Cyfrowa Etnografia

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Part of Why Is It the Way it Is? / Polska Sztuka Ludowa - Konteksty 2014 Special Issue

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ust a minute! Can everything be mathematised?
Does there exist in the world something that could
not become the object of mathematical theory?1

J

A math movie?
Just a single letter “n” -probably the shortest ti­
tle in the history of the cinema. A t the same time,
rather perverse and ambiguous: we know that apart
from being a particle of one of the natural languages
this letter from the Greek alphabet is also a cryptonym
of a certain number significant in mathematics. Basi­
cally, therefore, the title-letter proves to be actually
a title-number. In addition, it is a strange and mys­
terious number. That last circumstance could prove
to be even more curious. We remember from elemen­
tary school mathematics that n describes the ratio of a
circle’s circumference to its diameter, is constant, and
- in an approximation needed for the purpose of cal­
culations - totals 3,14. What is so extraordinary about
this? For those whose mathematical knowledge does
not exceed the elementary level (and be honest - that
means for the majority of us) the answer is: probably
nothing.
For mathematicians, however, n, once also known
as the Ludolphian number,2 does not cease being puz­
zling and disturbing, and remains a challenge for the
inquisitive analytical mind. It turns out that its expan­
sion after the comma is not a recurring decimal; in
other words, no constant regularities can be observed
in its course. Although it pertains to definite objects
the number n is indefinite. It is also irrational. Despite
the fact that with the assistance of the computer bil­
lions of numbers after the decimal comma have al­
ready been identified,3 a complete and finitely closed
sequence is still missing. So far, everything seems to
indicate that it is uncountable. The sequence of num­
bers after the decimal comma is infinitely open: writ­
ing down all those numbers would take up an eterni­
ty.4 Putting it succinctly: due to its very essence n aims
at infinity.
For science n does not cease being an enigma. A l­
though it appears to be a purely human construct it
is regarded as a number from beyond human order.
The biologist Darryl Rainey drew attention to the
amazing affiliation between mythological imagery and
mathematical intuition indicating the relations of the
circle as a basic figure in the mythologies of assorted
cultures and the mysterious value of n. The number
3,1415926... is infinite, and in mathematics consti­
tutes the so-called value n, the ratio of a circle’s cir­
cumference to its diameter. Looking at a circle we see
one of the most constant values in mathematics. We
may ask whether it is an accident that the circle is a
symbol regarded in the myths of numerous cultures as
the most magnificent and impeccable. Carl Jung was
of the opinion that the mandala (Sanskrit for circle,
303

DARIUSZ

CZAJA

Cipher and Epiphany.
Several Remarks on n

hence the motifs containing this scheme) is the most
important religious symbol of mankind. Whenever the
inner eye looks at a circle, e.g. a mandala, and gains
the impression of perfection, then it sees the infinite
number 3,1415926..., albeit from another level. It is
quite possible that we correctly describe such numbers
as transcendental.5 Therefore, n contains the idea of
perfection and completeness and carries the promise of
transcending beyond the finite, temporal dimension.
Within the context of such statements it becomes less
surprising that scholars decided to establish contact
with extra-human intelligence, and in the hope of
coming across a non-terrestrial civilisation transmit
into space numbers of the decimal expansion of n.6 A p­
parently, n evades simple assignments and is situated
somewhere along the border between “hard” science
and quests that we are in the habit of describing as
“paranormal”. From the cultural point of view its pres­
ence in both domains is important. There can be no
doubt that our ordinary schoolroom: “three/fourteen
hundred and sixteen” possesses a secret profoundness
and an almost hypnotically powerful impact.
Regardless, therefore, of its purely mathemati­
cal parameters the number n has attained a certain
autonomous value in contemporary symbolic space.
The same thing happened to it as to Einstein’s famous
equation: E = mc2, whose mythological value was bril­
liantly disclosed by Roland Barthes. Both the brain of
the creative physicist and his immortal product were
rapidly inserted in the old esoteric image of science.
The equation gained the status of a magic spell open­
ing the door to the Sesame of wisdom: There is a single
secret to the world, and the secret is held in one word; the
universe is a safe of which humanity seeks the combina­
tion: Einstein almost found it, this is the myth of Einstein.
In it, we find all the Gnostic themes: the unity of nature,
the ideal possibility of a fundamental reduction of world,
the unfastening power of the world, the age-old struggle be­
tween a secret and an utterance, the idea that total knowl­
edge can only be discovered all at once, like a lock which
suddenly opens after a thousand unsuccessful attempts.

