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Keywords: Complexity, genetic algorithms, emergence Title: Complexity : A Guided Tour Author: Melanie Mitchell Publisher: OUP USA ISBN: 0195124413 Media: Book Level: Introductory Verdict: Interesting overview

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For a while 'complexity theory' was going to be the next big thing. It was claimed that complexity theory would shine a light on areas that traditional physics and mathematics found too intractable: economics, genomics, climate, even human societies as whole. Complexity was the buzz-word of the moment and was popularised in a spate of best-selling pop science books, including Mitchell Waldrop's outstanding 'Complexity'. It promised to revolutionise science once and for all. That was then, and now? Where has complexity theory taken us since the field first gained popular prominence in the early 1990s? Melanie Mitchell, a name well-known in the field, aims to provide us with an updated sweep through complexity theory, and as such offers the reader a chance to gauge where things are at.

As one would expect, this guided tour opens with a bit of a history lesson, introducing the background so that it is possible to understand the historical context. Science had taken us to the arcane world of the sub-atomic and to the relativistic universe at the cosmological scale. This 'reductionist' science had served us well, what need was there for the different approach that complexity theory promised? Mitchell outlines the historical roots and the problems of emergent phenomena that conventional scientific approaches could not easily accommodate. An individual ant is a simple organism that can be dissected and prodded and analysed with the existing tools of science. But put the ant in a colony several million strong and that colony can evolve, solve problems and analysing the colony is no longer so simple and straightforward. The behaviour of the colony is emergent, it is qualitatively different to the individual components that make the whole - the whole is no longer simply the sum of the parts.

It is not just ants, immune systems, economies, societies all of these display emergent behaviour that is not easily amenable to conventional analysis. Mitchell outlines some of these in her introduction before moving on to look at how these questions were initially addressed and how this early thinking on dynamic systems evolved. She provides a crash course in complex adaptive systems, genetic algorithms, evolutionary computation, self-organised complexity, cellular automata, scale free networks and more. If these are new to you then this makes for a good introduction, however, for those already familiar with the subject from reading previous books on the subject, then this is all going to be ground already covered.

It is clear that Mitchell is a practitioner and not a professional science writer. She obviously has a good handle on the material, but the quality of the writing suffers a bit. This is interesting material but the writing doesn't really bring it to life. Compared to Waldrop's book or Emergence: The Connected Lives of Ants, Brains, Cities and Software by Steven Johnson this book just isn't such a good read. And for those interested in the applications of complexity theory to economics then The Origin Of Wealth by Eric Beinhocker provides a wider range of material in an accessible manner. It's not that Mitchell's book is overly technical, this is well within pop science territory, it's that her book simply does grab the reader.

However, her book does bring things more up-to-date than some of the previously mentioned books. And here we see that the revolutionary promise that many felt in complexity theory has not materialised. There is no doubt that it is a rich source of metaphor that can be applied across multiple disciplines - particularly in the social sciences - but it has not lead to any great advances in science. Particular techniques, such as genetic algorithms, ant colony optimisation and evolutionary approaches to computation have moved from the research lab and out into industry. We see the fruits of scale free networks around us on the web and in the advance of social networking sites. But the big theoretical advances in evolutionary theory, in understanding immunity or consciousness have yet to happen. In the meantime, for those wanting to get a current view of what complexity theory is about then this is worth checking out, even if the writing isn't up to the standard of some of the other books on the subject.