The incest paradox, revisited

“You have 2 parents. You have 4 grand-parents. You have 8 grand-grand-parents. In each step you go back in time, the number of your ancestors is doubled.

Imagine 3 generations per century. You go back in time 30 generations (1 millennium), and the number of ancestors you had around year 1000 AC is 2^30 = 1073 millions. But wait, the estimated Earth population in year 1000 is just 320 millions! How can it be possible? The only possible explanation is that people committed incest and/or had multiple relations in that time.”

This was one of my posts in my first blog, in 2004. Pretty funny idea, but intriguing!

However, I didn’t realize, at that time, that you can apply the same idea to the future: if a baby will be born around year 3100, his nowadays ancestors should be 2^33 = 8589 millions, more than the current world population (6700 millions). So we are currently committing incest and having multiple relations!

Data extracted from Wikipedia’s Word population article.