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

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.

I am frankly shocked by the negative reviews, although it could be that the reviewers are math-lovers who just find the stories too basic or something. For me, a relative novice to math thinking, the book is a delight. Bruce manages to capture much of the tone of the original Holmes books and works interesting math illustrations (some, to be fair, a little contrivedly) into the stories. Minus the math, the stories still have enough whimsy, flair, and character development to warrant reading them. Perhaps my expectations were so low for anything to do with a subject I avoid that "Conned Again" is getting all but a free pass from me, but I really enjoy this work and will look for more of Bruce's writing.

Some time ago, Lamarr Widmer, the editor of the problem column of "Journal of Recreational Mathematics" submitted a review of this book to me, in my capacity as book reviews editor of JRM. As soon as I read the first two paragraphs of the review, I knew that I had to read the book. Sherlock Holmes is without question the greatest character to appear in fiction, the style of the stories still inspire many spin-offs. In the science fiction television series, "Star Trek: The Next Generation", the Holmes style of problem solving is used in many episodes. This book presents several stories where Holmes solves problems with a mathematical theme. Each of them is a delight to read and I did a good deal of head scratching as I tried to anticipate the solution to the puzzle. My favorite story in the collection is "The Case of the Martian Invasion", which, set at the turn of the twentieth century, covers the possibility of heavier-than-air flying machines, "Martian" images on the Moon, crop circles and secret messages being embedded in biblical verse. The proponent of a Martian invasion believes that heavier-than-air machines are possible, putting forward the fundamental principle of using complex machines. That is of course redundancy, where multiple engines are placed on the aircraft in such a way that it can fly with any subset above a certain size. The explanation of the "secret messages" is easy, nothing more than a simple exercise in the probability of the frequency of the appearance of letters and looking hard enough. The other stories were nearly as interesting and cover many areas of life, the probability of various events being the most common scenario. Game theory and decision theory is also used to solve the cases brought before the greatest detective of all time. Although they are set in the time of Holmes, the events described in the puzzles can still be applied to life in the twenty-first century. I found this to be one of the best demonstrations of logical deduction based on sound mathematical principles that I have ever seen. Although he is constantly praised for his skill in logical deduction, Holmes also possesses another talent, that of a master teacher.Published in the recreational mathematics newsletter, reprinted with permission.

The author does a marvelous job of presenting Sherlock Holmes stories through the thought of Dr. Watson, never much in the style of Sir Arthur Conan Doyle. However instead of simple detective mysteries each story has a probabilistic theme. After reading 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 they 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.

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 su