Complexity. A guided tour.

*(English)*Zbl 1215.00003
Oxford: Oxford University Press (ISBN 978-0-19-512441-5/hbk). xvi, 349 p. (2009).

The idea of writing this book came when the author was invited to give the Ulam Memorial Lectures at the Santa Fe Institute, an annual series of lectures on complex systems for a general audience. The book is meant to be a much extended version of those lectures and, as Professor Mitchell describes, it is “a guided tour, flavoured with my own perspectives, of some of the core ideas of the science of complexity – where they came from and where they are going. Above all else, I hope to communicate the deep enchantment of the ideas and debates and the incomparable excitement of pursuing them.”

The material in the book is organized into five parts. The first part describes the content and history of four subject areas that play the key role in the theory of complex systems: dynamics and chaos, information, computation, and evolution. Identification of common properties of complex systems such as complex collective behavior, signaling and information processing, and adaptation naturally leads to the definition of a complex system as “a system in which large networks of components with no central control and simple rules of operation give rise to complex collective behavior, sophisticated information processing, and adaptation via learning or evolution.”

Parts II to IV describe in more detail the interplay between the four fundamental subject areas. Namely, Part II addresses the self-reproducing computer programs and genetic algorithms. Cellular automata, information processing in living systems, and prospects of computer modeling are among the topics discussed in Part III. A complex world of networks embracing such sophisticated objects as the brain, genetic regulatory networks, or food webs is dealt with in Part IV. In the final Part V, the author briefly discusses the past and the future of the sciences of complexity. In the end of the book, the reader can find explanatory notes with additional details, a very impressive bibliography and a detailed index.

The book is richly illustrated, the exposition is transparent and easy to follow. The narration is so skillfully organized that no specific knowledge in science or mathematics is required for understanding the details; the text appeals to a very wide audience. Written in a lively manner, this delightful book provides an accessible introduction to the complexity theory; it educates and entertains at the same time.

The material in the book is organized into five parts. The first part describes the content and history of four subject areas that play the key role in the theory of complex systems: dynamics and chaos, information, computation, and evolution. Identification of common properties of complex systems such as complex collective behavior, signaling and information processing, and adaptation naturally leads to the definition of a complex system as “a system in which large networks of components with no central control and simple rules of operation give rise to complex collective behavior, sophisticated information processing, and adaptation via learning or evolution.”

Parts II to IV describe in more detail the interplay between the four fundamental subject areas. Namely, Part II addresses the self-reproducing computer programs and genetic algorithms. Cellular automata, information processing in living systems, and prospects of computer modeling are among the topics discussed in Part III. A complex world of networks embracing such sophisticated objects as the brain, genetic regulatory networks, or food webs is dealt with in Part IV. In the final Part V, the author briefly discusses the past and the future of the sciences of complexity. In the end of the book, the reader can find explanatory notes with additional details, a very impressive bibliography and a detailed index.

The book is richly illustrated, the exposition is transparent and easy to follow. The narration is so skillfully organized that no specific knowledge in science or mathematics is required for understanding the details; the text appeals to a very wide audience. Written in a lively manner, this delightful book provides an accessible introduction to the complexity theory; it educates and entertains at the same time.

Reviewer: Svitlana P. Rogovchenko (Umeå)

##### MSC:

00A09 | Popularization of mathematics |

68Q12 | Quantum algorithms and complexity in the theory of computing |

81P45 | Quantum information, communication, networks (quantum-theoretic aspects) |

90C60 | Abstract computational complexity for mathematical programming problems |

91D10 | Models of societies, social and urban evolution |

92B20 | Neural networks for/in biological studies, artificial life and related topics |

92C42 | Systems biology, networks |