Discussion session on information theory:
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*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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