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August 19, 2007

Nickelback If Everyone Cared

I heard the song "If Everyone Cared" by Nickleback on the radio the other day. It is a bit of a modern version of Lennon's Imagine, and a very pretty song. It contains the lyric "Then we'd see the day, when nobody died " Which made me wonder, when was the last day that nobody died?

Low genetic diversity is a major reason why the human population is believed to have been through several bottlenecks where the population of humans was just a few thousand (average of 10) for a million years.
Maximum life expectancy was about 40 for all of prehistory, with an average of 20 years. So what if we treated life expectancy as binomial, so that your probability of dying on any one day was 1/average life expectancy or in this case, measured in days, 1/7305. The probability of a population of 10,000 having no deaths would be (7304/7305)^10000 = 0.25. That means that for most of human history on average 1/4 days no one died.

But by 9000 B.C.E there were 5 million people and the exercise becomes almost surely impossible. Let's say that then they had today's Global life expectancy of 66 years, which is way to high, and we use that same approximation as before.
It is hard to standardize what one means by possible, but I think of is as equvilent to was it likely that it I'd like to happened at least once in a thousand years which is 0.000274% of days. If we can agree on that, then even by 9000 BCE if there were more than 300,000 people then this was not possible even at today's health. Prehistoric health obviously makes that less likely.

If we choose a conservative value of 30 for life expectancy in late prehistory, then the criticical point occurred when the population moved from 100k to 150k. At that point it went from happening once every 25 years to happening once every 2000 years. Exponentials will do that to you. I figure (using groth rate math on census data) that human population crossed this threshold about 12 or 13 thousand BCE. So some day in 12500 BCE, most likely a temperate spring day in the northern hemisphere, nobody died.

Posted by OneEyedMan at August 19, 2007 11:47 AM

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