How I solved The Library of Babel

Borges, heaven and hell, and the Lord of All Words

In a postscript to an essay he wrote aged thirty Jorge Luis Borges relates a dream. He woke from “an uproar of chaos and cataclysms—into an unrecognisable room”, not knowing where or who he was. “My fear grew. I thought: This desolate awakening is in Hell, this eternal vigil will be my destiny.”¹

Chaos, desolation, eternal vigils haunt his other dreams, one short story in particular. ‘The Library of Babel’ is maybe the most essential Borges. It’s the best of his what I call ‘awesome implications’ stories. In just seven pages, the narrator - unidentified beyond being a sort of librarian² - describes a universe.

The whole universe is a library composed of hexagonal cells, linked by doorways, spiral stairs and air-shafts. In each cell four of the six walls have bookshelves, each of those walls have five shelves, each shelf thirty-five books, each book four hundred and ten pages, each page forty lines, each line eighty symbols: a period, comma, space, or any of the twenty-two letters of the alphabet. This set-up is the same in every hexagon, yet there are no duplicate books in the Library, which itself is eternal. Combining these “few axioms… allowed a librarian of genius” to deduce that the Library is total. It contains every permutation of text possible according to the above parameters. In it is everything “that is able to be expressed, in every language.”³

Recent ‘multiplicity’ stories - Everything Everywhere All At Once, the interdimensional cable TV in Rick and Morty - have with their zaniness slightly cheapened how awesome the idea of everything is. In the Library you can find:

the detailed history of the future, the autobiographies of the archangels, the faithful catalog of the Library, thousands and thousands of false catalogs, a proof of the falsity of those false catalogs, the proof of the falsity of the true catalog… the true story of your death, the translation of every book into every language, the interpolations of every book into all books.

Hardly surprising that summaries of the story dwell on its stupendous ramifications, or that computer scientists and mathematicians are fans. But the allure of the story comes just as much from its atmosphere, from the mood Borges suffused it with, like the light in the Library, “insufficient and incessant”. It refutes any image of him as a rarefied author of ‘the literature of ideas’ like some fusty antiquarian out of M. R. James. The ideas are soul-shaking; the story’s narrator is filled with longing. For being a librarian of Babel is a kind of Hadean torment.

At first, on realising the Library was total the librarians felt “unbounded joy.” Sure the books around them were filled with jumbled, junk text; but there “was no personal problem, no world problem, whose eloquent solution did not exist—somewhere in some hexagon.” The librarians abandoned their native hexagons in search of these vindicating books.

Instead they discovered what Borges had warned of in his essay ‘The Total Library’, which prefigured the short story: “For every sensible line or accurate fact there would be millions of meaningless cacophonies, verbal farragoes, and babblings.”⁴

“Millions” is something of a low-ball. The vast majority, to reclaim a cliché, of the permutations of twenty-five symbols within four hundred and ten page books would be cacophonies. And the total number of possible books is so huge that the chances of finding even one line you could parse - let alone entire “books of apologiae and prophecies that would vindicate for all time the actions of every person”- would be infinitesimal. Over the barren years the librarians’ numbers dwindle; the narrator’s memory of walking for nights on end without meeting anyone is “unspeakably melancholy”. Some die of lung disease, others by suicide; the rest continue their search, though “no one expects to discover anything.”⁵ It is after all the Library of Babel—of babble.

For the most part. The narrator cites some of the few, what we’d call, ‘statistically significant’ texts he’s known in his lifetime. There was a book his father ‘read’ that repeated the same three letters from the first to last line: an incredibly rare sustained pattern but content-free nevertheless, since “four hundred ten pages of unvarying M C V’s cannot belong to any language, however dialectical or primitive.” Then, on the penultimate page of a gibberish book, the phrase “O Time thy pyramids”—complete words, albeit without complete sense.

The second example is in fact the secret key to the whole story.

Where there’s a will

Since I first read it I’ve found the phrase “O Time thy pyramids” evocative without quite knowing what it evoked. It’s at once lyrical and gnomic, it has a C=D-style itchy inscrutability. I used to doodle it in margins and gouge it into desks.

What the phrase isn’t, so the narrator infers, is “absolute nonsense”—the Library has “not one single example” of that. Since it “contains all verbal structures, all variations allowed by the twenty-five orthographic symbols” then it “must surely have produced the extraordinary language that is required” to decipher the likes of “O Time thy pyramids”. Such phrases:

at first apparently incoherent, are undoubtedly susceptible to cryptographic or allegorical ‘reading’; that reading, that justification of the words’ order and existence, is itself verbal and, ex hypothesi, already contained somewhere in the Library.⁶ There is no combination of characters one can make… that the divine Library has not foreseen and that in one or more of its secret tongues does not hide a terrible significance…

Like what though? The eminent Dictionary of Borges glosses “O Time thy pyramids” as an allusion to Borges’s poem ‘Del Infierno y del Cielo’, “referring to the Day of Judgement when time will cease.” Borges’s English translator, Andrew Hurley, cites the phrase in his parody story ‘The Zahir and I’ as an example of the “untranslatable.” Its seeming point is to put the reader in the narrator’s place: tantalised by the odd random scrap of recognisable language, as though we’re dogs watching TV who hear among all the babble a single bark and so perk up. Like the narrator, we’ll never know what significance “O Time thy pyramids” might have behind its “verbal nonsense and incoherency.”

