Jorge Luis Borges

Jorge Luis Borges
 Jorge Luis Borges was an Argentinian writer, essayist, poet and translator. He was tremendously influential, writing intricate poems, short stories, and essays that instantiated concepts of dizzying power. His work embraced the "character of unreality in all literature."
The essay collection Borges y la Matemática by Guillermo Martínez outlines how Borges used concepts from mathematics in his work. Other books such as The Unimaginable Mathematics of Borges' Library of Babel by William Goldbloom Bloch, and Unthinking Thinking: Jorge Luis Borges, Mathematics, and the New Physics by Floyd Merrell also explore this relationship.
Some of his short stories, from which we have drawn inspiration in this project, are reproduced below - The Library of Babel, On Exactitude in Science, and The Aleph.


By this art you may contemplate the variations of the 23 letters...
The Anatomy of Melancholy, part 2, sect. II, mem. IV

The universe (which others call the Library) is composed of an indefinite and perhaps infinite number of hexagonal galleries, with vast air shafts between, surrounded by very low railings. From any of the hexagons one can see, interminably, the upper and lower floors. The distribution of the galleries is invariable. Twenty shelves, five long shelves per side, cover all the sides except two; their height, which is the distance from floor to ceiling, scarcely exceeds that of a normal bookcase. One of the free sides leads to a narrow hallway which opens onto another gallery, identical to the first and to all the rest. To the left and right of the hallway there are two very small closets. In the first, one may sleep standing up; in the other, satisfy one's faecal necessities. Also through here passes a spiral stairway, which sinks abysmally and soars upwards to remote distances. In the hallway there is a mirror which faithfully duplicates all appearances. Men usually infer from this mirror that the Library is not infinite (if it were, why this illusory duplication?); I prefer to dream that its polished surfaces represent and promise the infinite ... Light is provided by some spherical fruit which bear the name of lamps. There are two, transversally placed, in each hexagon. The light they emit is insufficient, incessant.

Like all men of the Library, I have traveled in my youth; I have wandered in search of a book, perhaps the catalogue of catalogues; now that my eyes can hardly decipher what I write, I am preparing to die just a few leagues from the hexagon in which I was born. Once I am dead, there will be no lack of pious hands to throw me over the railing; my grave will be the fathomless air; my body will sink endlessly and decay and dissolve in the wind generated by the fall, which is infinite. I say that the Library is unending. The idealists argue that the hexagonal rooms are a necessary form of absolute space or, at least, of our intuition of space. They reason that a triangular or pentagonal room is inconceivable. (The mystics claim that their ecstasy reveals to them a circular chamber containing a great circular book, whose spine is continuous and which follows the complete circle of the walls; but their testimony is suspect; their words, obscure. This cyclical book is God.) Let it suffice now for me to repeat the classic dictum: The Library is a sphere whose exact center is any one of its hexagons and whose circumference is inaccessible.

There are five shelves for each of the hexagon's walls; each shelf contains thirty-five books of uniform format; each book is of four hundred and ten pages; each page, of forty lines, each line, of some eighty letters which are black in color. There are also letters on the spine of each book; these letters do not indicate or prefigure what the pages will say. I know that this incoherence at one time seemed mysterious. Before summarizing the solution (whose discovery, in spite of its tragic projections, is perhaps the capital fact in history) I wish to recall a few axioms.

First: The Library exists ab aeterno. This truth, whose immediate corollary is the future eternity of the world, cannot be placed in doubt by any reasonable mind. Man, the imperfect librarian, may be the product of chance or of malevolent demiurgi; the universe, with its elegant endowment of shelves, of enigmatical volumes, of inexhaustible stairways for the traveler and latrines for the seated librarian, can only be the work of a god. To perceive the distance between the divine and the human, it is enough to compare these crude wavering symbols which my fallible hand scrawls on the cover of a book, with the organic letters inside: punctual, delicate, perfectly black, inimitably symmetrical.
Second: The orthographical symbols are twenty-five in number. (1) This finding made it possible, three hundred years ago, to formulate a general theory of the Library and solve satisfactorily the problem which no conjecture had deciphered: the formless and chaotic nature of almost all the books. One which my father saw in a hexagon on circuit fifteen ninety-four was made up of the letters MCV, perversely repeated from the first line to the last. Another (very much consulted in this area) is a mere labyrinth of letters, but the next-to-last page says Oh time thy pyramids. This much is already known: for every sensible line of straightforward statement, there are leagues of senseless cacophonies, verbal jumbles and incoherences. (I know of an uncouth region whose librarians repudiate the vain and superstitious custom of finding a meaning in books and equate it with that of finding a meaning in dreams or in the chaotic lines of one's palm ... They admit that the inventors of this writing imitated the twenty-five natural symbols, but maintain that this application is accidental and that the books signify nothing in themselves. This dictum, we shall see, is not entirely fallacious.)

