The Small Steps Principle

Clues allow us to reconstruct hidden structures. When a structure is complex we need many clues. For clues are the characteristics of structures. When a structure is complex, to mark it off from others like it--to mark it off, that is to say, from neighbouring structures--we will need as many of these characteristics / clues as we can. This is to say, in a complex investigation each clue can only give us a small piece of information about the structure which we want to reconstruct--small, that is to say, in relation to the whole. From footprints Sherlock Holmes can estimate a person's height. Now this is useful information but just one small item. He will need many more items, many more clues, if he is to identify the person.

In investigations our steps forward are guided by clues. When the structure we want to reconstruct is complex, to reconstruct this structure we will need many steps, each small. When playing Sherlock Holmes we therefore have to observe a Small Steps Principle: we take only small steps, never huge leaps. Failure to observe this principle will mean failure in the reconstruction.

The name the Small Steps Principle is my creation but its content is recognized in practice. In practice people know there is a limit to how much one can read into a clue. When an investigator exceeds the limit, we say he / she is taking too large a leap. In our cryptanalytic example used in earlier posts (reproduced below), to say SB might mean SH or TH or AR is permissible. But to say that SB alone tells us that the first two words are ARE AREAR is too large a leap.

SBR SBCTU DBCKERVS FCGG WTTCXR SFH FRRJD YTHE SHUWI

The Small Steps Principle applies only to complex investigations, investigations in which there is a lot to be found out. But in the statement of the Principle given above, I said nothing about complex investigations. I will explain why later on.

The Small Steps Principle is important because it is easy to breach--not only by novices but even experienced investigators. Success can go to a person's head. An accomplished investigator, having met with success after success and perhaps too impatient for the next one, might let his / her guard down and, basing themselves on just one or two clues, start pronouncing how the investigation will turn out. This happens to Sherlock Holmes in The Yellow Face.

The events Sherlock Holmes were asked to investigate in The Yellow Face happened in a village called Norbury. Before he left London Sherlock Holmes already had a 'theory' as to what happened, a theory based on the interview he had with the client, a Mr. Munro. The surprising thing about this theory is that it is full of details but no explanation as to where these details come from.

“The facts, as I read them, are something like this [Sherlock Holmes says to Watson]: This woman was married in America. Her [first] husband developed some hateful qualities, or shall we say he contracted some loathsome disease and became a leper or an imbecile? She flies from him at last, returns to England, changes her name, and starts her life, as she thinks, afresh. She has been married three years [to Mr. Munro, her second husband] and believes that her position is quite secure, having shown her husband the death certificate of some man whose name she has assumed, when suddenly her whereabouts is discovered by her first husband, or, we may suppose, by some unscrupulous woman who has attached herself to the invalid. They write to the wife and threaten to come and expose her. She asks for a hundred pounds and endeavours to buy them off. They come in spite of it, and when the husband mentions casually to the wife that there are newcomers in the cottage, she knows in some way that they are her pursuers. She waits until her husband is asleep, and then she rushes down to endeavour to persuade them to leave her in peace. Having no success, she goes again next morning, and her husband meets her, as he has told us, as she comes out. She promises him then not to go there again, but two days afterwards the hope of getting rid of those dreadful neighbours was too strong for her, and she made another attempt, taking down with her the photograph which had probably been demanded from her. In the midst of this interview the maid rushed in to say that the master had come home, on which the wife, knowing that he would come straight down to the cottage, hurried the inmates out at the back door, into the grove of fir-trees, probably, which was mentioned as standing near. In this way he found the place deserted. I shall be very much surprised, however, if it is still so when he reconnoitres it this evening. What do you think of my theory?”

--The Yellow Face

Watson was surprised that his friend could have inferred so much from the interview and moreover be so certain about it. To the question, 'What do you think of my theory?' Watson had to answer the only way he could: “It is all surmise.”

Sherlock Holmes arrived at his theory right after the interview with his client. He had not yet set foot at Norbury; he had not yet examined 'the scene of the crime'. What did Norbury tell him when he got there? How did events turn out? Was blackmail involved?

At Norbury Sherlock Holmes discovered one of his biggest mistakes ever. In propounding his theory he breached the Small Steps Principle. Instead of small steps he was taking huge leaps.

Not another word did he say of the case until late that night, when he was turning away, with his lighted candle, for his bedroom.
“Watson,” said he, “if it should ever strike you that I am getting a little over-confident in my powers, or giving less pains to a case than it deserves, kindly whisper ‘Norbury’ in my ear, and I shall be infinitely obliged to you.”

--The Yellow Face

Let me now turn back to a point I raised earlier. The Small Steps Principle applies only to complex investigations but in my statement of the Small Steps Principle earlier, I said nothing about complex investigations. I think it is unnecessary because it can be taken as understood. For in simple investigations the only steps we can take are necessarily and in an absolute sense small. We need only two points to reconstruct a straight line. In a ten-letter word in which nine are known it takes one step to fill in the missing letter. In a simple investigation it is not likely that anyone who has any idea about clues would start on a long story after detecting one or two of them.

Even with complex investigations there is an exception to the Small Steps Principle. However, this exception is also well known and therefore can be taken as understood as well. The exception occurs in the case of a clue which represents a unique characteristic. Now the structure may be complex but once we recognize the clue to be the unique characteristic of this structure, we should be able to rattle off the rest of the characteristics / details of this structure if we know of them already. Alfred Hitchcock has a trademark silhouette. Give this to a cinema buff together with the question, who is this person? and the cinema buff will be able to tell you a long, long story.