In the words of the story, “this incoherence at one time seemed mysterious”⁷; but the mystery has a solution. And not merely the one the narrator infers must exist but never imagines he’d find. It’s in Shakespeare’s sonnets—specifically Sonnet 123. Draw a triangle over its opening lines and you get:

That Borges’s eye might’ve been caught by these words is more apparent when we look at the 1609 quarto edition of the sonnets. The typesetting of the first line uses a drop-cap, which by its very prominence withdraws itself from focus, emphasising “O! Time” and “Thy pyramids”:

For years I’ve wondered whether this triangular quotation was a wink from Borges via Shakespeare, like the eye on the pyramid on a one-dollar bill, or just a cute coincidence. Not least since the phrase in the story is not a contiguous quote of any of the sonnet. And in the quarto edition, there’s an exclamation mark after ‘No’ (the phrase the narrator cites is not “O! Time thy pyramids”). Later editions, like the first given above, did lose the exclamation mark but they put commas around the word Time, neither of which appear in the story’s quotation, if that’s what it is. Maybe I wasn’t “looking at a real clue” but “only at one of these elegant lures that tease our appetite for meaning.”⁸

I let the mystery slide. I stopped scrawling the phrase everywhere and tried to put it out of mind. Till one day I myself was wandering around a library and had my own skin-prickling Borgesian moment.

Gleaming on a shelf amid other books was a white copy of his Selected Poems. I took it down and it opened straight on the verse: “O Time, all your ephemeral pyramids”.

Or say can you see?

Why had Borges in this poem, ‘Of Heaven and Hell’, quoted a variation of the line from his short story? In art, repetition’s not inelegant; it’s emphasis. What was Borges emphasising, what drift was he hoping a reader might catch that’d been missed?

Or did his story simply quote his poem? At the time I didn’t know of the Dictionary of Borges gloss, which sources the poem to the ‘El otro, el mismo’ section of his Obra poética, published in 1964 and covering his poetry from 1923. The poem itself isn’t dated in the Selected Poems, though the Dictionary of Borges implies it came before the short story was published in 1941.

Whichever order they came in, I don’t think Borges was making a circular self-reference. Could a man who once said Shakespeare had been his destiny write the line in the story and the one in the poem doubly deaf to their chimes with Sonnet 123? The alternative is they’re not variations of each other but are both diffuse quotations of the sonnet.⁹

Still, there’s a problem. So far I’ve been connecting Sonnet 123 with the English translations of Borges’s story. But he wrote the original in Spanish, where the scrap of text the narrator cites reads, “Oh tiempo tus pirámides” [my italics]. Which doesn’t transpose back onto the opening lines of Sonnet 123; it’s not like they read “Noh, Time…/ Thy pyramids” as though Shakespeare had somehow known about contemporaneous Japanese theatre. If Borges, as I claim, did make a sort of triangular screen-grab of the sonnet for his example of rare legible-but-inscrutable text found in the Library, then why did he write ‘Oh’ and not ‘O’?

Because there’s no real convention in literary Spanish for a declarative ‘O’. Keats’s “O, for a draught of vintage,” gets put into Spanish as “Oh, si un trago de vino”. There’s otherwise already an ‘O’ in Spanish—it means ‘Or’. Had Borges spliced the English ‘o’ from the sonnet into his story, he’d have given his original, Spanish readers the phrase “O tiempo tus pirámides”, which English translators would have put as “Or time thy pyramids”, inadvertently letting the reference to Shakespeare slip through the cracks forever. (Odysseus returns to Ithaca unrecognised because he’s now called Ordysseus.)

So in Spanish Borges had to use ‘Oh’. His first translators into English such as J E Irby wrote it as ‘Oh’ too (as did the Dictionary of Borges) since the English ‘Oh’ is a sufficient equivalent to the Spanish one. His ill-fated translator Norman Thomas di Giovanni detected the poetic tone but not the Shakespeare, translating the phrase as “O time your pyramids”, as if it were a command. However, subsequent translators - Kerrigan, Hurley - detected the tone and personification in the phrase, and translated ‘Oh’ (back) into ‘O’, capitalising the ‘t’ in time to boot.¹⁰ And so the scrap of Sonnet 123 survived repatriation to fulfil its greater purpose.

It wasn’t rocket science

Subtler evidence (weirdly enough, evidence by omission) that “O Time thy pyramids” comes from Shakespeare can be found in a forgotten short story, bowdlerised by one author and more than a little influencing another.

In ‘The Total Library’ Borges traces the history of an idea he would later riff on himself. One precursor was German author Kurd Lasswitz, who wrote the short story ‘The Universal Library’ in 1904. In it, a professor, his wife, niece, and friend discuss how running all combinations of letters, spaces and punctuation in books of a given size would produce the “collected works of everything that has ever been written in the past or can be written in the future.”¹¹

Reading the story, you get a sense it was more than just a previous version of an idea Borges would also explore. Notwithstanding what he did with the idea was whole orders more creative than Lasswitz, his story is also a version of Lasswitz’s story. There are too many parallels, one of which might be crucial.

Both stories have lists of books that must exist in their respective libraries. Both lists mention the lost works of Tacitus¹² as well as a catalogue of all books. And both stories provide obliquely related examples of the wider-spread gibberish that overwhelms any sense found. Compare this from ‘The Universal Library’: “After reading a little bit, all of a sudden the text goes on, ‘Abracadabra, there’s nothing’s here!’” with this from ‘The Library of Babel’: “The finest volume of all the many hexagons that I myself administer is titled… Axaxaxas mlö.”¹³ The relation is via ‘Abraxas’, the gnostic term that gave us the magic word ‘abracadabra’—from abracadabra to Abraxas to Axaxaxas. Borges’s use of the term is not incidental, as we shall see.

If I’m right and he repurposed ideas from Lasswitz’s story, then the most intriguing one of all depends on whether he read him in the German original or in English translation.

He could’ve done either; in his ‘Autobiographical Essay’, he mentions reading Schopenhauer in English and in German. However, the first English translation of Lasswitz’s story, by rocket scientist and SF writer Willy Ley, was published in the anthology Fantasia Mathematica in 1958, long after Borges had published his story in 1941. But the anthology doesn’t indicate whether Ley ever published the translation anywhere else beforehand. Having fled Germany for England in 1935, he’d been writing for Anglophone science fiction magazines since 1937. If this included his translation of ‘The Universal Library’, then Borges would’ve had time to sample it before writing ‘The Library of Babel’.

