Saturday, August 11, 2007

Ancestors

I'm here catching up? at work, listening to Mike Marshall's very cool mandocello performance at the D'addario website(type in Marshall). Absolutely worth seeing all of those clips. A friend here at DRI is also working, an archeologist, and stopped by. Turns out she was at the same and only concert that I've seen Mike Marshall three years ago. He filled in for Tony Rice in Chico while appearing with Peter Rowan. I was with my neotec colleague Rich Briggs. Spiderwebs anyone?

So her stopping by at the printer on my desk, her interest in mankind, and my recently posed mathematics, got me to finish up these thoughts.

Before I go into it, I am into my family history. I am American to the point until records are untraceable in every single direction. People always want to claim some foreign nationality, but in my case, I am American, pure and simple. I've been wondering 'how many generations could I conceivably keep track of?'. If I had total accounting of all ancestors, my answer is about 9 generations. That only gets back a few hundred years. Coincidently, to the American Revolution.

- - -

At the family reunion, I got to talking to a brilliant electrical engineer relative Jerry Wells; a great guy too. Talking about this question I realized the number of direct ancestors for each of us is a power function of 2 raised to what I'll call the 'generation number'. That should makes sense - two people are required to make a new one, hence the base of 2. As a reasonable convention, I have two parents. So they are 2^1, generation 1.Generations go up by one: grandparents 2, great-grandparents 3.

Number of direct ancestors = 2^(Generation Number)

For six generations I have 64 direct ancestors. 7 generations is 128 folks, 8 generations is 256 folks, and so on. Taking things a lot further, suppose that new generations occur, on average, at 25 years old. Then:

Generation number = years considered / 25

There are 4 generations per 100 years, Let's look at the Mayflower, landing in 1620. That's about 400 years ago, and 16 generations ago, yielding 65,536 direct ancestors from that time.

Now if we take 2,000 years ago (an obvious choice) that is 80 generations. The number of direct ancestors whose DNA each of us carry is on the order of:

Generation number = (2,000 / 25) = 80
Ancestor count = 2^80 = a huge number. How huge?

Well, I get 1.2 x 10^24. When you consider that a billion is 1 x 10^9, it is an incomprehensible number of ancestors. Other incomprehensible numbers are found in geologic time on earth, on the order of 4 billion years. So the number of billions in 10^24 is way way too many to think about. It's more than a billion squared (a billion billion).

Again, in 2,000 years (who will argue that people haven't been here since then?) =1.2 x 10^24 reproducing people. To go back to 200,000 years, the dawn of homo sapiens, Excel blows up. I can get it to calculate 10,000 years ago, the beginning of the Holocene, at 400 generations and get 2.6 x 10^120 ancestors. The highest even numbered generations Excel will calculate is 1,023 (or -1 + 2^10), corresponding to 25,600 years ago. The result here 9 x 10^307 people reproduced to make me!

It's been 14 years since my real introduction to geologic time as a geology undergrad, and by now I'm pretty comfortable with geologic time scales. To add in 111 additional exponents to the number (10^9 and 10^120), just to go back 10,000 years of humans? Yikes.

Well, given that the world population is currently on the order of 7 billion, (7 x 10^9), And just for me, one person, there are 10^24 people responsible only in the last 2,000 years! Makes you wonder.

Just some thought for food, er, food for thought.

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