In the second place, we must not misinterpret the nature of the publicity in the case of physical phenomena. The publicity consists in the fact that a number of people make closely similar reactions at a given moment. Suppose, for example, that twelve men are told to watch a screen for the appearance of a bright light, and to say “now” when it appears. Suppose the experimenter hears them all just when he himself sees the light; then he has good reason to believe that they have each had a stimulus similar to his. But physics compels us to hold that they have had twelve separate stimuli, so that when we say they have all seen the same light we can only legitimately mean that their twelve stimuli had a common causal origin. In attributing our perceptions to a normal causal origin outside ourselves, we run a certain risk of error, since the origin may be unusual: there may be reflection or refraction on the way to the eye, there may be an unusual condition of the eye or optic nerve or brain. All these considerations give a certain very small probability that, on a given occasion, there is not such an outside cause as we suppose. If, however, a number of people concur with us, _i.e._ simultaneously have reactions which they attribute to an outside cause that can be identified with the one we had inferred, then the probability of error is enormously diminished. This is exactly the usual case of concurrent testimony. If twelve men, each of whom lies every other time that he speaks, independently testify that some event has occurred, the odds in favour of their all speaking the truth are 4095 to 1. The same sort of argument shows that our public senses, when confirmed by others, are probably speaking the truth, except where there are sources of collective illusion such as mirage or suggestion.