Why does this matter? Because, as related by Erik Born for Mithila Review, Ley’s English translation slightly deGermanised the story (it was post-war). In the original, the characters discuss how their private letters must exist in the Universal Library, but signed by the likes of Goethe. Ley changed this to: “under the byline of William Shakespeare”.

Our dates are brief

Borges makes Kabbalists of his readers. Maybe you think these links are tenuous, verging on pareidolia, that I deserve the Always Sunny in Philadelphia conspiracy-board meme.¹⁴ It might even gall some readers I’ve been trying to Da-Vinci-decode an august masterpiece of 20th century literature. You’re like the librarians in the story who “repudiate ‘the vain and superstitious habit’ of trying to find sense in books, equating such a quest with attempting to find meaning in dreams.”

The narrator does entertain “the possibility of codes”; but although such a “conjecture has been universally accepted” it is “not in the sense in which its originators formulated it.” He means the way that even gibberish must somewhere in the enormous Library have its inadvertent cipher. But what if his author meant another sense, which we’ve missed?

I went back to the passage with the supposed scrap of Shakespeare to apply some of what the story calls “combinatory analysis.” I re-read the passage to Buddhist mantra lengths—and got my thunderclap:

One book, which my father once saw in a hexagon in circuit 15-94, consisted of the letters M C V perversely repeated from the first line to the last. Another (much consulted in this zone) is a mere labyrinth of letters whose penultimate page contains the phrase O Time thy pyramids.

Did you see it too?

In the original text, Borges wrote the number as “quince noventa y cuatro”—not how you’d typically write the number 1594 in Spanish; that would be “mil quinientos noventa y cuatro”. Irby translated it as “fifteen ninety-four”, while Hurley even puts the number in numerals, split by a dash.

Why would Borges have phrased a four-digit number in this - for Spanish - atypical way? The way in which, for example in English we phrase many of our years? That’s because “quince noventa y cuatro” is a year: one within Shakespeare’s lifetime.

And not just any either. 1594 was the breakout year for Shakespeare: when his so-called lost years had come to an end, the year his plays went exclusive with The Lord Chamberlain’s Men, the year he first performed for Queen Elizabeth, the year his first play was in print (the Quarto of Titus Andronicus), the year the last of his three main rivals, Thomas Kyd, had died (following Robert “upstart crow” Greene and Christopher Marlowe in ’92 and ’93)—and when, with the theatres shut because of the plague, he’d been focussing on his poetry: the narrative poems Venus and Adonis and The Rape of Lucrece (1593/94), and, you guessed it, the sonnets.

There’s never been stone-set dates for when each was written (not least because their first edition was published without Shakespeare’s go-ahead). But Borges would have good reason to date the 123rd sonnet to 1594. Current scholarship holds that “while [Shakespeare] may have experimented with the form earlier, [he] most likely began writing sonnets seriously around 1592.”¹⁵ While by 1598 we get our first historical record of them, from Clergyman Francis Meres: “the sweete wittie soule of Ouid liues in mellifluous and hony-toungued Shakespeare, witness… his sugred Sonnets among his private friends.” Borges had read these words (though whether or not before he wrote ‘The Library of Babel’ is unclear); in his 1964 lecture ‘The Enigma of Shakespeare’ he spoke of how, “outside of an ambiguous accolade that speaks of his ‘sugar sonnets’, [Shakespeare’s] contemporaries do not seem to have had him much in view.” If Shakespeare had written sonnet 123 in 1594 he’d have been the same age as Borges when he had his vigil dream. Best of all, though, Borges mentions the number again (repetition is emphasis) in his essay ‘A New Refutation of Time’, writing that the “universe, the sum total of all events, is no less ideal than the sum of all the horses—one, many, none?¹⁶—Shakespeare dreamed between 1592 and 1594.”

Scouring the scholarship while writing this, I learnt of a note in the critical edition of Borges’s Obras Completas that hazards, “Oh tiempo tus pirámides” is “posiblemente una referencia al soneto 123 de Shakespeare”. But if it is indeed the case that Borges paired his reference to the sonnet with the number 1594 as his estimate for when Shakespeare wrote it¹⁷, then that possibility becomes, to me anyway, a certainty. More to the point, pairing the reference and year doesn’t just reinforce the reference, for the two things don’t co-exist just in the same paragraph of the story…

Its narrator told us how his father had seen the book with the repeated M C V’s in “circuito quince noventa y cuatro”—circuit 1594. As for “O Time thy pyramids” it was in another book “(much consulted in this zone)”—“en esta zona”. I love that parenthetical “much consulted”, as if Borges was nudging for more consultation. Because where does “this zone” actually refer to?

Beyond those words the narrator doesn’t specify another, separate circuit number for the location of “O Time thy pyramids”. By “this zone” he could just mean where he’s writing from; he gave a rough idea of that location towards the start of the story: “I am preparing to die just a few leagues from the hexagon in which I was born.” But he never refers additionally to that location as “this zone”. Besides he already told us about the best scraps of text in his own hexagons (The Combed Thunderclap; The Plaster Cramp; Axaxaxas mlö). The last option is that “this zone” with the “O Time thy pyramids” refers to the same circuit with the “M C V’s”. (The word “zone”, the Spanish “zona”, derive from the Greek zōnē meaning ‘a belt or girdle’, linking us back to a circuit.) And if that option is the right one, then the scrap of Shakespeare being found in circuit 1594 has truly awesome implications—for the story’s narrator and its readers.

Of Heaven and/or Hell

The narrator’s cri de coeur is the heart of the story. Deducing the existence of a “Crimson Hexagon” that must contain, in Goethe’s words, the book of all books, he prays:

to the unknown gods that some man - even a single man, tens of centuries ago! - has perused and read that book. If the honor and wisdom and joy… are not to be my own, then let them be for others. Let heaven exist, though my own place be in hell. Let me be tortured and battered and annihilated, but let there be one instant, one creature, wherein thy enormous Library may find its justification.

