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Reviewer: H. Van Dyke Parunak

Phrases such as "chaos theory," "complex adaptive systems," and "complexity science" have become increasingly common over the past three decades. Catalyzed by the Santa Fe Institute, this interdisciplinary movement has brought together ideas from fields as diverse as mathematics, physics, computer science (CS), biology, and sociology. Mitchell, who spent ten years at the Santa Fe Institute and continues as an external faculty member, brings together the various strands that contribute to this new approach. This book is an expanded version of Mitchell's Ulam Memorial Lectures at the Santa Fe Institute [1]. Mitchell's task is a daunting one; as she acknowledges in the last chapter, there is no single science of complexity, although a number of common themes appear over and over in the work of researchers who self-identify with complexity. Mitchell's tour will be a helpful introduction to those in various disciplines who seek a gentle introduction to this emerging specialty. Part 1, chapters 1 to 7, introduces the concept of complexity through a series of examples, and outlines some of the individual disciplines that interact under the rubric of complexity, including nonlinear dynamics and chaos from physics; information and computation from CS; and evolution and genetics from biology. Chapter 7 surveys various attempts to quantify complexity. The next 11 chapters illustrate how these component ideas come together in various ways. Chapters 8 and 9 discuss self-reproducing and evolving automata that illustrate the fruitfulness of crossing biology with CS. Chapters 10 to 14 show how the notion of computation can be applied to systems that seem quite remote from the common laptop. These include cellular automata (a highly parallel system of simple interacting components), interacting particles, and living systems. Mitchell describes her own innovative research in computational models of analogy-making, and also discusses the usefulness of computer models in studying a variety of social and economic systems. Many disciplines use network diagrams in various forms to represent structures of interest to them. The study of these networks has recently become a unifying theme in the complexity community. Chapters 15 to 18 introduce recent developments in this field, and then show how they can be used to articulate complex genetic interactions. The complexity enterprise has not been without its detractors. The book's final chapter confronts some of these criticisms and speculates on how the field will evolve. Mitchell writes for a popular audience. Along with technical ideas, she regularly introduces the reader to the human side of complexity, providing brief biographical introductions to key researchers who have contributed both to the underlying ideas and to their modern synthesis. In addition to over 90 figures and charts that support the technical exposition, she includes over 30 portraits of people whose work underlies complexity. For those who want to dig deeper, there are 22 pages of endnotes with further technical detail, and references to the research literature. Although the book includes a detailed index and bibliography, it only goes up to the year 2007. Online Computing Reviews Service