Physicists often make discrete space-time models. These models can be programmed on a computer as a digital approximation of a continuous model. Space and time are discrete in these models in the form of a lattice of points. For example, a computer can use difference equations on a lattice to approximate partial differential equations in a continuum. The values at each cell in the lattice are typically computer numbers with about 20 digits of precision. The ad hoc nature of such discrete models relegates them to their role as approximations to physical reality.
Finite Nature (FN) is the hypothesis that assumes space; time and all other quantities of physics are ultimately discrete and finite. [1] Digital Philosophy is certain to come into vogue if we were to discover that Finite Nature is true. If all were digital, our views as to how all things work, microscopically, would have to change. In any case, we can still understand the nature of Digital Philosophy before we know whether or not FN is a true fact of Nature. Digital Philosophy suggests that not only can computers model all aspects of physics, but in theory, a computer could model those aspects exactly. It is clear that for much of physics, the idea of an exact computer model can never be realized, as the physical size of such a computational process would simply be to large to implement.
DM models are meant to be simple models but not directly based on differential equations or even ordinary difference equations. Automata Theory, on which DM is based, defines such concepts as Finite State Machine [2] , Automata, Cellular Automata [3] , Universal Computer [4] and the Speed-Up Theorem. The Finite State Machine is the mathematical model that deals with the most microscopic behavior of automata. FN implies certain other restrictions such as no infinities and no infinitesimals. DM models do not have infinities, infinitesimals, continuity or locally determined random variables, but microscopic randomness is everywhere from the continual inflow of information, orthogonal to any local process.
Research in DP has addressed the following questions: Are there reasonable models of reversible computation? How might Cellular Automata models (DM) capture more and more attributes of physics? What can we learn by trying to create DM models of physics? How might we verify the FN hypothesis? We have so far discovered that we can easily create DM models of many laws and characteristics of physics. We are encouraged by the steady progress that DM has made. We will be trying to convey more of the flavor of Digital Philosophy by explaining in some detail the interesting characteristics of one class of DM models.
