MULTIPLICITY AND INDETERMINACY IN THE DYNAMICS OF FORMAL INDICATIONAL AUTOMATA
Gary C. Berkowitz, David R. Greenberg, Charles A. White · Cybernetics & Systems · 1991
Virtually all dynamic phenomena exhibit quasi-stable fluctuation that admits a self-referent or recursive description. A qualitative mathematics with unique power to capture the unity of static and dynamic aspects of recursion is the Extended Calculus of Indications (ECI) of Kauffman and Varela. The ECI is a topological algebra built upon self-referent diagrammatic structures termed reentrant forms. A reentrant form viewed as a generator of state-dependent symbol sequences is a Formal Indicational Automaton (FIA). FIAs embed multiple concurrent dynamic configurations with a well-defined stochastic character. In this paper, we investigate multiplicity and indeterminancy in reentrant form dynamics. In particular, we develop statistical measures of entropy and temperature for FIAs. Further, we extract a Boltzmann distribution for the probability of observing an FIA in one of its possible states, as a function of energy and temperature. This lays a foundation for future investigation of interaction between reentrant forms.