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Tuesday, October 19, 2010

Where does the 1,000 year life expectancy come from?

I recently ran across a reference to a startup company called Halcyon Molecular, which I might blog about after further investigation. The company's CEO, William Andregg, says in a video interview he wants to live for "millions, billions, hundreds of billions of years."

Well, he does think big. I have to admire him for that. Cosmology might make the upper figures difficult, however.

Andregg refers to the claim that if we stopped aging in the current sort of environment, we might have a life expectancy of circa 1,000 years before a misadventure kills us. I've heard that figure before, so I wonder if it comes from actuarial considerations.

According to the actuarial table, a 10 year old boy has a 1 - 0.000085 = 0.999915 probability of surviving in a year. That probability decreases every year after that. Assuming that you had a population of people who consistently had the probability of surviving every year like a 10 year old boy, then it looks like that population would have a half life Lhalf, the length of time by which half of the population dies, calculated as follows:

Lhalf = (ln 0.5)/ln 0.999915) = 8,154 years.


That seems nearly an order of magnitude too high. What if you assume the survival probability of a 20-year-old man? The actuarial table gives that as 1 - 0.001343 = 0.998657. In that case, you'd have a half life:

Lhalf = (ln 0.5)/(ln 0.998657) = 516 years


And that figure gets to the right order of magnitude. So, apparently, the 1,000 year life expectancy figure must assume something like the survival probability of people in their teen years.

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