Moriarity's Greatest Con [Hardcover]

Bruce's approach is to teach concepts in statistics and probability through mystery stories written around the characters of Sherlock Holmes and Dr. Watson. At first I was a bit skeptical, wondering if something this non-traditional might be just a gimmick. I was pleasantly surprised to discover that the book not only has real intellectual merit, but that Bruce is a pretty good mystery writer to boot.

Holmes solves most of the mysteries in this book by using analysis grounded in the mathematics of statistics. Some of the solutions to these mysteries are non-intuitive, and may trip up even those who consider themselves to be experts. Gambling fallacies are a common theme, including the mistaken idea that the "law of averages" somehow decrees that, after a string of one type of random event, another type of independent random event becomes more probable. This error is rooted in the mistaken notion that if the ratio of two numbers approaches 1, then the difference between the two numbers approaches 0. For example, if you toss a fair coin N times, the ratio of the total number of heads, divided by the total number of tails, approaches 1 as N becomes very large. However, the difference between the number of heads and the number of tails can (and usually does) diverge. There is nothing in the laws of statistics that says that, after a string of 10 heads, the next throw of the coin is more likely to come up tails (if the coin is fair). Yet this common fallacy persists among many gamblers. This is closely related to the mathematics of the drunkard's walk, which is the centerpiece of another mystery unraveled by Holmes as he investigates the case of an unfortunate sailor and the insurance money pursued by his distraught sister.

In another caper, Holmes uses his knowledge of the well-known birthday paradox (given N people in a room, what is the probability that two or more of them will share a common birthday) to expose a fake genealogy at the heart of a dispute over a wealthy inheritance. The real lesson of this mystery, however, is that the human mind is a poor random-number generator that inevitably fails to appreciate the nuances of truly random events. In this story, Holmes uses the tell-tail signs of a concocted distribution of birthrates to deduce that a particular document is a forgery.

Who hasn't been exposed to supposed messages of seemingly profound importance, found encoded in the Bible? In the case of the foolish graduate student, Holmes exposes the mathematics of hidden messages and prophecies coded in religious texts (or any other type, for that matter). The main point is that, in almost any large body of text, the number of possibilities is so large as to make such coded messages a virtual certainty - if you look long and hard enough (you can even find them in things like software manuals).

There is hardly a more common human tendency than placing complicated entities in a linear hierarchy. Witness, for example, the Sunday college-football rankings and the linear ranking of IQ scores. The tendency is possibly rooted in our basic understanding of such things as elementary mathematics, where we are taught that if A is greater than B, and B is greater than C, then A is greater than C. This is true for the set of real numbers, but is hardly true in general. Bruce points out that in higher mathematics, A may be greater than B, and B may be greater than C, yet C may be greater than A. It's really not a difficult concept. Every child knows it well. Paper wraps rock, rock breaks scissors, and scissors cuts paper. The problem comes in internalizing the concepts and understanding where linear hierarchies don't apply. Con men make use of this error with simple games in which the mark gets to pick one of three dice. Unsuspectingly, he fails to appreciate that, no matter which dice he picks, the con man can pick one of the remaining two, that will beat (on average have a higher score) whichever one the mark chooses. The villain is no match for Holmes, though, who sees through the scam with clarity and dispatches his trademark logic to save a friend from his folly.

Many of the mysteries solved by Holmes have implications for public policy. One such example is a case in which Holmes calculates the probability of a particular outcome of a drug test involving one of Dr. Watson's patients. The results have wide application in public policy regarding drug testing. The central theme is that it's possible for some tests to sound very reliable, and yet a large number of the positive tests are false, or a large number of the negative tests are true. The results depend, in part, on the relative number of samples in the population that are using the drug, or have the illness that the drug is supposed to cure.

This book is easy to read, has no equations, and only a few figures. It looks like, feels like, and reads like an honest-to-gosh mystery novel, but manages to illuminate many important aspects of logic and statistics at the same time. I enjoyed reading it, and I'll bet you will, too.

I have to say I disagree. There are just no "AHA!" moments in the book - an element that I enjoy myself in recreational mathematics and seek to bring to my math classroom. I wholly expected the Holmes metaphor to create some captivating mathematical mysteries with more than a few twists. Instead I found leaden storylines and transparent mathematics.

I can't guarantee this complaint because, uncharacteristically, I haven't finished the book (and probably won't); I have so far only read two of the "stories." I found the first one, which ought to be the "hook", to be absolutely flat... nada. Holmes explained a not-especially-intriguing concept of logic or probability to Watson and then stated it again and again and again as they move through some inconsequential action in an uninteresting narrative. Right to the end I kept waiting for the clever twist - in vain. I sighed and set the book aside, then, and did not plan to read any more. Of course there's nothing like having already paid for a book to bring one back to it. The second piece, exploring some rather counter-intuitive elements of probability that many gamblers fall prey to was a tad more engaging - but not close to gripping.

Bruce seems to have the Holmes'ian character and language down pretty well. So what? That establishes a baseline tonality for the book that Holmes fans might enjoy, but it does not supply the oomph that the real Holmes mysteries provide; and Conan Doyle managed that even though we all knew that Holmes would, in the end, get the bad guy and do it in a characteristic way.

There are no mathematical or more traditional mysteries solved here. I guess the "bad guy" in these stories is supposed to be generic ignorance and some sort of innumerate tendency in the reading population (expressed via the straw-man "Watson"). Math literate readers will, perhaps, enjoy the poke at the widespread probabilistic ignorance of Watson's "everyman", but where's the fun (or the discovery) in that? In the two pieces I read, Bruce repeated the pattern of giving away the point in the first bit and then just pounding it in to poor Watson's head and the helpless reader. This seemed a clumsy attempt to copy the original in which Holmes would drop some sly suggestion of his focal point and elegantly uncover it for Watson and the reader.

For more engaging mathematics I'd suggest Ivars Peterson's "The Jungles of Randomness"... for critiques of mathematical blindspots and cultural ignorance, John Paulos' s work.