Original by Chris Hillman.
Last modified by Roland Gunesch on May 7, 2001.
One of the most interesting (and best justified) applications of entropy to the humanities
involves pattern matching and entropic measures of dissimilarity to help answer questions like
- which sections of the Bible were written by which authors? (Biblical scholars long ago
identified at least four different authors, and now still more are emerging).
- who wrote which sections of the Federalist Papers?
- was the Illiad composed by one author or many?
- were Shakespeare's plays written by (fill in the blank)?
For a very nice introduction to these ideas, see
Typical Sequences and All That: Entropy, Pattern Matching, and Data Compression,
by the late
Aaron D. Wyner.
The problem of recovering a lost language from written inscriptions is
one on which entropy theory can quite possibly shed some light. An
interesting problem is for example the following:
- do we have enough information to even try to decipher Minoan Linear A?
I should perhaps explain this a little further.
Linear B was deciphered by the remarkable amateur Michael Ventris,
who proved it was a written form of ancient Greek.
The known inscriptions turn out to mostly be product inventories; not very useful for understanding
the political situation when Linear B was in use, but painting a remarkably clear picture of the
economy of ancient Crete. Nonetheless, the mere fact that the official language of Crete was Greek
proved for the first time that, as had long been suspected, the Greeks had wrested political control
of the island from the Minoans, sometime around 1070 BC.
The Linear A script is similar in appearance to the Linear B script
but it is believed to represent the original Minoan language.
Various eminent epigraphers have claimed to decipher the available tablets,
but unfortunately, not only did their readings differ completely,
they even disagreed over the fundamental issue of whether ancient Minoan belonged to
the Indo-European family, the Hamito-Semitic family, or to still another language group!
I conjecture that the trouble may be that unlike the tablets written in Linear B,
some of which were fairly lengthy documents,
the known Linear A inscriptions are (so far as I am aware) at most a few lines long.
And as Shannon showed, a sufficiently short message simply cannot be
understood in a meaningful
way.
Psychologists have long attemped to apply entropy concepts to define and compute
"sensory capacities" or (more dubiously) "cognitive capacities"; such applications have
generally been criticized by information theorists as embarrasingly naive.
In a famous lament, Shannon himself cautioned that "workers in other fields
should realize that the basic results of the subject are aimed in a very specific
direction, a direction that is not necessarily relevant to such fields as psychology,
economics, and other social sciences" (IEEE Transactions on Information Theory, December 1955).
For a recent survey,
see the book by Norwich below (I haven't had a chance to examine this,
so I don't know if the psychophysicists have grown more sophisticated
since the demise of the unfortunate Zipf's Law.)
More ambitiously, psychologists have attempted to apply information theory to
the study of the human brain; see for instance these
abstracts
from a Workshop on Information Theory and the Brain.
Sociologists have applied entropy concepts in various ways, ranging from the use of
statistical entropies to help interpret statistical patterns in voting records
to vague and apparently vacuous speculations concerning
a sort of grand unified social theory (e.g. Bailey's book below; I have not examined
the books by Forse or Geiger). For more on Coleman's work see his book and the
following paper:
-
A Test for Conformity in Voting Behavior,
by Stephen Coleman (Program Evaluation Division,
Office of the Legislative Auditor, St. Paul, MN).
Coleman views behaviors such as the decision to vote for a minority party
candidate (or not to vote at all) as a form of communication and accordingly
attempts to quantify the "conformity" of voter behavior using Shannon's discrete entropy
measure.
Further Reading
Stephen Coleman suggested the following references
(but he doesn't endorse these books, other than the one he wrote himself!):
-
Social Entropy Theory, ,
by Kenneth D. Bailey, State University of New York Press, 1990.
-
Measurement and Analysis of Political Systems: A Science of Social Behavior,
by Stephen Coleman, Wiley, 1975.
-
L'Ordre Improbable. Entropie et Processus Sociaux,
by Michel Forse, Presses Universitaires de France, 1989.
-
Erkennen und Wahlen,
by Siegfried Geiger, Kiepenheuer und Witsch, Berlin, 1970.
-
Information, Sensation and Perception,
by Kenneth H. Norwich, Academic Press, 1993.
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