Saturday, July 16, 2011

Back to the apes

Richard Dawkins has been having a little trouble lately with feminists. He may think back with nostalgia to earlier decades when the world was marginally saner and marginally more intelligent and he was an evolutionary biologist who wrote popular books on evolutionary biology.

I was browsing through one of these older books recently, an elegant little tract entitled River out of Eden: a Darwinian view of life. The book is full of fascinating material, but let me focus here on a section showing that we are all more closely related than most people think.

"You have two parents, four grandparents, eight great-grandparents and so on. With every generation, the number of ancestors doubles. Go back g generations and the number of ancestors is 2 multiplied by itself g times: 2 to the power g. Except that, without leaving our armchair, we can quickly see that it cannot be so. To convince ourselves of this, we have only to go back a little way - say, to the time of Jesus, almost exactly two thousand years ago. If we assume, conservatively, four generations per century ... two thousand years amounts to a mere eighty generations... Two multiplied by itself 80 times is a formidable number, a 1 followed by 24 noughts, a trillion American trillion. You had a million million million million ancestors who were contemporaries of Jesus, and so did I! But the total population of the world at that time was a fraction of a negligible fraction of the number of ancestors we have just calculated.

Obviously we have gone wrong somewhere, but where? We did the calculation right. The only thing we got wrong was our assumption about doubling up in every generation. In effect, we forgot that cousins marry. I assumed that we each have eight great-grandparents. But any child of a first-cousin marriage has only six great-grandparents, because the cousins' shared grandparents are in two separate ways great-grandparents to the children. 'So what?' you may ask. People occasionally marry their cousins ... but it surely doesn't happen often enough to make a difference? Yes it does, because 'cousin' for our purposes includes second cousins, fifth cousins, sixteenth cousins and so forth. When you count cousins as distant as that, every marriage is a marriage between cousins. You sometimes hear people boasting about being a distant cousin of the Queen, but it is rather pompous of them, because we are all distant cousins of the Queen, and of everybody else, in more ways than can ever be traced."

Seeking to get one of his students to reason along these lines, Dawkins asked her "to make an educated guess as to how long ago her most recent common ancestor with me might have lived. Looking hard at my face, she unhesitatingly replied, in a slow, rural accent, 'Back to the apes.' An excusable intuitive leap, but it is approximately 10,000 percent wrong. It would suggest a separation measured in millions of years. The truth is that the most recent ancestor she and I shared would possibly have lived no more than a couple of centuries ago, probably well after William the Conqueror. Moreover, we were certainly cousins in many different ways simultaneously."

Classic Dawkins.