GCC References to Math in Borges Article & Coding Notes Discussion

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Ohooyrongu111

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Glendale Community College

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As we mentioned, Borges is often called a "mathematical" writer. Clearly, there are multiple reasons for this label. First, he alludes to math and mathematical principles in many of his stories, but he also writes with a precision that is mathematical. He is able to align the sequence of his ideas with the sequence of his sentences.

Have you ever read an essay -- yours or anyone else's -- and noticed gaps in the reasoning or flow? Do you ever feel like you think faster than you type? As I mentioned on the Canvas homepage for this course, writing code helped me sequence my ideas and eliminate gaps in reasoning. If you miss a beat when programming, your program won't run. It simply won't work. Programming is never wrong. Programmers are wrong, so it trains you to write for an audience that needs ideas to be presented sequentially and logically.

This assignment has two parts.

Part 1: Write down 20 references to mathematics, geometry, or calculus from the stories by Borges we have read so far. You can must put them down as a list in note format with page numbers. I'll do the first one for you.

1. Geometry of Tlon (visual and tactile) (12)

Now you do 19 more. What we're doing here is using our active reading and annotation to isolate a specific topic. As a general rule, when you want to analyze a text or a novel, you can't analyze ALL of it. You have to isolate a portion of it -- a topic, character, theme, or motif -- so you can focus your analysis on a specific idea. I'm helping you focus on a specific motif now: mathematics.

Part 2: Next, we're going to work on writing sequentially and methodically. Go to this website (Links to an external site.). Once there, get Elsa to level 20. To do this, you need to help her achieve her goals in each level by moving coding blocks to the workspace. So, for the first level, you move the block that reads "Move forward by 100 pixels" to the workspace under "Run." Then, click the button that reads "Run" under the picture of Elsa on ice on the left-hand side of the screen.

If you code successfully, Elsa will accomplish her goal for that session. If you don't code effectively, you'll have to start that level over again.

While you're doing this, take notes. At which level(s) did you fail to help Elsa meet her objective? Why do you think you made this mistake? Was it a silly mistake? Do those ever happen in your essays? If you never made a mistake and helped Elsa meet each objective on the first try, keep going to level 50 until you run into a problem.

In this part, jot down some notes about where you stumbled, and write about why you think you made this mistake. Then, in no more or less than three sentences, explain how this assignment can make you a better writer.

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Labyrinths Selected Stories & Other Writings Jorge Luis Borges Edited by Donald A. Yates & James E. Irby Preface by André Maurois a.b.e-book v3.0 / Notes at EOF Back Cover: Although his work has been restricted to the short story, the essay, and poetry, Jorge Luis Borges of Argentina is recognized all over the world as one of the most original and significant figures in modern literature. In his preface André Maurois writes: "Borges is a great writer who has composed only little essays or short narratives. Yet they suffice for us to call him great because of their wonderful intelligence, their wealth of invention, and their tight, almost mathematical style." Labyrinths is a representative selection of Borges' writing, some forty pieces drawn from various of his books published over the years. The translations are by Harriet de Onís, Anthony Kerrigan, and others, including the editors, who have provided a biographical and critical introduction, as well as an extensive bibliography. Copyright © 1962, 1964 by New Directions Publishing Corporation Library of Congress Catalog Card Number: 64-25440 (ISBN: 0-08112-0012-4) All rights reserved. Except for brief passages quoted in a newspaper, magazine, radio, or television review, no part of this book may be reproduced in any form or by any means, electronic or mechanical, including photocopying and recording, or by any information storage and retrieval system, without permission in writing from the Publisher. This augmented edition was first published in 1964. Labyrinths, Selected Stories & Other Writings, by Jorge Luis Barges, has been translated and published by agreement with Emecé Editores, S, A., Bolivar 177, Buenos Aires, Argentina. All selections here included and translated into English have been taken from the following volumes originally published in Spanish by Emecé: Ficciones (1956), El Aleph (1957), Discussión (1957), Otras Inquisiciones (1960) and El Hacedor (1960). 2 Contents Preface Introduction Fictions Tlön, Uqbar, Orbis Tertius The Garden of Forking Paths The Lottery in Babylon Pierre Menard, Author of the Quixote The Circular Ruins The Library of Babel Funes the Memorious The Shape of the Sword Theme of the Traitor and the Hero Death and the Compass The Secret Miracle Three Versions of Judas The Sect of the Phoenix The Immortal The Theologians Story of the Warrior and the Captive Emma Zunz The House of Asterion Deutsches Requiem Averroes' Search The Zahir The Waiting The God's Script 3 Essays The Argentine Writer and Tradition The Wall and the Books The Fearful Sphere of Pascal Partial Magic in the Quixote Valéry as Symbol Kafka and His Precursors Avatars of the Tortoise The Mirror of Enigmas A Note on (toward) Bernard Shaw A New Refutation of Time Parables Inferno, 1, 32 Paradiso, XXXI, 108 Ragnarök Parable of Cervantes and the Quixote The Witness A Problem Borges and I Everything and Nothing Elegy Chronology Bibliography 4 Preface Jorge Luis Borges is a great writer who has composed only little essays or short narratives. Yet they suffice for us to call him great because of their wonderful intelligence, their wealth of invention, and their tight, almost mathematical, style. Argentine by birth and temperament, but nurtured on universal literature, Borges has no spiritual homeland. He creates, outside time and space, imaginary and symbolic worlds. It is a sign of his importance that, in placing him, only strange and perfect works can be called to mind. He is akin to Kafka, Poe, sometimes to Henry James and Wells, always to Valéry by the abrupt projection of his paradoxes in what has been called "his private metaphysics." I His sources are innumerable and unexpected. Borges has read everything, and especially what nobody reads any more: the Cabalists, the Alexandrine Greeks, medieval philosophers. His erudition is not profound -- he asks of it only flashes of lightning and ideas -- but it is vast. For example, Pascal wrote: "Nature is an infinite sphere whose center is everywhere, whose circumference is nowhere." Borges sets out to hunt down this metaphor through the centuries. He finds in Giordano Bruno (1584): "We can assert with certainty that the universe is all center, or that the center of the universe is everywhere and its circumference nowhere." But Giordano Bruno had been able to read in a twelfth-century French