You have two parents, four grandparents, eight great grandparents, 16 great-great-grandparents, 32 great-great-great grandparents - the numbers tend to get a little blurry if you go much further, but the idea is very simple and very familiar. Most people know the parable of the Chinese philosopher who asks the Emperor for a simple reward, one grain of rice on the first square of the chess board, two on the second, four on the third, doubling with each square until there isn't enough rice in the world to pay him. (Presumably, the Emperor then has the philosopher torn apart by wild dogs.) The same principle, and the same scale, operates with ancestors. Assuming a conservative three generations per century, around the year 1000 AD, 30 generations ago, you should have 1,073,741,824 ancestors, more than a billion. This is at least three times the entire population of the planet in 1000 AD. Where did they all go?
The answer is straightforward. The calculation assumes that none of the couples over those thirty generations was in any way related. If you marry your second cousin, your children will only have 14 great-great-grandparents, not 16, 28 great-great-greats, instead of 32, and so on. At a stroke, you will have removed more than 130 million of those notional ancestors a thousand years ago. Marry your third cousin and you lose almost 70 million putative forebears, and that still presumes that none of the intervening couples was related. If just one set of grandparents in that third-cousin marriage were also third cousins, another 4 million ancestors vanish.
In fact, the chances are that almost all of your ancestors were related to each other in some way. Uncomfortable as it is, until relatively recently, cousin marriages were the norm, not the exception.
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