Discussion session on information theory:


*Mark Burgin*
Professor & Visiting Scholar
Department of Mathematics
University of California at Los Angeles

On the one hand, information is the basic phenomenon of our world. We live in the world where information is everywhere. All knowledge is possible only because we receive, collect and produce information. People discovered existence of information and now talk of information is everywhere in our society. As Barwise and Seligman write (1997), in recent years, information became all the rage. The reason is that people are immersed in information, they cannot live without information and they are information systems themselves. The whole life is based on information processes as Loewenstein convincingly demonstrates in his book (1999). Information has become a key concept in sociology, political science, and the economics of the so-called information society. Thus, to better understand life, society, technology and many other things, we need to know what information is and how it behaves. Debons and Horne write (1997), "if information science is to be a science of information, then some clear understanding of the object in question requires definition."

On the other hand, the actual nature and essence of the information, as well as of knowledge produced and distributed by information technology, remains abstract and actually unknown to the majority of people. Even more, many researchers assume that the diversity of information types and uses forms an insurmountable obstacle to creation of a unified comprehensible information theory. For instance, Shannon (1993) wrote: "It is hardly to be expected that a single concept of information would satisfactorily account for the numerous possible applications of this general field." Other researchers, such as Goffman (1970) and Gilligan (1994), argued that the term /information/ has been used in so many different and sometimes incommensurable ways, forms and contexts that it is not even worthwhile to elaborate a single conceptualization achieving general agreement. Capurro, Fleissner, and Hofkirchner (1999) even give an informal proof of the, so-called, /Capurro trilemma/ that implies impossibility of a comprising concept of information. According to his understanding, information may mean the same at all levels (/univocity/), or something similar (/analogy/), or something different (/equivocity/). In the first case, we lose all qualitative differences, as for instance, when we say that e-mail and cell reproduction are the same kind of information process. Not only the "stuff" and the structure but also the processes in cells and computer devices are rather different from each other. If we say the concept of information is being used analogically, then we have to state what the "original" meaning is. If it is the concept of information at the human level, then we are confronted with anthropomorphisms if we use it at a non-human level. We would say that "in some way" atoms "talk" to each other, etc. Finally, there is equivocity, which means that information cannot be a unifying concept any more, i.e., it cannot be the basis for the new paradigm...

The Capurro trilemma is a valid scientific result if it is assumed that researchers tried to elaborate a definition of information in the traditional form. Indeed, in this case, the trilemma clearly explains and grounds why it is impossible to achieve a comprising definition of information.

At the same time, utilization of a new type of definition, which is called a parametric definition, made it possible to adequately and comprehensively define information and build its unifying theory called the general theory of information (GTI) (Burgin, 2010).

Parametric systems (parametric curves, parametric equations, parametric functions, etc.) have been frequently used in mathematics and its applications for a long time. For instance, a parametric curve in a plane is defined by two functions /f/(/t/) and /g/(/t/), while a parametric curve in space has the following form: (/f/(/t/), /g/(/t/), /h/(/t/)) where parameter /t/ takes values in some interval of real numbers.

Parameters used in mathematics and science are, as a rule, only numerical and are considered as quantities that define certain characteristics of systems. For instance, in probability theory, the normal distribution has the mean m and the standard deviation s as parameters. A more general parameter, functional, is utilized for constructing families of non-Diophantine arithmetics (Burgin, 1997; 2001). In the case of the general theory of information (GTI), the parameter is even more general. The parametric definition of information utilizes a system parameter. Namely, an infological system plays the role of a parameter that discerns different kinds of information, e.g., social, personal, chemical, biological, genetic, or cognitive, and combines all existing kinds and types of information in one general concept "information".

This parametric approach provides tool for building the general theory of information as a synthetic approach, which organizes and encompasses all main directions in information theory (Burgin, 2010). On the meta-axiomatic level, it is formulated as 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 model of information are constructed. One type of these models bases the mathematical stratum of the general theory of information on category theory (Burgin, 2010a). Abstract categories allow us to develop flexible models for information and its flow, as well as for computers, networks and computation. Another type of models establishes functional representation of infological systems representing information as an operator in functional spaces. Namely, a Banach or Hilbert space serves as the state space of an infological system. Then transformations of infological systems are mathematically modeled by operators in Banach/Hilbert spaces (Burgin, 2010).

Taking into account the current situation and active quest for a unified theory of information (UTI) (Hofkirchner, 1999), it is natural to suggest the following questions for the discussion, answers to which may clarify the current situation in information theory and pave the way to new achievements in this area:

1. Is it necessary/useful/reasonable to make a strict distinction between information as a phenomenon and information measures as quantitative or qualitative characteristics of information?

2. Are there types or kinds of information that are not encompassed by the general theory of information (GTI)?

3. Is it necessary/useful/reasonable to make a distinction between information and an information carrier?

 Primary source:

Burgin, M. /Theory of Information/: /Fundamentality/,/ Diversity and Unification/, New York/London/Singapore: World Scientific, 2010

 Additional sources:

Burgin, M. (2003) Information Theory: A Multifaceted Model of Information, /Entropy/, 5(2), pp. 146-160

Burgin, M. (2003a) Information: Problem, Paradoxes, and Solutions, /Triple*C*/, v. 1(1), pp. 53-70

Burgin, M. (2010a) Information Operators in Categorical Information Spaces, /Information/, v. 1, No.1, pp. 119-152

Capurro, R., Fleissner, P., and Hofkirchner, W. (1999) Is a Unified Theory of Information Feasible? In /The Quest for a unified theory of information/, Proceedings of the 2^nd International Conference on the Foundations of Information Science, pp. 9-30

Hofkirchner, W. (Ed.) (1999) /The Quest for a Unified Theory of Information/, Proceedings of the Second International Conference on the Foundations of Information Science, Gordon and Breach Publ.

Marijuán, P.C. (2009) The Advancement of Information Science, /Triple*C*/, v. 7(2), pp. 369-375 Shannon, C. E. (1993) /Collected Papers/, (N. J. A. Sloane and A. D. Wyner, Eds) IEEE Press, New York


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