For a long time it was believed that these impenetrable books corresponded to past or remote languages. It is true that the most ancient men, the first librarians, used a language quite different from the one we now speak; it is true that a few miles to the right the tongue is dialectical and that ninety floors farther up, it is incomprehensible. All this, I repeat, is true, but four hundred and ten pages of inalterable MCV's cannot correspond to any language, no matter how dialectical or rudimentary it may be. Some insinuated that each letter could influence the following one and that the value of MCV in the third line of page 71 was not the one the same series may have in another position on another page, but this vague thesis did not prevail. Others thought of cryptographs; generally, this conjecture has been accepted, though not in the sense in which it was formulated by its originators.

Five hundred years ago, the chief of an upper hexagon (2) came upon a book as confusing as the others, but which had nearly two pages of homogeneous lines. He showed his find to a wandering decoder who told him the lines were written in Portuguese; others said they were Yiddish. Within a century, the language was established: a Samoyedic Lithuanian dialect of Guarani, with classical Arabian inflections. The content was also deciphered: some notions of combinative analysis, illustrated with examples of variations with unlimited repetition. These examples made it possible for a librarian of genius to discover the fundamental law of the Library. This thinker observed that all the books, no matter how diverse they might be, are made up of the same elements: the space, the period, the comma, the twenty-two letters of the alphabet. He also alleged a fact which travelers have confirmed: In the vast Library there are no two identical books. From these two incontrovertible premises he deduced that the Library is total and that its shelves register all the possible combinations of the twenty-odd orthographical symbols (a number which, though extremely vast, is not infinite): Everything: the minutely detailed history of the future, the archangels' autobiographies, the faithful catalogues of the Library, thousands and thousands of false catalogues, the demonstration of the fallacy of those catalogues, the demonstration of the fallacy of the true catalogue, the Gnostic gospel of Basilides, the commentary on that gospel, the commentary on the commentary on that gospel, the true story of your death, the translation of every book in all languages, the interpolations of every book in all books.

When it was proclaimed that the Library contained all books, the first impression was one of extravagant happiness. All men felt themselves to be the masters of an intact and secret treasure. There was no personal or world problem whose eloquent solution did not exist in some hexagon. The universe was justified, the universe suddenly usurped the unlimited dimensions of hope. At that time a great deal was said about the Vindications: books of apology and prophecy which vindicated for all time the acts of every man in the universe and retained prodigious arcana for his future. Thousands of the greedy abandoned their sweet native hexagons and rushed up the stairways, urged on by the vain intention of finding their Vindication. These pilgrims disputed in the narrow corridors, proferred dark curses, strangled each other on the divine stairways, flung the deceptive books into the air shafts, met their death cast down in a similar fashion by the inhabitants of remote regions. Others went mad ... The Vindications exist (I have seen two which refer to persons of the future, to persons who are perhaps not imaginary) but the searchers did not remember that the possibility of a man's finding his Vindication, or some treacherous variation thereof, can be computed as zero.
At that time it was also hoped that a clarification of humanity's basic mysteries -- the origin of the Library and of time -- might be found. It is verisimilar that these grave mysteries could be explained in words: if the language of philosophers is not sufficient, the multiform Library will have produced the unprecedented language required, with its vocabularies and grammars. For four centuries now men have exhausted the hexagons ... There are official searchers, inquisitors. I have seen them in the performance of their function: they always arrive extremely tired from their journeys; they speak of a broken stairway which almost killed them; they talk with the librarian of galleries and stairs; sometimes they pick up the nearest volume and leaf through it, looking for infamous words. Obviously, no one expects to discover anything.
As was natural, this inordinate hope was followed by an excessive depression. The certitude that some shelf in some hexagon held precious books and that these precious books were inaccessible, seemed almost intolerable. A blasphemous sect suggested that the searches should cease and that all men should juggle letters and symbols until they constructed, by an improbable gift of chance, these canonical books. The authorities were obliged to issue severe orders. 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 disks in a forbidden dice cup and feebly mimic the divine disorder.

Others, inversely, believed that it was fundamental to eliminate useless works. They invaded the hexagons, showed credentials which were not always false, leafed through a volume with displeasure and condemned whole shelves: their hygienic, ascetic furor caused the senseless perdition of millions of books. Their name is execrated, but those who deplore the "treasures" destroyed by this frenzy neglect two notable facts. One: the Library is so enormous that any reduction of human origin is infinitesimal. The other: every copy is unique, irreplaceable, but (since the Library is total) there are always several hundred thousand imperfect facsimiles: works which differ only in a letter or a comma. Counter to general opinion, I venture to suppose that the consequences of the Purifiers' depredations have been exaggerated by the horror these fanatics produced. They were urged on by the delirium of trying to reach the books in the Crimson Hexagon: books whose format is smaller than usual, all-powerful, illustrated and magical.

