Nov 07 2011

Holmesian Deduction

Sherlock Holmes is perhaps the most iconic detective in literature. His character continues to enthrall – there is a new BBC series with a modern Sherlock Holmes, and other popular TV characters, such as House, are significantly based on Holmes. What I think is endlessly compelling about Holmes is the seemingly preternatural skill with which he “deduces” specific facts about people and situations, based upon careful observation and a rigorous thought process. But then he makes it all seem so easy in retrospect when he reveals his method.

Because Holmes is such a fascinating character and Doyle wrote prolifically about this character, Holmes is also a useful and frequently used example of logic and the process of detective work. I took a course on Holmes in medical school, using Sherlock Holmes short stories as examples of diagnostic principles (Arthur Conan Doyle was a physician, and clearly drew upon this experience in writing Holmes). A recent Scientific American article, for example, used Holmesian logic as an example of how not to make several common fallacies of thinking – falling for the conjunction fallacy, the representativeness heuristic, and failure to consider the base-rate.

Briefly, we tend to assume that someone belongs to a category if they have features we find representative of that category, or if we can readily bring to mind similar examples. We tend not to consider the base rate – what percentage of the relevant population belongs to that category. Sherlock Holmes encapsulated part of this idea with his famous quip to Watson that if you hear clopping on a cobblestone street in London, think horse, not zebra. This principle is common in medical diagnosis, and in fact we call rare diseases (those with a low base-rate) “zebras” after Holmes’ example. In other words – even if a person has signs and symptoms that resemble a specific disease, the probability of that diagnosis is still low if the base rate is very low – it’s a rare disease. In fact, an atypical presentation of a very common disease may be more likely than a typical presentation of a rare disease.

But we tend to be more compelled by the representativeness of a person or situation than the base rate. Our evolved innate calculations of probability are flawed in this way.

The article also discusses the conjunction fallacy – the tendency to think that two likely conclusions are more likely that either alone. Mathematically, this cannot be true – the probability of A+B must be less than the probability of either A or B. This is easy enough to understand, but we tend to ignore this when confronted with a representative example. For example, if I describe for you a typical nerd and ask about the probability that they work in IT and play video games, your naive logic tells you that the probability of both is greater than the probability of either by itself, because they are both representative of the typical nerd.

Holmes is able to arrive at such accurate statements about those he observes partly because he does not fall for all the typical fallacies and heuristics that hamper our thinking. When they are explained, they make perfect logical sense. The average person, however, is typically not aware of all the flaws in logic that plague our thinking day to day.

However, I have to point out that the process that Sherlock Holmes engages in is usually not deduction, even though that is the term the character Holmes uses to describe his process. The new BBC Holmes series, for example, has a website called The Science of Deduction (which exists also in the world of the series as Holmes’ website).

Deduction is the logical process of going from the general to the specific. If one or more premises – general statements about the world – are true, then a specific conclusion must also be true. This is deduction. The textbook example of this is: Premise 1: All men are mortal; Premise 2: Socrates is a man; Conclusion: Socrates is mortal.

There are times when Holmes does indeed use deduction, but not when he is coming to conclusions based upon his careful observations. Some logicians have referred to what Sherlock Holmes does as “Holmesian deduction” to distinguish it from deduction itself. What Holmes is largely doing is well-informed inference. He begins with careful observation of details. He then uses base rate knowledge (rather than superficial representativeness thinking) to make specific high probability guesses. Watson, he observes, has a tan. He did not get the tan in London, so he must have recently arrived from a tropical location. He puts this together with other bits of information to infer that Watson probably served in Afghanistan.

Holmes also uses a great deal of inductive knowledge. Induction is the process of going from the specific to the general – which is mostly what scientific investigation involves. We might note that every swan observed is white, and induce the general principle that all swans are white. While deductive conclusions must be true, inductive conclusions are tentative – they are extrapolations from limited data. They are also falsifiable (at least in principle) as was demonstrated by the discovery of black swans in Australia. Holmes develops general principles from inductive processes (science) and then applies them to his inferences. He spends much of his time between cases doing detailed analyses of cigar ash and other such things, providing knowledge he can then use in his investigations.

In many ways what Holmes does is very similar to the cold reading of fake psychics and real mentalists. A skilled cold reader will be armed with knowledge of the base rate of many things, such as male and female names. They will use observation and feedback in order to feed the process with information, and then make inferences about what is likely to be true. Just as with Holmes, they have the ability to amaze their target, seemingly pulling very specific information out of thin air. But just like Holmes, they are really just using a process of observation and inference.

Regardless of the purpose (medical diagnosis, entertainment, investigation, or fraud) what the character Holmes does aptly demonstrate is the power of substituting rigorous logical methodology for the naive reasoning that humans evolved.

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