Which place is the narrator’s though? The one Borges wrote about in ‘Poem of the Gifts’ with its too-famous line about having always imagined Paradise as a kind of library? Or is it the hell he dreamed of when he was thirty-years-old, and the eternal vigil his librarians’ destiny?

“The mind has invented Hell,” he wrote, “it has invented predestination to Hell”; in that spirit he “tried to rescue from oblivion a subaltern horror: the vast, contradictory Library, whose vertical wildernesses of books run the incessant risk of changing into others that affirm, deny, and confuse everything like a delirious god.” These words from his essay ‘The Total Library’ he re-used in his short story (“la Biblioteca febril… como una divinidad que delira”). Except the narrator of the story scoffs at the words and people who hold by them; they “not only proclaim disorder but exemplify it as well, prove, as all can see, the infidels’ deplorable taste and desperate ignorance.”

It’d seem, then, the story remains equivocal on the matter of its setting. In Borges’s poem ‘Of Heaven and Hell’, he wrote that neither place needs any of their legendary extravagances; the same eternal sight of your beloved’s sleeping face would be enough: “for the rejected, an Inferno, / and, for the elected, Paradise.”¹⁸ So too the narrator of the story combines opposites, synthesises a theory:

The Library is unlimited but periodic. If an eternal traveler should journey in any direction, he would find after untold centuries that the same volumes are repeated in the same disorder—which, repeated, becomes order: the Order.

His “solitude is cheered by that elegant hope.” It’s only a hope, the kind sinners might feel being purified in purgatory. Indeed, more than heavenly or hellish the desolate atmosphere of the Library seems purgatorial—The Limbo of Babel.¹⁹

And in limbo is where most critics leave the story. Chris Power for The Guardian quotes DL Shaw on how labyrinths “combine an appearance of design with an implied reality of futile chaos”, then quotes Borges on Kafka and Henry James, who “thought of the world as being at the same time complex and meaningless.” In the end, the Library is contradictory; its “divine staircases” are where librarians strangle one another; it is, in Power’s words, “fundamentally unstable”—its infernal disorder and divine order superposed.²⁰

But the critics overlooked something. The story doesn’t hang on such a fine point. It hints, and this before the narrator’s consoling theory of ordered disorder, at a grander design. It’s like the librarians had hoped, “[t]he fundamental mysteries of mankind - the origin of the Library and of time - might be revealed”. Not by them and their eternal vigil but by the structure of the story.

A pyramid scheme

To take Borges’s hint, to appreciate why he paired the Library and time, we have to go back to Shakespeare.

If Borges wanted to smuggle a Shakespeare reference into his story, he could’ve chosen from any of the poems let alone plays. And out of the 154 sonnets there are others that’d more obviously suit a story about searching for “the one creature, wherein thy enormous Library may find its justification”—Sonnet 59, say, with its “O, that record could with a backward look, / Even of five hundred courses of the sun, / Show me your image in some antique book”. So why pick the sonnet Borges did?

There is a primally catchy ring to ‘123’ (as well known by The Jackson 5).²¹ It’s not a triangular number, though it does count off the sides of a triangle, which is the shape of Borges’s visual quotation of the sonnet, as well as one side of a pyramid, in which shape we find the word ‘pyramid’. (Compare with Radiohead’s ‘Pyramid Song’ which got its name from its ‘triangular’ 4/3 time signature.)

Pyramids belong to time in Borges’s story and his poem, and in Shakespeare’s sonnet. In all the sonnets, time is the villain: “wasteful Time”; “devouring Time”; “bloody tyrant Time”; even “sluttish time.” (In wedding-cliché Sonnet 116 it’s Time whose fool love is not.) And in Sonnet 123 time is trickier still:

1    No, Time, thou shalt not boast that I do change: 
  2    Thy pyramids built up with newer might 
  3    To me are nothing novel, nothing strange; 
  4    They are but dressings of a former sight. 
  5    Our dates are brief, and therefore we admire 
  6    What thou dost foist upon us that is old, 
  7    And rather make them born to our desire 
  8    Than think that we before have heard them told.
  9    Thy registers and thee I both defy,
 10    Not wond'ring at the present, nor the past, 
 11    For thy records and what we see doth lie,
 12    Made more or less by thy continual haste.
 13      This I do vow and this shall ever be:
 14      I will be true, despite thy scythe and thee.

Time here is at once mutable - its records lie; its “continual haste” distorts history and experience - and “nothing novel”: its pyramids “but dressings of a former sight.” When the speaker says they’re “built up with newer might” he even implies they’re not the monuments of the ancient world but contemporaneous buildings; Elizabethan English allowed ‘pyramids’ to mean towers, steeples, spires. This backs the accusation that Time’s novelty is a sham foisted upon us (“foist” in the sonnet doesn’t mean our modern sense of ‘force upon us’ but ‘try to pass off’) as old. There’s nothing new under the sun—or in the Library.

Which, subtly, Borges equates with pyramids. His story mentions them a second time²² (repetition is emphasis) when the narrator points out the redeeming polysemy of every word in the Library:

An n number of possible languages use the same vocabulary; in some of them, the symbol library allows the correct definition a ubiquitous and lasting system of hexagonal galleries, but library is bread or pyramid or anything else.²³

There’s a third mention of pyramids too, not in the story, but in Borges’s ‘Prologues to The Library of Babel’, which prologues include Arthur Machen’s short story ‘The Shining Pyramid.’ An early example of folk horror, the story is like a 19th century cross between The Descent and The Wicker Man; its “shining pyramid” turns out to be, in the story’s most poetic image, a sacrificial fire. Long-lasting pyramids likened to that which in its wildest dreams - its wildest fires - lasts no longer than a few months!²⁴O Fire thy ephemeral pyramids.

