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Noted coastal geologist Orrin Pilkey and environmental scientist LindaPilkey-Jarvis show that the quantitative mathematical models policy makers andgovernment administrators use to form environmental policies are seriously flawed.Based on unrealistic and sometimes false assumptions, these models often yieldanswers that support unwise policies.Writing for the general,nonmathematician reader and using examples from throughout the environmentalsciences, Pilkey and Pilkey-Jarvis show how unquestioned faith in mathematicalmodels can blind us to the hard data and sound judgment of experienced scientificfieldwork. They begin with a riveting account of the extinction of the NorthAtlantic cod on the Grand Banks of Canada. Next they engage in a general discussionof the limitations of many models across a broad array of crucial environmentalsubjects.The book offers fascinating case studies depictinghow the seductiveness of quantitative models has led to unmanageable nuclear wastedisposal practices, poisoned mining sites, unjustifiable faith in predicted sealevel rise rates, bad predictions of future shoreline erosion rates, overoptimisticcost estimates of artificial beaches, and a host of other thorny problems. Theauthors demonstrate how many modelers have been reckless, employing fudge factors toassure "correct" answers and caring little if their models actuallyworked.A timely and urgent book written in an engaging style,Useless Arithmetic evaluates the assumptions behind models, thenature of the field data, and the dialogue between modelers and their"customers."

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Orrin H. Pilkey is the James B. Duke Professor of Geology emeritus and director emeritus of the Program for the Study of Developed Shorelines at Duke University's Nicholas School of the Environment. He has written numerous books, including A Celebration of the World's Barrier Islands, and is the editor of the twenty-four-volume series, Living with the Shore. Linda Pilkey-Jarvis is a geologist in the State of Washington's Department of Ecology, where she helps manage the state's oil spills program.

Preface	p. ix
Mathematical Fishing	p. 1
Mathematical Models: Escaping from Reality	p. 22
Yucca Mountain: A Million Years of Certainty	p. 45
How Fast the Rising Sea?	p. 66
Following a Wayward Rule	p. 92
Beaches in an Expected Universe	p. 114
Giant Cups of Poison	p. 140
Invasive Plants: An Environmental Apocalypse	p. 164
A Promise Unfulfilled	p. 182
Appendix	p. 205
References	p. 213
Index	p. 223
Table of Contents provided by Ingram. All Rights Reserved.

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Preface

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According to Greek mythology, Zeus once released two eagles in order to find the center of the earth. One flew east and the other west. The birds met at Delphi, which lies on the slopes of Mount Parnassus. From about 1400 b.c. to a.d. 381, the Oracle of Delphi held sway at what was the most important shrine in all of Greece. The oracle could be more accurately described as a succession of priestesses, each given the title of Pythia. For twelve centuries the oracle played an influential role in ancient history and determined the course of empires.

Built around a sacred spring, the shrine to the oracle attracted people from all over Greece and far beyond, who came to pose their questions about the future to the Pythia. Her cryptic answers covered everything from optimal sowing and harvesting times to when an empire should declare war. As she responded to questions, seemingly in a trance, her inarticulate cries were interpreted and written down by an official scribe. In early times this transcription was rendered in hexameter verse, but later it was written in prose. The priest Plutarch said that the trance was the result of vapors, and indeed this may have been the case, for according to a recent geologic study, the presence of ethylene gas (once used as an anesthetic) has been detected in the vicinity of the spring.

The oracular responses were notoriously ambiguous, and their interpretation was often "deduced" only after the event to which they referred. Arguments over the correct interpretation of an oracle were common, but the oracle could always clarify or give another prophecy if more gold was provided. A good example is the incident before the Battle of Salamis, in which the Greeks defeated the Persians. The Pythia first predicted doom and later predicted that a "wooden wall" (interpreted by the Athenians to mean their ships) would save them.

Fast-forward 2,300 years and we find a world that still highly values and relies on prediction. Modern-day oracles are expected to provide predictions over a much wider range of things than the Oracle of Delphi could ever have imagined. In fact, with all the politicians, pundits, government agencies, stockbrokers, scientists, and academics offering their views today, we citizens are inundated with advice and suggestions derived from predictions about the future.

