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


Writing for the general reader and using examples from the environmental sciences, Orrin Pilkey and Linda Pilkey-Jarvis show how unquestioned faith in mathematical models can blind us to the hard data and sound judgment of experienced scientific fieldwork. They begin with the extinction of the North Atlantic cod on the Grand Banks of Canada, and then they discuss the limitations of many models across a broad array of crucial environmental subjects. Case studies depict how the seductiveness of quantitative models ...

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

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Writing for the general reader and using examples from the environmental sciences, Orrin Pilkey and Linda Pilkey-Jarvis show how unquestioned faith in mathematical models can blind us to the hard data and sound judgment of experienced scientific fieldwork. They begin with the extinction of the North Atlantic cod on the Grand Banks of Canada, and then they discuss the limitations of many models across a broad array of crucial environmental subjects. Case studies depict how the seductiveness of quantitative models has led to unmanageable nuclear waste disposal practices, poisoned mining sites, unjustifiable faith in predicted sea level rise rates, bad predictions of future shoreline erosion rates, overoptimistic cost estimates of artificial beaches, and a host of other problems. The authors demonstrate how many modelers have been reckless, employing fudge factors to assure "correct" answers and caring little if their models actually worked.

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Editorial Reviews

Library Journal
Environmental models are critical to understanding and predicting natural phenomena. Geologists Pilkey (emeritus, Duke Univ. Sch. of the Environment; A Celebration of the World's Barrier Islands) and Pilkey-Jarvis (department of ecology, Washington State) have written a fascinating book on the issues surrounding the mathematical models used to formulate environmental policies. To reflect better the book's content, its title should be Environmental Policies and Mathematical Models: Reliability, Issues, and Case Studies. The authors discuss the relevance of mathematical modeling as a means to predict future large, complex, and evolving environmental issues; chapters as case studies explore such issues of regional and global importance as invasive species, groundwater contamination, beach erosion, global warming and rising sea levels, underground storage of nuclear waste, and depleted ocean fish stocks. The strongest sections address the history and development of environmental issues central to understanding the reliability, appropriateness, and assumptions behind modeling behavior. Written for nonspecialists, this book is devoid of mathematics and easy to read, yet it includes a limited number of pictures, notes, references, and figures. Recommended for all undergraduate academic libraries supporting environmental and ecology programs.-Ian D. Gordon, Brock Univ. Lib., St. Catharines, Ont. Copyright 2006 Reed Business Information.
American Scientist
This book is a welcome antidote to the blind use of supposedly quantitative models.

— Carl Wunsch

New Scientist
This is an easy and persuasive read.

— Fred Pearce

The Midwest Book Review

Useless Arithmetic dispels many myths and is a 'must read' packing in case studies and insights on faulty thinking.

Earth Island Journal

[This] readily accessible book should be read by any activist who's ever had to face off against the opposition's engineers.

Issues in Science and Technology
A concise, powerful, and readable book.

— Steven R. Carpenter


This book should be in every library... Essential.

Useless Arithmetic will surely excite any reader.

— David Simberloff

American Scientist - Carl Wunsch

This book is a welcome antidote to the blind use of supposedly quantitative models.

New Scientist - Fred Pearce

This is an easy and persuasive read.

Issues in Science and Technology - Steven R. Carpenter

A concise, powerful, and readable book.

BioScience - David Simberloff

Useless Arithmetic will surely excite any reader.


This book should be in every library... Essential.

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Product Details

  • ISBN-13: 9780231132121
  • Publisher: Columbia University Press
  • Publication date: 1/2/2007
  • Pages: 248
  • Product dimensions: 6.30 (w) x 9.10 (h) x 1.00 (d)

Meet the Author

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.

Columbia University Press

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Read an Excerpt

The reliance on mathematical models has done tangible damage to our society in many ways. Bureaucrats that don't understand their limitations often use modeled predictions … 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."-from Useless Arithmetic

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Table of Contents

Preface ix

one Mathematical Fishing 1

two Mathematical Models: Escaping from Reality 22

three Yucca Mountain: A Million Years of Certainty 45

four How Fast the Rising Sea? 66

five Following a Wayward Rule 92

six Beaches in an Expected Universe 114

seven Giant Cups of Poison 140

eight Invasive Plants: An Environmental Apocalypse 164

nine A Promise Unfulfilled 182

Appendix 205

References 213

Index 223

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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.

