Jason Kuznicki asks a question:
Using mathematical models, it is easy to demonstrate that every human being alive today is likely to be a direct descendant of Confucius, even using mathematical models that assume an extremely small amount of cross cultural mating, since any human alive today would have had 1.5 sextillion ancestors alive at the time of Confucius, over a quadrillion times more than the population of the earth at the time, making descent from Confucius a mathematical certainty, even accounting for consanguinity and geographical and cultural barriers, as noted by Yale professor Joseph T. Chang.
Seriously? Are we all direct descendants of every individual living at that time? Or of every individual who managed to leave descendants? I find it hard to believe, but it would be excellent if it were true.
We are overwhelmingly likely to be descended from any individual--as long as they managed to leave some descendants at all alive today.
Think of it this way: there were roughly 750M people alive in 1800, 500M people alive in 1500, maybe 250M people alive back in the time of Confucius.
That was 4 x 25 = 100 generations ago. The number of "slots" in the family tree for your ancestors doubles every generation:
2^100 = 1,267,651,000,000,000,000,000,000,000,000. That's how many slots in the family tree for ancestors you have back at the time of Confucius.
There were only 250,000,000 people alive at the time of Confucius.
That means that the average person back at the time of Confucius fills 5,070,062,000,000,000,000,000 slots in your ancestral family tree.