Akinbo
To reply to your main question: I do not know the answer.
I do not see how the code could be required to know and cater for how many points there are on a line and on a plane, but I am not an expert on Clifford Algebra.
I will read your essay soon, but will first respond to your post.
My view is that all the contents of the universe were present in one state at one point at the beginning of a Penrose cycle or Big Bang. Space, then, only had one point. Was that point plotted at some place in a greater environment outside our universe? Probably yes as it does not make sense to plot a point in the middle of nowhere. If the point was plotted in the middle of nowhere then the idea of it having a size is odd as it may only have a size in relation to something external.
I view the universe as having finite contents. That assumes that there exist "smallest possible particles". A smallest possible particle (e.g. an electron) may have an unknown, possibly immense, amount of content in it, but I can treat it as finite because I have no access to any subdivision of it. (Finiteness probably also requires a similar assumption about a largest possible particle. )
So the origin of space has one large particle at a point and then space grows by sub-division and interaction of particles to give more points with less content per point, I believe that this corresponds to an n-folding and decreasing vacuum energy.
In my view, the contents have three colour charges requiring at least three sets of 3D per colour. That is equivalent to three colour branes of string theory. So even at the origin, there could be at least nine dimensions within the starting point. As I do not think dimensions are easily created, I assume that our 3D of space is a compactified set of additional dimensions also contained within the origin. So I seem to be saying that I believe that the universal 'computer screen' needs to pre-exist, though it can be compactified to be as small as is required.
I meant that macroscopic objects are combinations of points, not some unknown coverage of points.
I do not consider 'collapse to nothing' as in my view, particles have contents which can collapse to a point which still holds all the contents. If the point has a very small size, then collapse to nothing may possibly be side-stepped. In the Rasch computer program to plot points on a physical scale, the distances between points are what makes the scale a physical one, with points assumed to be mathematical points.
Joy's Figure 1: I know very little topology but http://en.wikipedia.org/wiki/Homeomorphism states that the 2-sphere with a single point removed is homeomorphic to a 2-D plane. So if you insert that single point then the correspondence vanishes. I simply assumed that Joy meant that the line and plane both had an infinite number of points.
