Chapter II

Probability is, of course, the guide of life. If all our assumptions were expressed, we should find the phrase “it is reasonable to suppose” occurred more frequently than any other, whether we were engaged in crossing a street or in writing a philosophical essay. Yet our perception of the reasonableness of anything rests on a sentiment which is often very delicate and extremely difficult to define. The mathematicians have succeeded in giving exact expression to some of the simplest manifestations of this sentiment, but most of the cases we are called upon to solve in ordinary daily life cannot be dealt with by their analysis. It is the great strength of science that it builds wholly upon this sentiment. We are not called upon to “transcend” reason by faith; we are asked to believe nothing that sins against our sense of probability. It is admitted, of course, that there are scientific theories that do not sound reasonable on a first hearing; indeed, they sometimes outrage common sense, and every scientific engineer knows the difficulty of persuading the “practical” man that the obvious thing is not always the right thing. Nevertheless, it is claimed for science that, on the evidence, its conclusions are the most reasonable ones even when they are wrong. The sense of what is reasonable depends upon the evidence, but the word “evidence” must often be taken to include a great deal of which the mind is not fully conscious. It was at one time thought quite reasonable that the heavenly bodies should move in circles round the earth. The belief was not wholly a matter of astronomical evidence. It was considered that there was something peculiarly and inherently reasonable in circular motion for heavenly bodies. We can see that this expectation was connected with the æsthetic properties of the circle, and we now think that expectations based on such considerations are, in astronomical matters, illegitimate. Something akin to such considerations still plays a part in science, however, although in a less obvious form. Other things being equal, a simple explanation of natural phenomena is preferred to a more complicated one, although, as Fresnel remarked, there is no _a priori_ reason to suppose that Nature takes any account of analytical difficulties. The history of the Copernican theory of the solar system is instructive from this point of view. The notion that the Earth and other planets went round the sun immediately made a number of puzzling things clear. It seemed, on the whole, a very reasonable notion. It was attended, however, by one great difficulty. If, at the end of six months, the earth were really at opposite ends of a long line, it should follow that the stars, viewed from these two points, should seem to shift their relative positions in the sky, just as the trees in a wood seem to change their relative positions as we pass them in a train. Tycho Brahe, one of the greatest astronomers who ever lived, was so impressed by the fact that this expected change does not occur, that he could not accept the Copernican theory as it stood. He invented a curious hybrid theory of his own, according to which, while the other planets went round the sun, they, together with the sun, revolved round the earth. He does not seem to have made many converts to this view; it somehow offends one’s sense of probability. The Copernican hypothesis persisted, in spite of the difficulty we have mentioned, but not without causing considerable mental discomfort. When Horrebow at last thought that he had obtained evidence of the apparent annual motion of the stars he published his discovery under the title _Copernicus Triumphans_. It was found, however, that the supposed differences were caused by temperature changes affecting the observer’s clock, and the old difficulty persisted. It might be thought that the correct solution was obvious; one had only to assume that the stars are so far away that, with such instruments as were then used, their apparent motion is imperceptible. We now know that this solution is the right solution, but in the eighteenth century it did not appear a reasonable solution. It was felt that if the stars were really at such immense distances as this hypothesis required, then Nature showed a grave lack of economy in space. Such enormous stellar distances pointed, so far as these astronomers could see, to a most unreasonable waste of space. No farmer would behave in such a fashion, and although the eighteenth-century astronomers would have denied that they viewed the universe as a gigantic farm, yet this delicate and elusive notion of what is reasonable was, in this case, greatly influenced by farming considerations. It is not possible to form reasonable expectations except on the basis of experience, and sometimes the most irrelevant considerations play a part in our estimate.

As instruments improved, however, the expected motion was observed, and the distances of some stars calculated. They proved to be enormous; the great waste of space does occur. God is not a farmer. This being established, one could approach the general problem of stellar distribution free from certain prepossessions. One’s sense of the reasonable acquired a different orientation, as it were. But it still remains reasonable to suppose that the brighter stars are, on the whole, nearer to us than the fainter stars. This assumption must, however, be employed with caution. If a list be formed of the nearest stars from amongst those whose distances have actually been determined, we reach some rather unexpected results. Knowing the apparent magnitudes of these stars, and their distances, we can calculate their actual luminosity compared with the sun as a standard. The apparent magnitudes range from Sirius, which is considerably brighter than a first-magnitude star, to stars of more than the ninth magnitude, that is, to stars quite invisible to the naked eye. Some of the nearest stars may be fainter yet, for determinations of the distances of stars fainter than magnitude 9.5 are lacking. The actual luminosities of these stars range from forty-eight times that of the sun to four-thousandths that of the sun. The actual distribution of the nearer stars is not at all that which would appear reasonable if we were guided by considerations of apparent brightness. Some of the very brightest stars, such as Canopus, must be at inconceivable distances, and their actual brightness must be thousands of times, perhaps very many thousands of times, that of the sun. Here again our unsophisticated notion of what is reasonable is apt to be more of a hindrance than a help. Excellent as a guide through not too unfamiliar country, it is apt to lead us sadly astray when we advance into completely unknown territory. Nevertheless, it is the only guide we have.