Universal Rewrite and Self-Organization

The conventional approach to computer programming using rewrite systems can be extended to create a universal rewrite system, which provides a computational approach to both physics and mathematics, based on the idea of a zero totality alphabet. Mathematics emerges from the system in the form of a Clifford-type algebra, while physics takes the form of nilpotent quantum mechanics (NQM). The most significant characteristic of NQM is that the quantum system (fermion state) and its environment (vacuum) are mathematical mirror images of each other. So a change in one automatically leads to corresponding changes in the other. We have used this characteristic as a model for self-organization, which has applications well beyond quantum physics. The nilpotent structure, seen as emerging from two commutative vector spaces, has a number of identifiable characteristics which we can expect to find in systems where self-organization is dominant; a recent case involves the neurons in the visual cortex. We expect to find many complex systems where our general principles, based, by analogy, on NQM, will apply.