Treebeard's Stumper Answer 22 October 1999

Too Many Ancestors

I have two parents, and so do they. That gives me four grandparents and eight great-grandparents. Details get fuzzy after that, but I'm sure my family tree keeps doubling every generation: 16, 32, 64, 128, 256, and so on. After 10 generations, I'm back to the founding of our country with 1,024 of my ancestors on the loose. After 20 generations, I have over a million ancestors. After 30 generations, I have a billion ancestors. But that's far more than the (then) population of the world! That's impossible! How does my family tree narrow down?

Everyone has two parents, but we soon find too many ancestors! The answer must be that our ancestors are not all distinct. I might be descended from more than one child of a couple. The same person may turn up twice in my family tree by remarrying. People do sometimes marry "distant cousins," and I'm sure this was more common in the past when people were more tied to small town life with limited populations and social opportunities. There must be many such duplications to prune down every family tree. Perhaps we really are all related?

Notes:

I think we're all cousins on this bus...

Ancestors pile up quickly as we go back in time. Figuring 25 years per generation (20 or even 15 years might be a better guess as we go further back), I get:

Generation	My Ancestors	Date
Me	-	1950
My parents	2	1925
My grandparents	4	1900
3rd generation	8	1875
4th generation	16	1850
5th generation	32	1825
6th generation	64	1800
7th generation	128	1775
8th generation	256	1750
9th generation	1,024	1725
10th generation	2,048	1700
11th generation	4,096	1675
12th generation	8,192	1650
13th generation	16,384	1625
14th generation	32,768	1600
15th generation	65,536	1575
16th generation	131,072	1550
17th generation	262,144	1525
18th generation	524,288	1500
19th generation	1,048,576	1475
20th generation	2,097,152	1450
21th generation	4,194,304	1425
22th generation	8,388,608	1400
23th generation	16,777,216	1375
24th generation	33,554,432	1350
25th generation	67,108,864	1325
26th generation	134,217,728	1300
27th generation	268,435,456	1275
28th generation	536,870,912	1250
29th generation	1,073,741,824	1225

Graybear gives this elegant answer:

We will find, as we fill in our trees, that we are soon able to trace back to a particular ancestor by more than one path. A friend of mine has traced her geneology back to Pocahontas in three different ways. In other words, our ancestors are cousins. If you go back far enough, each path will connect through Noah and his wife, and we will realize we are all (distant) cousins. This is one of the reasons that people who claim to believe the Biblical account of the flood have no excuse for prejudism. (The other reason is the second greatest commandment - Love your neighbor as yourself.) When we entered the space-age, we became aware that we are all neighbors on little blue-green island in the Milky Way. Maybe we should invite all of our neighbors for a world party...

Whether we trace our roots back to Adam or Lucy, I think the results are the same. Every duplication prunes the tree. In the end, we're all cousins, and our family trees will show it if we look close enough.

The first story I ever read by R.A. Lafferty was his "Nine Hundred Grandmothers" in his 1970 ACE story collection of the same name. Nobody tells a tale like R.A. Lafferty! In this story, explorers find the planet Proavitus where the inhabitants are immortal. But they get smaller and smaller as they grow older, and mostly sleep. They live on shelves in the basement: Smaller and older the creatures had been getting... The wren-sized grandmother talked and laughed and nodded that there were those far older than herself, and in doing so she nodded herself back to sleep... What was that sound - too slight, too scattered to be a noise? It was like a billion microbes laughing. It was the hilarity of little things waking up to a high time... Imagine all your ancestors in one place, and you can ask them questions! Read this story to find what the oldest grandmother says! There's a web site dedicated to R.A. Lafferty's great stories. Many of his books are now out of print, but try an author search at Amazon.Com.

This stumper has been discussed on the Web, and there are many geneology sites:

• The Newton Ask-A-Scientist archive answers the question "An Infinite Number of Ancestors?"
• Lorine McGinnis Schulze has a page on How many ancestors do we have?
• The Relatively Speaking and the Cousins and Cousinhood sites have info and links on cousins: "It's all relative!"

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