*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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