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“As you move further back in genealogical time, an even bigger paradox looms into view. We think of genealogy as a simple forking tree, our two parents the product of four grandparents, who are descended from eight great-grandparents, and so on. But such a tree eventually explodes into impossibility. By the time you get back to the time of, say, Charlemagne, you have to draw over a trillion forks. In other words, your ancestors from that generation alone far outnumber all the humans who ever lived. The only way out of that paradox is to join some of those forks back together.

...in 1999 a Yale mathematician named Joseph Chang created the first statistical model of it. He found that it has an astonishing property. If you go back far enough in the history of a human population, you reach a point in time when all the individuals who have any descendants among living people are ancestors of all living people.

Ralph and Coop identified 1.9 million chunks shared by at least two of the 2,257 people.
..
Everyone alive a thousand years ago who has any descendants today is an ancestor of every living person of European descent.

Everyone who was alive five thousand years ago who has any living descendants is an ancestor of everyone alive today. ”

-- Carl Zimmer. “She Has Her Mother's Laugh.”

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