Sigh. Your point is not valid. Here are some links that try to explain it.
You have two parents, four grandparents, eight great-grandparents, and so on. Each generation back the number of ancestors you have doubles. But this ancestral expansion is not borne back ceaselessly into the past. If it were, your family tree when Charlemagne was Le Grand Fromage would harbor around 137,438,953,472 individuals on it—more people than were alive then, now, or in total. What this means is that pedigrees begin to fold in on themselves a few generations back, and become less arboreal, and more a mesh or weblike. You can be, and in fact are, descended from the same individual many times over.
"But when we get to 40 generations ago, in the time of Charlemagne, we arrive at a trillion ancestors and that is a problem because we now have more ancestors than there were people. Thus one can deduce that a lot of those ancestors must be the same person."
Not a few. I just checked again and i'm related to 37 former Presidents, the Queen of England, Wilt Chamberlain, Ty Cobb, Donald Trump, Abe Lincoln, Obama, Jesse James, and Martin Luther King Jr (but not Joe Biden, thank God!!!).
A few presadents is a lot different form every presadent.
My point is valid.
Sigh. Your point is not valid. Here are some links that try to explain it.
https://www.popsci.com/descended-from-royalty/
https://phys.org/news/2013-08-dna-earth.html
Not a few. I just checked again and i'm related to 37 former Presidents, the Queen of England, Wilt Chamberlain, Ty Cobb, Donald Trump, Abe Lincoln, Obama, Jesse James, and Martin Luther King Jr (but not Joe Biden, thank God!!!).