      is 3 dimensions
     Hypercube is 4 dimensions

     A point has no extension (not zero extension mind you, NO
extension) because it has no dimensions in which to have extension.

     A line can be 0 inches long.  It has one dimension, so it can
have 0 extension.  0 extension is not NO extension, 0 extension is
quite some extension, it just happens to be zero.

     A line that is 0 inches long is not the same as a point that has
no dimension in which to have extension.

     Having a dimension with zero extension along it is different then
not having the dimension in the first place.

     Look at it this way.

     We see a 3 dimensional spatial world around us.

     So you have a chunk of gold that is {2 x 2 x 2} or 8 cubic
inches, that's a lot of gold, has weight, value etc.
     OK, assume there is a 4th dimension we just can't see it.
     How thick is your gold in the 4th dimension?

     If its 0 thick in the 4th dimension, then we have a 4 dimensional
piece of gold that is 2 x 2 x 2 x 0 which is 0 hypercubic inches of
     That's no gold dude.
     So if there IS a 4th dimension to our universe it HAS to have
SOME finitely large non zero thickness, or else the whole universe is
reduced to nothing.
     If the universe is 3 dimensional, your gold cube is {2,2,2}.

     If the universe is 4 dimensional, then your gold cube is
{2,2,2,x} where x must be greater than zero.

     Having a dimension, and then having zero extension along that
dimension reduces the whole object to nada.

     So if you want to keep your objects around, make sure that when
you give them another dimension you give them SOME non zero extension
in that dimension, otherwise with zero extension along any dimension,
they become nothing.

>- CBW

Homer Wilson Smith     The Paths of Lovers    Art Matrix - Lightlink
(607) 277-0959 KC2ITF        Cross            Internet Access, Ithaca NY
homer@lightlink.com    In the Line of Duty    http://www.lightlink.com