I note that there has been some relatively recent work bridging Shannon's theory (and probabilistic theories more generally) and the Channel Theory of Jon Barwise and Jeremy Seligman.
• Allwein, Gerard. 2004. A qualitative framework for Shannon information theories. In Proceedings of the 2004 workshop on New security paradigms , 23-31. Nova Scotia, Canada: ACM. doi:10.1145/1065907.1066030. http://portal.acm.org/citation.cfm?id=1065907.1066030&coll=Portal&dl=GUIDE&CFID=22417089&CFTOKEN=87154842. • Allwein, G.T., Moskowitz, I.S., Chang, L.W.: A new framework for Shannon information theory. Technical Report A801024, Naval Research Laboratory (2004) • Seligman, Jeremy. 2009. Channels: From Logic to Probability. In Formal Theories of Information , 193-233. http://dx.doi.org/10.1007/978-3-642-00659-3_8. and some intriguing work approaching quantum mechanics via Chu spaces, which are of course related to channel theory: • Abramsky, Samson. 2011. “Big toy models.” Synthese . doi:10.1007/s11229-011-9912-x. http://www.springerlink.com.hmlproxy.lib.csufresno.edu/content/073455w4h5u4588h/. These may be of interest to some. =================================================== Jacob Lee ttp://www.jacoblee.net/ ----- Original Message ----- From: "Loet Leydesdorff" <l...@leydesdorff.net> To: "joe brenner" <joe.bren...@bluewin.ch>, firstname.lastname@example.org Sent: Sunday, May 8, 2011 12:16:01 PM Subject: Re: [Fis] replies to several Dear Joe: 1. If I follow Loet, I must accept that Information Theory is essentially a mathematical theory that requires abstractions for extension to complex contexts. But Bob says that the mathematically derived “meaning” for antibodies is a pale representation of meaning in the human context and only reflects how wanly quantitative models in general prefigure more complicated human situations. CONCLUSION: something else that is non-mathematical and non-abstract beyond IT as so defined is required to capture meaning. Yes, I would agree. Shannon-type information is yet meaningless. Information can only be provided with meaning by the substantive specification of a system of reference. For this reason, one needs not only a formal theory of the exchange, but also substantive theories. For example, a theory about the exchange of molecules in biology, and of atoms in chemistry, or of transactions in economy. These theories of specific communications cannot be expected to be unified because the substances (of “what is communicated and why”) are different. The formal theory of communication serves us, among other things, for moving from one substantive theory to another and for developing metaphors that can thus heuristically be transported, because of the abstraction involved. Additionally, these confrontations can lead to further developments of the algorithms that are relevant for studying the dynamics. The dynamics in the communication of meaning is different from the communication of information! Information can also circulate as noise (without meaning). I doubt it that meaning can be communicated without communication of information. Meaning is generated when information can be related by “an observing system” or more precisely in a discourse. It seems to me that semioticians focus exclusively on the communication of meaning without relating it to the communication of information. The latter, for example, has to confirm to the entropy law, while the former does not. The possibility of generating negative information has first been discussed by Brillouin as negentropy (- Delta H). Meaning circulation generates redundancies because the historical case is one of possible cases from the perspective of hindsight and thus the maximum entropy (of possible states) can be continuously enlarged. This is further reinforced when meanings are codified in terms of models. Models enable us to consider more possible case in the future. Such systems – e.g., scientific discourses – can be considered as strongly anticipatory. They act against the axis of time. […] 3. Two aspects of the exchange between Koichiro and Loet merit attention: 1) Loet said that his point of replacing “why” with “what” did not seem necessary to him. In my mind, however, when Koichiro refers to “what is communicated by what”, he is insisting on not losing the qualitative components of the information involved. This seems confused to me. What is the qualitative aspect of “information”? (As a sideline: you did not answer any of my questions!) The qualitative aspect can only be the system of reference attributed to the information which provides the information with meaning. This system of reference is qualitative and therefore a qualitative and substantive theory of communication is then needed. This theory is different from the formal theory of communication. “By what” refers to the carriers of the information. Emphasis on the “why” instead provides focus on the theory about the dynamical system under study. For example: Why are molecules communicated in the autopoiesis of life? How is this different from the communication of atoms? And why? 2) Loet seems to think that the role of time is covered by the following: “ Meaning is communicated incursively, whereas information is communicated recursively, that is, with reference to a previous state (t-1). Meaning is provided to the events from the perspective of hindsight, and with reference to other possible meanings (at t +1). ” This suggests a background framework and a world (or model of a world) limited to a state-transition concept of time, where, in addition, only Markovian processes occur. Koichiro envisages times that are closely related to or perhaps dependent on the actual communication processes in progress. CONCLUSION: Is there anyone in the group besides me who could say that both of these perspectives are necessary for a satisfactory IT? “satisfactory” is not an analytical category, but an emotional one. Do you wish to vote on these issues? Your “seems to think” is not such a nice formulation. Let’s keep the discussion rational! My example, indeed, was a (first-order) Markovian process, but it does not follow from the example, that “I seem to believe that only Markovian processes occur”. I have a preference to understanding first the simplest processes before moving towards the more complex non-Markovian ones because otherwise one may lose analytical clarity and empirical relevance. J It seems to me that the Markovian processes against the order of time are far from solved in the computation of anticipatory systems. We are only at the beginning. Best wishes, Loet _______________________________________________ fis mailing list email@example.com https://webmail.unizar.es/cgi-bin/mailman/listinfo/fis
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