Enhanced descriptions from Syndetics:

Optimists believe this is the best of all possible worlds. And pessimists fear that might really be the case. But what is the best of all possible worlds? How do we define it? Is it the world that operates the most efficiently? Or the one in which most people are comfortable and content? Questions such as these have preoccupied philosophers and theologians for ages, but there was a time, during the seventeenth and eighteenth centuries, when scientists and mathematicians felt they could provide the answer.

This book is their story. Ivar Ekeland here takes the reader on a journey through scientific attempts to envision the best of all possible worlds. He begins with the French physicist Maupertuis, whose least action principle asserted that everything in nature occurs in the way that requires the least possible action. This idea, Ekeland shows, was a pivotal breakthrough in mathematics, because it was the first expression of the concept of optimization , or the creation of systems that are the most efficient or functional. Although the least action principle was later elaborated on and overshadowed by the theories of Leonhard Euler and Gottfried Leibniz, the concept of optimization that emerged from it is an important one that touches virtually every scientific discipline today.

Tracing the profound impact of optimization and the unexpected ways in which it has influenced the study of mathematics, biology, economics, and even politics, Ekeland reveals throughout how the idea of optimization has driven some of our greatest intellectual breakthroughs. The result is a dazzling display of erudition--one that will be essential reading for popular-science buffs and historians of science alike.

Table of contents provided by Syndetics

• Introduction (p. 1)
• 1 Keeping the Beat (p. 3)
• 2 The Birth of Modern Science (p. 24)
• 3 The Least Action Principle (p. 44)
• 4 From Computations to Geometry (p. 79)
• 5 Poincare and Beyond (p. 102)
• 6 Pandora's Box (p. 117)
• 7 May the Best One Win (p. 129)
• 8 The End of Nature (p. 145)
• 9 The Common Good (p. 166)
• 10 A Personal Conclusion (p. 182)
• Appendix 1 Finding the Small Diameter of a Convex Table (p. 193)
• Appendix 2 The Stationary Action Principle for General Systems (p. 195)
• Bibliographical Notes (p. 197)
• Index (p. 199)

Reviews provided by Syndetics

CHOICE Review

What is the best of all possible worlds? How does nature work? Is ours perhaps a world in which phenomena are optimized? Ekeland (Univ. of British Columbia) leads us from Maupertuis to Popper in studying this problem. Pierre-Louis Moreau de Maupertuis posited the principle of least action; i.e., nature is organized along the principle of efficiency. Ekeland traces the mathematization of science by analyzing contributions of seminal figures such as Galileo, Descartes, Leibniz, Fermat, Huygens, Bohr, and Feynman. Although some phenomena are explainable via minimizing "action," most classical mechanical systems are chaotic. Systems of nonlinear differential equations describing such systems seldom have exact solutions; probabilistic system models tend to work best. Though Maupertuis may seem naive in retrospect, it is clear that this early model was the impetus for study, refutation, and eventually more coherent, albeit complex, explanations of natural phenomena. In the last chapter, Ekeland relates the idea of optimization to the social issue of "the common good." Readers will wish that there were more such chapters, and will not regret a minute spent on reading this book. This intelligent, eloquent, very accessible work will make new connections for virtually every reader. Ekeland is clearly a master teacher. Summing Up: Essential. Upper-division undergraduates through professionals; two-year technical program students. R. L. Pour Emory and Henry College

Author notes provided by Syndetics

Ivar Ekeland is professor of mathematics and economics at the University of British Columbia and director of the Pacific Institute for Mathematical Sciences