Mathematical Approaches to Culture Change

Publisher Summary This chapter reviews two general categories of mathematical methods that are suitable in some measure for modeling cultural transformations. The first type includes methods of dynamical systems theory in which influences causing short-term changes are specified and the long-term behavior from these is derived. The second class of methods is directed more toward discrete entities and the structural relations or patterns among them. The theory of games, mathematical theories of optimization, and graph theory are among the fields included here. A study of the dynamics of large systems that contain complex interconnections or feedbacks among the constituent parts falls within the domain of systems theory. An important aspect of human cultural systems is their orientation toward achieving goals. Various mathematical theories have been proposed to provide a framework for analyzing phenomena of this sort. Generally, these may be called prescriptive or optimization models, in contrast to descriptive or predictive models. Dynamic programming introduces a dynamic element in mathematical programming permitting decisions to be made on the basis of a current assessment of the situation at each stage. The mathematical theory of games is another method available for the study of decision making.