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Six Sources of Collpase

Charles R. Hadlock
Mathematical Association of America
Publication Date: 
Number of Pages: 
[Reviewed by
William J. Satzer
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This book is an attempt to describe the phenomenon of collapse and catastrophic risk for civilizations, businesses, industries, economies and biological systems. You wouldn’t have to be a disaster junkie to enjoy it. The style is informal, and the writing thoughtful.

The author is an applied mathematician with a breadth and variety of experience that includes consulting and collaboration across several industries and technical fields. He writes that he spent many years in the world of industrial disasters and risk analysis (Three Mile Island, Bhopal, Exxon Valdez and “too many others”). In an understated way he offers justification for the value of mathematical modeling in understanding some critical systems in the world. The book is intended for a broad range of readers, and much of it is accessible to those without any particular mathematical background beyond some high school work.

A collapse, as the author loosely defines it, is a “relatively rapid process that leads to a significant reduction in quantity, quality, or level of organization.” That seems pretty vague, but it does have to stretch quite a ways to encompass the fall of the dinosaurs, the implosion of Enron, the disaster at Chernobyl, and the extinction of the passenger pigeon.

What does he propose as the six sources of collapse?

  • Chance — an apparently random perturbation of a system that is sufficient to alter its behavior in a significant way;
  • Group behavior — the independent emergence of patterns in the behavior of a large number of people or agents;
  • Competition and evolution — evolution of strategies by agents that operate in a competitive environment that is itself evolving;
  • Instability — iterative exchange between two or more agents in which differences tend to magnify rapidly;
  • Nonlinearity — system changes, sometimes small, that lead to completely different behavior paths; and
  • Network effects — propagation of an effect through a network, often in rapid or unexpected ways.

Like Hadlock’s definition of “collapse”, these are pretty general. Good specific examples are what it takes to make them real. For the most part the author does this in a rather casual way. For example, when he talks about chance, the author first provides some background in probability, and then discusses several of the many consequences we have seen in recent years of the poor estimation of risk. These include incautious drilling into an underground mine (leading to the flooding of the mine and the disappearance of the lake above it), the catastrophic losses of Long Term Capital Management, and of course the mortgage fiasco of the last several years.

Collapse resulting from group behavior is illustrated by the fall of the Anasazi culture and an agent-based model that’s used to try to understand it. Each category of collapse receives a similar treatment: some examples and a related discussion of whatever mathematical modeling technique is appropriate.

I very much wanted to like this book, but in the end I have a hard time recommending it without reservations. It is perhaps too low key and too casual. The introduction and title suggest ambitions that the book fails to fulfill in the end. For example, we are hooked in the introduction by a description of the extinction of the passenger pigeon, but the follow-up is meager indeed — a few sentences.

The treatment throughout is so diffuse and wanders so frequently from the nominal subject that I had to wonder what the author was really trying to do. There is a relatively long discussion of the flocking behavior of birds, which I agree is a fascinating subject, but also seems curiously placed. Yes, it’s about coordinated behavior of organisms in a crowd, but what does it have to do with the author’s main subject? The author never fails to be readable and frequently interesting, but he is often distractingly discursive.

Bill Satzer ( is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.

1. Introduction
2. Predicting Unpredictable Events
3. Group Behavior: Crowds, Herds, and Video Games
4. Evolution and Collapse: Game Playing in a Changing World
5. Instability, Oscillation, and Feedback
6. Nonlinearity: Invitation to Chaos and Catastrophe
7. It’s All About Networks
8. Putting It All Together: Looking at Collapse Phenomena in '6-D"
About the Author