Aug 03

Excellent post by the On Gravity and Levity blog discussing the actuarially inspired “Gompertz Law of human mortality”, which predicts the probability of dying during a given year doubles every 8 years.

Below are some statistics for mortality rates in the United States in 2005, as reported by the US Census Bureau (and displayed by Wolfram Alpha):

usa-death_rates

This data fits the Gompertz law almost perfectly, with death rates doubling every 8 years.  The graph on the right also agrees with the Gompertz law, and you can see the precipitous fall in survival rates starting at age 80 or so.  That decline is no joke; the sharp fall in survival rates can be expressed mathematically as an exponential within an exponential:

P(t) \approx e^{-0.003 e^{(t-25)/10}}

Exponential decay is sharp, but an exponential within an exponential is so sharp that I can say with 99.999999% certainty that no human will ever live to the age of 130.  (Ignoring, of course, the upward shift in the lifetime distribution that will result from future medical advances)

Especially intriguing is the ending of the article – in which the author discusses a “cops and criminal” model and leads to a discussion on telomere shortening. It would be interesting to see if the telomere error rate is anywhere close to the Gompertz Law.

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