An algebraic approach to modelling humanistic processes

Abstract

A "humanistic process" is a process in which a population of "individuals" ("life forms" of some sort, capable of observation, thought, and action), evolve in time, within some environment. In this work, we model such a process by associating with each individual (in the population, at each point in time), a state vector which includes their belief, and their decision function. Individuals are assumed to take actions (at each point in time), the action taken being determined by their decision function on the basis of their belief. We restrict our attention to deterministic processes evolving in discrete time. The objects we develop as models are algebraic in nature, and a portion of our work is concerned with an analysis of the mathematical structure of these objects. This analysis is along basic Universal Algebra lines, and includes definitions and results concerning sub-objects, morphisms, congruences, and quotient-objects. Work of an interpretive nature is also begun, where we build "real-world" concepts into our models by appropriate definition. A circumstance (representing a set of individuals and their corresponding actions, at some point in time), is defined, and techniques for analysing such are developed. In particular creation (of "new" individuals) and the identification of "creative processes" within a given circumstance are looked at closely. Also "cause and effect" and "isolation" (between circumstances), are briefly examined.