D ariusz C zaja • CIPHER AND EPIPHANY. SEVERAL REMARKS ON

The historic equation E =m c2 by its unexpected simplicity,
almost embodies the pure idea of the key - bare linear,
made of one metal, opening with a wholly magical ease a
door which had resisted the desperate efforts of centuries .7
Somewhat similarly to Einstein’s equation the mysteri­
ous and unsolvable n functions at present as a sign of
something more than a purely digital characteristic. It
offers a tempting promise of breaking the code of “vis­
ible and invisible things” and of solving the mystery
of existence. This key seems to be even simpler and
less sophisticated than Einstein’s equation: it suffices
to merely discover certain regularity in the decimal ex­
pansion of n and we shall attain the threshold of the
secret. The cultural significance of “3,14” bypasses the
whole complication and finesse of mathematical cal­
culations and has been as if added “above” the number
itself. Unclear and puzzling, surrounded with a certain
emotional aura, it became one of the recognisable
numbers of contemporary anthology. In one of his
interviews Darren Aronofsky admitted: n has always
fascinated me as a number. It’s a really wild concept.8 His
film consciously refers to numerical mythology.
A t the very onset let us exclude a certain misun­
derstanding that could emerge in the course of watch­
ing the film. Despite distinct cognitive ambitions and
certain necessarily abbreviated references to numbers
and mathematical searches this is no “math film”, as
film critics sometimes describe it, that would aspire to
compete with mathematics taught at university. To
put it in plain terms: the film might be quite boring
and obvious for the average student of mathemat­
ics just as it could prove to be boring and obvious for
every person with an even average knowledge of the
secrets of Cabbalistic gematria. It is difficult to believe
that such persons would regard information about the
existence of the Fibonacci sequence or an elementary
presentation of the principles of gematric correspon­
dence as discoveries. One can, however, assume - and
this is not an excessively light-hearted premise - that
the percentage of mathematicians and Cabbalists in
each population is not very high and, consequently,
relatively low among the film audience. Aronofsky
certainly did not produce his film with them in mind.
The recipients are aptly described by the authors of
an excellent book on the construction of computa­
tional complexity: the majority of people with at least
elementary scientific training disclose an astonishing
belief in the power of mathematics, envisaged as a tool
that makes it possible to calculate the very essence of
reality. One and one are two regardless whether we
add ounces of flour or gunshots. The ratio of a circle’s
circumference to its diameter is a mathematical con­
stant and the magical number n (3,1315...). 9 The film
refers to precisely such a state of common conscious­
ness. It is not a presentation of mathematics intended
for mathematicians (just imagine such a plot!) but of
304

mathematics in a simplified dimension, a popular vi­
sion.
Aronofsky is perfectly well aware of the fact that
the presented level of mathematical knowledge is
rather unsophisticated: It’s pop math, really, everyone
bought Chaos, that chaos book that everyone got stuck
on the first three pages and then it became a doorstop or
something. That’s what the film is. It’s like the first three
pages of those cool math books.10 A brief and, of neces­
sity, superficial introduction to the world of numbers
and Cabalistic calculations - remember that the cin­
ema cannot stand lectures - is composed of merely
slogans, call signs of the problems announced in the
film. This is the beginning of a thread that we can fol­
low in order to reach the heart of the story. Aronofsky
does not resolve mathematical equations but uses an
analytical probe to examine the state of contemporary
awareness. That is his real theme.
The début film contains a distinctive stylistic sig­
nature. The rather simple story about an accomplished
Jewish mathematician is told brilliantly. Aronofsky in­
scribes serious reflections about the condition of con­
temporaneity into a rather trivial scheme of an ordi­
nary thriller. Nonetheless, he does so with enormous
virtuosity. The convention of a thriller is treated with
a certain distance and we are actually dealing more
with a pastiche. What sort of a thriller is this in which
a dubious Wall Street gang wishes to win the coop­
eration of a famous mathematician, and in which the
thrills are produced at best by his periodic migraines?
And yet the film adheres to the elementary determi­
nants of the genre. The selection of such a convention
and style of telling a story is, on the one hand, a film
homage paid to the cinema of genres and, on the other
hand, a vehicle that is only to tempt the spectator.
Aronofsky’s ascetic and formally disciplined film
builds an extremely evocative world of madness and
hallucination. Numerous cuts produce an impressive
and violent image capturing the senses and inten­
sively penetrating the mind. Maintained consistently
in a kaleidoscopic, uneven rhythm it matches ideally
the progressing insanity of a brilliant mind, a process
occurring right in front of us. The spectator is instant­
ly compelled to examine reality through the eyes of
a madman whose desperate and fragmented mind is
vividly visualised by the frames of the depicted world,
sometimes blurred and “upside down”. If this is expressionistic poetics, and numerous stylistic elements indi­
cate that this is the case, then it should be described
more accurately as “hysterical expressionism”.
This is a claustrophobic world, cramped and tightly
clamping the protagonist’s head in the manner of a
steel band. The black-and-white tape and the sound
track recalling indistinctly articulated industrial mur­
murs, clusters and sequences reinforce the impression of
alienness, the unreal quality of the portrayed reality.

D ariusz C zaja • CIPHER AND EPIPHANY. SEVERAL REMARKS ON

New York in n is a space of alienation and fear. To­
tally different from the warm and nostalgic New York
in Allen’s Manhattan, it is filmed as a city-Moloch
without any of its emblematic buildings but with unat­
tractive streets and empty, suspicious looking subway
passages. In contrast to Auster’s Brooklyn Boogie with
a local community of residents sharing daily, mun­
dane problems we are shown a community devoid of
all bonds; each person lives on his own and for him­
self, each takes part in an isolated world of nomadic
beings. This is a gloomy, dark, and cold world. Or, in
reference to the film’s Cabbalistic motif, it is a world
of broken vessels, a distant echo of shevirat ha-kelim,
remote but maintaining a connection with its source.

