An Infinite Number of Ancestors?|
How many man and woman are needed to come to me from the year 500 AC?
How is it possible? Do you know the answer, mail it to:
Interesting answers will be written here.
Genealogy Tip of the Day
Have you ever wondered how many ancestors you have? Many new genealogists learn quickly that you start with yourself and that you have two parents, four grandparents, eight great-grandparents, and so on - the number doubling with each generation. The problem with this theory, however, is that by the time you take your family tree back 32 generations you have 8,589,934,592 ancestors - greater than the population of the world today or at any other point in history.
Is it possible that we could have more ancestors than there are people? Of course not! The error in this calculation is that it assumes that all of the ancestors in your family tree are distinct individuals, with no duplication. Yet some names appear on your pedigree more than once. Cousins have married and, if they were first cousins, their children only have six great-grandparents instead of the usual eight since their parents have two grandparents in common. This means they have a 25% decrease in the number of ancestors in the fourth generation back, and this decreased percentage will have an impact on each successive generation going back in time. Multiply that effect by the many marriages between relatives, close or distant, which likely exist in your family tree, and you can begin to see why our ancestors do not multiply to infinity.
It is estimated that as many as 80% of the marriages in history were between cousins (first, second, third, etc.). Until recent times, most of our ancestors lived in small towns and sparsely populated communities where the opportunities for marriage were somewhat limited. Consequently, consanguineous marriages were inevitable. In marriages between distant relatives, they may have even had common ancestors from different generations and not even known they were related.
The consequence of all of this math is that your pedigree, instead of getting wider as you go back (like a triangle) actually widens to a point and then begins to narrow (like a diamond) as the number of distinct ancestors decreases. This important point emphasizes the fact that we are all considerably more inter-related than we might think. You share many of your ancestors with millions of people around the world today - ancestors who were members of nationalities, cultures, ethnic groups, and religions that might surprise you.
An infinite number of ancestors? Cannot be
I have two parents, four grandparents, eight grandparents, etc. By the time I get 27 generations back, it is more than the population of the earth, yet we all go farther back than that. Please explain how my ancestor tree must narrow down instead of expanding infinitely.
Response #: 1 of 1
HOW MANY ANCESTERS DO YOU HAVE?
"Every person has two immediate parents, four ancestors in the second degree, eight in the third, and so the pedigree ascends, doubling at every step, till, in the twentieth (twenty-first*) generation, he has no fewer than 1,048,576 ancestors; and in the thirtieth, (thirty-first,*) 1,073,741,824, a number which exceeds the present population of the globe."
The above statement would be correct, provided there had been no intermarriages among a person's ancestors to the 21st and 31 generations.
*These generations are the twenty-first and thirty-first, as usually reckoned, counting the person himself the first generation, his parents the second, and so on; but they are really the twentieth and thirtieth generations of one's ancesters."
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?
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
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...
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:
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?"