In a similar fashion, Borges undercuts pyramids and Time - their supposed longevity together with their sham novelty - both in his poem ‘Of Heaven and Hell’ and in his story via the sonnet it carries inside like a germ. He defines time this way to defy it, like the speaker of the sonnet does to Time’s “registers” and “records” (meaning, significantly, books). After all Borges did write an essay called ‘A New Refutation of Time’. But why would refuting or defying time be relevant to ‘The Library of Babel’?

From heaven’s heart I dab at thee

The answer lies in how the Library is a kind of poetic illustration of idealism. It has existed “ab aeternitate” and is “the future eternity of the world.” All possible texts in it exist already and always. (Even books that fanatical librarians have destroyed persist in variorum, not to mention throughout the infinitely repeated Library.)

A word about that ‘already’; it might imply precedence. But there’s no before or after in the world of monads or forms. There’s not a first time a triangle had three sides. Saying triangles or numbers or the Library came before people is like saying ‘red is bigger than 100’. The narrator recounts past activities of the librarians; but the Library itself has no history. As with supposed novelty in Sonnet 123, none of the books in it - none of its registers or records - were ever new.

When author Jonathan Basile learned how to code in order to turn the story’s concept into an algorithm, he quickly found there wasn’t enough server space in the world to store his ‘eLibrary of Babel’; instead of an archive he had to run it as a text generator: press a button, get a page. Meanwhile other fans of the story treat the Library like the professor’s friend does in Lasswitz’s story, as a “combinatorial machine! A triumph of technology!” which can sift from the chaos new answers to age-old questions.

But the Library is not potential text; it’s what has been ‘written’. There’s a reason Borges didn’t choose a printing press or a lettered fruit machine or the immortal monkey he pointed out would suffice in place of infinite monkeys on typewriters, and instead a library.

Such a total eternal Library would seem to us, whose “dates are brief”, both static and chaotic, as though full of “continual haste”: everything, everywhere, all at once. It’s like how we think of time as change - both ever-changing and all-changing, fluctuating and corrupting like some amalgam of mercury and lead - and how only through change can we perceive the passage of time, or for that matter can there be any passage of it in the universe, hence ‘space-time’. But in an idealist sense space-time is more like braille, and time’s passage the successive, various sensations on our fingertips, while the braille itself is always there and never changes.

This idea of eternal, predestined totality can - especially in a materialist meaningless universe - be galling for being so arbitrary.²⁵ The universe, Time, the Library: nothing but the sum of permutations of particles. (Democritus, co-founder of atomism, was according to Borges among the first to prefigure the Library idea.) And whether the universe is some eternal four-dimensional form - a rugby ball of space-time with the Big Bang at one end and the Big Crunch at the tip - or it has no beginning and no end, it’s still all just there: convoluted, fathomless and already over. (It’s like the fatalist shrug in the cod-Eastern idiom ‘It is written.’)

This “certainty that everything has already been written annuls” the librarians, renders them “phantasmal.” Even in the real world the immensity of the already-written can feel this way. (Is this how Borges felt when he was tracing the confines, high and profound, of his blind National Library?²⁶)

But totality and eternity don’t have to annul us. It’s in a kind of eternal return that the narrator finds hope.²⁷ What’s more, ‘The Library of Babel’ goes beyond this in-story consolation. By smuggling in Shakespeare’s sonnet, by equating (Time’s) pyramids with the Library, the story defies time as conceived above: the paradox of its endless churn combined with the brute, all-is-written fact of it. The Library, that is the universe, is neither arbitrary nor chaotic, nor is its justification to be found only in the narrator’s hopes. He had it right in front of him.

The Lottery of Babel

Since the Library contains every book it contains everything Shakespeare wrote: what he would’ve written had Hamnet lived, the sonnets addressed not to the Fair Youth or Dark Lady but Anne Hathaway - his wife and also the actress, etc. So it’s tritely inevitable that the Library contains our fragmented scrap of Sonnet 123, and only a little more surprising that somebody like the narrator one day (though ignorant of its origin) came across it.

In a truly infinite library, not just one periodically repeated but whose books were composed of however many characters and were however many pages long, this happy accident would be necessary. In infinity there are no surprises. But the narrator specifically told us the sum total of the Library’s books is not infinite. He hopes the Library is repeated but believes each discrete iteration of it is indefinite but finite.

Nevertheless the Library is still stupendously large. Just how large would it have to be to contain all possible books according to the parameters the narrator gave? In ‘The Total Library’ Borges wrote that its shelves would obliterate the day. He’s being modest; they’d obliterate every star.

The Library contains 25^131200 books (or to put it another way, a 3 followed by 2.3million zeroes). By comparison the number of atoms in the universe is a meagre 10^78. Adam Lee for Patheos points out that even “all the books that were exact duplicates of War and Peace, save for a mere twelve or fewer single-character differences somewhere in the text, would more than fill the observable universe.” And what he dubs Tolstoyspace is a “vanishingly small fraction of Babelspace.”

Yet where in all of Babelspace did Borges put the scrap of Sonnet 123?

We’ve already deduced the scrap’s circuit number, but the story never indicates how many hexagons make up each circuit. A single one might contain a quadrillion hexagons. In which case, the significance of a scrap of cut-up Shakespeare existing in circuit 1594 would be much diminished (in a quadrillion hexagons there’d probably be more than that scrap, and wholesale passages too, not just a triangular quotation of some opening lines).

There is, though, a lower limit to how many hexagons make a circuit. Programmer Jamie Zawinski modelled how the hexagonal cells of the Library could be arranged going by Borges’s parameters—with some difficulty. Hexagons tessellate in 2D space but not 3D volume. Whether Zawinski modelled the spiral stairs - described by the story as passing through the inter-cell vestibules - as wide ones that circle a whole hexagon or the more traditional drill-bit kind running straight up and down, the smallest circuits he and his commenters could fit together were six hexagons large.