All is number
Now, return to numbers, that astonishing cosmos
of beings with a curious ontology. on ly habit forces
us to seek knowledge about the nature of contempo­
raneity in books written by researchers specialising in
culture. After all, they too - whether they know it or
not - are in the grasp of a paradigm, which they try to
describe and analyse. Contrary to the meta-descrip­
tive character of science they do not succeed in per­
forming the Baron Munchhausen trick all that often.
Sometimes, intuition preceding the findings of those
who deal with culture professionally is preceded by lit­
erature. In Bohumil Hrabal’s excellent autobiographi­
cal essay the enthralling motif of the number appears
upon several occasions.11
Hrabal’s intuition reactivates daily reality but also
places it in another light. We live in a world composed
of numbers. Every day we move in space peopled with
numbers. The hypertrophy of numbers each step of
the way, almost everywhere, is so great that we almost
fail to notice this fact and accept it as “natural” and as
something that does not require reflection. Everything
is weighed, measured, counted, as if contemporary cul­
ture had written its (ill-bidding?) Mane, Tekel, Fares...
in all possible places and with multiplied effort.
What are these numbers? What is their nature?
What does it mean: “our epoch is expressed only in
numbers”? Had we, unconsciously, returned to old Py­
thagorean intuitions according to which the world is a
number and can be described and comprehended via
numerical relations?
The writings of Pythagoras of Samos are non-ex­
tant and their content is known only from secondary
sources. Therefore, recall the concise and apt charac­
teristic of Pythagorean ideas contained in Aristotle’s
Metaphysics: The so-called Pythagoreans, who were the
first to take up mathematics, not only advanced this study,
but also having been brought up in it they thought its prin­
ciples were the principles of all things. Since of these prin­
ciples numbers are by nature the first, and in numbers they
seemed to see many resemblances to the things that exist
305

and come into being-more than in fire and earth and water
(such and such a modification of numbers being justice,
another being soul and reason, another being opportunity
and similarly almost all other things being numerically
expressible); since, again, they saw that the modifications
and the ratios of the musical scales were expressible in
numbers; since, then, all other things seemed in their whole
nature to be modeled on numbers, and numbers seemed to
be the first things in the whole of nature, they supposed the
elements of numbers to be the elements of all things, and
the whole heaven to be a musical scale and a number. And
all the properties of numbers and scales which they could
show to agree with the attributes and parts and the whole
arrangement of the heavens, they collected and fitted into
their scheme; and if there was a gap anywhere, they readily
made additions so as to make their whole theory coherent
(I, 985 b and sqq.).
In other words, Pythagoras and his followers regard­
ed the number as sacred (to mention perfect numbers
or tetraktys) and as a tangible confirmation of the won­
der of the divine-human world. In the spirit of the two
halves of the Greek symbolon it was a keystone linking
two realities. The Pythagorean maxim: all is number
meant that the number was conceived as the begin­
ning and the end, the pre-foundation, the arche of the
whole comprehensible reality. In this magical-religious
conception the cosmos of numbers created, slightly in
the manner of Platonic paradeigmata, a world of ideal
pre-models. The number makes possible cognition
and leads to the discovery of the truth of reality. The
condition for learning anything from existing things is
pre-established harmony, the model of measure and
proportion. Harmony is the source of the organisation
of the world since we can become familiar only with
that, which is orderly.
Hrabal’s enumeration seems to suggest that the re­
ality in which we live is Pythagorean, albeit à rebours.
In daily experience the number fulfils only pragmatic,
orientating functions. More, it conceals the truth of
the thing despite the fact that according to the inten­
tions of the collective, anonymous author, numerically
marking all and everyone, the number was supposed to
cast light on truth and accentuate and confirm it with
an undisputed mathematical certificate. The number
often becomes the name of a thing, its variable re­
placement (not to mention people-numbers from the
horrific past of concentration camps). Those numbers
from our daily life offer a semblance of precision, a
commonplace equivalent of a scientific interpreta­
tion of the world. The aphorism created by common
sense about the existence of small lies, big lies, and
statistics corroborates this obvious fact by means of its
curious gradation. The world of everyday experience
is a world of numerical illusion. It creates a vast space
built of numbers, a monstrous - in both meanings of
that word - simulacrum. To put it more explicitly: it is

D ariusz C zaja • CIPHER AND EPIPHANY. SEVERAL REMARKS ON

an unintentional joke about the eternal claims to pre­
cise reasoning made by mathematics and the desire to
offer a true description of reality. The daily world full
of digital references is a perverse variant of Pythagoreanism. True, we “actually” live in an anti-Pythagorean
world. For us a number deprived of all sacral references
fulfils the function of merely an ordinary identifier. It
is a firm scaffold supporting elementary orientation in
the world, without which life appears to be impossible.
After all, it would be difficult to say that behind those
orientation indices there stands some sort of cosmic
harmony that binds all and everyone. The numerical
world plays rather the role of a protective umbrella
and is one of the means that tame the unknown and
provide an illusion of controlling things.
Heidegger accused contemporary science of a simi­
lar attitude. Science, he claimed, does not think, but
calculates. The effect of such an approach is a purely
subjectivising attitude towards things. Nature and his­
tory become the objects of a representing that explains.12
He who counts and subjectivises being seeks predomi­
nantly certainty.
Heidegger also drew attention to the fact that to­
day the essence of the material is defined primarily by
numbers. Meanwhile, the Greek ta mathemata origi­
nally denoted that, which is known a priori to a person
co-existing with things, i.e. the corporeality of bodies
or the plant-like character of plants. The same holds
true for numbers. Discovering three apples on a table
we know that there are three of them because we al­
ready knew the number three, “tertiary nature”. It is
precisely in this non-quantifying sense that it is math­
ematical. Contrary to school routines mathematics
does not find fulfilment in the vulgar gesture of count­
ing and calculating: Mathematics is mathematisation, to
paraphrase Heidegger’s celebrated: die Sprache spricht.
It is thus both the conception and the birth of something
essential (i.e. beings) “produced” by mankind and at the
same time viewed and contemplated. It is theory, theorein
—creative imagination.13 Let it be stressed clearly: in its
innermost, spiritually comprehended act mathematics
is essentially contemplation.

