http://popups.lib.uliege.be/1373-5411/index.php?id=3911 Index terms fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=4483 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. Fri, 11 Oct 2024 15:43:24 +0200 Fri, 11 Oct 2024 15:43:44 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=4483 http://popups.lib.uliege.be/1373-5411/index.php?id=4457 The universal rewrite system, which has previously been applied especially to the generation of the number system and to nilpotent quantum mechanics, not only provides a generalised description for all natural processes but also creates a direct measure of entropy increase and of information transfer, which is especially significant for systems on the edge of chaos. Entropy and information can be shown to have a direct connection with the concept of the generation of the number field at a very fundamental level. Fri, 11 Oct 2024 11:05:08 +0200 Fri, 11 Oct 2024 11:05:28 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=4457 http://popups.lib.uliege.be/1373-5411/index.php?id=3910 While nonlocality has been considered by some to be a problem for quantum physics, it is, in fact, an essential component of understanding how local interactions actually operate. Locality and nonlocality are fundamental components of a dual system in which each determines the behaviour of the other. The exact characteristics of the different local interactions (weak, strong and electric) can be shown to be completely determined by the nonlocal vacuum structures with which they are associated. At the same time, gravity provides a nonlocal dual to the combined interactions, which has inertia as its local manifestation. A completely integrated description of local interactions and nonlocal vacuum structures is proposed, based on nilpotent quantum mechanics and its unique algebraic structure. Tue, 01 Oct 2024 14:21:27 +0200 Tue, 01 Oct 2024 14:21:35 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3910