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Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin
Lawrence Weinstein and John A. Adam
Publisher: Princeton University Press (2008)
Details: 336 pages, Paperback
Topics: Mathematics for the General Reader, Estimation
MAA Review[Reviewed by Andrew Ross, on 04/19/2008]
How many tons of batteries would you need to equal the energy contained in one tank of gasoline? How much farmland would be needed to grow enough crops for ethanol to run all the cars in the US? If you placed all the pickles sold in the US in a year end-to-end, how far would they reach?
Guesstimation teaches you to find approximate answers for these problems, and many others. Many of the problems in this book are related to important public policy questions, like the first two questions above. Others are just for fun. Many would be appropriate for a quantitative literacy class, while others would only go well in a class for math/science/engineering majors. Some middle- and high-school science contests, such as Science Olympiad, also have events that use these kinds of problems.
The key to doing one of these approximations is to break it into a sequence of easier estimation problems, then combine those results. Part of the aim is that you won’t need to look up anything; each part of the estimation is either a common physical constant or estimated from daily experience. For example, you could answer the pickle problem by estimating the number of pickles each person eats per year (or month), the number of people in the US, and the average length of a pickle. You would probably then convert the result from inches to feet, and then to miles.
These sorts of problems are known as Fermi problems, after the physicist Enrico Fermi, who was fond of them. The usual goal is to get within a factor of 10 of the true value. Guesstimation does a good job of checking the answers obtained with more accurate answers looked up elsewhere, and indeed accuracy to a factor of 10 is almost always achieved. It has good supporting material on the use of scientific notation and a list of numbers to know approximately (US population, world population, chemical reaction energy in electron-volts, etc.). It also has a good discussion on using upper and lower bounds to estimate average values, and on the importance of using the geometric mean rather than the arithmetic mean.
The book generally does a good job putting its answers into context. For example, the total yearly energy output of the sun is compared to the current global human demand for energy. The interesting twist comes if we assume a 2% growth per year in energy demand; in what year would we need to consume the entire energy output of the sun?
Some problems (such as the farmland-for-ethanol question) could use a better context for their answer. Perhaps this is part of the fun for readers. In particular, some of the questions involving energy end with an answer in joules, or sometimes kilowatt-hours, which might still be too abstract for some people. In those cases, I prefer to convert these answers to dollar amounts. For example, if you had to supply the energy by buying food and using its caloric content, how much would it cost? Or, if you were allowed to supply the energy using household electricity (at 10 cents per kilowatt-hour), how much would it cost? What if you had to use AA batteries?
Guesstimation makes for entertaining reading, as well as having important insights on public policy questions. The bulk of the book consists of questions, hints, and well-reasoned, worked-out answers. It is an excellent sourcebook for teachers who want their students to learn estimation. Since most of the questions are worked out, however, it’s not clear that students should have a copy if the teacher intends to assign the questions (though the book does have a list of 33 questions with no hints or answers). Overall, it is a very good book, and I have been recommending it to many of my colleagues in a variety of fields.
Andrew Ross is an assistant professor of mathematics at Eastern Michigan University. He works on many areas of operations research: queueing theory, applied probability, and optimization, focusing on the telecommunications and electric power industries. He notes that a AA battery contains about 0.003 kilowatt-hours and suggests that you calculate the cost per kilowatt-hour of AA batteries.