Today's special guest is Harvard professor Steven Pinker. Dr. Pinker, an experimental cognitive scientist and linguist, has written several best-selling popular science books including The Language Instinct, The Blank Slate: The Modern Denial of Human Nature, and most recently The Better Angels of Our Nature: Why Violence Has Declined. In addition to all these accomplishments, he has, quite possibly, the greatest scientist/rockstar hair one can imagine and was deservingly chosen as the original member of the Luxuriant Flowing Hair Club for Scientists.1
Dr. Pinker writes,
How many people died during the 20th century?
If the world's population was X at time t, and Y at time v, how many distinct individuals were alive between t and v? This question obviously presupposes another one, namely, what other variables does one need to compute an estimate (birth rate? Average age of death?)
All of us have, at one time or another, suffered the misfortune of being born.2 As such, we can answer the first of Dr. Pinker's questions by knowing what the population was at midnight on New Year's Eve 1899 and adding to that any births that occurred during the next one hundred years. The first of these is easy to look up (about 1.6 billion), and I'll discuss the latter shortly. Before getting to that though, I should point out that once you have this answer, the answer to the second question is easy to find. Since another unfortunate consequence of birth is, of course, the inevitable death that follows, all you have to do is subtract the world population at midnight on New Year's Eve 1999 (about 6 billion) from the number of people who "lived in the 20th century" and you'll have found the number of people who croaked during this time. The only tricky step is figuring out how many people were born in the meantime.
|A nice "world population vs. time" plot courtesy of Wikipedia.|
There's an old statistics joke about the average family having 2.3 kids. While it's fun to imagine the extra three-tenths of child as a torso-less pair of legs constantly running around and bumping into walls, the statistic itself will be useful here.3 Let's say people reproduce on average once every 25 years. Assuming no one dies, you should have 4.3/2 = 2.15 times the original population (about 6.9 billion people) by the time you reach 1925.4 Since there will be about four generations, you would have to repeat this procedure four times to get roughly the total number of people who lived during the 20th century. We can write this using a formula that contains only three variables:
[(2 + average number of children) / 2](number of generations) × (original world population)
= 2.154 × (1.6 billion)
= 34 billion people.
That's about 34 billion people who lived at some point during the 20th century. Since there were only about 6 billion people living at the end of the century, it stands to reason that roughly 28 billion deaths occurred during the 20th century.5
Dr. Pinker, it has been an honor having you and your awesome hair on the blog today. Thanks for a great question!
 To quote the Improbably Research website, "From that lone, Pinkerian seed, there has grown a spreading chestnut, black, blond, and red-haired membership tree."
 Birth is, of course, a vital prerequisite for living, but that fact does not make the matter any more pleasant or less messy.
 The exact number might be closer to 2.1 kids or 3.1 kids. Fortunately, most of us aren't the Duggars, so we should be good to at least an order of magnitude here.
 For those who have a hard time seeing why it's 2.15 and not just 2.3, consider a world with only 20 people. If those people reproduce at the assumed rate, they will have 23 kids giving a total population of 43 people, or roughly 2.15 times the original population.
 This means that roughly 18% of the people who were alive at some point during the 20th century were alive at the end of it. Avid readers of this blog will note that one of the first calculations I did was determining what fraction of people that have ever lived are still living. I got about 30%, but a more reasonable number is 6%. I'll leave it as a challenge for you to figure out why that's still not a bad estimate in light of today's result.
Aaron Santos is a physicist and author of the books How Many Licks? Or How to Estimate Damn Near Anything and Ballparking: Practical Math for Impractical Sports Questions. Follow him on Twitter at @aarontsantos.