Some interesting things come to light when you look at the math of genealogy. People know they have two parents and four grandparents. People question when you explain they have eight grandparents or even sixteen great great grandparents. But it becomes very hard to convince someone that only 20 generations ago they have 1 million grandparents! That is unbelievable:
ancestors number years ago
How can this be? There are more grandparents for one person 860 years ago (43 generations x 20 years per generation) than there were people in the world 860 years ago.
Here’s why. The table above shows a mathematical series which is correct but considers only unique values. From Wikipedia, under the definition of ancestors: Assuming that all of an individual’s ancestors are otherwise unrelated to each other, that individual has 2n ancestors in the nth generation.
For example, if we take our 10th generation (includes parents and grandparents) from the table above n=10. Two raised to the 10th power is 1024 and you can see 8x great grandparents equals 1024.
The math is right but the condition is not. People are related, so there is much overlap and the occurrences are not unique. Your great grandparents are probably not blood related. Going further back though, the possibilities increase with the number of occurences. So while the recent math is true, the older math is repeating over the same people multiple times.