The Mathematics of Ancestry

The other day I was playing around on Ancestry.com, and I traced one of my mother’s grandparents all the way back to Charlemagne. Ancestry.com is as addictive as any video game, and it was like I had made it to the last round of Mario and finally defeated Bowser when I made the leap from England into France from the generation that was born just after the Norman invasion and the generation that was born before. Getting to Charlemagne from there was just extra minutes tacked onto recess.

But then I started thinking about how many people probably are descendants of Charlemagne. My brother, who got all of my math genes and his as well, told me the number of great grandparents you would have by the time you went back the 30+ generations it would take to reach Charlemagne would number in the billions. I am here today to correct his math. In his defense, he did this calculation off the top of his head without even pausing in the conversation to think. I, however, have gone the extra step in looking it up on someone’s personal website.

And the answer is…

Assuming you were born in the middle of the 20th century and that there was an average of 30 years between generations, you would need to go back 40 generations to your 38th great grandparents in order to reach Charlemagne in the middle of the 8th century. At that point, you would have more than one trillion 38th great grandparents.

The population of all of Europe at that time was probably somewhere between 20 and 30 million.

Charlemagne’s progeny wouldn’t even have needed to have multiplied as prolifically as they did for nearly everyone of European descent to trace back to him.

The thing about family trees is that you can only branch them out so far before they start narrowing back down. This is one place where science and religion agree. All of us are related somehow.