From: John Conover <john@email.johncon.com>
Subject: David McCullum
Date: Sun, 4 Jan 1998 15:54:53 -0800
I was watching the historian David McCullum, one of my favorite
authors, give a lecture on C-SPAN today. He made an interesting
observation:
History is not about the past. History is about the present in
the past, which is a different present than ours. History could
have taken a different path at every juncture, and its outcome was
not foreseeable in the present that was the past any more than it
is foreseeable in the present that is today.
Besides being an eloquent definition of the concept of history, it
struck me as a prescription for a non-linear dynamical system, (ie.,
specifically, a fractal.) Why? because that is the way fractal
structure is created; starting at any point, attempt to define a
future outcome. If the outcome is not foreseeable, then there will be
a randomness in the outcome; repeat the process indefinitely.
Why make this distinction? Because, it is a distinction that is
formally verifiable. If we analyze the duration-in centuries-of
societies/cultures throughout recorded civilization, the durations
assemble into a 1 / (2 * (t^(3/2))) distribution. The cumulative
distribution will be the integral of this formula, or 1 / sqrt (t),
meaning that half of the societies/cultures lasted less than four
centuries, and half more. (The Egyptians had the culture with the
longest run length, followed by the Romans. Although we are working
with a limited data set size, derived through inconsistent metric
methods-ie., for example, exactly when the Mayan culture in the
Yucatan begin, and ended is not precisely known-the shape of the
distribution is very assertive, with an average of about four
centuries. Exactly what would be expected from a fractal system.)
Interesting.
John
BTW, there are many other characteristics of fractal systems in the
dynamics of the history of civilization. A society's/culture's wealth
and power, (irregardless of how it is measured, as long as it is
consistent,) will increase with the sqrt (t) through the run length of
its duration, (which the metrics seem to confirm,) and the wealth and
power will be distributed through the society/culture in a 1 / (f^2)
distribution, (which also seems to be confirmed by the metrics.) I am
not certain of the implications of all of this, but one interpretation
could be that that we have less influence over the future than we care
to admit, and we have no guarantees that the societies/cultures of the
past did have.
--
John Conover, john@email.johncon.com, http://www.johncon.com/