Daniel Dockery's Portfolio

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Ex Bibliotheca

February 21st, 2012

On Tumblr, earlier, I saw this:

Here is a site that offers digital renderings of some of the books in the unimaginably vast universe of information (and un-formation) described in Jorge Luis Borges’ story the Library of Babel

Explore, but remember that the possibility of of discovering your Vindication within the Universal Library “can be computed as zero.”

An interesting idea, but given Borges’ kabbalistic leanings, his remark that there is no form of capital lettering, no digits, and his insistence on the twenty-two letters and their fixed, symmetrical forms, it is most likely that he meant for the Library’s volumes to be expressed in the block Hebrew script, which he has admired in other places, though any language might be encyphered in that alphabet in the Library’s vast holdings, such as his “Samoyed-Lithuanian dialect of Guarani, with classical Arabic inflections” (“un dialecto samoyedo-lituano del guaraní, con inflexiones de árabe clásico“) mentioned in the story.

Other possibilities do present themselves, however, for clues suggest the language of the southern hemisphere of Tlön. How so? In “The Library of Babel”, Borges gives us explicit “titles” for three volumes: “trueno peinado“, “el calambre de yeso” and “axaxaxas mlö“. The first could be the “Combed Thunder”, the second “The Plaster Cramp”, but what of the third? If one were to read “Tlön, Uqbar, Orbis Tertius“, from the same 1944 collection (Ficciones [Spanish, English]) in which “The Library of Babel” appeared, one would encounter a passage reading, “Surgió la luna sobre el río se dice hlör u fang axaxaxas mlö“, “‘The moon rose over the river’ would be said hlör u fang axaxaxas mlö.” In the additional text, he indicates all words are verbs in that language, and that “axaxaxas” would mean something resembling “flowing like a river”, while “mlö” would be “shining (or perhaps rising) like the moon”. Translate it however we will, there remains the point that at least one book in the Library is titled by one of the Tlönistas. Or by coincidence would appear to be.

This provides much of a proposed alphabet: in addition to the three titles, Borges also wrote that the combination of letters “dhcmrlchtdj” would appear in the Library and that there is one volume that consists of endlessly repeated “mcv”s. Taken together, sorted alphabetically with duplicate letters removed, this leaves us with 20 or perhaps 21 letters: a, b, c, d, e, h, i, j, l, m, n, o, p, r, s, t, u, v, x, y—and, as he does distinguish it, possibly ö. The alphabet in use on the above linked site adds f, g and q but omits the u needed for “trueno” and doesn’t distinguish the ö from o. If we accept that the line from the story of Tlön is of the same language or alphabet, as at least the title seems to be, then we also see evidence of the f and g in use. If we adapt those, but hesitantly combine the o and ö, we will have another set of twenty-two letters.

It likely doesn’t matter:

Un número n de lenguajes posibles usa el mismo vocabulario; en algunos, el símbolo biblioteca admite la correcta definición ubicuo y perdurable sistema de galerías hexagonales, pero biblioteca es pan o pirámide o cualquier otra cosa, y las siete palabras que la definen tienen otro valor. Tú, que me lees, ¿estás seguro de entender mi lenguaje? (Borges, “La biblioteca de Babel”)

An n number of possible languages use the same vocabulary: in some, the symbol “library” admits the correct definition: “an enduring, ubiquitous system of hexagonal galleries”, but “library” is “bread” or “pyramid” or anything else [in others], and the seven words that define it have other meanings. You who are reading me, are you certain you understand my language?

Many years ago (2003) my fascination with the idea of this library, from Kurd Laßwitz’s much earlier story (“Die Universalbibliothek“, 1904) on through Borges’ (whose 1941 variant of the tale I prefer by far) and similar themes (e.g., Arthur C. Clarke’s “The Nine Billion Names of God“, 1954), etc., had me working out the elaborate mathematics of the whole and being in awe at the staggering numbers. For instance, given that Borges explicitly defined the volumes of the library as containing 410 pages, each page containing 40 rows of text with 80 characters per line (including punctuation and spaces), defined there to be exactly 25 possible characters, and said that the library contained exhaustively everything it is possible to express with them and that no two books were identical, we can calculate that the library must have exactly 25^(80*40*410), or 25 to the 1,312,000th power volumes. To put that in perspective, that is 1.956 x 10^1834097 books, a number 1,834,098 digits long. If you were to write out five digits a second, it would take you more than four days of non-stop writing just to transcribe the whole number.

