On the Moen page I posted yesterday, I made mention of a mathematical quandry rooted in the powers of two. That is, genetically, each of us has exactly two parents, four grandparents, eight great-grandparents, 16 great-great and so on. By then it’s going up really fast: ten generations, over a thousand; twenty generations, over a million; thirty generations, a billion (4 times the estimated world population at that time). At 65 generations (the Emperor Claudius), the number is practically inconceivable: 36,893,488,147,419,103,232.
Of course that number is reduced by intermarriage of cousins; it is hard to fathom but obvious that the number is reduced by a factor of hundreds, or thousands. It also strongly implies that a relatively high percentage of the reproductive population were indeed ancestors of any given person living today. That is, the probability of, for example, Charlemagne being a direct ancestor of anyone on earth today, is great. Narrow the field just to anyone of partial or fully European descent, and it becomes even more probable.
But documenting it, that is another matter. Especially if your ancestors at some time in between were poor, which is the case for most of us Euro-Americans. Next post: What documents there are.