Gauge theory of things alive and universal dynamics

Positing complex adaptive systems made of agents with relations between them that can be composed, it follows that they can be described by gauge theories similar to elementary particle theory and general relativity. By deenition, a universal dynamics is able to determine the time development of any such system without need for further speciication. The possibilities are limited, but one of them-reproduction fork dynamics-describes DNA replication and is the basis of biological life on earth. It is a universal copy machine and a renormalization group xed point. A universal equation of motion in continuous time is also presented. All known interactions between fundamental particles are described by gauge theories, as we know, including Einsteins theory of gravity, general relativity. Here we argue that the scope of gauge theory is much wider, including physical systems biological organisms Organizations of human society spiritual ediices: Minsky's "society of mind""1], languages, evolutionary algorithms, etc. Example: Gauge theory of swimming of microorganisms 2]. Gauge theory can describe complex adaptive systems, i.e. anything alive in the widest sense, especially autopoietic systems which "make themselves" in an approximately autonomous fashion 3]. All these systems consist of agents and their relations. Both evolve in time. Agents organize themselves into larger structures as a consequence of the relations between them which determine their interaction. I will give the argument for gauge theory, present examples for various of its aspects, and add remarks on important ramiications. An expanded discussion of the contents of the rst two sections is found in 4]. 1 Structure: What is a thing? The state of a system at time t may be considered as a category K. In this way structure can be described. Figure 1: The structure of a brick wall determines a category Agents become objects X of a category, Relations become arrows f : X 7 ! Y of a category The basic postulates of mathematical category theory are Example: brick wall. Its objects are the bricks and the fundamental arrows specify the translation of a brick to the position of a nearest neighbour. These arrows specify the structure of the wall. They can be composed to yield translations to other bricks' positions. Composability of relations is our central postulate. This postulate leads to gauge theory. Examples: friend of a friend, husband of a sister = brother-in-law. In a *-category a relation f of X to Y deenes a possible relation f …