Chapter 2 — The Rigged Universe

Chapter 2 — The Rigged Universe

Here is a game you cannot lose. I will flip a coin; if it comes up heads, you win; and if it comes up tails, we simply agree not to speak of it and I flip again. Play this game long enough and you will develop an unshakeable, statistically flawless reputation as a caller of coins. You will also be a fraud, though possibly a sincere one — you may genuinely forget the tails ever happened.

Sherlock Holmes has been playing this game for a hundred and thirty years. It is time somebody counted the tails.

Crime, built backwards

A real detective and a fictional detective face problems that only look alike. The real detective is handed a mess — a body, some noise, a scatter of facts most of which mean nothing — and must grope forward toward a solution that may not exist and can never be fully confirmed. The fictional detective is handed something entirely different: a solution that already exists, in the author's notebook, from which the mess was manufactured in reverse.

Doyle wrote solution-first. He decided who did it and how, and then he strewed the story with exactly the clues that would let Holmes recover the answer — and, crucially, no clues that would mislead a sufficiently clever man. Every bootprint in a Holmes story is a load-bearing bootprint. Every speck of cigar ash is diagnostic. This is not how the physical world behaves. The physical world is almost entirely noise: your shoes right now carry mud and dust and fibres from a dozen places that mean nothing, tell no story, and would send an over-eager Holmes galloping toward a dozen wrong towns. Doyle's universe has had the noise deleted at the factory. In it, significance is guaranteed. A clue cannot be a coincidence, because the author does not deal in coincidences; he deals in a tidy machine wearing the mask of a messy world.

Give a real detective a world where every detail is a genuine clue placed by a benevolent god specifically so it can be read, and that detective would look like Sherlock Holmes too. Take away that god and Holmes would look like the rest of us: right sometimes, wrong often, and never quite sure which he was being today.

The eighty men in the ditch

There is a beautiful and terrible idea from the Second World War. The story — polished over the years, so take the details as a parable rather than a deposition — concerns the statistician Abraham Wald and the returning bombers. The military, wanting to add armour, mapped the bullet holes on planes that came back and proposed armouring the spots that were hit most. Wald's insight was to invert the whole picture: armour the places with no holes. The planes in front of you are the survivors. The holes they carry are the survivable holes. The fatal wounds are invisible precisely because the planes that received them are at the bottom of the Channel, and nobody surveyed them.

This is survivorship bias, and it is the exact mechanism by which Sherlock Holmes convinces you he is infallible. Every Holmes story is a plane that came back. Doyle never publishes the case where Holmes reads the tan line, announces "Afghanistan," and is told, coolly, that the gentleman runs a tanning salon in Brighton. Those cases are at the bottom of the Channel. In the real profession of detection they are the majority of cases — the confident inference that curdles, the theory that fit until one more fact arrived — and their absence from the canon is not an oversight. It is the product. You are reading a highlight reel and mistaking it for a batting average.

I want you to actually picture them, the men in the ditch, because Doyle never will. For every gleaming inference that lands, imagine the ones that don't: the returned soldier who was actually a sunburnt vicar; the "obvious" strangler who was home with his mother; the innocent man arrested with total confidence over a misread scuff. In our world these are not comic footnotes. They are wrongful convictions, ruined lives, the specific human wreckage that a science of inference exists to prevent. Part II of this book is largely the story of people who took the men in the ditch seriously — who built their entire discipline around the tails of the coin. Holmes never had to. Holmes lives in the reel.

The base rate that never comes up

Let me put a number on the swindle, because numbers are where the fantasy goes to die.

Suppose a tan line with fair wrists really is a decent clue for "recently returned from somewhere sunny." Fine. Now ask the question Holmes never asks — the question his author has arranged for him to never need to ask: of all the people in London with that particular tan, how many are soldiers back from a colonial war, and how many are simply holidaymakers, gardeners, sailors, bricklayers, and men who fell asleep in a deck-chair? If the sunburnt population of Victorian London runs to the hundreds of thousands and the invalided-Afghan-veteran population runs to the low thousands, then the tan line, however real, points at "soldier" only a sliver of the time. The base rate — how common the explanation is in the first place, before any clue — is doing most of the work, and it is doing that work against Holmes. He should be wrong most of the time. He is wrong none of the time. The difference is Doyle's thumb on the scale.

We will meet this failure in its clinical form soon enough — a mind so mesmerised by a vivid clue that it forgets to ask how common the thing being pointed at actually is. Doctors do it with test results. Juries do it with courtroom statistics. You do it every time a single striking detail about a stranger convinces you that you have understood them. It has a name — base-rate neglect — and Holmes is its patron saint, precisely because his universe has been engineered so that neglecting the base rate never once punishes him.

Exhibit A: the one time the author let him lose

I promised you fairness, and fairness requires admitting that Doyle, on exactly one well-documented occasion, opened the trapdoor and let his creation fall.

The story is "The Adventure of the Yellow Face" (1893). Holmes, presented with a wife's strange secrecy and a shuttered cottage with a livid yellow face at the window, constructs a confident and sinister theory: blackmail, he decides — the woman's first husband, presumed dead, is alive and extorting her. It is a fine piece of Holmesian reasoning. It is also completely, humiliatingly wrong. The truth, when the door is finally opened, is tender rather than sinister — the yellow "face" is a mask, and behind it is the woman's daughter from a first marriage, a child she had hidden not out of terror but out of shame at the prejudice she feared. Holmes has misread a story of love as a story of crime. He is so struck by the failure that he asks Watson, in the story's closing line, to whisper "Norbury" in his ear whenever he seems to be growing overconfident — a private word to puncture his own vanity.

It is the most honest moment in the entire canon, and it proves the case for the prosecution more decisively than any clever argument could. Because "The Yellow Face" is the control group. It is the one experiment Doyle ran with the rig switched off — and the instant he did, his infallible reasoning machine produced exactly what abduction produces in the wild: a confident, coherent, well-supported leap to the wrong explanation. Sixty-odd stories with the thumb on the scale, and one without, and it is only in the one without that we glimpse the real error rate of the method. The tragedy is that Doyle wrote "Norbury" as a charming exception. It was never the exception. It was the truth about every other case, briefly allowed out of the cellar.

The mask and the method

So this is the shape of the rig, and it has three struts. Doyle builds crime backwards, so that clues are guaranteed to mean something. He publishes only the survivors, so that the misses are never counted. And he suspends the base rate, so that the vivid clue always beats the boring odds. Remove any one strut and Holmes wobbles. Remove all three and he is a very fast, very observant man who would be right rather more than average and wrong rather more than he could bear to admit — which is to say, he would be a person.

None of which makes the stories less wonderful. I reread them every year. But we are no longer reading for pleasure; we are performing an autopsy, and the autopsy has now established cause of death. The great detective did not reason his way to certainty. He was granted certainty, by an author, as a gift — and then he pretended, with immense charm, that he had earned it.

There is a whole industry that runs on exactly this pretence — earning applause for certainty that was never earned. It does not wait for a novelist. It works a live audience, in real time, for money. To understand just how cheaply the Holmesian miracle can be manufactured, we need to leave the library and visit the séance.