One of the most enchanting things about the library is, of course, that in its seemingly endless volumes you may find everything that it is possible to write down—including your own life story (your “vindication”), perhaps spanning multiple volumes in elaborate detail, as well as countless millions of erroneous copies whether differing by a single letter or missing entire events or with events that end otherwise than reality’s version, the answer to every mystery or riddle that it’s possible to answer, truly everything. The damning part is that these volumes can be scattered anywhere throughout the universal library and your chance of finding the one you seek is only 1 in 25^1312000, which is so incredibly small it is for all practical senses zero. Should you by luck find one good volume of a multivolume set, you have again those vast odds against your ever finding the next.

Yet perhaps the most damning, or tantalizing, aspect of it all is that you could calculate any or all of these volumes and discern the universal order of the whole by a task no more arduous than counting by ones.

In Tlön, etc., Borges mentioned in passing various numerical bases, touching on the base 12 system (duodecimal) of one of the Tlönistas and the base 60 system (sexagesimal) of ancient Sumeria and Babylon (and in its way even today in our system of minutes and seconds). This is the essential clue. While base 10 (decimal) seems to have conquered all others today, other bases have been in use elsewhere: the now infamous Mayan calendar system, for instance, uses base 20; and in computing, we sometimes use base 16 (hexadecimal), base 8 (octal) or at the lowest possible level base 2 (binary). We can conceive of the Library as being expressed in base 25 (quinquevigesimal) notation, but instead of mixed case, such as with base 16 (where the “digits” are 0 through 9, then A through F, such that the decimal number 190 is expressed as BE in hexadecimal), we can define our 25 digits to be the twenty-five symbols set out by Borges, the twenty-two letters of the alphabet, the comma, the period and the space. Each volume in the library then is merely a number, and the order of their seemingly entropic arrangement is numerical. Which is also suggested in the story when he writes how some have asserted that while the books are written in the “natural symbols” of written language, any appearance of meaning is coincidental, a side effect of using those symbols. To demonstrate, we can see the same thing in hexadecimal, such as above when I pointed out that the number 190 is “BE” which could be interpreted as an English verb; or the number 57,005 is DEAD in hexadecimal, again a “word” in appearance though a number in intent, like the dreadful notion of DECAF, which represents the number 912,559. Treating the volumes as natural numbers also explains the Library’s first axiom, that it exists “ab æterno“, just as the numbers.

An example, to demonstrate. If we take the numerical order of the characters to be that in which Borges gave them in his text—to wit, “the space, the period, the comma, the twenty-two letters of the alphabet”—and set them, in the natural arrangement, as being equal to our base 10 values of 0 through 24, then our first book, corresponding to 0 would be an entirely blank volume. The second, corresponding to 1, would be entirely blank but for a single final period. The next would be the same, but with a comma. Then an “a”, a “b” and so on for the first twenty-five books, one for each symbol. The twenty-sixth would be blank but for the last two symbols which would be a period followed by another space. The sequence would continue, almost forever. In the 9,752nd volume we’d find it blank but for the last letters “mm.”; the next would be “mm,”; the next, “mma” then “mmb” and so on again. At the end of the 19,370,996,558th volume, we would find “abula‘fia”, the name of the 13th century kabbalist renowned for his combinatorial ability. The numbers have grown enormous by the time we even get beyond single sentences. And it continues, letter combining with letter, line with line, page with page, growing and growing, as the early kabbalist text, the Sefer Yetzirah, has it (IV:16, dealing with permutations):

מכאן ואילך צא וחשוב מה שאין הפה יכול לדבר ואין האוזן יכולה לשמוע׃

“From here on go out and calculate that which the mouth cannot speak and the ear cannot hear.”

Unfortunately, even with the fastest computing systems in operation today, our sun would burn out before we could generate a fraction of the library, which is moot anyway since with even the best possible compression available today, the library would require more storage space than currently exists or will exist for likely ages to come, if ever. The most recent figures I’ve seen suggest that as of 2011, the global data storage demands for all digital media of any kind covers “only” about 940 exabytes (for those of you playing along at home, that’s roughly 985,661,440 terabytes), with that number essentially doubling every two years—and with it generally pushing the limits of the amount of storage capacity we actually have available globally. Another way to look at data amounts, if every one of the 6,995,685,817 people of the current estimated world population had a full terabyte of data, the total would be roughly 6.5 zettabytes, a vast number far, far beyond current global capacity (there are 1024 exabytes in a zettabyte). At the expected rate of growth, it should take us almost six years to reach that capacity. Yet a complete digital copy of the Library of Babel, at ideal, maximum compression, would require something to the effect of 4.24562416107 x 10^1,834,075 yottabytes—where a single yottabyte is 1024 zettabytes or 1,125,899,906,842,624 gigabytes! At that projected growth rate, it should take a measly 12 million years for us to reach that capacity.

