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An Infinite Number of Ancestors?
How many man and woman are needed to come to me from the year 500 AC?
the year needed
persons
25%
decrease
after
4 gen.
generation
after
30 years
-------- -------- -------- --------
1970 1 1 1
1940 2 2 2
1910 4 4 3
1880 8 8 4
1850 16 12 5
1820 32 18 6
1790 64 27 7
1760 128 *40,5=40 8
1730 256 60 9
1700 512 90 10
1670 1.024 135 11
1640 2.048 *202 12
1610 4.096 303 13
1580 8.192 *454 14
1550 16.384 681 15
1520 32.768 *1021 16
1490 65.536 *1531 17
1460 131.072 *2296 18
1430 262.144 3444 19
1400 524.288 5166 20
1370 1.048.576 7749 21
1340 2.097.152 *11623 22
1310 4.194.304 *17434 23
1280 8.388.608 34868 24
1250 16.777.216 52302 25
1220 33.554.432 78543 26
1190 67.108.864 *117679 27
1160 134.217.728 *176518 28
1130 268.435.456 264777 29
1100 536.870.912 *397165 30
1070 1.073.741.824 *595747 31
1040 2.147.483.648 *893.620 32
1010 4.294.967.296 1.340.430 33
980 8.589.934.592 2.010.645 34
950 17.179.869.184 *3.015.967 35
920 34.359.738.368 4.523.950 36
890 68.719.476.736 6.785.925 37
860 137.438.953.472 10.178.888 38
830 274.877.906.944 15.268.322 39
800 549.755.813.888 22.902.498 40
770 1.099.511.627.776 34.353.747 41
740 2.199.023.255.552 51.530.621 42
710 4.398.046.511.104 77.295.931 43
680 8.796.093.022.208 115.943.896 44
650 17.592.186.044.416 173.915.844 45
620 35.184.372.088.832 260.873.766 46
590 70.368.744.177.664 391.310.649 47
560 140.737.488.355.328 586.965.973 48
530 281.474.976.710.656 880.448.959 49
500 562.949.953.421.312 1.320.673.438 50
So may people didn't existed then.
How is it possible? Do you know the answer, mail it to:
WeikoPiebes@CS.com
Interesting answers will be written here.
Some Answers
http://genealogy.about.com/library/tips/blancestors.htm?terms=generation
Or
http://genealogy.about.com/library/tips/blancestors.htm

Genealogy Tip of the Day

Infinite Ancestors

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.


http://newton.dep.anl.gov/newton/askasci/1995/math/MATH001.HTM
An infinite number of ancestors? Cannot be
Author: unterman
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
Author: chaffer
An assumption in your analysis is that all the ancestors in your tree are distinct. That is, your great-great-great-great grandfather on your father's side is not the same person as your great-great-great-great-great grandfather on your father's side. The mathematics and the population size on earth shows that there are indeed many duplications in yours and every body else's family tree. It may be necessary to go back quite a few genera- tions to find the duplication but it WILL be there.


http://freepages.genealogy.rootsweb.com/~walkersj/surnames.htm
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.
But, a single intermarriage in the fourth geneation, may make the number of ancestors in the next, and all succeeding generations, an eighth less; while one in the third generation may reduce it a quarter. Where intermarriages occur frequently, as they generally do among families that have long been located in one neighborhood, the number of one's ancesters is lessened very materially thereby.
If we should carry our calculation back to our first parents, what an infinite number of ancestors, in that generation, we should be supposed to have had; and yet, there really would be but two of them.

*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."
(From an article stuck in the book, EARLY SETTLERS OF ESSEX AND OLD NORFOLK, ca. 1852, author unknown)


http://www.rain.org/~mkummel/stumpers/22oct99a.html
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!"