theologian, Alain de Lille, a formulation borrowed from the Corpus Hermeticum (third century): "God is an intelligible sphere whose center is everywhere and whose circumference is nowhere." Such researches, carried out among the Chinese as among the Arabs or the Egyptians, delight Borges, and lead him to the subjects of his stories. Many of his masters are English. He has an infinite admiration for Wells and is indignant that Oscar Wilde could define him as "a scientific Jules Verne." Borges makes the observation that the fiction of Jules Verne speculates on future probability (the submarine, the trip to the moon), that of Wells on pure possibility (an invisible man, a flower that devours a man, a machine to explore time), or even on impossibility (a man returning from the hereafter with a future flower). Beyond that, a Wells novel symbolically represents features inherent 5 in all human destinies. Any great and lasting book must be ambiguous, Borges says; it is a mirror that makes the reader's features known, but the author must seem to be unaware of the significance of his work -which is an excellent description of Borges's own art. "God must not engage in theology; the writer must not destroy by human reasonings the faith that art requires of us." He admires Poe and Chesterton as much as he does Wells. Poe wrote perfect tales of fantastic horror and invented the detective story, but he never combined the two types of writing. Chesterton did attempt and felicitously brought off this tour de force. Each of Father Brown's adventures proposes to explain, in reason's name, an unexplainable fact. "Though Chesterton disclaimed being a Poe or Kafka, there was, in the material out of which his ego was molded, something that tended to nightmare." Kafka was a direct precursor of Borges. The Castle might be by Borges, but he would have made it into a ten-page story, both out of lofty laziness and out of concern for perfection. As for Kafka's precursors, Borges's erudition takes pleasure in finding them in Zeno of Elea, Kierkegaard and Robert Browning. In each of these authors there is some Kafka, but if Kafka had not written, nobody would have been able to notice it -- whence this very Borgesian paradox: "Every writer creates his own precursors." Another man who inspires him is the English writer John William Dunne, author of such curious books about time, in which he claims that the past, present and future exist simultaneously, as is proved by our dreams. (Schopenhauer, Borges remarks, had already written that life and dreams are leaves of the same book: reading them in order is living; skimming through them is dreaming.) In death we shall rediscover all the instants of our life and we shall freely combine them as in dreams. "God, our friends, and Shakespeare will collaborate with us." Nothing pleases Borges better than to play in this way with mind, dreams, space and time. The more complicated the game becomes, the happier he is. The dreamer can be dreamed in his turn. "The Mind was dreaming; the world was its dream." In all philosophers, from Democritus to Spinoza, from Schopenhauer to Kierkegaard, he is on the watch for paradoxical intellectual possibilities. II There are to be found in Valéry's notebooks many notes such 6 as this: "Idea for a frightening story: it is discovered that the only remedy for cancer is living human flesh. Consequences." I can well imagine a piece of Borges "fiction" written on such a theme. Reading ancient and modern philosophers, he stops at an idea or a hypothesis. The spark flashes. "If this absurd postulate were developed to its extreme logical consequences," he wonders, "what world would be created?" For example, an author, Pierre Menard, undertakes to compose Don Quixote -- not another Quixote, but the Quixote. His method? To know Spanish well, to rediscover the Catholic faith, to war against the Moors, to forget the history of Europe -- in short, to be Miguel de Cervantes. The coincidence then becomes so total that the twentiethcentury author rewrites Cervantes' novel literally, word for word, and without referring to the original. And here Borges has this astonishing sentence: "The text of Cervantes and that of Menard are verbally identical, but the second is almost infinitely richer." This he triumphantly demonstrates, for this subject, apparently absurd, in fact expresses a real idea: the Quixote that we read is not that of Cervantes, any more than our Madame Bovary is that of Flaubert. Each twentiethcentury reader involuntarily rewrites in his own way the masterpieces of past centuries. It was enough to make an extrapolation in order to draw Borges's story out of it. Often a paradox that ought to bowl us over does not strike us in the abstract form given it by philosophers. Borges makes a concrete reality out of it. The "Library of Babel" is the image of the universe, infinite and always started over again. Most of the books in this library are unintelligible, letters thrown together by chance or perversely repeated, but sometimes, in this labyrinth of letters, a reasonable line or sentence is found. Such are the laws of nature, tiny cases of regularity in a chaotic world. The "Lottery in Babylon" is another ingenious and penetrating staging of the role of chance in life. The mysterious Company that distributes good and bad luck reminds us of the "musical banks" in Samuel Butler's Erewhon. Attracted by metaphysics, but accepting no system as true, Borges makes out of all of them a game for the mind. He discovers two tendencies in himself: "one to esteem religious and philosophical ideas for their aesthetic value, and even for what is magical or marvelous in their content. That is perhaps the indication of an essential skepticism. The other is to suppose in advance that the quantity of fables or metaphors of which man's imagination is capable 7 is limited, but that this small number of inventions can be everything to everyone." Among these fables or ideas, certain ones particularly fascinate him: that of Endless Recurrence, or the circular repetition of all the history of the world, a theme dear to Nietzsche; that of the dream within a dream; that of centuries that seem minutes and seconds that seem years ("The Secret Miracle"); that of the hallucinatory nature of the world. He likes to quote Novalis: "The greatest of sorcerers would be the one who would cast a spell on himself to the degree of taking his own phantasmagoria for autonomous apparitions. Might that not be our case?" Borges answers that indeed it is our case: it is we who have dreamed the universe. We can see in what it consists, the deliberately constructed interplay of the mirrors and mazes of this thought, difficult but always acute and laden with secrets. In all these stories we find roads that fork, corridors that lead nowhere, except to other corridors, and so on as far as the eye can see. For Borges this is an image of human thought, which endlessly makes its way through concatenations of causes and effects without ever exhausting infinity, and marvels over what is perhaps only inhuman chance. And why wander in these labyrinths? Once more, for aesthetic reasons; because this present infinity, these "vertiginous symmetries," have their tragic beauty. The form is more important than the content. III Borges's form often recalls Swift's: the same gravity amid the absurd, the same precision of detail. To