Davis’s Law

Conversation 6

SOCRATES. Good morning Adeimantus. Your brow is furrowed, you have some weighty matter on your mind, I think.

ADEIMANTUS. Yes, good morning Socrates. Perhaps you could explain a mystery for me?

S. I will do my best, Adeimantus. What is this mystery?

A. Well, we have a little dog who does his business on the back lawn at our place. I carefully search the lawn to remove all his deposits but, you know, every time I look again, I always find another one. How can this be?

S. Ah, Adeimantus, you have come up against Davis’s Law!

A. Davis’s Law? I’ve never heard of it.

S. It was first formulated by a chap I used to work with at the Pencil Sharpness Analysis Division. Chris Davis was his name. He called it, ‘The Law of Futile Exhaustive Search’.

A. Pencil Sharpness Analysis Division? What is that?

S. That’s a story for another day¹, Adeimantus. For now, let me outline Davis’s Law. Davis was one of our best analysts, and once he was tasked with developing a technique for ensuring that every blunt pencil belonging to an organisation had been located so it could be sharpened in readiness for future use.

A. Incredible!

S. You may find it so, Adeimantus, but I can assure you that the readiness of its pencils is a matter that has troubled many a bureaucracy. But let me continue. Having a sound grasp on probability theory, Davis knew that sampling techniques could never deliver absolute certainty, so he developed procedures for exhaustive search. Basically, you had to look everywhere that a blunt pencil might be concealed. To test his procedures, Davis designed an extensive series of trials. Of course, these were ‘in-depth’ trials. A very curious finding emerged from the trials. No matter how carefully and thoroughly the trial participants searched for blunt pencils and claimed to have found them all, whenever they looked again, they always found at least one more. It was almost as if blunt pencils were materialising out of thin air.

A. I see. How did Davis account for the finding?

S. He never arrived at a conclusive explanation, but he became convinced that it was more to do with the vagaries of human perception and subjective estimation of probabilities than with the mathematical description of the search procedures. It was what, in analytical circles, we called a ‘human factors problem’.

A. Are you suggesting that Davis’s Law applies to dog poos, as well as to pencils?

S. Yes, Davis himself made that observation. He was a wizard for seeing applications of the most arcane theories to everyday life. He quickly realised that the law applied equally well to land mines and dog poos. In fact, he used to refer to dog poos as ‘land mines’, having stepped on a few in his own back yard. He had that sort of dry sense of humour.

A. So, I am wasting my time trying to find every single dog poo.

S. Yes, that’s why Davis called exhaustive search ‘futile’. His implication was that you should decide how long you are prepared to spend searching and be content with the results you achieve in that time. Of course, his actual formulation of the law was couched in highly technical language, and I’m afraid I no longer remember the precise details.

A. That’s a pity.

S. Not to worry! Davis developed some more colloquial, if less precise, formulations to suit the ‘man in the street’. Here are two I remember:

‘No matter how hard you look, the next time you look you will find another one.’

Or more emphatically, ‘If you think you’ve found them all, you haven’t.’

A. When you think of it, it is remarkable that Davis’s Law is not more widely known.

S. Yes, it pops up everywhere. Just yesterday I was picking scale insects off one of Petal’s indoor plants and, just when I thought I had got them all, sure enough, there was another whole tribe of them! ‘Leave me alone, Davis!’ I shouted.

A. I will never be able to search in peace now that I have heard of it.

S. Join the club, Adeimantus, a sadder and a wiser man!

A. What became of Davis?

S. The last I heard, he had retired and was applying his considerable skills to researching the medicinal applications of broad beans.

A. Quite a career change!

S. Yes, I heard that his broad bean crops were magnificent.

1. See the conversation on The Pencil Sharpness Analysis Division.