Part 2

We have treated this point at some length because Dr. Campbell, in a recent valuable book on the Elements of Physics, insists that the physics he is talking about is that of physicists. He has endeavoured to supply a criticism of the terms used in Physics, to find what is meant by a Law, by a Theory, what a physicist means when he says a proposition is “true,” or that something “exists,” or that a theory has “meaning.” Mr. Campbell is perfectly aware that all these subjects have already been treated by the professional metaphysician, but he claims, and we have no doubt that his claim is just, that he is speaking not only for himself but for the great majority of scientific men when he says that in these discussions he not only does not recognise the subject-matter, but he does not recognise any subject-matter. Such words as “reality” and “existence,” as they are employed by metaphysicians, he finds productive of nothing but great discomfort and intense mental confusion. As he unhesitatingly rejects the hypothesis that metaphysicians are imbeciles, he thinks this confusion can be due only to the fact that these words are used by metaphysicians in senses quite different from those they bear to men of science. He has not been able to explain precisely in what the difference consists, since he has not been able to discover what meanings metaphysicians attach to these words. Accordingly he has confined himself to explaining the meanings these words have in science. The result is a subtle, fairly clear, and frequently entertaining piece of analysis. He acknowledges that his two masters have been Poincaré and Bertrand Russell, and he shows complete familiarity with other writers of the kind. But part of his reason for publishing the book, he tells us, is that even the mathematical philosophers occasionally misrepresent science as the experimental physicist knows it. That they are mathematicians and not physicists is a little too evident in some of their conclusions. Thus Mach’s idea that the object of science is to economise thought is only plausible, he thinks, to a mathematician; and a fundamental proposition that Russell and Whitehead find quite necessary to thought Mr. Campbell does not find necessary at all. He thinks it quite likely, also, that scientific thinking is illogical, but not therefore invalid. The point of view, in fact, is that there are different kinds of minds with different needs and different satisfactions, and Mr. Campbell claims that physicists, for example, belong to a certain species and that the science of physics is something which exists in the minds of physicists. Therefore this book, as he insists, is not only written by a physicist, but it is written for physicists. He is confident that what he has to say will be found an explicit statement of their instinctive processes, and he thinks the highest compliment that could be paid to his book would be for physicists to say they knew it all before.

Now it is true that nobody but a physicist could have written this book and that nobody ignorant of physics could understand it. It may also be true that none but a practising physicist could understand it with the intimacy that Mr. Campbell desires. But any reader who is not, in Mr. Campbell’s sense, half-educated (the other half consists of science--preferably physics) will find the book not only valuable, but delightful. The slight touch of _brusquerie_ that the metaphysician or the equally unfortunate “half-educated” person might attribute to Mr. Campbell from the above exposition is not in the least that of the horny-handed son of toil, but is the half-humorous impatience of a subtle and vigorous thinker who is by no means naïve. There is no reason why the audience that reads Poincaré’s popular four volumes should not also read this book, and there are many reasons why it should. Many of the questions raised there are here developed more fully; most of the questions, in fact, raised by the speculations of such men as Poincaré, Russell, Mach, etc., in so far as they affect science, are here given systematic treatment. We hope to devote a future article to the exposition of some of Mr. Campbell’s more interesting results; we are concerned here to indicate the nature and scope of the book.

The present volume is in two pretty distinct parts, the first part being concerned with the propositions of science, and the second part with measurement. These are to be followed by Part III. on Space and Time, Part IV. on Force, and Part V. on Energy, although, regarding these parts, Mr. Campbell says: “I have not the remotest idea when, if ever, they will be published.” Without anticipating a future discussion of the more technical parts of Mr. Campbell’s work, we may refer here, because of the general interest taken in the subject, to the explanation he gives of the fact that while the outside world resolutely marks off Science from Art, yet this distinction is not at all clear to scientific men. It is difficult, for example, in studying the life of a great man of science, to resist the conclusion that his incentives and satisfactions are indistinguishable from those of a great artist. Yet it seems to be undoubtedly true that a work of Art is something personal, whereas Science is obviously impersonal. Mr. Campbell asks us to distinguish between truth and meaning. The truth of science is something impersonal, but its meaning is personal. The achievement of Newton and Maxwell is as personal as that of Giotto, Shakespeare and Bach. Their dreams were not less personal, nor less delightful, and it is nothing to their discredit that their dreams also came true. And the fact that the meaning of a scientific theory is something that exists, perhaps, only for men of science, has an obvious parallel in Art. The following passage from Mr. Campbell’s book is one to which every man of science would give instant assent:

Nobody who has any portion of the scientific spirit can fail to remember times when he has thrilled to a new discovery as if it were his own. He has greeted a new theory with the passionate exclamation, “It must be true!” He has felt that its eternal value is beyond all reasoning, that it is to be defended, if need be, not by the cold-blooded methods of the laboratory or the soulless processes of formal logic, but, like the honour of a friend, by simple affirmation and eloquent appeal. The mood will and should pass; the impersonal enquiry must be made before the new ideas can be admitted to our complete confidence. But in that one moment we have known the real meaning of science, we have experienced its highest value; unless such knowledge and such experience were possible, science would be without meaning and therefore without truth.

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.