Dear Bob,
I now understand clearly what you mean to say. The Kullback-Leibler
information always increases the uncertainty (because the second law; Theil,
1972). While the mutual information between two distributions reduces the
uncertainty, however, the consequent conditionality in the probability
distribution seems not a sufficient condition for defining "meaning". One
needs a kind of feedback on the positive generation of probabilistic entropy
along the time axis. Meaning is provided from the perspective of hindsight,
i.e., against the axis of time. Dubois has called this incursion (as
different from recursion), and developed algorithms for the computation of
anticipatory systems.
Your measure of the mutual information in three dimensions ("configurational
information"; McGill, 1954) is very beautiful for this purpose. It makes the
generation of positive or negative entropy an empirical question. I used it,
for example, for measuring the knowledge base of the German and Dutch
economies. [Loet Leydesdorff and Michael Fritsch, Measuring the Knowledge
Base of Regional Innovation Systems in Germany in terms of a Triple Helix
Dynamics, Research Policy, 35(10), 2006, 1538-1553; at
www.leydesdorff.net/germany/index.htm ] We are currently involved in a
project where we use it to distinguish fields of science in terms of whether
knowledge is generated endogenously by using the mutual information among
three or more textual indicators. Knowledge can be defined as a meaning
which makes a difference. Meaning is defined as soon as a system of
reference is specified for the (Shannon-)information processing.
All these questions thus can be made empirical ones.
Best wishes,
Loet
________________________________
Loet Leydesdorff
Amsterdam School of Communications Research (ASCoR)
Kloveniersburgwal 48, 1012 CX Amsterdam
[EMAIL PROTECTED] <http://www.leydesdorff.net/>
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