The mad geometrician
Max Cohen, a brilliant Jewish mathematician, is
obsessed with the world of numbers. He concentrates
his entire life on studying numerical functions and
finds fulfilment in mathematical calculations. Con­
sumed by this preoccupation, he spends whole days in
front of his super-computer in the hope of discovering
a secret sequence of numbers describing the order of
the world. Apparently, the old Pythagorean intuitions
have found in him a brilliant performer. Cohen un­
doubtedly displays a reverent attitude towards num­
bers and their explanatory properties. The point of
departure of the celebrated syllogism consists of three
306

premises: 1. Mathematics is the language of Nature,
2. The world can be presented and comprehended
with the assistance of numbers, 3. Diagrams of system
numbers reveal regularities. The conclusion is as fol­
lows: Nature is the domain of regularities. Evidence
for their existence can assume the form of a number
of phenomena whose occurrence seems not to be sub­
jected to any regularities: recurring disease epidemics,
the wax and wane of caribou populations, sunspot cy­
cles or the rise and fall of the Nile. In each of those
natural phenomena, at first glance chaotic and with­
out any conspicuous order, it is possible to trace peri­
odic repetitions.
Cohen discerns regularities in almost all natural
phenomena and the arts. In this respect, detailed
proof is supplied by the intriguing presence of phe­
nomena from assorted orders, numbers from the socalled Fibonacci sequence (1, 2, 3, 5, 8 , 13... etc., each
successive number being the sum of the two previous
ones). Fibonacci numbers actually occur universally
in Nature: leafs on branches grow at intervals, whose
relations correspond approximately to the relations of
Fibonacci numbers. Numerous flowers have a perma­
nent number of petals: lilies - three, buttercups - five,
calendulas - 13, asters - 21, etc., with all numbers be­
longing to the above-mentioned sequence. Sunflower
seeds are arranged in the shape of spirals: as a rule,
there are 34 dextrorotary spirals and 55 laevorotary
ones, and both numbers come from the Fibonacci se­
quence. More: the quotients of two adjoining numbers
from the same sequence (e.g. 144:133) consistently
approach the golden ratio coefficient to be found in
numerous examples of architecture (the Parthenon,
the Pyramid of Giza); the golden ratio was applied by
Leonardo ... It is simply impossible not to assume that
numbers or, more exactly, certain particular numeri­
cal sequences govern the world.
Cohen becomes intrigued by the question whether
stock market predictions are not subjected to identical
dependencies that can be calculated. A world order, if
it exists, must reveal itself not only in Nature but also
in the world of human activity. After all, if one takes
a closer look at the stock market it becomes appar­
ent that it too is some sort of an organism. Just like a
natural organism it is subjected to the law of growth
and necrosis, and incessantly changes. The fact that
it is a permanently living network legitimises a new
hypothesis: the stock market is governed by a certain
pattern concealed by numbers, a constant algorithm
that has to be deciphered. Cohen embarks upon
countless attempts to discover a numerical sequence
describing the chaos of stock market oscillations of
the prices of stocks and shares. The unearthing of this
magic formula would mean not only comprehension of
the present-day state of things but also the possibility
of predicting future results on the stock market. The

D ariusz C zaja • CIPHER AND EPIPHANY. SEVERAL REMARKS ON

goal appears to be quite close but Cohen’s computer
does not tolerate the calculation overload. The row of
numbers appearing on the screen a moment prior to
the collapse seems to be accidental. The printout with
an incomprehensible sequence of slightly more than
200 numbers lands in a wastepaper basket.
Cohen’s innovative works on statistics written
during his early youth become universally known. His
mathematical talents are so valuable that he unex­
pectedly becomes the object of interest of two entirely
different milieus. He is pursued by analysts from a
forecast office at the New York stock market and by a
certain rather suspicious character named Lenny Mey­
er, who turns out to be an envoy of a Chassidic sect.
Meyer presents the elementary principles of Hebrew
gematry, according to which each letter corresponds
to a certain numerical value. He cites the example of
the Hebrew version of “The Garden of Eden”, which
in a numerical transcription totals 144, and “The Tree
of the Knowledge of Good and Evil” - a total of 233.
In passing, Cohen notices that these are numbers from
the Fibonacci sequence. Meyer likens the Torah to a
cipher given by God, a holy writ with an unclear mes­
sage that calls for exegesis. The Torah also contains
the Name of God composed of 216 numbers but, un­
fortunately, the key to it had been lost. The situation
becomes complicated and it appears that there is no
return. Cohen starts to assume that there exists a sin­
gle regularity governing reality as a whole. It could be
applied not only in the case of the stock market but
also to describe an essential characteristic and, finally,
as a numerical cryptonym of God’s name. He does not
heed the warnings of his mentor - you will start to see
numbers in everything and as soon as you discard scientific
rigor, you’re no longer a mathematician, you’re a numerologist - and becomes immersed in his obsession with
numbers, imagining that he is a mere few steps away
from discovering the contemporary Holy Grail. Insan­
ity is close.
For the Cohen dramatis persona Aronofsky applied
a certain essential Faustian motif: insatiable desire
for knowledge. But is Max Cohen simply a presentday Faust? Undoubtedly, his story contains distinct
echoes of the Faustian myth.14 Apparently, Cohen’s
Faustian traits constitute an interpretation trail not so
much misleading as unaware of what is most sympto­
matic in this character. We are tempted to perceive
the brilliant mathematician through the prism of the
land surveyor from Kafka’s The Castle, who resembles
him in many respects. The heart of the matter is not
merely a simple directive that could guide us to such
a trail: after all, Cohen’s computer is named “Euclid”
after the great legislator of geometry. There are also
more important reasons: Cohen is not concerned with
knowledge conceived as the growth of information. He
wants to introduce order into reality, to capture it in
307

