Part 4

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.

ON LEARNING SCIENCE

It is a well-known fact that a really intelligent child finds great difficulty in believing that the earth is round. Stupid children, on the other hand, believe anything they are told. The difficulty experienced by the first child is due to the fact that, in however elementary a way, it is conscious of the implications of the statement. The stupid child seems to be unaware that the statement has any implications; it seems able to accept almost any statement in some curiously bare, unrelated fashion. Hermann Bahr has an interesting and amusing story of how profoundly his faith in his father was shaken when the latter, _à propos_ of a sunset, told the young boy that in reality it was the earth that turned round and not the sun. Completely overwhelming objections to this statement rose instantly in young Hermann’s mind, and, outraged by this insult to his intelligence, he preserved a hurt and dignified silence that lasted for days.

We notice the same essential difference in schoolboys and university students, and, in fact, in men of any age. Perhaps the majority of men, and less certainly of children, have but little sense of the implications of a statement. The sense of implications does not necessarily involve the ability to discover the implications--that is a comparatively rare gift. It acts rather in a negative manner, making the student restless under a subtly illogical presentation of a case, or leaving the schoolboy frankly mutinous at the end of a sermon. It is not a gift which makes a rapid learner, although its absence will prevent a man from ever knowing a subject properly. It is unfortunate that education, as practised in this country, does not sufficiently take into account this very desirable inhibition. The text-book plays a very large part in contemporary education, and most text-books are designed for those who can swallow statements at great speed. That delicate web of doubt, of half-seen alternative explanations, which comes into the mind of the intelligent student when confronted with the highly dogmatic statements and somewhat perfunctory “proofs” of many modern text-books, counts as sheer loss in the examination race. This is especially true of scientific text-books, which are usually conceived on an entirely wrong plan, judged from the standpoint of rational education. Statements which are the final expression of very difficult and slowly acquired abstractions are presented in all their nakedness, and followed by a collection of “examples.” The glib student learns these statements as if he were learning a foreign language, and soon masters the tricks necessary to apply them. I have known such students able to solve very difficult problems and yet entirely unable to meet, in any way, a sceptical attack upon the fundamental theorem they employ. The fact is that this method of teaching science is psychologically unnatural, and the knowledge acquired on this method is largely sham knowledge. While it may not be true that the child passes through “cultural epochs” in its mental growth, it is true that it will feel many of the hesitations and difficulties experienced by the men who first formulated the concepts now presented to it for its instant acceptance. It is for this reason that the best method of teaching a science is probably the historic method. In this way not only are many doubts fairly met instead of being merely repressed, but the exact _portée_ of a statement and possible lines of extension are much more clearly seen. The effect of the modern text-book is to make the intelligent student feel that he is remarkably unintelligent; the text-book writer is so terribly cocksure.

But if the historic method must be rejected as too lengthy one may plead for its partial application. Let the text-book give the broad outlines, and let the student supplement these by reading, wherever possible, the standard memoirs written by the original discoverers. In this way he will gain something much more valuable than a more thorough acquaintance with his subject; he will learn something of the mental gesture of the true man of science, something very different from the glittering efficiency of the text-book writer. Consider, for instance, the following passage from Newton, writing on the theory of light: He discusses a corpuscular theory, and continues:

But they, that like not this, may suppose light any other corporeal emanation, or any impulse or motion of any other medium or æthereal spirit diffused through the main body of æther, or what else they can imagine proper for this purpose. To avoid dispute, and make this hypothesis general, let every man here take his fancy; only whatever light be, I suppose it consists of rays differing from one another in contingent circumstances, as bigness, form, or vigour.

The subject here becomes alive in a way it never does in the text-book. It is of the greatest importance that the student should see, not merely the results, but the avenues of approach. He will gain more confidence in his own powers and more interest in the subject.