THE DOCTRINE OF CYCLES
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by Jorge Luis Borges
Excerpt from Jorge Luis Borges Selected
Non-Fictions, Edited by Eliot Weinberger
I
This doctrine (whose most recent inventor
called it the doctrine of the Eternal
Return) may be formulated in the following manner:
The number of all the atoms that compose
the world is immense but finite,
and as such only capable of a finite (though also immense) number of
permutations.
In an infinite stretch of time, the number of possible permutations
must be run through, and the universe has to repeat itself. Once again
you will
be born from a belly, once again your skeleton will grow, once again
this same
page will reach your identical hands, once again you will follow the
course of
all the hours of your life until that of your incredible death. Such is
the customary
order of this argument, from its insipid preliminaries to its enormous
and threatening outcome. It is commonly attributed to
Nietzsche.
Before refuting it -- an undertaking of
which I do not know if I am
capable -- it may be advisable to conceive, even from afar, of the
superhuman
numbers it invokes. I shall begin with the atom. The diameter of a
hydrogen
atom has been calculated, with some margin of error, to be one hundred
millionth of a centimeter. This dizzying tininess does not mean the atom
is
indivisible; on the contrary, Rutherford describes it with the image of
a solar
system, made up of a central nucleus and a spinning electron, one
hundred
thousand times smaller than the whole atom. Let us leave this nucleus
and this electron aside, and conceive of a frugal universe composed of
ten
atoms. (This is obviously only a modest experimental universe;
invisible,
for even microscopes do not suspect it; imponderable, for no scale can
place
a value on it.) Let us postulate as well -- still in accordance with
Nietzsche's
conjecture -- that the number of possible changes in this universe is
the
number of ways in which the ten atoms can be arranged by varying the
order
in which they are placed. How many different states can this world
know before an eternal return? The investigation is simple: it suffices
to
multiply 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10, a tedious operation
that
yields the figure of 3,628,800. If an almost infinitesimal particle of
the
universe is capable of such variety, we should lend little or no faith
to
any monotony in the cosmos. I have considered ten atoms; to obtain two
grams of hydrogen, we would require more than a billion billion atoms.
To
make the computation of the possible changes in this couple of grams -- in
other words, to multiply a billion billion by each one of the whole
numbers
that precedes it -- is already an operation that far surpasses my human
patience.
I do not know if my reader is convinced;
I am not. This chaste, painless
squandering of enormous numbers undoubtedly yields the peculiar pleasure
of all excesses, but the Recurrence remains more or less Eternal, though
in the most remote terms. Nietzsche might reply: "Rutherford's spinning
electrons are a novelty for me, as is the idea -- scandalous to a
philologist -- that
an atom can be divided. However, I never denied that the vicissitudes
of matter were copious; I said only that they were not infinite." This
plausible
response from Friedrich Zarathustra obliges me to fall back on Georg
Cantor and his heroic theory of sets.
Cantor destroys the foundation of
Nietzsche's hypothesis. He asserts
the perfect infinity of the number of points in the universe, and even
in one
meter of the universe, or a fraction of that meter. The operation of
counting
is, for him, nothing else than that of comparing two series. For
example, if
the first-born sons of all the houses of Egypt were killed by the Angel,
except
for those who lived in a house that had a red mark on the door, it is
clear that as many sons were saved as there were red marks, and an
enumeration
of precisely how many of these there were does not matter. Here the
quantity is indefinite; there are other groupings in which it is
infinite. The
set of natural numbers is infinite, but it is possible to demonstrate
that,
within it, there are as many odd numbers as even.
This proof is as irreproachable as it is
banal, and is no different from
the following proof that there are as many multiples of 3018 as there
are
numbers -- without excluding from the latter set the number 3018 and its
multiples.
The same can be affirmed of its
exponential powers, however rarefied
they become as we progress.
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THE DOCTRINE OF CYCLES
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