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Humanist Discussion Group, Vol. 13, No. 453.

Centre for Computing in the Humanities, King's College London

<http://www.princeton.edu/~mccarty/humanist/>

<http://www.kcl.ac.uk/humanities/cch/humanist/>

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)

variable)

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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