demonstrate an impossible discovery, he will adopt the tone of the most scrupulous scholar, mix imaginary writings in with real and erudite sources. Rather than write a whole book, which would bore him, he analyzes a book which has never existed. "Why take five hundred pages," he asks, "to develop an idea whose oral demonstration fits into a few minutes?" Such is, for example, the narrative that bears this bizarre title: "Tlön, Uqbar, Orbis Tertius." This concerns the history of an unknown planet, complete "with its architectures and quarrels, with the terror of its mythologies and the uproar of its languages, its emperors and seas, its minerals and birds and fish, its algebra and fire, its theological and metaphysical controversies." This invention of a new world appears to be the work of a secret society of astronomers, engineers, biologists, metaphysicians and geometricians. This world that they have created, 8 Tlön, is a Berekeleyan and Kierkegaardian world where only inner life exists. On Tlön everyone has his own truth; external objects are whatever each one wants. The international press broadcasts this discovery, and very soon the world of Tlön obliterates our world. An imaginary past takes the place of our own. A group of solitary scientists has transformed the universe. All this is mad, subtle, and gives food for endless thought. Other stories by Borges are parables, mysterious and never explicit; still others are detective narratives in the manner of Chesterton. Their plots remain entirely intellectual. The criminal exploits his familiarity with the methods of the detective. It is Dupin against Dupin or Maigret against Maigret. One of these pieces of "fiction" is the insatiable search for a person through the scarcely perceptible reflections that he has left on other souls. In another, because a condemned man has noticed that expectations never coincide with reality, he imagines the circumstances of his own death. Since they have thus become expectations, they can no longer become realities. These inventions are described in a pure and scholarly style which must be linked up with Poe, "who begat Baudelaire, who begat Mallarmé, who begat Valéry," who begat Borges. It is especially by his rigor that he reminds us of Valéry. "To be in love is to create a religion whose god is fallible." By his piled-up imperfects he sometimes recalls Flaubert; by the rarity of his adjectives, St. John Perse. "The inconsolable cry of a bird." But, once these relationships are pointed out, it must be said that Borges's style is, like his thought, highly original. Of the metaphysicians of Tlön he writes: "They seek neither truth nor likelihood; they seek astonishment. They think metaphysics is a branch of the literature of fantasy." That rather well defines the greatness and the art of Borges. ANDRÉ MAUROIS of the French Academy Translated by Sherry Mangan Introduction Jorge Luis Borges was born on 24 August 1899 in Buenos Aires, of Spanish, English and (very remotely) Portuguese Jewish 9 origin. His parents were of the intellectual middle class and descended from military and political figures prominent in the struggles for Argentine national independence and unity that occupied most of the nineteenth century. After completing his secondary education in Geneva and then spending some three years in Spain associated with the avant-garde ultraísta group of poets, Borges returned to Buenos Aires in 1921. There he immediately became the leading exponent and theorist of Argentine ultraísmo, distinguished from its Spanish counterpart by a peculiar fusion of modern expressionist form and anachronistic nostalgia for certain national values -- values most palpably embodied for those writers in the old criollo quarters of Buenos Aires -- which were by then disappearing amid the postwar boom and rush of foreign immigration. Borges's and his companions' situation was not unlike that of some North American writers of the same generation who suffered the impact of war, industrialism and modern European art on a tranquil Midwestern or Southern heritage. But out of these general conditions, shared by many in our time, Borges has created a work like no other. Perhaps the most striking characteristic of his writings is their extreme intellectual reaction against all the disorder and contingency of immediate reality, their radical insistence on breaking with the given world and postulating another. Born into the dizzying flux and inconstancy of a far-flung border area of Western culture, keen witness of the general crisis of that culture, Borges has used his strangely gifted mind -- the mind of a Cabalist, of a seventeenth-century "metaphysical," of a theorist of pure literature much like Poe or Valéry -- to erect an order with what Yeats called "monuments of unageing intellect." Borges is skeptical as few have ever been about the ultimate value of mere ideas and mere literature. But he has striven to turn this skepticism into an ironic method, to make of disbelief an aesthetic system, in which what matters most is not ideas as such, but their resonances and suggestions, the drama of their possibilities and impossibilities, the immobile and lasting quintessence of ideas as it is distilled at the dead center of their warring contradictions. Until about 1930 Borges's main creative medium was poetry: laconic free-verse poems which evoked scenes and atmospheres of old Buenos Aires or treated timeless themes of love, death and the self. He also wrote many essays on subjects of literary criticism, metaphysics and language, essays reminiscent of Chesterton's in their compactness and unexpected paradoxes. The lucidity and verbal precision of these 10 writings belie the agitated conditions of avant-garde polemic and playfulness under which most of them were composed. During these years Borges was content to seek expression in serene lyric images perhaps too conveniently abstracted from the surrounding world and have all his speculations and creations respond primarily to the need for a new national literature as he saw it. The years from 1930 to 1940, however, brought a deep change in Borges's work. He virtually abandoned poetry and turned to the short narrative genre. Though he never lost his genuine emotion for the unique features of his native ground, he ceased to exalt them nationalistically as sole bulwarks against threatening disorder and began to rank them more humbly within a context of vast universal processes: the nightmarish city of "Death and the Compass" is an obvious stylization of Buenos Aires, no longer idealized as in the poems, but instead used as the dark setting for a tragedy of the human intellect. The witty and already very learned young poet who had been so active in editing such little reviews as Martín Fierro, Prisma and Proa, became a sedentary writer-scholar who spent many solitary hours in reading the most varied and unusual works of literature and philosophy and in meticulously correcting his own manuscripts, passionately but also somewhat monstrously devoted to the written word as his most vital experience, as failing eyesight and other crippling afflictions made him more and more a semi-invalid, more and more an incredible mind in an ailing and almost useless body, much like his character Ireneo Funes. Oppressed by physical reality and also by the turmoil of Europe, which had all-too-direct repercussions in