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Untangling Complex Systems

Pier Luigi Gentili
CRC Press
Publication Date: 
Number of Pages: 
[Reviewed by
David S. Mazel
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This book has been a challenge to review because it is so wide ranging in topics that I found it difficult to follow at times. The author seeks to introduce the reader to a plethora of examples of complex systems. He discusses thermodynamics, chemical reactions, bifurcations, predator-prey models, economics, and cellular systems, to name just the first few. In each case the author describes the system, provides equations to represent the behavior of the system, and gives the reader what seems to be a thorough discussion of the topic. The difficulty is the material is so broad in scope as to require a reader to be well-versed in many scientific topics to understand the discussion. 
Let me illustrate this thought with a discussion of Chapter 9 titled “The Emergence of Order in Space.” The contents of this chapter (and the rest of the book really) are nothing short of stunning. A reader will find chemical waves, Turing patterns, and periodic precipitations. There is a lovely image in the book, and although the image is in black & white, this figure demonstrates chemical waves, Turing patters, and periodic precipitation. There is a pattern of each from nature and from a laboratory. The image connects what we do inside a building and what goes on outside the building. One can sense the connections the author is drawing of how nature behaves and its beauty therein. 
A turn of the page leads to the Divergence Theorem which requires the reader to be familiar with partial differential equations—an area of mathematics known to be difficult. A page later are chlorine-dioxide-iodine-malonic acid reactions in relation to Turing patterns. Unfortunately, I am not familiar with this topic and the discussion was beyond me. To the author’s great credit though, he does find a way to bring this less than knowledgeable reader back to his work. 
Gentili moves on to biology (still in the same chapter) with a discussion of embryos, specifically that of the Drosophila, a vinegar fly. We learn that the diffusion of the bicoid protein across an egg determines the final development of the creature. Should this diffusion be disturbed the creature may lack a head and thorax. The book illustrates this idea with an image of the fly and its embryo. The author shows the connections between the embryo and fly so the reader sees how the structure of the embryo maps to the final creature. Again I found this discussion beyond me but it was fascinating even with my superficial understanding. 
This same chapter continues with chemical waves forming a target pattern or a spiral.  For an added example of the breadth of this book, this chapter introduces an axon model consisting of variable resistors, voltage sources, and a capacitor. These axons lead to hearts and a discussion of chemical waves in the human heart. The chapter (we are still in just this one chapter of thirteen) goes on to Liesegang patterns. These are waves produced from two strong electrolytes with different concentrations in a gel. New salts are formed in the gel and yield a lovely pattern of striations and layers as shown in an image of a test tube. There are similar patterns in geology and biology. The breadth of discussion is staggering in this and every chapter.
In fairness, the book includes more conventional ideas about complexity when the author discusses the double pendulum, the logistics map, and the Lorenz equations for weather models. He has a few paragraphs on the Chua circuit for even more variety and appeal to a broader audience. The discussions are not always deep but they are a welcomed sight to see. I found many of the discussions quite familiar and a respite from chemistry and biology. 
The last few chapters return to more conventional topics such as fractals (for example, the Koch curve) and power laws. There is even something in this book for the computer scientists with discussions of computational complexity, Hamiltonian paths in graphs, and even a pinch of agent-based modeling. 
I wish I understood all that I read. Despite that, however, to see all these topics in one reference, and to see, even superficially, the connections and variety is to gaze upon what is certainly a rich and diverse field. It is worth the reader’s time to see this landscape of complex systems and explore whatever piece of it he can.
Each chapter contains recommended exercises sprinkled throughout the text to motivate the reader to learn on his own. There are problems at the end of each chapter which are challenging and informative. These problems are worth reading even if the reader has no intention of solving any of them. It’s evident the author put time into developing the problems and they really do add to the material. The author provides MATLAB scripts to help the reader conduct his/her own computer-based experiments and the bibliography is extensive pointing the way for more details and research.
Finally let me end with the author’s definition of a complex system and what he means by the title of this book.  It is the best definition of complex systems I have had the pleasure to see:
A Complex System consists of many elements, often diverse, if not unique. For example, the components of an ecosystem are plainly diverse, and those belonging to a human community are evidently unique. The elements of a Complex System are also highly interconnected. Complex Systems are networks. They are intertwined systems. In fact, the etymology of the adjective “Complex” derives from the Latin verb cum-plectere that means ``to intertwine together.’’ It is different from the etymology of “complicated.” “Complicated’’ derives from the Latin verb cum-plicare that means ``to fold together.’’ Anything that is “complicated,”’ is “folded” and can be “unfolded.” On the other hand, anything that is “complex,” is interwoven and cannot be “unfolded.” Instead it needs to be untangled. 
If you want a survey of the many of the topics in complex systems, this book will be of service to you. I found it intriguing and I suspect others will as well.
David S. Mazel is a practicing engineer in Washington, DC. He welcomes your thoughts and feedback. He can be reached at [email protected].