The count of my ancestors

I thoroughly enjoy the Last Word feature of New Scientist where the readers pose and answer questions amongst themselves. The questions are hilarious sometimes and always informative. Case in point: The question about the awful smell of human droppings.

Another question asked and yet unanswered is this. I am paraphrasing here. "If I try to calculate the number of my ancestors starting with my parents, the numbers don't add up. [My parents + their parents + their parents + .. ] is: [2 + 4 + 16 + ... and so on]. If I continue adding, very soon - within a few generations - I end up with an insanely large number of ancestors. I couldn't have possibly had so many ancestors. Heck, there never existed so many people to satisfy my ancestoral math. What's wrong with this calculation?" (Some of you may have read a similar question in one of Dawkins books. I remember reading this but forgot which book it was).

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Inbreeding is exactly right. If you (meaning anyone) trace your family tree back far enough, you'll see the same people occuring more than once.

what you have here is an upper bound on no. of ancestors at each level. and offcourse some of your ancestors from both sides overlap.