The Broken Dice:
And Other Mathematical Tales of Chance

Ivar Ekeland

translated from the French by Carol Volk
The University of Chicago Press 1993
A book review by Danny Yee © 1997
With essays on chance, fate, anticipation, chaos, risk, and statistics, The Broken Dice is as much philosophy as mathematics. Each of its essays begins with a story taken from the Icelandic sagas or the Bible and is illustrated with examples from elsewhere in literature, history, and everyday life.

In "Chance", Olaf Haroldsson's dicing for an island with the king of Sweden (from the Heimskringla) is connected, via a Borgesian tale of a now-lost monastic manuscript, to the problem of pseudo-random number generation. "Fate" looks at contingency and determinism in mathematics, exploring regularity in sequences, entropy, and contingent series and touching on the possible contingency of mathematics itself. "Anticipation" considers expectations and how they influence their own accuracy; Ekeland weaves examples from markets, poker, and soccer in with stories from The Saga of Olaf Trygvesson and Rabelais. The longest essay, "Chaos", is a brief introduction to chaos theory, to the concepts of exponential instability and attractors; examples include the stability of the solar system and Gylippus' meeting of the Peloponnesian fleet in 413 BC. Gunnar's abrupt decision not to go into exile in Njal's Saga is the starting point for "Risk", which examines the psychology of human risk-avoidance and risk-taking, ranging from the Athenian decision to fight at Marathon to the hazards of nuclear technology. And a brief piece on "Statistics" exposes its philosophical and mathematical foundations — having started with Joseph, Pharaoh, and the seven years of famine and plenty.

The Broken Dice is a wonderful work, an exploration of the ties between mathematics and philosophy (outside mathematical logic). The essays vary in their assumption of mathematical knowledge: anyone totally unfamiliar with chaos theory will not find "Chaos" an ideal introduction, for example, but no mathematics at all is needed to follow "Risk" and the other essays assume no more than basic high school mathematics. The Broken Dice will entertain mathematicians and non-mathematicians alike, but especially those with a humanities background, who will most appreciate the historical and literary references.

June 1997

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%T The Broken Dice
%S And Other Mathematical Tales of Chance
%A Ekeland, Ivar
%M French
%F Volk, Carol
%I The University of Chicago Press
%D 1993
%O paperback, index
%G ISBN 0226199924
%P 183pp