An Angry Indictment of Mathematical Modeling
On the basis of an analytic model, the US Environmental Protection Agency approved a site at Yucca Mountain, Nevada, as a repository for radioactive waste, stipulating that leakage could expose humans to no more than 15 millirems of radiation in any year for the next 10,000 years. Later, a federal appeals court increased the safety window to hundreds of thousands of years. The authors of Useless Arithmetic: Why Environmental Scientists Can't Predict the Future, a prominent coastal geologist and his geologist daughter, aim to show that environmental science models purporting to predict the future beyond a few decades are inevitably incorrect—often drastically so—and frequently harmful, in that they lead to bad policy and convey an unwarranted sense of certainty and control.
To exemplify the problem, Orrin H. Pilkey and Linda Pilkey-Jarvis examine the use of such models in seven fields: radioactive waste disposal, fisheries, global sea-level change, plant invasions, beach nourishment, shoreline erosion, and mine-pit water quality. As they see it, in each instance, there are so many variables and stochastic inputs that predictions of any analytic (as opposed to statistical) model will quickly go awry. Contributing to the erroneous results at Yucca Mountain were climate change over a long time frame, insufficient empirical study of the chemical reactions of the waste or the degradation of waste containers and a titanium shield, and magnification of errors through the interdependence of hundreds of sub-models. Any policy decision based on the results of such a model would be unwarranted.
This is not to say that analytical models cannot be useful in other ways—for example, it would seem that comparing model predictions to subsequent observations could help scientists understand a phenomenon better. Not necessarily so, according to the authors of Useless Arithmetic, who argue that beach nourishment, shoreline erosion, and mine-pit water models have not done even that. In these and other fields, reification of model variables has, in their view, not only led to unjustified policy decisions but also discouraged the gathering of empirical data that would enhance scientific understanding.
In contrast to those areas, the use of models in plant invasions is exemplary, Pilkey and Pilkey-Jarvis point out, lauding a National Research Council report (2002) and other invasion-biology publications for being forthright about the severe limitations of predictive models and advocating caution in applying models to policy decisions. They thus turn what is perhaps the main criticism of modern invasion biology—that it lacks a theoretical basis with quantitative, predictive, generally applicable models—into a virtue.
The chief villains in the piece, according to the authors, are engineers, and they see it as no coincidence that the National Research Council committee on predicting plant invasions consisted wholly of academic scientists—it had no engineers. Modeling in the other fields, except for fisheries and global sea-level change, is dominated by engineers. Pilkey and Pilkey-Jarvis believe that the very nature of engineering models renders the models incapable of adequately representing the complexity and stochasticity of many environmental phenomena. Concrete and steel structures are immeasurably simpler than the physical and biological processes that operate all over Earth.
The other main factor contributing to the dominance of misleading mathematical models is “political pollution,” the authors' term for the pressure on modelers to produce a prediction compatible with the desires of political and economic interests, and the ability of mathematical modelers to adapt to that pressure. For a particularly good example of political pollution, consider how quantitative models abetted the collapse of the Canadian cod fishery.
This is a very angry book. Like Michael Crichton (2004), the authors accuse global-change modelers of being concerned primarily with their own funding. They call the coastal engineering profession a disgrace. They say the field of pit-lake chemistry is in a woeful state. They label much of the mathematical modeling community an unassailable and untouchable priesthood that, by virtue of being a priesthood, has avoided the criticism and debate that characterize normal science. They attack prominent approaches to policy-relevant modeling, such as meta-analysis and cost-benefit analysis. They regard many of the costly, even disastrous failures of military policies as the results of bad modeling. And they name names, identifying many of the villains in the fields they criticize and detailing their sins.
The authors go so far as to open themselves to the charge of settling scores, quoting from critical reviews of a rejected manuscript of the senior author, and assailing the journal to which the paper was submitted and its editors. The vitriol is sufficiently stark and unrelenting that a casual reader, with no expertise in the specific fields under discussion, might suspect the book is the work of neo-Luddites (an epithet Pilkey proudly admits to having been called by one of the coastal engineers he criticizes).
For readers who are scientists, the authors do not help themselves by striving to present their criticism of mathematical models wholly verbally, with almost no equations except for those in an appendix that presents several beach models. Further, they could have clarified their case for both scientists and lay readers with several straightforward, definitional treatments. Importantly, rather than defining “model” and discussing the (valid) uses of models at the outset, and then considering the differences between mathematical and statistical modeling, Pilkey and Pilkey-Jarvis approach these matters tangentially and almost casually in several chapters. Nor do they describe exactly the differences between engineering and science, which they see as a crucial component of the issues they discuss. Similarly, their definition of adaptive management is informal and incomplete and does not address the substantial published criticisms of this approach to resource management (e.g., fisheries and forests); this lapse is striking, given their enthusiasm for adaptive management as a good alternative, in some settings, to mathematical models. Many scientists will perhaps be familiar with most or all of these definitions and the literature surrounding them, but for a targeted readership of “nonspecialists and nonmathematicians,” these are serious lacunae.
And yet, this is a compelling book, hard to put down and impossible to dismiss on the merits of the case. The authors often score telling points, as when they show how standard coefficients in equations widely used to decide policy are often only fudge factors to make the equations produce a desired answer. Similarly, the details of many disasters make for gripping reading: the descriptions of the relationships between modeling and the decisions that led to these disasters are chilling, and often little-known matters are brought to light. The discussion of why a discredited model of shoreline retreat with sea-level rise—the Bruun rule—continues to be widely used is perceptive and broadly applicable to a number of environmental and ecological fields.
Useless Arithmetic will surely excite any reader. Some will be angry, others skeptical, many shocked and dismayed. No one will be bored, and most will want to read further. Anyone who reads policy decisions based on models will inevitably think back to the issues raised here.
- M. Crichton. 2004. State of Fear. New York, Harper-Collins.
- National Research Council 2002. Predicting Invasions of Nonindigenous Plants and Plant Pests. Washington (DC), National Academy Press.