[This is a back-issue of one of this site’s newsletters]
I got an interesting question by email the other day.
It was from someone who had just read my rice and chessboard page. That’s the story about a king who offered a reward to the man who had taught him the game of chess. Have a read!
Here’s the question that was asked:
I have two parents. They each had two parents, so that’s four grandparents.In turn, there were eight great-grandparents, sixteen great-great grandparents, and so on.
Fifty generations back, this means there were one quadrillion, one hundred and twenty five trillion, eight hundred and ninety nine billion, nine hundred and six million, eight hundred and forty two thousand, six hundred and twenty-four great-great-great-…-great grandparents. However, there’s never been anywhere near so many people in the world. So what happened to them all?
Fifty generations is not a long time – only about 1500-2000 years at most. The answer, you probably guessed, is some of them married their distant cousins. Or, rarely, not-so-distant.
The right way to think about this is not that you definately have eight great-grandparents, but rather that out of the multiple millions of people alive back then, there were 8 chances for each of them to be one of your great grandparents. So most people from the 19th century are not your great grandparent, because eight chances out of hundres of millions is pretty slim odds.
Go back 2000 years, though, and each person who has any descendants at all has about a quadrillion chances to have you as one. Quadrillions of chances out of mere millions is a near certainty.This means, for example, you are, almost certainly, direct descendants of (say) Julius Caesar. And so am I.
You can substititute basically any historical figure for Julius Caesar here. Either almost everyone is descended fromt hem, or nobody is.
So, think about that, have a good week, and Ave, patreulis, mathematicus te salutant!