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The article in the issue 1:

The date of the publication:
2012-05-08
The number of pages:
103
The issue:
1
Commentaries:
2
The Authors
Igor Dzhadan, Alex Shkotin, Vladimir Ryakhovsky, Nicholas N. Zhaldak, Petr Kusliy, Vsevolod Ladov, Alexander Boldachev, Andrej Ule, Andrew Schumann, András Máté, Péter Szegedi, Andrei Krennikov, Andy Adamatzky,

Andrei Khrennikov studied at Moscow State University, Department of Mechanics and Mathematics, in the period 1975–1980. In 1983 he received a PhD in mathematical physics (quantum field theory) from the same department. He started his teaching and research career at Moscow University for Radio-Electronics and Automatics and in 1990 he became full professor at Moscow University for Electronic Engineering. He started his career abroad at Bochum University and since 1997 he is professor of applied mathematics at Linnaueus University, South-East Sweden, since 2002, the director of the multidisciplinary research center at this university, International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science. His research interests are multi-disciplnarity, e.g., foundations of quantum physics and quantum information, foundations of probability (in particular, studies on negative probabilities), cognitive modeling, ultrametric (non-Archimedean) mathematics, dynamical systems, infinite-dimensional analysis, quantum-like models in psychology, economics and finances. He is the author of about 400 papers and 16 monographs in journals in mathematics, physics, biology, cognitive science, economics, and finances.

Email: Andrei.Khrennikov@msi.vxu.se

Andrew Schumann worked at the Belarusian State University, Minsk, Belarus. His research focuses on logic and philosophy of science with an emphasis on non-well-founded phenomena: self-references and circularity. He contributed mainly to research areas such as reasoning under uncertainty, probability reasoning, non-Archimedean mathematics, as well as their applications to cognitive science. He is engaged also in unconventional computing, decision theory, logical modelling of economics.

Email: andrew.schumann@gmail.com
 

ARTICLE:

Interview: P-Adics: Mathematics for Sigmund Freud?

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).

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