Part 3

SCIENCE AND CULTURE

The influence of scientific discoveries on that vaguely defined complex of beliefs and intellectual interests called culture seems, at first sight, to have something paradoxical about it. There can be no question that this influence is very widespread, and there can be as little question that ignorance of scientific discoveries is equally widespread. If our admittedly cultured classes were submitted to such a questionnaire as the workers in Sheffield were recently called upon to answer, we should doubtless find that such questions as Who was Dante? Who was Plato? would act like holes in a dam; but it is to be feared that the questions under the heading Science would evoke the merest trickle of information. And yet many of the questions in other parts of the questionnaire would be answered very differently were it not for those scientific discoveries of which the examinee can give no satisfactory description. The apparent paradox is resolved by remembering that it is only the broadest generalisations of science, and only certain aspects of those, which exert a marked influence on the rest of a man’s beliefs. The varied and highly complicated studies which make up modern astronomy, for instance, can be known, in any real sense, to but a few specialists; the one significant thing, for purposes of general culture, that emerges from these studies, is that the earth is materially insignificant in the universe. We need not mind if so much knowledge and no more percolates through the barriers of a literary education; the damage is done; the rest of the man’s beliefs begin to be profoundly affected. In the papers on geology and biology the majority of cultured people would fail; they would all be amused, however, at the idea that the earth was formed in 4004 B.C. and that man was a special and separate creation. Psychological studies have not yet reached, perhaps, a great and easily understood generalisation, but there is a growing charity vis-à-vis the “criminal classes” and other moral outcasts. Our Victorian parents’ hearty condemnation of everybody they disliked is now just a little more difficult. Such generalisations as we have been mentioning are important to general culture because of what we may call their perspective effect. Their bearing on the rest of a man’s mental furniture is not direct; they put the furniture in a different setting. A change of residence, if the difference between the two houses be sufficiently marked, may well lead to a change of habits, and the furniture which looked quite well in four rooms may seem a little inadequate in forty. Those writers who declare that there is no “real” conflict between science and religion, for instance, may be perfectly good logicians; the point is whether a particular religion looks adequate in the modern universe of science. It is not a question of destroying the furniture; it is whether the contents of a bijou villa adequately furnish Salisbury Plain. The influence of science on philosophy is similarly indirect. Perhaps there is no philosophy which does not still find defenders; our objection to many of these philosophies is not that they are illogical, but that they look so funny.

When we come to study the influence of science on the arts we see that there is yet another way in which science modifies culture. Many of the pleasurable emotions associated with the arts are not unknown to the student of science. The study of such sciences as astronomy, physics or biology awakens emotions not readily distinguishable from those evoked by even the greatest works of art. It is as if the universe with which science deals was itself a work of art; it is, to an increasing number of people, the greatest of all works of art. Such students often acquire a new standard of æsthetic excellence. Darwin’s indifference to poetry in his later years was probably the result, not of the atrophy of a faculty, but of its fuller exercise elsewhere. The young William Thomson, reading at night in the library, and drawing great breaths of rapture over Lagrange’s Mécanique Analytique, was experiencing emotions probably not very different from those of Swinburne when reading Shakespeare. Before such satisfactions become accessible to the ordinary cultured classes more is required than that vague acquaintance with outstanding generalities to which we have referred. In such a science as astronomy the mere results are often sufficiently attractive to rouse pleasurable emotions in the reader, although the actual march of the investigation by which the results were obtained is often of equal interest. At the present day both results and the broad lines of the investigations are in many cases accessible to the ordinary cultured person, with the result that his intellectual interests are added to, or at least find a new field for deployment. A greater number of æsthetic objects people his world, and it may even happen that the new arrivals affect the estimate in which he held the old. He may discover an unsuspected futility in some of his earlier occupations; he may, in fact, change his ideals of culture.

But it is, in truth, impossible to trace precisely the effect on an individual of a new belief or of a new interest. Psychologists have made us aware of the fact that the mind is not only immensely complex, but that the connections between its elements are often of the most unsuspected character. Destruction of an old belief or the grafting of a new interest may issue in results as unlike their cause as the butterfly is unlike the chrysalis. The effect of the impact of science on the old culture cannot be foreseen; it has, however, already produced such changes that the culture of the comparatively near future will probably differ from ours by more than ours differs from that of Babylon.

