American Scientist

How Nature Works: The Science of Self-organized Criticality. Per Bak. 212 pp. Copernicus (Springer-Verlag), 1996. $27.

How Nature Works is a bold effort to show how some general concepts for defining complex systems might be applied to astrophysics, geology, biology or sociology. Because such a model must be very general, we look for the fundamental property of a useful model—what it is able to predict. Can we predict earthquakes or the stock market?

Specific predictions will never be possible for complex systems, no matter how much computer power is available. This is itself an important understanding, since it dooms many such attempts. What Bak seeks to demonstrate is that complex systems, at whatever level, have common underlying features and that complexity leads to criticality. Bak, a physicist and expert at computer simulations, minimizes mathematical details by using metaphors and stories to illustrate the meaning and significance of a few general, but abstract, concepts.

The easiest metaphor is the sandpile. At some point, as grains of sand are slowly and steadily added, the pile becomes "critical" or unstable, and an avalanche occurs spontaneously. Now, this visual and obviously simple system is, in fact, complex (there are truly many sandgrains interacting), and, as the pile grows, it must attain the point of criticality, which initiates the dramatic reorganization caused by the avalanche. So what? Well, Bak and his colleagues developed a simple mathematical model to simulate a growing sandpile, and it also produced avalanches.

From this model we are introduced to the concept of self-organized criticality: Systems with interacting components will spontaneously change to become critical and then experience a catastrophe that reorganizes them. Bak applies this concept in modeling the Big Bang, the human brain and traffic jams, leading to a discussion of fractals and power laws. Many things can be characterized on a scale that is fractal, meaning that it can be measured on smaller and smaller units. When various natural phenomena are defined by some size unit and sorted into bins, the distribution of bins by size follows a power law that is remarkably similar whether the object being examined is the length of coastline segments in fjords, the magnitude of earthquakes or the number of species extinctions over time. Such data plots are "similar" in that the slope of the plots often has a value in the range of 1.2–1.7. To Bak, this reflects a basic universal principle of self-organized criticality.

In the rest of the book, Bak seeks to develop the connection between fractal systems and power laws. He tells this story as a first-person narrative of his discovery of the models and concepts, with anecdotes of frustration and dismay, success and joy. More than 30 individuals from around the globe are identified as having made contributions or collaborated with the author, leading to a sense that when Bak is not on the road himself, visitors are continually stopping by his institute.

I had conflicting feelings about Bak's models. On the one hand, it appears significant that some type of model could be formulated to approximate specific features of a particular complex system, be it neural function or general economics. On the other hand, since, by necessity, the computational model had to be defined very specifically, its relevance to the real world is questionable. For example, Bak finds that earthquakes are clustered in time, and that it is more likely that an earthquake will not occur at a given time if a long time has elapsed since the last earthquake. Likewise, species that have been in existence for a long time are more likely to persist in the future.

These are clearly very generic predictions. Nevertheless, even such modeling has predictive significance in the general sense. In the United States we currently have several mechanisms for preventing a stock market crash. Since Bak can model simple economic systems and show them to be complex and critical, then it is predicted that a market crash (an avalanche) is inevitable, and that the Federal Reserve Board must fail in its efforts to stabilize the stock market. Although Bak can predict the inevitability of an event, he cannot predict the time.

Readers will find this book controversial and challenging. Bak's effort to extend this basic modeling concept to diverse disciplines may spark resistance when applied in a reader's field of personal expertise. In at least one example, he may have overextended himself. A lot of evidence associates the mass extinction event at the Cretaceous/Tertiary boundary (K/T) with an asteroid impact. Whether we think evolution proceeds gradually or in a pattern of punctuated equilibrium, mass extinctions are dramatically catastrophic events that may require some unusual outside perturbation—a condition clearly satisfied by an asteroid impact. Bak, however, seeing mass extinctions as inherent in a self-organized system that must occasionally reach the critical point, suggests that the asteroid impact at the K/T extinction was a fortuitous event but not necessarily the major causative factor! This may be an important example that alternative solutions to a problem need not be mutually exclusive.

This book presents us with an interesting narrative in how to apply abstract concepts to the real world. It helps us to think about the distinction between predictability as "something must happen" and predictions that specify time, place, or extent. More important, it seeks to show the implications inherent in self-organized complexity and criticality as applied to remarkably different systems.—Thomas W. Traut, Biochemistry and Biophysics, University of North Carolina School of Medicine