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/

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