ASSUMPTIONS
I
It has been remarked that man’s senses were given him, not to philosophise with, but to help him in the struggle for existence; Boltzmann, the great German physicist, was frankly distrustful of many of the natural motions of the mind. He could admit that Science, although often very abstract, had a certain validity, since it issues in the prediction of events which are accessible to sense perception. But philosophy, he insisted, was in an altogether different case, and he thought the chances considerable that its impalpable conclusions were the merest moonshine. It is a speculation that must have exercised everyone who has whole-heartedly accepted the evolutionary account of the rise of intelligence. Why should this instrument be adapted to other than its original uses? Doubts of this kind, however, are both too vague and too comprehensive to serve any useful purpose. They do not tell us in what way and to what extent our intelligence is untrustworthy; they do not enable us to make one step towards drawing up an Index of Forbidden Subjects. At the most they enable a man with a constitutional dislike of philosophic speculations to indulge his contempt for that occupation with an easy conscience. Nevertheless, a tincture of this doubt is very wholesome, and more particularly if it be the result of an acquaintance with the history of human thought rather than the product of a kind of lazy a priori scepticism. A student of the history of science, for instance, is inevitably led to reflect on the curious nature of the barriers to further advance which the mind itself has set up. It is as if the mind could only take exercise within some imaginary prisoner’s yard, and that the great advances were really the result of liberations. These liberations are only partial; the mythical boundaries are set a little further off, but it is agreed that the high walls exist.
It is interesting to review the progress of Science from this point of view, to see it as a gradual secession from unwarrantable assumptions. The exceedingly cautious, the almost groping character, of the advance of knowledge, becomes very apparent. And, although such a survey may lead us to become very conscious of this particular mental limitation, we are not one whit nearer being enfranchised. It is still the prerogative of genius to be innocent, to turn surprised eyes on one of our most arbitrary assumptions, and to say: But that is not necessary. The history of Astronomy, of course, provides some of the best examples of mental prison yards. That the planets must move in circles because the circle is the perfect figure is an assumption now sufficiently remote from our acquired sense of probability to seem exceedingly strange. That it was an assumption possessing a high degree of obviousness is apparent from the fact that even Copernicus did not question it. The attempt to enter into this assumption, to see it as obviously reasonable, would be a useful exercise for the historian, since it involves, very largely, a reconstitution of the mental life of that age. It acquired its obvious character from the fact that it fitted in; it was the natural companion of a great number of other equally obvious assumptions; it was not an isolated eccentricity of the mind. It is for that reason that Copernicus never freed himself from it, and that Kepler only succeeded after a difficult struggle. Kepler was required to question not merely an isolated doctrine, but to escape from a veritable Zeitgeist. The Inquisitorial examination of Galileo, also, was not directed merely to correcting the erroneous statement of an isolated fact; it was, in truth, a whole system of thought that stood on trial. It is this double aspect of any given abandoned assumption that accounts for our unimaginative surprise on learning that very intelligent men once mistook it for an obvious truth. We are judging the assumption, not on its own merits, as it were, but from the standpoint of an alien system of thought.
We can form a juster estimate of the degree of credulity manifested by the contemporaries of Copernicus by considering assumptions that have been but recently questioned, or rather, which have only recently been generally questioned. The assumptions regarding animal psychology form a vivid example. Such men as Darwin and Romanes found it quite natural to assume that the emotions and many of the intellectual processes of which they were conscious in themselves furnished an adequate key to animal behaviour. It is an assumption which the average educated man of to-day makes quite readily, although he may not share Aristotle’s views on the perfection of circles. We now know that there is no reason whatever to suppose, for example, that the psychology of snails has the slightest resemblance to the psychology of human beings. We may be confident that, in a very few years, the assumptions of Darwin and most other people will appear almost inexplicably gratuitous. It will take longer, we think, for the Freudian ideas about man himself to become acclimatised; man will take a long time to learn that in trusting his immediate awareness of himself he is making a number of unwarrantable assumptions. The system of thought into which his present assumptions fit is so profound and extensive that it is impossible, even now, to picture the thoroughly enfranchised man.
A general acceptance of the Einsteinian ideas of space and time is easier to predict. The current conceptions of space and time, although Euclidean when reduced to a logical scheme, are not, in fact, present as a logical scheme in the mind of the ordinary man. He is sufficiently vague about his fundamental assumptions to offer no strenuous resistance to their subtle modification. We think that part of his general bewilderment about Einstein’s space and time is due to his bewilderment on thinking about space and time at all. His assumptions on these questions, whatever those assumptions may be, are not really part of a general scheme of beliefs. Nothing that greatly concerns him is incompatible with non-Euclidean geometry, and we confidently expect that the grandchildren of the ordinary man will as blandly believe they have swallowed Einstein as the contemporary ordinary man believes he has swallowed Euclid. For an assumption which is not an integral part of a general scheme of thought is readily abandoned. It is the lopping of connections which the mind resists. It is no paradox to say that the mathematician and philosopher finds it harder to accept Einstein than does the ordinary man. That is because the mathematician’s acceptance involves both believing more and disbelieving more.
