This article takes as its point of departure the view that the discovery of the mathematical formalism of quantum mechanics (QM) was not merely a discovery of a new mathematical way of dealing with physical, and specifically quantum, processes in nature. It was also a discovery of a general mathematical formalism (in part discovered in mathematics itself earlier), which, supplemented by certain additional rules, consistently described the processing of incomplete information about certain events and contexts in which these events occur. This article proposes a quantum-like (QL) model of the functioning of the brain based on the (Hilbert-space) formalism of quantum mechanics, but now used as part of a QL mathematical model of neural processes in the brain, rather than for describing quantum physical processes. This model is, thus, fundamentally different from the (reductionist) quantum model of the brain and consciousness, according to which cognition arises by virtue of physical quantum processes in the brain. In the present view, the brain is an advanced biological system that developed the ability to create a QL representation of contexts, which, thus, allows one to describe a significant part of its functioning by the QM mathematical formalism. The possibility of such a description has nothing to do with the constitution and workings of the brain as a quantum system (composed of photons, electrons, protons, and so forth). The QL model offered here is based instead on conventional neurophysiological model of the functioning of the brain, even though the brain, the article suggests, does use the QL rule (given by von Neumann trace formula, used in QM) for the calculation of approximate averages for mental functions. The QL model developed in this article has a temporal basis, based on a (hypothetical) argument that cognitive processes are based on at least two time scales: a (very fine) subcognitive one and a (much coarser) cognitive one.
Document Type: Research Article
Center for Mathematical, Modelling in Physics and Cognitive Sciences, University of Växjö, S-35195, Sweden., Email: Andrei.Khrennikov@msi.vxu.se