With all the focus on Ancestry and 23andme these days, I thought a post from 2005 might need to be brought forward. Let me correct a myth that has sprung up by people who can at least do simple arithmetic (these days I should be grateful), but have not thought things through - that everyone can't be at least 20th cousins on the basis of mere multiplying by two and comparing that to the population of the world. The Native Americans really are separated from Europeans and even Asians by thousands of years, never mind the Africans and Aboriginal Australians. When cultures did not write things down and had limited contact with anyone but related tribes, there were lots of third through fifth cousins marrying each other. Even now, if there is no shared surname in the immediate families (Oh, Whittemore was my grandmother's maiden name...), would you know if you were marrying a fifth cousin? Especially when they crossed the Atlantic, people lost track of who aunts and uncles, great aunts and great uncles were.
2 parents, 4 grandparents, 8 grandparents… 1024 gggggparents after 10 generations (about 300 years in my family)… over a million after 20 generations (about 1400AD)…a billion in 1100 – wait, that can’t be right. There weren’t a billion people then. Not in the whole world.
Before the 10th generation (usually), the ancestral lines cross. Old Amos Peacham had 9 children, and you’re descended from 3 of them in different lines. Third or fifth cousins married each other, usually without knowing it. Before 1900, people didn’t move much. Families remember the exceptions: the two consecutive generations which moved from the old country and spread out a bit here. But before your people were chased, lured, or brought here they had pretty much stayed put, and after arriving, pretty much stayed put as well. Moving to Seattle is a recent phenomenon.
There are always interesting additions – a Dutch soldier or some unexplained woman with a Portuguese name wanders into your line somewhere. George from the Isle of Wight just showed up in my Nova Scotian line. Huh. We've got two consecutive generations of Larkins - an Irish name - marrying in in the early 1800s. There were only about ten surnames in the East Pubnicos in NS. (And ten more surnames in the West Pubnicos, all Acadian French. They apparently didn't mix much.) But your various lines will quickly develop nodes, where four generations are all from Woburn or a village outside of Warsaw. Ancestors don’t keep doubling forever.
If you are from some smaller group, Ashkenazi Jewish, Old Amish, Dominican, Gypsy, your line folds back in more quickly. There might be surprising branches sprouting out of your ancestry (it happens in the best of families), but that is out of a core of many second and fourth cousins marrying each other.
Around 1200 AD or so for those of European descent, the foldovers start outnumbering the doublings, and you actually start having slightly fewer ancestors each generation back. There weren't that many people in the area. The standard line is “Everyone is descended from Charlemagne.” I would add “by dozens or thousands of different paths.”