Conned Again, Watson consists of twelve short stories. Each story has a paragraph or three of explanation (sometimes including book recommendations) in the book's afterword.
After inheriting a cab business, Watson's cousin James attempted to emulate
how the Americans have reduced company management to a science. However, he botched it so badly that his company was nearing bankruptcy. He then was taken in by a con man. Watson encourages him to go to Holmes regarding the con, and Holmes informs James that he was such a perfect mark that the con man probably will approach him again, at which point Holmes will aid in the criminal's capture. Holmes then inquires as to how James actually implemented the
modern American management methods.
I really must congratulate you, Watson. In the course of one morning's ordinary domestic decisions, you have managed to replicate on a small scale every one of the errors that brought your cousin's business to its knees!
A woman affianced to a nobleman seeks Holmes's help. Her husband-to-be is low on cash, but has thought of a
foolproof system to get a new fortune at the roulette table.
Perhaps people unconsciously assume that Fortune has a finite number of outcomes in the sack of black and white pebbles she arries. Then the more black pebbles you are dealt, the higher the proportion of white remain in her sack, and the more likely you are to get white. But in truth her supply is infinite, and she can always continue to give black or white at perfect whim. Failure to understand that is the first great human fallacy in misunderstanding the Laws of Chance.
The second great fallacy is to think that you can ignore a very tiny chance of a very large loss or gain. A mathematician would warn you of the meaninglessness of multiplying zero by infinity, but we did not have to venture into such abstractions to see that the Marquis's second system would have come to grief eventually.
The ageing (and seemingly-benign) leader of a small cult seeks Holmes's help. According to her faith, she must bequeath her
church to a descendant of her great-grandfather (the cult's founder). She has 61 candidates. However, the 61st, an infidel who mocks the cult, lives in Canada, and has written back to say that there are 59 more descendants in Canada. The cult leader must choose which candidate is the best, based on which of them has a particular mystically-significant birthday.
The Canadian relative sends over a list of birthdays, but refuses to give the corresponding names and addresses. Instead, the Canadian insists that the cult leader must tell the mystically-significant date to the Canadian, after which the Canadian will contact whichever American relative matches it. However, it's the cult leader's suspicion that there are no other American relatives, and the Canadian is plotting to take over the church (using a non-relative accomplice with a fake birthday) and milk its followers for money. The cult leader wants to know whether or not the Canadian's list of birthdays looks fake, and gives to Holmes two lists of birthdays—one for the 60 British candidates, and one for the 60 alleged American candidates, but neither is marked. She expects Holmes to tell her which one
looks suspicious in its very nature.
Not a bad simile, Watson: real randomness is a sharp and spiky place, which will cut the unwary as surely as sharp rocks rip apart the boots and hands of the ill-equipped cave explorer. We are unaccustomed to such roughness because processes human and artificial so often give nonrandom pattern to the world we encounter, and uniformity is a simple pattern to generate, and therefore commonplace.
Holmes raised a long finger.Never mistake uniformity for the product of randomness.
But you are not alone in your error: mistaking a uniform distribution for a random one is a common blunder. Indeed, it is worthy of being tagged as the third great human fallacy in misunderstanding the Laws of Chance! You had better start making a list. It is as ever most instructive to talk to you, Watson.
Compare the following sentence, which wouldn't look out of place in Harry Potter and the Methods of Rationality:
A drunken sailor whom Holmes and Watson saw
walking a perfect mathematical Drunkard's Walk in Chapter Two apparently fell off a pier and drowned shortly after they observed his stumbling. However, he recently took out a large life insurance policy, with his sister as the sole beneficiary. The insurance company suspects fraud, and refuses to pay out. Inspector Lestrade is sympathetic toward the sister, and has asked Holmes to investigate.
Why, confound it, Holmes, I have once again drawn Napoleon's hat!
Quite so, Watson. You have indeed chosen a fitting name for the Normal Distribution. Just as Napoleon sought to conquer all the populations he encountered, so the Napoleon's hat curve tends to dominate all random populations encountered in nature. But remember this: Napoleon ultimately failed in his quest—he never ruled all of Europe, despite his ambition. And similarly, not every imaginable population conforms to the normal distribution, although student mathematicians sometimes fall into the trap of thinking that all must.
Watson goes to visit an old college friend who wants to undertake some excavations in order to uncover possible Arthurian artifacts. (The friend, named Prendergast, thinks that he may be a descendant of King Arthur Pendragon.) However, the friend's father (whose line has held the title of Mage since before the Norman Conquest) has forbidden any excavation unless Prendergast can prove that the chance of turning up something important is better than one in two. Charles Dodgson (Lewis Carroll) also has been invited.
The Mage looked at scornfully.One-half to two-thirds, he said savagely.That seems to be your theme song, Reverend.
After seeing a horrific face on the surface of the Moon, hearing about crop circles in nearby fields, and finding the message ARES COMES in the Bible, an aspiring engineer thinks that a Martian invasion is imminent.
ticked off points on his fingers.First, you showed us how the human eye and brain can detect pattern where there is none. It is understandable design by evolution, for it is better to be frightened by ten shadows than to overlook one actual tiger, but it often trips us up in modern life.
