Melanie Mitchell’s expanded version of her invited Ulam Memorial Lectures, “The Past and Future of the Sciences of Complexity” successfully meets the ambitiously stated goal of introducing “nonspecialists to the vast territory of complexity” (p. xii). Mitchell, Professor of Computer Science at Portland State University and External Professor at the Santa Fe Institute adopts the role of tour guide in an attempt to introduce new readers to some of the core historical and current sites of interest and samples of the biographical and cultural history of the sciences of complexity. For the traveler who is already somewhat familiar with the landscape there are few new insights to be gleaned. These are contained mostly in the second half of the book as open questions and ideas that require further development. However, the book does present opportunities for these travelers to revisit and renew old acquaintances in a refreshing manner. The tour is divided into five excursions (Sections) covering the breadth of the terrain across its 19 chapters. That being said, this is a tour and not a field expedition into the territory. Readers looking for details or depth on the most recent advances are advised to look elsewhere. Her up-to-date bibliography is perhaps a good starting point.

Part 1, Background and History (Chapters 1 to 7), and Part 2, Life and Evolution in Computers (Chapters 8 and 9) are the first stops on the tour. They constitute one of the most succinct, accessible and reader friendly introductions to a wide range of foundational concepts, controversies and researchers across a variety of complex (adaptive) systems drawn from physics, biology, and computer science. These include chaotic dynamics, linear and non-linear models, the logistic equation, period-doubling, Feigenbaum’s constant, information theory, the theory of computation, quantum uncertainty, Gödel’s theorem, Turing machines, the second law of thermodynamics, evolution, heredity, and the modern synthesis, the mechanics of molecular genetics, competing measures of complexity (complexity as: size, entropy, algorithmic information content, logical depth, thermodynamic depth, statistical, fractal dimension and degree of hierarchy), von Neumann’s self-reproducing automaton, artificial life and genetic algorithms. Mitchell sets up the necessary foundations, laying out essential conceptual hubs with which the remainder of the book connects, in a breezy 142 pages. These sections are pedagogically satisfying, introducing, exemplifying and elaborating necessary concepts like fractal dimension and fitness functions only at the points where they become necessary to the unfolding narrative and utilizing only sufficient mathematics (and if necessary, equations) to illuminate the content. This will appeal to the many lay readers to whom the book is primarily pitched. She defers deeper mathematical explanations to the end-notes.

Whereas Part 2 develops important ideas relating to modeling life and evolutionary processes in silico, Part 3, Computation writ Large (Chs. 10 to 14) moves to examine the extent to which nature computes. With the same effectiveness and economy as the two first Parts, Mitchell presents a concise and potent introduction to cellular automata and the work of Stephen Wolfram which opens the door to a discussion of computation/information processing in the immune system, ant colonies, cellular metabolism and unresolved questions around what constitutes consciousness and how meaning might be made in living and artificial intelligence systems through analogy and conceptual slippage. The final chapter in this section is devoted to providing important caveats and clarifications of the purposes and limitations of idea models in the complexity sciences using research on The Prisoner’s Dilemma and its extensions regarding the evolution of cooperative behavior to exemplify.

The final major excursion, Network Thinking (Chs. 15 to 18), provides a foundation for lay readers on advances in Network Theory, whose significance for the complexity sciences Mitchell describes as providing “a novel language for expressing commonalities across complex systems in nature, thus allowing one area to influence other, disparate areas” (p.252). Applications of concepts such as small world networks, scale-free networks, power law distributions, preferential attachment, scaling, random Boolean networks and resilience, are applied in discussing biological examples which include brain function, genetic regulation, metabolism, epidemiology and ecological food webs. As in the previous section Mitchell does not shy away from presenting important skeptical, alternative or oppositional positions. This deliberate attention to the ongoing controversies is one of the features that make this text stand apart from others in this field. She portrays the reality, undecidedness, and complexity of an as yet nascent field in which many terms, including complexity itself, are not well defined and where concepts are still contested and require further evidence. Additionally, she highlights important open problems such as: understanding the origins of power-law distributions across disciplines, determining how, why, and if evolution creates complexity and hints at the significant impact that future work in this area is likely to have across all knowledge domains and in social and political life. This is the section most likely to stimulate those new to the field and inspire renewed inquiry from those already working in it.

In bringing the tour to a close, Mitchell as guide offers a timely historical warning for complexity scientists as they look to the future namely the overshadowing, fragmentation and loss of enthusiasm for parental disciplines such as cybernetics and general systems theory which she suggests had more “extent than content…ranged over too disparate an array of subjects, and [whose] theoretical apparatus was too meager and cumbersome” (p.297) to achieve their ends. She also identifies what she believes is needed— “the right vocabulary to precisely describe what we’re studying…that not only captures the conceptual building blocks of self-organization and emergence but can also describe how these come to encompass what we call functionality, purpose, or meaning” (p. 301, italics in original).

There have been many excellent introductions to the various “sciences of complexity” written over the last quarter-century by pioneers in the field. Mitchell’s adds another, though one that pays attention to some of the pedagogical and conceptual difficulties that have limited laypersons’ understanding of the content, controversies and significance of the complexity sciences especially in their potential to radically alter the reductionist ethos in science, transform the disciplinary divides among academic disciplines and change the way we think about social institutions and relationships. The book will be of interest to students and instructors at the undergraduate and upper high school levels across a wide range of disciplines. The freshness of the book’s presentation of the core ideas of the main branches of the complexity sciences, its deliberate attempt to foreground the ongoing debates in the field, its reminders of the limitations of models, cautions, and its pointing out important future directions that the field might take, or needs to take, is likely to render it an oft-recommended starting point and perhaps one of this generation’s standard introductions to the exciting worlds of the sciences of complexity.