Genealogy math

I recently discovered that my parents were 24th cousins, once removed. That's the closest known link, anyway, and even that link supposes that birth certificates, gravestones, oral family history, professional genealogists, and Google searches can be trusted, which of course, they can't, except for the last one. I had a point here, and I'm coming to it as soon as I remember what it was.

Oh yeah. When I mentioned this fact to my niece, her response was "gross", or perhaps some more contemporary version thereof. She didn't like it any better when I pointed out that her own parents are fifteenth cousins.

What bothered me about her reaction was that she apparently thinks that everyone must have these pure, unadulterated ancestral lines, when math screams to me that this would be impossible.

If you go back one generation from yourself, you have two parents. At least I do. Two equals 2 to the 1st power. Go back two generations and you have four grandparents (2 to the 2nd power). Three generations give eight great-grandparents (2 to the 3rd power). In general, going back n generations gives 2 to the nth ancestors.

Let's assume a generation averages about 25 years. So going back 10 generations (say, the American Revolution), you have 1024 ancestors. Go back 20 generations (Queen Elizabeth I) and you have about 1,000,000 ancestors. Go back to Jesus (maybe 80 generations) and you end up with 2 to the 80th (about 1 sextillion, or 1,000,000,000,000,000,000,000,000) ancestors.

That's a lot. Now, the total number of people who have ever lived is a much discussed question. The commonly repeated "fact" that half of the people who have every lived are alive today is just silly, but the actual value is tough to calculate. This website estimates there have been about 100,000,000,000.

Clearly something is wrong here. You have a hundred trillion times more ancestors than have ever lived on the earth. The only way to account for this (well, other than virgin birth) is by massive intermarriage. So get used to it.

It's not even icky. Second cousins (same great-grandparents) can legally marry in the U.S. I have some just a few generations back. First cousins (same grandparents) can, and do, legally marry in many countries, including Spain and most Spanish-speaking countries. And there are plenty of closer cases than that, including one in a collateral line of mine that involved double-first cousins marrying -- two brothers married two sisters, and their children married. Their offspring had only four great-grandparents! Ok, maybe that is a bit icky.

The upshot of this post is that this was obvious to me even when I was quite young. Math is innate to me, and I wish it were to everyone. Of course, my niece has the innate ability to carry herself well in social situations, while I stumble through conversations, unable to express myself and inadvertently insulting others. *sigh* I suppose I could prove mathematically that her skills are more important.