The Finite State Machine

In order to better understand Finite Nature, we can look to examples of simple systems with similar properties.  A digital computer, exclusive of its input and output facilities (with just a processor and memory), has many of the same properties that we find in Finite Nature.  In particular, if we concentrate on a computer hardware technique called single clock, it will be easy to see why.  Single clock means that when the computer is in a state, a single clock pulse initiates the transition to the next state.  After the clock pulse happens, various changes propagate through the computer until things settle down again.  Just after each clock pulse the machine lives for a short time in the messy real world of electrical transients and noise.  At the points in time just before each clock pulse the computer corresponds exactly to the workings of a theoretical automaton or Finite State Machine. 

The main point is that a computer is an embodiment of a system where Finite Nature is true (just before each clock pulse) [8] .  Every such system has the property that it evolves by progressing from one state to the next state.  Computers and all other such finite systems would eventually cycle around a closed trajectory if they ran long enough.  Reversible systems are always on such a closed cycle, while an irreversible system can start down a path that will not repeat until finally entering a closed cycle.  This is the informational viewpoint, as contrasted from the matter and energy viewpoint.

A computer needs to be able to perform three primitive functions: it must remember, communicate and compute.  If we turn tables, systems of particles can model computers.  An example is the Billiard Ball Model [9] of computation; an idealized 2-D billiard ball table with balls in motion that can exactly mimic the behavior of any computer.  Particles remember by existing, communicate by moving and compute by interacting.  A good understanding of what's happening reveals that communicating and remembering are the identical process (related by a space-time transformation) from the perspective of the physics involved.