The Wheat and Chessboard Problem Applied to Ancestry

Going back in your ancestry, every generational step (N) yields (in theory) a doubling of ancestors, mathematically expressed as 2^N

• N=0 : 2^0 = 1 you
• N=1 : 2^1 = 2 parents
• N=2 : 2^2 = 4 grandparents
• N=3 : 2^3 = 8 great-grandparents

..and so on.

Those familiar with the nature of the "Wheat and chessboard problem" will immediately realize that the amount of ancestors quickly spirals out of control. Let's assume for the sake of mathematical convenience that the average maternal age at birth equals 33 years,

• 330 years ago (~1690 CE) N=10 : 2^10 = 1,024 ancestors
• 660 years ago (~1360 CE) N=20 : 2^20 = 1,048,576 ancestors
• 990 years ago (~1030 CE) N=30 : 2^30 = 1,073,741,824 ancestors

So you only have to go back to the early 11th century to end up with more than a billion ancestors, which would exceed the generally estimated total world population at that time.

What can we conclude from this absurdity?

• The limitations of the gene pool means that in reality people are forced to interbreed with their (hopefully) distant relatives. The same ancestors appear multiple times in your family tree.
• The exponential growth of ancestors going back in time gives credence to the notion that "we are all related".
• With that many ancestors, and with people being more related to each other than we tend to realize, it is really no big deal to have historically noteworthy people in your family tree, be it Charlemagne or Ghengis Khan. On the contrary, it would be a very special case for someone to have no medieval aristocracy at all in their family tree.