numerical parameters, to describe it with a digital se­
quence. In an excellent exegesis of The Castle Walter
Hilsbecher, who perceives this novel predominantly as
a drama of an impatient mind, describes the meaning
of the work performed by K: His profession consists of
introducing order into that, which is disorderly, of measur­
ing and dividing land and metaphorically: in the introduc­
tion into the uncertainty of being a particle of certitude, a
guarantee of order, of granting structure to that, which is
distant from structural order, and contours to that which
is deprived of them, human contours comprehended in the
manner of men and accessible to man.15 Their prime aim
is also similar - here the homonym of the Polish word:
zamek proves to be helpful - to open a lock (zamek),
i.e. to decode, and to capture a castle (zamek)...
Both experience their profession as a calling of
sorts. Cohen seems to be chosen by the very fact of
possessing a brilliant mind, a feature that gradually
intensifies. The longer he works on discovering nu­
merical regularities the stronger the feeling of a voca­
tion (in a discussion held with a rabbi he shouts: The
number is nothing. It’s the meaning. The syntax. It’s what’s
between the numbers. You haven’t understood it. It’s be­
cause it’s not for you. I’ve got it. I’ve got it! I understand it.
I’m gonna see it. Rabbi, I was chosen. The characteristic
of K is similar: He is a land surveyor. Nothing indicates
that he would ever resign from the right to measure land,
to carry out his profession, to fulfil his vocation (in a dual
sense: also in the one stemming from the fact that the castle
‘called’ him). He is a man whose calling is to measure the
unmeasurable even though it would prove impossible to be
measured. It is precisely the unmeasurable that calls him
and tempting him evades him —just like the castle.16
Hilsbecher proposed an extremely original inter­
pretation of the meaning of Kafka’s castle, the object
of the land surveyor’s admiration: The castle is the cen­
tre, the inaccessible stronghold of the irrational, which chal­
lenges ratio and evades it, the principal and contemnor of
ratio, an extraordinary reality (judging by the effects) and
mirage. The key to its secret remains unapproachable and
the battle is waged in the forefield.17 It would be difficult
to seek a more adequate description of the sense and
goal of Cohen’s hopeless quest. Similarly, a characteris­
tic of the surveyor’s personality is an adequate portrait
of the behaviour of Max Cohen: K. is a man who takes
things to heart. Since he frets about life his very existence
becomes a heavy burden. He suffers because of existence,
its non-transparency and irrationality, although it is precisely
the immeasurability of being that should be a cause for merri­
ment. This is not to say that he should resign from his attempt
at rationalising: this is his calling. But he treats it much too
seriously and devotes all his zeal, causing him to be suspected
of impatience. Impatience is one of the cardinal sins.18
Hilsbecher aptly extracted K’s deadly sin: impa­
tience. By introducing into his remarks the aphorism
formulated by Kafka in Reflections on Sin, Suffering,

D ariusz C zaja • CIPHER AND EPIPHANY. SEVERAL REMARKS ON

Hope, and the True Way, he commented the signifi­
cance of the surveyor’s failure: “It was because of impa­
tience that they were expelled from Paradise; it is because
of indolence that they do not return”, Kafka wrote about
people. Then he corrected himself:” Perhaps there is only
one cardinal sin: impatience. Because of impatience we are
driven out of Paradise; because of impatience we cannot
return".
What did their impatience consist of? They wished to
know. And in order to know, they ate from the Tree of
Knowledge.
Did Kafka, while performing a salto morale of resigna­
tion thus condemn the desire for knowledge, ratio? This
assumption is negated by K .’s resentment of the peasants’
comatose state and by his vocation. An impatient longing
for knowledge is the essence of people’s “cardinal sin". Who
can say that access to the tree of knowledge has been re­
fused for all eternity? Or that patience will not be reward­
ed by a slow alleviation of the prohibition, a slow maturity
towards cognition? This is certainly an infinite process but
patience could offer it peaceful progress. (...) Ratio also
must develop and the possibilities of its employment have to
be carefully considered; it too must control itself —oppose
the danger of conceit and impatience, mindful of the fact
that it is traversing an endless path.19
This pride and impatience are confirmed also in
the most important story, a sui generis biographical
myth of Cohen: When I was a little kid, my mother told
me not to stare into the sun. So once, when I was six, I did.
As a result he almost became blind and started suf­
fering persistent headaches, which recurred when he
was an adult. This story, however, can be interpreted
less literally and in a symbolic perspective be seen as a
pre-figuration of essential moments in the boy’s later
life. Hence the legible motifs of the Sun and the viola­
tion of the prohibition will become a discernible film
variation of the tragic myth of Icarus. Cohen certainly
possesses some of the traits of Faust. But an even more
apt characteristic seems to be: a geometrician with the
Icarus complex. It is difficult not to notice that the
protagonist of n bears the same sort of tragic stigmata,
a pre-established fatalism.

