The Broken Dice: And Other Mathematical Tales of Chance

by Ivar Ekeland, Carol Volk (Translator)

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

Genres: Mathematics, Science, History, Philosophy

183 pages, Hardcover

First published January 1, 1993

Reviews

[Bruce · Rating 3 out of 5]

For anyone embedded in historical determinism, there is nothing more troubling than the interference of an unexplained phenomenon, of pure contingency. Since the first anthropoid walked the earth, man has sought to survive by… drawing lessons from experience to anticipate the future. Accepting the inexplicable, resigning oneself to the unpredictable, means… perhaps compromising the survival of the species. As a result, we feel obliged to attribute occult meanings to events that have no apparent meaning…. In such circumstances, primitive man will invoke the gods and try to appease them, while modern man will invoke chance and make statistical calculations.… [A]s long as this explanation has not been found, no scientist can claim to be truly satisfied. (p. 126)

This passage fairly sums up Ivar Ekeland's rambling (but short!) collection of essays. Ekeland admits to their rambling nature in his prologue: "Reader, this book has six chapters. Choose your die; you know what to do." It's an easy read, but a bit unsatisfying for the lack of any sustained argument. Ekeland begins each chapter with an excerpt from Norse tradition (!) to launch into an associative tangent about a specific mathematical principle: chance events and probability theory, fate and determinism, information theory and decision-making (as these effect expectation and risk), the unpredictability caused by exponentially exploding minutiae (chaos), and the uncertain role statistics has to play in interpreting both objective reality and the narrow slice of it which we actually experience.

Toss these aside. Throughout, the author seems to be grappling with the relevance of the pursuit of knowledge, a relevance brought into question by the pursuit's apparent futility. So he swings from despair to determination to awe to acceptance, considering summaries of Newton, Poincare, Godel, Shannon, etc. alongside anecdotal recitations ranging from Theucydides, the Arabian Nights, and "The China Syndrome" (and mathematical illustrations of course). It's a disjointed but extremely literary road, one which radiates the elegance of its sources. This is a very zen work. For me, appreciation of its meaning arises through the experience of reading it rather than from its explicit content; Ekeland quotes Antonio Machado at p. 56:

Wanderer, your footsteps are
the road, and nothing more;
wanderer, there is no road,
the road is made by walking.

*

We should enjoy in the moment whatever it is that life has to offer, for the path itself leads nowhere.


[*original in Spanish]

[Mark · Rating 3 out of 5]

Readability 4. Rating 5. I have mixed feelings about this one. First, it’s a translation, and I think some of its essence may have been lost. Second, Ekeland weaves a great deal of Scandinavian folklore/mythology into his discussions of “chance”, broadly defined, often with only tenuous connections. Finally, the notation in many of his math forays is poor, and obscures his points. In all, the topics are intriguing and difficult, but I am not convinced that his discussions are the most transparent and lucid (I feel this because some of the topics – statistics and human attitudes toward ambiguity and risk – I have covered in GSB classes, without which his points would have been lost).

[Rebeka · Rating 2 out of 5]

Ένα βιβλίο που σε παραπλανεί λίγο με τον τίτλο του. Αναφέρεται σε μαθηματικές ιστορίες και περίμενα όντως μαθηματικές ιστορίες που όμως δεν είδα. Παρόλα αυτά καταπιάνεται με κάποια θέματα, όπως είναι η τύχη, το πεπρωμένο, η πρόβλεψη, το χάος, ο κίνδυνος και η επιστήμη της στατιστικής, που αν μη τι άλλο σχετίζονται άμεσα με τα Μαθηματικά. Θεωρώ ότι κάποιες γνώσεις σε θέματα μαθηματικών είναι απαραίτητες ώστε κάποιος να κατανοήσει πλήρως αυτό το βιβλίο.
Σε κάποια σημεία πλατιάζει αρκετά και κουράζει.

[Deqlan · Rating 3 out of 5]

This book attempts to debunk 'chance' mathematically, meeting with some success and some insurmountable obstacles. Meanwhile, the writer recounts old world myths to portray the role that chance, game theory and number statistics play in our collective cultural conciousness. The math is dense and dry, but the rest of the book is thought provoking.