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The book Conned Again, Watson consists of twelve short stories of “rationalist” Sherlock Holmes fanfiction, published for profit with the blessing of the copyright holder (since, at the time of publication, the franchise still was far from entering the public domain). Each story is accompanied by a paragraph or three of explanation (sometimes including book recommendations) in the book's afterword.
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.
The Case of the Unfortunate Businessman (Chapter 1)
Framing Story
After inheriting a cab business, Watson's cousin James attempted to emulate “how the Americans have reduced company management to a science”. However, James 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”.
Topics
Author's Book Recommendations
Quotes
[Sherlock:] “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!”
The Case of the Gambling Nobleman (Chapter 2)
Framing Story
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.
Topics
Author's Book Recommendations
Quotes
[Sherlock:] “Perhaps people unconsciously assume that Fortune has a finite number of outcomes in the sack of black and white pebbles she carries. 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 Case of the Surprise Heir (Chapter 3)
Framing Story
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). The leader must choose which candidate is the best, based on which of them was born on a particular mystically-significant date, which is known only to her. She knows of 61 candidates, 60 in Britain and one in Canada. However, the one in Canada is an infidel who mocks the cult. In response to the leader's inquiries, the Canadian has written back to say that there are 59 more candidates, “living in various parts of the Americas”, of whose identities the leader is ignorant.
The Canadian 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 candidate matches it. However, it is 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), squander its assets (“large houses in London and New York, and also a fund of several thousand pounds”), and milk its members. The cult leader wants to know whether the Canadian's list of birthdays looks fake. She gives to Holmes two lists of birthdays—one for the 60 British candidates, and one for the 60 alleged American candidates. She has not labeled the two lists, as she expects Holmes to tell her which one “looks suspicious in its very nature”.
Topics
Quotes
[Sherlock:] “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:
Harry's brain complained that it never would have encountered a random distribution in the ancestral environment.
The Case of the Ancient Mariner (Chapter 4)
Framing Story
A drunken sailor whom Holmes and Watson saw “walking a perfect mathematical Drunkard's Walk” in chapter 2 apparently fell off a pier and drowned shortly after they observed his stumbling. However, he had recently taken 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.
Topics
Quotes
“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.”
The Case of the Unmarked Graves (Chapter 5)
Framing Story
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.
Topics
Author's Book Recommendations
Quotes
The Mage looked at [Dodgson] scornfully. “One-half to two-thirds,” he said savagely. “That seems to be your theme song, Reverend.”
The Case of the Martian Invasion (Chapter 6)
Framing Story
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.
Topics
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Compound probability
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Dependency of events
Quotes
[Holmes] 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.”
Three Cases of Unfair Preferment (Chapter 7)
Framing Story
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 2 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.
Topics
Quotes
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 Execution of Andrews (Chapter 8)
Framing Story
The lone survivor of a ten-thousand-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.
Topics
- Bayes's theorem, with helpful visualizations that continue to be presented in later chapters
Author's Book Recommendations
Quotes
“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.”
Three Cases of Relative Honor (Chapter 9)
Framing Story
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 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.
Topics
Author's Book Recommendations
Quotes
I blinked at the complex array of figures.
[Sherlock:] “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 [from The Einstein Paradox, this book's physics-focused prequel] 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.
The Case of the Poor Observer (Chapter 10) and The Case of the Perfect Accountant (Chapter 11)
The afterword advises that these chapters “should be taken together”.
Framing Story
A businessman (the son of a person who died in The Einstein Paradox) comes to Holmes for advice on how he should manage his business.
Topics
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Misleading observations and statistics
Author's Book Recommendations
Quotes
From the afterword:
[These chapters] 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?
Three Cases of Good Intentions (Chapter 12)
Framing Story
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 5) 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.
Topics
Author's Book Recommendations
Quotes
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 Wednesday Wellness threads are meant to encourage users to ask for and provide advice and motivation to improve their lives. It isn't intended as a 'containment thread' and any content which could go here could instead be posted in its own thread. You could post:
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Requests for advice and / or encouragement. On basically any topic and for any scale of problem.
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