We also know of another superstition of that time: that of the Man of the Book. On some shelf in some hexagon (men reasoned) there must exist a book which is the formula and perfect compendium of all the rest: some librarian has gone through it and he is analogous to a god. In the language of this zone vestiges of this remote functionary's cult still persist. Many wandered in search of Him. For a century they have exhausted in vain the most varied areas. How could one locate the venerated and secret hexagon which housed Him? Someone proposed a regressive method: To locate book A, consult first book B which indicates A's position; to locate book B, consult first a book C, and so on to infinity ... In adventures such as these, I have squandered and wasted my years. It does not seem unlikely to me that there is a total book on some shelf of the universe; (3) I pray to the unknown gods that a man -- just one, even though it were thousands of years ago! -- may have examined and read it. If honor and wisdom and happiness are not for me, let them be for others. Let heaven exist, though my place be in hell. Let me be outraged and annihilated, but for one instant, in one being, let Your enormous Library be justified. The impious maintain that nonsense is normal in the Library and that the reasonable (and even humble and pure coherence) is an almost miraculous exception. They speak (I know) of the "feverish Library whose chance volumes are constantly in danger of changing into others and affirm, negate and confuse everything like a delirious divinity." These words, which not only denounce the disorder but exemplify it as well, notoriously prove their authors' abominable taste and desperate ignorance. In truth, the Library includes all verbal structures, all variations permitted by the twenty-five orthographical symbols, but not a single example of absolute nonsense. It is useless to observe that the best volume of the many hexagons under my administration is entitled The Combed Thunderclap and another The Plaster Cramp and another Axaxaxas mlö. These phrases, at first glance incoherent, can no doubt be justified in a cryptographical or allegorical manner; such a justification is verbal and, ex hypothesi, already figures in the Library. I cannot combine some characters


which the divine Library has not foreseen and which in one of its secret tongues do not contain a terrible meaning. No one can articulate a syllable which is not filled with tenderness and fear, which is not, in one of these languages, the powerful name of a god. To speak is to fall into tautology. This wordy and useless epistle already exists in one of the thirty volumes of the five shelves of one of the innumerable hexagons -- and its refutation as well. (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 pyramidor anything else, and these seven words which define it have another value. You who read me, are You sure of understanding my language?)

Immersive 3D map
The methodical task of writing distracts me from the present state of men. The certitude that everything has been written negates us or turns us into phantoms. I know of districts in which the young men prostrate themselves before books and kiss their pages in a barbarous manner, but they do not know how to decipher a single letter. Epidemics, heretical conflicts, peregrinations which inevitably degenerate into banditry, have decimated the population. I believe I have mentioned suicides, more and more frequent with the years. Perhaps my old age and fearfulness deceive me, but I suspect that the human species -- the unique species -- is about to be extinguished, but the Library will endure: illuminated, solitary, infinite, perfectly motionless, equipped with precious volumes, useless, incorruptible, secret.

I have just written the word "infinite." I have not interpolated this adjective out of rhetorical habit; I say that it is not illogical to think that the world is infinite. Those who judge it to be limited postulate that in remote places the corridors and stairways and hexagons can conceivably come to an end -- which is absurd. Those who imagine it to be without limit forget that the possible number of books does have such a limit. I venture to suggest this solution to the ancient problem: The Library is unlimited and cyclical. If an eternal traveler were to cross it in any direction, after centuries he would see that the same volumes were repeated in the same disorder (which, thus repeated, would be an order: the Order). My solitude is gladdened by this elegant hope.

Translated by J. E. I.


1 The original manuscript does not contain digits or capital letters. The punctuation has been limited to the comma and the period. These two signs, the space and the twenty-two letters of the alphabet are the twenty-five symbols considered sufficient by this unknown author. (Editor's note.)
2 Before, there was a man for every three hexagons. Suicide and pulmonary diseases have destroyed that proportion. A memory of unspeakable melancholy: at times I have traveled for many nights through corridors and along polished stairways without finding a single librarian.
3 I repeat: it suffices that a book be possible for it to exist. Only the impossible is excluded. For example: no book can be a ladder, although no doubt there are books which discuss and negate and demonstrate this possibility and others whose structure corresponds to that of a ladder.
4 Letizia Álvarez de Toledo has observed that this vast Library is useless: rigorously speaking, a single volume would be sufficient, a volume of ordinary format, printed in nine or ten point type, containing an infinite number if infinitely thin leaves. (In the early seventeenth century, Cavalieri said that all solid bodies are the superimposition of an infinite number of planes.) The handling of this silky vade mecum would not be convenient: each apparent page would unfold into other analogous ones; the inconceivable middle page would have no reverse.


…In that Empire, the Art of Cartography attained such Perfection that the map of a
single Province occupied the entirety of a City, and the map of the Empire, the entirety of a Province. In time, those Unconscionable Maps no longer satisfied, and the Cartographers Guilds struck a Map of the Empire whose size was that of the Empire, and which coincided point for point with it. The following Generations, who were not so fond of the Study of Cartography as their Forebears had been, saw that that vast Map was Useless, and not without some Pitilessness was it, that they delivered it up to the Inclemencies of Sun and Winters. In the Deserts of the West, still today, there are Tattered Ruins of that Map, inhabited by Animals and Beggars; in all the Land there is no other Relic of the Disciplines of Geography.

