REVIEW - COMPLEXITY EXPLAINED BY PETER ERDI By Karl Friston FRS, University College London This is a charming and engaging book. It treats the reader with perspectives on complexity from nearly all possible angles. This rounded approach works extremely well and highlights the connections between different formulations of complexity, both in terms of their application and historical development. The book is clearly written by someone who delights in the challenges posed by complexity research and has spent a lot of time teaching in this area. The book is written in an intuitive and accessible way; although there are mathematical expositions, they are not intimidating for the non-mathematical reader. The book is organised in a clear and purposeful way; as if it was based on a mature series of lectures. It stars from the historical fundaments of complexity theory and ends with cutting-edge research into things like evolutionary game theory. The writing style is endearingly idiosyncratic; disclosing the author's Hungarian background. Peter Erdi's ethnic and intellectual roots show themselves through the balanced references to Eastern block and Western contributions, through his Hungarian anecdotes and metaphors, through his syntax and finally through his humour. There are several nice examples of the latter; his preference for the term "player" over "agent" is not left implicit. Sometimes it is difficult to tell whether something has been lost or gained in translation, for example I had assumed that "out of ouch" meant "out of touch". However, the context in which this phrase was used (the resolution of unrequited love) made me think twice. In short, the book had great substance and made me smile a lot. The book is organised into ten chapters; the first three deal with the history of complex systems and theory. I found these chapters very illuminating. They gather together names and concepts that one has come across before and place them in useful relationship to each other. There is lots of fascinating detail about the growth of the ideas considered in later chapters. These chapters are underpinned by some excellent tutorials in relevant basics in the physical and life-sciences (e.g., Hamiltonian dynamics, statistical thermodynamics, chaotic itinerancy and so on). In areas that I am familiar with, I was impressed by the clarity and depth of this background material. This made me take the treatment of other areas equally seriously. The middle part of the book deals with the phenomenology and application domains of complexity theory; ranging from chemical kinetics to the epidemic propagation of infections and ideas. Some of the examples are a prelude to the final chapters that focus on the complexity of the brain and related models of decision making and prediction. There is diversity and coherence in these chapters, for example we move gracefully from stock-market crashes to epileptic seizures, which take us straight back to earlier chapters dealing with single-cell modelling in the brain and neuronal rhythms. As with the historical chapters, the coverage was impressive for its balance and breadth. As someone who has dealt with complex systems in a somewhat piece-meal fashion, I was impressed that nearly every relevant contribution I know about was covered in a brief but useful way. Even in areas I was familiar with, I learned a lot, particularly about the origins of some of the ideas. Most of this was scientific but sometimes it was historical (e.g., the contributions F Ventriglia to mean-field theories of statistical neurodynamics); sometimes it was personal (e.g., learning that, sadly, Esther Thelen had died). I am not sure whether this book 'explains' complexity. It certainly explains the genesis of the complexity sciences with a compelling and useful focus on the history of these ideas and the rhetoric needed to articulate them. This is a very worthwhile read for any student considering an academic career in complexity or, senior scientists who want to place their corner of enquiry in a larger context. On finishing the book, I wondered whether a better title would have been "Complexity Celebrated". From the reviews: "In Complexity Explained, Erdi (Kalamazoo College) traces in great detail the path that complexity theory followed from classical mathematics onward. ... The list of references is extensive and may be useful for researchers. Summing Up ... Researchers/faculty." (J. A. van Reenen, CHOICE, Vol. 45 (11), July, 2008) "Erdi covers such a great deal of important data on complexity that a shorter review cannot do justice to this excellent book ... . The 581 References are one indication of his inclusive broad coverage. ... graduate students, researchers and teachers in any of the numerous sciences, technologies and humanities, as well as the general educated public are addressed. ... Any researcher planning to write a book ought to copy Erdi's styles: the English is superbly conversational, clear, uncomplicated and logically compressed ... ." (Karl H. Wolf, International Journal of General Systems, 2008) "This book has many advantages ... . It is an excellent introduction to CS for specialists in many fields. ... Summarizing, this is an excellent introduction to CS. I strongly recommend it to anyone who wants to learn CS seriously. At a more advance level, it should be followed by deeper books in individual fields e.g. CS in biology, CS in social sciences etc... I thank the author for this enjoyable and useful book." (E. Ahmed, Zentralblatt MATH, Vol. 1162, 2009) "This book is written for anyone interested in the meaning of complexity. ... the book uses mathematical notions of dynamical systems theory to show that very different complex phenomena of nature and society can be analyzed and understood by nonlinear dynamics." (IEEE Control Systems Magazine, Vol. 29, October, 2009)
