Re: [Fis] Derrida's diferAnce and Kolmogorov's Information Operator
Dear Joe, Dear FISers, I would like to add a short remark. In fact, I repeat a fact that I mentioned several times in the past. We often miss to list a very simple form of information among the others, namely that, what I call information on existence. This is a double-valued property, with the words of Joe, binary opposition. Something exists here and now, or does not. E.g., I am here or I am not here; you are hungry or you are not hungry; it is red or not red, that object has the same colour like this, or has different colour, etc. (Note, difference is not certainly a binary category in itself, because it compares two things, where one of the compared things has one property, while the other side - asymmetrically - is many-valued. These many values may be finite, discrete infinite, or may belong to a smooth continuum.) This observation comes for me from my experience with the description of symmetries in physics. For decades, there were described different kinds of symmetry by discrete groups, then by (continuous) Lie groups - more and more complicated appearances of symmetry phenomena. The significance of parity was recognised late, in the nineteen fifties, and I would say, that there are even now (fortunately not all, only) many physicists who are surprised when meet the difference between the behaviour of parity in odd and even dimensional spaces. This is caused by lack of general knowledge about the nature of paritiy. Nevertheless, the most simple appearance of the phenomenon. Something similar happened around existence type information. It is important, it is lovely, worthy of affection. Let us not forget/neglect it. Gyuri At 06:43 22.02.2010, you wrote: Dear FIS Colleagues and Friends, As you have for a long time before me, I have been trying to tame (I prefer the French make private â apprivoiser) the notion of information. One thought was suggested by Batesonâs seemingly generally accepted dictum of âa difference (and/or distinction) that makes a difference. But I think this difference is no ordinary âdeltaâ; this is an active referring or better differing term like the différance of Derrida. Iâm sure someone has made a reference to this before Iâm new here â but then Derrida uses différance to question the structure of binary oppositions, and says that différance âinvites us to undo the need for balanced equations, to see if each term in an opposition is not after all an accomplice of the other. At the point where the concept of différance intervenes, all of the conceptual oppositions of metaphysics, to the extent that they have for ultimate reference the presence of a present (signifier/signified; diachrony/synchrony; space/time; passivity/aactivity, etc.) become non-pertinent. Since most of the usual debates about information are based on such conceptual oppositions, and classical notions of here and now, it may be high time to deconstruct them. I am sure you are familiar with this, but I found it rather interesting to read that Kolmogorov had given one definition of information as âany operator which changes the distribution of probabilities in a given set of eventsâ. (Apparently, this idea was attacked by Markov.) Différance in the informational context then started looking to me like an operator, especially since in my process logic, where logical elements of real processes resemble probabilities, the logical operators are also processes, such that a predominantly actualized positive implication, for example, is always accompanied by a predominantly potentialized negative implication. At the end of all this, then, one has, starting from the lowest level: a) information as what is processed by a computer; b) information as a scalar quantity of uncertainty removed, the entropy/negentropy picture; c) semantic information as well-formed, meaningful data (Floridi); d) information as a process operator that makes a difference to and for other processes, including above all those of receivers and senders. A first useful consequence is that information âoperationsâ with my operator are naturally polarized, positive, negative or some combination which Iâll leave open for the moment. The negative effects of some information follow naturally. Many of you may conclude Iâm doing some oversimplification or conflation, and I apologize for that in advance. But I believe that Kolmogorovâs original idea has been neglected in the recent discussions of information Iâve seen, and I would very much welcome comments. Thank you and best wishes. Joseph ___ fis mailing list fis@listas.unizar.es https://webmail.unizar.es/cgi-bin/mailman/listinfo/fis http://symmetry.hu/coming-meetings.htmlBridges Conference 2010, Pecshttp://symmetry.hu/coming-meetings.html, 24-28 July http://vod.niif.hu/symmetry2009/Symmetry Festival
Re: [Fis] Derrida's diferAnce and Kolmogorov's Information Operator
At the end of all this, then, one has, starting from the lowest level: !--[if !supportLists]--a) !--[endif]--information as what is processed by a computer; !--[if !supportLists]--b) !--[endif]--information as a scalar quantity of uncertainty removed, the entropy/negentropy picture; !--[if !supportLists]--c) !--[endif]--semantic information as well-formed, meaningful data (Floridi); !--[if !supportLists]--d) !--[endif]--information as a process operator that makes a difference to and for other processes, including above all those of receivers and senders. Dear Joseph and colleagues, I agree with the distinction of four operations, but it seems to me that this can be expressed more parsimoneously using information theory. Given Bateson's (1972) formulation that information can be considered as a difference which makes a difference, one should distinguish between the first type of differences and the second. Let's say difference(1) and difference(2). (I'll need difference(3) and difference(4) below.) A difference(1) can only make a difference(2) for a system (or more generally the expectation of a system). This difference(2) is analytically preceded by difference(1), that is, pure differences. Shannon-type information is contained in probability distributions. In the binary case, this is only one difference (Y/N, F/T, open/closed); in the non-binary case probability distributions provide us with sets of differences(1). These differences(1) can only make a difference(2) for a system which contains other (orthogonal) differences. In this case one needs one-more (orthogonal) dimension of the probability distribution that positions the incoming (Shannon-type) information