Formal-language-oriented foundation of dynamics of human crowds using topos-theory

Abstract

In contemporary neuro-quantum studies, the following main idea has been established: motion of a human body obeys the laws of Newtonian physics, while motion of human mind can be formally described only by the laws of quantum physics. From this psycho-physical modeling perspective, a general dynamics of human crowds can be divided into two categories: a relatively simplistic crowd mechanics, concerning only with the physical motion of individual agents, aggregates and a crowd as a whole; and a complex cognitive behavior of a crowd, which incorporates motivational cognition into the crowd mechanics. In this paper we will attempt to provide a topos-theoretic foundation for both crowd mechanics and general crowd behavior. For this we will use a general formal-language framework, in which crowd mechanics is described by a propositional language, while crowd behaviour is described by a higher-order typed language. This framework naturally leads to the category of complex systems and general crowd behavioral dynamics in a general topos. © 2011 Springer-Verlag Berlin Heidelberg.