The Quantum-Like Brain Operating on Subcognitive and Cognitive Time Scales

Abstract

We propose a {\it quantum-like} (QL) model of the functioning of the brain. It should be sharply distinguished from the reductionist {\it quantum} model. By the latter cognition is created by {\it physical quantum processes} in the brain. The crucial point of our modelling is that discovery of the mathematical formalism of quantum mechanics (QM) was in fact discovery of a very general formalism describing {\it consistent processing of incomplete information} about contexts (physical, mental, economic, social). The brain is an advanced device which developed the ability to create a QL representation of contexts. Therefore its functioning can also be described by the mathematical formalism of QM. The possibility of such a description has nothing to do with composing of the brain of quantum systems (photons, electrons, protons,...). Moreover, we shall propose a model in that the QL representation is based on conventional neurophysiological model of the functioning of the brain. The brain uses the QL rule (given by von Neumann trace formula) for calculation of {\it approximative averages} for mental functions, but the physical basis of mental functions is given by neural networks in the brain. The QL representation has a {\it temporal basis.} Any cognitive process is based on (at least) two time scales: subcognitive time scale (which is very fine) and cognitive time scale (which is essentially coarser).