The Broken Dice, and Other Mathematical Tales of Chance [Hardcover]

Ivar Ekeland (Author), Carol Volk (Translator)

Book Description

ISBN-10: 0226199916 | ISBN-13: 978-0226199917 | Publication Date: November 22, 1993 | Edition: 1

Ivar Ekeland extends his consideration of the catastrophe theory of the universe begun in his widely acclaimed Mathematics and the Unexpected, by drawing on rich literary sources, particularly the Norse saga of Saint Olaf, and such current topics as chaos theory, information theory, and particle physics.

"Ivar Ekeland gained a large and enthusiastic following with Mathematics and the Unexpected, a brilliant and charming exposition of fundamental new discoveries in the theory of dynamical systems. The Broken Dice continues the same theme, and in the same elegant, seemingly effortless style, but focuses more closely on the implications of those discoveries for the rest of human culture. What are chance and probability? How has our thinking about them been changed by the discovery of chaos? What are all of these concepts good for? . . . Ah, but, I mustn't give the game away, any more than I should if I were reviewing a detective novel. And this is just as gripping a tale. . . . Beg, borrow, or preferably buy a copy. . . . I guarantee you won't be disappointed."—Ian Stewart, Science

Editorial Reviews

From Publishers Weekly

This elegantly written essay is a subtle philosophical meditation on the role of chance, risk, fate and uncertainty in mathematics, physics, nature and our daily lives. Modern civilization "moves forward without measuring the risks incurred, and without thinking globally," warns Ekeland ( Mathematics and the Unexplained ), president of the Universite Paris-Dauphine. Stressing that chance is an inescapable, fundamental part of the universe, he examines its workings in subatomic physics, card playing, weather prediction, at Chernobyl and Three Mile Island, in chaos theory, statistics and information theory. Leavening his occasionally technical presentation with literary examples ranging from Norse sagas to Rabelais, Isaac Asimov and Jorge Luis Borges, Ekeland concludes that every decision-making problem has a moral dimension--and the more important the decision, the larger this dimension. Illustrated.
Copyright 1993 Reed Business Information, Inc.

From Library Journal

In this book, Ekeland confronts some of the questions faced by people who must use probability and statistical theory. He begins each section with a tale drawn from Norse legends, the Bible, or other sources and segues into mathematics. Starting with the problem of generating "random" numbers by nonrandom procedures, Ekeland then poses the philosophical question, "Is there really such a thing as chance or is it simply a manifestation of our own ignorance?" He later looks into the underlying ideas behind many branches of mathematics that deal with chance: information theory, game theory, chaos, statistics, evaluation of risk, even probabilistic number theory. The book's technical content is quite limited, frustrating the reader who would like to see more detailed examples. Nevertheless, these metaphysical musings by a knowledgeable probabilist make intriguing reading.
- Harold D. Shane, Baruch Coll., CUNY
Copyright 1993 Reed Business Information, Inc.

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Product Details

• Hardcover: 190 pages
• Publisher: University Of Chicago Press; 1 edition (November 22, 1993)
• Language: English
• ISBN-10: 0226199916
• ISBN-13: 978-0226199917
• Product Dimensions: 8.3 x 5.6 x 0.9 inches
• Shipping Weight: 12.2 ounces (View shipping rates and policies)
• Average Customer Review: 4.3 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #577,943 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

10 of 11 people found the following review helpful:

5.0 out of 5 stars intellectual fun, August 20, 2002

By A Customer

This review is from: The Broken Dice, and Other Mathematical Tales of Chance (Paperback)

If you had to go through it in graduate school you'd probably agree with me that behaviour under uncertainty is usually handled rather mechanically by professors. You may even have considered that, anyway, not much intuition could be behind those theories. Ivar Ekeland shows in this book that dealing with the fundamentals of expectations, probabilities, games, and risk can be fun, and you get the intuition to start thinking by yourself as well. Early morning reading, though.

7 of 7 people found the following review helpful:

5.0 out of 5 stars Even better than his first book, March 2, 2003

By 

Bukkene Bruse (Iowa) - See all my reviews
(VINE VOICE)   

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This review is from: The Broken Dice, and Other Mathematical Tales of Chance (Hardcover)

Ivar Ekeland is one of the better writers of popular mathematics. In "The Broken Dice," he continues with the themes explored in "Mathematics and the Unexpected." Divided into six chapters (Chance, Fate, Anticipation, Chaos, Risk and Statistics) the book is an elegant examination of the human struggle to find order in the seeming contingency that is the natural world. Mixed with the mathematical discussions are excerpts from Icelandic sagas, the Bible, and Shakespeare that reinforce the message that our analytical search for meaning is still fundamentally a humanistic endeavor.

0 of 4 people found the following review helpful:

3.0 out of 5 stars Elegant prose covers lack of novel insight, May 19, 2008

By 

David J. Aldous "gentleman scholar" (Alameda, CA USA) - See all my reviews
(REAL NAME)   

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This review is from: The Broken Dice, and Other Mathematical Tales of Chance (Hardcover)

As an aficionado of Norse sagas, I was intrigued to find that a mathematician wrote a book on probability framed by Saint Olaf's saga. Six essays on popular science topics, with clear explanations and interestingly non-standard historical and literary detours. But the choice of math topics (random number generators vs true randomness vs Kolmogorov complexity; random strategies in game theory; chaos, attractors, fractals and ergodicity; risk aversion and underestimation of rare serious events) seems in 2008 very unimaginative, and despite its colorful background the book brings no new insight or individualistic perspective to the science.