—Suarez Miranda,Viajes de varones prudentes, Libro IV,Cap. XLV, Lerida, 1658

Translated by Andrew Hurley


O God! I could be bounded in a nutshell, and count myself a King of infinite space... 
Hamlet, II, 2

But they will teach us that Eternity is the Standing still of the Present Time, a Nunc-stans (as the schools call it); which neither they, nor any else understand, no more than they would a Hic-stans for an Infinite greatness of Place. 
Leviathan, IV, 46

In search of the site of the Aleph, Buenos Aires 2007
On the burning February morning Beatriz Viterbo died, after braving an agony that never for a single moment gave way to self-pity or fear, I noticed that the sidewalk billboards around Constitution Plaza were advertising some new brand or other of American cigarettes. The fact pained me, for I realised that the wide and ceaseless universe was already slipping away from her and that this slight change was the first of an endless series. The universe may change but not me, I thought with a certain sad vanity. I knew that at times my fruitless devotion had annoyed her; now that she was dead, I could devote myself to her memory, without hope but also without humiliation. I recalled that the thirtieth of April was her birthday; on that day to visit her house on Garay Street and pay my respects to her father and to Carlos Argentino Daneri, her first cousin, would be an irreproachable and perhaps unavoidable act of politeness. Once again I would wait in the twilight of the small, cluttered drawing room, once again I would study the details of her many photographs: Beatriz Viterbo in profile and in full colour; Beatriz wearing a mask, during the Carnival of 1921; Beatriz at her First Communion; Beatriz on the day of her wedding to Roberto Alessandri; Beatriz soon after her divorce, at a luncheon at the Turf Club; Beatriz at a seaside resort in Quilmes with Delia San Marco Porcel and Carlos Argentino; Beatriz with the Pekingese lapdog given her by Villegas Haedo; Beatriz, front and three-quarter views, smiling, hand on her chin... I would not be forced, as in the past, to justify my presence with modest offerings of books -- books whose pages I finally learned to cut beforehand, so as not to find out, months later, that they lay around unopened.
Beatriz Viterbo died in 1929. From that time on, I never let a thirtieth of April go by without a visit to her house. I used to make my appearance at seven-fifteen sharp and stay on for some twenty-five minutes. Each year, I arrived a little later and stay a little longer. In 1933, a torrential downpour coming to my aid, they were obliged to ask me for dinner. Naturally, I took advantage of that lucky precedent. In 1934, I arrived, just after eight, with one of those large Santa Fe sugared cakes, and quite matter-of-factly I stayed to dinner. It was in this way, on these melancholy and vainly erotic anniversaries, that I came into the gradual confidences of Carlos Argentino Daneri.

Beatriz had been tall, frail, slightly stooped; in her walk there was (if the oxymoron may be allowed) a kind of uncertain grace, a hint of expectancy. Carlos Argentino was pink-faced, overweight, gray-haired, fine-featured. He held a minor position in an unreadable library out on the edge of the Southside of Buenos Aires. He was authoritarian but also unimpressive. Until only recently, he took advantage of his nights and holidays to stay at home. At a remove of two generations, the Italian "S" and demonstrative Italian gestures still survived in him. His mental activity was continuous, deeply felt, far-ranging, and -- all in all -- meaningless. He dealt in pointless analogies and in trivial scruples. He had (as did Beatriz) large, beautiful, finely shaped hands. For several months he seemed to be obsessed with Paul Fort -- less with his ballads than with the idea of a towering reputation. "He is the Prince of poets," Daneri would repeat fatuously. "You will belittle him in vain -- but no, not even the most venomous of your shafts will graze him."

On the thirtieth of April, 1941, along with the sugared cake I allowed myself to add a bottle of Argentine cognac. Carlos Argentino tasted it, pronounced it "interesting," and, after a few drinks, launched into a glorification of modern man.

"I view him," he said with a certain unaccountable excitement, "in his inner sanctum, as though in his castle tower, supplied with telephones, telegraphs, phonographs, wireless sets, motion-picture screens, slide projectors, glossaries, timetables, handbooks, bulletins..."
He remarked that for a man so equipped, actual travel was superfluous. Our twentieth century had inverted the story of Mohammed and the mountain; nowadays, the mountain came to the modern Mohammed.

So foolish did his ideas seem to me, so pompous and so drawn out his exposition, that I linked them at once to literature and asked him why he didn't write them down. As might be foreseen, he answered that he had already done so -- that these ideas, and others no less striking, had found their place in the Proem, or Augural Canto, or, more simply, the Prologue Canto of the poem on which he hd been working for many years now, alone, without publicity, with fanfare, supported only by those twin staffs universally known as work and solitude. First, he said, he opened the floodgates of his fancy; then, taking up hand tools, he resorted to the file. The poem was entitled The Earth; it consisted of a description of the planet, and, of course, lacked no amount of picturesque digressions and bold apostrophes.

