7. Scaling, anti-scaling and common sense

The whole of science is nothing more than a refinement of everyday thinking.

— Albert Einstein

DM has one set of properties that scale and an­other that do not scale. The informational pro­cesses that look like field equations must be able to scale because there is not always an intrin­sic size associated with the process. The informa­tional process that constitutes a particle must not scale, because there is only a very small number of sizes associated with a particular particle. An electron-like particle comes in only a few masses and charges. These quantities do not scale because they would be a direct consequence of the rule and the lattice size. If you could erase physics from the mind of a computer scientist, he or she would be hard pressed to imagine how a particle could emerge from a programmed model of physics if there were no fundamental unit of length, nor could he or she imagine how uniform motion could occur without a fixed reference lattice. Finite na­ture would mean that our world is an informational process - there must be bits that represent things and processes that make the bits do what we perceive of as the laws of physics. This is true, because the concept of computational universality guarantees that if what is at the bottom is finite, then it can be exactly modelled by any universal machine. Finite nature does not just hint that the informational aspects of physics are important, it insists that the informational aspects are all there is to physics at the most microscopic level. What is speculative is that a (3 + 1)-dimensional RUCA can be a good model of physics even if finite nature is true.

A scientist steeped in the field of computation who happens to believe in finite nature begins to understand certain laws of nature that have not yet been formalized. For example, "What cannot be programmed, given the necessary resources, cannot be physics." What this means is that if we can prove that we cannot program any kind of computer to model telepathy in accordance with the laws of physics, then telepathy cannot be part of physics. No physics experiment can, in general, give an answer to the halting problem [3]. We believe that we cannot program rectilinear mo­tion without a fixed reference frame. We cannot program particles without a unit of length. We cannot program angular orientation (and conse­quently angular momentum) without coordinate axes. In short, as an informational scientist it is not that we see DM as a possible model of physics, rather it is that we see no way to model physics without the incorporation of much of what is in DM. In other words, to a programmer who be­lieves in finite nature, physics cannot be imagined in microscopic detail without its having most of the characteristics of DM; unless one resorts to magic. A programmer who does not believe in fi­nite nature, knows that he can only model physics on a computer by making the same kinds of as­sumptions that DM makes. The author believes that if finite nature is false, then there are not yet enough ideas in contemporary physics to ade­quately explain from first principles such questions as conservation of momentum or small number phenomena ranging from group theory to spin or charge quantization. Unfortunately, explanations of the most fundamental aspects of physics either do not exist or they are tautological in nature.

[3]  M. Minsky, Computation, Finite and Infinite Machines (Prentice Hall, Englewood Cliffs, NJ, 1967)