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.
The clash between Cantor's lovely game
and Zarathustra's lovely game
is fatal to Zarathustra. If the universe consists of an infinite number
of
terms, it is rigorously capable of an infinite number of combinations --
and
the need for a Recurrence is done away with. There remains its mere
possibility,
which can be calculated as zero.
II
Nietzsche writes, in the autumn of 1883:
"This slow spider dragging itself
towards the light of the moon and that same moonlight, and you and I
whispering at the gateway, whispering of eternal things, haven't we
already
coincided in the past? And won't we happen again on the long road, on
this long tremulous road, won't we recur eternally? This was how I
spoke,
and in an ever lower voice, because my thoughts and what was beyond
my thoughts made me afraid." Writes Eudemus, a paraphraser of Aristotle,
three centuries or so before the Cross: "If the Pythagoreans are to
be believed, the same things will return at precisely their time and you
will be with me again and I will repeat this doctrine and my hand will
play with this staff, and so on." In the Stoic cosmogony, "Zeus feeds on
the world": the universe is cyclically consumed by the fire that
engendered
it, and resurges from annihilation to repeat an identical history. Once
again the diverse seminal particles combine, once again they give form
to stones, trees, and men -- and even virtues and days, since for the
Greeks
a substantive number was impossible without some corporeality. Once
again every sword and every hero, once again every minutious night of
insomnia.
Like the other conjectures of the school
of the Porch, that of a general
repetition spread across time entered the Gospels (Acts of the Apostles
3:21), along with its technical name, apokatastasis, though with
indeterminate
intent. Book XII of St. Augustine's Civitas Dei dedicates several
chapters
to the refutation of so abominable a doctrine. Those chapters (which I
have before me now) are far too intricate for summary, but their
author's
episcopal fury seems to fix upon two arguments: one, the gaudy futility
of
this wheel; the other, the ridiculousness of the Logos dying on the
cross like
an acrobat in an interminable sequence of performances. Farewells and
suicides
lose their dignity if repeated too often; St. Augustine must have
thought the same of the Crucifixion. Hence his scandalized rejection of
the
viewpoint of the Stoics and Pythagoreans, who argued that God's science
cannot understand infinite things and that the eternal rotation of the
world's process serves to allow God to learn more and familiarize
Himself
with it. St. Augustine mocks their worthless revolutions and affirms
that Jesus
is the straight path that allows us to flee from the circular labyrinth
of
such deceptions.
In the chapter of his Logic that
addresses the law of causality, John Stuart
Mill maintains that a periodic repetition of history is conceivable --
but
not true -- and cites Virgil's "Messianic eclogue":
Can Nietzsche, the Hellenist, have been
ignorant of these "precursors"?
Was Nietzsche, author of the fragments on the pre-Socratics, perhaps
unaware
of a doctrine learned by the disciples of Pythagoras?' This is hard to
believe -- and futile. True, Nietzsche has indicated, in a
memorable page, the
precise spot on which the idea of the Eternal Return visited him: a path
in
the woods of Silvaplana, near a vast pyramidal block, one midday in
August
1881 -- "six thousand feet beyond men and time." True, this instant is
one of
Nietzsche's great distinctions. "Immortal the instant in which I
engendered
the eternal recurrence. For that instant I endure the Recurrence," were
the
words he would leave (Unschuld des Werdens II, 1308). Yet, in my
opinion,
we need not postulate a startling ignorance, nor a human, all too human,
confusion between inspiration and memory, nor a crime of vanity. My key
to this mystery is grammatical, almost syntactical. Nietzsche knew that
the
Eternal Recourse is one of the fables, fears, diversions, that eternally
recur,
but he also knew that the most effective of the grammatical persons is
the
first. Indeed, we would be justified in saying that, for a prophet, the
only
grammatical person is the first. It was not possible for Zarathustra to
derive
his revelation from a philosophical compendium or from the Historia
philosophiae graeco-romanae of the surrogate professors Ritter and
Preller,
for reasons of voice and anachronism, not to speak of typography. The
prophetic style does not allow for the use of quotation marks nor the
erudite
attestation of books and authors ....
