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Borges and Mathematics

GUILLERMO MARTÍNEZ
Translated by Andrea G. Labinger
Copyright Date: 2012
Published by: Purdue University Press
https://www.jstor.org/stable/j.ctt6wq5rd
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    Borges and Mathematics
    Book Description:

    Borges and Mathematics is a short book of essays that explores the scientific thinking of the Argentine writer Jorge Luis Borges (1899-1986). Around half of the book consists of two “lectures” focused on mathematics. The rest of the book reflects on the relationship between literature, artistic creation, physics, and mathematics more generally. Written in a way that will be accessible even to those “who can only count to ten,” the book presents a bravura demonstration of the intricate links between the worlds of sciences and arts, and it is a thought-provoking call to dialog for readers from both traditions. The author, Guillermo Martínez, is both a recognized writer, whose murder mystery The Oxford Murders has been translated into thirty-five languages, and a PhD in mathematics. Contents: Borges and Mathematics: First Lecture; Borges and Mathematics: Second Lecture; The Golem and Artificial Intelligence; The Short Story as Logical System; A Margin Too Narrow; Euclid, or the Aesthetics of Mathematical Reasoning; Solutions and Disillusions; The Pythagorean Twins; The Music of Chance (Interview with Gregory Chaikin); Literature and Rationality; Who’s Afraid of the Big Bad One?; A Small, Small God; God’s Sinkhole. This book was originally published in spa as Borges y la matemática (2003). It has been translated with generous support from the Latino Cultural Center at Purdue University. Key points: • Presents complex mathematical and literary concepts in a way that is accessible to non-specialists. • Promotes dialog between readers from both humanist and scientific traditions. • Expands understanding of the Argentine writer, Jorge Luis Borges, including presenting some never-before-translated work.

    eISBN: 978-1-61249-251-3
    Subjects: Mathematics, Language & Literature

Table of Contents

  1. Front Matter
    (pp. i-iv)
  2. Table of Contents
    (pp. v-vi)
  3. ACKNOWLEDGMENTS
    (pp. vii-viii)
  4. PREFACE
    (pp. ix-xii)
  5. 1 BORGES AND MATHEMATICS: FIRST LECTURE: February 19, 2003
    (pp. 1-24)

    Whenever one chooses an angle or a theme, the phenomenon to be studied is often distorted, something physicists know well. It also happens whenever one tries to approach an author from a particular angle: one finds oneself mired in the quicksand of interpretation. In this regard, it’s good to keep in mind that the game of interpretation is a balancing act that allows for errors of omission or of commission. If we approach a Borges text, let’s say, from a purely mathematical, very specialized standpoint, we may end up above the text. Here, “above” really means outside: we might skew...

  6. 2 BORGES AND MATHEMATICS: SECOND LECTURE: February 26, 2003
    (pp. 25-60)

    I’d like to begin with a brief recapitulation of what we’ve seen in the first chapter; then I will bring in additional evidence to support what we’ve already said. I want to call your attention to the bookBorges: Textos recobrados, part of an effort to collect all his writings. It contains some truly remarkable essays, and Borges the polemicist is revealed. At the very beginning we spoke of Borges’ mathematical education. InTextos recobrados, there is a fairly technical article called “La cuarta dimensión,” which allows us to appreciate the fact that Borges was capable of reading mathematical texts,...

  7. 3 THE GOLEM AND ARTIFICIAL INTELLIGENCE
    (pp. 61-66)

    Although it is not yet clear if something that might properly be called “artificial intelligence” really exists (beyond certain possible, convincing simulations), through the miracle of theorizing specialists now speak of an “ancient era” and a “modern era” in this quest. In the “ancient era,” investigators tried to model intelligence as an algorithm distinct from the physical, a gigantic program designed for an ideal computer. In the “modern era,” efforts are being made to “embody” intelligence within an organic-spatial context through robots, the latter-day golem.

    Now I’d like to remind you of some verses from Borges’ poem about the Rabbi...

  8. 4 THE SHORT STORY AS LOGICAL SYSTEM
    (pp. 67-70)

    There are certain elements in the structure of the short story—brevity and rigor, for example—that too easily tempt us into formulating rules for the genre and dreaming up possible classifications and commandments. These efforts usually turn out either too vague and general to be of interest or else, regardless of how many carefully thought-out axioms are presented and precautions taken, they fail to consider some perfectly legitimate example of a short story that mocks the laws. And just as in that old-fashioned bookOne Hundred Ways to Say NO to a Sexual Proposition,the hundredth answer is YES;...

  9. 5 A MARGIN TOO NARROW
    (pp. 71-80)

    A man leans over a book at night. He is a high-ranking official in the court system in seventeenth-century France who filters petitions to the king and can send the accused to the bonfires of the Inquisition. His name is Pierre Fermat. Due to the gravity of his role and so as to avoid bribes or favoritism, he is not permitted a social life, but this proscription, far from being disturbing, allows him to devote himself to a secret passion for numbers. He spends his nights making notations in the margins of his copy of Diophantus’Arithmetica.

    On one of...

