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.