Contextual Geometric Structures: modeling the fundamental components of cultural behavior

The structural complexity of culture cannot be characterized by simply modeling cultural beliefs or inherited ideas. Formal computational and algorithmic models of culture have focused on the inheritance of discrete cultural units, which can be hard to define and map to practical contexts. In cultural anthropology, research involving structuralist and post-structuralist perspectives have helped us better understand culturally-dependent classification systems and oppositional phenomena (e.g. light-dark, hot-cold, good-evil). Contemporary research in cognitive neuroscience suggests that complementary sets may be represented dynamically in the brain, but no model for the evolution of these sets has of yet been proposed. To fill this void, a method for simulating cultural or other highly symbolic behaviors called contextual geometric structures will be introduced. The contextual geometric structures approach is based on a hybrid model that approximates both individual/group cultural practice and a fluctuating environment. The hybrid model consists of two components. The first is a set of discrete automata with a soft classificatory structure. These automata are then embedded in a Lagrangian-inspired particle simulation that defines phase space relations and environmental inputs. The concept of conditional features and equations related to diversity, learning, and forgetting are used to approximate the goal-directed and open-ended features of cultural-related emergent behavior. This allows cultural patterns to be approximated in the context of both stochastic and deterministic evolutionary dynamics. This model can yield important information about multiple structures and social relationships, in addition to phenomena related to sensory function and higher-order cognition observed in neural systems.