From Chaos to Complexity

book reviews , quently from Krishnan as from her nemeses. Y But after the first 90 pages, apart from a AR

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stealing, the novel takes a more mundane HO turn and becomes a description of the biotechnology business plan to capitalize on Krishnan’s discoveries. The interesting human aspects of the characters, the inner Y SAMS,/SCIENCE P conflicts of scientists succumbing to com- petitive drives and the temptations of com- 8 mercialization, become secondary to the not-so-suspenseful fate of their stock options.

Overall, the reader is most likely to be T CAMAZINE, , GREGOR gripped by the well-researched biology of T NO and the “jouissance” derived from read- YK, SCO ing about the science of sex, a term that, according to Djerassi, was fashionable U KUL

among undergraduates at Wellesley College, MEHA Massachusetts, circa 1970. Frances M. Brodsky is in the Departments of Biopharmaceutical Sciences, Pharmaceutical Chemistry and Microbiology and Immunology at the University of California, 513 Parnassus Avenue, San Francisco, California 94143-0552, USA. She is the author of the scientific mystery Out of the chaos: clockwise from top left are a Lyapunov space (used to study how enzymes break down Principal Investigation by B. B. Jordan (Berkley carbohydrates), the Lorenz Attractor and fractal images entitled Overseer and Scorpio’s Tail. Prime Crime, 1997). orbits-within-orbits of the standard and learned, and a similar limitation has not Zaslavsky maps. deterred cosmologists. Williams succeeds in his goal, with a Yaneer Bar-Yam’s intriguing Dynamics From chaos to carefully written, thoughtful exposition of of Complex Systems goes beyond chaos the- standard topics (such as the logistic map, ory to the broader field of complex systems. complexity strange attractors, routes to chaos and He does not define complexity, but consid- Chaos Theory Tamed Poincaré sections) and tools of the trade ers mainly systems with a large number of by Garnett P. Williams (including attractor reconstruction, Kol- interacting parts, and seeks to discover per- Taylor & Francis: 1997. Pp. 499. £19.95, mogorov–Sinai entropy, fractal dimensions vading themes, such as memory, adapta- $34.95 and Lyapunov exponents). Equations are tion, evolution and self-organization, and Dynamics of Complex Systems included, but they are developed using then to model these phenomena. by Yaneer Bar-Yam careful discussion, rather than detailed The book begins with a 294-page intro- Addison-Wesley: 1997. Pp. 848. $56 mathematics. The first 158 pages of his duction — a veritable book within a book Michael F. Shlesinger book cover background information, — covering basic topics such as iterative including vectors, Fourier analysis, proba- maps, Monte Carlo techniques, random Chaos is no longer a new field. It has already bility theory and time series. A good deal of walks, phase transitions, activated process- been 35 years, and several generations of discussion is given to the logistic map as a es and fractals. These topics form an exten- students, since Edward Lorenz discovered simple model to demonstrate many ideas of sive toolkit, providing the reader with the the strange attractor. Neither is chaos a fad chaos. Those unfamiliar with the basic top- means to characterize, model and simulate or a dead end. It is based on the rock-solid ics of nonlinear dynamics in dissipative sys- aspects of complex systems. foundation of physics, Newton’s laws, and tems would do well to study this friendly, In the body of the book, Bar-Yam begins on tackling the nonlinear, non-integrable self-contained book. with neural networks, then moves up the equations whose solution had to wait for an The success of nonlinear dynamics in scale of complexity to protein folding, evo- appreciation of unstable behaviour, new handling chaos in systems with few degrees lution, developmental biology and, finally, mathematical tools and the advent of com- of freedom has led some to believe that human civilization. The book does not try puter visualization. these methods can be extended all the way to have the last word on these vast fields, but The thesis of Garnett Williams’s Chaos to understanding complex social systems, introduces the reader to aspects that can be Theory Tamed is that enough wisdom has such as economics, war strategy, psycholo- modelled and explored. Throughout, ques- accumulated to give an account of chaos gy and city planning. But the ultimate suc- tions and their answers are folded into the theory mostly in words and pictures, with- cess of the ideas of chaos in physics has been text, and the many mathematical tech- out resorting to deep and sophisticated based on experimental verification of the niques and arguments are clearly present- mathematics. existence of nonlinear instabilities and ed. This book is an excellent place to start Williams is careful to focus on standard behaviours in well-controlled, repeatable exploring the concepts and techniques of theoretical topics related to low-dimen- experiments — in other words, the scientif- complex systems and provides an effective sional dissipative systems, and opts not to ic method. Like the proverbial river into springboard to further studies. broach the rich, complex subject of Hamil- which one cannot step twice, one cannot Michael F. Shlesinger is in the Office of Naval tonian systems, thereby omitting topics repeat a social experiment, because the first Research, Physical Sciences Division 331, such as the three-body problem and the experiment changes the conditions under 800 North Quincy Street, Arlington, Virginia strange kinetics associated with the fractal which it was executed. But much can be 22217-5660, USA.