One type of prediction that the original Pythia seldom had to worry about has to do with processes on the surface of the earth. During the time of the Pythia, the earth was far less densely populated, and society had fewer machines to move soil, fight wars, or pollute the air and water. In the days of the American frontier you could start excavating a mine shaft in Montana whenever you wished, provided you could file the claim and pay for the dynamite. If you could make or buy a boat, all the fish in the sea were yours, provided you could catch them. And if you had an eroding shoreline in front of your house, you could build a seawall at will or dump a few dozen truckloads of sand or construction debris on the beach.

Times have changed. Before we can develop a new mine now, a vast amount of paperwork is required, including an environmental impact statement. Such statements are predictions of the ways in which the proposed project could affect the quality of air and water in the neighborhood, and the quality of life for plants and animals and humans alike. Shored up by the cries of distress from the mostly wealthy people who live next to beaches, the federal government began funding beach nourishment projects on Great Lakes and ocean shorelines. In order for a community to receive federal funding for an artificial beach, the calculation of a cost-benefit ratio is required, which in turn assumes an accurate prediction of how rapidly the artificial beach will disappear. Shock waves from the demise of the Grand Banks cod fishery, perhaps the world's greatest fishery for more than five hundred years, have bolstered the requirements for accurate estimates of fish stocks as a basis upon which to regulate fishing.

The widespread availability of computers, the requirement for environmental impact statements and cost-benefit ratios, and the dawn of mathematical models all arrived on the scene simultaneously in the final quarter of the twentieth century. Scientists in the 1960s and 1970s assured bureaucrats that the computer would make it possible to predict the outcomes of natural processes accurately. We don't know how to do it right now, they said, but fund us and we'll figure it out. There are still some scientists who claim successes -- undaunted by several decades of the failure of certain mathematical models to provide the accurate answers that society needs.

At the beginning of the twenty-first century, predictive models of processes on the surface of the earth have come into widespread use. The recognition of complexity and chaos seems not to have diminished the still-rising star of modeling. Every year hundreds of cost-benefit ratios roll off the presses for federal engineering projects involving beaches, rivers, lakes, and groundwater flow. Engineers who have found great success in the use of models to predict the behavior of steel and concrete have applied modeling to the natural environment just as if nature were made up of construction materials with well-defined properties.

The environmental impact of various engineering activities 50 years into the future is calculated even more frequently than cost-benefit ratios are. The mother of all environmental impact predictions is the required assurance of 10,000 years of safety from the Yucca Mountain repository of the nation's radioactive waste. Billions of dollars have been spent at Yucca Mountain on the unrealistic goal of predicting what the climate and groundwater flow will be thousands of years from now. The American judiciary apparently is even more clueless than the scientists of the Department of Energy who are charged with proving the safety of Yucca Mountain -- recently a federal court decreed that the prediction must cover 300,000 to 1 million years! The New York Times quotes an incredulous bartender in Las Vegas as saying, "The earth might not even be here a million years from now." The disappearance of the earth is perhaps not likely, but certainly over the next several hundred thousand years there will be two or three ice ages, the sea level will fall and rise by hundreds of feet, and Yucca Mountain will experience major changes in climate, perhaps an earthquake or two, maybe even a volcanic eruption. Undying faith in mathematics stilled the voice of scientific caution and skepticism that should have warned Congress and the judiciary that the predictive requirements they established for a repository at Yucca Mountain were impossible to achieve.

The reliance on mathematical models has done tangible damage to our society in many ways. Bureaucrats who don't understand the limitations of modeled predictions often use them. That was why the Bureau of Land Management allowed open-pit mines that, once abandoned, would eventually become "giant cups of poison." Models act as convenient fig leaves for politicians, allowing them to put off needed action on controversial issues. Fishery models provided the fig leaf for Canadian politicians to ignore the dying Grand Banks cod fishery. Agencies that depend upon project approvals for their very survival (such as the U.S. Army Corps of Engineers) can and frequently do find ways to adjust models to come up with correct answers that will ensure project funding. Most damaging of all is the unquestioning acceptance of the models by the public because they are assured that the modeled predictions are the state-of-the-art way to go.