John M. Henshaw
Johns Hopkins University Press 2014, 200 pages
PRICE (HARDBACK) £30.00 ISBN 978-1-421-41491-1
This book is written for a general audience. The preface opens with the words: ‘This is not a math book. It’s a storybook’. There are fifty-two stories each inspired by an equation from mathematics or science. ‘Equation’ is interpreted quite widely to include the statement of a constant (π or the speed of light) or a conversion factor. About half of the equations are derived from physics, with others from biology, finance, geometry, statistics and pure mathematics. Each chapter is given a title which relates more to the story than the formula.
In many cases the equation is a mere catalyst for a discussion of a topic – ‘The Mars Curse’ uses the equation to convert the imperial pound-force to the metric Newton and explores the failure of the 1999 Mars Climate Orbiter mission due to inconsistency in units. The origin of the title lies in the disturbing fact that of some 42 unmanned missions to Mars since 1960 more than half have ended in failure.
There is a good balance between formulae of a specialist nature and those related to everyday life. ‘Dog Days’ considers the well-known adage that multiplying a dog’s actual age by seven gives us the age in ‘dog years’ (comparable to human years) and explores the science of ageing in different species. ‘A House of Cards’ takes the formula for geometric progression and uses pyramid selling as an example. The original Ponzi scheme from 1920 is described and compared with the later more sophisticated, and more lucrative, Bernie Madoff scandal. ‘Take Two Aspirins…’ is inspired by the equation for calculating the z statistic to compare two means. The specific examples explored are clinical trials and in particular the placebo effect.
Some everyday quantities are explored which may be of interest beyond mathematicians: the definitions of Body Mass Index, Intelligence Quotient and Sun Protection Factor. In each of these cases the quantity can be easily defined and calculated, but the question is whether it conveys a useful metric of the intended property. For BMI (given by mass/height2) it is argued that an exponent of 2.6 instead of 2 would give a more meaningful figure. With modern calculators this is easy, but the original formula was published in 1870. The chapter on IQ explores how the original ideas of psychologist Binet for measuring intelligence were amended by Stern (who defined IQ) and were then widely misapplied in the United States.
The author does not avoid controversial topics. ‘Fracking Unbelievable’ uses the equation for Breakdown Pressure to Initiate Rock Failure to discuss various aspects of fracking including greenhouse gas emissions and the possible stimulation of earthquakes. ‘Zero, One, Infinity’ considers very diverse possible outcomes of the Drake equation for numbers of extra-terrestrial civilizations and the associated Fermi paradox. There are some gems for the pure mathematician – such as the Golden Ratio, Euler’s Identity and the Fermat-Wiles theorem with discussion of unsolved problems in number theory and why mathematicians tackle them.
Several subsets of chapters cover common ground, for example the equations explored in six chapters: on exponential growth, compound interest, geometric progression, radioactive decay, decay heat and the Von Bertalanffy equation are actually variations on the same theme. Two distinct topics, the definition of power and Faraday’s Law of Induction each lead to discussion of certain aspects of electric vehicles. The grading of students is mentioned in chapters on Normal Distribution and IQ.
Each of the topics is very well explained with historical and cultural background as well as theory. Arguably there is some over-representation of physics as against other topics such as financial mathematics. Possibly an overall summary bringing common themes together would be helpful. However it is a very entertaining text, well indexed and referenced with a bibliography for each chapter. I would recommend it as a text for anyone who is interested in the relevance of mathematics to our daily life.
Francis McGonigal CMath MIMA
Birmingham City University
Book review published directly onto IMA website (August 2015)
