Aspects of science

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:

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.