Complexity: A Guided Tour

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Reviewed by John Bragin
UCLA Human Complex Systems: Computational Analysis of Social and Organizational Dynamics

The strength of Complexity: A Guided Tour arises from the author's clear and concise presentation of the family of concepts and methods that make up the less-than-unified sciences of complexity. In five parts and 19 chapters the tour visits a variety of places (topics). Given the space available (349 pages, including end-notes, bibliography and index) and the aim of producing a work accessible to the layperson (which nonetheless requires careful reading and re-reading as with any science book that is not merely anecdotal) Melanie Mitchell has done an excellent job of describing, analyzing and explaining each of these topics. However, as with most package tours (even the best) this one suffers from the lack of a theme-based, narrative arc that takes us from the basics and then develops these, as a true grows from its roots and shoots out branches that depend on the whole, and maintain the life of the whole tree.

This is the case not because of any shortcomings in Ms Mitchell's expertise in complexity matters nor lack of talent as a communicator, but rather because of two facts that bedevil anyone attempting an introduction to the subject. First, as her last chapter entitled "The Past and Future of the Sciences of Complexity" declares, we need to speak of the sciences of complexity in the plural, not the singular. It is not now the case, and may never be, that complexity concepts and methods hang together in the same way as classical mechanics or even the looser framework of evolutionary biology.

Second, the sciences of complexity as a recognized discipline are barely 25 years old (even though individual work on some of its aspects go back to the 1930s). Perhaps its beginning as an organized discipline could be dated to the founding of the Santa Fe Institute and its first conference on the economy as an evolving complex system in 1987. We are barely out of infancy and just becoming toddlers. Unlike classical mechanics and evolutionary biology, where the subject itself and its teaching at an introductory level have been refined in hundreds of books and undergraduate courses, no such refinement of presentation exists for complexity.

I've reviewed about two dozen course syllabi for undergraduate, introductory courses given at colleges and universities across the United States, and unlike analogous introductions to physics or evolutionary biology, there is no broad agreement on necessary and sufficient fundamentals, even though many courses contain similar topics, such as fractals, networks, and agent-based models, but often with different emphases on what is basic about these and their relative importance. It is the same for books. There are no general undergraduate textbooks in the field. Instructors rely on journal articles, and individual book chapters, most of which are also heterogeneous in the topics they cover, their order and relative emphasis.

That much said, here is a description and evaluation of the preface and the five parts of the Mitchell book. After a "Preface" that covers the topic of traditional reductionist ideas and the anti-reductionist stance of complexity, Mitchell highlights her own entry to the field through computation, and then gives a brief description of each part of the book which in its entirely deals with complex adaptive systems. Part Two, "Life and Evolution in Computers", and Part Three, "Computation Writ Large", both deal with Mitchell's primary expertise in computation and information. Part One, "Background and History", presents seven core ideas: the characteristics of complex adaptive systems, dynamics, information, computation, genetics, and a further definition of complexity and its measurement. The first chapter is an excellent introduction, because it describes a wide variety of complex adaptive systems at different scales (from the brain and insect colonies, to economies and the world wide web) as well as giving the several common properties of such systems and proposing a definition of them along with a brief look at the problems of measuring complexity.

The second chapter on dynamics is more limited and of less use to understanding complexity. The chapter considers only deterministic chaos and focuses solely on the logistic difference equation as an example that illustrates some of its concepts. Mitchell does not deal with these important facts: Chaos is deterministic, while complexity is often stochastic. Chaos deals with a few macro-variables that are strongly interdependent. Complexity deals with a large number of micro-variables that are networked and thus connected with varying degrees of strength. Chaos starts with one or a few equations and evolves into a pattern of apparent randomness in a deterministic system bounded by a strange attractor. Complexity starts with a highly distributed set of agents in apparently and often random arrangement and interactions, and evolves into emergent patterns of macro order, which is not necessarily bounded by an attractor. All these differences make chaos a cousin to complexity, but not a sibling.

The third chapter on information begins with classical thermodynamics, moves on to statistical dynamics, and finishes with Shannon information entropy as he derived it from Boltzmann's entropy. The introductory concepts on information particularly find application in Chapter Twelve, "Information Processing in Living Systems". As far as non-equilibrium thermodynamics goes, there is too little in the book about dissipative structures and their role in order creation within living organisms, ecosystems, and social systems.

Chapter four focuses on computation and is one of the best in the book. It It deals principally with Gödel and Turing. The Turing proof that not all propositions are decidable (i.e. effectively computable) is difficult, but she takes the reader with little math or computer science through it step-by-step in layperson's terms. Carefully following her guide here is well worth the effort. I have not found a better explanation anywhere else.

Chapter five on evolution is likewise very good. But perhaps there is too much emphasis on the polemics against a strong and exclusive selectionist explanation for evolution. A stance that "complexity proposes and selection disposes" gives a better picture of how the two work together. The knowledge here is needed to make sense of its application particularly in Part Two, "Life and Evolution in Computers" (chapters eight on self-reproducing computer programs and nine on genetic algorithms), and chapter eighteen "Evolution, Complexified".

Chapter six on genetics provides a very short introduction to the structure and mechanics of DNA replication, and its translation into proteins. The knowledge here is also needed to make sense of its application particularly in chapters eight, nine and eighteen.

Chapter seven deals with a number of proposed measures for the complexity of a given system, their strengths and limitations, and the problem of comparing the complexity of various systems. These are notoriously thorny problems, and no solution is reached, but Mitchell, again, does an excellent job of presenting each in the brief space of one chapter.

Part II, "Life and Evolution in Computers" is an area of Mitchell's particular expertise. She uses her own work (particularly in chapter nine on genetic algorithms) to give concrete examples of the concepts and methods of self-reproducing programs (with a concise overview of Von Neumann), and of how she and Holland use the principles of variation and selection to find solutions to problems. Patience, attention and careful re-reading are unnecessary for those unfamiliar with the material in this and subsequent parts of the book, but the effort is well worth it.

Part III, "Computation Writ Large" deals with cellular automata, information processes in living systems, Mitchell's own efforts at tackling analogy and meaning via Artificial Intelligence, and the prospects of computer modeling with particular attention to Axelrod's work on cooperation with various forms of the Prisoner's Dilemma problem. The chapter ends with a description of four basic roles Mitchell sees as involved with computational experiments: 1) showing that a proposed mechanism for a phenomena is plausible or implausible; 2) exploring the effects of variations on a simple model and priming one's intuitions about complex phenomena; 3) inspiring new technologies; and 4) leading to mathematical theories. Followed by discussion of the limitations of models and the need for replication to test them. The book lacks a chapter on agent-based simulation modeling and this is a serious fault in any introduction to complexity.

Part Four, "Network Thinking", covers the basic definitions and metrics of network science, scaling phenomena, and the evolution of genetic networks, with particular focus on the new field of evolutionary development, and to Stuart Kauffman's work on random Boolean networks of "genes" where different levels of connectedness result in different macro behaviors of the network.

In the final chapter, Mitchell takes a short look back into the roots of the new sciences of complexity, including the strengths and limitations of cybernetics; some criticisms of complexity science; and the views of a number of complexity workers about the reasons for their involvement in the field and its future prospects. If there is to be a grand unified science of complex adaptive systems, she writes that we need a more precisely defined set of concepts such as 'complexity', 'self-organization', and 'emergence'; and how these encompass functionality, purpose, and meaning. We are "waiting for a Carnot", who can do for complexity what Sadi Carnot did for thermodynamics.

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© Copyright Journal of Artificial Societies and Social Simulation, 2010