Crowd dynamics, dating, war - all in a single theory

Two's Company, Three Is Complexity has three underlying goals: to present an enjoyable introduction to complexity for the general reader, to provide an overview of the work of the author's complexity research group and to argue that "complexity is indeed the science of all science" (the book's final sentence).

As a complexity convert for the past eight years and a strong believer in the importance of making science more accessible and popular, I tend to commend most efforts in this direction. Unfortunately, Neil Johnson's book is neither a very good introduction to complexity nor a good overview of how the field is developing. Hence, its occasional grandiose claims are not really justified. However, what it does do well is provide a good introduction and overview to the complexity-based work of Johnson's research group, including a long list of web-based papers on aspects of complexity in physics and mathematics.

The book begins with a brief definition of complexity and then examines various aspects of complexity thinking, fractals, chaos, networks, power laws and so on. These are explained using accessible examples (particularly crowd dynamics, traffic flow and financial fluctuations) and occasional illustrations. As Johnson states from the beginning, most examples used come from the work of his research team. Unsurprisingly, coming from a physics and maths-based research group, most of the examples have a strong quantitative orientation and do little directly to explore the much wider interdisciplinary implications of complexity. Judged from this perspective, it is a good layman's introduction to the work of a particular research group, and for students in physics or maths it would be worthwhile.

However, as a general introduction to complexity it lacks both history and breadth. With only passing mention of the traditional linear or Newtonian paradigm that went before, it would be very difficult for a lay reader to see what was so new and exciting about complexity.

Moreover, the book implies in the preface that complexity started developing "at the beginning of the 21st century". No attempt is made to show how concepts of complexity have been emerging throughout the 20th century and that its early roots could easily be found in the 19th-century work of the mathematician Henri Poincaré.

Likewise, in terms of breadth, although the book looks at various aspects of the human and health implications of complexity and briefly touches on a number of popular themes (globalisation, inequality, war, dating and so on), all of these aspects rest on a fundamentally quantifiable and mathematical view of the world and complexity. Obviously, this reflects the nature of the research group.

However, complexity thinking has gone far beyond these boundaries through the work of people such as Brian Goodwin in biology, Peter Coveney in chemistry, Ralph Stacey in management, Eric Beinhocker in economics and John Gaddis in history, to name just a few. Even in the appendix, which claims to provide further information, only 15 books and five centres of complexity are mentioned. There are now hundreds, if not thousands, of books on complexity and dozens of complexity centres throughout the world.

In the end, maybe I find this book disappointing because I am so excited about complexity and its vast interdisciplinary implications that I really do believe that it may be a new sort of "science of all science". Though providing a good accessible overview of the work of a particular physics and maths-oriented research group, this book is unlikely to convert many lay readers or interested academics to the fascinating world of complexity.

Robert Geyer is professor of politics and international relations, Lancaster University, and co-editor of Complexity, Science and Society , 2007.