This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

A review of a major, definitive source book on the basis of information theory is presented.

Mark Burgin’s

The result is that the

The originality of this book lies in the author’s ability to integrate perspectives on information from logic, epistemology and systems theory in a rigorous mathematical framework. For example, for a long time, parametric systems have been frequently used in mathematics and its applications but the parameters are, as a rule, only numerical and are considered as quantities that define certain characteristics of systems. In the case of the general theory of information (GTI), the parameter is very general. The parametric definition of information utilizes a system parameter called an

This parametric approach provides a tool for building the GTI as a synthetic approach, which organizes and encompasses all main directions in information theory. In Burgin’s next step, on the meta-axiomatic level, it is formulated as a system of principles, explaining what information is (by means of Ontological Principles) and how to measure information (by means of Axiological Principles). On the level of science, mathematical models of information are constructed. One type of model bases the mathematical stratum of the general theory of information on category theory. Abstract categories allow one to develop flexible models for information and its flow, as well as for computers, networks and computation. Another type of model establishes functional representation of infological systems representing information as an operator in functional spaces.

The book is organized as a three-component system. At first (in Chapter 1), contemporary interpretations and explications of the term

In more detail, Chapter 2 contains an informal exposition of the GTI and its applications to the theory of knowledge and psychology. Section 2.1 develops theoretical and methodological foundations for the GTI. These foundations include the general structures of the world, mathematical definition of the concept

Sections 2.2 and 2.3 contain the basics of the general theory of information, giving its conceptual and methodological foundations. In order to develop the general theory of information, three levels of formalization are used:

Chapter 3 contains a brief exposition of several directions and applications of statistical information theory. The relationships between information and communication are studied in Section 3.1. The relationships between information, uncertainty and entropy are considered in Section 3.2. The problem of the difference between information in conventional systems and quantum information is treated in Section 3.3. Section 3.4 demonstrates what relations exist between information and problem solving. Section 3.5 describes axiomatic foundations of the statistical theory of information. How the theory of information is used in physics is explained in Section 3.6.

In contrast to statistical theories of information, the semantic theories of information, which are described in Chapter 4, study the meaning of information. The meaning of information is generally understood as the assumption that every piece of information has the characteristic that it makes a positive assertion and at the same time clearly denies the opposite of that assertion. However, meaning is a more complicated phenomenon and to understand it in the context of information theory, Chapter 4 starts with a study of three communicational aspects, or dimensions, of information: syntax, semantics and pragmatics (

Chapter 5 provides a broad perspective on algorithmic information theory with its main peculiarities and constructions. In comparison with the majority of sources on algorithmic information theory, the exposition of this theory is given on several levels. At first, the conventional level of recursive algorithms is considered in Sections 5.1 and 5.2. Burgin is able to upgrade the usual recursive algorithmic approach to information to a next, super-recursive level of the algorithmic universe in Section 5.3. This is a necessary step as super-recursive algorithms are essentially more efficient in processing information than recursive algorithms and give more adequate models for the majority of information systems. Section 5.4 contains a relativized version of algorithmic information theory. Finally, the highest level is presented in the form of an axiomatic algorithmic information theory considered in Section 5.5.

Chapter 6 contains an exposition of pragmatic theories of information. Section 6.1 considers the economics of information developed by Marschak, Arrow, and others, the role of information in economic activity and measures for estimation of the economic value and cost of information and information sources. Section 6.2 further studies such important characteristics as value, cost, and quality of information. Section 6.3, which was one of those of the most interest to this reviewer, contains elements of the qualitative information theory developed by Mazur [

Dynamic theories of information are presented in Chapter 7 starting with, in Section 7.1, the theories of information flow developed by Dretske, Barwise and Seligman. Section 7.2 contains an exposition of the operator theory of information developed by Chechkin [

Section 7.3 exhibits information algebra and geometry. Elements of the mathematical component of the GTI are expounded in Subsection 7.3.1. This mathematical theory is based on functional models where information dynamics is represented by operators in function spaces. Other publications by Burgin show that it is also possible to develop a mathematical component of the GTI based on category theory.

Abstract information algebra in the sense of Kohlas, which captures a variety of formalisms in computer science, is presented in Subsection 7.3.2. For instance, abstract information algebras can model operations and processes with information carriers, such as data, texts, and documents. Information geometry is discussed in Subsection 7.3.3, demonstrating the application of geometrical methods and structures to information studies.

The last Chapter, Chapter 8 contains conclusions and directions for future research, and a series of valuable Appendices on the Mathematical Foundations of Information Theory, set theoretical, logical, algorithmic, number theoretical

The exposition of the material is such that different groups of readers will each find something of interest and value. Those who want to know more about the history of information studies and get a general perspective of the current situation in this area can skip proofs and even many results that are given in the strict mathematical form. Those who have a sufficient mathematical training and are interested in formalized information theories can skip the preliminary discussions and go directly to the sections that contain the mathematical expositions.

If there is any criticism to be made of this

In conclusion, I feel that this book masterfully presents and organizes the bulk of the major existing directions in information theory, giving a broader picture than any other published book in this area. Its new approach drastically changes how information should be viewed and studied, showing, for example, that what is commonly termed “

Thus, this detailed foundational exposition of a General Theory of Information, supported by numerous examples and illustrations, can serve as the basis for the development of a new paradigm for information science and information practice including information retrieval, processing and transmission. Researchers and advanced students of information theory and practice will find the book an essential resource for a large variety of methods, techniques and theories in information studies. In my view, the

In conclusion, Burgin’s GTI reveals fascinating relations between matter, knowledge, energy, and information and makes it possible to discuss new types of information such as affective information and effective information in an organized fashion. Both the expert and the general reader will gain an essential set of new ideas and tools with which to understand, use and further develop the concept of information.

One reviewer has asked for some additional information in very pertinent areas that I am pleased to include in this review:

Infological systems: Burgin proposes the concept of “infological systems” as part of the characterization of informational systems and processes that emphasizes their ontological aspects (the term is a contraction of informational-ontological). The information involved in an infological system is, roughly, defined as both constituted by and acting upon structural subsystems which one designates as its infological system. For example, systems of knowledge are infological systems.

Energy: With regard to energy, suggests that the phenomena of physical, mental, and emotional energy, and information itself as structural energy, are all particular cases of information in broad sense. However, Burgin does not undertake, in this book, a detailed analysis of information processes in biological systems in which information and energy problems must be looked at in tandem. The suggestion that he could do so elsewhere is noted.

Observer dependence of information:

Finally, another reviewer criticized my book review, and thus by implication the Burgin book, for not referring to the work of some authors, say A and B. My reply to him is that Burgin’s