Similarly, when a book is opened, there are a limited number of possibilities as to which page will fall into view; this, of course, is true of any book including such works as the Bible and the I Ching26. Opening a philosophical work at random, the reader may sometimes be confronted with a passage which appears to be relevant to personal circumstances at a particular time; and sometimes, the words may indicate some course of action which might be taken. In fact some people utilise this method, which is really a type of divination, to enquire and seek after God. But because of the ultimate certainty of coincidence, the approach is flawed.

The futility of this is neatly illustrated in the following story. A person who had just begun to study the Bible opened the book at random, and read the following extract from The Gospel According to St Matthew, ‘and Judas went out and hanged himself27’ .Thinking that this was rather a bad start, he closed the book and opened it once more at random. This time he read from The Gospel According to St Luke, ‘go and do thou likewise28’ .Wisely, he did not accept the readings to have been divinely inspired. In fact, the chance of any particular page coming up, in the Bible, is approximately one in 1200. But, of course, if you have a favourite passage, it is much more likely to occur at an apparently random opening; this is simply dictated by the condition of the spine of the book. On occasions, a particular concatenation of circumstances just seems too unlikely to have occurred solely by chance: take the story of Albert and Betty Cheetham for example. This couple met another Albert and Betty whilst on holiday in Tunisia; it turned out that both couples had been married at 2 p.m. on August 15th, 1942; both men had been coach builders; both women had worked for the General Post Office; both women had lost their engagement rings; the women had identical 1930’s watch bracelets, with the same link repaired; both families have two sons, born in the same years; both couples have five grandchildren; and the couples booked their Tunisian holiday on the same day, choosing the same outward and return holiday dates29.

Although we may be predisposed to the notion that coincidence is rare, in fact, coincidence is actually much more likely than we sometimes are prepared to concede; since for any given set of possible outcomes, the coincidence is an equally likely outcome. If coincidences never happened, the only satisfactory explanation would be that some outside influence was at work leveraging events. Now, whereas coincidence is indeed a likely and possibly inevitable outcome in many situations, naturally, as the mathematical odds lengthen, the less likely it becomes that a coincidence will occur; until eventually, if we continue to lengthen the mathematical odds indefinitely, the situation will occur in which the probability of coincidence will become almost, though never quite, zero.

If a single die is thrown once, any number between one and six, inclusive, may come up. The odds of any particular number occurring is therefore exactly one in six; or in the parlance of the bookie, five to one against. This means that there is a statistical probability that the number six, for example, will come up at least once in six successive throws of the die. It is however also possible for the number to not come up at all within the six throws. The mathematical theory dealing with the subject of randomness, which was developed jointly by Pierre de Fermat and Blaise Pascal, can only help us to decide what is most likely to happen but not what will in fact happen.