JAMES CLERK MAXWELL

The place that will be held by James Clerk Maxwell in the history of physics is not easy to determine. That it will be a very high place is obvious, that he will emerge as the greatest of the physicists of the nineteenth century is probable, but the student of Maxwell must feel that this kind of ranking is somehow irrelevant, or likely to become irrelevant, to his peculiar effect. The unique impression produced by Maxwell’s achievement is not adequately described by being referred to his “originality.” There are different ways of being original; it is not a sufficiently penetrating term. A number of Maxwell’s scientific contemporaries were original men, but one is conscious that they had more in common with one another than Maxwell had with them. An exception from this statement is found in W. K. Clifford, who, as has often been remarked, had a genius curiously akin to Maxwell’s. Both men were exceptionally independent thinkers, both men resisted the attraction of the high road; both men, if the term may be permitted, had a personal and unique angle of approach to the problems of their time. But this, though true, is not a sufficient description. It is important that in neither case do we feel their individual quality to be an eccentricity; their work has a power, and, still more, a comprehensive serenity, which is never the product of mere oddity--the oddity, for instance, of a Samuel Butler. If we try to get closer to this elusive and important characteristic we do not meet with much success; but we may suggest that the ideas of these men have the effect of springing from an unusually rich, subtle and comprehensive context. The fundamental ideas of the science of their time were subtly modified by reception into these minds; they were connected in a personal and unusual web of implications.

It is doubtless worth noting in this connection that Maxwell, unlike most of the scientific men of his time, was genuinely interested in metaphysical speculation. This was not merely another interest of his; it was, at most, another field of attention; he brought the same attitude of mind to all the objects with which he was concerned. We cannot make an exception even in the case of his religious views; to this man the problems of metaphysics, of physics, of morality, are almost arbitrary divisions of the one object of his thought. He was expressing a real difference from himself when he said that some men seem to have water-tight compartments in their minds. When we study the kind of homogeneity characteristic of Maxwell’s mental life it is easy to understand those who call him a mystic. Even as a purely scientific man, his rational faculty, as evidenced by his mathematical reasoning, was a distinctly more fallible thing than his intuition. This is not to say that he was not a fine mathematician, but it is his intuitive grasp of a physical problem which gives him his high position, and not his purely mathematical verifications. His mathematics, in fact, was not always impeccable, as Sir Joseph Larmor points out in the new edition of Matter and Motion. But it is characteristic of Maxwell, that, even when his proofs were faulty, his results were usually sound. His own way of confirming a difficult intuition was not to provide a formal mathematical verification, but to make appeal to easier intuitions--in fact, to construct mechanical models. He always liked to see the way things worked. It is important to remember that this desire for a particular kind of verification was not due to any lack of power to form abstractions; it was due to something quite different, to a lack of ease when faced by a purely logical chain of deduction. On Maxwell’s famous Treatise on Electricity and Magnetism, Poincaré comments that its difficulty resides precisely in its great abstraction. It is this presentation of his theory to which one has to turn; nevertheless Maxwell, as if for his private satisfaction, developed some extremely complicated models which seemed to him to make his theory clearer. It was doubtless this combination, a great power of abstraction on the one hand, and a desire for very definite, even unnecessarily definite, confirmation on the other, which enabled him to be at once extremely original and remarkably sound.

