With the doubling factor, if you go back about 30 generations, you'll have more relatives than world pop. How?

Question

You have 4 grand-parents, 8 great-grand parents, etc. If it keeps doubling, after about 30 generations (about 1300 A.D.), you'll have more relatives than the population of the earth. Of course, this can't be! What is wrong with my logic?

Answer 1

As you go back, the number of individuals you directly descend from pyramids.  

For instance, you have 2 parents, 4 grandparents, 8 great grandparents,16 great great grandparents, 32 3xgreat grandparents, 64 4xgreat grandparents, 128

5 x great grandparents, 256 6xgreat grandparents. That already totals 510 individuals. I've never figured it back to 30 generations but I know it is a whole lot of people.

Answer 2

Your math is not faulty at 30 generations we have more BLANKS in our family tree than are currently living and at 31 generations we have more than have ever lived on earth.

In reality though we have duplicates in those blank spaces. Whenever there is more than one way we are related to any person on our tree that also causes all the blank spaces above them also to have duplicate persons with other spaces in our family tree.

My wife's mother married her sister's brother in law, so all of her cousins are double cousins and all of the blanks of all of her ancestors are duplicated at least once, leaving her with only half as many distinct ancestors as blanks in our family tree. Add to that both her and I are related to ancestors in more than one way. Like great aunt Tessie being related to great aunt Hepsaba, there again is a place in our pedigree where all the spots are duplicates with all of the great aunts ancestry and all of the pedigree blanks that were already duplicated twice, so quad duplicates for most of her ancestry. Now she not only has (half plus two divided by (one sixteenth plus thirty two)) as many ancestors as blanks in her pedigree. Can you see where this is going? Just a few repeats decrease the number of different people a lot.

In practice by about ten generations this duplicating factor is happening faster than the doubling factor so the reverse pyramid that was occurring has turned around into a diamond shaped mathematical model.

Answer 3

With the doubling factor, you are assuming a person's family tree is pyramid-shaped.  However, with marriage between 2nd (or even third or fourth) cousins, a person's family tree is more likely to be diamond-shaped.  Remember, before automobiles, people lived, married, and died within a relatively small geographical location.  

There's a good explanation on the Olive Tree Genealogy site, linked below.

Answer 4

Why can't that be?  About every generation , you figure that the entire world population has died and been reborn (and then some!).  And when you figure it mathematically like this, you have to remember that this is counting out to branches of the family that you are not even aware of now.  It is perfectly logical that someone could have millions of people in their extended family over the last 700 years!  You have to remember that they didn't all live a the same time!