Re: [Fis] the religion of probability

Various contributors have emphasized the probabilistic nature of
reality and the beauty of probability theory. I concurr with both
sentiments. I thought before we moved off completely to new topics,
however, I would like to add a few of my own opinions about the
necessity of aleatoric events that transcend probability theory. The
usual assumptions that enable one to address and quantify chance are
that unpredictable events are both simple and repeatable.
Repeatability is especially important, for if anything were to occur
that is truly unique, it simply could not be treated by conventional
statistical techniques. I would like to suggest, however, that with
complex systems we must face the possibility that *many* events
occurring are singular and unique for all time.

To see why unique events are not only likely but inevitable, I invoke
an argument formulated several decades ago by Walter Elsasser. Elsasser
sought to delimit what he called an "enormous" number. By this he was
referring to numbers of possibilities so large that they must be
excluded from physical consideration, because they greatly exceed the
number of physical events that possibly could have occurred since the
Big Bang. To provide an estimate of the threshold for enormous numbers
Elsasser reckoned the number of simple protons in the known universe to
be about 10^85. He then noted as how the number of nanoseconds that
have transpired since the beginning of the universe is about 10^25.
Hence, his rough estimate of the upper limit on the number of
conceivable events that could have occurred in the physical world is
about 10^110. Any number of possibilities much larger than this value
simply loses any meaning with respect to physical reality.

Anyone familiar with combinatorics immediately will realize that it
doesn't take very many identifiable elements or processes before the
number of possible configurations among them becomes enormous. One
doesn't need Avagadro's Number of particles (10^23) to produce
combinations in excess of 10^110 -- a system with merely 80 or so
distinguishable components will suffice. In probabilistic terms, any
event randomly comprised of more than 80 separate elements is almost
certain never to have occurred earlier in the history of the universe.
Such a constellation is unique once and for all time. It follows, then,
that in the ecosystems I deal with, involving hundreds or thousands of
distinguishable organisms, one must reckon not just with the occasional
unique event, but with legions of them. Unique, singular events are
occurring all the time, everywhere!

One is suddenly confronted by the sheer ubiquity of the aleatoric. The
fabric of causality manifests holes everywhere, at all levels. In the
full panoply of events, arbitrarily close to any phenomenon that
conforms to a law, one can find gaps that, by virtue of their
uniqueness, never can be covered by any conceivable law. One is
reminded of the Born-Caratheodory formulation of the second law of
thermodynamics, which says that arbitrarily close to any state of a
system lies another state that cannot be reached by a reversible
process. Similarly, one could argue that arbitrarily close to any event
that is lawful in either the deterministic sense, one can find singular
events. Hence, reality is not a compact continuum, but resembles rather
a "complex manifold" in the fractal sense

The best to all,
Bob Ulanowicz

-------------------------------------------------------------------------
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 |
--------------------------------------------------------------------------

_______________________________________________
fis mailing list
fis@listas.unizar.es
http://webmail.unizar.es/mailman/listinfo/fis
Received on Thu Apr 29 17:30:09 2004