With six-hexagon circuits, there’d be 840 books in each. The fraction one such circuit would be of the whole Library is 840 over a 3 followed by 2.3million zeroes—a fraction that is, in Adam Lee’s words, “vanishingly small.” So if the circuits are made up of their structural minimum of six hexagons, and if 1594 is when Borges dates the composition of Sonnet 123, then the chance the story’s narrator, that anyone, would locate “O Time thy pyramids” in that circuit is infinitesimally, subatomically small. The words could’ve been in any book in any of the googols upon googols of circuits - anywhere - in a Library that is far, far bigger than our universe (but that isn’t, remember, infinite, so all its eventualities aren’t necessary but remain in the realm of probability). And yet of all places, all the so many places, the words just happen to be in circuit 1594, the same year Shakespeare wrote them! What, as they dryly say, are the odds?

Our universe’s parts are too few for me to give a suitable comparison of unlikelihood. There’s more chance you’d keep winning the lottery till they had to stop holding lotteries. There’s more chance you’d drop a bowl of jelly beans and they’d spell out DEFINITELY NOT A MESSAGE FROM GOD. The odds of the story’s coincidence are so statistically insane as to constitute for any sane mind a miracle.²⁸ To make you believe, I’m sorry to say, in intelligent design.

The miracle isn’t that there is a God or that God and not odds were behind the Library. The narrator already told us how “the universe… can only be the work of a god.” Neither is the miracle that the cacophonies have a hidden meaning; he’d inferred this, he just never imagined finding it. Nor that there might be a higher order to the Library’s disorder; he ends the story hoping as much. The point is that he’d prayed for the Library’s justification, a librarian whom he likens to a god who’s read the book of books, that “[m]any wandered in search of Him”, but that “[i]n adventures such as these” he’d “squandered and wasted” his years. It was to salvage something of those years that he formed his elegant (and slightly pat) hope: of periodic infinity, which would justify the Library’s disorder via a meta-Library order: “the Order.”

But he’d already gotten a peek of the Orderer. He himself had been glanced by the Author—of All Things, meaning both God and Borges, who, since this is a story, are one and the same. Time and the Library weren’t just the sum of arbitrary permutations; heaven did exist and the narrator’s place wasn’t hell²⁹—yet he was going to die without ever having realised it, as the general readership and anglophone scholarship have never realised, so far as I know. (How many of our own dreams have graced us with miraculous reunions and earth-shattering insights which we simply forgot before we woke up?)

All the signs of a Sign were there. In ‘A Defense of Kabbalah’ Borges imagined the Holy Scriptures as a “mechanism of infinite purposes, of infallible variations, of revelations lying in wait”… And ‘The Library of Babel’ itself clued us in, reminding us, “There is no syllable one can speak… that is not, in one of those languages, the mighty name of a god.”

We’d already read one such name. The word Axaxaxas was taken by translator Andrew Hurley as a pronunciation of Borges’s “cruel, mocking laughter”, but it also chimes, as we saw, with ‘Abraxas’—a name of God in the Gnostic system of Basilides. In case of doubt, Borges mentions the Gnostic Gospel of Basilides twice: in the story and in his essay ‘The Total Library’. Repetition is… you get the picture. And how fitting for God to steal into Borges’s story via Shakespeare. In a lecture, Borges relayed an idea of Paul Groussac³⁰ that many writers:

have made a display of their disdain for literary art… But… all of them have given expression to their disdain, and all of those expressions are inexpressive if we compare them to Shakespeare’s silence. Shakespeare, lord of all words,³¹ who arrives at the conviction that literature is insignificant, and does not even seek the words to express that conviction; this is almost superhuman.

The Secret Miracle

If all of this had been Borges’s aim, why not “seek the words to express that conviction” and make it more noticeable? Why hide it instead? Out of elitist obscurity or pretentiousness? If he’d taken ideas from Ley’s translation of Lasswitz why make a point of not incorporating Ley’s mention of Shakespeare, of not calling him by name? A name conspicuously absent from a story that otherwise roll-calls such important literary figures as Bede and Tacitus. And why leave the identity and profound location of the reference to Shakespeare’s sonnet, as it were, off-page?

It’s almost like Borges treated the reference in such a way as to hamper future search engines. The words aren’t a string of complete text, they’re typographically adjacent, something more easily seen looking at the printed page than read in code. The quasi-quotation isn’t case sensitive and omits the Quarto’s exclamation mark and the later editions’ commas.

Borges had accounted for any such smudging of the quotation’s identity. Since the Library is total, “there are always several hundred thousand imperfect facsimiles: works which differ only in a letter or a comma.” Then there was his ingenious subterfuge with the back-and-forth-translations and their compounding error, turning the English ‘O’ into the Spanish ‘Oh’, which returned into English either bare or with a camouflaging ‘h’. (With apologies to The Anatomy of Melancholy, which provides the story’s epigraph: “By this art Borges concealed the variation of one letter.”) Did he anticipate that one of his English translators would eventually split the right way? Or hope none would, as if the secrecy was part of the design? Either way, his foresight is almost superhuman.

In The Magician’s Doubts Michael Wood points out that:

[t]he way we feel about the improbable, even the statistically insane, may have to do with the lightness or heaviness of our interpretation of it, the tone rather than the truth of the claims we make.

Borges was too much of an artist to have built in a heavier, less ambiguous message from the Author to the narrator. (Perhaps as well why he wrote Axaxaxas and not Abraxas.) The clues are faint enough to be tantalising and grounded enough to not be dismissible. The story’s ‘miracle’, like even the most improbable in the real world, isn’t proof. It could still just be a coincidence. A man struck by lightning a dozen times has no special proof of the supernatural—though you can forgive him for going a bit nuts about it. Found on the penultimate page of a book, “O Time thy pyramids” is - to steal from Philip K Dick - a penultimate truth. It’s provisional, a glint of heaven in a chaotic hell, “a promise,” in the words of Michael Wood “of sense in what seems to be noise and nonsense.”³²

Moreover, Borges was too much of an artist to have been cryptic out of mere literary trickery. This wasn’t all some easter egg, a smug in-joke. The hidden import of “O Time thy pyramids” may well have been his story’s lasting point. (“The Library… incorruptible, and secret—will endure.”) To be, like the title he gave to another story, a secret miracle.

