Hi Akinbo,
I liked your essay but I am still not fully convinced that a discrete physical model cannot be possible... although some of your ideas really made me think!
I must admit, I was almost ready to give up trying to make sense of some of your points because I wasn't really following exactly what you were getting at. But then I think I got a better understanding... Please correct me if I'm wrong, but I believe your view is that in order for space/distance/point to exist in this universe, it must be constructed of something, or else it doesn't really exist in this universe. I think too many people will find it hard to abandon the notion of a background space that exists independent of matter, just like they might picture the big bang in their head as a point that explodes in a background space, rather than a point that expands and creates space itself. So from your perspective, to talk about a point between two objects in the physical world, that point must exist "on top of something", or else it really isn't a point in our universe. Maybe stated another way, you theory supposes that you can't have a true vacuum devoid of matter. I don't think you said some of this stuff, but I have a feeling like this is what you were getting at... but maybe I'm completely off.
You said this with regard to dividing:
"Physics does not fair better, even in the models where there is finite divisibility of length. In those models, there is a limit to the number of extended points or fundamental lengths, but there is also no distance between those points, since that distance will also consist of points. Further, one cannot resort to cutting at the boundary since as fundamental objects, both the boundary and its object are one and cannot be separate parts. So like, the case for math, where to cut is a problem."
But what about a discrete physics model where there is a network of nodes, like what Stephen Wolfram postulates? I think in his model, 3-D space and matter is emergent, so that may be a loophole in your theory that allows for a discrete physical model. Maybe in this kind of network model, network connections(1) and non-connections(0) could combined to lead to emergent properties, which I think is similar to the idea you were describing in your theory when you tried to account for distinct properties in a physical continuum. In this type of network, I believe the lines/edges just help to define a "distance" in metric space between the nodes/verticies, and don't represent a 3-D distance at the most fundamental level... So maybe your ideas would gel with this type of network model since the lines in this model don't really contain any points.
Maybe even imagining this kind of model pictorially is a little misleading. Maybe each node should be given a number and the structural relationship could be represented as sets of numbers, similar to how a graph is defined in graph theory. So rather than picturing a triangular network composed of three "points" and three "lines", you could consider the following isomorphic numerical representation:
Vertex 1 connections: {2,3}
Vertex 2 connections: {1,3}
Vertex 3 connections: {1,2}
I have more thoughts on this, but I don't want to get carried away and write more if I didn't get some of your ideas right in the first place.
Please send a note to my essay forum when you respond so I get an email notification, and know when to check back on your page.
Thanks,
Jon