First and Last Things

I would like in a parenthetical section to expand and render rather more concrete this idea of the species as one divaricating flow of blood, by an appeal to its arithmetical aspect. I do not know if it has ever occurred to the reader to compute the number of his living ancestors at some definite date, at, let us say, the year one of the Christian era. Everyone has two parents and four grandparents, most people have eight great-grandparents, and if we ignore the possibility of intermarriage we shall go on to a fresh power of two with every generation, thus: --

Column 1: Number of generations.

Column 2: Number of ancestors.

 3 :             8 
 4 :            16 
 5 :            32 
 7 :           128 
10 :         1,024 
20 :       126,976 
30 :    15,745,024 
40 : 1,956,282,976 

I do not know whether the average age of the parent at the birth of a child under modern conditions can be determined from existing figures. There is, I should think, a strong presumption that it has been a rising age. There may have been a time in the past when most women were mothers in their early teens and bore most or all of their children before thirty, and when men had done the greater part of their procreation before thirty-five; this is still the case in many tropical climates, and I do not think I favor my case unduly by assuming that the average parent must be about, or even less than, five and twenty. This gives four generations to a century. At that rate and DISREGARDING INTERMARRIAGE OF RELATIONS the ancestors living a thousand years ago needed to account for a living person would be double the estimated population of the world. But it is obvious that if a person sprang from a marriage of first cousins, the eight ancestors of the third