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 gold. 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. Homer >- 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