The Chaos Avant-Garde: Memories of the Early Days of Chaos Theory Ralph Abraham and Yoshisuke Ueda. World Scientific (2000), price $58.00, ISBN: 9810244045.
Reviewer: R. Ghrist, University of Illinois Urbana-Champaign, USA.

This book is the result of the editors' querying various pioneers in dynamical systems theory for memoires of their experiences. The time frame of the remembrances is from 1959 (Smale's arrival in Rio) through 1974 (the ascendancy of the word chaos in the scientific and mathematical community). The raison d'etre for the avant garde moniker stems from the editorial decision to "invite only the avant-garde, the people who had struggled with chaos concepts before the acceptance of the new paradigm."

The contributing authors are S. Smale, Y. Ueda, R. Abraham, E. Lorenz, C. Mira, F. Takens, T. Y. Li, J. Yorke, and O. Rossler. The articles written by Smale, Ueda, and Lorenz are reprinted from various existing sources. The lengths of the articles vary dramatically. Takens' submission clocks in at approximately 500 words. Mira's submission encompasses over 100 pages.

The book is not technical; neither is it meant for the layperson, since it has little expository component. Several of the articles freely assume familiarity with dynamical systems terminology and history. The articles themselves range in style from being terse and factual to being eerily purple. Example: "The observer-centered light bubble which unites relativity and quantum mechanics would then no longer be only a prison to fear: Any better-understood bondage provides the seeds for its own undoing. A `technology of liberation' would join the theology of liberation."

First-hand history is always the most fascinating, if not the most detached and comprehensive. The reader of this text will not get a comprehensive history lesson in dynamical systems research from 1959-1974. But the reader will be treated to a wealth of fascinating anecdotes coupled with personal perspectives. Several of the articles reproduce early drawings and computer plots of now well-understood dynamical phenomena. These are especially heartening to see as an indication that dynamical systems has indeed matured.

Most readers will likely chafe at a few of the statements made in these memoires. More than one additional book could easily be filled with the contributions of the less-avant of the Old Guard of dynamical systems pioneers who were not invited to contribute. Nevertheless, as a window on the workings of the contributors, this book is an entertaining and informative sample.