In the Arthur Conan Doyle story, “The Silver Blaze,” Sherlock Holmes discusses the theft of a race horse from a country estate that is guarded by a fierce watch dog.
"Is there any point to which you would wish to draw my attention?"
Holmes: "To the curious incident of the dog in the night-time."
"The dog did nothing in the night-time."
Holmes: "That was the curious incident.”
Holmes later explains how the “dog that didn’t bark” helped him to solve the crime:
I had grasped the significance of the silence of the dog, for one true inference invariably suggests others… A dog was kept in the stables, and yet, though someone had been in, and had fetched out a horse, he had not barked enough to arouse the two lads in the loft. Obviously the midnight visitor was someone whom the dog knew well.
This is an example of abductive reasoning: an inference is made based on known facts, in an effort to explain them. It certainly sounds good here. Holmes is working on the premise that because (a) dogs bark loudly at strangers, but not at people they know; and (b) the dog didn’t bark loudly, if he barked at all; then (c) the dog knew the intruder. This is how many detectives and police officers work out a problem. But this reasoning contains fundamental flaws, claims Dr. Robin Bryant, Director of Criminal Justice Practice at Christ Church University, in Canterbury, England, a criminologist with an expertise in how detectives think.
With the new season of the hugely-popular Sherlock television series just kicking off, it seems like an apt time to consider the question: outside the realm of fiction, where Holmes’ “deductions” all seem to end up correct, would Conan Doyle’s detective be considered a sound, logical thinker in today’s world of policing?
A new book, Master-Mind: How To Think Like Sherlock Holmes by Maria Konnikova takes the famous fictional detective’s problem-solving skills and transforms them into a sort of self-help book. That sounds fine at first, and of course Holmes is a renowned problem-solver, at least in the world of fictional ink. But this raises the question: If Sherlock Holmes worked for a modern police force, would he be considered a good detective? According to Dr. Bryant, alas, he would not. His over-reliance on abductive reasoning, at the sacrifice of more powerful logical tools, make his conclusions suspect at best. Dr. Bryant could teach Sherlock Holmes a thing or two. He now travels Europe, teaching police how to analyze their own problem-solving processes, helping them to understand how they make decisions, where there are opportunities for logical inconsistencies, and how to avoid such pitfalls.
“In the 21st century, with the advent of large databases and mathematical modeling, inductive forms of reasoning have become the more reliable methods of criminal investigation,” explains Dr. Bryant, when asked what lessons he might give, should Sherlock Holmes one day show up in his class.
Under the cold light of mathematical logic, there are holes in Holmes’ conclusion (despite the fact that, in the novel, he solved the case). Holmes assumes that dogs behave in a rational manner when, in fact, there might be various reasons why the dog wouldn’t bark, even at a stranger. The stranger might have brought a sausage to appease the dog. The dog might have barked, but no one heard. The dog might even have been drugged (we might call this the Scooby Doo explanation). Because Holmes did not take these variables into consideration, one might conclude that the logic of Holmes’ argument is flawed. It is based on probability (dogs normally bark at strangers), not absolute fact.
In film and fiction, the mental process of moving from observation (clues at a crime scene, the behavior of a suspect in an interrogation) to conclusion is presented in a dramatically foreshortened manner. The problem is that most real-life detectives attempt a Holmesian method, rather than the other logic methods in one’s mental arsenal.
To demonstrate the sort of flexible thinking Dr. Bryant and other mental processes specialists advocate, consider a mathematical puzzle. Based on the following numbers, what would you guess comes next in this sequence:
2, 4, 8, 16, X.
Most people guess that the next number, X, will be 32, each number doubling. That’s a fair guess. But the answer to this particular question is not 32. The next most common estimate is 8, respondents concluding that the sequence will reverse itself. This is also reasonable, but incorrect. The correct answer is 31.
This defies our logic when we consider a sequence of numbers like this, but it does make sense as a plausible answer, if we reveal that the sequence refers to the number of points on a circle, and the number of sections into which the circle is divided. Sometimes called Moser’s Circle Problem, this determines the number of sections into which a circle is divided, if X number of points on its circumference are joined by lines.
If you place two points along the circle, connecting them with a line, then you will have divided the circle into two sections. Add a third point to the circle and connect all three points and you will have created a triangle, dividing the circle into four sections. If you add a fourth point to the circle and connect all the points with lines, then the circle is divided into eight regions. This continues until you have six points along the circle which, when lines connect each of them, leaves you with 31 sections within the circle.
The point of this exercise is not mathematical, nor does it have anything to do with circles or slices of apple pie. When used by Dr. Bryant, it is employed in the hope to demonstrate that there are multiple ways of looking at a problem, and that the most obvious solution, our instinctive reaction, is not necessarily the correct one. Look at the problem from one angle only, and you risk getting it wrong. That is the most frequent logical pitfall into which Sherlock Holmes falls. But because Holmes’ fate was in the hands of Sir Arthur Conan Doyle, he was set up to always succeed. Real-life detectives and amateur problem-solvers do not have that advantage.
Whenever there is a problem to be solved, a decision to be made, we already use the logical methods (abduction, deduction) that neurologists use as categories—we just don’t tend to think of them in those terms. By considering the strengths and weaknesses of various logical methods, we can identify our own built-in prejudices and come to clearer, more logical conclusions.
Dr. Bryant recommends that his students imagine growing a second brain, one whose role is to double-check the assumptions of one’s primary brain. The second brain is there to challenge how conclusions were reached, to ask “what form of reasoning is this?” and “How do I know that if a then b must be true?” This is a point that Maria Konnikova makes in her book: that we would do well to question what we hear immediately, rather than absorbing it as fact and only then questioning it in reflection. By way of example, consider hearing someone mention a “pink elephant.” We instantly imagine an elephant with pink skin, before we “engage in disbelieving it.” Konnikova writes “Holmes’ trick is to treat every thought, every experience, and every perception the way he would a pink elephant…begin with a healthy dose of skepticism instead of credulity…” The implication is that our instinctive credulity puts us at a disadvantage—when we accept what is said (an eyewitness account of a crime, for example), we absorb the prejudice of at first believing what we hear, and only later considering how we might change our mind. Skip this initial step of believing what you hear, and you’ll think more clearly.
That sounds good on paper, but Sherlock Holmes did not regularly follow the advice that Maria Konnikova teaches based on Holmesian examples. In the instance of the dog in the night, Holmes solved the crime, but did so with flawed logic.
Sherlock Holmes should have asked himself why he concluded that a dog not barking meant that the race horse thief was someone the dog knew. Holmes did not consider alternative explanation for why the dog might not have barked, just like Holmes might have assumed that the solution to Moser’s Circle Problem is 32, and have therefore gotten it wrong.
I teach criminology as well as art history, and criminological techniques, of the sort that Dr. Bryant teaches and that we might apply to everyday life, as Konnikova seeks to do in her book, recommend the following method to avoid logical traps. Instead of going with the most obvious and immediate explanation for any action, try to first set that explanation aside and see whether the same facts fit an alternative explanation. For Holmes, this would mean considering all of the various ways in which a theft could occur without the guard dog barking. For a mathematician, it would mean accepting that there are various solutions to Moser’s Circle Problem: 32 is correct if you are doubling each number in the sequence. 8 is correct if the sequence is reversing. But the answer we’re looking for is 31.
Would Holmes have solved Moser’s Circle Problem? He would likely have concluded 32 or 8, long before he reached the “right” answer of 31. Sometimes the answer lies not with what you conclude, but with how you approach the question.