Gompertz Law of Human Mortality

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Gravity and Levity has a concise, informative summary of the Gompertz half of the Gompertz-Makeham Law of Mortality.

In the early part of the 19th century, mathematician Benjamin Gompertz proposed that mortality rates increased exponentially over time. Specifically, any individual’s odds of dying double every 8 years. As Gravity and Levity summarizes it,

For me, a 25-year-old American, the probability of dying during the next year is a fairly miniscule 0.03% — about 1 in 3,000.  When I’m 33 it will be about 1 in 1,500, when I’m 42 it will be about 1 in 750, and so on.  By the time I reach age 100 (and I do plan on it) the probability of living to 101 will only be about 50%.  This is seriously fast growth — my mortality rate is increasing exponentially with age.

And if my mortality rate (the probability of dying during the next year, or during the next second, however you want to phrase it) is rising exponentially, that means that the probability of me surviving to a particular age is falling super-exponentially.

Why would this be the case? There is a longer explanation at Gravity and Levity, but the short version is that the human body simply wasn’t engineered by evolution to survive all that long. Accumulated injuries, disease and other things that impact health eventually exhaust the body’s ability to overcome the damage.

On the one hand, this is a bit depressing to see our odds of surviving decreasing super-exponentially. On the other hand, it means there is something that could potentially be done about it if better technologies are developed to repair or avoid the damage that the body itself cannot repair (for example, a medical advance that all but eliminated breast or colon cancer).

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