at specific moments in time. Thus, difference(2) presumes at least a dimensionality of two in the probabilistic entropy. When the system develops, difference(3) can be defined with reference to the time axis (recursion). This is Brillouin's (1962) Delta H. The difference(1) that made a difference(2) for the system makes a difference(3) over time. When the system operates as a self-organizing, autonomous or autopoietic system it is additionally able to provide the information with a meaning from the perspective of hindsight, that is, against the axis of time. This incursion can make a difference(4). In other words, one needs at least a vector (one dimension of the entropy) for containing an uncertainty. One needs (at least) two dimensions of the probabilistic entropy for positioning the information in a network (matrix) at specific moments of time. Three dimensions are needed when the time axis is additionally included; four when the direction in the time axis can be considered as another degree of freedom. The two approaches seem very akin to me, but I claim that mine is more strict and parsimoneous because I only need numbers of dimensions of the probabilistic entropy and not concepts like differance. The next-order probability distributions can be considered as the probability of probability distributions, etc. Best wishes, Loet _ Loet Leydesdorff Amsterdam School of Communications Research (ASCoR), Kloveniersburgwal 48, 1012 CX Amsterdam. Tel.: +31-20- 525 6598; fax: +31-20- 525 3681 mailto:l...@leydesdorff.net l...@leydesdorff.net ; http://www.leydesdorff.net/ http://www.leydesdorff.net/ ___ fis mailing list fis@listas.unizar.es https://webmail.unizar.es/cgi-bin/mailman/listinfo/fis
Re: [Fis] Derrida's diferAnce and Kolmogorov's Information Operator
Dear Joseph - once again your post was most stimulating, provocative and enjoyable. Kolmogorov's definition of information that you quote is most interesting but like Shannon's definition incorporates the notion that information is a quantitative concept that can be measured. The Bateson definition that you refer to was a critique of this notion of information as a quantitative measure. The criticism began with MacKay (1969 Information, Mechanism and Meaning. Cambridge MA: MIT Press.) who wrote Information is a distinction that makes a difference which Bateson (1973 Steps to an Ecology of Mind. St. Albans: Paladin Frogmore.) then built on to come up with the more popular: Information is a difference that makes a difference. MacKay was the first to critique Shannon's quantitative definition of information when Shannon wrote his famous definition: We have represented a discrete information source as a Markoff process. Can we define a quantity, which will measure, in some sense, how much information is ‘produced’ by such a process, or better, at what rate information is produced? – Shannon (1948 . A mathematical theory of communication. Bell System Technical Journal, vol. 27, pp. 379-423 and 623-656, July and October, 1948.) According to Claude Shannon (1948, p. 379) his definition of information is not connected to its meaning. Weaver concurred in his introduction to Shannon’s A Mathematical Theory of Communication when he wrote: “Information has ‘nothing to do with meaning’ although it does describe a ‘pattern’. Shannon also suggested that information in the form of a message often contains meaning but that meaning is not a necessary condition for defining information. So it is possible to have information without meaning, whatever that means. Not all of the members of the information science community were happy with Shannon’s definition of information. Three years after Shannon proposed his definition of information Donald Mackay (1951) at the 8th Macy Conference argued for another approach to understanding the nature of information. The highly influential Macy Conferences on cybernetics, systems theory, information and communications were held from 1946 to 1953 during which Norbert Wiener’s newly minted cybernetic theory and Shannon’s information theory were discussed and debated with a fascinating interdisciplinary team of scholars which also included Warren McCulloch, Walter Pitts, Gregory Bateson, Margaret Mead, Heinz von Foerster, Kurt Lewin and John von Neumann. MacKay argued that he did not see “too close a connection between the notion of information as we use it in communications engineering and what [we] are doing here… the problem here is not so much finding the best encoding of symbols… but, rather, the determination of the semantic question of what to send and to whom to send it.” He suggested that information should be defined as “the change in a receiver’s mind-set, and thus with meaning” and not just the sender’s signal (Hayles 1999b, p. 74). The notion of information independent of its meaning or context is like looking at a figure isolated from its ground. As the ground changes so too does the meaning of the figure. The last two paragraphs are an excerpt from my new book What is Information? to be published by the University of Toronto Press in late 2010 or early 2011. Your post Joseph has stimulated the following thoughts that I hope to add to my new book before it is typeset. As MacKay and Bateson have argued there is a qualitative dimension to information not captured by the Shannon Weaver quantitative model nor by Kolmogorov's definition. Information is multidimensional. There is a quantitative dimension as captured by Shannon and Kolmogorov and a qualitative one of meaning as captured by MacKay and Bateson but one can think of other dimensions as well. In responding to a communication by Joseph Brenner on the Foundations of Information (FIS) listserv I described the information that he communicated as stimulating, provocative and enjoyable. Brenner cited the following Kolmogorov definition of information as “any operator which changes the distribution of probabilities in a given set of events.” Brenner's information changed the distribution of my mental events to one of stimulation, provocation and enjoyment and so there is something authentic that this definition of Kolmogorov captures that his earlier cited definition of information as the minimum computational resources needed to describe a program or a text does not. We therefore conclude that not only is there a relativistic component to information but it is also multidimensional and not uni- dimensional as is the case with Shannon information. Joseph - many thanks for your stimulating post - I look forward to your comments on this riff on your thoughts. - Bob
