Customer Reviews

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

5 star:		(8)
4 star:		(6)
3 star:		(1)
2 star:		(1)
1 star:		(1)

 

 

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.

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.

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.

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.

Unlike some other reviewers, I am neither a statistitian nor a Sherlock Holms lover. I never cared much for murder mysteries perse, but as a tool for exploring such interesting concepts I thought it worked well. Yes he took a few liberties with history (as he pointed out in the end notes)--so what?

The stories were not designed to top those of doyle but to make some interesting probability and decision making concepts approachable, relevent, and enjoyable. This they did wonderfully. As someone who was turned off to math after years of dull, abstract school lecture, my interest arose from my work in business and computer science. Some of these concepts were not new to me, but all were from new angles. I found .the math easy to follow(depressingly difficult to predict!) and only wished I had not run out of pages. I plan not only to check out the author's other work, but some of the additional reading he kindly suggests in the notes. Thank you Mr. Bruce for and enjoyable read.

This is good enough at what it does: illustrating mathematical concepts under the guise of Sherlock Holmes stories. However, I have one beef and that is that Bruce, perhaps through lack of information on his own part, makes Holmes less intelligent than he should be.

My main example is that throughout the book, Holmes and Watson make reference to the year 1900 (their present year) as being the beginning of a new century. I feel certain that Holmes at least would know that centuries do not begin until the year one, in this case 1901. When Watson mentioned it, I felt sure that Bruce was taking the normal tack of making him obviously less intelligent than his partner (the man *is* a doctor, for crying out loud, give him *some* credit), but when Holmes mentions it later, I was duly perturbed.

Bruce also uses characters purely to tack on surprise endings to his stories, one of which did not work for this reviewer. In one story, the pair meet the Reverend Charles Dodgson, which any bibliophile knows is the real name of Lewis Carroll, but does not present this information until the last paragraph of the story. The surprise ending, using the pseudonym, was therefore lost on me.

In another story, there is no solution presented to a murder. This irked me no end at first, but then I realized that there being no solution to the mystery better illustrated the mathematical principle being explained. I still prefer my murders to have solutions, however.

All in all, this is an entertaining book. Bruces skills as a storyteller and his ability to mix lessons into his stories is commendable. The stories, as Holmes pastiches, ring true overall, only clunking during the details I have mentioned, such as certain actions that seem totally out of character. One other example is when Sherlock and Mycroft are explaining a principle and Sherlock pulls out a graph to illustrate. Bruce (as Watson) writes the following (to the best of my memory): I jumped up, knocking over my chair, and cried, I have a horror of algebra! I couldnt help but laugh! This behavior from one of the most beloved characters in literature?

But, as I said, as a whole the book succeeds, and if you can overlook these details and engross yourself in the superb storytelling, you will enjoy yourself, and probably be educated in the process.

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.

Twelve short Sherlock Holmes stories challanging logic, probability, statistic, game theory, more or less relevant to daily life. The authors approach of telling the story seen through Holmes and Watson is brilliant (incl. the dialogue between the two). Some stories are a bit simple and boring while others were quite amazing. Example Chapter 7 illustrates the error of assuming that a well-defined ordering retlation must also define a unique hierarchy. In higher mathematics it is quite possible to have x greater than y, y greater than z, and yet z greater than x! Last but not least, the afterword is extremely useful where the author sheds more light on each chapter.

This book teaches about pratical math applications through the characters of Sherlock Holmes and Watson. We the readers get to identify with Watson, who blunders and then is set straight by Holmes. I think this way of presenting math makes it more fun. Otherwise mathematical ideas run the risk of being too dry.

Some of the ideas explored in this book are: gambler's fallacy (a long run of bad luck does not make one due for good luck), sunk costs, (sunk costs are sunk costs, don't throw good money after bad). If this sounds interesting to you, then you'd probably like it.

The book is a list of biases and fallacies clothed in the English and London universe of 1899-1900. For a 2011 reader, this makes the stories a bit more difficult to follow given the somewhat archaic environment and language.

For instance, the simple Wason Test is described in a convoluted story around some graveyard stones. Bruce explains in the Afterword that the decision was thus made to prevent the reader from distinguishing an abstract Wason test (the odd/even number vs. vowel/consonant cards) from a realistic one (cheating about one's age to drink alcohol). I found this device to be ineffective. In my opinion, you're better off reading about the Wason Test and the Monty Hall problem on Wikipedia than reading Chapter 5 of the book.

That said, there are interesting morsels throughout the book: why buses tend to come in pairs much more often than regularly spaced in time; the minimax method; how to calculate the numbers of wild populations of animals; why picking the shortest checkout line if often a bad idea; why the most common first digit of prices is 1; how self-interest is more effective than altruism for equitable outcomes.