# Why I Don’t Have 1.6 Novemdecillion Ancestors

I was going to call this “Fun with Genealogy, Math, and Data” but then I’d have even fewer readers. (Darn, I said it! There go the readers!)

### Lots of Boxes in the Family Tree

The odd thing about family trees is that the number of people gets larger as you go back through the generations, but the population of the world is smaller as you go back through the generations. If my family tree had no repetition, meaning that every spot in the tree held a different person, I’d have 1.6 novemdecillion ancestors by the time you go back to about 4000 BCE. That’s 16 followed by 59 zeros, which is vastly, hugely, astronomically more than the world population 6000 years ago of around 7 million people. It’s vastly more than the estimated number of stars in the universe.

The explanation, of course, is that a family tree must have tons of repetition when you go that far back. Somewhere back in ancient Europe, where DNA testing places my heritage, there are couples who must show up trillions of trillions of times in my family tree.

### The Crossover Point

The next question is: Where’s the crossing point between the size of my family tree and the population of the world? At which generation in the family tree does the size of that generation exceed the world population? It turns out to fall somewhere around the year 1100. I’m estimating 30 years per generation. Look back 28 generations before my year of birth and we hit the year 1118. That 28th generation of the family tree has more than a quarter of a million people in it. The world population back then was a little more than that, somewhere around 320 million. Look back 29 generations to about 1088, and we’ve got over half a billion people in the family tree, but the world population was smaller than that. That’s the crossover, then. Somewhere around the turn of the 12th century, my family tree is larger than the population of the world. There are more spots to fill than people to fill them.

What does that mean? Although anyone could have repetition in the family tree more recently than that, it’s guaranteed to happen by the time you reach back to the Middle Ages. It also means that if your ancestors and a friend’s ancestors were from the same general region back then, there’s a very real possibility that you’re very distant cousins. If two people today have an ancestor in common from 29 generations ago, they’re 28th cousins.

That crossover point is where your family tree must have repetitions. Most likely, you’ve got repetitions that are much more recent, because you’re not descended from everyone who was alive back then. Some of those people didn’t have kids, or didn’t have family lines that survived until the present day, and some simply aren’t your ancestors.

### Repetition in Our Family Trees

Both my wife and I have known repetitions in our family trees. Phillip Harmon (1803-1853) and Nancy Jackson (1801-1885) are my 4th great-grandparents in two different places. Their daughter’s son married their son’s daughter – cousin married cousin – back in southern Indiana. In my wife’s family tree, Pierre Georges Riffaud (1834-1890) and Marie Elisabeth Zélie (1833-1893) are her great-great-grandparents twice over (life on a small island, Martinique). Two of their descendants got married and became my wife’s ancestors.

We also found potential common ancestors in medieval Europe (because European nobility and royalty kept careful track of their lineage). Our evidence isn’t rock solid every step of the way, but it’s mostly pretty good, so we might well be distant cousins through some medieval ancestor. The math above makes this a rather unsurprising result. Just about all of European royalty was descended from Charlemagne, and there’s a decent chance that if you have European heritage, you’re descended from some European royal too, and therefore also from Charlemagne. If you have French heritage in particular, you’re probably descended from Charlemagne. Roughly 30% of today’s African-Americans also have European ancestry, so if you’re descended from slaves in the US, you too could be one of Charlemagne’s descendants.

If you are indeed descended from Charlemagne, you’ve got lots of repetition in your family tree. If he’s there at all, he’s probably there in multiple places.

### 30 Years per Generation?

Earlier, I estimated 30 years per generation. That’s a common genealogical estimate, but can we test it? Sure, with more math and more data! Yay! The average generation interval between an ancestor and a descendant is: (descendant’s birth year – ancestor’s birth year) / (number of generations between them). My 3rd great-grandfather Mathias Becker was born in 1814. I was born in 1958. That’s (1958 – 1814)/5 = 28.8 years. That’s one line. When I average out the 4 generations behind our kids, I get 30.4 years. Our family trees have complete birth info on everyone for those 4 generations. Our info gets more sparse as you go back. When I average what we have for 5 generations, I get 30.6 years. When I throw in the 6th generation, where the birth dates fall in the late 18th century, I get an average of 29.8 years. Those averages are all in the neighborhood of 30 years, so the estimate seems like a decent one, at least for the last few centuries of European heritage.

To go back farther in time, I looked at the oldest line I could trace with any kind of data, to Pepin of Landen, Charlemagne’s 3rd great-grandfather. (Once your family tree ties into European royalty, the family tree grows a lot.) For the sake of the exercise, let’s accept the path leading to dear old Pepin without pointing out where the weak links are, and see what this does to the average generation interval. He was born in about the year 580. In the family tree data we’ve accumulated, he shows up 24 times as an ancestor of my kids: 4 times as their 41st great-grandfather, 15 times as 42nd, and 5 times as 43rd. He’s 43-45 generations behind my kids. Five of those 24 ancestral spots are on my wife’s side, 19 on mine. He’s probably there in a lot more places that we don’t know about.

For my youngest, the average generation interval between her and Pepin of Landen is 31.4, 32.1, or 32.8 years, depending on the path you take. A rule of thumb of 30 years per generation still seems about right, all the way back to the early Middle Ages.

### Genealogy. Math. Data.

Genealogy. Math. Data. This is how I have fun.

Thank you both for listening.

Jim