Argentina, Borges sought to create a coherent fictional world of the intelligence. This world is essentially adumbrated in "Tlön, Uqbar, Orbis Tertius." As Borges slyly observes there, Tlön is no "irresponsible figment of the imagination"; the stimulus which prompted its formulation is stated with clarity (though not without irony) toward the end of that story's final section, projected as a kind of tentative Utopia into the future beyond the grim year 1940 when it was written: Ten years ago any symmetry with a semblance of order -- dialectical materialism, anti-Semitism, Nazism -- was sufficient to charm the minds of men. How could one do other than submit to Tlön, to the minute and vast evidence of an orderly planet? It is useless to answer that reality is also orderly. Perhaps it is, but in accordance with divine laws -- I translate: inhuman laws -- which we never quite grasp. Tlön is surely a labyrinth, but it is a labyrinth devised by men, a labyrinth destined to be deciphered by men. 11 Borges's metaphysical fictions, his finest creations, which are collected in the volumes Ficciones (1945) and El Aleph (1949), all elaborate upon the varied idealist possibilities outlined in the "article" on Tlön. In these narratives the analytical and imaginative functions previously kept separate in his essays and poems curiously fuse, producing a form expressive of all the tension and complexity of Borges's mature thought. His fictions are always concerned with processes of striving which lead to discovery and insight; these are achieved at times gradually, at other times suddenly, but always with disconcerting and even devastating effect. They are tales of the fantastic, of the hyperbolic, but they are never content with fantasy in the simple sense of facile wish-fulfillment. The insight they provide is ironic, pathetic: a painful sense of inevitable limits that block total aspirations. Some of these narratives ("Tlön, Uqbar, Orbis Tertius," "Pierre Menard, Author of the Quixote" "Three Versions of Judas," "The Sect of the Phoenix") might be called "pseudo essays" -- mock scrutinies of authors or books or learned subjects actually of Borges's own invention -- that in turning in upon themselves make the "plot" (if it can be called that) an intricate interplay of creation and critique. But all his stories, whatever their outward form, have the same self-critical dimension; in some it is revealed only in minimal aspects of tone and style (as, for example, in "The Circular Ruins"). Along with these "vertical" superpositions of different and mutually qualifying levels, there are also "horizontal" progressions of qualitative leaps, after the manner of tales of adventure or of crime detection (Borges's favorite types of fiction). Unexpected turns elude the predictable; hidden realities are revealed through their diverse effects and derivations. Like his beloved Chesterton, who made the Father Brown stories a vehicle for his Catholic theology, Borges uses mystery and the surprise effect in literature to achieve that sacred astonishment at the universe which is the origin of all true religion and metaphysics. However, Borges as theologian is a complete heretic, as the casuistical "Three Versions of Judas" more than suffices to show. Borges once claimed that the basic devices of all fantastic literature are only four in number: the work within the work, the contamination of reality by dream, the voyage in time, and the double. These are both his essential themes -- the problematical nature of the world, of knowledge, of time, of the self -- and his essential techniques 12 of construction. Indeed, in Borges's narratives the usual distinction between form and content virtually disappears, as does that between the world of literature and the world of the reader. We almost unconsciously come to accept the world of Tlön because it has been so subtly inserted into our own. In "Theme of the Traitor and the Hero," Borges's discovery of his own story (which is worked up before our very eyes and has areas "not yet revealed" to him), Nolan's of Kilpatrick's treason, Ryan's of the curious martyrdom, and ours of the whole affair, are but one awareness of dark betrayal and creative deception. We are transported into a realm where fact and fiction, the real and the unreal, the whole and the part, the highest and the lowest, are complementary aspects of the same continuous being: a realm where "any man is all men," where "all men who repeat a line of Shakespeare are William Shakespeare." The world is a book and the book is a world, and both are labyrinthine and enclose enigmas designed to be understood and participated in by man. We should note that this all-comprising intellectual unity is achieved precisely by the sharpest and most scandalous confrontation of opposites. In "Avatars of the Tortoise," the paradox of Zeno triumphantly demonstrates the unreality of the visible world, while in "The Library of Babel" it shows the anguishing impossibility of the narrator's ever reaching the Book of Books. And in "The Immortal," possibly Borges's most complete narrative, the movements toward and from immortality become one single approximation of universal impersonality. Borges is always quick to confess his sources and borrowings, because for him no one has claim to originality in literature; all writers are more or less faithful amanuenses of the spirit, translators and annotators of pre-existing archetypes. (Hence Tlön, the impersonal and hereditary product of a "secret society"; hence Pierre Menard, the writer as perfect reader.) By critics he has often been compared with Kafka, whom he was one of the first to translate into Spanish. Certainly, we can see the imprint of his favorite Kafka story, "The Great Wall of China," on "The Lottery in Babylon" and "The Library of Babel"; the similarity lies mainly in the narrators' pathetically inadequate examination of an impossible subject, and also in the idea of an infinite, hierarchical universe, with its corollary of infinite regression. But the differences between the two writers are perhaps more significant than their likenesses. Kafka's minutely and extensively established portrayals of degradation, his irreducible and enigmatic situations, contrast strongly with Borges's compact but 13 vastly significant theorems, his all-dissolving ratiocination. Kafka wrote novels, but Borges has openly confessed he cannot; his miniature forms are intense realizations of Poe's famous tenets of unity of effect and brevity to the exclusion of "worldly interests." And no matter how mysterious they may seem at first glance, all Borges's works contain the keys to their own elucidation in the form of clear parallelisms with other of his writings and explicit allusions to a definite literary and philosophical context within which he has chosen to situate himself. The list of Pierre Menard's writings, as Borges has observed, is not "arbitrary," but provides a "diagram of his mental history" and already implies the nature of his "subterranean" undertaking. All the footnotes in Borges's fictions, even those marked "Editor's Note," are the author's own and form an integral part of the works as he has conceived them. Familiarity with Neo-Platonism and related doctrines will clarify Borges's preferences and intentions, just as it will, say, Yeats's or Joyce's. But, as Borges himself has remarked of the theological