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Conned Again, Watson: Cautionary Tales of Logic, Math, and Probability

Colin Bruce
Perseus Books Group
Publication Date: 
Number of Pages: 
[Reviewed by
Daniel H. Cohen
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Colin Bruce has once again called upon Sherlock Holmes to solve a vexing mystery, viz., how to introduce some important concepts and lessons from statistics, probability, logic, and game theory. These lessons, presented as cases written by the indomitable Dr. Watson, are all well written and well constructed. Since Dr, Watson comes across as an earnest student, albeit of rather modest abilities, he serves as an effective vehicle for pedagogy.

The result is an introductory text with significant virtues. The stories are quite accessible and quite engaging. They elegantly exemplify the situations to which the probabilities and mathematics rightly apply. Typically, the lessons include two examples. The first is in the form of a case for Holmes to solve, explain, or illuminate. The other is a structurally identical situation in Watson's life. The amiable but bumbling doctor misconstrues things initially, but he sorts things out in the end, correctly deploying the mathematical lessons just earned.

On the other hand, as an introductory text in mathematics, it may be too informal. There are no formulas anywhere in the book and relatively few charts or tables. Thus, the burden falls entirely on the descriptions and explanations. This works pretty well as an introduction to the broad outlines of the ideas behind probabilities and statistical sampling, and does quite a nice job with several specific points, e.g,, how random processes can yield bunched-up distributions and Benford's Law of the most common first digit (which, out of respect for historical accuracy, is properly attributed to Simon Newcomb). The main points concerning the Prisoner's Dilemma, assorted gambler's fallacies, the truth-conditions for conditionals, the apparent presence of patterns in randomly generated sequences, and even some important elements of Bayesianism are well served by Bruce's narratives.

Still, the gain in accessibility is paid by some cost to pedagogical efficiency. It might be easier to illustrate the statistical significance of, say, false positives in testing for a disease formally. On the other hand, the effects of a narrative presentation may be longer lasting, so the circumlocutions needed to express the ideas are justified. It seems odd, however, to talk about standard deviations or expected values, for example, without ever giving their exact, formal definitions, even as an aside. Perhaps the sensitivities of the symbol-shy are over-respected here, because Bruce seems determined to avoid formulas at costs.

It is worth remarking on the steady stream of anachronisms throughout the book. Many are only mildly disconcerting and would not be likely to bother any students. For example, the Victorian logician Charles Dodgson, a k a Lewis Carroll, appears two years after his actual death and Karl Marx appears 17 years after his. Others that may give more pause, e.g., Holmes' reference to quantum physics and Watson's ridiculing of his contemporaries' wild predictions for the twentieth century (now all recognizable as unrealistically prescient). Still others involve the presentation of ideas to which Sir Arthur Conan Doyle would not have had access, e.g., game theory. The author does note these in the Afterword, citing literary license and begging the readers' indulgence — which should be forthcoming, for the charm they add and the pleasure that can be had from finding them first.

The Afterword is a valuable addition to the reading for other reasons, too. It adds some helpful discussions that elaborate and historically contextualize the main ideas in the different chapters. It also provides references to further readings of the kind that would be needed to complement this book, should one choose to use this as a classroom text. While it would not be suitable as a text by itself, there are several classes of readers would be able to take something from reading this book: those who are completely ignorant about the topics covered, and would otherwise remain so; those who would use this as an invitation and a springboard to further exploration; and those who are familiar with the issues at hand, but who have the capacity to appreciate a witty and clever re-packaging.

Daniel H. Cohen ( is professor of philosophy at Colby College.

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