Five Brothers and a War

The“Ancestor Paradox”

On one hand, it seems to be somewhat scandalous to have family members marrying other family members, even when they are not immediate family. Yet the reality is that it is impossible, from a purely mathematical perspective, for this not to happen. If everyone always has purely distinct non-related ancestors, then the mathematical equation would require a function of 2 gen , meaning that a person has two parents (2 1 ), four grandparents (2 2 ), eight great-grandparents (2 3 ), 16 great-great-grandparents (2 4 ), and so on. On the assumption that there are about 3.6 generations per century, after four centuries, a person would have 21,619 (2 14.4 ) direct ancestors. After one millennium, that number balloons to 68,719,476,736 (2 36 ) . In the time since the year 1 AD, this would require at least 47,223,664,828,696,452,136 (2 72 ) , more than 47 quintillion. On the top end, the estimate of people who have ever lived on Earth, for any lifespan, is 100 billion. The delta between that number and the number of discrete ancestors is 470 million times. In other words, all of this is mathematically impossible. Two conclusions must be true: many of our ancestors are shared, meaning they have inter-married (a lot) somewhere along the line, and everyone on Earth is in some way related. The other major issue is that people will tend not to even notice cousins whose names are even slightly different, particularly if they do not share the same surname. Most people do not even know their great-grandparents’ surnames, much less take that into account when choosing a mate, especially when growing up in a closed geographic community where the choices are very limited. The other side of the issue is that had each and every of those tens of thousands of ancestors not lived exactly as they did, and not procreated precisely when they did, none of us would be here today.

Ancestors

THEN

van Pelt

TIME

Population of the World

NOW

Five Brothers and a War

Page 120