Chapter II

What kind of Physics would be developed by a man alone on an island? We are assuming, of course, that this favourite figure of speculative writers enjoys the properties usually attributed to him; he is remarkably intelligent, and can create by a word any scientific apparatus he requires. The point is that he has no need to take into account the judgments of other people. Let us choose an experiment designed to make clear the consequences of his isolated state. Suppose our islander, after looking at a red patch, glances at a white ceiling. He sees a green patch. Now suppose that he heats a copper wire in the flame of a Bunsen burner. The flame turns green. Will our islander proceed to construct a physics which shall embrace both these observations? Before we can answer this question we must consider why our own physics distinguishes so sharply between them. In the first place, it may be said that all observers, except the man who contemplated a patch of red, agree that the colour of the ceiling is unchanged, whereas, in the case of the copper wire, all observers agree that the flame has turned green. In the first case, therefore, we say that there has occurred a change in the observer, and in the second case a change in the flame. We invoke the criterion of universal assent. But it can readily be shown that we have not, in fact, invoked this criterion, for in saying that the flame has turned green, we have left out the testimony of colour-blind persons. Not everybody would agree that the flame has turned green, and on what principle are we to decide between the conflicting opinions of different observers? Mr. Campbell’s examination of this question appears to take us to the root of the matter. Universal assent is involved, but also something more, and it is the something more which will probably enable our islander to form a physics like our own. Let us first consider the way in which universal assent is involved in science.

We must obviously leave out judgments of colour; similarly, science does not now measure electrical quantities in the manner of Cavendish, by comparing the intensities of electric shocks experienced by the observer. Science makes a choice of the judgments it shall consider; it does not even embrace all judgments for which universal assent may be obtained. The judgments on which science is based, and for which universal agreement may be obtained, are divided by Mr. Campbell into three groups: (1) Judgments of simultaneity, consecutiveness and “betweenness” in time;[1] (2) Judgments of coincidence and betweenness in space; (3) Judgments of number, such as, The number of the group A is equal to, greater than or less than, the number of the group B. Now it is judgments of this kind that are involved in physical observations: the deflection of a spot of light on a scale, the reading of a stop-watch, and so on. These judgments are fundamental to science and are such that universal assent may be obtained for them. Let us now consider the case of the copper wire in the Bunsen flame. We have said that not all people will agree that the flame has turned green. But the light from the Bunsen has other properties than its colour; it has a measurable refrangibility and a measurable wave-length. The important point for physics is that all observers, both “normal” and colour-blind, would agree on these measurements, since they are connected with the fundamental judgments mentioned above. The fact that different observers associate these same measurements with different colours is a fact of no importance for physics; “colour” is not a notion essential to physics at all; when phrases containing such words as “red” or “yellow” occur in physics they may always be replaced by words depending for their meaning solely on fundamental time, space and number judgments. It is for this reason, then, that science builds on perfectly sure foundations; its foundations can only be denied by an imposter, that is, by one whose actions show that he actually believes what he says he denies. Now, how does this apply to our islander? We may assume that he can measure refrangibility and wave-length. He finds that, in these particulars, the light from the ceiling is unaltered, while the light from the Bunsen flame is altered. But these observations have no greater support than his colour judgments. On both occasions the only testimony is his own. But he would notice a great difference directly he began to establish the laws connecting these phenomena. The laws derived from the second set of observations would be much more satisfactory than those derived from the first set. He would undoubtedly prefer them and would unhesitatingly adopt them. When it is put in this way, there certainly seems something arbitrary about the process by which science selects its fundamental judgments. They are selected because they fall neatly and satisfactorily into laws. Mr. Campbell further suggests that the laws used in science are selected from amongst other possible laws because the selected laws fit into theories, “the form of which is dictated chiefly by preconceived ideas of what a theory should be.” It may be stated at once that Mr. Campbell admits the presence of an arbitrary element in science, but it is precisely his case that this arbitrary element gives to science its value.

We cannot here summarise his exposition, because it would be unintelligible except to readers with a scientific training, since Mr. Campbell has adopted the very sound method of analysing the actual laws and theories current in physics. We may indicate, however, the general lines of his investigation. He attempts to analyse the kind of relation involved in a scientific “law.” It has been generally assumed by philosophers that this relation is the “causal” relation, but, in fact, it is very doubtful whether this relation is ever used in the statement of laws. It is a very special kind of relation, and its supposed importance to science seems to rest on a confusion between the psychological process in an observer performing an experiment and the relation stated to exist between his observations. Thus, in Ohm’s Law, does the potential difference enter as cause or effect of the current? The question is sufficient to show that the causal relation is not concerned. Mr. Campbell admits that he has not succeeded in making a final analysis of the propositions called laws, but we think that he has certainly established several points of great value. It is more to our present purpose, however, that this analysis shows more clearly how an arbitrary element enters into scientific laws. A law does not simply relate concepts in a manner consistent with observation; it would be perfectly possible, for instance, to replace Ohm’s Law, expressing simple proportionality between current and potential difference, by a much more complicated expression which should agree equally well with observation. There are always several laws which will satisfy the observations; the one that is chosen is chosen for its simplicity, i.e., because of the mental satisfaction it affords. The fact that it does fit the observations gives it what Mr. Campbell calls its “truth,” and the fact that it affords intellectual satisfaction gives it what he calls its “meaning.”

When we pass from laws to theories we find that the element of “meaning” becomes much more prominent. Now the truth of a law is something that rests on universal assent; this is not the case, however, for the meaning of a law. It may be that the contemplation of Ohm’s Law gives you no satisfaction whatever; if it satisfies me, however, then to me it has meaning. It is only necessary, therefore, that scientific laws should have meaning for scientific men; their truth, however, is the same for all. When we come to consider theories we find that, concerning their meaning, there is much more difference of opinion. This difference, in fact, almost follows national lines, so that of the two great classes of theories, the “mechanical” and the “mathematical,” the former is largely a product of British physicists, while continental physicists prefer the second type. Mr. Campbell analyses very acutely the differences between the two classes as well as the elements they have in common. As he says, there may be a “taste” for certain kinds of theories, as there is a taste for oysters. The result of this analysis is to show very clearly in what respects science is impersonal and in what respects personal; it also helps to make clear what science is. It is true that the impersonal element in science is the most important, in this sense, that if any law or theory can be shown not to be true, then, however much meaning it may have, it must be at once rejected. It is also true that it is the meaning of laws and theories, particularly theories, which gives them their value to scientific men. We therefore reach once more the conclusion, sufficiently familiar, but seldom so satisfactorily prepared, that the value of science is in the æsthetic satisfactions it affords. In Mr. Campbell’s words, “Science is the noblest of the arts.”

FOOTNOTES:

[Footnote 1: Assuming, in accordance with the principle of Relativity, that all observers have the same motion.]

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