One of the greatest capabilities of the digital computer is its ability to execute computational models of complex systems. Applied to systems as diverse as the weather, economics, biology, and geology, these models have become an integral part of modern life and policy making. Commonly, they are used to predict how the system being modeled will behave in the future. These two volumes survey the success of such predictive models from two very different perspectives: that of scientists in the domain being modeled (Pilkey and Pilkey-Jarvis) and that of an applied mathematician concerned with the mathematics of modeling, independent of domain (Orrell). Despite their different approaches, the authors agree that the trust placed by modern society in predictive computational models is wildly overoptimistic and that the scientists who offer such models are less than objective about their limitations.

Orrell’s book rests on his own technical studies that compare different sources of error in computational models. Errors can originate either with the structure of the model itself (say, ignoring a key process or variable) or with noise in the measurement of model inputs; the chaos endemic to nonlinear models can amplify both kinds of errors exponentially. Orrell presents two approaches for comparing the impact of model error with chaotic amplification of input uncertainty. The shadowing approach explores a range of starting values for the model, to see if an initial condition can be found that enables the model to track reality. Success implies that the basic structure of the model is adequate. The model drift approach advances the model by short intervals, resetting to truth at the start of each interval, and accumulates the error. Since the model is continuously reset, chaos cannot amplify the starting error, and the drift reflects model error.

Orrell’s first section reviews the history of prediction. The second section begins by applying his methods to weather prediction. He finds that (contrary to the received wisdom) weather models are dominated by model error, not chaotic divergence. He goes on to explore biological and economic models. Similarly to the weather models, they make so many approximations and generalizations that it is likely they will also be dominated by model error. The third section of the book comments on long-range predictions; it finds them liable to the same kinds of uncertainty as the shorter-term models discussed in the second section. He speculates that lack of predictability is a deep property of living systems, providing another line of evidence for the Gaia hypothesis. The final chapter concludes that the value of models is not as much in predicting the future, as it is in understanding the present and evaluating hypotheses about processes and their interacting outcomes.

Pilkey and Pilkey-Jarvis examine the history of modeling in six domains of earth science, with illustrated case studies. These include fishery models (the collapse of the cod fishery in the Grand Banks of Canada), geological structure (the evaluation of Yucca Mountain as a repository for nuclear waste), sea level change, coastal erosion (D. Pilkey’s specialty, supported by numerous examples), development of toxic water in abandoned pit mines (Berkeley Pit), and invasive organisms (the brown tree snake of Guam). Their documented discussions of numerous model failures support Orrell’s emphasis on model error: models leave out too many contributing causes, many of which are not understood well enough to be included. Additionally, they illuminate the complex political forces and funding channels that compromise the supposed objectivity of the scientists who promote and execute models.

Mathematically, Pilkey and Pilkey-Jarvis’ book has two shortcomings. First, it repeatedly contrasts the complex systems studied in the earth sciences with systems studied by physicists and astronomers, which it considers not complex. In fact, complexity was first discovered by physicist Henri Poincaré in the late 19th century, in the context of astronomy. Physicists have developed most of the concepts and mathematical tools through which we understand complex systems. Second, while it consistently condemns quantitative models, which aim at numerical predictions, it strongly advocates what it calls qualitative models, which predict the direction and general magnitude of changes. The distinction is spurious. Any computational model is quantitative. Every model has a limit to its precision. What Pilkey and Pilkey-Jarvis call a qualitative model is simply a quantitative model with a lower level of precision than other models; it works the same way and is subject to the same weaknesses. In particular, whether an environmental variable (say, sea level) will increase or decrease over the next 100 years is a quantitative distinction that depends on whether the first derivative of the quantity is greater or less than zero. In fact, the book itself gives numerous examples of “qualitative” predictions that have failed in exactly the same way as quantitative ones. The book is on firmer ground when it advocates the use of models to anticipate multiple possible ways that the world could develop to support contingency planning. This recommendation is closely related to Orrell’s observation that models help us understand how processes interact.

Because they come from complementary perspectives, the general agreement of these two books is striking and sobering. Predictive models have failed in domain after domain. Confronting the evidence of these failures is painful for those whose professional careers depend on modeling, but it is essential, if we are to make appropriate use of computational models. If the modeling profession honestly owns up to what it cannot do, it will be in a much better position to encourage society to take advantage of what it can do well.