A Great Code
Films do not arise in a mental void. To a lesser
or greater degree they are a visual exteriorisation of
that, which is “in the air”, with which contemporary
thought is concerned. The questions that n proposes
for consideration coincide with a special moment in
Western culture. For some time since the discover­
ies made by Crick and Watson we have been aware
of four basic components of the genetic code and the
relations between them. We are also familiar with a
model of the atom discovered by Rutherford. Today,
the years-long project of deciphering the biochemical
contents of the human genome is coming to an end.
308

A group of outstanding Jewish mathematicians has
announced the outcome of its research - up to now
not undermined by anyone - into the existence of a
Biblical code. Certain physicists maintain that the socalled general theory of everything is already within
our reach. We live at a time of impatient expectation.
We are waiting for the breaking of the last code, the
removal of the last seal from a parcel containing data
about ultimate meaning. Apparently, we believe that
we are participating in the final act of a great drama of
depriving the world of its secret. The curve of cogni­
tion is asymptotically coming close to the line mark­
ing Truth, and almost touching its edge. One moment
more and the impossible will become the possible.
There will come a time of great decoding. The rev­
elation of all mysteries and the announcement of the
sense of Everything - those are the legible signs of ulti­
mate times. The Greek apocalypsis means “revelation”
but also the “disclosure” of the meaning of a certain
secret. It is also in this etymological sense that we can
describe the present-day moment in culture as a time
“just before” the apocalypse. Aronofsky’s film without
doubt intentionally refers to this state of the aware­
ness of the contemporary world. The director has
brilliantly sensed the atmosphere of anticipation for
a spectacular grande finale dominating in the Western
world, and has noticed an almost universal Kafkaesque
impatience, that deadly sin of mankind. Aronofsky, a
New York Jew from Coney Island, attaches particular
importance to the discovery of Biblical codes in the
Torah and the ensuing intellectual foment (together
with its eschatological subtexts) amidst the Jews of
America and Israel.20 This was, he confirms, one of
the essential points of departure for the construction
of the scenario.
And yet the answer proposed by Aronofsky as re­
gards the necessity and possibility of cognition appears
to be distant from unambiguity.
First take a look at several doubts. n forces to
tackle a number of elementary questions concerning
the nature of reality. Does Someone send us letters
written in invisible ink and telegrams with an unclear
content, or do we grant them meaning by asserting
ex post that these are communiqués “not from this
world”? Doing so, we submerge ourselves in signs that
we had produced, rather unconvincing proof for the
existence of a Source dispatching coded letters in bot­
tles. In other words: does reality disclose holy contents
in an unknown language requiring interpretation and
behave like the Delphi oracle that “gives signs”, or is
the world suffering from an ontological muteness and
all that we decipher from it tells us exclusively about
the contents of our cognitive apparatuses? To put it
in yet another way: is Someone really writing texts in
a secret language addressed to us - in that case read­
ing them seems to be a serious undertaking worth the

D ariusz C zaja • CIPHER AND EPIPHANY. SEVERAL REMARKS ON

effort - or does this correspondence have the same
author and addressee and thus all endeavours at de­
coding its transcendent sense resemble a tragic farce?
A genuine metaphysical horror.
The rationalistic decree describes doubts of this
sort as childish. While discussing man’s “hermeneutic”
inclination towards deciphering profound meanings
produced by the world Leszek Kołakowski defended
the stance of the “cryptologists” and “coders”. He con­
ducted a fervent polemic with the Enlightenment tra­
dition, which imposed harsh restrictions upon ques­
tions of this sort: We have never stopped asking such
questions, and most likely never will. We shall never be
free of the temptation to perceive the universe as a book in
secret code to which somewhere they is a key... And why
indeed should we want to be free of this temptation, which
has proved the most fruitful source of cultural growth in all
civilizations except our own (at least insofar as its domi­
nant trend is concerned)? And what is it that confers su­
preme validity on the verdict that forbids us this research?
Only the fact that our civilization, that has to large extent
abandoned this, has proved immensely successful in some
respects but in many others it has failed pathetically.
One might ask why, if the universe is indeed a secret
book of the gods with a coded message for us, this mes­
sage is not written in ordinary language rather than in hi­
eroglyphics whose decoding is discouragingly arduous and,
above all, never results in certainty ?
But this question is futile for two independent reasons.
First, it assumes that we do know, or can imagine what
the universe were like if its message and meaning were
clearly readable and unambiguously displayed before our
eyes. But we do not know this, and we lack the kind of
imagination. Second, it is possible that if we knew why the
message is hidden, or partly hidden —that concealment of
the reasons for which it is hidden is a necessary part of its
being hidden.21
Naturally, Kołakowski is right. The temptation to
treat the world as a code, a puzzle to be solved, appears
to be a non-reducible disposition and no Enlighten­
ment-era decrees can alter a single thing. After all, we
can ask whether it follows that in our task of reading
the “sacred ciphers” were are doomed to only two pos­
sible hermeneutic stands: the optimistic vision, whose
sign could be Champollion, and the degenerate version,
whose emblematic figure is Daniken? Is there no other
way out than those two possibilities? Must the decipher­
ing of “holy signs”, the reversal of the matter of real­
ity “to the right side”, be always accused of naïveté and
suspected of gnostic pride and cheap exclusivism? A
certain response is offered by the final, ambiguous and
symbolically open scene of the film,22 whose entire force
comes from the fact that it is also semantically open.
Having already completed homemade “lobotomy”
(the removal of a mysterious bulge from his temple)
and thus having ended his suffering, Max Cohen sits
309

