Lucretius called a fool someone who believes that the tallest mountain that exists in the world and the tallest mountain he has ever observed are one and the same. We’d probably brand someone who thought that way foolish as well. And yet we do the same thing every single day. Author and mathematician Nassim Taleb even has a name for it, inspired by the Latin poet: the Lucretius underestimation. (And back in Lucretius’s day, was it so strange to think that your world was limited to what you knew? In some ways, it’s smarter than the mistakes we make today given the ease of knowledge at our disposal.)
Simply put, we let our own personal past experience guide what we perceive to be possible. Our repertoire becomes an anchor of sorts; it is our reasoning starting point, our place of departure for any further thoughts. And even if we try to adjust from our egocentric perspective, we tend not to adjust nearly enough to matter, remaining stubbornly skewed in a self-directed approach. It’s our storytelling proclivity in another guise: we imagine stories based on the ones we’ve experienced, not the ones we haven’t.
Learning of historical precedent as well matters little, since we don’t learn in the same way from description as we do from experience. It’s something known as the description-experience gap. Perhaps Watson had read at one time or another about a daring rooftop entrance, but because he has never had direct experience from it, he will not have processed the information in the same way and is not likely to use it in the same manner when trying to solve a problem. Lucretius’s fool? Having read of high peaks, he may still not believe they exist. I want to see them with my own two eyes, he’ll say. What am I, some kind of fool? Absent a direct precedent, the improbable seems so near impossible that Holmes’s maxim falls by the wayside.
And yet distinguishing the two is an essential ability to have. For, even if we have successfully separated the crucial from the incidental, even if we’ve gathered all of the facts (and their implications) and have focused on the ones that are truly relevant, we are lost if we don’t let our minds think of the roof, however unlikely it is, as a possible entry point into a room. If, like Watson, we dismiss it out of hand—or fail to even think about—we will never be able to deduce those alternatives that would flow directly from our reasoning if only we’d let them.
We use the best metric of the future—the past. It’s natural to do so, but that doesn’t mean it’s accurate. The past doesn’t often make room for the improbable. It constrains our deduction to the known, the likely, the probable. And who is to say that the evidence, if taken together and properly considered, doesn’t lead to an alternative beyond these realms?
Let’s go back for a moment to “Silver Blaze.” Sherlock Holmes emerges triumphant, it’s true—the horse is found, as is the trainer’s murderer—but not after a delay that is uncharacteristic of the great detective. He is late to the investigation (three days late, to be specific), losing valuable time at the scene. Why? He does just what he reprimands Watson for doing: he fails to apply the precept that the improbable is not yet the impossible, that it must be considered along with the more likely alternatives.
As Holmes and Watson head to Dartmoor to help with the investigation, Holmes mentions that on Tuesday evening both the horse’s owner and Inspector Gregson had telegraphed for his assistance on the case. The flummoxed Watson responds, “Tuesday evening! And this is Thursday morning. Why didn’t you go down yesterday?” To which Holmes answers, “Because I made a blunder, my dear Watson—which is, I am afraid, a more common occurrence than anyone would think who only knew me through your memoirs. The fact is that I could not believe it possible that the most remarkable horse in England could long remain concealed, especially in so sparsely inhabited a place as the north of Dartmoor.”
Holmes has dismissed the merely improbable as impossible and has failed to act in a timely fashion as a result. In so doing, he has reversed the usual Holmes-Watson exchange, making Watson’s reprimand uncharacteristically well warranted and on point.
Even the best and sharpest mind is necessarily subject to its owner’s unique experience and world perception. While a mind such as Holmes’s is, as a rule, able to consider even the most remote of possibilities, there are times when it, too, becomes limited by preconceived notions, by what is available to its repertoire at any given point. In short, even Holmes is limited by the architecture of his brain attic.
Holmes sees a horse of exceptional appearance missing in a rural area. Everything in his experience tells him it can’t go missing for long. His logic is as follows: if the horse is the most remarkable such animal in the whole of England, then how could it go under the radar in a remote area where hiding places are limited? Surely someone would notice the beast, dead or alive, and make a report. And that would be perfect deduction from the facts, if it happened to be true. But it is Thursday, the horse has been missing since Tuesday, and the report has failed to come. What is it then that Holmes failed to take into account?
A horse couldn’t remain concealed if it could still be recognized as that horse. The possibility of disguising the animal doesn’t cross the great detective’s mind; if it had, surely he wouldn’t have discounted the likelihood of the animal remaining hidden. What Holmes sees isn’t just what there is; he is also seeing what he knows. Were we to witness something that in no way fit with past schemas, had no counterpart in our memory, we would likely not know how to interpret it—or we may even fail to see it altogether, and instead see what we were expecting all along.
Think of it as a complex version of any one of the famous Gestalt demonstrations of visual perception, whereby we are easily able to see one thing in multiple ways, depending on the context of presentation.