explications of Kafka's work, the full enjoyment of his writings precedes and in no way depends upon such interpretations. Greater and more important than his intellectual ingenuity is Borges's consummate skill as a narrator, his magic in obtaining the most powerful effects with a strict economy of means. Borges's stories may seem mere formalist games, mathematical experiments devoid of any sense of human responsibility and unrelated even to the author's own life, but quite the opposite is true. His idealist insistence on knowledge and insight, which mean finding order and becoming part of it, has a definite moral significance, though that significance is for him inextricably dual: his traitors are always somehow heroes as well. And all his fictional situations, all his characters, are at bottom autobiographical, essential projections of his experiences as writer, reader and human being (also divided, as "Borges and I" tells us). He is the dreamer who learns he is the dreamed one, the detective deceived by the hidden pattern of crimes, the perplexed Averroes whose ignorance mirrors the author's own in portraying him. And yet, each of these intimate failures is turned into an artistic triumph. It could be asked what such concerns of a total man of letters have to do with our plight as ordinary, bedeviled men of our bedeviled time. Here it seems inevitable to draw a comparison with Cervantes, so apparently unlike Borges, but whose name is not invoked in vain in his stories, essays and parables. Borges's fictions, like the enormous fiction of Don Quixote, grow out of the deep 14 confrontation of literature and life which is not only the central problem of all literature but also that of all human experience: the problem of illusion and reality. We are all at once writers, readers and protagonists of some eternal story; we fabricate our illusions, seek to decipher the symbols around us and see our efforts overtopped and cut short by a supreme Author; but in our defeat, as in the Mournful Knight's, there can come the glimpse of a higher understanding that prevails, at our expense. Borges's "dehumanized" exercises in ars combinatoria are no less human than that. Narrative prose is usually easier to translate than verse, but Borges's prose raises difficulties not unlike those of poetry, because of its constant creative deformations and cunning artifices. Writers as diverse as George Moore and Vladimir Nabokov have argued that translations should sound like translations. Certainly, since Borges's language does not read "smoothly" in Spanish, there is no reason it should in English. Besides, as was indicated above, he considers his own style at best only a translation of others': at the end of "Tlön, Uqbar, Orbis Tertius" he speaks of making an "uncertain" version of Sir Thomas Browne's Urn Burial after the manner of the great Spanish Baroque writer Francisco de Quevedo. Borges's prose is in fact a modern adaptation of the Latinized Baroque stil coupé. He has a penchant for what seventeenth- and eighteenth-century rhetoricians called "hard" or "philosophic" words, and will often use them in their strict etymological sense, restoring radical meanings with an effect of metaphorical novelty. In the opening sentence of "The Circular Ruins," "unanimous" means quite literally "of one mind" (unus animus) and thus foreshadows the magician's final discovery. Elevated terms are played off against more humble and direct ones; the image joining unlike terms is frequent; heterogeneous contacts are also created by Borges's use of colons and semicolons in place of causal connectives to give static, elliptical, overlapping effects. Somewhat like Eliot in The Waste Land, Borges will deliberately work quotations into the texture of his writing. The most striking example is "The Immortal," which contains many more such "intrusions or thefts" than its epilogue admits. All his other stories do the same to some degree: there are echoes of Gibbon in "The Lottery in Babylon," of Spengler in "Deutsches Requiem," of Borges himself in "The Library of Babel" and "Funes the Memorious." Borges has observed that "the Baroque is that style which deliberately exhausts (or tries to exhaust) its possibilities and borders on its own caricature." A self-parodying tone 15 is particularly evident in "Pierre Menard, Author of the Quixote," "The Zahir," "The Sect of the Phoenix." In that sense, Borges also ironically translates himself. Most of the present volume is given over to a sizable selection of Borges's fictions. The essays here represent only a very small portion of his production in that form; they have been chosen for the importance of their themes in Borges's work as a whole and for their relevance to the stories, which were written during the same years. All are taken from his best essay collection, Otras inquisiciones (1952), with the exception of "The Argentine Writer and Tradition" (originally a lecture), which is contained in the revised edition of another collection entitled Discusión (1957). Because of his near-blindness, Borges ceased to write stories after 1953 (though "Borges and I" suggest other reasons for the abandonment of that genre), and since then he has concentrated on even shorter forms which can be dictated more easily. The parables concluding this collection are examples of that later work. They are all found in the volume El hacedor (1960). Borges's somewhat belated recognition as a major writer of our time has come more from Europe than from his native America. The 1961 Formentor Prize, which he shared with Samuel Beckett, is the most recent token of that recognition. In Argentina, save for the admiration of a relatively small group, he has often been criticized as non-Argentine, as an abstruse dweller in an ivory tower, though his whole work and personality could only have emerged from that peculiar crossroads of the River Plate region, and his nonpolitical opposition to Perón earned him persecutions during the years of the dictatorship. Apparently, many of his countrymen cannot pardon in him what is precisely his greatest virtue -- his almost superhuman effort to transmute his circumstances into an art as universal as the finest of Europe -- and expect their writers to be uncomplicated reporters of the national scene. A kind of curious inverse snobbism is evident here. As the Argentine novelist Ernesto Sábato remarked in 1945, "if Borges were French or Czech, we would all be reading him enthusiastically in bad translations." Not being French has undoubtedly also relegated Borges to comparative obscurity in the English-speaking countries, where it is rare that a Hispanic writer is ever accorded any major importance at all. Perhaps this selection of his writings will help correct that oversight and justify the critical judgments of René Etiemble and Marcel Brion, who have found in Borges the very perfection of the cosmopolitan spirit, and in his work 16 one of the most extraordinary expressions in all Western literature of modern man's anguish of time, of space, of the infinite. J. E. I. Tlön, Uqbar, Orbis Tertius I I owe the discovery of Uqbar to the conjunction of a mirror and an encyclopedia. The mirror troubled the depths of a corridor in a country house on Gaona Street in Ramos Mejía; the encyclopedia is fallaciously called The Anglo-American Cyclopaedia (New York, 1917) and is a literal but delinquent reprint