A Mathematician Tries to Clear Up a Difficulty In Family Descent.
It goes without saying that a man has two parents, four grandparents, eight great grandparents, and so on, so that if we go back, say, ten generations, doubling at each stop, we have 2,048 ancestors. This sort of argument has been used by superficial genealogists to show that at the time of William the Conqueror each of us had more ancestors than the total population of England; hence we must each be descended from every Englishman of that day, including the immortal William himself.
The absurdity of this sort of reasoning has been pointed out by Professor Brooks of Johns Hopkins. His immediate object is to establish a point in the theory of evolution, but he confutes all silly genealogists at the same time. While it is true that we do have four grandparents they need not be four separate and distinct persons. First cousins have not more than three separate grandparents. If they are doubly cousins, they have but two. So in the tenth generation one's 2,048 ancestors are never 2,048 separate persons. They abound in "duplicates," so to speak, as every one knows who has tried to trace his descent, not in one line, but in all possible lines. These duplicates abound especially in small communities whose inhabitants have intermarried for years.
Besides this the lines from a given pair of ancestors tend to become extinct sooner or later, so as ancestry is traced back the probability is that all the persons living in a given community will be found to be descended, not from all, but from a very few — perhaps only one or two — of the inhabitants of the community as they were centuries ago. So, instead of having all Englishmen of the year 1000 for our ancestors, the probability is that we are descended from comparatively few of them — the number may be technically many thousands, but one individual does duty for several scores, or even several hundreds of these, the lines of ancestry converging upon him from many different directions. This is what Professor Brooks calls the "convergence of ancestry." — Exchange.
Monday, June 30, 2008