Mathematical Philosophy of Consciousness

Abstract

We propose a mathematical model of consciousness and information and use it to formulate empirical and theoretical approaches to both. Starting with previously introduced definition of information as a vector of concepts we extend it to a matrix. The diagonal elements of the matrix are identical to the original concepts of the vector and represent pure reactions, while the off-diagonal elements are correlators of concepts and represent associations. While transformation of information within a particular nervous system occurs due to numerous internal (biological, psychological, behavioral, individual history, and etc.) factors we nevertheless can consider all these factors as a combined force acting on information and causing its change. Thus we define consciousness as a matrix operator acting on matrix of information. Under adiabatic approximation we derive a Schrodinger-type equation governing dynamics of consciousness and information. In equilibrium (calm, normal) state all new information falls into expected range. When deviation from equilibrium state exceeds some critical value the system becomes unstable (alert, concerned) and resolves the instability by creating a new concept, which is a phase transition. We also suggest that feelings correspond to a partial loss of consciousness and mathematically represented by off-equilibrium values of correlators of concepts.