Second, there is the fallacy of retrodiction—conducting a blanket search of a great number of possibilities, and claiming subsequently how unlikely it is to get just that message in just that position. It is more often done by numerology: measure every possible dimension of the Great Pyramid, say, in every system of units known to you, and then try dozens of possible numerical combinations of the results to see whether any of the numbers that emerge seem significant, such as being a famous year in the Christian calendar. But your Bible messages have that beat all hollow.
First, Watson reads about a parlor game in which three people must pretend to be historical figures (e. g., Newton, Caesar, and Socrates) and argue over which of the three should be thrown out of a sinking hot-air balloon. Second, Lestrade calls Holmes out to investigate the murder of a philanthropist, in which three attractive young women whom he was considering for a scholarship are suspects. Third, the woman from Chapter Two writes to ask for advice, as her husband-to-be, while having vowed to stay away from casinoes forever, has fallen in with a peculiar gentleman's club that supposedly deals solely in games of skill.
I shook my head.Really, this seems like black magic, Holmes.
Not so, Watson. But it does go against a false intuition that Nature has hard-wired firmly into our brains: the fallacy of judgement, that people or objects can always be ranked in order of value, from best to worse, in a sort of beauty contest. Let us be thankful that it is not true.
The lone survivor of a 10 000-man army killed by ambush in the backwoods of British Burma is being slaughtered by the newspapers just as badly as his comrades were by the Burmese, and is expected to be convicted of desertion and hanged.
Bayes's theorem sets out formally the criteria for calculating probability ratios such as those we have been encountering today.
I will be sure to credit him if I write up today's events. If you show me it, perhaps I should reproduce his formula to illustrate the point.
Holmes turned the book toward me to reveal, I must say, a rather intimidating piece of algebra.
I would not advise it, Watson. I have heard it said that every equation appearing in a popular book halves its sales: your fear of algebra is not unique. I confidently predict that if this formula appears in all its glory, your sales will be decimated—and in the modern sense of the word! No, you should confine yourself to illustration by example. Those window-frame-shaped diagrams I have been drawing for you summarize Bayes's approach exactly.
First, Mycroft calls in Holmes to investigate a diplomatically-sensitive burglary at the French Embassy, in which two suspects have been caught but refuse to talk. Second, an officer about to be court-martialed for indirectly causing the deaths of the men under his command asks Holmes whether or not he made the correct decision under the circumstances in which he found himself. Third, Holmes contemplates the similarity of the officer's situation to Holmes's own decision in The Final Problem—of whether, in attempting to flee to the continent, he should have gone directly to Dover or left the train at Canterbury after he learned that Moriarty was chasing him in a special train.
I blinked at the complex array of figures.
Henderson wants to choose a column that maximizes his chance of survival. But the Mauras will pick the row that minimizes it. Hence arises the concept of the minimax, beloved of game theorists. We must look for the column in which the lowest value is as high as possible.
Well, it does not matter now, Holmes. As it turned out, you went to Canterbury, and survived; Moriarty is dead, and can never tell us on what basis he chose Dover. All else is moot.
Holmes looked at me without seeming to see me, his gaze focused somewhere beyond infinity.Is it, Watson? Do you remember the many-worlds view of reality, endorsed by Challenger and many other clever physicists, that arises out of quantum theory?
In that case, the original Sherlock Holmes who tossed a coin on the way to Canterbury gave rise to a huge (but not infinite) number of subsequent versions. Call that number a zillion if all had survived. If I had rolled a die as I should have done, a third of a zillion would be alive now. As it is, there are only a quarter of a zillion. One-twelfth of those other versions of myself were killed by my stupidity.
I gazed into the fireplace for some time, musing like Holmes on philosophical realities almost impossible to grasp.
A businessman (the son of a person who died in The Einstein Paradox, this book's prequel) comes to Holmes for advice on how he should manage his business.
From the afterword:
deal with the same problem: How do you construct an accurate picture of the world, given that your subjective impressions may be misleading, and second-hand reports deliberately selective?
First, someone is poisoning people accused of criminal deeds with butterscotch sweets, in a procedure that looks something like Russian roulette. Second, Watson has discovered that nightshade extract seems to be an effective treatment for Baird's disease—but it seems to help only half of the patients to whom he prescribes it. Third, Reverend Dodgson (fron Chapter Five) has devised a way to extend I cut, you choose to disputes between three or more parties, and offers his services to help in a territorial dispute between three nations in the Balkans who are negotiating under British oversight.
From the afterword:
Game theory and related branches of mathematics have made great strides in recent decades. Perhaps where the visionaries of the early twentieth century fell short in their attempts to design new and better societies in which war and want would be unknown, those of the twenty-first, equipped with better knowledge, may yet succeed.
The URL given for the author's site in the book's afterword has been dead for quite a few years, but the Internet Archive has a copy saved.