In his boyhood he was constantly making all kinds of experiments with common substances, drawing complicated diagrams, constructing solid geometrical figures, even knitting elaborate pieces of wool-work; practically all these pursuits were dictated by the same desire, the desire to see an abstract principle embodied in a concrete instance. No man was less at the mercy of words. But it was, nevertheless, the abstract principle with which Maxwell was concerned; he merely wished to be quite sure that he understood it. His occasional trick of supplying an unexpectedly simple proof of a difficult theorem is due to this habit of realisation. Platitudes acquired a wealth of implication in Maxwell’s hands. During his student life at Cambridge, when he seems to have been chiefly occupied in making a survey of things in general, we find the same desire to reduce everything to a few principles; but the principles must first stand a rigorous examination. Merely vague unifications provoked his irony, and where no principle could be made to work, then, in spite of his love for coherent and inclusive systems, he would admit ignorance. And, in spite of his need for principles, and the tenacity with which he clung to those that met his need, he claimed no “absolute” quality for his beliefs. In his own words, “Nothing is to be holy ground consecrated to Stationary Faith, whether positive or negative.” And, later, “Again, I assert the Right of Trespass on any plot of Holy Ground which any man has set apart....” Such questioning as Maxwell applied to himself was to be applied to all other men. He was conservative, but not on exterior authority. His scepticism was, in truth, very profound, and it was always present. It informs his criticism, which is often extremely penetrating. The letters he wrote on the death of his friend Pomeroy, shortly after Maxwell had become a Fellow of Trinity, are very instructive from this point of view. His distrust of the “rationalisations” that men give of their beliefs extends to the beliefs themselves. As he says, men “are ignorant even of their own true faith till something brings it into action.” This was a deep-rooted conviction with him, and is responsible for the flavour of irony which is never long absent from his comments on philosophic matters, indefatigable student as he was. He can direct this scepticism against himself, as in the entry in his programme of future study: “4. Metaphysics--Kant’s Kritik of Pure Reason in German, read with a determination to make it agree with Sir W. Hamilton.” On another occasion he writes to a friend pointing out that, in reading an author, he had to find out first of all, not what the author meant, but that it was not what he was convinced must be meant. A little experience of criticism persuades us that this is, indeed, a very necessary procedure.

This aspect of Maxwell, as a critic at large, as it were, would well repay study, and it is unfortunate that our material for it is contained in a scarcely ideal biography. He differed from the run of scientific men, whose absorption in one pursuit makes their mental life unrepresentative; his chief problems are not found in his scientific writings, and they are the problems of us all. There was nothing superficial in Maxwell, and he had no easily won conclusions. It is the path he followed that gives interest to his goal. We should like to know, for instance, what experiences, what reflections, enabled him to write: “Long ago I felt like a peasant in a country overrun with soldiers, and saw nothing but carnage and danger. Since then I have learned at least that some soldiers in the field die nobly, and that all are summoned there for a cause.” That Maxwell, either suddenly or gradually, developed a mystic consciousness of life, is borne out by many passages of his correspondence. We can attach no other significance to his description of his “nostrum”: “an abandonment of wilfulness without extinction of will, but rather by means of a great development of will, whereby, instead of being consciously free and really in subjection to unknown laws, it becomes consciously acting by law, and really free from the interference of unrecognised laws”; and his letters to his wife, dealing with passages from the Bible, abound in interpretations which are indubitably mystical. Yet we have no evidence that he was acquainted with the literature and terminology of mysticism; he is speaking of personal experiences, not of acquired doctrines.

The maintenance of a mystical outlook on life, together with a perfect realisation of the implications of physical science, was accomplished, in Maxwell’s case, by denying the ordinary conception of the direction of scientific progress. It is the idea which would inevitably occur to him, for it is the peculiar merit of his own work that it was not the result of straightforward progress. He made a new way of thinking necessary just as, in our own time, Quantum Theory and Relativity Theory have fundamentally disturbed our most unquestionable assumptions. The way Maxwell actually approached the problem we have mentioned was by insisting on what he called, by a mathematical analogy, the “singular points” of existences, that is, the points where the equations break down, and he postulated that the more there were of these singular points the higher the rank of the existence. At a “singular point” influences which are usually negligible may assume a dominating importance, and Maxwell saw the science of the future as being largely concerned with these lapses in continuity--as, in fact, science since his time has been. In this way he escaped determinism. In his own words:

If, therefore, those cultivators of physical science from whom the intelligent public deduce their conception of the physicist, and whose style is recognized as marking with a scientific stamp the doctrines they promulgate, are led in the pursuit of the arcana of science to the study of the singularities and instabilities, rather than the continuities and stabilities of things, the promotion of natural knowledge may tend to remove that prejudice in favour of determinism which seems to arise from assuming that the physical science of the future is a mere magnified image of that of the past.

This speculation, the problem of evil, and in what sense the individual may be said to persist in Time, are the kind of questions which concerned him during the last years of his life. It would be merely fanciful to mention these things as evidence of that “context” of which we spoke, but we think it is possible to understand more intimately the origin of the Electromagnetic Theory of Light if we remember that it originated in a mind which also constantly entertained these other, and apparently disconnected, speculations.

ASSUMPTIONS

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.

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.”

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.

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.