The Assumption: Finite Nature
If we could look into a tiny region of space with a magic microscope, so that we could see what was there at the very bottom of the scale of length, we would find something like a seething bed of random appearing activity. This would not be locally generated randomness. While the state of a particular bit is the immediate, deterministic function of its neighborhood, it is also functionally related to approximately 1/2 of all of the bits in the entire space-time history of the entire universe. This means that if one could magically reach back into the past and change any one of those functionally related bits, it would change the state of that particular bit. Because quantum mechanics limits our knowledge of the exact state of microscopic events, the state of such a bit can be perfectly random with regard to any kind of test that can be administered from within the system.
Space would be divided into cells and at each instant of time each cell would be in one of a few states. A snapshot would reveal patterns of two (or three or four or some other small integer) kinds of distinguishable states. It would be either pluses and minuses, blacks and whites, seven shades of gray, ups and downs, pluses and neutrals and minuses, clockwises and anticlockwises or whatever. The point is that it would be equivalent to digits. If every cell was either a black or a white, then we could rename them "1" and "0" or " " and "-". It wouldn't matter.
What we would discover is that there is a rule that governs the behavior of the cells. It is logical to suspect that the state of each cell is some kind of function of a neighborhood; for each cell, a set of neighbor cells with some particular space-time relationship to the cell. We don't yet know what the rule is, or even the exact nature of the rule, but we know many kinds of rules it could be. The fact that each cell is like a digit and that the overall behavior is a consequence of a rule where the next state of each cell depends on some function of the neighborhood cells is why the underlying mechanism must be some kind of cellular automaton.
The meaning of the digits in Finite Nature is that the information process that the digits and cells are engaged in define the space and time and matter and energy of our world. It is important to understand that while the cellular space may normally resemble the space of physics, the two kinds of space would become very different under certain conditions such as near a black hole. The same is true for the passage of time. An ordinary clock might, if unaccelerated and far from a strong gravitational field, keep reasonable time with respect to the goings on in the cells, However, strong gravitational fields or velocities near the speed of light would cause an ordinary clock to slow down with respect to the events in the cellular space.