For a countering thought, Seth Lloyd, in an article (“Computational Capacity of the Universe”) in the science journal Physical Review Letters, in 2002, asserted that the total information capacity of the observable universe is only 10^92: the capacity necessary for the complete Library is over 10^1,834,099. Borges equated the Library with the Universe, yet it seems the Library is greater in scope. By far.

So it seems very possible that while the mind can conceive of the Library, can understand it, can know how to create it, its actual creation is beyond the scope not just of human ability but also beyond the scope of universal capacity, beyond the time scale of our solar system. We have to be satisfied with only knowing that these things “exist” in some abstract sense, our vindication, the answer to every pressing problem, to every question that’s ever passed our mind or anyone’s, every great novel (and every awful one!), even this post I’m writing now, exist, waiting for someone to discover them, yet outside the possibility of truly being able to search or find them in any clear or orderly fashion.

Perhaps we should, after the fashion of the site at the beginning, pick up our own “forbidden dice cup”…

“A blasphemous sect suggested that” [rather than searching for meaningful volumes] “all men should juggle letters and symbols until they constructed, by an improbable gift of chance, these canonical books.” […] “The sect disappeared, but in my childhood I have seen old men who, for long periods of time, would hide in the latrines with some metal discs in a forbidden dice cup and feebly mimic the divine disorder.”

J.L. Borges’ “A quien está leyéndome”

June 14th, 2011

The poem:

Eres invulnerable. ¿No te han dado
los númenes que rigen tu destino
certidumbre de polvo? ¿No es acaso
tu irreversible tiempo el de aquel rio
en cuyo espejo Heráclito vio el símbolo
de su fugacidad? Te espera el mármol
que no leerás. En él ya están escritos
la fecha, la ciudad y el epitafio.
Sueños del tiempo son también los otros,
no firme bronce ni acendrado oro;
el universo es, como tú, Proteo.
Sombra, irás a la sombra que te aguarda
fatal en el confin de tu jornada;
piensa que de algún modo ya estás muerto.

The translation, “To whomever is reading me”:

You’re invulnerable. Haven’t they given you—
the powers that govern your destiny—
the certainty of dust? Isn’t your own time
as irreversible as that river in which
Heraclitus saw in his reflection the symbol
of impermanence? A marble stone awaits you
that you will not read. On it’s already written
the date, the city and the epitaph.
Others are also only dreams of time,
not enduring bronze or unblemished gold;
the universe is, like you, Proteus.
A shadow, you’ll go to the shadow waiting
at the fatal end of your journey;
know that in some way you’re already dead.

Twenty-five years ago today (Jun 14), Borges passed away.


December 24th, 2010

nec tamen, ut lauder, uigilo curamque futuri
nominis, utilius quod latuisset, ago.
detineo studiis animum falloque dolores,
experior curis et dare uerba meis.
quid potius facam desertis solus in urbe,
quamue malis aliam quærere coner opem?

Ovid, Tristia, V. vii. 39–40.

It’s not for praise I stay awake and toil for the future of a name best forgotten. I busy my mind with studies, sidetracking sorrows, trying to give voice to my concerns. What else can I do alone in this forsaken town, what other help to this should I seek?

I wish I had some such study tonight to drive myself to like distraction, that I would not now be sitting here brooding as I am, under full sway of this sad, sorrowful season’s selection of spectres. This flu business hardly helps.

Last night, I lost myself in music, or my fumbling attempts thereat. As they did not turn out well—they seldom do—I do not wish to pursue the same fruitless path tonight. The goal, as with Ovid, is to forget my frustrations, not encourage them. Yet running through my options now, I’m coming to a dreary conclusion: everything I know how to do is an equal frustration.

Writing, art, music, any of it, all of it—equally flawed, equally disappointing. I’m tired of this; I need a new outlet.

Fazer uma obra e reconhecê-la má depois de feita é uma das tragédias da alma. Sobretudo é grande quando se reconhece que essa obra é a melhor que se podia fazer. Mas ao ir escrever uma obra, saber de antemão que ela tem de ser imperfeita e falhada; ao está-la escrevendo estar vendo que ela é imperfeita e falhada—isto é o máximo da tortura e da humilhação do espírito. Não se os versos que escrevo sinto que me não satisfazem, mas sei que os versos que estou para escrever me não satisfarão, também.

Por que escrevo então? […] Tenho de escrever como cumprindo um castigo. E o maior castigo é o de saber que o que escrevo resulta inteiramente fútil, falhado e incerto.