of the Encyclopaedia Britannica of 1902. The event took place some five years ago. Bioy Casares had had dinner with me that evening and we became lengthily engaged in a vast polemic concerning the composition of a novel in the first person, whose narrator would omit or disfigure the facts and indulge in various contradictions which would permit a few readers -very few readers -- to perceive an atrocious or banal reality. From the remote depths of the corridor, the mirror spied upon us. We discovered (such a discovery is inevitable in the late hours of the night) that mirrors have something monstrous about them. Then Bioy Casares recalled that one of the heresiarchs of Uqbar had declared that mirrors and copulation are abominable, because they increase the number of men. I asked him the origin of this memorable observation and he answered that it was reproduced in The Anglo-American Cyclopaedia, in its article on Uqbar. The house (which we had rented furnished) had a set of this work. On the last pages of Volume XLVI we found an article on Upsala; on the first pages of Volume XLVII, one on UralAltaic Languages, but not a word about Uqbar. Bioy, a bit taken aback, consulted the volumes of the index. In vain he exhausted all of the imaginable spellings: Ukbar, Ucbar, Ooqbar, Ookbar, Oukbahr. . . Before leaving, he told me that it was a region of Iraq or of Asia Minor. I must confess that I agreed with some discomfort. I conjectured that this undocumented country and its anonymous heresiarch were a fiction devised by Bioy's modesty in order to justify a statement. The fruitless examination of one of Justus Perthes' atlases fortified my doubt. 17 The following day, Bioy called me from Buenos Aires. He told me he had before him the article on Uqbar, in Volume XLVI of the encyclopedia. The heresiarch's name was not forthcoming, but there was a note on his doctrine, formulated in words almost identical to those he had repeated, though perhaps literarily inferior. He had recalled: Copulation and mirrors are abominable. The text of the encyclopedia said: For one of those gnostics, the visible universe was an illusion or (more precisely) a sophism. Mirrors and fatherhood are abominable because they multiply and disseminate that universe. I told him, in all truthfulness, that I should like to see that article. A few days later he brought it. This surprised me, since the scrupulous cartographical indices of Ritter's Erdkunde were plentifully ignorant of the name Uqbar. The tome Bioy brought was, in fact, Volume XLVI of the Anglo-American Cyclopaedia. On the half-title page and the spine, the alphabetical marking (Tor-Ups) was that of our copy, but, instead of 917, it contained 921 pages. These four additional pages made up the article on Uqbar, which (as the reader will have noticed) was not indicated by the alphabetical marking. We later determined that there was no other difference between the volumes. Both of them (as I believe I have indicated) are reprints of the tenth Encyclopaedia Britannica. Bioy had acquired his copy at some sale or other. We read the article with some care. The passage recalled by Bioy was perhaps the only surprising one. The rest of it seemed very plausible, quite in keeping with the general tone of the work and (as is natural) a bit boring. Reading it over again, we discovered beneath its rigorous prose a fundamental vagueness. Of the fourteen names which figured in the geographical part, we only recognized three -- Khorasan, Armenia, Erzerum -- interpolated in the text in an ambiguous way. Of the historical names, only one: the impostor magician Smerdis, invoked more as a metaphor. The note seemed to fix the boundaries of Uqbar, but its nebulous reference points were rivers and craters and mountain ranges of that same region. We read, for example, that the lowlands of Tsai Khaldun and the Axa Delta marked the southern frontier and that on the islands of the delta wild horses procreate. All this, on the first part of page 918. In the historical section (page 920) we learned that as a result of the religious persecutions of the thirteenth century, the orthodox believers sought refuge on these islands, where to this day their obelisks remain and where it is not uncommon to unearth their stone mirrors. The section on Language 18 and Literature was brief. Only one trait is worthy of recollection: it noted that the literature of Uqbar was one of fantasy and that its epics and legends never referred to reality, but to the two imaginary regions of Mlejnas and Tlön. . . The bibliography enumerated four volumes which we have not yet found, though the third -- Silas Haslam: History of the Land Called Uqbar, 1874 -- figures in the catalogues of Bernard Quaritch's book shop.* The first, Lesbare und lesenswerthe Bemerkungen über das Land Ukkbar in Klein-Asien, dates from 1641 and is the work of Johannes Valentinus Andreä. This fact is significant; a few years later, I came upon that name in the unsuspected pages of De Quincey (Writings, Volume XIII) and learned that it belonged to a German theologian who, in the early seventeenth century, described the imaginary community of Rosae Crucis -- a community that others founded later, in imitation of what he had prefigured. * Haslam has also published A General History of Labyrinths. That night we visited the National Library. In vain we exhausted atlases, catalogues, annuals of geographical societies, travelers' and historians' memoirs: no one had ever been in Uqbar. Neither did the general index of Bioy's encyclopedia register that name. The following day, Carlos Mastronardi (to whom I had related the matter) noticed the black and gold covers of the Anglo-American Cyclopaedia in a bookshop on Corrientes and Talcahuano. . . He entered and examined Volume XLVI. Of course, he did not find the slightest indication of Uqbar. II Some limited and waning memory of Herbert Ashe, an engineer of the southern railways, persists in the hotel at Adrogué, amongst the effusive honeysuckles and in the illusory depths of the mirrors. In his lifetime, he suffered from unreality, as do so many Englishmen; once dead, he is not even the ghost he was then. He was tall and listless and his tired rectangular beard had once been red. I understand he was a widower, without children. Every few years he would go to England, to visit (I judge from some photographs he showed us) a sundial and a few oaks. He and my father had entered into one of those close (the adjective is excessive) English friendships 19 that begin by excluding confidences and very soon dispense with dialogue. They used to carry out an exchange of books and newspapers and engage in taciturn chess games. . . I remember him in the hotel corridor, with a mathematics book in his hand, sometimes looking at the irrecoverable colors of the sky. One afternoon, we spoke of the duodecimal system of numbering (in which twelve is written as 10). Ashe said that he was converting some kind of tables from the duodecimal to the sexagesimal system (in which sixty is written as 10). He added that the task had been entrusted to him by a Norwegian, in Rio Grande do Sul. We had known him for eight years and he had never mentioned his sojourn in that region. . . We talked of country life, of the capangas, of the Brazilian etymology of the word gaucho (which some old Uruguayans still pronounce gaúcho) and nothing more was said -- may