Complexity: A Guided Tour , MelanieMitchell Oxford U. Press , New York , 2009. $29.95 (349 pp.).  ISBN 978-0-19-512441-5

The notion of complexity is one of the most controversial and debated issues of scientific inquiry, and the chances are slim that the debate will be resolved anytime soon. Essentially, complexity is a collective noun for those uneasy feelings people have when faced with a system whose components and interactions are known but whose behavior adds up to more than the sum of its parts. But just what is it that makes us uncomfortable? Is it solely the system, or is it also our physical inability to make sense of the spectrum of behaviors produced by an interacting multicomponent system? Even the human brain, with its vast number of representational degrees of freedom, is limited by biophysical constraints.

Writing a book on complexity is a brave undertaking—anyone who chooses to do so becomes a target for criticism from both experts and journalists who feed on controversies. In Complexity: A Guided Tour, accomplished computer scientist Melanie Mitchell courageously takes the reader on an entertaining and illuminating journey through the jagged world of complex-systems research. Mitchell’s writing on each topic she addresses is lucid and factual, based on research by her and others in the field and reported on in peer-reviewed journals. When discussing a controversial idea, she gives a balanced presentation of the views of both its proponents and opponents.

Mitchell suggests—in my opinion, rightfully so—that researchers should focus on “common principles” and pull back from talking about things that must hold “generally” in complex systems. Her philosophy echoes Nigel Goldenfeld and Leo Kadanoff’s conclusion, expressed 10 years ago at the end of their article “Simple Lessons from Complexity”: “But each complex system is different; apparently there are no general laws for complexity. Instead, one must reach for ‘lessons’ that might, with insight and understanding, be learned in one system and applied to another” (Science, volume 284, page 89, 1999). Complex behavior could then be interpreted as emerging from a network interaction of those principles, as implicitly suggested in the book’s penultimate section and explicitly discussed in its concluding chapter.

Complexity: A Guided Tour occasionally reads as a list of seemingly unrelated topics, including universal computation, emergence, chaos, self-representation, species and genetic-level evolution, and complex networks. However, in some cases, Mitchell carefully chooses examples to illustrate the connection between complex behaviors in different systems; for instance, her computer model for making analogies (which only humans do well) is based on genetic algorithms and has much in common with models of how ants forage for food. She then considers a number of common principles that could be used as building blocks for a complexity science. That approach will inspire the reader to search for additional commonalities and principles.

Naturally, given the author’s background, the book provides a computer-science-like view of complex systems and emphasizes information processing (that is, computing) in various systems. That, I would argue, is the main strength of the book. As Mitchell asserts throughout the text, our brains are themselves complex systems, where we store, access, represent (or simulate), and generate information. And in part, learning and understanding occur through pattern matching between internal neuronal activity and external input. So it may not be surprising that representation and information theory will have a large role in foundations of complexity science, as suggested by Mitchell’s focus on the works of mathematicians and computer scientists such as Alan Turing, John von Neumann, Claude Shannon, and Norbert Wiener.

Although the emphasis on information and computation is, in my opinion, one strength of the book, I feel that the author could have explored its basic aspects in greater detail. In particular, two key issues deserve further discussion: the hierarchical (or terraced) encoding of information that occurs, for example, in the primate cerebral cortex, as shown by neuroscientists David Van Essen and Daniel Felleman; and the separation of scales in complex systems. Regarding the latter, I again quote Goldenfeld and Kadanoff: “Don’t model bulldozers with quarks” (page 88). In general, there’s no need to, because many complex systems exhibit a separation of scales—length, time, energy—that allows one to replace complex dynamics at a certain scale with effective models that statistically mimic the system’s behavior at that scale. Those models are then hierarchically put together (the brain processes information that way) to produce a multiscale description of the system. A section on how such models are generated could have included current research by practitioners and further strengthened an already solid book.

Complexity: A Guided Tour is well written and engaging, laced with candid humor and occasional blunt remarks about some of the major characters in the field. It is a fine introduction to complexity science and could serve as a first-rate text for an advanced course for undergraduates and an excellent guide for courses at the graduate level. Experts and nonspecialists alike will have a hard time putting it down.