If all this is true, how can people counteract the modeling craze? The supposition is that there is no way that ordinary people can argue with such sophisticated mathematics. But there is more to models than mathematics. There are parameters such as water velocity, temperature, wave height, rock composition and porosity, and many other factors that make natural processes work. And each of the parameters is represented in a model by simplifications and assumptions. This is the point at which the mathematically challenged among us can evaluate models and even question the modelers.

For example, the height of the waves striking a beach is an important control on the velocity of currents that carry sand away. Anyone who has spent time on a beach, however, knows that the waves vary widely from day to day and, of course, during a storm can be huge. So what number do you use in a model to represent such a variable parameter? The volume and flow rate of groundwater is an important factor in controlling the fate of nuclear waste at Yucca Mountain, Nevada, and the amount of rainfall will be critical in determining that rate. What number do you use in the model for the annual rainfall 100, 1,000, 10,000, or 1,000,000 years from now? After an open-pit mine is abandoned, the rate of flow of groundwater into the pit is critical to understanding whether or not the pit will be an environmental hazard, but the rate of flow into the pit will vary as acidic waters either dissolve rock and enlarge pores or precipitate minerals and reduce pores. Future rainfall amounts are also important. OHow do you put all of this together and come up with a prediction of the composition of the pit lake 50 years from now? Or 100 years from now?

Years ago, in his capacity as a professor at Duke University, Orrin organized a graduate seminar in the Nicholas School ofthe Environment to look at mathematical models used in coastal geology. None of the class participants (including the professor) knew much about mathematical models. They decided to get to the bottom of the question of why the models seemed to come up with inaccurate predictions of the behavior of beaches.

What a revelation that seminar turned out to be! It became clear that beach modelers used models that had no demonstrable basis in nature. They employed “coefficients” that in reality were fudge factors to assure that the “correct” answer would be found, and no one looked back to see if the models actually worked. And no one was complaining. Neither the public nor the politicians knew or particularly cared, since the models were providing them with federal funds to stop beach erosion. And when the scope of the seminar was broadened beyond beaches, it became apparent that the problem existed in a wide variety of modeling efforts involved with all kinds of physical and biological processes concerned with the surface of the earth.

Clearly, the mathematical modeling community believed so strongly in models that it insisted on using them even when there was no scientific basis for their application. The discredited Bruun Rule model predicts how much shoreline erosion will be created by sea-level rise, and since no other model claims to do this, the Brunn Rule remains in widespread use. The maximum sustainable yield is a concept that fishery models are still using as a means to preserve fish populations despite the fact that the concept was discredited thirty-five years ago.

Participants in the seminar came to believe that an amazing statement by Jim O’Malley, a representative of the fishing industry, could be applied on a much broader front than fish models:
I stress that the problem was not mathematics per se but the place of idolatry we have given it. And it is idolatry. Like any priesthood, it has developed its own language, rituals and mystical signs to maintain its status and to keep a befuddled congregation subservient, convinced that criticism is blasphemy. . . . Most frightening of all, our complacent acceptance of this approach shows that mathematics has become a substitute for science. It has become a defense against an appropriate humility, and a barrier to the acquisition of knowledge and understanding of our ocean environments. . . . When used improperly, mathematics becomes a reason to accept absurdity.
Linda has worked for both federal and state governments. Quantitative modelers, she independently observed, have an almost religiously fanatic outlook on the veracity of their models and brook little criticism. It is a characteristic we believe can be applied broadly to many natural-process modelers. The modeling modus operandi is shrouded in mystery, with necessary though poorly communicated assumptions made at each step along the way. In Linda’s view, those who rely on the models for making policy decisions rarely understand the limitations of the models, much less are prepared to communicate such information to the public.

Qualitative models are used in trying to understand natural processes; here precise answers are not sought. Such models seek only trends, relative impacts, probable causes, directions of flow, timing of events. They consider and incorporate only the most important parameters of a process. They are not expected to produce accurate answers. These models often work and can be very useful. In this book we are concerned with the quantitative, “accurate” predictions made by mathematical models that are applied to societally important issues involving natural surface events on the earth. These models are expected to produce answers that are accurate enough to use for engineering and other applied societal purposes.