I asked him to read me a passage, if only a short one. He opened a drawer of his writing table, drew out a thick stack of papers -- sheets of a large pad imprinted with the letterhead of the Juan Crisóstomo Lafinur Library -- and, with ringing satisfaction, declaimed:
Mine eyes, as did the Greek's, have known men's
towns and fame,
The works, the days in light that fades to amber;
I do not change a fact or falsify a name --
The voyage I set down is... autour de ma chambre.
"From any angle, a greatly interesting stanza," he said, giving his verdict. "The opening line wins the applause of the professor, the academician, and the Hellenist -- to say nothing of the would-be scholar, a considerable sector of the public. The second flows from Homer to Hesiod (generous homage, at the very outset, to the father of didactic poetry), not without rejuvenating a process whose roots go back to Scripture -- enumeration, congeries, conglomeration. The third -- baroque? decadent? example of the cult of pure form? -- consists of two equal hemistichs. The fourth, frankly bilingual, assures me the unstinted backing of all minds sensitive to the pleasures of sheer fun. I should, in all fairness, speak of the novel rhyme in lines two and four, and of the erudition that allows me -- without a hint of pedantry! -- to cram into four lines three learned allusions covering thirty centuries packed with literature -- first to the Odyssey, second to Works and Days, and third to the immortal bagatelle bequathed us by the frolicking pen of the Savoyard, Xavier de Maistre. Once more I've come to realise that modern art demands the balm of laughter, the scherzo. Decidedly, Goldoni holds the stage!"

He read me many other stanzas, each of which also won his own approval and elicited his lengthy explications. There was nothing remarkable about them. I did not even find them any worse than the first one. Application, resignation, and chance had gone into the writing; I saw, however, that Daneri's real work lay not in the poetry but in his invention of reasons why the poetry should be admired. Of course, this second phase of his effort modified the writing in his eyes, though not in the eyes of others. Daneri's style of delivery was extravagant, but the deadly drone of his metric regularity tended to tone down and to dull that extravagance.
[Among my memories are also some lines of a satire in which he lashed out unsparingly at bad poets. After accusing them of dressing their poems in the warlike armour of erudition, and of flapping in vain their unavailing wings, he concluded with this verse: 
But they forget, alas, one foremost fact -- BEAUTY!
Only the fear of creating an army of implacable and powerful enemies dissuaded him (he told me) from fearlessly publishing this poem.] Only once in my life have I had occasion to look into the fifteen thousand alexandrines of the Polyolbion, that topographical epic in which Michael Drayton recorded the flora, fauna, hydrography, orography, military and monastic history of England. I am sure, however, that this limited but bulky production is less boring than Carlos Argentino's similar vast undertaking. Daneri had in mind to set to verse the entire face of the planet, and, by 1941, had already dispatched a number of acres of the State of Queensland, nearly a mile of the course run by the River Ob, a gasworks to the north of Veracruz, the leading shops in the Buenos Aires parish of Concepción, the villa of Mariana Cambaceres de Alvear in the Belgrano section of the Argentine capital, and a Turkish baths establishment not far from the well-known Brighton Aquarium. He read me certain long-winded passages from his Australian section, and at one point praised a word of his own coining, the colour "celestewhite," which he felt "actually suggests the sky, an element of utmost importance in the landscape of the Down Under." But these sprawling, lifeless hexameters lacked even the relative excitement of the so-called Augural Canto. Along about midnight, I left.

Two Sundays later, Daneri rang me up -- perhaps for the first time in his life. He suggested we get together at four o'clock "for cocktails in the salon-bar next door, which the forward-looking Zunino and Zungri -- my landlords, as you doubtless recall -- are throwing open to the public. It's a place you'll really want to get to know."

More in resignation than in pleasure, I accepted. Once there, it was hard to find a table. The "salon-bar," ruthlessly modern, was only barely less ugly than what I had excepted; at the nearby tables, the excited customers spoke breathlessly of the sums Zunino and Zungri had invested in furnishings without a second thought to cost. Carlos Argentino pretended to be astonished by some feature or other of the lighting arrangement (with which, I felt, he was already familiar), and he said to me with a certain severity, "Grudgingly, you'll have to admit to the fact that these premises hold their own with many others far more in the public eye."
He then reread me four or five different fragments of the poem. He had revised them following his pet principle of verbal ostentation: where at first "blue" had been good enough, he now wallowed in "azures," "ceruleans," and "ultramarines." The word "milky" was too easy for him; in the course of an impassioned description of a shed where wool was washed, he chose such words as "lacteal," "lactescent," and even made one up -- "lactinacious." After that, straight out, he condemned our modern mania for having books prefaced, "a practice already held up to scorn by the Prince of Wits in his own grafeful preface to theQuixote." He admitted, however, that for the opening of his new work an attention-getting foreword might prove valuable -- "an accolade signed by a literary hand of renown." He next went on to say that he considered publishing the initial cantos of his poem. I then began to understand the unexpected telephone call; Daneri was going to ask me to contribute a foreword to his pedantic hodgepodge. My fear turned out unfounded; Carlos Argentino remarked, with admiration and envy, that surely he could not be far wrong in qualifying with the ephitet "solid" the prestige enjoyed in every circle by Álvaro Melián Lafinur, a man of letters, who would, if I insisted on it, be only too glad to dash off some charming opening words to the poem. In order to avoid ignominy and failure, he suggested I make myself spokesman for two of the book's undeniable virtues -- formal perfection and scientific rigour -- "inasmuch as this wide garden of metaphors, of figures of speech, of elegances, is inhospitable to the least detail not strictly upholding of truth." He added that Beatriz had always been taken with Álvaro.