Pessoa, Livro do desassossego, 231

To write something and recognize afterward that it’s bad is one of the tragedies of the soul. It’s especially terrible when we recognize that the work is the best we could do. But when we write something knowing beforehand that it has to be imperfect and flawed, seeing as we write it that it’s imperfect and flawed—that is the spirit’s maximum torture and humiliation. Not only do I feel that the verses I write do not satisfy me, I know that neither will the verses I’m about to write.

So why do I write? I must write—it’s like carrying out a punishment. And the greatest punishment is knowing that what I write will be entirely futile, flawed and uncertain.

As it’s said that “the truth is established” by “two witnesses”, these two botcheries of last night’s effort will be mine.

The basic study of the intended melody, meant to be a throw-away piece, though it’s perhaps the better of the two in the end.

Black Keys

A more elaborate work on the same melodic material, passing through a number of modulations into other tonal areas than the basic F# minor of the original, though beginning and ending with it.

Further work and revision has—perhaps, or hopefully—improved this latter work, so I have removed the earlier recording; the new incarnation has been premiered on the Facebook “fan” page, under the title “A Waltz in Winter“.

He cometido el peor de los pecados
que un hombre puede cometer. No he sido
feliz. […] Mi mente
se aplicó a las simétricas porfías
del arte, que entreteje naderías.
No me abandona. Siempre está a mi lado
la sombra de haber sido un desdichado.

Borges, “El remordimiento”

I have committed the worst sin a man can commit: I have not been happy. I gave my mind to the symmetric stubbornness of art and all its webs of pettiness. It never leaves me. It is always at my side, the shadow of having been a brooding man.


July 28th, 2010

Borges, “El laberinto” y “El suicida”

Zeus no podría desatar las redes
de piedra que me cercan. He olvidado
los hombres que antes fui; […]
Sé que en la sombra hay Otro, cuya suerte
es fatigar las largas soledades
que tejen y destejen este Hades
y ansiar mi sangre y devorar mi muerte.
Nos buscamos los dos. Ojalá fuera
éste el último día de la espera.

No quedará en la noche una estrella.
No quedará la noche.
Moriré y conmigo la suma
Del intolerable universo.
Borraré las pirámides, las medallas,
Los continentes y las caras.
Borraré la acumulación del pasado.
Haré polvo la historia, polvo el polvo.
Estoy mirando el último poniente.
Oigo el último pájaro.
Lego la nada a nadie.

A fragment, inspired by the preceding Borges and named “Nada a Nadie” for the last line, which I once meant to complete. I no longer have such expectations and present here only the surviving trifle, so truly lego la “Nada a Nadie”.


June 22nd, 2009

The poem:

Yo que soy el que ahora está cantando
seré mañana el misterioso, el muerto,
el morador de un mágico y desierto
Orbe sin antes ni después ni cuándo.
Así afirma la mística. Me creo
indigno del Infierno o de la Gloria,
pero nada predigo. Nuestra historia
cambia como las formas de Proteo.
¿Qué errante laberinto, qué blancura
ciega de resplandor será mi suerte,
cuando me entregue el fin de esta aventura
la curiosa experiencia de la muerte?
Quiero beber su cristalino Olvido,
ser para siempre; pero no haber sido.


I who am singing today, tomorrow will be dead,
the mysterious inhabitant of a magical, lonely
orb without a past, future or when.
So says the mystic. I think myself unworthy
of Hell or Glory, but I predict nothing.
Our stories shift like the shapes of Proteus.
What wandering labyrinth, what blinding brilliance
will be my fate when I surrender
at the end of this adventure
to the curious experience of death?
I want to drink its crystalline Oblivion,
to be forever; but never to have been.

J.L. Borges’ “A quien ya no es joven”

June 20th, 2009

The poem:

Ya puedes ver el trágico escenario
y cada cosa en el lugar debido;
la espada y la ceniza para Dido
y la moneda para Belisario.
¿A qué sigues buscando en el brumoso
bronce de los hexámetros la guerra
si están aquí los siete pies de tierra,
la brusca sangre y el abierto foso?
Aquí te acecha el insondable espejo
que soñará y olvidará el reflejo
de tus postrimerías y agonías.
Ya te cerca lo último. Es la casa
donde tu lenta y breve tarde pasa
y la calle que ves todos los días.

The translation, “To one no longer young”:

Already you can see the tragedy,
everything in its place:
the sword and ash for Dido,
an obolus for Belisarius.
Why do you keep searching for conflict
in the hexameters’ hazy bronze
when here can be found
the seven feet of ground,
the sudden blood and open grave?
Here watching you is the unfathomable mirror
that will dream and forget the reflection
of your agonies and final years.
Already the last one hems you in.
It’s the house where you spend
your slow, brief evening
and the street you see every day.

