Dear Joe, The semantic aspects are external to the Shannon perspective (by definition). However, Weaver (1949) gives openings. (I discuss this extensively in the paper at http://arxiv.org/abs/1507.05251.) "Mutual redundancy" can be defined as a measure of the imprint of meaning processing on the communication of information. Meaning itself cannot be measured, but hypothesizing meaning processing enables one to specify expectations about higher order loops.
The dimensionality remains in bits of information. The probability distribution, however, becomes multi-variate when next-order loops are added: instead of p(i), for example, p(ijk....) Best, Loet Loet Leydesdorff Emeritus University of Amsterdam Amsterdam School of Communication Research (ASCoR) l...@leydesdorff.net ; http://www.leydesdorff.net/ Honorary Professor, SPRU, University of Sussex; Guest Professor Zhejiang Univ., Hangzhou; Visiting Professor, ISTIC, Beijing; Visiting Professor, Birkbeck, University of London; http://scholar.google.com/citations?user=ych9gNYAAAAJ&hl=en -----Original Message----- From: Joseph Brenner [mailto:joe.bren...@bluewin.ch] Sent: Tuesday, July 28, 2015 9:07 AM To: u...@umces.edu; John Collier Cc: l...@leydesdorff.net; 'Fernando Flores'; fis@listas.unizar.es Subject: The Same and Not the Same Dear Bob and All, I have found many useful things in the recent postings, especially Bob U.'s point about the parsing of entropy into two components, mutual information and residual entropy; /qualitatively/, information and entropy are (epistemologically) antithetical, and, I might add, ontologically contradictorial. Also John's point about loops not being computable, as one might expect if they reflect the evolution of real processes. But what about mutual information itself? Mutual information is defined, I believe, as a measure of the mutual dependence of random variables. But suppose the variables or process elements are not random, but there is still mutual dependence. What about the information content here? Perhaps in this context, I can ask again the question of whether it makes sense to 'parse' /information/ itself into two interactive components that differ in their dimensionality, with meaning associated with the emergent component with the higher dimensionality. Curious, Joseph ----- Original Message ----- From: "Robert E. Ulanowicz" <u...@umces.edu> To: "John Collier" <colli...@ukzn.ac.za> Cc: <l...@leydesdorff.net>; "'Joseph Brenner'" <joe.bren...@bluewin.ch>; "'Fernando Flores'" <fernando.flo...@kultur.lu.se>; <fis@listas.unizar.es> Sent: Monday, July 27, 2015 9:25 PM Subject: Re: [Fis] Answer to the comments made by Joseph > Folks > > I know there is a long legacy of equating information with entropy, > and dimensionally, they are the same. Qualitatively, however, they are > antithetical. From the point of view of statistical mechanics, > information is a *decrease* in entropy, i.e., they are negatives of each other. > > This all devolves back upon the requirement that *both* entropy and > information require a reference state. (The third law of > thermodynamics.) Once a reference distribution has been identified, > one can then quantify both entropy and information. It actually turns > out that against any reference state, entropy can be parsed into two > components, mutual information and conditional (or residual) entropy. > Change the reference state and the decomposition changes. > <http://people.clas.ufl.edu/ulan/files/FISPAP.pdf> (See also Chapter 5 > in > <http://people.clas.ufl.edu/ulan/publications/ecosystems/gand/>.) > > Cheers to all, > Bob > >> Folks, >> >> Doing dimensional analysis entropy is heat difference divided by >> temperature. Heat is energy, and temperature is energy per degree of >> freedom. Dividing, we get units of inverse degrees of freedom. I >> submit that information has the same fundamental measure (this is a >> consequence of Scott Muller¡¯s asymmetry principle of information. So >> fundamentally we are talking about the same basic thing with >> information and entropy. >> >> I agree, though, that it is viewed from different perspectives and >> they have differing conventions for measurement. >> >> I agree with Loet¡¯s other points. >> >> John > > _______________________________________________ Fis mailing list Fis@listas.unizar.es http://listas.unizar.es/cgi-bin/mailman/listinfo/fis
