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| MatrixEvolutions Quote | Reply | This message was updated on 8/13/2008 3:20:32 PM by MatrixEvolutions | THE EVOLUTION OF INFORMATION: posted on: 8/13/2008 3:19:33 PM A Unified Mathematical Science of Physical, Biological and Human Nature Abstract and introduction. A new general function for information is derived able to explain information in every form it takes in nature including visual information, verbal information, communicated information, emotional information and thermodynamic entropy. As such this new information function. which we call the bentropy, meaning benthic or deep entropy or fundamental entropy, provides the basis of a unified understanding of all things. The bentropy is a mathematical relative of the Shannon entropy, the central information function in information theory. To paraphrase A. Dukkipati (PhD Thesis, Electrical Engineering, Indian Institute of Science, Bangalore, 2006), “the fact that the Shannon entropy has performed so well in deriving the coding theorems of information theory that explain man-made communication systems would seem to provide such overwhelming evidence for the adequateness of Shannon’s information measure that to look for essentially different measures of information might appear to make no sense at all. Still, all the evidence that Shannon’s information measure is the only possible one, is valid only within the restricted scope of coding problems considered by Shannon. As the Hungarian mathematician, Alfred Renyi, pointed out in his fundamental paper on generalized information measures, in other sorts of problems other quantities may serve just as well or even better as measures of information.” In particular, because of the abstruse non-intuitive way it is derived, (Mathematical Foundations of Information Theory, Aleksandr Khinchin, Dover, 1957), there is a problem using the Shannon entropy to explain information as we generally understand it. Indeed Khinchin himself stated: “The reader will see that the path to the Shannon theorems is long and thorny, but apparently science, at this time, knows no shorter path….” Bentropy derives, rather, in a most direct and clear way from a simple matrix operation on a natural number set. This derivation of information shows information to be underpinned by distinction rather than the more restrictive concept of uncertainty which the Shannon entropy and other information theory functions such as the Renyi entropy, and the Tsallis entropy arise from. Indeed the bentropy shows uncertainty to be a subset notion of the broader, indeed universal concept, of distinction. Further, bentropy, in being the most general function for information, both derives and can be derived from all of the above entropies of information theory. The sense of distinction the bentropy represents includes visual distinctions we intuitively make between objects we see, verbal distinctions we think and communicate with, uncertainty understood as the distinction between anticipations and contradictory outcomes, emotional distinctions between things pleasant and unpleasant and the tacit distinctions that inherently exist between interacting entities in physical and biological systems. To read more visit our Website. |