Part 3

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

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