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.
III
If we contrast ancient with modern scientific theories we find that the chief distinguishing characteristic of the former is that they employ principles drawn from other branches of knowledge or speculation. It would be, perhaps, rash to say that modern science, in all its branches, is yet completely autonomous; sometimes, for instance, it seems to make assumptions which are the result of an uncritical philosophy, but even the grossest of these examples, compared with many celebrated early scientific theories, shows how great is the purification that has been effected. The chief error of the old speculators consisted in imagining that the world is a more obvious unity than we have now any reason to suppose. Hence they were always willing to argue by “analogy,” comparing terms between which we cannot now find the slightest resemblance. The method was not only illegitimate, but sometimes led to quite unnecessary complexities of explanation. The Ptolemaic system of astronomy, for instance, conceived as the theory that the heavenly bodies revolve round the earth, was a perfectly reasonable and satisfactory theory. It was capable of explaining all the observed planetary motions, except a few minute irregularities requiring precise measurements for their detection. Its proper development required, of course, complete docility in face of the facts. But in its actual development it was forced to accommodate itself to quite other considerations. It had to take into account the venerable principle that, the celestial bodies being obviously sublime, incorrupt and perfect, their orbits must be perfect and described with uniform velocities. The only possible perfect orbit was as obviously a circle. Hence the Ptolemaic theory was loaded with the task of explaining the observed heavenly motions on two grounds: first, that the earth was stationary and at the centre of the system, and second, that the planetary orbits were circular and described with unvarying velocities. Alternative hypotheses were not only stupid but impious. The task thus set to the early astronomers was one of considerable difficulty.
The observed path of a planet, say Mars, or Jupiter, or Saturn, is by no means simple. If its motion amongst the stars be watched from night to night it is seen to be moving sometimes from east to west and sometimes from west to east. Further, in changing its direction of motion it does not retrace its path amongst the stars. Its actual observed path exhibits irregular loops, and, more rarely, a twisted line. It was at once obvious that a circular orbit, traversed with uniform velocity, would not suffice to explain these appearances. Nevertheless, the principle must be preserved. The astronomers overcame this difficulty by a device that strikes one as being almost disingenuous. They imagined a small circle whose centre traversed the circumference of the big circle with a constant velocity and round whose own circumference the planet moved with a constant velocity. By assigning suitable velocities to these two motions the crude features of the planet’s actual observed motion could be represented—it would sometimes be retrograde and sometimes direct. This is ingenious, but it is questionable whether it preserves the principle. The planet’s motion is obtained by circular motions, it is true, but it is not itself a circular motion with reference to the earth as centre. The astronomers have entered on a slippery path. We view them with the same suspicion with which we watch a Broad Churchman expounding the Thirty-Nine Articles. But they had to go further. The theoretical and the observed motions did not fit well enough. On the little circle it was necessary to imagine a still smaller circle, and to place the planet on its circumference. After all, this interpretation of “circular motion” once admitted, there was no reason why it should not be followed up. But progress in this direction soon came to a halt. It became evident that this method would not, by itself, reconcile observation and theory. The principle had to be strained again, and this time in an almost indefensible manner. It was declared that the big circle was eccentric with respect to the earth and that the little circles were eccentric with respect to their supposed former centres. This assertion must have been a great strain on the faith of the orthodox believer. He may well have wondered whether, by this time, the pure doctrine of his fathers had not been subtly undermined. Circular motion was still preserved, in a way, it is true, but with so many circles, and their centres all over the place—this must have appeared something very different from what he supposed the principle to mean.
The same difficulty was felt by simple minds in modern times, when the correct explanations of statements in Genesis were worked out by the theologians. And just as the simple story of the Creation in Genesis became transformed into an extremely obscure and ambiguous anticipation of the discoveries of Geology, so the interpretation of circular motion advanced from complexity to complexity. Immutable principles must exist, of course—it is part of the glory of man that he should have been able to discover so many of them—but they sometimes seem more trouble than they are worth. The old astronomers found that yet again a more liberal interpretation must be given to the principle of circular motion. This time it was found that the circles do not all lie in one plane. Each circle has its own plane, which may be inclined at any angle to the others. By this time the theorists, whom we might call the “commentators,” had forged a very powerful method. Circles could be multiplied; their centres could be placed anywhere; their planes could be inclined at any angle. The rich content of the principle of circular motion was now fully revealed. With all these variables to play with a very close correspondence between theory and observation was effected.