For instance, consider this picture:
Do you see the middle figure as a B or a 13? The stimulus remains the same, but what we see is all a matter of expectation and context. A disguised animal? Not in Holmes’s repertoire, however vast it might be, and so he does not even consider the possibility. Availability—from experience, from contextual frames, from ready anchors—affects deduction. We wouldn’t deduce a B if we took away the A and C, just like we’d never deduce a 13 were the 12 and 14 to be removed. It wouldn’t even cross our minds, even though it is highly possible, merely improbable given the context. But if the context were to shift slightly? Or if the missing row were to be present, only hidden from our view? That would change the picture, but it wouldn’t necessarily change the choices we consider.
This raises another interesting point: not only does our experience affect what we consider possible, but so, too, do our expectations. Holmes was expecting Silver Blaze to be found, and as a result he viewed his evidence in a different light, allowing certain possibilities to go unexamined. Demand characteristics rear their ugly head yet again; only this time they take the guise of the confirmation bias, one of the most prevalent mistakes made by novice and experienced minds alike.
From early childhood, we seem to be susceptible to forming confirmatory biases, to deciding long before we actually decide and dismissing the improbable out of hand as impossible. In one early study of the phenomenon, children as young as third grade were asked to identify which features of sports balls were important to the quality of a person’s serve. Once they made up their minds (for instance, size matters but color does not), they either altogether failed to acknowledge evidence that was contrary to their preferred theory (such as the actual importance of color, or the lack thereof of size) or considered it in a highly selective and distorted fashion that explained away anything that didn’t correspond to their initial thought. Furthermore, they failed to generate alternative theories unless prompted to do so, and when they later recalled both the theory and the evidence, they misremembered the process so that the evidence became much more consistent with the theory than it had been in reality. In other words, they recast the past to better suit their own view of the world.
As we age, it only gets worse—or at the very least it doesn’t get any better. Adults are more li
kely to judge one-sided arguments as superior to those that present both sides of a case, and more likely to think that such arguments represent good thinking. We are also more likely to search for confirming, positive evidence for hypotheses and established beliefs even when we are not actually invested in those hypotheses. In a seminal study, researchers found that participants tested a concept by looking only at examples that would hold if that concept were correct—and failed to find things that would show it to be incorrect. Finally, we exhibit a remarkable asymmetry in how we weigh evidence of a hypothesis: we tend to overweight any positive confirming evidence and underweight any negative disconfirming evidence—a tendency that professional mind readers have exploited for ages. We see what we are looking for.
In these final stages of deduction, System Watson will still not let us go. Even if we do have all the evidence, as we surely will by this point in the process, we might still theorize before the evidence, in letting our experience and our notion of what is and is not possible color how we see and apply that evidence. It’s Holmes disregarding the signs in “Silver Blaze” that would point him in the right direction because he doesn’t consider it possible that the horse could remain undetected. It’s Watson disregarding the roof as an option for entrance because he doesn’t consider it possible that someone could enter a room in that fashion. We might have all the evidence, but that doesn’t mean when we reason, we’ll take into account that all of the evidence is objective, intact, and in front of us.
But Holmes, as we know, does manage to catch and correct his error—or have it caught for him, with the failure of the horse to materialize. And as soon as he allows that improbable possibility to become possible, his entire evaluation of the case and the evidence changes and falls into place. And off he and Watson go to find the horse and save the day. Likewise, Watson is able to correct his incomprehension when prompted to do so. Once Holmes reminds him that however improbable something may be, it must still be considered, he right away comes up with the alternative that fits the evidence—an alternative that just a moment ago he had dismissed entirely.
The improbable is not yet impossible. As we deduce, we are too prone to that satisficing tendency, stopping when something is good enough. Until we have exhausted the possibilities and are sure that we have done so, we aren’t home clear. We must learn to stretch our experience, to go beyond our initial instinct. We must learn to look for evidence that both confirms and disconfirms and, most important, we must try to look beyond the perspective that is the all too natural one to take: our own.
We must, in short, go back to that CRT and its steps; reflect on what our minds want to do; inhibit what doesn’t make sense (here, asking whether something is truly impossible or merely unlikely); and edit our approach accordingly. We won’t always have a Holmes prompting us to do so, but that doesn’t mean we can’t prompt ourselves, through that very mindfulness that we’ve been cultivating. While we may still be tempted to act first and think later, to dismiss options before we’ve even considered them, we can at least recognize the general concept: think first, act later, and try our utmost to approach every decision with a fresh mind.
The necessary elements are all there (at least if you’ve done your observational and imaginative work). The trick is in what you do with them. Are you using all available evidence, and not just what you happen to remember or think of or encounter? Are you giving it all the same weight, so that you are truly able to sift the crucial from the incidental instead of being swayed by some other, altogether irrelevant factors? Are you laying each piece out in a logical sequence, where each step implies the next and each factor is taken to its conclusion, so that you don’t fall victim to the mistake of thinking you’ve thought it through when you’ve done no such thing? Are you considering all logical paths—even those that may seem to you to be impossible? And finally: are you focused and motivated? Do you remember what the problem was that got you there in the first place—or have you been tempted off course, or off to some other problem, without really knowing how or why?
