I've been reading "Hyperspace"; also been reading Peat's "Superstrings And The Search For The Theory Of Everything"; so I appreciated your very interesting post about different ways of looking at a rolled up grid. (Have no computer so can be long gaps between my posts).
Here's a curious thought:
The "Standard Model" of physics is known to be artificially 'taped together' and too rough to be right- involves 19 differenr constants 'put in by hand'; three different symmetry systems 'taped' together, etc., etc. Works experimentally but obviously suspect.
Well, the physicists found that pieces of the puzzle suddenly started falling much more neatly together when they invoked additional dimensions- especially a total of 10.
Now they ask: why don't we see the other 6?
I think 'time'; is not no.4; but merely a way of matching two patterns (before and after) with respect to a third pattern (reference pattern - 'clock'). The concept of 'synchronicity' enters the picture; and the more basic concepts of 'match'; 'freedom', and 'structure'. To be free to drive a car, you've got to have a structure 'car' to start with.
You can 'match' car-here to car-there; and car-this to car-that; car-red to car-yellow, etc. etc. so we have 'car' in the dimension 'location', in the dimension 'who's car?'; in the dimension 'color'; etc.? Dimensions as 'freedom-spaces to match patterns'?
Well, I think the physicists may be making a big mistake postulating that the 'other 6' dimensions are curled up so 'we don't see them'. We? Or they?
What if newborn babies DO see them? What if shortly after birth, those other 6 dimensions curled up IN THE OBSERVER (physicist)?
So he could no longer see them (match them)?
The physicist needs to be alert to'the beam in his eye' before assuming a 'mote in nature's eye'?
Just floating ideas there.