The rise of the “higher criticism” of this system leads to the history of modern astronomy. It is to be noted, however, that the first higher critic, like the first higher critics in other departments, was not wholly emancipated from his early teaching. Copernicus effected the immense revolution of placing the sun in the centre of the system, but he did not abandon circular motion. So he had to retain parts of the epicyclic apparatus. The revolution was first completely effected by Kepler, but even he conducted his early researches as a semi-believer, a kind of very Broad Churchman. He made nineteen successive attempts to explain the motions of Mars by the arrangements of eccentric and epicyclic motions, and only then did he frankly throw the great principle of circular motion overboard, and state that the actual paths of the planets were ellipses. And so, in a few years, a great immutable principle, a whole system of beliefs, the industry and thought of generations went for nothing, and now exist merely as an occasional cold reference in a treatise on Astronomy to the Ptolemaic system as a “monument of misplaced ingenuity.”
IV
We may divide scientific theories into two classes, which have recently been distinguished by Einstein as theories of construction and theories of principle. His own theory of relativity is a theory of principle, and its attraction resides in its logical perfection. Such theories, whatever charm they may have for the logician, are not, man being constituted as he is, felt to be sufficient. A principle which natural phenomena obey, and which enables equations to be deduced expressing the relations between phenomena, is, to a few austere souls, all with which science need concern itself, but the majority of men require, in addition, something they call an “explanation” of the relations deduced from the principle. They desire to see events described in terms with which they are familiar. Thus, a description of the behaviour of the material universe in terms of the mutual impacts of little billiard balls would afford genuine satisfaction to the mind, and important advances have been made in science by the attempt to describe phenomena in these terms. The assumptions which underlie some such attempts may seem, to the logician, preposterous, but there is no doubt that the mind is impelled to make such assumptions. Our familiarity with the motions of matter in bulk makes it quite natural that we should endeavour to give, as far as possible, dynamical explanations of events, although, if we stop to ask ourselves why nature should be flexible enough to admit of descriptions in such terms, we are at a loss for an answer.
The history of theories of the æther is particularly instructive from this point of view, because the irrational nature of the impulse is here most clearly apparent. The attempt to explain phenomena in terms of an æther has led to some very remarkable theories of the nature of matter itself. It has been supposed, for instance, that the ultimate particles of matter are vortical whirls in the æther, or, again, points of a very special kind of strain in the æther. Nevertheless, a theory of the æther is regarded as unsatisfactory which is not couched in terms of the observed behaviour of ordinary matter as we know it. A dynamical explanation is always sought after, and a great part of the scientific effort of the nineteenth century was devoted to describing the æther as an elastic solid. But men of science were not content with showing that the laws of dynamics could be applied to the æther; many of them endeavoured to devise models which should represent, on a large scale, the actual construction of the æther. It is difficult to know to what extent their authors supposed these models to correspond to the reality; it is probably not sufficient, however, to say that they regarded them merely as furnishing useful tools for subsequent investigations. The models were usually extremely complicated, for, from the very beginning, the æther proved somewhat recalcitrant to this attempt to represent it as an elastic solid. The most obvious objection to this representation was provided by the observed motions of the planets. It could be proved that, if there were any resistance to their motions round the sun, it must be excessively minute, and how was this to be combined with the hypothesis that they were moving with great speed through an elastic solid? The answer was found in cobbler’s wax. Sir George Stokes noticed that cobbler’s wax, although rigid enough to be capable of elastic vibration, is yet sufficiently plastic to permit other bodies to pass slowly through it. We have only to imagine that in the æther these qualities are much exaggerated, and the motion of the planets presents no difficulty. If no substance like cobbler’s wax happened to be known it is difficult to know what satisfactory answer could be returned to the objection. Here we have the first glimpse of the remarkable combination of qualities with which it was found necessary to dower the æther. The mathematical examination of the properties of the æther, undertaken by such men as Navier, Cauchy, Poisson, Green, was continually leading to queer and unsatisfactory results, unsatisfactory, that is, in the light of our experience of the properties of matter. Cauchy, in particular, deduced a number of remarkable physical properties which were irreconcilable with one another, although one of his theories, that of the æther considered as a kind of foam, attracted the attention of Lord Kelvin.
With the rise of Maxwell’s electromagnetic theory, the elastic solid æther received less attention. Maxwell himself, in his great treatise, gives no mechanical explanation of his theory; he merely shows that an infinite number of mechanical explanations are possible. With the publication of Einstein’s first principle of relativity in 1905, however, the æther began to disappear; and now, with the generalised theory of relativity, it has become a mere ghost. There are still sturdy champions of the æther, and, indeed, it seems a pity to have to abandon the mechanical explanations it promised. But possibly the attempt to find dynamical explanations of this kind is doomed to failure; perhaps, after all, nature is not flexible enough. The orientation of modern science is in another direction. It is towards a more abstract class of theories altogether—theories which tell us nothing about the mechanism of a process, but tell us the principles the process must obey. Such theories effect a vast unification of knowledge. They are magnificently comprehensive, and it is possible that they contain all that we can really know, although men will long be reluctant to abandon all hope of ever approaching reality with the intimacy that the theory of the æther seemed to promise.
