Project Title: Modeling Cognitive Structures and Dynamics on Topological Domains
Project Directors: Brett Sims
Project Summary: This research on modeling cognitive and social dynamics will expand on conjectures developed during the 2016 NREUP at BMCC. In 2016, students developed a homomorphism that maps over interpretations to define the “gluing” of two philosophical substructures, they also described coordinated social action, via homotopy lifting. In this work students will apply theory of a simplicial complex with attention to affine groups, G-sets, and deck transformations to describe and analyze autonomous and externally stimulated cognitive dynamics. In addition, students will explore applications in homology theory, with the objective of developing a consistent definition for an “orientable or non-orientable” psychological substructure. Analysis will include the effects of specific types of philosophical “gluing” on individual or social “orientation”. Students will define qualitative psychological substructures (philosophical, attitudinal, motivational) and their relations based on existing empirical research. The “total” psychological space will be treated as an n-sorted topological structure under such theory as model theory, theory of a simplicial complex, and group theory. Topological representation of the, generally non-metricizable, psychological space permits a mathematical characterization of qualitative cognitive dynamics that can be coordinated with the metricizable physical spatio-temperal (behavioral) space.
