Biomedical subjects

A Khrennikov

Publications and source records attributed to A Khrennikov.

4 recordsLinked to original sources

PubMed1999

A p-Adic model for the process of thinking disturbed by physiological and information noise.

We develop a model of the process of thinking in the presence of noise (which is produced by the simultaneous action of a huge number of neurons in the brain as well as by external information and internal cognitive processes). Our model is based on Freud's idea on the splitting of cognitive processes into two (closely connected) domains: consciousness and subconsciousness. We represent the process of thinking as a random dynamical process in a space of ideas endowed with a non-Euclidean geometry (which differs extremely from the ordinary Euclidean geometry of spatial location of neurons in the brain). The so-called p-adic geometry on a space of ideas describes the ability of cognitive systems to form associations. We show that random dynamical thinking systems on a p -adic space of ideas still generate only deterministic ideas. We also study positive and negative effects of noise (in particular, creativeness and stress).

Brain↗

PubMed1999

Memory retrieval as a p-adic dynamical system.

We propose a mathematical model of the memory retrieval process based on dynamical systems over a metric space of p-adic numbers representing a configuration 'space of ideas' in which two ideas are close if they have a sufficiently long common root. Our aim is to suggest a new way of conceptualizing human memory retrieval that might be useful for simulation purposes or for the construction of artificial intelligence devices, as well as for a deeper understanding of the process itself. The dynamical system is assumed to be located in a blackbox processing unit (the 'subconscious') and controlled by an interface control unit (the 'conscious') that fixes parameters in the dynamical system and starts its iteration by sending an initial generating idea to it. We show that even simple p-adic dynamical systems admit behavioral scenarios that could explain some of the essential features of the human memory retrieval process.

Humans↗

PubMed1998

Human subconscious as a p-adic dynamical system.

We propose a mathematical model of the process of thinking based on dynamical systems over a configuration space of ideas. These dynamical systems are assumed to be located in the human subconscious and are controlled by the human conscious which fixes parameters of the dynamical systems in the subconscious and transmits to the subconscious generating ideas which initiate iterations of the dynamical systems in the subconscious. Thus, we present the mathematical model which is not based on the rule of reason. Mathematically the space of ideas is described by so-called p-adic numbers. In fact, a p-adic metric on the space of ideas corresponds to the following nearness between ideas: two ideas x and y are close if they have sufficiently long common root. Already the simplest p-adic dynamical systems might describe some sides of human psychological and social behaviour.

Bipolar Disorder↗

PubMedDate not supplied

Classical and quantum dynamics on p-adic trees of ideas.

We propose mathematical models of information processes of unconscious and conscious thinking (based on p-adic number representation of mental spaces). Unconscious thinking is described by classical cognitive mechanics (which generalizes Newton's mechanics). Conscious thinking is described by quantum cognitive mechanics (which generalizes the pilot wave model of quantum mechanics). The information state and motivation of a conscious cognitive system evolve under the action of classical information forces and a new quantum information force, namely, conscious force. Our model might provide mathematical foundations for some cognitive and psychological phenomena: collective conscious behavior, connection between physiological and mental processes in a biological organism, Freud's psychoanalysis, hypnotism, homeopathy. It may be used as the basis of a model of conscious evolution of life.

Cognition↗