If my human flesh can assimilate the
brute flesh of a sheep, who can
prevent the human mind from assimilating human mental states? Because
he rethought it at great length, and endured it, the eternal recurrence
of
things is now Nietzsche's and does not belong to some dead man who is
barely more than a Greek name. I will not insist; Miguel de Unamuno
already
has his page on the adoption of thoughts.
Nietzsche wanted men who were capable of
enduring immortality. I say
this in words that appear in his personal notebooks, the Nachlass,
where he
also inscribed these others: "If you envision a long peace before you
are reborn,
I swear to you that you are thinking wrongly. Between the final
instant of consciousness and the first gleam of a new life there is 'no
time' --
the lapse lasts as long as a bolt of lightning, though billions of years
are insufficient
to measure it. If a self is absent, infinity can be the equivalent of
succession."
Before Nietzsche, personal immortality
was no more than a blundering
hope, a hazy plan. Nietzsche postulates it as a duty and gives it all
the
ghastly lucidity of insomnia. "Waking, by reason of their continual
cares,
fears, sorrows, dry brains," (I read in Robert Burton's antique
treatise) "is a
symptom that much crucifies melancholy men." We are told that Nietzsche
endured this crucifixion and had to seek deliverance in the bitterness
of
chloral hydrate. Nietzsche wanted to be Walt Whitman; he wanted to fall
minutely in love with his destiny. He adopted a heroic method: he
disinterred
the intolerable Greek hypothesis of eternal repetition, and he contrived
to make this mental nightmare an occasion for jubilation. He sought
out the most horrible idea in the universe and offered it up to
mankind's
delectation. The languid optimist often imagines himself to be a Nietzschean;
Nietzsche confronts him with the circles of the eternal recurrence
and spits him out of his mouth.
Nietzsche wrote: "Not to yearn for
distant ventures and favors and
blessings, but to live in such a way that we wish to come back and live
again,
and so on throughout eternity." Mauthner objects that to attribute the
slightest moral, in other words practical, influence to the hypothesis
of eternal
return is to negate the hypothesis -- since it is comparable to
imagining
that something can happen in another way. Nietzsche would answer that
the formulation of the eternal return and its extensive moral (in other
words, practical) influence and Mauthner's cavils and his refutation of
Mauthner's cavils are naught but a few more necessary moments in the
history
of the world, the work of atomic agitations. He could, with reason,
repeat
the words he had already written: "It suffices that the doctrine of
circular repetition be probable or possible. The image of a mere
possibility
can shatter and remake us. How much has been accomplished by the
possibility
of eternal damnation!" And in another passage: "The instant that this
idea presents itself, all colors are different -- and there is another
history."
III
At one time or another, the sensation of
"having lived this moment already"
has left us all pensive. Partisans of the eternal recurrence swear to us
that it
is so and investigate a possible corroboration of their faith in these
perplexed
states of mind. They forget that memory would import a novelty
that negates the hypothesis, and that time would gradually perfect that
memory until the distant heaven in which the individual now foresees his
destiny and prefers to act in another way. ... In any case, Nietzsche
never
spoke of a mnemonic confirmation of the Recurrence. [2]
Nor -- and this deserves to be emphasized
as well -- did he speak of the
finiteness of atoms. Nietzsche negates the atom; atomic theory seemed to
him nothing but a model of the world made exclusively for the eyes and
the
mathematical mind .... To ground his hypothesis, he spoke of a limited
force, evolving in infinite time, but incapable of an unlimited number
of
variations. His procedure was not without perfidy: first he sets us on
guard
against the idea of an infinite force -- "let us beware such orgies of
thought!" --
and then he generously concedes that time is infinite. Similarly, it
pleases
him to fall back on the Prior Eternity. For example: an equilibrium of
cosmic
forces is impossible, since if it were not it would already have
occurred
in the Prior Eternity. Or: universal history has happened an infinite
number
of times -- in the Prior Eternity. The invocation seems valid, but it
should be
repeated that this Prior Eternity (or aeternitas a parte ante, as
the theologians
would call it) is nothing but our natural incapacity to conceive of a
beginning to time. We suffer the same incapacity where space is
concerned,
so that invoking a Prior Eternity is as decisive as invoking the
Infinity To My
Right. In other words, if time is infinite to our intuition, so is
space. This
Prior Eternity has nothing to do with the real time that has elapsed; we
go
back to the first second and note that it requires a predecessor, and
that that
predecessor requires one as well, and so on infinitely. To close off
this regressus
in infinitum [regression into infinity], St. Augustine declares that
the
first second of time coincides with the first second of the Creation:
"non in
tempore sed cum tempore incepit creatio" [The Creation begins not in
time
but with time].
