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Krulwich Wonders: Are You Related To King Charlemagne?

Thursday, February 16, 2012 - 10:50 AM


Here's the riddle.


An illustration by Wendy MacNaughton posing the question who is related to Charlemange.

Wendy MacNaughton

The answer is at the bottom of this post. But first, a story.

It's from my friend Jack Hitt, who says that when he was 17 he was fascinated by ancestors. In particular, his own. He wondered if he was descended from a king, maybe a Founding Father. Anybody who's a Somebody would be good. He was looking for fabulousness.

His mother sent him to a cousin. The cousin was an amateur genealogist. And she started working her way backward up Jack's family tree and discovered — oh my God — that Jack is a direct descendant of Charlemagne, the great medieval king of France. And when she said straight, she meant it: Jack is 48 generations straight down, a direct descendant of the king!

Jack was thrilled. But then, he went to college. (Where so many things take on a different aspect.) As he tells the story in a new book, Bunch of Amateurs, to be released this spring, one day he is sitting in a calculus class that's about factoring large numbers, and the teacher says he wants to demonstrate something called "Pedigree Collapse."

"Pedigree Collapse" is something great-great-grandsons of Charlemagne don't want to experience.

The teacher says if you count your direct ancestors backward through time, the further back you go, obviously, the more ancestors you have. But when you do the numbers, something queer happens.

Go back to 800 A.D., he said, and the number of direct ancestors is, well, puzzling. You start with two grandparents, then four great-grandparents, then on to eight, 16, etc., and by the time you get to 800 A.D., the number averages to about 562,949,953,421,321. That's a lot of people. In fact, that's more people than have ever lived.

So something's wrong.

What's wrong is at some point up the line, people get counted twice, or three times. Your great-great-great-great-grandma on one line turns out to also be a great-great-great-great-grandma on another line. The same person can show up multiple times. You get duplicates. And way back, when the population of humans was much smaller, pretty much every line is duplicating heavily till at some point, everybody is your direct ancestor.

A drawing of Charlemange, King Charles, The Hammer, by Wendy MacNaughton.

Wendy MacNaughton

So let's be careful. Even if we zero in on 1300 A.D., well after Charlemagne's reign, it turns out Jack has about 268 million people who are his direct ancestors. This is also an awkwardly big number since Jack says, that's "roughly the total population of humans on the planet at that time."

Which means, said the teacher, "that nearly everyone currently living anywhere on the planet can claim [and he paused for emphasis] to be the direct descendant of Charlemagne."


But consider the irony: If you want to be truly Fabulous, "the mathematical distinction," said the teacher, "would be to not have Charlemagne as a direct ancestor.

This is what is meant by "Pedigree Collapse" — when the luckiest guy in the room can say: "Guess what? You can shake my family tree till everybody falls out, and I'm the only one here who is NOT RELATED to Charlemagne, or Cleopatra or Genghis Khan!"

And we all think: "Awesome!"

Meantime, here's the answer to our riddle.

Answer key to a riddle posing the question who is related to Charlemange by Wendy MacNaughton.

Wendy MacNaughton

Jack Hitt's new book, Bunch of Amateurs, will be published in May.


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Comments [5]

Justin from Salem, Oregon USA

Lol, this is great. I remember reading someplace a long time ago that genetically no two people on the face of the planet can be more than a 36 times removed cousin....its a small genepool people.

Feb. 21 2012 01:45 PM
Robert from Berkeley

This story is cute, but the mathematics of it is incorrect. First, however, a simple example: there are no known living descendants of Abraham Lincoln. The last living descendant of Lincoln died in the 1980's, childless. So, it turns out the mathematics of extinction of family lines is better described by stochastic branching theory than by calculus. Stochastic branching theory has its own interesting history: its discovery has often been attributed to Francis Galton (Darwin's cousin, and the discoverer of the method of regression) to answer a problem in lineal extinction. (In fact, Bienayme had described the method about four decades before Galton but unfortunately published his results in an obscure journal). Stochastic branching processes are characterized by whether they are subcritical, critical, or supercritical processes. If subcritical or critical, they eventually go extinct while if supercritical they grow. Sadly, stochastic branching theory is now best known not by its original application to lineal growth or extinction but rather because it describes nuclear fission and atomic bombs. The words "critical" and "supercritical" have now entered the popular lexicon in that context.

Feb. 19 2012 11:13 PM

Whether you believe certain religious texts, the principles of evolution, or a combination of both, we are ALL related!

Feb. 19 2012 01:41 AM

Hi, Heres a thought for you and request!

I found it weard how your podcast can receive a healthy number of well written comments directly on each one and yet without any written feedback from you or your partner, yet here on your blogg were you do write your thoughts there are no comments at all?

Maybe you should/could reply more on all the long comments made there already?
Great show because of the delivery of the info as an experiance, yet think it would have been nicer to have seen 2-3 replies to follow up on the thoughts of your listeners? I think that would be an insentive to write even more ^^

Feb. 18 2012 09:00 AM
Matthew Van Dusen from New York, NY

Jack Hitt's essay in Harper's Magazine, from which he got the book idea, was a classic and inspired me to write this guest post not long ago for Scientific American.
To summarize, my great forefather, appropriately titled (for someone from olden times) Abraham the Miller, was an original settler of New York who issued forth many notable progeny. The New York Times wrote about the prolific and distinguished Van Dusens, but ultimately I concluded I was common as dirt.
All thanks to Jack, who made it safe to lay claim to nothing greater than oneself.
Matt Van Dusen

Feb. 16 2012 05:15 PM

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