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Full Description
In this book we develop various mathematical models of information dynamics, I -dynamics (including the process of thinking), based on methods of classical and quantum physics. The main aim of our investigations is to describe mathematically the phenomenon of consciousness. We would like to realize a kind of Newton-Descartes program (corrected by the lessons of statistical and quantum mechanics) for information processes. Starting from the ideas of Newton and Descartes, in physics there was developed an adequate description of the dynamics of material systems. We would like to develop an analogous mathematical formalism for information and, in particular, mental processes. At the beginning of the 21st century it is clear that it would be impossible to create a deterministic model for general information processes. A deterministic model has to be completed by a corresponding statistical model of information flows and, in particular, flows of minds. It might be that such an information statistical model should have a quantum-like structure.
Contents
1. Processing of Information on P-Adic Trees.- 2. Hierarchy of Information.- 3. P-Adic Dynamical Systems.- 4. Random Processing of Information.- 5. Information Quantum Mechanics.- 6. Bohmian Mechanics on Information Spaces.- 7. Abstract Ultrametric Information Spaces.- 8. Pathway Representation of Cognitive Information.- 9. Contextual Approach to Quantum Theory.- 10. Frequency Analysis of Foundations of Quantum Mechanics.- 11. Bohmian Mechanics for Financial Processes.- References.
