Millions, Billions, Zillions: Defending Yourself in a World of Too Many Numbers

The purpose of this small book is to help people process and develop a feeling for, the barrage of numbers, often very big numbers, that they typically encounter in their daily lives. Assuming no background beyond grade school arithmetic, the author does a commendable job of instilling in the reader a “number sense”—i.e., an ability to understand big numbers, distinguish between sensible and fallacious arguments, avoid making mistakes in interpreting numbers, and to estimate large quantities. 

 

Because this book has essentially no prerequisites, portions of it may strike many readers as just common sense: the author points out explicitly, for example, that when comparing data, one needs to be sure the units are the same, and that if there seems to be an inconsistency in two statistics, looking for other sources may suggest which of the two is correct. But there is also a good amount of material here that may be new to some readers, including discussions of Little’s Law, the Rule of 72, and some basic statistics. There are also lots of examples scattered throughout the text, illustrating incorrect uses of numbers.

 

Kernighan’s writing style is clear, and the examples are helpful, so this book definitely achieves its stated objective of helping people cope with the numbers they deal with ordinary life and recognizing when mistakes have been made.  The last chapter of the book is an interesting, and I thought very useful, assortment of “Fermi problems” (such as “how many golf balls can fit inside a school bus?”) along with the author’s suggested estimates.

 

One small caveat is that the author’s writing style, and the examples given, can sometimes be a bit dry; reading about one newspaper typo after another can grow wearisome after a while. Another, much more pressing, concern is the total lack of an index. This is a worrisome feature that I am noticing more and more in books. 

 

There are, of course, other books addressing the sort of issues discussed here. One that comes to mind immediately is the well-known Innumeracy by John Paulos, written about thirty years ago. Innumeracy, however, differs in a number of respects from the book now under review. Kernighan’s book seems to be more suitable for a genuinely innumerate audience; it is written in a style that is more accessible to people with little mathematical training. It does not address things like the well-known “birthday problem” in probability, which are interesting but not really relevant to the subject of the text, and which take at least some degree of mathematical maturity to appreciate. The Paulos book also contains chapters on topics that are not discussed by Kernighan, including a chapter on the causes of innumeracy and one on “pseudoscience”—for example, astrology and numerology. Finally, the book now under review may lack some of the flash of the Paulos text, but, on the plus side, it also lacks a condescending tone that I thought was occasionally evident in the latter.  

 

To summarize and conclude: an inability to deal intelligently with numbers is a definite problem in American society, and this book does, I think, help address that issue. It should, however, have an Index.

---

Mark Hunacek (mhunacke@iastate.edu) teaches mathematics at Iowa State University.