Dear Joe, 5. The description of differences in terms of levels of complexity and recursion affecting Shannon-type information is essential because it provides an analytical basis of meaning also. Perhaps the sequence goes from vector to tensor to spinor (?) as you go up in dimensionality of the entropy to yield valuedness or valence?
Yes, it yields valuedness because the differences(1) make a difference(2), etc. For example, the information contained in a vector is positioned in the network/matrix, and this position has a value. The operation is recursive. But it closes itself off at the level of four. First, there are only difference(s)(1): expected information content of a distribution. This can make a difference(2) to an extension. Difference(3) when this is not only once, but repeated over time, that is, in a three-dimensional array. (Is that a 3-dimensional tensor?) In the next recursion, difference(4) has the additional degree of freedom of playing with the direction of time: incursion versus recursion becomes possible. Let us reformulate this in terms of evolution theory: differences(1) is only variation. Difference(2) positions the variation selectively. The structure of the system determines the value of the variation. Difference(3) adds the time axis and therefore stabilization: some selections are selected for stabilization. Difference(4) adds globalization: some stabilizations are selected for globalization. Globalization means that a next-order systems level folds back on the system, closes it of, and makes it a possible carrier for a next order systems dynamics. In other words: stabilizations can be at variance and thus provide a next-order variation with reference to difference(1). Difference(4) can analogously be considered as a next-order selection mechanism. But the system now already contains time (difference(3)) and performs by using also time as a degree of freedom. The monad is constituted. It closes off --performing its own autopoiesis-- but remains open in terms of its stablizations (= second order variations) for other systems dimensions to build further upon. Because of its fourth dimension it is not subsumed but remains as an independent reality. Is this consonant with Logic in Reality? 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/ _____ From: fis-boun...@listas.unizar.es [mailto:fis-boun...@listas.unizar.es] On Behalf Of joe.bren...@bluewin.ch Sent: Tuesday, February 23, 2010 7:33 PM To: lo...@physics.utoronto.ca Cc: fis Subject: Re: [Fis] Derrida's "diferAnce" and Kolmogorov's Information Operator Dear Bob, Loet, Gyuri and All, Progress?! Between Bob, Loet, and something of my logical approach, I see the art of understanding information developing in its necessarily dialectically connected synthetic and analytical aspects. Here are a few of the ideas suggested by Bobs historical notes, very useful for me, and by Loets elaboration of the complexity of difference. 1. The quantitative characteristics of information are more or less clear. My list of definitions was not intended to be exhaustive. 2. The semantic question of MacKay of what to send and where to send it is a process taking place in the senders mind. His definition of information as the change in a receivers mind-set and thus (concerned) with meaning also describes a dynamic process. He should have added simply that there is, when the signal is finally sent, a change in the senders mind-set also. These relations and changes can be described in my logical terms. 3. The Gestalt description of sufficiently complex information and meaning connected as figure and ground should have been obvious to me long ago, it wasnt, but it certainly is now. Logic in Reality provides a principled dynamic description of the linked changes of figure and ground, alternately predominating in the mind in two dimensions. The analogy is not perfect, however. One needs to keep in mind, here, the vertical, inter-level relation between information and meaning. It is this kind of information, and that in point 2., that I would like to describe as logical information operators. 4. Information without meaning, (Bobs paragraph 2) is information that is incapable of making a direct causal difference, to all intents and purposes, such as a data base. 5. The description of differences in terms of levels of complexity and recursion affecting Shannon-type information is essential because it provides an analytical basis of meaning also. Perhaps the sequence goes from vector to tensor to spinor (?) as you go up in dimensionality of the entropy to yield valuedness or valence? 6. The concept of allegedly self-organizing, autonomous and autopoïetic systems, however, requires the further explication of the origin of these wonderful properties in reality. Loets statement that the two approaches are very akin is very welcome in the analytic domain, since it is indeed more strict and parsimonious and différance is only a philosophical concept. However, différance is in a sense directly related to complex real physical systems, such as information producers and receivers. Ascription of autonomy, etc. where it does exist complicates things. I am trying to get a handle on information as an ontological operators, not one related to epistemic or doxastic differences. 7, From this perspective, a clarification to Gyuris note about the simple form of information to which he gives the very intriguing designation information on existence. Everything that has to do with existence is of interest to me, but my Logic in Reality does not and is not intended to apply to the entire extant domain. The examples you give, Gyuri, are binary or in other cases in a one-to-many relation. There is existence here, double-valuedness and information and at an even more fundamental level parity, as a property of quantum entities. But this is not binary opposition; there is no opposition here, no exchange of energy, no caused differences. At the limit, there is no physical change at all of the duals as such, or if there is, it is only of the state-transition type (cf. Loets Y/N, F/T, open-closed and your same color different color, presence - absence). So by all means lets discuss the concept of existence type information,. For me the test of its utility would be the extent to which it might apply to or be included in (as lowest level semantic information is) something complex and interactive. Many thanks. Best, Joseph ----Message d'origine---- De: lo...@physics.utoronto.ca Date: 22.02.2010 15:07 À: <joe.bren...@bluewin.ch> Copie: "Pedro Clemente Marijuan Fernandez"<pcmarijuan.i...@aragon.es>, "fis"<fis@listas.unizar.es> Objet: 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 Shannons 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 Shannons 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 Wieners newly minted cybernetic theory and Shannons 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 receivers mind-set, and thus with meaning and not just the senders 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 ______________________ Robert K. Logan Chief Scientist - sLab at OCAD Prof. Emeritus - Physics - U. of Toronto www.physics.utoronto.ca/Members/logan On 22-Feb-10, at 12:43 AM, joe.bren...@bluewin.ch 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 apprivoiser) the notion of information. One thought was suggested by Batesons seemingly generally accepted dictum of a difference (and/or distinction) that makes a difference. But I think this difference is no ordinary delta; this is an active referring or better differing term like the différance of Derrida. Im sure someone has made a reference to this before Im new here but then Derrida uses différance to question the structure of binary oppositions, and says that différance invites 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/activity, 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 any operator which changes the distribution of probabilities in a given set of events. (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: <!--[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. A first useful consequence is that information operations with my operator are naturally polarized, positive, negative or some combination which Ill leave open for the moment. The negative effects of some information follow naturally. Many of you may conclude Im doing some oversimplification or conflation, and I apologize for that in advance. But I believe that Kolmogorovs original idea has been neglected in the recent discussions of information Ive 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
_______________________________________________ fis mailing list fis@listas.unizar.es https://webmail.unizar.es/cgi-bin/mailman/listinfo/fis