in front of his house. He gazes upwards with a rather
absent, otherworldly glance, observing, as he did once
before, branches swinging in the treetop. A shaft of light
is trapped between the branches. It is this image that
previously suggested the existence of patterns in N a­
ture. But this time things are not the same. They have
become an illegible hieroglyph, an equation without
clear-cut properties. Cohen’s face, however, lights up
with a mysterious smile. Enlightened ignorance? This
“comprehending” smile appears to contain knowledge
about the hopelessness of efforts aimed at interpreting
the mystery of the world in a numerical algorithm as
well as a conviction that despite serious premises the
world is not a key to the code. The sense of a thing
does not have to be concealed and sometimes appears
within the range of sight. The response to the worldcode is the world conceived as epiphany. We witness
an almost alchemical and spiritual transmutation: as
if the Tree of Knowledge changed at this exact mo­
ment into the Tree of Life. Cohen seems to finally un­
derstand the teachings of his mentor, Robeson, who
while playing go drew his attention to the need of not
thinking too much, indicating intuition as the key to
profoundest cognition.
Now the heart of the matter is not to perceive the
world as a code, a puzzle, and a hieroglyph to which
one matches a key, gives the correct result or produces
an adequate translation into a comprehensible lan­
guage and thus reduces the unknown to the known
and actually appropriates the mystery; it is a special
sort of “reading”. This process of reading and deci­
phering has nothing in common with decoding a ci­
phered message. We use the conceit of a code in those
situations when we know that the concealed meaning
can be basically, sooner or later, grasped. It consists
rather of an exteriorisation of the spiritual message,
entrusting its secret and following its voice. Decipher­
ing is not tantamount to breaking a code, the destruc­
turisation or deconsolidation of a secret. On the con­
trary: deciphering the world revealed in a hieroglyph
respects the existence of the secret and its essential
imperviousness to any sort of explanation. To “read”
the hieroglyph in the above-presented fashion means
to continue existing in the interior of the secret, to be
not before it or in relation to it, but within it.
There exists such a meaning of reality that cannot
be calculated and enclosed in a numerical formula.
There also exists such a meaning of reality whose pri­
vate deciphering does not provide convincing inter­
subjective proof that something is really “there”. There
is also such a meaning of reality, which cannot be re­
solved as if it were a puzzle but can be comprehended
by intensive, earlier prepared perception. In order to
be cognitively productive the latter must possess all
the features of ecstatic contemplation. It seems futile
to add that the condition for such contemplation is

D ariusz C zaja • CIPHER AND EPIPHANY. SEVERAL REMARKS ON

approximations to the Babylonians and Egyptians of the
second millennium B.C. I n te r e st in th is n u m b e r is c o n ­
n e c t e d n a tu r a lly w ith th e in v e n tio n o f th e w h e e l. They
took it as roughly three, and it arose naturally as a conse­
quence of the discovery of the wheel. Pi also arose in various
measurements of a pyramid. Pi is even alluded to in the Old
Testament —in Kings I, 7-23 we read about a circular wall
being constructed. From the given number of units for the
circumference and the diameter, we can conclude that the
ancient Israelites took it to be roughly three, A c z e l, o p . c it.,

total and unconditional impartiality. Thanks to it, and
in it, one can simply see sense that does not succumb
to discursive tooling or numerical calculations. Rilke’s
Introduction to The Book of Images, and in particular
the captivating fragment that literally concerns the
act of seeing a tree, is an excellent account of such
experience and its essential impermanence:
Whosoever thou art! Out in the evening roam,
Out from thy room thou know’st in every part,
And far in the dim distance leave thy home,
Whosoever thou art.
Lift thine eyes which lingering see

p. 3 0 .
4
5

A c z e l, o p . c it., p. 29.
D . R e an n e y , Śmierć wieczności. Przyszłość ludzkiego umy­

słu, tra n sl.

W

S z ele n b e rg e r,

M . S z w e d -S z e le n b e rg e r,

W a rsz a w a 1 9 9 3 , p. 2 0 9 a n d 2 2 6 .
6
7

The shadows on the foot-worn threshold fall,
Lift thine eyes slowly to the great dark tree
That stands against heaven, solitary, tall,
And thou hast visioned Life, its meanings rise
Like words that in the silence clearer grow;
As they unfold before thy will to know
Gently withdraw thine eyes.23

S . S t e in , Potęga liczb, W a rsz a w a 1 9 9 7 , p. 2 0 8 .
R . B a r th e s,

Mitologie, tra n sl. A .

D z ia d e k , in tr o d . K .

K ło siń sk i, W a rsz a w a 2 0 0 0 , p p . 1 2 3 -1 2 5 .
8

J. B e r a rd in e lli, Darren Aronofsky’s Piece of the n.

9

E C o v e n e y , R . H ig h fie ld , Granice złożoności. Poszukiwania
porządku w chaotycznym świecie, tra n sl. E A m ste r d a m s k i,
W a rsz a w a 1 9 9 7 , p. 4 0 .

