13.0453 more on the Met algorithm

From: Humanist Discussion Group (willard@lists.village.virginia.edu)
Date: Tue Feb 29 2000 - 06:51:52 CUT

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                   Humanist Discussion Group, Vol. 13, No. 453.
           Centre for Computing in the Humanities, King's College London

             Date: Tue, 29 Feb 2000 06:46:34 +0000
             From: "Osher Doctorow" <osher@ix.netcom.com>
             Subject: Two additional items for the Metamorphoses

    Dear Colleagues:

    a. I would add two more entries to the Metamorphoses Algorithm (items 9 and
    10 below).
    b. Since the Metamorphoses are considered to require analysis as a whole in
    order to understand them, I would suggest considering logic-based
    probability operating on the union (or in propositional terms, the
    disjunction) of all the parts or their complements (negations). Such a
    union can be expressed in terms of sets of form A-->B-->C...-->N, etc., or
    even forms such as A<-->B which equals A-->B intersected with
    B-->A. Researchers could consider implementing models of this form. There
    might be a remarkable number of different models since so many combinations
    are possible, but it would be quite interesting.

    9. Maxima (maximum points) and minima (minimum points) and inflection
    points (points where curves change from concave up to concave down)
          A. time (maxima and minima of some (random) variable in time, etc.
          B. space (maxima and minima of some (random) variable in space, etc.
          C. conceptual (cognitive highest and lowest points of some (random)

    10. Percentiles, deciles, etc. (essentially points of equal subdivision of
    data or equal subdivisions of areas under curve representing probability
    density or cumulative distribution function of random variable).

    With 9 and 10, a certain similarity is beginning to emerge with fuzzy set
    and fuzzy logic theory. It is possible to argue that fuzzy sets and fuzzy
    logic involve conceptual graphs of high, low, intermediate levels of
    (random) variables. This would make fuzzy sets and fuzzy logic a
    subcategory of logic-based probability. It is not suggested that fuzzy
    techniques be abandoned, but it would place things in perspective by
    revealing why fuzzy techniques give useful results in many cases - namely,
    because they (among other methods) maximize logic-based probability.

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