Discussion session on information theory:

* * *INFORMATION: MYSTERY SOLVING* *Mark Burgin* Professor & Visiting Scholar Department of Mathematics University of California at Los Angeles http://www.math.ucla.edu/~mburgin/ mbur...@math.ucla.edu

`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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