IN the last chapter I discussed how science teaches us to decide that a particular set of events has occurred accidentally, rather than because certain laws of nature, which these events seem to confirm, are in fact valid. I now want to urge that any such decision is based on two different but mutually correlated appraisals. When I say that an event is governed by chance, I deny that it is governed by order. Any numerical assessment of the probability that a certain event has occurred by chance can be made only with a view to the alternative possibility of its being governed by a particular pattern of orderliness.
It may help to bring out my point better and at the same time to extend its generality if I introduce a fresh example of the kind of statistical judgment I have in mind here. At the border between England and Wales you pass a small town called Abergele. Its railway station has a beautifully kept garden in which, sprawling across the lawn, you are faced with the inscription, set out in small white pebbles: ‘Welcome to Wales by British Railways. ’ No one will fail to recognize this as an orderly pattern, deliberately contrived by a thoughtful station-master. And we could refute anyone who doubted this by computing as follows the odds against the arrangement of the pebbles having come about by mere chance. Suppose that the pebbles had originally all belonged to the garden and would, if left to chance, be found in any part of this area with equal probability; we could compare the large number of arrangements open to the pebbles, if distributed at random all over the garden, with the incomparably smaller number of arrangements in which they would spell out the inscription ‘Welcome to Wales by British Railways’. The ratio of the latter small number over the former very large number would represent the fantastically small chance of the pebbles having arranged themselves in the form of the inscription merely by accident; and this would crushingly refute any supposition of this having been the case.