Borges and Mathematics

Front Cover

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Frontmatter

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Table of Contents

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Acknowledgments

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pp. vii-

To my patient mathematics professors, Roberto Cignoli, Marta Sagastume, and Hernán Cendra; to Professor Alicia Borinsky, who invited me to lecture on Borges and mathematics for the first time at Boston University; to Soledad Costantini and Ana Quiroga of the Department of Literature at MALBA for...

Preface

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pp. ix-xi

I owe the impulse and initial idea for this book to a trip I made to the United States in 2001, and more specifically to an invitation by Professor Alicia Borinsky during that visit to lecture at Boston University on the connection between Borges and mathematics...

1. Borges and Mathematics: First Lecture: February 19, 2003

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pp. 1-23

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...

2. Borges and Mathematics: Second Lecture: February 26, 2003

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pp. 25-59

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 book Borges: Textos recobrados, part of an effort to collect all his writings. It contains some truly remarkable essays, and...

3. The Golem and Artificial Intelligence

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pp. 61-65

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...

4. The Short Story as Logical System

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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...

5. A Margin Too Narrow

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pp. 71-79

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...

6. Euclid, or the Aesthetics of Mathematical Reasoning

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pp. 81-85

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...

7. Solutions and Disillusionment

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pp. 87-89

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...

8. The Pythagorean Twins

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pp. 91-99

In May 2003 I had the opportunity to review Oliver Sacks’ The Man Who Mistook His Wife for a Hat for the Argentine newspaper La 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...

9. The Music of Chance (Interview with Gregory Chaitin)

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pp. 101-112

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...

10. Literature and Rationality

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pp. 113-117

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...

11. Who’s Afraid of the Big Bad One?

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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...

12. A Small, Small God

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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...

13. God’s Sinkhole

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pp. 127-129

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, physics will arrive at a unified theory of the laws of the universe, with a mathematical explanation of the first moment of Creation...

Appendix A

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pp. 131-134

Appendix B

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pp. 135-137

Appendix C

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pp. 139-140