  10. 6 EUCLID, OR THE AESTHETICS OF MATHEMATICAL REASONING
    (pp. 81-86)

    At the end of the 1930s, a diminutive man with a fragile demeanor and a broad forehead arrived at the Universidad Nacional del Litoral, persecuted by Mussolini. He was Beppo Levi, among the most important mathematicians of the twentieth century. He had been hired as a researcher at one of the first specialized institutes in Argentina, but, due to a typical Argentine paradox, there was a sudden, devastating intervention, and Levi ended up teaching ordinary classes in mathematical analysis to first-year students. It was also in the city of Rosario in Argentina where hisLeyendo a Euclides(Reading Euclid) was...

  11. 7 SOLUTIONS AND DISILLUSIONMENT
    (pp. 87-90)

    In mathematics there is an elitist moment that corresponds to the correct intuition of the solution to a problem and is reserved for the enlightened few, and a second, genuinely democratic moment when that solution is revealed to one and all through a proof. On closer inspection, a mathematical proof is a succession of small, logical steps, connected to one another so that anyone may examine the links as thoroughly as possible. Ideally, each one of the steps should be so simple that any person possessing even the most basic acquaintance with symbols could check it almost automatically, verifying each...

  12. 8 THE PYTHAGOREAN TWINS
    (pp. 91-100)

    In May 2003 I had the opportunity to review Oliver Sacks’The Man Who Mistook His Wife for a Hatfor the Argentine newspaperLa Nación.Among this extraordinary collection of clinical tales, one of the most astonishing for any mathematician is “The Twins,” which reveals an unexpected source of “biological,” or more precisely, “neurophysiological” evidence for the formulation of a critical, stillunanswered question in the history of mathematics about prime numbers.

    Sacks relates that “The Twins . . . had been variously diagnosed as autistic, psychotic, or profoundly retarded” (195). In 1966, when Sacks began observing them, most of...

  13. 9 THE MUSIC OF CHANCE (INTERVIEW WITH GREGORY CHAITIN)
    (pp. 101-112)
    GREGORY CHAITIN

    Gregory Chaitin is an extraordinary mathematician. He spent half his youth in Manhattan and the other half in Buenos Aires. In 1957, when the Russians succeeded for the first time in placing a satellite in space, the North Americans, alarmed, created a series of advanced courses for students who were interested in science. So it was that at age twelve, and despite the fact that his father is a playwright, Chaitin began to study quantum physics and the theory of relativity at Columbia University. At fifteen he discovered a variation of Gödel’s theorem that allowed him to define the idea...

  14. 10 LITERATURE AND RATIONALITY
    (pp. 113-118)

    A particularly extremist thesis of our modern age, yet one that is widely accepted and repeated like a bromide of the times, proclaims all philosophical systems ineffective, all great syntheses of thought impossible, and reason’s ambition to account for reality unfeasible. It’s not hard to imagine why this thesis is so popular: there are too many philosophers; philosophy books are long; thinking is exhausting and causes headaches. And then, of course, in order to read Schopenhauer, we need to go back to Hume and Kant; in order to read Sartre, we must return to Heidegger; and we can’t get to...

  15. 11 WHO’S AFRAID OF THE BIG BAD ONE?
    (pp. 119-122)

    It’s well known that there is only one more effective way to kill conversation in a waiting room than to open a book, and that is to open a book of mathematics. The mere mention of the word “mathematics” induces chills and terror and can reduce the most confident adult to the tremors of division of fractions and other numerological nightmares of childhood. And despite the fact that mathematical thought has left its fingerprints all over the so-called humanities, from the Pythagoreans to the Vienna Circle, from Pascal’s theological wager to ethics according to Spinoza’s geometrical order, from Descartes’ first...

  16. 12 A SMALL, SMALL GOD
    (pp. 123-126)

    How many possible choices did God have in constructing the universe? This question, posed by Einstein, which in other eras might have been of concern to philosophers or theologians, through a paradox of postmodernism is about to be answered by modern physics. The point of departure for this journey to the end of night is a crucial astronomical observation made in 1929: no matter where a telescope is pointed, distant galaxies move away from us. Or, to express it more dramatically: the universe is expanding.

    It took physicists several decades to process this news theoretically; the belief in an essentially...

  17. 13 GOD’S SINKHOLE
    (pp. 127-130)

    I remembered this little story recently when I heard Stephen Hawking predict in an interview that soon, perhaps in the first decade of the millennium,² physics will arrive at a unified theory of the laws of the universe, with a mathematical explanation of the first moment of Creation.

    I recalled, as the reporter asked Hawking the inevitable question about what role would be left for God to play, Professor Katz’s cosmology classes at the Facultad de Ciencias Exactas and the terror he instilled in his students. Katz had studied at Oxford with Roger Penrose, Hawking’s dissertation director, and during his...

  18. APPENDIX A: MATHEMATICAL THEMES IN BORGES’ WORK
    (pp. 131-134)
  19. APPENDIX B: MATHEMATICAL BIBLIOGRAPHY OF WORKS CONSULTED BY BORGES
    (pp. 135-138)
  20. APPENDIX C: SOURCES OF ENGLISH TRANSLATIONS AND EXCERPTS
    (pp. 139-140)
  21. Back Matter
    (pp. 141-141)