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Natural complexity : a modeling handbook
Charbonneau P., Princeton University Press, Princeton, NJ, 2017. 376 pp. Type: Book (978-0-691170-35-0)
Date Reviewed: Dec 4 2017

Author Paul Charbonneau defines science as “a way of knowing.” Since the Renaissance, the natural sciences have had two main ways of knowing: empirical analysis of observational data from the real world, and theoretical arguments (in the most rigorous form, mathematical proofs) about causal models explaining the observations. The advent of the computer has made feasible a third way of knowing: detailed simulations that can explore models intractable to formal proof. These simulations have revealed unexpected behaviors from large collections of interacting elements, behaviors that are borne out in empirical observations and that give us a much richer toolbox for understanding nature.

Charbonneau is concerned with what are commonly called “complex systems,” though he resolutely refuses to define the word “complex.” But he does characterize the systems that he describes as exhibiting the emergence of macroscopic patterns and behaviors without external macro-level control, through the microscopic interaction of many individual components, a characterization that fits well with the broader literature in complex systems. He is a physicist, and his concern is not simply to exhibit simulations, but to characterize them in physical terms, such as critical points, ensembles, dissipative systems, universality, and power laws.

An introductory chapter disclaims any definition of complexity but does outline what complexity is not (randomness, chaos, large numbers). The next ten chapters offer a series of computational models, based on simple Python programs, that increase in their relevance to real-world systems and introduce a growing range of analytic techniques. With one exception, the core Python program for each chapter fits on a single page (though in six-point font that makes one wish the author had made machine readable files available online). The book assumes readers with no background in programming, and the programs give simplicity and clarity priority over computational efficiency and pure Pythonic idioms. Charbonneau provides a line-by-line commentary on each program. Each chapter ends with a collection of exercises to extend and explore the model, including one grand challenge per chapter to encourage more open-ended exploration. The text does not give footnotes to individual technical concepts, but does include references at the end of each chapter.

The first model introduces one-dimensional and two-dimensional cellular automata and explores their behavior. These models are an excellent introduction to the programming idioms used throughout the book and also give some initial examples of unexpected emergent behavior.

The next model introduces diffusion-limited aggregation and uses its behavior to introduce fractal structure and the resulting self-similarity across different scales. The discussion becomes more formal with the third model, on percolation. By focusing on the distribution of cluster sizes, the student can observe a phase transition with associated power law behavior at the critical point. The fourth model is the venerable self-organizing sandpile, with discussion of a range of relevant measures that can be observed on the model and a discussion of its critical behavior. This exploration of alternative measures (in the case of the sandpile, total mass, mass displaced at each iteration, and avalanche energy, peak, and duration) is characteristic of the discussion of the later models and reflects the practicing physicist’s preoccupation with finding the right observable on which to focus analysis. At this point, the reader has begun to see the relevance of a basic set of themes (such as criticality, power law behavior, and self-organization) to multiple models, a lesson that is reinforced in the subsequent chapters dealing with forest fires, traffic jams, earthquakes, epidemics, and flocking. The final model, on pattern formation, explores excitable systems such as the Belousov–Zhabotinsky reaction, using the hodgepodge machine as a model. A concluding personal chapter documents some of the author’s personal encounters with complexity and seeks to cement the student’s intellectual commitment to further exploration. Appendices deal with the Python programming language, probability density functions, random numbers and random walks, and computational techniques on lattices.

This book is a clear introduction to experimentation with complex systems that will appeal to multiple audiences. It is accessible to lay people with an interest in physics but limited formal training, and it might stimulate students at the high school level to contemplate a physics major. It would make an excellent undergraduate introduction to computational physics for nonphysicists and could very well supplement an undergraduate class in statistical physics, allowing students to gain intuition into phenomena such as phase transitions. In addition, it will serve as an example of pedagogical clarity and skill for anyone responsible for teaching the physical sciences.

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Reviewer:  H. Van Dyke Parunak Review #: CR145693 (1802-0060)
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