# Ancestors and population paradox: exponential growth

If I have 2 parents, and each of them have 2 parents, each generation back has double the number of members. Thus there are 2^n members n generations ago. 10 generations ago there were about one thousand (1024) people, 20 back were 1 million, and 30 back were 1 billion.

If each generation is about 25 years, then 30 generations ago is around 750 years ago, or around 1250 AD. The entire world population is estimated to be around 300 million people around 1300 AD.

This implies that the number of people in my family tree 30 generations ago (1 billion) is larger than the number of people who existed (0.3 billion).

Does that means that I am equally likely to be descended from everyone who lived 700 years ago?

We’re all cousins!

If my wife and I have 2 kids, and they each have 2 kids, and they each have 2 kids….

My dad, a human geneticist from Honolulu, is visiting me in Seattle. He (and my mom) broke the two kids per family rule: he had five boys.