Tossing a Coin
Trevor Leggett was head of the Japanese Department of the BBC.
This is one of his broadcasts to Japan
Zubari (undated)
Hello listeners.
Hello listeners.
Today I am going to say something about tossing a coin in order to get a decision.
The most well-known cases are the beginning of a sports match: the captains of the two sides at cricket, for instance, toss a coin to decide who will bat first. But here there are no other factors.
I want to speak of cases where we do know some evidence, but we cannot come to a decision; so we toss a coin.
Take an early story by Edgar Allan Poe, called the ‘Purloined Letter’. In this story, Poe talks about reasoning, and he gives an example of a schoolboy who excelled in predicting what an opponent would do in a simple game. The game was played with marbles, which in many schools at that time were like money for the children.
In the game, one boy faces another. The first boy shows a closed fist, and asks: “Are the marbles in my fist odd, or even, in number?” If the second boy accepts the challenge, he guesses; if he is right in his guess, he wins a marble. If he is wrong, he must give a marble to the other boy. Then he may try again.
Poe describes how one boy, aged about 8, won all the marbles in the school. He had a system, which was this: “Suppose I guess even, but the other boy opens his fist, and the number is odd. Then I must give him a marble. Now the other boy turns away, and puts some more marbles in his fist so that I cannot see how many they are. He faces me again, holding up a fist.
I look at him, and see that he is a very simple boy. I can tell what he is thinking. Because he is simple, he simply changes the previous odd to even this time. So, I guess even, and I win.
But suppose that I am facing a boy a little more clever. My first guess is the same – pure chance. I guess even, but his fist actually contains an odd number of marbles. So, I lose. Now we try again. I can see that he will think of simply changing from odd to even, but then the thought will occur to him: ‘That would be too simple.’ So, he decides to keep the same, namely odd. So, this time I guess odd, and I win.”
By reasoning on these lines, and measuring the intelligence of the opponent, he won all the marbles in the school.
But we notice that Poe has stopped his analysis here. After these two very elementary steps, how does the ‘successful guesser’ proceed? He is imagining the thought of the other boy: He will think first: ‘I will change them. No, that will be too simple, I will keep them as before.’ A more intelligent boy will think: ‘No, that too would be too obvious. I will change them after all. No… I will keep them….’ and so on, endlessly.
We can see that there will be no predictable decision. The ultimate decision will be something like change chance. It will be impossible to ‘win all the marbles in the school’.
Perhaps a boy could decide what to do by thinking: ‘If the next man or woman who passes in the road outside comes from the left, I will hold up an odd number: if from the right, even.’ That is like tossing a coin.
Well listeners, have you ever had to toss a coin on a very important occasion? In my final Law examination at London University I had to study Roman Law, which is very boring. I wrote out some of the subjects on big cards, and learnt the cards by heart. For instance, the powers of a Trustee in Roman Law changed during the centuries: I wrote out the changes, with the dates when they changed. I hoped to get a question in which I could somehow bring in this list. To my delight, I found that in the examination paper, one question was: ‘DESCRIBE THE CHANGES IN THE POWERS OF TRUSTEES DURING THE ROMAN REPUBLIC AND EMPIRE.’ This was exactly what I had learnt by heart! I had written on the card: Houses… BC 160, Slaves AD 20…. Jewellery…… AD 85 and so on. I remembered it all perfectly.
Then to my horror I realised that I did not know whether these changes were a widening of the powers, or a progressive restriction of them! I knew it would be useless just to write the list without saying exactly what the changes were. I began to sweat. I tried and tried to remember, but it had not been on the card. When I had copied out the card from the text book, it had been obvious to me – but I had not read the book since, and I had forgotten.
Finally, I took out a coin, and spun it on the desk. One of the inspectors looked at me with curiosity, but said nothing. I looked at the coin – it was Heads. And I had decided: ‘If it is Heads, the powers extended; if it is Tails, they contracted.’ I wrote: ‘The extensions of the powers of Trustees were these,’ and then put my list.
When I got out of the exam room, I ran to the University Law Library, and with trembling hands took down History of Roman Law. I nearly fainted with relief when I saw the Section heading: ‘Extensions of the Powers of Trustees.’
I have tried to find out what was the traditional Japanese method in Tokugawa times, for instance, of coming to a decision for when it is impossible to decide on the evidence. I could not find one – the modern Japanese is willing to toss a coin. I suppose in the old days the equivalent of tossing the coin was: Ask a Senpai.
© Trevor Leggett