Nietzsche appeals to, energy; the second
law of thermodynamics declares
that some energetic processes are irreversible. Heat and light are no
more than forms of energy. It suffices to project a light onto a black
surface
to convert it into heat. Heat, however, will never return to the form of
light.
This inoffensive or insipid-seeming proof annuls the "circular
labyrinth" of
the Eternal Return.
The first law of thermodynamics declares
that the energy of the universe
is constant; the second, that this energy tends toward isolation and
disorder, though its total quantity does not decrease. This gradual
disintegration
of the forces that make up the universe is entropy. Once maximum
entropy is reached, once different temperatures have been equalized,
once
any action of one body on another has been neutralized (or compensated
for), the world will be a random assemblage of atoms. In the deep center
of
the stars, this difficult, mortal equilibrium has been achieved. By dint
of
constant interchange, the whole universe will reach it, and will be warm
and
dead.
Light is gradually lost in the form of
heat; the universe, minute by
minute, is becoming invisible. It grows more inconstant, as well. At
some
point, it will no longer be anything but heat: an equilibrium of
immobile,
evenly distributed heat. Then it will have died.
A final uncertainty, this one of a
metaphysical order. If Zarathustra's hypothesis
is accepted, I do not fully understand how two identical processes
keep from agglomerating into one. Is mere succession, verified by no
one,
enough? Without a special archangel to keep track, what does it mean
that
we are going through the thirteen thousand five hundred and fourteenth
cycle and not the first in the series or number three hundred twenty-two
to
the two thousandth power? Nothing, in practice -- which is no impairment
to the thinker. Nothing, for the intellect -- which is serious indeed.
[1936]
Among the books consulted for the
foregoing article, I must make mention of the
following:
Die Unschuld des Werdens von Friedrich
Nietzsche. Leipzig, 1931.
Also sprach Zaarathustra von Friedrich Nietzsche. Leipzig, 1892.
Introduction to Mathematical Philosophy by Bertrand Russell. London,
1919.
The ABC of Atoms by Bertrand Russell. London, 1927.
The Nature of the Physical World by A. S. Eddington. London, 1928.
Die Philosophie der Griechen von Dr. Paul Deussen. Leipzig, 1919.
Worterbuch der Philosophie van Fritz Mauthner. Leipzig, 1923.
La ciudad de Dios par San Agustin. Version de Diaz de Beyral. Madrid,
1922.
_______________
Notes:
1. This perplexity is futile. Nietzsche,
in 1874, jeered at the Pythagorean thesis that history
repeats itself cyclically (Vom Nutzen und Nachteil der Historie).
(Note added in 1953.)
2. Of this apparent confirmation, Nestor
Ibarra writes: "It also happens that some
new perception strikes us as a memory, and we believe we recognize
objects or accidents
that we are nevertheless sure of meeting for the first time. I imagine
that this
must have to do with a curious operation of our memory. An initial
perception, any
perception, takes place, but beneath the threshold of consciousness.
An instant later, the
stimulus acts, but this time we receive it in our conscious mind.
Our memory comes
into play and offers us the feeling of deja vu, but situates the
recollection wrongly. To
justify its weakness and its disturbing quality, we imagine that a
considerable amount
of time has passed, or we may even send it further, into the repetition
of some former
life. In reality it is an immediate past, and the abyss that separates
us from it is that of
Our own distraction."
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THE DOCTRINE OF CYCLES
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