Interview: P-Adics: Mathematics for Sigmund Freud?

Abstract

The interview of Andrew Schumann, the managing editor of Studia Humana, with Andrei Krennikov, professor of applied mathematics at Linnaueus University, South-East Sweden, the director of the International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science.

Andrew Schumann: According to Galileo Galilei’s famous claim, the book of nature is written in the language of mathematics. Hence, mathematics has been regarded as cornerstone tool in physics since Galilei. His claim is self-evident for physicists till now, but not for philosophers. What do you think how far math can be applied in cognitive sciences? If there are any limits?

Andrei Khrennikov: One of the sources of the extremely successful mathematical formalization of physics was the creation of the adequate mathematical model of physical space, namely, the Cartesian product of real lines. This provides the possibility for “embedding” physical objects into a mathematical space. Coordinates of physical systems are given by points of this space. Rigid physical bodies are represented by geometric figures (cubes, balls, etc.). By describing dynamics of coordinates, e.g., with the aid of differential equations, we can describe dynamics of bodies (from falling stones to Sputniks). For 15 years I have advocated a similar approach to description of mental processes in cognitive sciences and psychology (and even information dynamics in genetics).