By Andrei Khrennikov (auth.)
In this ebook we boost a variety of mathematical versions of knowledge dynamics, I -dynamics (including the method of thinking), according to equipment of classical and quantum physics. the most target of our investigations is to explain mathematically the phenomenon of recognition. we want to gain one of those Newton-Descartes application (corrected by way of the teachings of statistical and quantum mechanics) for info tactics. ranging from the information of Newton and Descartes, in physics there has been constructed an sufficient description of the dynamics of fabric platforms. we wish to advance an identical mathematical formalism for info and, specifically, psychological strategies. in the beginning of the twenty first century it's transparent that it'd be most unlikely to create a deterministic version for basic details procedures. A deterministic version should be accomplished via a corresponding statistical version of knowledge flows and, specifically, flows of minds. it would be that such a knowledge statistical version must have a quantum-like structure.
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Extra info for Information Dynamics in Cognitive, Psychological, Social and Anomalous Phenomena
In principle we can do this. However, the corresponding number system is not in general a field. , division is not well defined. The field structure is very important for developing analysis. Therefore the main part of investigations have been performed for prime p. The construction of new fields Qp induced strong interest in number theory and algebra. For practically one hundred years p-adic numbers were intensively used only in pure mathematics, mainly in number theory; see, for example, the classical book of Borevich and Schafarevich .
Thus 7rl automatically produces a nonzero attractor ° x = (0, ... ,aa, ... ,ad, 0, ... ). Here a religious input gives a sexual output. Such an output will be rather abnormal, because the digits aa, . 4. (Conflict of dynamical systems). Let us consider again the functioning of two dynamical systems which has been described above. Suppose that the input or output channels of the processor 7rl are blocked for a long time. The neurons a = nt, . ,d = n;d (on the intersection of the sexual and religious hardware) do not receive any signal from neighbouring neurons in N 1 .
The completion of Q with respect to the metric pp(x, y) = Ix - yip is the locally compact field of p-adic numbers Qp. The number fields Rand Qp are unique in a sense, since by Ostrovsky's theorem  I . I and I . Ip are the only possible valuations on Q, but have quite distinctive properties. The field of real numbers R with its usual valuation satisfies Inl = n -+ 00 for valuations of natural numbers n and is said to be Archimedean. By a well known theorem of number theory  the only complete Archimedean fields are those of the real and the complex numbers.