I first read Sherlock Holmes in Russian because that was the language of my childhood and of all of my childhood books. Think back to the clues I’ve left for you. I’ve told you that my family is Russian, and that both my sister and I were born in the Soviet Union. I’ve told you that the stories were read to me by my dad. I’ve told you that the book in question was old—so old that I wondered if his dad had, in turn, read it to him. In what other language could it have possibly been, once you see everything laid out together? But did you stop to consider that as you were seeing each piece of information separately? Or did it not even cross your mind because of its . . . improbability? Because Holmes is just so, well, English?
It doesn’t matter that Conan Doyle wrote in English and that Holmes himself is so deeply ingrained in the consciousness of the English language. It doesn’t matter that I now read and write in English just as well as I ever did in Russian. It doesn’t matter that you may have never encountered a Russian Sherlock Holmes or even considered the likelihood of his existence. All that matters is what the premises are and where they take you if you let them unwind to their logical conclusion, whether or not that is the place that your mind had been gearing to go.
SHERLOCK HOLMES FURTHER READING
“ ‘Elementary,’ said he.” “I smoked several pipes over them, trying to separate those which were crucial from others which were merely incidental.” from The Memoirs of Sherlock Holmes, “The Crooked Man,” p. 138.
“Every instinct that I possess cries out against it.” from The Return of Sherlock Holmes, “The Adventure of the Abbey Grange,” p. 1158.
“It is one of those cases where the art of the reasoner should be used rather for the sifting of details . . .” “I confess that any theories which I had formed from the newspaper reports were entirely erroneous.” from The Memoirs of Sherlock Holmes, “Silver Blaze,” p. 1.
“How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?” from The Sign of Four, chapter 6: Sherlock Holmes Gives a Demonstration, p. 41.
CHAPTER SIX
Maintaining the Brain Attic: Education Never Stops
A lodger’s behavior has been markedly unusual. His landlady, Mrs. Warren, hasn’t seen him a single time over a period often days. He remains always in his room—save for the first evening of his stay, when he went out and returned late at night—pacing back and forth, day in, day out. What’s more, when he needs something, he prints a single word on a scrap of paper and leaves it outside: SOAP. MATCH. DAILY GAZZETTE. Mrs. Warren is alarmed. She feels that something must be wrong. And so she sets off to consult Sherlock Holmes.
At first, Holmes has little interest in the case. A mysterious lodger hardly seems worth investigating. But little by little, the details begin to grow intriguing. First, there is the business of the printed words. Why not write them normally instead? Why choose such a cumbersome, unnatural all-caps means of communication? Then there is the cigarette, which Mrs. Warren has helpfully brought along: while the landlady has assured Holmes that the mystery man has a beard and mustache, Holmes asserts that only a clean-shaven man could have smoked the cigarette in question. Still, it is not much to go on, so the detective tells Mrs. Warren to report back “if anything fresh occurs.”
And something does occur. The following morning, Mrs. Warren returns to Baker Street with the following exclamation: “It’s a police matter, Mr. Holmes! I’ll have no more of it!” Mr. Warren, the landlady’s husband, has been attacked by two men, who put a coat over his head and threw him into a cab, only to release him, roughly an hour later. Mrs. Warren blames the lodger and resolves to have him out that very day.
Not so fast, says Holmes. “Do nothing rash. I begin to think that this affair may be very much more important than appeared at first sight. It is clear now that some danger is threatening your lodger. It is equally clear that his enemies, lying in wait for
him near your door, mistook your husband for him in the foggy morning light. On discovering their mistake they released him.”
That afternoon, Holmes and Watson travel to Great Orme Street, to glimpse the identity of the guest whose presence has caused such a stir. Soon enough, they see her—for it is, in fact, a she. Holmes’s conjecture had been correct: a substitution of lodger has been made. “A couple seek refuge in London from a very terrible and instant danger. The measure of that danger is the rigour of their precautions,” Holmes explains to Watson.
“The man, who has some work which he must do, desires to leave the woman in absolute safety while he does it. It is not an easy problem, but he solved it in an original fashion, and so effectively that her presence was not even known to the landlady who supplies her with food. The printed messages, as is now evident, were to prevent her sex being discovered by her writing. The man cannot come near the woman, or he will guide their enemies to her. Since he cannot communicate with her direct, he has recourse to the agony column of a paper. So far all is clear.”
But to what end? Watson wants to know. Why the secrecy and the danger? Holmes presumes that the matter is one of life and death. The attack on Mr. Warren, the lodger’s look of horror when she suspects someone might be looking at her, everything points to a sinister cast.
Why, then, asks Watson, should Holmes continue to investigate? He has solved Mrs. Warren’s case—and the landlady herself would like nothing more than to force the lodger out of the boardinghouse. Why involve himself further, especially if the case is as risky as it sounds? It would be easy enough to leave and let events take their course. “What have you to gain from it?” he asks the detective.
Mastermind: How to Think Like Sherlock Holmes Page 21