To the individual who is inclined to proclaim, “math is too rigid!” I would hand over a copy of Göran Grimvall’s Quantify! A Crash Course in Smart Thinking. The notation, language and even ideas of mathematics, it turns out, are a little messier — and can handle a little more messiness — than many are inclined to believe.
Consider, as Grimvall asks us to do in Chapter One, the humble dot versus the unassuming comma. What, precisely, does 3,175 mm mean? According to the English version of the ISO standards, a comma is used as a decimal sign. Therefore, 3,175 could signify a decimal amount between the integer three and the integer four. Meanwhile, in the US, it is an “unofficial convention” to separate groups of three digits with a comma. By this standard, 3,175 is the single integer that lies between the numbers 3174 and 3176. Usually the context hints at the appropriate interpretation, but not always.
The content of Grimvall’s book, however, does not only concern notation. Grimvall deftly explains why it might be easier to set a triple jump record in Brazil than in Germany or how it came to pass that the number of fatalities in Sweden declined in the year after the change from left-hand to right hand traffic. The discussions of how to determine the carrying capacity of an elevator and the load limit of a rope were particularly thought-provoking. Meanwhile, the section concerning how to determine what constitutes a lethal dose of a given poison was as matter-of-fact as it was chilling. Factors such as the size of the individual who is poisoned, the time after exposure and the way in which the poison made contact with the body — through inhalation, ingestion or intravenously — must be considered. Even so, these factors must be weighed in light of observable, counterintuitive evidence. For example, a single bite from Australasian funnel web spider means instant death for a human but not necessarily for a rabbit, dog or cat.
The book is a model of organization: each of the seven chapters has exactly four sections and each section offers precisely three, seemingly-divergent essays on a single theme. While each essay could easily stand on its own, together they offer more than the sum of their parts. Chapter 6, “The Real World,” for example, has four subsections, one of which is called, “Plausible, but Not Correct.” In this subsection, the reader is treated to essays on the following three topics: “The Unridable Bicycle,” “Church Windows and Lead Roofs” and “The Bathtub Vortex.” It is here that the reader learns that balance on a bicycle has little to do with gyroscopic effects from the spinning wheels, uneven glass on church windows has little to do with the fact that glass is a liquid and the direction of water spiraling down a bathtub drain has little to do with relative position from the equator. Each essay gets right to the point — few are longer than three pages — and offers the reader witty, detailed and interesting material for spurring mathematical thought.
While Quantify! is accessible to anyone with a high school background in math, it also has the potential to speak to those with more advanced training in mathematics. The absence of problems on which to work makes the book inappropriate as a primary text for most math classes. However, the book could serve as a provocative supplement to any math course that treats topics concerning counting, measure, accuracy, extrapolation and models. Overall, I heartily recommend Goran Grimvall’s Quantify! A Crash Course in Smart Thinking to anyone who might appreciate — if not enjoy — evidence that math can accommodate the messiness of everyday, real life situations.
Susan D’Agostino is an Assistant Professor of Mathematics at Southern New Hampshire University. She has written articles for The Chronicle of Higher Education, MAA Focus and Math Horizons. She is currently writing a book with mathematical themes intended for an audience of nonmathematicians.