Chemical Education Today

www.JCE.DivCHED.org • Vol. 83 No. 4 April 2006 • Journal of Chemical Education 549

edited byJeffrey Kovac

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Book & Media Reviews

The Essential Exponential:For the Future of Our Planet

by Albert A. Bartlett

University of Nebraska Press: Lincoln, NE, 2004. 291 ppISBN 0975897306. $24.98

reviewed by Kevin M. Dunn

“The greatest shortcoming of the human race is our in-ability to understand the exponential function.” This is thecentral message of The Essential Exponential by Albert A.Bartlett, an emeritus professor of physics at the Universityof Colorado at Boulder. The book takes its title from a lec-ture Bartlett was invited to give in 1969 and that he woulddeliver more than 1500 times over a 35-year period. The talkled Bartlett to investigate the mathematics of populationgrowth and the depletion of non-renewable resources suchas fossil fuels. This research led to a long line of journal ar-ticles that collectively comprise The Essential Exponential.

The book is divided into chapters, most of which aresimply collections of journal articles on a common topic. Anexception is the first chapter, in which Bartlett recounts thehistory of the talk and his subsequent research on exponen-tial arithmetic. Chapter Two contains six articles on the en-ergy crisis spanning the years 1976–2001 in which Bartlettargues that the public has been given overly optimistic esti-mates of lifetimes for fossil fuels. One such estimate, for ex-ample, states that at current levels of output and recoveryU.S. coal reserves can be expected to last for more than 500years. What Bartlett points out is that even modest growthin the consumption of coal drastically reduces the expectedlifetime. At 1976 levels of consumption Bartlett estimates thatU.S. coal will indeed last between 780 and 2980 years. Butif consumption grows at an annual rate of 3 percent, thenthe estimates fall to between 105 and 149 years. If the growthrate is 10 percent, the estimates fall to between 43 and 57years. Bartlett rightly criticizes leaders from government andindustry who promulgate optimistic lifetimes “at current ratesof consumption” while at the same time pressing for increasedreliance on coal.

Bartlett builds on the work of M. King Hubbert, whoempirically modeled the full life cycle of the production ofnon-renewable resources. In this analysis, per-year produc-tion tends to follow a Gaussian curve, growing from year toyear, peaking at some point, and then declining eventuallytoward zero annual production. U.S. oil production peakedin 1970, and in a 2000 study Bartlett estimated that it willdecline to one-third of the peak value by 2020. World oilproduction is projected to peak some time between 2004 and2030.

Chapter Three contains four articles on populationgrowth, which in Bartlett’s view is the root of most of theworld’s problems, the energy crisis among them. Bartlett re-pudiates the popular view that overpopulation is mostly a

problem for the third world. In his view, the U.S. consumesthe lion’s share of the world’s finite resources and zero growthin the U.S. population is an absolute requirement if the fu-ture is to look anything other than dismal. In order to achievethis goal we would have to allow no immigration into theU.S. and reduce the birth rate to 59% of its 1992 value. Someimmigration could be allowed if the birth rate fell to evenlower values. The argument against immigration seems overlysimplistic; does a middle-class European automatically be-come more wasteful when he crosses the pond? Does a citi-zen of the U.S. acquire a social conscience when she emigratesto Australia? The argument for reduced birth rate would callfor a voluntary or mandatory limit of approximately one childper married couple. Since the zero-population-growth argu-ment is founded on the assumption of a fundamentally prodi-gal American character, neither voluntary nor mandatorylimits would seem to be on the horizon.

The final article of Chapter Three, “The Massive Move-ment to Marginalize the Modern Malthusian Message”, is anelaborate attempt to classify and categorize those who do notagree that population growth is the most pressing concernof the planet. Briefly, Believers are the good guys, those whoagree with Bartlett. Critics can be divided into Non-Believers(who, according to the article, are probably innumerate) andDiverters (who know the Truth but who, for a variety of rea-sons, try to convince others of its falsity). The tone of thearticle is less than charitable and might come off as a rant toreaders who are not already Believers.

