A Useless Case

June 12, 2007

Book Review
William Kolata

Useless Arithmetic: Why Environmental Scientists Can't Predict the Future. By Orrin H. Pilkey and Linda Pilkey-Jarvis, Columbia University Press, New York, 2007, $29.50.

Occasionally, a book arrives that is immensely frustrating but strangely fascinating. The Pilkeys' Useless Arithmetic is one such book. To get an idea of the book's style, imagine a sequence of medieval morality tales, told by a narrator but with the action and voices of the major heroes and villains kept, for the most part, offstage. For example, our imagined narrator might summarize the first chapter as follows. "The Canadian cod fishery collapses. A mathematical model must share the blame, according to journalist. The concept maximum sustainable yield appears to be a major culprit."

The Pilkeys wish to convince their intended readers ("non-specialists" and "non-mathematicians") that the "reliance on mathematical models has done tangible damage to our society in many ways," and to make the case that "applied quantitative mathematical models of earth processes cannot produce accurate answers." Be prepared, however, for a rather broad interpretation of "earth processes." Thrown into the mix are dubious "mathematical models," such as body counts during the Vietnam War and Enron's accounting standards. In the second chapter, the authors provide a largely muddled and often inaccurate description of quantitative mathematical modeling. They ignore the huge literature on the verification, validation, and testing of mathematical models and on the analysis of model uncertainties by the mathematical community in favor of their own cartoon version.

The Pilkeys suggest an alternative to quantitative modeling that they call "qualitative modeling" at times and "adaptive planning" or "scenario planning" at other times. They contrast the supposed vices of quantitative modeling with the virtues of their qualitative approach. But they do not convincingly explain why qualitative modeling isn't subject to many of the same problems as quantitative modeling. They imply that qualitative modeling can deal with complexity and "predict directions, orders of magnitude and the mechanisms behind natural processes" and yet never requires "arithmetic," especially not arithmetic on a computer.

Examples are usually helpful, and the Pilkeys suggest several, ranging from the admirable to the absurd. They claim that the successful hurricane frequency prediction for the 2005 season by William Gray is based on a "purely qualitative approach." A glance at a methodology document on Gray's Web site, however, shows that he uses a Poisson distribution model for landfall frequency and a binomial distribution for 50-year landfall probabilities; these are quantitative mathematical models based on parameters derived from data.

Looking back to the hurricane that devastated Galveston in 1900, on the other hand, the Pilkeys see an egregious example of the quantitative trumping the qualitative in the failure of the American Weather Service to take into account warnings from observers in Cuba who were "reading cloud patterns instead of using modern weather forecasting techniques"; consequently, they write, "no one left Galveston before the 1900 hurricane struck and 6,000 souls perished." This was more than 50 years prior to the introduction of electronic computers in numerical weather prediction. It also contradicts the report of a local forecast official who wrote* two weeks after the storm that "storm warnings were timely and received a wide distribution not only in Galveston but throughout the coast region. Warning messages were received from the Central Office at Washington on September 4, 5, 6, 7, and 8."

Most of the chapters describe models and their failures in the context of various public policy decisions. The descriptions are fascinating, and they hold several important lessons for modelers, whether quantitative or qualitative. The first is that modeling is a scientific discipline and must meet the standards of scientific peer review, and so modelers must be prepared to address uncertainties. The second lesson is that when modelers enter the public policy domain, they need to proceed with caution in order to avoid confusing science with politics. Had the Pilkeys concentrated on these chapters and attempted to rein in their righteous indignation and faintly Luddite rants against quantitative models, they would have written a much better book. As it is, their case against quantitative mathematical models is, well, useless.

William Kolata is SIAM's technical director.

*Special Report on the Galveston Hurricane of September 8, 1900, Isaac M. Cline, Local Forecast Official and Section Director, United States Weather Bureau Office, Galveston, Texas, September 23, 1900.

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