J. WICKEN states: "In communication theory, messages are conceived as generated from symbols sets through stochastic processes know as MARKOV's chains, wherein the presence of one symbol might or might not affect the identity of the following symbol, according to the grammmar of transmission. SHANNON (C. SHANNON & W. WEAVER, 1949) referred to this as the "residue of influence" of one symbol on another. The reach of this "residue of influence" defines the order of the Markov process. If the presence of one symbol has no influence on what comes next, one has identical conditional probabilities, p(i/j)=p(j) for any assignment of it, and the Markov order of the process is zero. If it influences only the identity of the immediately following element or symbol, the order is one and so on.
"The Markov order of a sequence chain is in turn reflected in its complexity and compressibility order" (1989, p.141).
This concept had already been applied in a very interesting way by W.R. ASHBY in his" Introduction to Cybernetics", specially when used to describe a system (as defined by the matrix of its states transitions) able to produce a great number of trajectories (1956, 9/4 to 9/10).
In another sense WICKEN consider that "the information of a paragraph is certainly not reducible to SHANNON's complexity of letters on a page… We can't compute the information content of a treatise any more than we can compute the information content of an organism by a SHANNON-complexity analysis of DNA sequences" (p.142).
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Bertalanffy Center for the Study of Systems Science (2020). Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]
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