Tuesday, February 26, 2008

10 Million People Could Do It

In my previous post, I claimed that it couldn't be done. Well, I was wrong.

One person could examine every (30 generation) ancestral line in 34 years, giving each line one second.

But, 10 million people could accomplish the same task in less than two minutes.

That's one dimension of the solution.

The other one is that it's not really 2 billion ancestors in a family tree, but 2 billion places or roles: Father, Mother, Paternal Grandfather, etc. We could represent, or name, these places with simple strings:

F and M
FF, FM, MF and MM

and so on. These are isomorphic to the binary strings that I constructed in an earlier post about the "Powers of two."

As a more intense example, in my family tree there is an ancestor at position FFMMMFFFFFFFFFFMMFFFMMMMMFFMFF, who happens to be William the Conqueror. I would be very surprised if this illustrious gentleman didn't pop up in at least one other place in my family tree.

The point is that sometimes the same person will be found at more than one place, playing more than one role in the same family tree. If my son were to marry one of my third cousins, his children would find that the person in position FFFMMF (Caspar Witsch) might be the exact same person as the one in position MxxxF (again, Caspar Witsch). This cuts out a huge section of his or her the family tree.

Replace each "x" with one of "F" for father or "M" for mother. I'm not going to say precisely which family of third cousins he might marry into! To his children, I will occupy position FF. Everyone descended from position FFF is either me or one of my sisters. Everyone descended from FFFM is one of my (paternal) cousins, from FFFMM a second cousin, and from FFFMMF a third cousin. From my hypothetical grandchild's point of view, all of my third cousins are descended from individuals in positions FFxxxx (of which there are 16 possible; in other words, any one of my great-great grandparents). The grandchild's mother, being one of my third cousins is a great-great grandaughter of one of these 16 people. This would make the child both a 3rd great grandchild and a 4th great grandchild of Caspar Wintsch--his or her own fourth cousin once removed.

Getting back to the work at hand, if we combined the family trees of all of the 10 million people, chances are really good that they would have a lot in common. My sisters' family trees are identical to mine. My cousins' (and nephews') family trees are half the same as mine, and so on.

How many people have lived in the world since the year 1000? Let's suppose 20 billion lived in the areas from which the 10 million people drew their 30 generations of ancestors.

So, these 10 million people have no more than 20 billion distinct ancestors shared among them. If we spread out the work, each ancestor could be contemplated for one second in under an hour.

But, one second isn't very much time to devote to another human life.

What if we wanted to see that each of the 20 billion ancestors got 3 whole hours of the undivided attention of one of our 10 million workers. The 60 billion hours, split 10 million ways, would require 6,000 hours of each worker's time. A full-time work-year contains 8 hours per day times 250 days per year, or 2,000 hours. So, if we could convince each of our 10 million workers to devote 3 years of full-time work, every person who ever lived could get 3 hours of attention. And the 10 million people could still take off nights, weekends, holidays and some vacation time.

So, it could be done, after all, if only we could convince 10 million people that it is that important.


Nancy said...

I'll make you a deal.

If you finish your family tree, I will just cross out your name, put in my mom's and add mine and Rachel's underneath.

Then all I need to do is find someone else to do my dad's side. ;)

Looks like I'm set. That's not a bad deal at all!

Myrna said...

You might want to look at my genealogy books: I was fascinated by just this idea, and wanted to see how many times mom and dad shared the same ancestors--especially after realizing that Colleen and LeRon were like 3rd cousins once removed or something--so I indexed their two sides so I could find intersecting names. Then I started an index of places, which I never finished, but just thinking that towns were pretty small, and trying to see who from all my lines were in the same place at the same time.

Bruce Conrad said...

Very funny, Nancy! Of course, since you're one of the 10 million, you have to put in your own three years. My records are just bookkeeping so that you don't redo the same work.

Myrna, I would love to look through your work!