Question: In considering tracing genealogy the problem of a large and growing number of direct (grandparent) ancestors arose. Since the number of grandparents in any given generation doubles, for a person born in 2000 and assuming 25 year generations, in the year 1000 that person would have over one trillion direct ancestors in that year alone. Since estimates I have read place the total world population in 1000 at 250-300 million, the one trillion figure cannot be correct. I must be missing something in my calculations. Can you help provide the answer? While I am unlikely to be able to trace back to 1000, there is reason to believe 1250 is possible. Even in that year there would exist over one billion direct ancestors. That is certainly rather daunting and unlikely to be achieved if correct. Thank you for your help.
The large numbers you calculated came from assuming that each ancestor is unique. What your calculation shows is that if you trace your ancestory back a few generation you will find the some people more than once.
Think of your genealogy as a tree with you at the root. Above you are two branches, your parents. Above each of them are two more branches, their parents, etc. When the same person appears twice you need to prune the tree since everyone above that person appears twice. This pruning removes an entire limb each time a person appears twice in the tree.I hope this helps,