The Life-Spans of Empires

Thursday, August 18th, 2011

The Life-Spans of Empires follow an exponential distribution; some empires last a long time, but most do not:

One of the interesting points about the exponential distribution is that it implies that the the duration of an empire at any given moment can’t tell you the probability that it’s going to collapse in the near future. The distribution is “memoryless.” In other words, the likelihood of doom striking isn’t greater as time passes. This seems somewhat counterintuitive. After all doesn’t the cohesion and elan of the a ruling caste of a given empire wane as the society slowly lose its vital force? Hasn’t the author read Spengler! Arbesman admits that there are more complex equations which can describe the distribution more precisely, but the exponential formula has only one parameter, so it’s quite parsimonious. But even if we have a first approximation we don’t have a total description.

In gamer terms, empires don’t have hit points; rather, they eventually fail a saving throw.  (See also: Gompertz Law of Human Mortality.)

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