Nobody in my past was hugely famous, at least that I know of. I vaguely recall that an ancestor of mine who shipped over on the Mayflowerdistinguished himself by falling out of the ship and having to get fished out of the water. He might be notable, I guess, but hardly famous. It is much more fun to think that I am a bloodline descendant of Charlemagne. And in 1999, Joseph Chang gave me permission to think that way.
Chang was not a genealogist who had decided to make me his personal project. Instead, he is a statistician at Yale who likes to think of genealogy as a mathematical problem. When you draw your genealogy, you make two lines from yourself back to each of your parents. Then you have to draw two lines for each of them, back to your four grandparents. And then eight great-grandparents, sixteen great-great-grandparents, and so on. But not so on for very long. If you go back to the time of Charlemagne, forty generations or so, you should get to a generation of a trillion ancestors. That’s about two thousand times more people than existed on Earth when Charlemagne was alive.
The only way out of this paradox is to assume that our ancestors are not independent of one another. That is, if you trace their ancestry back, you loop back to a common ancestor. We’re not talking about first-cousin stuff here–more like twentieth-cousin. This means that instead of drawing a tree that fans out exponentially, we need to draw a web-like tapestry.
In a paper he published in 1999 [pdf], Chang analyzed this tapestry mathematically. If you look at the ancestry of a living population of people, he concluded, you’ll eventually find a common ancestor of all of them. That’s not to say that a single mythical woman somehow produced every European by magically laying a clutch of eggs. All this means is that as you move back through time, sooner or later some of the lines in the genealogy will cross, meeting at a single person.
continue to source article at http://phenomena.nationalgeographic.com/2013/05/07/charlemagnes-dna-and-our-universal-royalty/