The Approach to Al-Anjilizia

Some secrets don’t want to be found; others leave a trail of clues. Going on such a trail has great mystical significance in many of the short stories of Borges.

The trail has to be obscure though—esoteric, difficult. The trail is also a trial. A clearer reference to Shakespeare, plus one found in a circuit 1564 or 1616, would’ve been too easy a giveaway and so not have fitted Borges’s plan. We’d have noticed the reference quickly, inevitably, long ago, and so not experienced what his narrator did.

For his and our experiences mirror each other too well to be unplanned. Both sides rummaged for signs of a higher design, wondered after the meaning of mysterious phrases but in the end had only theories and hopes. And both sides overlooked a secret that was always and will always have been there in the text, i.e. the Library, i.e. the universe. (Maybe the universe is dotted with such secret miracles. Maybe God’s silence is an epistemological, not ontological problem.) It’s as though Borges meant for us to miss it, for the secret to have endured as a secret, like that undiscovered book in the Crimson Hexagon—for its ongoing secrecy and our missing it to be the whole point. He - that is Borges, I think - meant for us to experience having not experienced something, which, as any good dialectician or Pierre Menard knows is not the same as experiencing nothing. There is hope, just not noticed by us.

Are there any other examples in literature of a story whose point was the reader didn’t notice something? Of an unknown unknown that wasn’t just a private joke but a profound metaphysical statement? I guess we wouldn’t be able to tell. Until now. Have I in fact spoiled the story?³³ 

Perhaps a useful comparison is Borges’s fragment, ‘Argumentum Ornithologicum’:

I close my eyes and see a flock of birds. The vision lasts a second or perhaps less; I don’t know how many birds I saw. Were they a definite or an indefinite number? This problem involves the question of the existence of God. If God exists, the number is definite, because how many birds I saw is known to God. If God does not exist, the number is indefinite, because nobody was able to take count. In this case, I saw fewer than ten birds (let’s say) and more than one; but I did not see nine, eight, seven, six, five, four, three, or two birds. I saw a number between ten and one, but not nine, eight, seven, six, five, etc. That number, as a whole number, is inconceivable; ergo, God exists.

Ordinarily the meanings authors put in their works they aim at least to be discernible and at most for the general reader to ‘get’ them. But in this story’s case Borges had a motive to hide his aim: because even when no reader noticed his secret miracle, it would still be there, in the way that an overlooked divine justification might be in our own universe, in the way that the momentarily imagined flock of birds has a definite number even if we could never name it.

This, then, was Borges’s truly genius artistic touch: that his story’s form would follow function, as with all great artworks; but, unlike them, for this to be hidden as part of that very function. In his essay ‘The Wall and the Books’ he wrote as if about the Library that “certain twilights and certain places, all want to tell us something, or have told us something we shouldn’t have lost, or are about to tell us something; that imminence of a revelation as yet unproduced is, perhaps, the aesthetic fact.” Which is what he achieved with his art. He had us pore over text fruitlessly, like his narrator, for some revelation which was under our fingertips all this time (immanence, then, as much as imminence); had us lose something we’d been told without us realising it while always yearning for it: that instant, that creature, that justification by the Author. Who, a year before publishing his story, closed his essay ‘Time and J. W. Dunne’ with words we now might read as a tip-off: “God and our friends and Shakespeare will collaborate with us.”

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Many thanks to my collaborators, friends and fellow librarians of Babel: Adam, Prof Bollig, Duncan, Fernando, Andrew Hurley, Mayte, and Sandeep

1. From ‘The Duration of Hell’. All essay quotations are from The Total Library: Non-Fiction 1922-1986, tr. Esther Allen, Suzanne Jill Levine & Eliot Weinberger.

2. I’ve gendered the narrator as ‘he’ from this point on, not because I haven’t thought through defaulting to the male as a neutral third person; it just felt appropriate seeing as Borges was such a complicatedly autobiographical writer.

3. All short story translations are from Andrew Hurley’s Viking/Penguin editions unless otherwise specified.

4. There’s no reason, however, the general cacophony and scraps of sense would be evenly distributed. Minus any design they’d be distributed at random, which, considering the cosmological size of the Library, would mean whole globes, whole solar systems of sense. The librarians there live happy lives reading the wisest books. Only occasionally are they troubled by rumours from “eternal travellers” who’ve arrived from or made it to the border: weird hinterlands where the great wise beautiful books glitch, fragment, blurt the odd line of gibberish. For the librarians of those zones the Library’s story is one of divine sense crumbling at the margins. For everybody else the story is one of default chaos with an odd crumb of sense—or so they think.

5. It’s like the Library is the one from The Scary Door. (Crass comparison aside, being a blind librarian was the very predicament Borges spoke of transcending in his ‘Poem of the Gifts’.)

6. Like this essay is.

7. Tr. J E Irby.

8. From The Magician’s Doubts, Michael Wood

9. That I’d reconnected via Borges’s poem with his story’s allusion to Sonnet 123 last year, which would’ve been his 123rd birthday, did edge me into paranoia.

10. The poem’s “¡oh Tiempo! tus efímeras pirámides” Alastair Reid translated as “Oh Time”, plus he used “your” and not “thy” for the “ephemeral pyramids”. Andrew Hurley suggested to me that, “with this sort of hyper-poetic address to Time, capitalized, I think one would want to use ‘thy/thine’ as a way of investing the phrase with gravity, sobriety, etc., and with age… it may simply not have occurred to Alastair in the moment that ‘thy’ might be appropriate… I must say that the phrase has the ring of something out of Shelley’s ‘Ozymandias,’ in which Shelley uses ‘ye’ to give the long-dead king’s inscription ‘age.’”

