Oh yeah... can the higher dimensions be specified as a single number (not necessarily discrete) like the first 4? Eg. (1, 2, 3, 4) would be 1 metre in x dir, 2m in y dir, 3m in z dir from say, the centre of the earth, and 4 seconds from beginning of time (arbitrarily chosen units and origins).
What in the world do you mean by that? If you're asking whether you can ask for the coordinates of a five or N dimensional point than of course... (x_0,x_1,x_2,x_3,x_4)=(1,52,21,-21,0)... easy, why wouldn't you? As far as declaring time as a unit of time, you can easily show that time is a unit of space as well by means of -c*t, where c is in m/s and t is in s... thus c*t=m/s*s=m resulting in the proper units. Time and space are combined into one concept by means of relativity. As a consequence of this, when you measure the length of a rod that's moving at v/c where v approaches c, the length of the rod appears to be stretched or contracted depending on whether the rod is approaching you or moving away. This isn't just an optical illusion either, as you would be able to touch and feel the rod there as well just as it appears, but it isn't because the rod itself changed in any manner either, as the rod measuring itself would still show that it had the same length it started out with. Thus the result is purely a consequence of the rod being an ellement within 4-space and not simple 3-space that we use to measure the rod in. The exact formula is,
L'=yL or L/y
Where, y=1/sqrt(1-v^2/c^2), L' is the length we measure and L is the length of the rod in it's own reference frame (or the rods length when it appears at rest with us), v is the rods velocity with respect to our reference frame and the formula uses y when the rod is moving away from us, and 1/y when the rod is moving towards us. c by the way is approximately 3.0E8 m/s and is the speed of light. Did I leave anything out?
Oh, but there is so much more! What about 1.25 fractal dimensions
. Yes, I said 1.25 dimensions! Of course, this makes use of a different definition than most people are used to working with to describe the term dimension... but it still yields 1, 2, 3 and 4 dimensions we know and love when describing spaces holding these dimensional rules. But when the rule is used on fractals, it results in non-integer dimensions.