One in a thousand million

It has been said that if we could search back a sufficient number of generations, we would reach a point where each of us would be able to claim more ancestors than actually lived in the world at that time. That's not quite true, but there’s a point there.

Those of us who happen to be able to trace our ancestry - or at least part of it - a long way back must have that ‘least part’ among the ancient nobility or royalty, simply because in the old days (up to the time of George III, say) few documents recorded other family trees.

So although I am lucky to be able to follow one line back through the nineteenth century to an ancestor with a ‘title’, and further back from there to medieval English royalty, and back through them to William the Conqueror - it’s no big deal.

If we reckon on 3.5 generations per century (and that may well be an underestimate), the period from William I to the present day gives us some 34 generations. Reckoning backwards, each generation will double the number of ancestors, male and female, that any of us had living at a certain time in the past. My calculator is able to accommodate ten digits, not quite enough to complete the sum, for doubling each generation 34 times gives us a grand total of eleven digits: seventeen thousand, one hundred and seventy-nine million; eight hundred and sixty-nine thousand, one hundred and eighty-four. This is the number of people alive in William’s day who were destined to be the ancestors of myself - and of course the same number (though potentially a different set) for my wife, and for each of my neighbours, and every person alive in Britain, Europe and the world today.

That’s the theory. But of course a very large number of anyone's ancestors would appear in several branches of the family tree. For instance, it is not impossible that some of William’s great-great-great-great-grandchildren (of whom there might well have been more than 100 living in the year 1300), may have been married to one another; and their great-great-great-grandchildren (of whom there may have been 3,000 - 4,000 by the time of Queen Elizabeth I) will certainly have done the same, so that by the eighteenth century their great-great-great-grandchildren might have numbered 256,000. And the same principle of inter-marriage among descendants can be applied to each of the 33 generations between William and me. So we don’t have to include the whole population of Europe after all. Many of my ancestors (and of your ancestors, and of everybody else's ancestors) will be our ancestors several times over, traceable (in theory) through dozens or hundreds of lines.

The other side of the coin is that today the number of William’s descendants (indirect, mostly, of course - that is, not in a purely uninterrupted male line) could be counted (if we could count them at all) possibly in thousands of millions. Not all in Britain, of course, but all over the world. And of course not all my ancestors - including William of Normandy - were British. I know that I have among my traceable ancestors not only Englishmen, Scots, Welsh and Irish, but Frenchmen (hence my surname), Italians, Spaniards, Eastern Europeans and Scandinavians.

Virtually all of us are mongrels, and probably the better for it.

One in a thousand million