07 April 2016

Cromwell’s Rule of Statistics

The new research on Lawrence disturbs our certainties

by Chin Chin

It quite ruined my breakfast. There I was, reading the newspaper, wrapped in that happy shroud of sneering cynicism which distinguishes the North Londoner, when my eye fell on an article about research done by the University of Bristol in the Arabian Desert. Apparently they have visited the scenes of some of the actions described by Lawrence of Arabia in his autobiography “Seven Pillars of Wisdom” and, after examining spent cartridge cases etc, have come to the conclusion that things happened very much as he reported them.

Well, what spoilsports!  It has always been the conventional view of Lawrence that his account was wildly exaggerated and, indeed, it was only that which made reading about him tolerable; a classical scholar and archaeologist who wrote like a god; an Arabist who understood the subtle relationships between the tribes; a man who could ride a camel across impassable deserts; so tough that when struck down by a fever he spent his illness planning his strategy against the Turks; a fellow of All Souls. Oh yes, I nearly forgot.  Wasn’t he the man who organised the Arab revolt and took Akaba and Damascus? After all that, a little human weakness such as a tendency to dramatize is needed to leaven the mix and to stop the rest of us from feeling painfully inferior. Now that is denied and we are left face to face with our mediocrity.

It is always unsettling when myths one had discounted as fiction turn out to be true. The discovery that Richard III really did have a deformed back is a good example.  We cynics had all written the story off as Tudor propaganda. “Oh, well”, we said, “Shakespeare would have had his pressures like the rest of us. He had to fill his theatres and attract patronage so naturally he would have gone with the politically acceptable version of events”.  Wrong again,  Romantics: 1, Cynics:0. I will never forget the television coverage of the American Richard III society being told that the body had been pulled out of its parking lot.  “Well that will get rid of that silly story about the deformity”, they crowed gleefully. “Well, er, I am not quite sure how to put this….” said the voice at the other end of the phone.

I have never thought Cromwell (Oliver, that is, not the Wolf Hall one) a particularly attractive man. He had warts for one thing and he closed the theatres for another, but perhaps when he wrote to the Church of Scotland: “I beseech you, in the bowels of Christ, think it possible that you may be mistaken”, he had something of a point.  Not that it will have had any effect on the Scottish Church mind you – try telling the successors to John Knox that they are mistaken about anything – but for those of us south of the border a little uncertainty is not a bad thing, which is what inspired the statistician Dennis Lindley to introduce “Cromwell’s rule”.  That says that you never assign anything a probability of zero unless you can actually prove that it is impossible.

There are plenty of practical examples of the rule’s application. Many of the most celebrated achievements have been accomplished “against the odds”. Who would have put any money on Cortes and his small band carving out an empire in South America?  The pundits would have laughed at the possibility of Foinavon[1] winning the Grand National in 1967.  Those who succeed against apparently impossible odds all depend on Cromwell’s rule. It was never impossible that they should succeed, merely very unlikely.

The trouble, however, is that once you start to apply Cromwell’s rule the world disappears into a cloud of uncertainty.  So many unlikely things must be regarded as possible after all. Perhaps Paris really did trigger the Trojan war by giving the apple to the wrong goddess.  Perhaps Elijah did make a grand exit in a fiery chariot.  Perhaps those feet did in ancient time….. Until now I had always dismissed the creationists as cranks but maybe, if Cromwell’s rule is right, my judgement was a little hasty.

It gets worse when you start putting your cynicism aside in other areas.  Maybe it is true after all that that nice man selling investments on the phone is genuinely concerned that you should not miss out because he has taken a liking to you. Or that the orange tie you are being sold is exactly the same shade as the one worn by Michelangelo when he was painting the ceiling of the Sistine Chapel. Do sophisticated women really like their men to wear smart brown acrylic suits? One had thought not, of course, but if Cromwell’s rule is right you cannot be quite sure.

The difficulty with believing that almost anything could happen becomes evident when a choice needs to be made between different courses of action. However unlikely an outcome may be, Cromwell’s rule says that it cannot be wholly discarded so how should you take it into account, particularly if it will have a drastic effect?

Statisticians will tell you to assess the probability and weight it for the seriousness of the result. That is fine in theory but I doubt if it works in practice. In his book “On War” the Prussian officer Karl von Clausewitz places emphasis on the importance of the “coup d’oeil” by which the successful leader determines what he will do. That is not a comparison of odds. It is an instinctive judgement. “Yes, the enemy could turn the flank but although it would mean disaster, actually I’m sure they won’t so I will forget that”.

You see something rather similar in successful property developers.  I once knew one who ran a big public company and when he went to look at a site he did so with an escort of surveyors and accountants. They would tell him what it was worth per square foot but he would often ignore them, take his own view and be right. That was not done through a weighing of odds but by an instinctive grip of where demand would be and then a confidently unCromwellian rejection of conflicting views.

It may be better, then, for us to forget Cromwell and retain our faith in judgement, something of which cynicism is a crucial part. Occasionally we will be wrong and the cynical view we have taken of Lawrence’s account of the Arab Revolt is an example of this. Still, there we should have known. The Shaw Sheet is named for Lawrence, who changed his name to Shaw when back in the UK.  If you go to our “About Us” page you will find the following quotation from his book:

“All men dream: but not equally. Those who dream by night in the dusty recesses of their minds wake in the day to find that it was vanity: but the dreamers of the day are dangerous men, for they may act their dream with open eyes, to make it possible.”

Whatever Cromwell’s rule may say, how could the man who wrote those glorious words be other than a beacon of truth?

 

 

[1]Foinavon was so slow that when all the runners were involved in a massive pile-up, its jockey had time to avoid the disaster by going round it.

 

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