Dear Mark, Pedro and FIS Colleagues, It is nice to talk about our common (future!) understanding of the phenomenon “information.
Dear Mark, Congratulations for your very good book (Burgin, 2010). It is proper example what we all need to do step by step. Thank you for pointing my work on GIT. Small misprinting at the page 12 It is written: “..., Markov, et al (2007) write that when a triad (source, evidence, recipient) exists, then the reflection of the first entity in the second one is called information. Thus, information is interpreted as a specific reflection.” The triad need to be written (source, recipient : evidence) No problems, the main meaning is clear. Now about your questions. In general, there are no answers to these questions. It is impossible to answer without pointing the paradigm to which the questions and answers belong to. We may stay at the point of view of GTI (Burgin, 2010) and to try to answer. However, we need to study in deep GTI, to understand and after that to try to answer the questions. The same is for any other theory, for instance GIT (Markov, et al, 2007). What to do? Dear Pedro, I am novice in FIS Group and maybe I do not know the accepted by FIS colleagues style of work in such difficult situations. Please help me. What I can do at this moment is to sketch my answers without deep explanation, which may be done in further discussion. My point of view is just the triad given above. The forth element is not included in it – the Subject (Infological System, Information Subject, INFOS). This means that we have quadruple ( source, recipient : evidence, Infos ) Now, I will answer the questions in the reverse order: 3. Is it necessary/useful/reasonable to make a distinction between information and an information carrier? One and the same source may be reflected in many different recipients, for which may exists again many evidences and Infoses. It means that as more different recipients and etc. we have so different information(s) about source will exists. The information is reflection IN the information carrier and destroying the carrier leads to loosing current reflection of the source. Now the answer: YES, Is it necessary/useful/reasonable to make a distinction between information and the information carrier, taking in account that the information is reflection in the carrier but not whole carrier. 2. Are there types or kinds of information that are not encompassed by the general theory of information (GTI)? Here the answer is simple: NO. The reason is in the definition of information in the frame of GTI (Burgin, 2010) . The other definitions lead to different types of information. 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? This is the most difficult question and I need more deep explanation for the answer. To measure means to have at least one measurement system. Again the variety is so great that it is impossible to answer simply. What we really may measure concerning the information phenomena? The source, the recipient, the evidence or the Infos characteristics (features)? Again, without concrete paradigm, there is no answer. In GIT (Markov, et al, 2007), we introduce the concept “Information Expectation” of the Infos as point in the multi-dimensional subjective ( mental ! ) attributive space of Infos. (Mark, do you remember the “ideal objects” and their materialization ?) The information, subjectively received by Infos, is another point in the same space. In this case we may introduce any measurement system, in which we may measure some characteristics of subjective reflection (information). Finally the answer is: YES, 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, because the information as phenomenon cover all instances of the quadruple “(source, recipient : evidence, Infos)”, but the information measures are closely depended on concrete instance of the quadruple, i.e. on concrete quadruple elements. Of course, there exist possibility to define measurement systems for classes of instances of the quadruple, for example see Shannon, C. E. (1993). Sorry to be so talkative :-) Friendly regards Krassimir Source: (Markov, et al, 2007) Markov, K., Ivanova, K. and Mitov, I. Basic structure of the general information theory, Information Theories and Applications, v. 14, 2007. pp. 5–19 http://www.foibg.com/ijita/vol14/ijita14-1-p01.pdf From: Pedro C. Marijuan Sent: Friday, April 08, 2011 11:08 AM To: fis@listas.unizar.es Subject: [Fis] ON INFORMATION THEORY--Mark Burgin 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: <!--[if !supportLists]-->1. <!--[endif]-->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? <!--[if !supportLists]-->2. <!--[endif]-->Are there types or kinds of information that are not encompassed by the general theory of information (GTI)? <!--[if !supportLists]-->3. <!--[endif]-->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, TripleC, 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 2nd 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, TripleC, 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 --------------------------------------------------------- -------------------------------------------------------------------------------- _______________________________________________ fis mailing list fis@listas.unizar.es https://webmail.unizar.es/cgi-bin/mailman/listinfo/fis
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