Ask A Scientist Mathematics Archive

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.