I agreed -- agreed profusely -- and explained for the sake of credibility that I would not speak to Álvaro the next day, Monday, but would wait until Thursday, when we got together for the informal dinner that follows every meeting of the Writers' Club. (No such dinners are ever held, but it is an established fact that the meetings do take place on Thursdays, a point which Carlos Argentino Daneri could verify in the daily papers, and which lent a certain reality to my promise.) Half in prophecy, half in cunning, I said that before taking up the question of a preface I would outline the unusual plan of the work. We then said goodbye.

Turning the corner of Bernardo de Irigoyen, I reviewed as impartially as possible the alternatives before me. They were: a) to speak to Álvaro, telling him the first cousin of Beatriz' (the explanatory euphemism would allow me to mention her name) had concocted a poem that seemed to draw out into infinity the possibilities of cacophony and chaos: b) not to say a word to Álvaro. I clearly foresaw that my indolence would opt for b.

But first thing Friday morning, I began worrying about the telephone. It offended me that that device, which had once produced the irrecoverable voice of Beatriz, could now sink so low as to become a mere receptacle for the futile and perhaps angry remonstrances of that deluded Carlos Argentino Daneri. Luckily, nothing happened -- except the inevitable spite touched off in me by this man, who had asked me to fulfill a delicate mission for him and then had let me drop.

Gradually, the phone came to lose its terrors, but one day toward the end of October it rang, and Carlos Argentino was on the line. He was deeply disturbed, so much so that at the outset I did not recognise his voice. Sadly but angrily he stammered that the now unrestrainable Zunino and Zungri, under the pretext of enlarging their already outsized "salon-bar," were about to take over and tear down this house.

"My home, my ancestral home, my old and inveterate Garay Street home!" he kept repeating, seeming to forget his woe in the music of his words.

It was not hard for me to share his distress. After the age of fifty, all change becomes a hateful symbol of the passing of time. Besides, the scheme concerned a house that for me would always stand for Beatriz. I tried explaining this delicate scruple of regret, but Daneri seemed not to hear me. He said that if Zunino and Zungri persisted in this outrage, Doctor Zunni, his lawyer, would sue ipso facto and make them pay some fifty thousand dollars in damages. Zunni's name impressed me; his firm, although at the unlikely address of Caseros and Tacuarí, was nonetheless known as an old and reliable one. I asked him whether Zunni had already been hired for the case. Daneri said he would phone him that very afternoon. He hesitated, then with that level, impersonal voice we reserve for confiding something intimate, he said that to finish the poem he could not get along without the house because down in the cellar there was an Aleph. He explained that an Aleph is one of the points in space that contains all other points.

"It's in the cellar under the dining room," he went on, so overcome by his worries now that he forgot to be pompous. "It's mine -- mine. I discovered it when I was a child, all by myself. The cellar stairway is so steep that my aunt and uncle forbade my using it, but I'd heard someone say there was a world down there. I found out later they meant an old-fashioned globe of the world, but at the time I thought they were referring to the world itself. One day when no one was home I started down in secret, but I stumbled and fell. When I opened my eyes, I saw the Aleph."
"The Aleph?" I repeated.
"Yes, the only place on earth where all places are -- seen from every angle, each standing clear, without any confusion or blending. I kept the discovery to myself and went back every chance I got. As a child, I did not foresee that this privilege was granted me so that later I could write the poem. Zunino and Zungri will not strip me of what's mine -- no, and a thousand times no! Legal code in hand, Doctor Zunni will prove that my Aleph is inalienable."
I tried to reason with him. "But isn't the cellar very dark?" I said.
"Truth cannot penetrate a closed mind. If all places in the universe are in the Aleph, then all stars, all lamps, all sources of light are in it, too."
"You wait there. I'll be right over to see it."

I hung before he could say no. The full knowledge of a fact sometimes enables you to see all at once many supporting but previously unsuspected things. It amazed me not to have suspected until that moment that Carlos Argentino was a madman. As were all the Viterbos, when you came down to it. Beatriz (I myself often say it) was a woman, a child, with almost uncanny powers of clairvoyance, but forgetfulness, distractions, contempt, and a streak of cruelty were also in her, and perhaps these called for a pathological explanation. Carlos Argentino's madness filled me with spiteful elation. Deep down, we had always detested each other.

On Garay Street, the maid asked me kindly to wait. The master was, as usual, in the cellar developing pictures. On the unplayed piano, beside a large vase that held no flowers, smiled (more timeless than belonging to the past) the large photograph of Beatriz, in gaudy colours. Nobody could see us; in a seizure of tenderness, I drew close to the portrait and said to it, "Beatriz, Beatriz Elena, Beatriz Elena Viterbo, darling Beatriz, Beatriz now gone forever, it's me, it's Borges."

Moments later, Carlos came in. He spoke dryly. I could see he was thinking of nothing else but the loss of the Aleph.

