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When the numbers don't add up

Useless Arithmetic: Why Environmental Scientists Can't Predict the Future

  • Orrin Pilkey &
  • Linda Pilkey-Jarvis
Columbia University Press: 2007. 230 pp. $29.50 £19 0231132123 | ISBN: 0-231-13212-3

The central thesis of Useless Arithmetic, by the father-and-daughter team of Orrin Pilkey and Linda Pilkey-Jarvis, is “the virtual impossibility of accurate quantitative modelling to predict the outcome of natural processes on the Earth's surface”. This is sure to cause cognitive dissonance among many readers — it simply does not seem to accord with our lived experience.

As I write this review, I'm sitting on an aircraft safely crossing the United States. The plane was created with quantitative aeronautical engineering design models, its flight path dictated by quantitative routing models, and the snowy weather I experienced at take-off was predicted by quantitative weather-forecasting models. Such experiences in successfully predicting and managing natural processes would seem to indicate that without mathematical models our twenty-first-century lives would simply be impossible. What could have influenced the authors to make claims so strongly contradicted by experience?


The authors answer this question unambiguously and definitively by discussing some two dozen instances (seven of which are examined in detail) in which decision-making, and in some cases science, based on mathematical modelling has gone awry, leading to undesired societal and environmental outcomes.

The difference between my flight and failed predictions and mismanagement of fisheries, say, is an important part of the book's argument. In engineering design, flight-path routing and weather prediction, quantitative models are produced and used in a different way from those used by policy-makers for fisheries management, sea-level rise, beach nourishment and the disposal of nuclear waste. However, many of the nuances and complexities involved in understanding these differences are hard to discern in the high-level, non-technical overview provided in Useless Arithmetic. For example, the book hints at the contextual importance of open and closed systems, consolidative and exploratory modelling, and epistemic (knowable) versus aleatory (random) uncertainties, but it does not provide the in-depth treatment needed to really understand these differences or their significance. Readers seeking to have their dissonance resolved may wish that the authors had explained these issues, rather than merely hinted at them. But those wanting more depth will find some useful pointers to accessible literature in a concise but useful bibliography.

The authors point out that modelling results “are easier to live with if they follow preconceived or politically correct notions”, and the chapter on sea-level rise related to human-caused global warming seems to bear this out. In most chapters, the authors focus on a critique of models, modellers and model users. On climate change they choose instead to sandwich their critique of sea-level-rise models with an even stronger critique of Republican senator James Inhofe and author Michael Crichton, both of whom have strongly taken issue with the science of climate modelling and action on climate change. Yet the following authors' comments would have been equally at home in one of Inhofe's speeches or in Crichton's sceptical novel State of Fear (HarperCollins, 2004): “the juggernaut, the large industry that has risen to answer questions about global climate change, global warming, sea level rise, and all their ramifications, has unstoppable momentum... leaders in global change studies tend to view as a primary task the maintenance of funding for the modelling juggernaut.” Have the authors lost their nerve when discussing the politically sensitive issue of climate change? Even so, their strong views on modelling in climate science are difficult to miss.

Despite these quibbles, this is a valuable book for the very reason that it causes dissonance. Using well-documented cases of policy failure, the authors have identified a critical challenge confronting the modern scientific enterprise: our ability to produce model-based predictions seems to have outpaced our ability to use such tools wisely in decision-making. The results are seen in bad policies and bad science.

So what to do? The authors' plea for a world without models is unrealistic, and not simply because scientists will continue to produce them. A story related by the Nobel Prize-winning economist Kenneth Arrow explains why. As a weather forecaster in the Second World War, Arrow and his colleagues were told that their commanding officer needed a long-term forecast. The forecasters knew from experience that such forecasts had little scientific basis, and related this up the chain of command. The reply that came back was this: no matter, the general needs the forecast for planning purposes. Quantitative predictions fulfil important political and social roles, regardless of their quality, accuracy or appropriateness, and will continue to be demanded by decision-makers and produced by scientists.

If quantitative models are here to stay, an important question to ask is how we can improve the way we create and apply models in science and policy. The authors provide some useful guidance by suggesting that we need to be more qualitative in how we model, for instance by recognizing that all current data and analysis point to sea levels rising for the foreseeable future, with some extreme scenarios that cannot be ruled out or even quantified probabilistically, but with a more honest admission that accurate prediction of long-term rates and totals is beyond our abilities. Qualitative modelling supports adaptive decision-making under uncertainty, where commitments are tentative and continuously re-evaluated in the light of experience. Adaptive management does not exclude long-term planning, but it could help us to avoid the big mistakes made when we act as if we know more than we actually do. And as Useless Arithmetic details, making big mistakes based on the misuse of quantitative models is far more common than it should be.

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Pielke, R. When the numbers don't add up. Nature 447, 35–37 (2007).

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