Exploring Complexity Country with a Local

	Book review on COMPLEXITY: A Guided Tour by Melanie Mitchell (2009) Reviewed by Max Boisot, 2009 published in Network Review No 101
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Although complexity is strongly associated with the emergence of life and intelligence, it constitutes a dimension of all phenomena: the purely physical, the biological, and the social. The vast increases in computing power achieved over the past four decades have allowed researchers to tackle complexity in its own right rather than artificially reducing it so as to achieve conceptual and computational tractability. This timely book by, Melanie Mitchell, one of the main players on the complexity scene, offers an elegant and accessible guide to the subject.

The book subdivides into five parts. In Part I Mitchell defines a complex system either as one "... 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" or as one "... that exhibits nontrivial emergent and self-organising behaviours". The first definition takes us from order to complexity, the second from complexity to order. Mitchell then offers some background on four of the subject areas that make up the complexity field: information, computation, dynamics and chaos, and evolution. She points out that since people will vary in the complexity that they will impute to an object or process, no one has yet been able to come up with a general measure complexity.

In Parts II to IV Mitchell describes how these four subject areas relate to each other, and in particular, how life and evolution can now be simulated in computers. In chapters 8 and 9, she shows how life and evolution might show up inside computers and in chapter 10 at how far computation might itself be said to occur in nature. With the development of Self-reproducing computer programmes and genetic algorithms, the notion of computation is increasingly being invoked to explain the behaviour of natural systems. This, of course, is hardly a new idea. What today we call 'complex systems' can trace its ancestry back to the work being carried out in the 1950s and 60s in cybernetics and the related field of systems science. Both dealt with systems, with their boundaries, and in the case of cybernetics, with their information-driven feedback processes.

Mitchell usefully points out that the major thrust of complex systems research has been the exploration of simple idea models, designed to gain insights into general concepts without the need to make detailed predictions about any specific aspect of their behaviour. This exploratory way of using models is relatively new and one of the fruits of the increased computational power at our disposal. Mitchell therefore looks at the prospects for the computer modeling of complex systems, as well as at some of the perils involved in applying such models. The power of computational modeling is further illustrated in Part IV of the book, where Mitchell explores the new science of networks. She brings out the deep commonalities being discovered among systems as disparate as social communities, the Internet, epidemics, and metabolic systems in organisms. Some of these commonalities have even suggested to the theoretical biologist Stuart Kauffman that natural selection is in principle not necessary to create a complex living creature.

Finally, in the last concluding Part, V, Mitchell discusses the search for general complexity principles. The book comes across as more focused on the natural than on the social sciences. Given that this is where complexity thinking has so far enjoyed its greatest successes, this seems reasonable. One criticism that a Europe-based (but not necessarily Eurocentric) reviewer might make of the book, however, is that the European contribution to the field is seriously underplayed. The Santa Fe Institute, created in 1984 to study complex systems, takes centre stage, and key figures like Prigogine, Haken, and Von Foerster, barely get a passing mention. At the end of the book, Mitchell briefly refers to Prigogine and Haken as the authors of "more recent approaches to general theories of complex systems".  More recent approaches? Their work predates the creation of the Santa Fe Institute - in Prigogine's case by more than a decade. Indeed, Prigogine was awarded a Nobel Prize for his work in non-equilibrium thermodynamics.

One the positive side, the book is clearly written and well furnished with examples. Mitchell explains the sophisticated concepts that underpin representations of chaotic systems such as the logistic map or bifurcation diagrams clearly and simply. She also offers a straightforward presentation of the second law of thermodynamics. Another merit of the book is that it introduces a historical and biographical element into the story of complexity together with photos of the individuals who contributed to it. This lightens up the text for those whose concentration might flag. It presents complexity as emerging naturally as a dimension of a range of problems that scientists in various disciplines are engaged with.

Complexity research is a broad church, accommodating a wide variety of interests. This is not really surprising since, in the absence of some single, overarching theory, it is not yet a unified discipline. Mitchell has provided a valuable overview of the diversity of its practices and practitioners in an accessible language that will appeal to academics and practitioners alike.

Max Boisot, ESADE, University of Ramon Llull Barcelona

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