God forgive me -- of duodecimal functions. In September of 1937 (we were not at the hotel), Herbert Ashe died of a ruptured aneurysm. A few days before, he had received a sealed and certified package from Brazil. It was a book in large octavo. Ashe left it at the bar, where -- months later -- I found it. I began to leaf through it and experienced an astonished and airy feeling of vertigo which I shall not describe, for this is not the story of my emotions but of Uqbar and Tlön and Orbis Tertius. On one of the nights of Islam called the Night of Nights, the secret doors of heaven open wide and the water in the jars becomes sweeter; if those doors opened, I would not feel what I felt that afternoon. The book was written in English and contained 1001 pages. On the yellow leather back I read these curious words which were repeated on the title page: A First Encyclopaedia of Tlön. Vol. XI. Hlaer to Jangr. There was no indication of date or place. On the first page and on a leaf of silk paper that covered one of the color plates there was stamped a blue oval with this inscription: Orbis Tertius. Two years before I had discovered, in a volume of a certain pirated encyclopedia, a superficial description of a nonexistent country; now chance afforded me something more precious and arduous. Now I held in my hands a vast methodical fragment of an unknown planet's entire history, with its architecture and its playing cards, with the dread of its mythologies and the murmur of its languages, with its emperors and its seas, with its minerals and its birds and its fish, with its algebra and its fire, with its theological and metaphysical controversy. And all of it articulated, coherent, with no visible doctrinal intent or tone of parody. In the "Eleventh Volume" which I have mentioned, there are 20 allusions to preceding and succeeding volumes. In an article in the N. R. F. which is now classic, Néstor Ibarra has denied the existence of those companion volumes; Ezequiel Martínez Estrada and Drieu La Rochelle have refuted that doubt, perhaps victoriously. The fact is that up to now the most diligent inquiries have been fruitless. In vain we have upended the libraries of the two Americas and of Europe. Alfonso Reyes, tired of these subordinate sleuthing procedures, proposes that we should all undertake the task of reconstrucing the many and weighty tomes that are lacking: ex ungue leonem. He calculates, half in earnest and half jokingly, that a generation of tlönistas should be sufficient. This venturesome computation brings us back to the fundamental problem: Who are the inventors of Tlön? The plural is inevitable, because the hypothesis of a lone inventor -- an infinite Leibniz laboring away darkly and modestly -- has been unanimously discounted. It is conjectured that this brave new world is the work of a secret society of astronomers, biologists, engineers, metaphysicians, poets, chemists, algebraists, moralists, painters, geometers. . . directed by an obscure man of genius. Individuals mastering these diverse disciplines are abundant, but not so those capable of inventiveness and less so those capable of subordinating that inventiveness to a rigorous and systematic plan. This plan is so vast that each writer's contribution is infinitesimal. At first it was believed that Tlön was a mere chaos, an irresponsible license of the imagination; now it is known that it is a cosmos and that the intimate laws which govern it have been formulated, at least provisionally. Let it suffice for me to recall that the apparent contradictions of the Eleventh Volume are the fundamental basis for the proof that the other volumes exist, so lucid and exact is the order observed in it. The popular magazines, with pardonable excess, have spread news of the zoology and topography of Tlön; I think its transparent tigers and towers of blood perhaps do not merit the continued attention of all men. I shall venture to request a few minutes to expound its concept of the universe. Hume noted for all time that Berkeley's arguments did not admit the slightest refutation nor did they cause the slightest conviction. This dictum is entirely correct in its application to the earth, but entirely false in Tlön. The nations of this planet are congenitally idealist. Their language and the derivations of their language -- religion, letters, metaphysics -- all presuppose idealism. The world for them is not a concourse of objects in space; it is a 21 heterogeneous series of independent acts. It is successive and temporal, not spatial. There are no nouns in Tlön's conjectural Ursprache, from which the "present" languages and the dialects are derived: there are impersonal verbs, modified by monosyllabic suffixes (or prefixes) with an adverbial value. For example: there is no word corresponding to the word "moon," but there is a verb which in English would be "to moon" or "to moonate." "The moon rose above the river" is hlör u fang axaxaxas mlö, or literally: "upward behind the on-streaming it mooned." The preceding applies to the languages of the southern hemisphere. In those of the northern hemisphere (on whose Ursprache there is very little data in the Eleventh Volume) the prime unit is not the verb, but the monosyllabic adjective. The noun is formed by an accumulation of adjectives. They do not say "moon," but rather "round airy-light on dark" or "pale-orange-of-the-sky" or any other such combination. In the example selected the mass of adjectives refers to a real object, but this is purely fortuitous. The literature of this hemisphere (like Meinong's subsistent world) abounds in ideal objects, which are convoked and dissolved in a moment, according to poetic needs. At times they are determined by mere simultaneity. There are objects composed of two terms, one of visual and another of auditory character: the color of the rising sun and the faraway cry of a bird. There are objects of many terms: the sun and the water on a swimmer's chest, the vague tremulous rose color we see with our eyes closed, the sensation of being carried along by a river and also by sleep. These second-degree objects can be combined with others; through the use of certain abbreviations, the process is practically infinite. There are famous poems made up of one enormous word. This word forms a poetic object created by the author. The fact that no one believes in the reality of nouns paradoxically causes their number to be unending. The languages of Tlön's northern hemisphere contain all the nouns of the Indo-European languages -- and many others as well. It is no exaggeration to state that the classic culture of Tlön comprises only one discipline: psychology. All others are subordinated to it. I have said that the men of this planet conceive the universe as a series of mental processes which do not develop in space but successively in time. Spinoza ascribes to his inexhaustible divinity the attributes of extension and thought; no one in Tlön would understand the juxtaposition of the first (which is typical only of certain states) and the second -- which is a perfect synonym of the cosmos. In other 22 words, they do not conceive that the spatial persists in time. The perception of a cloud of smoke on the horizon and then of the burning field and then of the half-extinguished cigarette that produced the blaze is considered an example of association of ideas. This monism or complete idealism