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2010/07/11-An annotation on the General Theory of Information (by Mark Burgin)

posted 11 Jul 2010, 14:50 by José María Díaz Nafría   [ updated 22 Oct 2011, 07:56 ]
The general theory of information has three parts:
  • Philosophical, which gives a new vision of information and its place in the modern world;
  • Methodological, which studies basic principles of information theory and information technology;
  • Theoretical, which is mathematically based making available different mathematical models of information, information processes and information processing systems.
Mathematical models are developed in various domains and employ different mathematical theories. Such an information space can be a logical system (in this model, logicians can contribute) or a Hilbert space, which is used in physics for representing observables (in this model, physicists can contribute). Actually observables (even by their name) are information operators. There are models based on functional analysis, in which information is represented by operators acting on information spaces, which are state spaces of infological systems. Other models use logic (logical models), theory of algorithms (constructive models), theory of categories (categorical models), topology (topological models), and some other mathematical theories.

The general theory of information provides a powerful base for obtaining a relevant solution to a variety of problems encountered by modern society because the vast majority of these problems are related to information (by the way, communication is also exchange of information). 

There are various journal publications on the general theory of information. The most developed exposition of this theory is given in the book Theory of Information: Fundamentality, Diversity and Unification, World Scientific Publishing, 2010.

The general theory of information is the most advanced direction in information theory because it encompasses all (!!!) other directions in information theory. A lot of supporting evidence is given in the book Theory of Information. The majority of popular and not so popular information theories (including Shannon theory of communication, Carnap and Bar-Hillel’s semantic information theory, Kolmogorov, Solomonoff and Chaitin’s algorithmic information theory, Dretske, Barwise and Seligman’s theory of information flow, and many others) are presented in the book and it is explained why all of them are particular cases of the general theory of information. 

Information is everywhere. So, experts in various fields (philosophers, mathematicians, physicists, biologists, computer scientists, economists, anthropologists, sociologists, etc.) can work in the general theory of information developing it and can use this theory in their studies in physics, biology, economics, anthropology, sociology, system theory, informatics, computer science, etc.
Now it is a good time to work in this area because the general theory of information is at the very beginning. Those who start earlier to work in a new ground-breaking theory have advantages and can easier obtain outstanding results, becoming authorities in information studies. For instance, brothers Bernoulli studied the calculus under Leibniz and became the top mathematicians in Europe developing and applying the calculus (a general mathematical theory for studying functions), which was at the very beginning at their time. German physicist Heinrich Rudolf Hertz discovered electromagnetic waves (namely, radio waves) when he used and expanded Maxwell’s electromagnetic theory (a general physical theory).
Mark Burgin