The mathematics of genealogy

I'm working a bit on the family tree again, with help from some expert friends. Thus far I can get Thompsons at Ballyfrench back into the 1760s, which is pretty good. It coincides with the family tradition of Thompsons arriving near Ratallagh in the mid 1700s, having come from between Kilmarnock and Troon in Scotland. But I'm doing what most people do, which is focus mainly on the strand of ancestors who passed down my surname.*

However, when you see the diagram expanding, the range of surnames increasing, and then do the maths, the number of ancestors that each of us has is mind-boggling.

I have two parents (obviously), and therefore four grandparents, and therefore eight great-grandparents, and therefore 16 g-g-grandparents. Most of them were born in the late 1880s, so that's 4 generations every 100-ish years.

But every time you go back a generation, the number doubles. 16 g-g-grandparents becomes 32 g-g-g-grandparents, which becomes 64 g-g-g-g-grandparents, which becomes 128 g-g-g-g-g-grandparents, which becomes 256 g-g-g-g-g-g-grandparents. So that's us now back another 120-ish years, to around the 1760 date mentioned above.

To leapfrog back another 120 years, to 1640, the numbers get scary: that 256 becomes 512, which becomes 1024, which becomes 2048, which becomes 4096.

So I had 4096 ancestors alive in 1640. Go back one more generation to around 1615 and it becomes 8192 ancestors. And then go back just one more, to before the magic date of 1606, and I had (theoretically, and give or take a generation or two for early mortality, or even possible longevity) 16384 ancestors on the planet.**

And, theoretically, so did you.

So, the odds of just ONE of my ancestors being on the first boats sent across from Scotland to Ulster by Hamilton & Montgomery in 1606 has got to be pretty good, eh?



* so the surname of just one line of descent is really a ridiculously limited picture.
** however, the tree does not expand endlessly, because the numbers don't tell the whole human story. Particularly in small communities, second cousins would have been marrying - in fact, some statisticians think that 80% of the marriages in world history were between second cousins. Google that for yourself!