I'm here - it's taken too long, but now is now :) Anyway, something struck me today while I was driving... however profound or mundane it is, and that was, is our present construction/conception of physical dimension necessarily correct. I mean, we start with a 0 dimensional point, build a 1 dimentional line by "lining up" points (although not necessarily in a line... consider a circle), then build 2 dimensional surfaces by "swiping" those "lines" (in quotes because they are not necessarily lines as noted), then 3 dimensional objects by "pushing" surfaces... what bothered me was that we seem to build fundamentally from those constructions (which are admittedly ok for me intuitively)... the question that came was... can we start in a different way and construct "dimensions" which are fundamentally different from those we now use intuitively? I have a feeling this is either something subtle and interesting, or simply nothing to consider at all... perhaps the current construction encapsulates all of what even I am thinking of as dimensionality... but something about the limitation of starting with points and getting to "lines" and building from there seems to be something of a choice... are there other creative choices for "starting" which yield parallels to what we now think of as dimensions? I think either there are OR the concept of dimension is something more fundamental as an idea, than simply to serve as an important construction for physics.
PS - we still have much more to discuss regarding the number of infinities which exist :) At our last meeting, we discussed the following:
1. things that are the size of the naturals (0, 1, 2, 3, 4, ...) - also same size as integers.
2. things that are the size of the reals (which is like the power set - set of all subsets - of the naturals)
We discussed much more, and I want to find the link to the formalism on that matter we found last time... there was a conjecture there that there were only "so many" infinities if I remember correctly.