The glimmer of momentary illumination reveals
- yes, reveals, and the ambiguity of this verb is sig­
nificant - the sense of the Whole, shattered into frag­
ments and thus earlier inaccessible. Emerging from
darkness it glistens for the blink of an eye in the fis­
sure of concealment, and then returns to it. The fleet­
ing character of this experience and its, by the very
nature of things, passing nature does not in any way
diminish its poignant reality. Contrary to assorted ide­
alisms, the truth - naturally, not in its aletheic mean­
ing but according to an adequacy comprehension - is
not concealed somewhere in an inaccessible cocoon
of the noumen nor does it lie “beyond the horizon”. It
is given “here and now” in rare revelations, in viewing
that annuls the customary subject-object, spiritualsensual, etc. contrasts, and which starts with sensual
observation but a moment later “leaves the senses” for
the sake of meaning and word that in the silence clearer
grow. It is in this single and indivisible act of cognition
that the sense of the word can reveal itself and exist in
the full meaning of the word.
The rest is... computation.

10

A . K a u fm a n , An Inteview with Darren Aronofsky and Sean

11

Gullette of “Pi”.
B. H r a b a l, Mój wiek, tra n sl. A . S . Ja g o d z iń sk i. W a rsz a w a

12

M . H e id e g g e r, Czas światoobrazu, tra n sl. K . W o lic k i, in:

1994, pp. 3 5 -3 6 , 39.

Drogi lasu, tra n sl. v a r io u s a u th o rs, W a rsz a w a 1 9 9 7 , p.
75.
13

K . M a u r in , Mistyka - matematyka - magia, “ G n o s is ” n o .

14

A r o n o fs k y h im s e lf d rew a t te n t io n t o th is r a th e r o b v io u s

15

W. H ilsb e c h e r, Tragizm, absurd i paradoks, se le c tio n a n d

1 1 :1 9 9 9 , p. 110.
p o ssib ility , se e : A . K a u fm a n , An Interview...
in tr o d u c tio n S . L ic h a ń sk i, tra n sl. S . B ła u t, W a rsz a w a
1 9 7 2 , p p . 1 1 0 -1 1 1 .
16

H ilsb e c h e r, op. cit., p p . 1 1 3 -1 1 4 .

17

Ib id ., p p . 1 1 3 -1 1 4 .

18

Ib id ., p p . 1 2 3 -1 2 4 .

19

Ib id ., p. 126.

20

O n B ib lic a l c o d e s se e th e w o rth le ss a n d se n sa tio n a l: M .
D r o sn in ,

Kod Biblii, tra n sl. J. Ja n n a s z , W a rsz a w a 19 9 8

a n d th e c le a r h e a d e d a n d e x tr a o r d in a r ily c o m p e te n t: J.
S a tin o v e r , Kod Biblii. Ukryta prawda, tr a n sl. D . K o n ie c z k a ,
B y d g o sz c z 1 9 9 9 .
21

L . K o ła k o w sk i, Horror metaphysicus, tra n sl. M . E an u fn ik ,
W a rsz a w a 1 9 9 0 , p p . 1 4 3 -1 4 4 .

22

A p p a re n tly , im p a tie n c e is n o t th e d o m a in o n ly o f b r il­
lia n t m a th e m a t ic ia n s b u t a lso o f film c ritic s. A n in te r ­
v ie w w ith D . A r o n o fsk y p o se s a rid ic u lo u s q u e stio n :

What is the meaning of the end?; it is d iffic u lt t o tell
w h e th e r it c o n ta in s a n u n u s u a l d o se o f o r d in a ry in a n ity
o r b o u n d le s s n a iv e te . F o rtu n a te ly , th e d ir e c to r d id n o t
fail: One can comprehend the end of the film in many ways

E n d n o te s
1

Ograniczenia matematyki,
Skarby matematyki, e d . T

A fte r : PJ. D a v is, R . H e r sh ,
tra n sl. J. S k o lim o w sk i, in:

F erris, W a rsz a w a 1 9 9 8 , p. 140.
2

F r o m th e n a m e o f th e D u tc h m a th e m a t ic ia n L u d o lp h

23

v a n C e u le n ( 1 5 3 9 - 1 6 1 0 ) .
3

Ja s tr u n , K ra k ó w 1 9 8 7 , p. 3 5 .

C f. I. E k e la n d , Chaos, tra n sl. M . Ja ro sie w ic z , K a to w ic e
1 9 9 9 , p. 2 7 ; A .D . A c z e l,

Wielkie twierdzenie Fermata,

tra n sl. P S tr z e le c k i, W a rsz a w a 1 9 9 8 . It is w o rth n o t in g
u p o n th is o c c a s io n th e a r c h a ic n a t u r e o f in te r e st in th e
n u m e r ic a l v a lu e o f n:

and I wanted people to propose various interpretations. Even
I, Sean Gulette and Eric Watson wondered what it really
signified, Wprawić widza w trans. Z Darrenem Aronofskym
rozmawia Anna Draniewicz, “ K in o ” n o . 5 :2 0 0 1 , p. 22.
R .M . R ilk e , Poezje, s e le c tio n , tra n sl. a n d fo re w o rd M .

PI was known to within various

310