J.L. Borges’ “El Despertar”

June 19th, 2009

The poem:

Entra la luz y asciendo torpemente
de los sueños al sueño compartido
y las cosas recobran su debido
y esperado lugar y en el presente
converge abrumador y vasto el vago
ayer: las seculares migraciones
del pájaro y del hombre, las legiones
que el hierro destrozó, Roma y Cartago.
Vuelve también la cotidiana historia:
mi voz, mi rostro, mi temor, mi suerte.
¡Ah, si aquel otro despertar, la muerte,
me deparara un tiempo sin memoria
de mi nombre y de todo lo que he sido!
¡Ah, si en esa mañana hubiera olvido!


The light enters and I rise slowly
from dreams into the shared dream
and things regain their proper
and expected place. And into this present
converges—overwhelming and vast—
the nameless past: the age-old migrations
of bird and man, the legions
ravaged by the sword, Rome and Carthage.
Back, too, comes my everyday life:
my voice, my face, my nervousness, my luck.
Ah, if only that other awakening, death,
would grant me a time without the memory
of my name and all that I’ve been!
Ah, would this morning brought forgetfulness!

J.L. Borges’ “El Sur”

June 19th, 2009

The poem:

Desde uno de tus patios haber mirado
las antiguas estrellas,
desde el banco de
la sombra haber mirado
esas luces dispersas
que mi ignorancia no ha aprendido a nombrar
ni a ordenar en constelaciones,
haber sentido el círculo del agua
en el secreto aljibe,
el olor del jazmin y la madreselva,
el silencio del pájaro dormido,
el arco del zanguán, la humedad
—esas cosas, acaso, son el poema.

“The South”:

To’ve watched from one of your yards
the ancient stars;
from a shaded bench to’ve seen
those scattered lights
which my ignorance has learned
neither to name nor arrange
in constellations;
to have experienced:
the circuit of water in the secret cistern,
the scent of the jasmine and honeysuckle,
the repose of the sleeping bird,
the entryway, the humidity—
these things, perhaps, are the poem.

y te puede matar una guitarra

June 25th, 2003


Ya no es mágico el mundo. Te han dejado.
Ya no compartirás la clara luna
ni los lentos jardines. Ya no hay una
Luna que no sea espejo del pasado,
cristal de soledad, sol de agonías.
Adiós las mutuas manos y las sienes
que acercaba el amor. Hoy sólo tienes
la fiel memoria y los desiertos días.
Nadie pierde (repites vanamente)
sino lo que no tiene y no ha tenido
nunca, pero no basta ser valiente
para aprender el arte del olvido.
Un símbolo, una rosa, te desgarra
y te puede matar una guitarra.


Ya no seré feliz. Tal vez no importa.
Hay tantas otras cosas en el mundo;
un instante cualquiera es más profundo
y diverso que el mar. La vida es corta
y aunque las horas son tan largas, una
oscura maravilla nos acecha,
la muerte, ese otro mar, esa otra flecha
que nos libra del sol y de la luna
y del amor. La dicha que me diste
y me quitaste debe ser borrada;
lo que era todo tiene que ser nada.
Sólo me queda el goce de estar triste.
Esa vana costumbre que me inclina
al Sur, a cierta puerta, a cierta esquina.

JL Borges, “1964”



Enchantment is gone from the world. They have left you.
No more will you share the clear moon or those gentle gardens.
There will be no moon that’s not a reminder of the past,
a lonesome reflection, a sun of agonies. Farewell to hands
and bodies united by love. Now, only your faithful memories
remain, and all your empty days. No one can lose anything
(you vainly repeat to yourself) but what they never truly had.
It’s not enough to be brave to learn this, the art of forgetting.
A symbol, a rose, can tear you up, and a guitar can kill.


I’ll never again be happy. It doesn’t matter.
There’s so much in the world besides this:
every moment has all the depth and diversity of the sea.
Though the hours are so long, this life is short,
watched by an obscure wonder: Death, that other sea,
that other arrow that frees us of Sun and Moon, and Love.
The happiness you gave and took away I must forget;
what meant to me everything must come to naught.
Now, I’ve only sorrow for joy, and that vain habit
inclining me to the South, a certain corner,
toward a certain door that never again will open.

An attempt at doing a guitar piece in the Argentinian zamba style, inspired by the Borges work cited.

This track may also be heard on Last.FM.

Daniel Dockery's Portfolio

animî nostrî dêbent interdum âlûcinâri