"First a glass of pseudo-cognac," he ordered, "and then down you dive into the cellar. Let me warn you, you'll have to lie flat on your back. Total darkness, total immobility, and a certain ocular adjustment will also be necessary. From the floor, you must focus your eyes on the nineteenth step. Once I leave you, I'll lower the trapdoor and you'll be quite alone. You needn't fear the rodents very much -- though I know you will. In a minute or two, you'll see the Aleph -- the microcosm of the alchemists and Kabbalists, our true proverbial friend, the multum in parvo!"

Once we were in the dining room, he added, "Of course, if you don't see it, your incapacity will not invalidate what I have experienced. Now, down you go. In a short while you can babble with all of Beatriz' images."

Tired of his inane words, I quickly made my way. The cellar, barely wider than the stairway itself, was something of a pit. My eyes searched the dark, looking in vain for the globe Carlos Argentino had spoken of. Some cases of empty bottles and some canvas sacks cluttered one corner. Carlos picked up a sack, folded it in two, and at a fixed spot spread it out.
"As a pillow," he said, "this is quite threadbare, but if it's padded even a half-inch higher, you won't see a thing, and there you'll lie, feeling ashamed and ridiculous. All right now, sprawl that hulk of yours there on the floor and count off nineteen steps."

I went through with his absurd requirements, and at last he went away. The trapdoor was carefully shut. The blackness, in spite of a chink that I later made out, seemed to me absolute. For the first time, I realised the danger I was in: I'd let myself be locked in a cellar by a lunatic, after gulping down a glassful of poison! I knew that back of Carlos' transparent boasting lay a deep fear that I might not see the promised wonder. To keep his madness undetected, to keep from admitting he was mad, Carlos had to kill me. I felt a shock of panic, which I tried to pin to my uncomfortable position and not to the effect of a drug. I shut my eyes -- I opened them. Then I saw the Aleph.

I arrive now at the ineffable core of my story. And here begins my despair as a writer. All language is a set of symbols whose use among its speakers assumes a shared past. How, then, can I translate into words the limitless Aleph, which my floundering mind can scarcely encompass? Mystics, faced with the same problem, fall back on symbols: to signify the godhead, one Persian speaks of a bird that somehow is all birds; Alanus de Insulis, of a sphere whose center is everywhere and circumference is nowhere; Ezekiel, of a four-faced angel who at one and the same time moves east and west, north and south. (Not in vain do I recall these inconceivable analogies; they bear some relation to the Aleph.) Perhaps the gods might grant me a similar metaphor, but then this account would become contaminated by literature, by fiction. Really, what I want to do is impossible, for any listing of an endless series is doomed to be infinitesimal. In that single gigantic instant I saw millions of acts both delightful and awful; not one of them occupied the same point in space, without overlapping or transparency. What my eyes beheld was simultaneous, but what I shall now write down will be successive, because language is successive. Nonetheless, I'll try to recollect what I can.
On the back part of the step, toward the right, I saw a small iridescent sphere of almost unbearable brilliance. At first I thought it was revolving; then I realised that this movement was an illusion created by the dizzying world it bounded. The Aleph's diameter was probably little more than an inch, but all space was there, actual and undiminished. Each thing (a mirror's face, let us say) was infinite things, since I distinctly saw it from every angle of the universe. I saw the teeming sea; I saw daybreak and nightfall; I saw the multitudes of America; I saw a silvery cobweb in the center of a black pyramid; I saw a splintered labyrinth (it was London); I saw, close up, unending eyes watching themselves in me as in a mirror; I saw all the mirrors on earth and none of them reflected me; I saw in a backyard of Soler Street the same tiles that thirty years before I'd seen in the entrance of a house in Fray Bentos; I saw bunches of grapes, snow, tobacco, lodes of metal, steam; I saw convex equatorial deserts and each one of their grains of sand; I saw a woman in Inverness whom I shall never forget; I saw her tangled hair, her tall figure, I saw the cancer in her breast; I saw a ring of baked mud in a sidewalk, where before there had been a tree; I saw a summer house in Adrogué and a copy of the first English translation of Pliny -- Philemon Holland's -- and all at the same time saw each letter on each page (as a boy, I used to marvel that the letters in a closed book did not get scrambled and lost overnight); I saw a sunset in Querétaro that seemed to reflect the colour of a rose in Bengal; I saw my empty bedroom; I saw in a closet in Alkmaar a terrestrial globe between two mirrors that multiplied it endlessly; I saw horses with flowing manes on a shore of the Caspian Sea at dawn; I saw the delicate bone structure of a hand; I saw the survivors of a battle sending out picture postcards; I saw in a showcase in Mirzapur a pack of Spanish playing cards; I saw the slanting shadows of ferns on a greenhouse floor; I saw tigers, pistons, bison, tides, and armies; I saw all the ants on the planet; I saw a Persian astrolabe; I saw in the drawer of a writing table (and the handwriting made me tremble) unbelievable, obscene, detailed letters, which Beatriz had written to Carlos Argentino; I saw a monument I worshipped in the Chacarita cemetery; I saw the rotted dust and bones that had once deliciously been Beatriz Viterbo; I saw the circulation of my own dark blood; I saw the coupling of love and the modification of death; I saw the Aleph from every point and angle, and in the Aleph I saw the earth and in the earth the Aleph and in the Aleph the earth; I saw my own face and my own bowels; I saw your face; and I felt dizzy and wept, for my eyes had seen that secret and conjectured object whose name is common to all men but which no man has looked upon -- the unimaginable universe.

