Re: [Fis] definition(s) of order/disorder ?

From: Robert Ulanowicz <[email protected]>
Date: Mon 24 May 2004 - 15:54:59 CEST

With regard to the distinction between order and disorder, several have
mentioned the relative nature of the cut. I will just offer the following
illustration:

If one observes a particular distribution, call it A, without reference to
any other distribution, the only measure one can make is the "entropy" of
A, or

        H(A) = - Sum Pi log (Pi)
                  i

As Bayseians are quick to point out, such a measure is always relative to
some other (implied) distribution (often the uniform distribution.) It is
better to make clear the reference distribution, call it B, and then one
may write

      H(A) = I(A;B) + H(A|B).

What one accomplishes thereby is the decomposition, or parsing, of the
complicatedness (I'll try to avoid the word "complexity", but some might
find it appropriate) into two distinct terms. The first measure, I(A;B),
tells us what part of the complicatedness of A appears to be ordered
(constrained) with respect to B. The second term H(A|B) (the conditional
or residual "entropy") reveals that part of H(A) that remains disordered
with respect to B.

Now, if one had chosen the distribution C instead of B, the decomposition
would have been

        H(A) = I(A;C) + H(A|C)

so that with respect to C, possibly two very different measures of what is
ordered and what remains disordered emerge.

Hence, the Bayesian word on order/disorder is that the distinction always
remains relative to the chosen reference.

Cheers to all,
Bob

-------------------------------------------------------------------------
Robert E. Ulanowicz | Tel: (410) 326-7266
Chesapeake Biological Laboratory | FAX: (410) 326-7378
P.O. Box 38 | Email <ulan@cbl.umces.edu>
1 Williams Street | Web <http://www.cbl.umces.edu/~ulan>
Solomons, MD 20688-0038 |
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Received on Mon May 24 15:56:05 2004

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