The book is intended to be read by non-specialists who are interested in nature and in the politics of working with the earth. We have not included equations here except (with some reluctance) for a few relatively simple examples in an appendix. Without resorting to mathematics, we make our point that applied quantitative mathematical models of earth processes cannot produce accurate answers. We evaluate assumptions behind the models, look at the nature of the field data that go into the models, evaluate model achievements, and examine the dialogue between modelers and their “customers.” We are speaking to non-mathematicians like ourselves.
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Interviews & Essays

Q: You've written numerous books on coastal hazards and how we should respond to them. Why did you want to write this book about the abuse of mathematic models?

Orrin H. Pilkey and Linda Pilkey-Jarvis: For more than twenty-five years we have monitored beach nourishment projects around the United States. In order to secure federal funding and justify the enormous costs of these projects, anyone undertaking one must make a prediction of how long the sand will last on the replenished beach. The predictions are based on mathematical models that are said to be sophisticated and state of the art, and yet are consistently, dramatically wrong—always in an optimistic direction. In the rare instances when communities questioned the models after the predictions of a long healthy replenished beach clearly failed, the answer typically was that an unusual and unexpected storm caused the error. Well, the occurrence of storms at any beach is neither unusual nor unexpected. Eventually we became interested in how models were used in other fields. When you start looking into it, you find that a lot of global and local decisions are made based on modeling the environment. There are some fascinating (and discouraging) stories of model misuse and misplaced trust in models in the book.

Q: What is the problem?

OHP and LP-J: The problem arises when we rely on quantitative models to find an accurate "when," "where," and "how much." We find that these types of applied models are frequently detached from reality—built on oversimplified and unrealistic assumptions about natural processes. Worse yet, we found that the modelers in many fields (global climate change being an exception) don't look back at the predictions to see if they were right. Instead they march forward, creating ever more sophisticated models. If your basic assumptions are wrong, it doesn't matter what the math does. By the way, the reader should not worry that this book is full of mathematical equations—it's not! This book is full of interesting stories and illustrates how the mathematically challenged can confront modeled predictions.

Q: You frequently use the term "fig leafs" throughout Useless Arithmetic. How does it apply to models?

OHP and LP-J: One example from our book is the "fig leaf" coverage provided by quantitative modeling in the Grand Banks fishery. The Canadian Grand Banks fishery has been described as the greatest in the world. It provided cod to the Western world for 500 years. In our lifetime, we watched the wild and senseless overfishing lead to the demise of an industry that employed as many as 40,000 people. The models, which many realized were questionable, provided a fig leaf behind which politicians could hide to avoid making the unthinkable decision to halt fishing.

Q: You also write about politics polluting mathematical models. How so?

OHP and LP-J: We tell the story of the selection of Yucca Mountain (Nevada) as the permanent repository for our nation's nuclear waste. Overconfidence in models caused the U.S. government and courts to set a ludicrously impossible standard of safety for the site. Now the federal government requires one million years of certainty that radioactive waste will not endanger the local communities. It should be obvious to all of us that there is no way to predict what will happen in the next million years—a time span longer than that of humans. During the next million years there will be several ice ages and vast changes in climate, and possibly earthquakes and volcanoes. The Yucca Mountain prediction is based on a precarious pyramid built by stacking hundreds of inaccurate models on top of each other.

Q. So what is the solution?

OHP and LP-J: The problem is not the math itself, but the blind acceptance and even idolatry we have applied to the quantitative models. These predictive models leave citizens befuddled and unable to defend or criticize model-based decisions. We argue that we should accept the fact that we live in a qualitative world when it comes to natural processes. We must rely on qualitative models that predict only direction, trends, or magnitudes of natural phenomena, and accept the possibility of being imprecise or wrong to some degree. We should demand that when models are used, the assumptions and model simplifications are clearly stated. A better method in many cases will be adaptive management, where a flexible approach is used, where we admit there are uncertainties down the road and we watch and adapt as nature rolls on.

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  • Anonymous

    Posted November 12, 2007

    A reviewer

    I highly recommend this book for engineers and modelers of natural systems who have dwelled too long in the world of fabricated realities and conflicted interests. You may not agree with everything the Pilkeys say - I didn't - but the book is sure to take off your rose-colored glasses and get your feet headed back towards the ground. This book encourages me, an ecologist who analyzes estuarine monitoring data, to keep questioning the assumptions and 'data' of fisheries and ecosystem models.

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  • Anonymous

    Posted October 24, 2008

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