V
Whether or not it be true that the proper study of mankind is man, it is certain that he finds great difficulty in studying anything else. His first impulse, when he thinks about the universe at large, is to consider it in reference to himself, and to explain it in terms of his own actions and desires. In Astronomy, for example, it long seemed quite reasonable that in the peculiarities of men’s bodies should be found the system on which the universe is constructed. The arguments of Galileo’s contemporaries amuse us now, for we have learned modesty, but the tendency to explain all things in purely human terms, as it were, is by no means yet extinct, and is still a hindrance to science. It is even hinted that man’s explanation of himself is not free from bias; psychologists inform us that a man’s account of his own actions is not always to be trusted, that the true springs of his conduct are usually those he would blush to own. But if we are to say that man’s speculations about the universe show an overwhelming sense of his own importance we must allow him also a certain generosity. Until quite recent times he was willing to dower almost anything, animate or inanimate, with his own attributes. He credited stones with life and trees with desire, while the whole animal world were his brothers. He could admire the loving sentiments of the dove and weep for the sorrows of the crab. A pathetic confidence in man as the type and exemplar of the universe informed nearly all the early writings on animal psychology, and Descartes’ theory that animals were automatic roused a sentimental indignation which has not yet subsided. Nevertheless, comparatively recent investigations tend to overthrow the natural assumption that worms and insects are little men inhabiting strange bodies. The modern biologist refuses to be conscience-stricken when referred to the industry of the bee or the conjugal perfections of the dove. It is only recently that he has become so heartless. Darwin, in a celebrated passage, describes with simple reverence the mutual affection existing between snails. The intelligence of these little creatures was also estimated highly by Romanes. Loeb, the great American biologist, did much to upset this naïve anthropomorphism. He took some worms who are “always attracted by light,” and showed that this movement did not testify to a “more light” cry in these little souls, but was a purely automatic proceeding. The worm places itself so that both sides of its body are equally illuminated. It is a mechanical action due to the influence of light on the living matter of its body. If there are two lights the worm passes between them, thus securing equal illumination of its two sides.
The crab which, being held by a claw, sheds that claw and hurries to the nearest rock for shelter, is found to do the same thing after its eyes or brain have been destroyed. Dr. Georges Bohn, who has made many experiments to determine how far the actions of the lower animals are purely mechanical, gives an interesting account of a certain parasitic worm which attaches itself to the fish called the torpedo. He finds (1) that if the amount of salt in the water be varied the reactions of the worm alter; (2) that if light be allowed to play first on one part and then on another part of the worm, its reactions alter; (3) if the animal has already taken up its position, attached to the glass, for instance, and a shadow be passed over the top of the vessel, the whole body of the worm turns itself into the vertical in such a way that if the shadow were caused by a passing torpedo, the worm could attach itself to the fish. If, however, it be already attached to a torpedo, it does not raise itself at a passing shadow. Here, then, is an association between the region of the body excited by light and the part fixed to the fish. It was found, also, that the crab which abandons its claw only does so when held by a certain part. The action appears to be purely automatic. If it were dependent in any way on the crab’s simultaneous visual perceptions, for instance, an associative phenomon would be established. But experimental tests find no such correspondence. As the result of numerous experiments of this kind biologists have become very wary of offering psychical explanations of the actions of the lower animals. Even when genuine associations are established one must be careful not to interpret them in terms of human psychology. In the very description of experiments an unwarrantable turn may be given to the phenomena by the fact that words of ordinary language inevitably call up associations which may be out of place in the discussion. To say that an amœba learns to reject certain foreign particles in a solution, for instance, is a statement that requires careful interpretation. How are we to picture an amœba learning something?
But, indeed, the danger of anthropomorphic interpretations becomes very obvious when we reflect on the purely physical phenomena which accompany man’s own emotions. If the James-Lange theory be correct, it is in terms of these physical phenomena that we must understand man’s emotions. Now consider the example given in Washburn’s book, The Animal Mind. An angry man has a quickened heartbeat, altered breathing, a change in muscular tension, and a change in the blood. Consider a wasp. It has no lungs, but breathes through its tracheæ; the circulation of its blood is fundamentally different from that in man; all its muscles are attached internally because its skeleton is everywhere external. What, then, is an “angry” wasp? It seems clear that if a man is to study anything but man he must forget himself as far as possible.