11. All quotations are taken from a new English translation of Lasswitz’s story by Erik Born for Mithila Review.

12. Isn’t it a paradox that the universe, which is only a Library, contains references to real-world historical figures? Not at all. First off, everyone who ever existed, never existed, could exist would be name-dropped by the totalising library. Second, anyone can be text-only. As Jonathan Swift’s narrator instructed in The Battle of the Books, “when Virgil is mentioned, we are not to understand the person of a famous poet, called by that name, but only certain sheets of paper, bound up in leather, containing in print the words of the said poet.”

13. Axaxaxas mlö is also a quotation of the Tlönic language from Borges’s story ‘Tlön, Uqbar, Orbis Tertius’. Another trace of the Author in the Library, and one appropriately twinned again with God.

14. In the short story ‘The Vane Sisters’ Nabokov spoofs a librarian who scries old books for prophetic misprints such as ‘hitler’ for hither. The narrator mocks this as “statistically insane”, though he himself later starts finding the name ‘Taft’ written acrostically in Shakespeare’s sonnets. Is this why the last line of Lolita mentions “prophetic sonnets”? (Source: The Magician’s Doubts.)

15. From The Shakespeare Birthplace Trust.

16. At least two. Horses are mentioned in Sonnets 51 and 91.

17. It doesn’t matter when Shakespeare really did write the sonnet. Future scholarship might yet prove it was 1590 or 1608. All that matters is when Borges estimated Shakespeare had written it, and what motive he had for secreting that date into the story, and what, within the universe of the story, it means for the date and the scrap of the sonnet to be found together.

18. Tr. Alastair Reid.

19. Not a dance.

20. Borges himself was ambivalent towards libraries. Long before he became director of Argentina’s National Library, a prestigious though honorific position, he worked at the Miguel Cané Municipal Library, a time he describes as “nine years of solid unhappiness” when he would walk to his tram-stop in tears. Worse, to punish him for pro-Allies sentiment the Peronist government ‘promoted’ him out of the library to inspector of poultry and rabbits. (Source: Culture Matters.)

21. 123 is also 3 x 41, and Borges published the story in ’41. OK we’re getting into Jim Carrey Number 23 territory here. Then again the story’s narrator does wonder whether humans are “about to be extinguished,” not a surprising worry for when, as Borges wrote in his essay ‘1941’ it looked like the Third Reich was “procuring a universal empire, the conquest of the world”…

22. Borges also mentions toilets two times—first euphemistically as one of the “gabinetes minúsculos” for “las necesidades finales”; second as latrines. Are we to scry for mystical meanings in that?

23. Tr. J E Irby.

24. There are exceptions. In Australia, about 5000 years ago - in fact as long ago as the first pyramids - lightning struck a coal seam. It still burns underground to this day.

25. See Jacob Howland for The New Criterion on ‘The Library of Babel’ as anti-materialist parable.

26. See Alastair Reid’s translation of ‘Poem of the Gifts’.

27. Borges wrote in his essay of the same name that “[the Total Library] is a typographical avatar of that doctrine of the Eternal Return which, adopted by the Stoics or Blanqui, by the Pythagoreans or Nietzsche, eternally returns.” For what it’s worth, Nietzsche says he discovered(/recovered) the idea of the Eternal Return next to a pyramidal mound…

28. In a Library of such multitudinous magnitude, wouldn’t this also be a banal coincidence? Think of how large a pool of potential Shakespeare references we’re working with. According to Marvin Spevack’s concordances, Shakespeare wrote 884,647 words. It wouldn’t stand out if one such word, say a ‘thy’ from Hamlet, appeared in circuit 1600. Having said that, other single words would be humanly detectable Shakespeare references since he coined so many words himself. And as for two words? Three, four? How far apart could the words get before they stopped being any kind of reasonable ‘reference’? And even if ours are a reasonable one when looked at visually, how do you quantify others of its kind? What’s the sum of the equivalents to “O Time thy pyramids” in all of Shakespeare, and what their chances of appearing in their native circuit-numbers between 1564 and 1616? And yet considering that in our estimation, the Library’s circuits (let alone books) far outnumber all the atoms in the universe, all the seconds in recorded time, the odds remain infinitesimal that any Shakespeare - from fragment to complete work - would just happen to sit in a circuit that shared a number with the year it was composed.

29. Maybe. Order and design don’t have to be benevolent, as Robert Frost warned: “What but design of darkness to appall?— / If design govern in a thing so small.”

30. Borges’s twinnish predecessor: also a writer, critic, director of Argentina’s National Library, and blind.

31. The pun is an Islamic one: Allah, the Lord of the Worlds.

32. Take the story’s title. Folk etymology falsely derives the word ‘babble’ from ‘Babel’, not least because of the Bible’s origin story of our multifarious languages in The Tower of Babel’s fall. The word ‘Babel’ does give us ‘Babylon’, but, more importantly, also derives from the Akkadian for ‘gate of God.’ Not revelation but the threshold of revelation. The ajar light. The Library of the gate of God…

33. I appreciate that my reasoning here is, like Borges’s ruins, circular. But let’s say I’m right and his aim was to have his narrator overlook a secret miracle, and to embody that in the story by having his readers overlook it too. How else to achieve that than by hiding a riddle in the story so subtly that almost no one would notice? And he didn’t do this, I believe, for his own personal gratification (it wasn’t a private joke on the reader nor is it indiscernible for anyone other than Borges). He did it to tie in with his wider metaphysical/theological theme: that the universe isn’t arbitrary but has signs of higher meaning in it; but just because we never even realise we’ve missed the signs, walked by them, read past them, doesn’t mean they’re not always there. Or to let Borges have the final words, taken from ‘Tlön, Uqar, Orbis Tertius’, tr. Norman Thomas di Giovanni: “[W]e’d lingered over a discussion on the mechanics of writing a novel… in which the narrator omitted or distorted events, thereby creating discrepancies that would allow a handful of readers - a tiny handful - to come to an appalling or banal realization.”