One of Bartlett’s pet peeves is the oxymoronic term “sus-tainable growth”. The four articles of Chapter Four deal withapplications and misapplications of the term “sustainable” asapplied to problems of population and finite resources. Thefirst article advocates a program for “sustained availability,”in which the rate of extraction of a resource declines eachyear at such a rate that the resource lasts “forever”. Whilethis is an interesting mathematical puzzle, the result does notseem to be fundamentally different from that which wouldcome about in a laissez-faire approach. In the “sustained avail-ability” future some kind of central planning authority de-creases the extraction quota each year according to amathematical projection. In the laissez-faire future, it becomesincreasingly expensive to extract the dwindling resource un-til it is no longer economical to do so on the same scale aspreviously. In neither future does the extraction rate neces-sarily fall to zero, and in both futures the population mustmake do with an extraction rate significantly less than thehistorical peak.

Chapter Five contains an article by M. King Hubbert,whose Gaussian model for resource depletion appears in manyof Bartlett’s articles. One article by physicist David Roperprovides a theoretical foundation for Hubbert’s empirical ob-servation. Another Roper article applies this theory to U.S.petroleum and natural gas depletion. Roper’s model allowsfor an asymmetric extraction curve in which the decline inthe extraction rate is not necessarily as rapid as the rise lead-ing up to the peak. This means that the modeled resource

Chemical Education Today

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Book & Media Reviewsmay last somewhat longer than would be predicted by theGaussian model. The end of the story is the same, neverthe-less; the resource is extracted at miniscule rates in the distantfuture.

Chapter Six consists of three articles previously publishedin Population & Environment. The first outlines the principlesof discrete and continuous compounding, describes the useof logarithmic scales for plotting data, and gives methods forcalculating doubling times. The second article is built aroundthe example from Life magazine of a 98-year-old man whohad 200 great-grandchildren and goes on to develop math-ematical models for determining the number of children,grandchildren, and great-grandchildren who would descendfrom a hypothetical person under various scenarios. The thirdarticle in the series compares the growth in profits and wagesfrom 1989 to 1997. Bartlett concludes that corporate profitsgrew 25 times as fast as wages during this time period.

Chapter Seven consists of 14 articles written for ThePhysics Teacher between 1976 and 1998 that develop themathematics of the exponential function and apply it to avariety of real-world problems, including compound inter-est, inflation, highway construction, population growth, post-age rates, gasoline shortages, and curve fitting. The materialfrom Chapters Six and Seven are among the most timelessin the book, applying exponential arithmetic to a variety ofmodel problems that are not necessarily tied to particular po-litical and economic messages.

Chapter Eight consists of endnotes by Robert Fuller,Vicki Clark, and John Rogers, who convinced Bartlett thatThe Essential Exponential deserved to be archived in book

form for the use of planet-conscious science teachers. Chap-ter Nine is an annotated bibliography of articles by Bartlett.

I suspect that The Essential Exponential will not be well-received by Non-Believers and Diverters. Bartlett is not shyabout expressing his disdain for “experts” who disagree withhis political and economic messages (p 98):

There seems to be a concerted effort, locally, nationally,and globally to marginalize the modern Malthusian mes-sage and to talk about sustainability, using terms and con-cepts which don’t offend anyone. This marginalizationrequires that we make no mention of the facts that at alllevels,

(a) Sustainability requires that both population and therates of consumption of resources be stabilized atlevels substantially smaller than those of today and,

(b) The world’s worst population problem is right herein the U.S.

Believers will appreciate these messages and admireBartlett’s tenacity in fighting the good fight for more thanthree decades. Scientists of all political stripes, however,should applaud him for bringing to these politically and emo-tionally charged debates the underlying central message thatmathematics is the language best suited to exploring issuesin which numbers really count.

Kevin M. Dunn is a member of the Department of Chem-istry, Hampden-Sydney College, Hampden-Sydney, VA 23943;kdunn@hsc.edu