The field of complex systems has formally existed for several decades, and many of its founders, including Nobel Prize winner Murray Gell-Mann, came from physics. Yet the field has recently flourished; it is experiencing a rise in practitioners, an expanding number of intriguing problems to address, and a commensurate increase in high-impact publications. In his new book An Introduction to Complex Systems: Making Sense of a Changing World, Joe Tranquillo joins a growing body of authors aiming to define complex systems and disseminate the field’s most important conclusions to the greater world. The text provides a useful overview of complex systems, with enough detail to allow a reader unfamiliar with the topic to understand the basics. The book stands out for its comprehensiveness and approachability. It will be particularly useful as a text for introductory physics courses.
Tranquillo’s strength is in delivering a vast amount of information in a succinct manner. Unlike Geoffrey West’s Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies (2017), Tranquillo’s book is not for general audiences. It does not dive deeply into individual subjects the way Mark Newman’s Networks (2nd edition, 2018) does, nor does it provide a how-to on a specific method, as Steven Railsback and Volker Grimm do in Agent-Based and Individual-Based Modeling: A Practical Introduction (2nd edition, 2019). Instead, Tranquillo has written a thorough textbook that gives a useful introduction to complex adaptive systems as a whole field. It can also serve as a quick reference for seasoned practitioners who need a refresher on a particular subject.
The field of complex systems does not fall within any one discipline. Its techniques and concepts are useful for various sciences and for making order out of seemingly disorderly structures and have been applied in physics, economics, biological systems, computer science, mathematics, and my own field of archaeology. Tranquillo, whose background is in engineering, touches on each of those applications in his text and demonstrates that to be a true scholar of complexity one needs to embrace interdisciplinarity. “It is not always clear where one discipline ends and the field of complex systems picks up,” he writes in the first chapter. “As an interdisciplinarity field … it has inherited tools, processes, ways of thinking, histories, tensions, and world views from other disciplines.”
The book is an excellent reference for many of the mathematical formalizations that provide the backbone for complex-systems study. Tranquillo’s text displays those formalizations seamlessly, in a way that will be useful for teaching students about the underlying thought processes. Yet, even though math is well-integrated into the text, a reader could skim over the equations and focus instead on the prose without losing much. Tranquillo’s presentation will allow math-phobes to be slowly exposed to equations—alongside good explanations—without being forced to read through proofs line by line; thus the book is a useful text for mixed-population undergraduate courses. Those who are looking for a more advanced text that delves deeply into a certain area of complex adaptive systems are likely to find An Introduction to Complex Systems a bit thin. However, it is not meant to be an in-depth guide, but rather a survey of the field.
What makes An Introduction to Complex Systems stand out is its thoroughness. The book is basically an encyclopedia of complex-systems studies. Need to quickly reference the equation for the first law of thermodynamics? Section 7.1.3. How about measures of information? Section 6.1.4. A reader can find information quickly and efficiently—that is, in my opinion, the book’s greatest value. If Tranquillo’s text ends up on your shelf, you’ll find that you thumb through it regularly for a pithy description of a particular complex-systems approach.
Stefani Crabtree is the ASU-SFI Center for Biosocial Complexity Fellow at the Santa Fe Institute and an assistant professor in social-environmental modeling in the department of environment and society at Utah State University. Crabtree has a background in archaeology, ecology, and computational modeling, and she uses complexity science approaches to understand the human–environment interface from deep time until today.
