“I think the next century will be the century of complexity.”

—Stephen Hawking, January 2000

What makes a popular science book exciting to non-specialists? It is not enough to be informative, it has also be lively and engaging. Melanie Mitchell’sComplexity: A Guided Tour”, is such a book. Melanie is a professor of computer science at Portland State University and Santa Fe Institute, specialised in the study of complexity. In her book, she explores dynamical systems, information technology, genetic algorithms, cellular automata, chaos, and network theory.

complexityMitchell is a wonderful writer and her love for the subject is evident and infectious. Complexity: A Guided Tour” is stimulating and fun; it is not an easy read, but it is immensely worthwhile.

Reductionism has been the dominant approach to science since the 1600s, but it has reached its limitation, argues Mitchell. There are phenomena that are better described from a complex perspective, such as incest swarms, the brain, the immune system, the ecosystems, the economic markets, the World Wide Web. Complexity science is a broad and multi-disciplinary subject, it touches on almost all aspects of modern technology and science. The rise of an interest in understanding general properties of complex systems has paralleled the rise of the computer, because the computer has made it possible for the first time in history to make more accurate models of complex systems in nature.

“I have learned” says Mitchell in the preface of the book, “that as the lines between disciplines begin to blur, the content of scientific discourse also gets fuzzier. People in the field of complex systems talk about many vague and imprecise notions such as spontaneous order, self-organization, and emergence (as well as “complexity” itself). A central purpose of this book is to provide a clearer picture of what these people are talking about and to ask whether such interdisciplinary notions and methods are likely to lead to useful science and to new ideas for addressing the most difficult problems faced by humans, such as the spread of disease, the unequal distribution of the world’s natural and economic resources, the proliferation of weapons and conflicts and the effects of our society on the environment and the climate”.

Up to this time, there is no consensus formal definition of complexity. Andrew Ilachinski defines it as the study of systems in which an “increasing number of independent variables are interacting in interdependent and unpredictable ways. Informally, “a complex system is a large network of relatively simple components with no central control, in which emergent complex behaviour is exhibited.” Relatively simple components” means that the individual components, or at least their functional roles in the system’s collective behaviour, are simple with respect to that collective behaviour. For example, a single neuron or a single ant are complicated entities in their own right. However, the functional role of these single entities in the context of an entire brain or an entire colony is relatively simple as compared with the behaviour of the entire system.”

The notion of nonlinearity is important here: the whole is more than the sum of the parts. The complexity of the system’s global behaviour is typically characterised in terms of the patterns it forms, the information processing that it accomplishes, and the degree to which this pattern formation and information processing are adaptive for the system, that is, increase its success in some evolutionary or competitive context. In characterising behaviour, complex-systems scientists use tools from a variety of disciplines, including nonlinear dynamics, information theory, behavioural psychology, and evolutionary biology, among others.*

Mitchell examines several proposals for common and universal principles that attempt to explain the regulation of all the diverse complex dynamical systems that we find in nature; John von Neumann’ s principles of self-reproduction; Robert Axelrod’s general conditions for the evolution of cooperation; West, Brown and Enquist’s proposal that fractal circulation networks explain scaling relations, et cetera. In chapter 12, she, herself, proposes a number of common principles of adaptive information processing in decentralised systems. “Randomness and probabilities are essential” she says.

Although, much of the science described in this book is still in its early stages, the discipline of complexity has enabled successful applications and breakthroughs in fields like biology, economics, and consciousness. Understanding the conditions required for systems self-organisation is crucial of the sustainability of these system over time.

*Complex Systems: Network Thinking,  Melanie Mitchell, SFI WORKING PAPER: 2006-10-036