I felt infinite wonder, infinite pity.

"Feeling pretty cockeyed, are you, after so much spying into places where you have no business?" said a hated and jovial voice. "Even if you were to rack your brains, you couldn't pay me back in a hundred years for this revelation. One hell of an observatory, eh, Borges?"
Carlos Argentino's feet were planted on the topmost step. In the sudden dim light, I managed to pick myself up and utter, "One hell of a -- yes, one hell of a."

The matter-of-factness of my voice surprised me. Anxiously, Carlos Argentino went on.
"Did you see everything -- really clear, in colours?"

At that moment I found my revenge. Kindly, openly pitying him, distraught, evasive, I thanked Carlos Argentino Daneri for the hospitality of his cellar and urged him to make the most of the demolition to get away from the pernicious metropolis, which spares no one -- believe me, I told him, no one! Quietly and forcefully, I refused to discuss the Aleph. On saying goodbye, I embraced him and repeated that the country, that fresh air and quiet were the great physicians.

Out on the street, going down the stairways inside Constitution Station, riding the subway, every one of the faces seemed familiar to me. I was afraid that not a single thing on earth would ever again surprise me; I was afraid I would never again be free of all I had seen. Happily, after a few sleepless nights, I was visited once more by oblivion.

Postscript of March first, 1943 -- Some six months after the pulling down of a certain building on Garay Street, Procrustes & Co., the publishers, not put off by the considerable length of Daneri's poem, brought out a selection of its "Argentine sections". It is redundant now to repeat what happened. Carlos Argentino Daneri won the Second National Prize for Literature. ["I received your pained congratulations," he wrote me. "You rage, my poor friend, with envy, but you must confess -- even if it chokes you! -- that this time I have crowned my cap with the reddest of feathers; my turban with the most caliph of rubies."] First Prize went to Dr. Aita; Third Prize, to Dr. Mario Bonfanti. Unbelievably, my own book The Sharper's Cards did not get a single vote. Once again dullness and envy had their triumph! It's been some time now that I've been trying to see Daneri; the gossip is that a second selection of the poem is about to be published. His felicitous pen (no longer cluttered by the Aleph) has now set itself the task of writing an epic on our national hero, General San Martín.

I want to add two final observations: one, on the nature of the Aleph; the other, on its name. As is well known, the Aleph is the first letter of the Hebrew alphabet. Its use for the strange sphere in my story may not be accidental. For the Kabbala, the letter stands for the En Soph, the pure and boundless godhead; it is also said that it takes the shape of a man pointing to both heaven and earth, in order to show that the lower world is the map and mirror of the higher; for Cantor's Mengenlehre, it is the symbol of transfinite numbers, of which any part is as great as the whole. I would like to know whether Carlos Argentino chose that name or whether he read it -- applied to another point where all points converge - - in one of the numberless texts that the Aleph in his cellar revealed to him. Incredible as it may seem, I believe that the Aleph of Garay Street was a false Aleph.

Here are my reasons. Around 1867, Captain Burton held the post of British Consul in Brazil. In July, 1942, Pedro Henríquez Ureña came across a manuscript of Burton's, in a library at Santos, dealing with the mirror which the Oriental world attributes to Iskander Zu al-Karnayn, or Alexander Bicornis of Macedonia. In its crystal the whole world was reflected. Burton mentions other similar devices -- the sevenfold cup of Kai Kosru; the mirror that Tariq ibn-Ziyad found in a tower (Thousand and One Nights, 272); the mirror that Lucian of Samosata examined on the moon (True History, I, 26); the mirrorlike spear that the first book of Capella's Satyricon attributes; Merlin's universal mirror, which was "round and hollow... and seem'd a world of glas" (The Faerie Queene, III, 2, 19) -- and adds this curious statement: "But the aforesaid objects (besides the disadvantage of not existing) are mere optical instruments. The Faithful who gather at the mosque of Amr, in Cairo, are acquainted with the fact that the entire universe lies inside one of the stone pillars that ring its central court... No one, of course, can actually see it, but those who lay an ear against the surface tell that after some short while they perceive its busy hum... The mosque dates from the seventh century; the pillars come from other temples of pre-Islamic religions, since, as ibn-Khaldun has written: 'In nations founded by nomads, the aid of foreigners is essential in all concerning masonry.'"
Does this Aleph exist in the heart of a stone? Did I see it there in the cellar when I saw all things, and have I now forgotten it? Our minds are porous and forgetfulness seeps in; I myself am distorting and losing, under the wearing away of the years, the face of Beatriz.

El Aleph, 1945. Translation by Norman Thomas Di Giovanni in collaboration with the author.