Conned Again, Watson! Cautionary Tales of Logic, Math, and Probability [Paperback]

Colin Bruce (Author)

Book Description

Publication Date: January 15, 2002

In Conned Again, Watson!, Colin Bruce re-creates the atmosphere of the original Sherlock Holmes stories to shed light on an enduring truth: Our reliance on common sense-and ignorance of mathematics-often gets us into trouble. In these cautionary tales of greedy gamblers, reckless businessmen, and ruthless con men, Sherlock Holmes uses his deep understanding of probability, statistics, decision theory, and game theory to solve crimes and protect the innocent. But it's not just the characters in these well-crafted stories that are deceived by statistics or fall prey to gambling fallacies. We all suffer from the results of poor decisions. In this illuminating collection, Bruce entertains while teaching us to avoid similar blunders. From "The Execution of Andrews" to "The Case of the Gambling Nobleman," there has never been a more exciting way to learn when to take a calculated risk-and how to spot a scam.

Editorial Reviews

Amazon.com Review

Some people who think they hate math are lucky to learn that they actually just can't abide its often dry, abstract presentation. Physicist Colin Bruce turns math teaching on its head by using conflict, drama, and familiar characters to bring probability and game theory to vivid life in Conned Again, Watson! Cautionary Tales of Logic, Math, and Probability. Using short stories crafted in the style of Sir Arthur Conan Doyle, he lets Sherlock Holmes guide Watson and his clients through elementary mathematical reasoning. This kind of thinking is growing more and more important as poll numbers, economic indicators, and scientific data find their way into the mainstream, and Bruce's gambit pays off handsomely for the reader. Delving into such arcana as normal distribution, Bayesian logic, and risk taking, the stories never dry up, even when presenting tables or graphs. Holmes's quick wit, Watson's patience, and their various friends' and clients' dubious decisions unite both to entertain and to illuminate tough but important problems. Even the cleverest numerophile will probably still find a nugget or two of hidden knowledge in the book, or at least a few new ways to explain statistical concepts to friends and students. The rest of us can relax, enjoy the tales, and come away a little bit tougher to con. --Rob Lightner --This text refers to an out of print or unavailable edition of this title.

About the Author

Colin Bruce is a physicist and science writer living in Oxford, England. He is an expert in mathematical paradoxes and a lover of mysteries.

Product Details

• Paperback: 304 pages
• Publisher: Basic Books; 1st edition (January 15, 2002)
• Language: English
• ISBN-10: 0738205893
• ISBN-13: 978-0738205892
• Product Dimensions: 8.2 x 5.4 x 0.9 inches
• Shipping Weight: 10.4 ounces (View shipping rates and policies)
• Average Customer Review: 4.1 out of 5 stars  See all reviews (17 customer reviews)
• Amazon Best Sellers Rank: #387,061 in Books (See Top 100 in Books)
  • #82 in Books > Mystery, Thriller & Suspense > Mystery > Reference

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Customer Reviews

Most Helpful Customer Reviews

26 of 26 people found the following review helpful:

5.0 out of 5 stars probability and statistics taught through the eyes of a detective, January 24, 2008

By 

Michael R. Chernick "statman31147" (Holland PA) - See all my reviews
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This review is from: Conned Again, Watson!: Cautionary Tales Of Logic, Math, And Probability (Hardcover)

The author does a marvelous job of presenting Sherlock Holmes stories through the thought of Dr. Watson, very much in the style of Sir Arthur Conan Doyle. However instead of simple detective mysteries each story has a probabilistic theme.

After reading the first couple of chapters I thought this is great for me but I am a statistician. Could a novice understand the complex explanations and story that enhances ones memory about the principles as the author suggests? I think so. The later chapters convince me.

There the author goes over the waiting time paradox, capture-recapture methods and other related problems in the chapter on the poor observer. The famous Monte Hall problem and the birthday problem are also covered and well explained through the eyes of Watson based on the work of Sherlock Holmes and his brother.

23 of 23 people found the following review helpful:

5.0 out of 5 stars Mathematics through the eyes of Sherlock Holmes, April 19, 2001

By 

Duwayne Anderson (Saint Helens, Oregon) - See all my reviews
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This review is from: Conned Again, Watson!: Cautionary Tales Of Logic, Math, And Probability (Hardcover)

This is one of the most interesting books I've read in a long time. I think it will be interesting reading for just about everyone, from the high school student with a penchant for mathematics to armchair intellectuals, statisticians, mathematicians, and scientists.

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.

45 of 51 people found the following review helpful:

2.0 out of 5 stars I was expecting a lot more  you probably are, too, July 11, 2001

By 

Daryl Anderson (Trumansburg, NY USA) - See all my reviews
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Amazon Verified Purchase

This review is from: Conned Again, Watson!: Cautionary Tales Of Logic, Math, And Probability (Hardcover)

I have not read any of Colin Bruce's previous books. They seemed to be highly acclaimed, and I bought this title based on that reputation and some strong reviews here at Amazon.

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.