invalidates all science. If we explain (or judge) a fact, we connect it with another; such linking, in Tlön, is a later state of the subject which cannot affect or illuminate the previous state. Every mental state is irreducible: the mere fact of naming it -- i.e., of classifying it -- implies a falsification. From which it can be deduced that there are no sciences on Tlön, not even reasoning. The paradoxical truth is that they do exist, and in almost uncountable number. The same thing happens with philosophies as happens with nouns in the northern hemisphere. The fact that every philosophy is by definition a dialectical game, a Philosophic des Ah Ob, has caused them to multiply. There is an abundance of incredible systems of pleasing design or sensational type. The metaphysicians of Tlön do not seek for the truth or even for verisimilitude, but rather for the astounding. They judge that metaphysics is a branch of fantastic literature. They know that a system is nothing more than the subordination of all aspects of the universe to any one such aspect. Even the phrase "all aspects" is rejectable, for it supposes the impossible addition of the present and of all past moments. Neither is it licit to use the plural "past moments," since it supposes another impossible operation. . . One of the schools of Tlön goes so far as to negate time: it reasons that the present is indefinite, that the future has no reality other than as a present hope, that the past has no reality other than as a present memory.* Another school declares that all time has already transpired and that our life is only the crepuscular and no doubt falsified and mutilated memory or reflection of an irrecoverable process. Another, that the history of the universe -- and in it our lives and the most tenuous detail of our lives -- is the scripture produced by a subordinate god in order to communicate with a demon. Another, that the universe is comparable to those cryptographs in which not all the symbols are valid and that only what happens every three hundred nights is true. Another, that while we sleep here, we are awake elsewhere and that in this way every man is two men. * Russell (The Analysis of Mind, 1921, page 159) supposes that the planet has been created a few minutes ago, furnished with a humanity that "remembers" an illusory past 23 Amongst the doctrines of Tlön, none has merited the scandalous reception accorded to materialism. Some thinkers have formulated it with less clarity than fervor, as one might put forth a paradox. In order to facilitate the comprehension of this inconceivable thesis, a heresiarch of the eleventh century* devised the sophism of the nine copper coins, whose scandalous renown is in Tlön equivalent to that of the Eleatic paradoxes. There are many versions of this "specious reasoning," which vary the number of coins and the number of discoveries; the following is the most common: *A century, according to the duodecimal system, signifies a period of a hundred and forty-four years. On Tuesday, X crosses a deserted road and loses nine copper coins. On Thursday, Y finds in the road four coins, somewhat rusted by Wednesday's rain. On Friday, Z discovers three coins in the road. On Friday morning, X finds two coins in the corridor of his house. The heresiarch would deduce from this story the reality -- i.e., the continuity -- of the nine coins which were recovered. It is absurd (he affirmed) to imagine that four of the coins have not existed between Tuesday and Thursday, three between Tuesday and Friday afternoon, two between Tuesday and Friday morning. It is logical to think that they have existed -- at least in some secret way, hidden from the comprehension of men -- at every moment of those three periods. The language of Tlön resists the formulation of this paradox; most people did not even understand it. The defenders of common sense at first did no more than negate the veracity of the anecdote. They repeated that it was a verbal fallacy, based on the rash application of two neologisms not authorized by usage and alien to all rigorous thought: the verbs "find" and "lose," which beg the question, because they presuppose the identity of the first and of the last nine coins. They recalled that all nouns (man, coin, Thursday, Wednesday, rain) have only a metaphorical value. They denounced the treacherous circumstance "somewhat rusted by Wednesday's rain," which presupposes what is trying to be demonstrated: the persistence of the four coins from Tuesday to Thursday. They explained that equality is one thing and identity another, and formulated a kind of reductio ad absurdum: the hypothetical case of nine men who on nine successive nights suffer a severe pain. Would it not be ridiculous -- they questioned -- to pretend that this pain is one and the same?* They said that the heresiarch was prompted only by the blasphemous intention of 24 attributing the divine category of being to some simple coins and that at times he negated plurality and at other times did not. They argued: if equality implies identity, one would also have to admit that the nine coins are one. * Today, one of the churches of Tlön Platonically maintains that a certain pain, a certain greenish tint of yellow, a certain temperature, a certain sound, are the only reality. All men, in the vertiginous moment of coitus, are the same man. All men who repeat a line from Shakespeare are William Shakespeare. Unbelievably, these refutations were not definitive. A hundred years after the problem was stated, a thinker no less brilliant than the heresiarch but of orthodox tradition formulated a very daring hypothesis. This happy conjecture affirmed that there is only one subject, that this indivisible subject is every being in the universe and that these beings are the organs and masks of the divinity. X is Y and is Z. Z discovers three coins because he remembers that X lost them; X finds two in the corridor because he remembers that the others have been found. . . The Eleventh Volume suggests that three prime reasons determined the complete victory of this idealist pantheism. The first, its repudiation of solipsism; the second, the possibility of preserving the psychological basis of the sciences; the third, the possibility of preserving the cult of the gods. Schopenhauer (the passionate and lucid Schopenhauer) formulates a very similar doctrine in the first volume of Parerga und Paralipomena. The geometry of Tlön comprises two somewhat different disciplines: the visual and the tactile. The latter corresponds to our own geometry and is subordinated to the first. The basis of visual geometry is the surface, not the point. This geometry disregards parallel lines and declares that man in his movement modifies the forms which surround him. The basis of its arithmetic is the notion of indefinite numbers. They emphasize the importance of the concepts of greater and lesser, which our mathematicians symbolize as > and
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20 References to math in Borges article:
1. Geometry of Tlon (visual and tactile) (12)
2. Duodecimal system of numbering (descriptive) (20)
3. Prime unit (descriptive) (22)
4. Algebra example (tactile) (24)
5. Logical reasoning about the labyrinth (descriptive) (33-34)
6. Infinity (tactile) (37)
7. Logic and symmetry (descriptive) (41)
8. ...


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