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Open Access Publications from the University of California

Human Complex Systems




We examine a theory of cultural rules as mathematical transforms. Certain cultural rules may be represented as set functions (called here “transforms”) between possible structures (called here “configurations” denoted “C”) on generations of an evolutionary sequence. If R is a rule and R its transform, the outcome of R acting of a starting configuration C is a set denoted RC of possible configurations. The smallest fixed point of the transform R of a rule R (called the “minimal structure” of that rule) is the descriptive diagram for illustration of the operation of certain rules traditionally used by ethnographers. A combinatorial density computing certain key population statistics of a cultural system is derivable from the minimal structure of the rule, enabling empirically testable (and successfully tested) predictions of observable population measures on systems using that rule. Therefore we may conclude that cultural structure and the uncertainty inherent in cultural systems are but two parts of one framework. Cultural theory thus has a structure in some ways like that of quantum theory, and is a physically testable physical theory. But quantum theory has been under development for a century. The task for a comparable cultural theory is simply to get started.

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