Wednesday, 11 May 2011
Hooptedoodle #24 - Who were you in the 12th Century?
We interrupt the trilogy with a small digression - something that I've been thinking about for a day or so. Nothing scientific, I promise - just something silly to mull over.
Each of us has, or had, 2 (biological) parents, and thus 4 grandparents, 8 great-grandparents and so on. You have no choice in the matter - that's the way it works. As you go back to each previous generation, the number doubles, for obvious reasons. If we assume, as a rough-but-handy approximation, that 10 generations take about 300 years, then you should have 1024 great-great-great-great-great-great-great-great-grandparents who were alive somewhere around 1700. Go back a further 300 years and you now have over 1 million direct ancestors; go back yet another 300 years - around 1100 AD - and there are over a billion. That is mind boggling enough, but we have hardly started yet - mankind has been around for far, far longer than that.
That's OK - let's stick at the year 1100. 1 billion people required for the family. Now, as far as I can determine, our current best estimate for the total population of the Earth in 1100 AD is only 300 million. That's everyone - all races, all religions, all over the globe. Is the difference between these numbers explained entirely by various degrees of inbreeding?
My assumptions are consciously simplistic, but the principle of the thing stands up. If, as you go back through the generations, you find the odd individual who (accidentally?) occupies more than 1 slot in your upside-down family tree (and this must get more likely as the numbers increase), then a whole section of the tree above him/her disappears, since we only need him/her to be conceived once. That would get the numbers down a bit, and let us not, gentle readers, distress ourselves by dwelling on just how he/she occupies the two slots. And so on. I guess that must be it - there doesn't seem to be another explanation.