JOHN SMITH’S ANCESTORS
READER mine, wisest of mortals that you are, do you feel sure that you know how to deal with a proposition, which is at the same time unquestionable and impossible—which must be true, yet can not be true? Do you know just what degree of intellectual hospitality to give to such a proposition—whether to receive and entertain it (and if so how) or cast it from you, and how to do that? Possibly you were never consciously at bay before a proposition of that kind, and therefore lack the advantage of skill in its disposal. Attend, then, O child of mortality—consider and be wise:
You have, or have had, two parents—whom God prosper if they live and rest if dead. Each of them had two parents; in other words, you had at some time and somewhere four grandparents, and right worthy persons they were, I’ll be sworn, albeit you may not be able to name them without stopping to take thought. Of great-grandparents you surely had no fewer than eight—that is to say, no further away than three generations your ancestors numbered eight persons, now in heaven. In countries which are pleased to call themselves civilized and enlightened “a generation” means about thirty-four years. Not long ago it meant thirty-three, but improved methods of distribution, sanitation and so forth have added a year to the average duration of human life, though they have not pointed out any profitable use to make of the addition. All this amounts to saying (acceptably, I trust) that at each remove of thirty-four years back toward Adam and his time you double the number of your ancestors. Among so many some, naturally, were truly modest persons, and I don’t know that you would care to have so much said about them as I shall have to say; so, if you please, we will speak of Mr. John Smith’s instead.
John Smith, then, whom I know very well, and greatly esteem, and who is approaching middle age, had, about 34 years ago, two ancestors. About 102 years ago, say in the year of grace 1792, he had eight—though he did not have himself. You can do the rest of the figuring yourself if you care to go on and are unwilling to take my word for what follows—the astonishing state of things which I am about to thrust upon your attention. Just keep doubling the number of John Smith’s ancestors until you get the number 1,073,741,824. Now when do you suppose it was that Mr. Smith had that number of living ancestors? Make your calculation, allowing 34 years for each time that you have multiplied by two, and you will find that it was about the year 879. It seems a rather modern date and a goodish number of persons to be concerning themselves, however unconsciously, in the begetting of Neighbor John, but that is not “where it hurts.” The point is that the number of his ancestors, so far as we have gone, is about the number of the earth’s inhabitants at that date—little and big; white, black, brown, yellow and blue; males, females and girls. I do not care to point out Mr. Smith’s presumption in professing himself an Anglo-Saxon—with all that mixed blood in the veins of him; perhaps he has never made this calculation and does not know from just what stock he has the honor to have descended, though truly this distinguished scion of an illustrious race might seem to be justified in calling himself a Son of Earth.
But is he not more than that? In the generation immediately preceding the one under consideration the number of the gentleman’s ancestors must have been twice as great, namely, 2,147,483,648—more than two thousand millions, or some five hundred millions more than Earth is infested with even now. Where did all those people live?—in Mars? And to what political or other causes was due the migration to Earth, en masse, of their sons and daughters in the next generation?
Does the reader care to follow up Mr. Smith’s long illustrious line any further—back to the wee, sma’ years of the Christian era, for example? Well and good, but I warn him that geometrical progression, as he has already observed, “counts up.” Long before his calculations have reached back to the first merry Christmas he will find Mr. Smith’s ancestors—if they were really all terrestrial in their habits—piled many-deep over the entire surface of all the continents, islands and ice-floes of this distracted globe. A decent respect for the religious convictions of my countrymen forbids me even to hint at what the calculation would show if carried back to the time of Adam and Eve.
It will perhaps be observed that I have left out of consideration the circumstance that John Smith (my particular John) is not the sole living inhabitant of Earth to-day: there are others, though mostly of the same name, whose ancestors would somewhat swell the totals. In mercy to the reader I have ignored them, one man being sufficient for my purpose.
Must not John Smith have had all those ancestors? Certainly. Could all those ancestors of John Smith have existed? Certainly not. Have I not, therefore, as I promised to do, conducted the reader against “a proposition which is at the same time unquestionable and impossible”—a statement “which must be true, yet can not be true”? According to the best of my belief he is there. And there I leave him. Any gentleman not content to remain there with his face to the wall is at liberty to go over it or through it if he can. Doubtless the world will be delighted to hear him expose the fallacy of my reasoning and the falsehood of my figures. And I shall be pleased myself.
1894.