Actually, it doesn't work that way, because you are assuming that the gene pols back in the 13th century weren't mostly idsolated grouops with limited crossing.

What you *really* get is that the family tree starts getting a lot of cross-links when you get basck to the "mostly isolated grouo" period. The number of ancestors doesn't increasde and can even decrease.

The powers of 2 bit *assumes* that each generation ancestors *not* shared between branches.