15. Memory and communication

Memory and communication, must be the same physical or informational process, differing only by a coordinate transformation.

We can define a fundamental act of communication as follows:

R_x',y',z',t' = S_x,y,z,t ; we Receive, at x',y',z',t' information Sent earlier at x,y,z,t.

We can define a fundamental act of memory as follows:

R_x',y',z',t' = S_x,y,z,t ; we Read, at x',y',z',t' information Stored earlier at x,y,z,t. Normally x',y',z' = x,y,z.

It should be clear that we can always transform memory into communication by means of a coordi­nate transformation, and similarly for transform­ing communication into memory. We normally think of memory as involving a system where we store information in a given place and later read it out at the same place. From a moving coordinate system of a different observer, it will not necessar­ily be the same place. For example, while the pilot thinks he is storing data in his navigation com­puter about flying from Boston to Paris, someone on the ground will see that he is communicating that information from Boston to Paris. A visitor to our solar system may think that everything saved on tape for 6 months is actually an attempt to communicate it to the other side of the sun. When we write on a floppy disk it is usually memory, but when we buy a program on a floppy disk, it serves as communication. Thus it is only our intent that separates memory and communication. From the point of view of physics, they must be seen as one and the same. If two processes are identical ex­cept for a coordinate transformation, they must be the same process. Within a DM, there is only one process, and it serves as memory and communica­tion. Computation is simply conditional memory-communication. This is clearly demonstrated by the conservative logic gate, which is a universal computation element. Anything may be computed if you have enough reversible devices (computer designers would call them "gates") that commu­nicate information from A to D if C is a 0, and from B to D if C is a 1, along with ways to inter-connect them.

In DM, there is an information cone that is loosely equivalent to our current idea of the light cone of ordinary physics. However, the informa­tion cone does not have the intuitive kind of lo­cal causality we sometimes attribute to the light cone. In DM it is simply incorrect to say that only events within the information cone of the past can influence an event in the present. This is surpris­ing, but really has to do with the nature of DM. The state of a particular cell is absolutely determined by the state of its immediate neighbors in space-time.

C_x,t = F₁(C_x-1,t , C_x+1,t , C_x,t-1 , C_x,t+1).

F can be an unusual function where the equation may be also written as follows:

C_x,t+1 = F₂(C_x-1,t , C_x+1,t , C_x,t-1 , C_x,t),

computing the future;

C_x,t-1 = F₃(C_x-1,t , C_x+1,t , C_x,t+1 , C_x,t),

computing the past;

C_x+1,t = F₄(C_x-1,t , C_x,t , C_x,t-1 , C_x,t+1),

computing right!;

C_x-1,t = F₅(C_x+1,t , C_x,t , C_x,t-1 , C_x,t+1),

computing left!

There must be an information cone similar to a light cone. The rub is that it might stretch out in 8 different directions. The function F for all DM systems must have an F₂ and an F₃. In many in­teresting DM models all eight versions of F exist. In any DM model, because the system is totally deterministic and reversible, no information ever gets lost despite its extreme quantization. Also, in every reversible CA, the space-time neighbors of a cell always include both the past and the fu­ture! As we shall see, this means that there are reasonable DM models where every cell is a deter­ministic function of cells through a region of space, the information cone, that includes parts of space not in the obvious light cone. Thus the language we use to describe situations where the concept of a light cone is used, may make little sense in DM. For example, consider the following state­ment, "Suppose something happens at x,y,z,t, will it affect things at x',y',z',t'?" This question poses many problems for DM. First, because of the nature of the reversible, deterministic system it is hard to understand exactly what is meant by "...something happens at x,y,z,t... ". Second, it is not as simple as in ordinary, intuitive physics where we might observe that x,y,z,t is outside of the x',y',z',t' light cone. We have to ask "is x,y,z,t outside of the x',y',z',t' information cone; and that is another question.