Chapter V (2)

I do not mean that very little happened, or that what did happen was always easy to explain. But most of the happenings were trifling, and not such as to preclude the idea of trickery. One’s coat-tails would be pulled, paper cutters, etc., would fly about, knocks would shake our chairs, and so on. I do not count messages, usually of no interest, which were spelt out alphabetically by raps that seemed to come from the neighbourhood of the medium’s feet. Perhaps what struck us most were lights which on one or two occasions floated about. They were real enough, but rather difficult to locate, though I do not think they were ever more than six or eight feet away from us.

Another incident was the gradual tipping over of a rather heavy table at which they had been sitting. “Mrs. Jencken, as well as ourselves [i.e. Lady Rayleigh and himself. The husband was not admitted to these séances] was apparently standing quite clear of it.” He found it very difficult to reproduce the phenomenon himself, using both hands. He endeavoured to “improve” the conditions for some experiments. After being shown some writing, “supposed to be spirit writing,” he arranged paper and pencils inside a large glass retort, which he then hermetically sealed. Nothing then appeared on the paper at these séances. “Possibly this was too much to expect. I may add that on recently inspecting the retort I find that the opportunity has remained neglected for forty-five years.”

And so he has left the matter. The experiences were certainly strange, yes, but in his judgment, not strange enough. On the other hand, he is reluctant to believe they were due to fraud, and he is quite convinced that he was not a victim of hallucinations. If Mrs. Jencken were a clever fraud “her acting was as wonderful as her conjuring.” She practically never made an intelligent remark on any occasion. “Her interests seemed to be limited to the spirits and her baby.” In investigating this subject he finds that the attitude of convinced believers makes a difficulty. They “take no pains over the details of evidence on which everything depends.” Others attribute all these phenomena to the devil and will have nothing to do with them. “I have sometimes pointed out that if during the long hours of séances we could keep the devil occupied in so comparatively harmless a manner we deserved well of our neighbours.”

The general disbelief in scientific circles that meteorites really came from outer space occurs to him. This disbelief was due, he points out, to the impossibility of producing the phenomena at pleasure in our laboratories. Nevertheless, the disbelief was unjustified. Spirit manifestations may be, he thinks, just such sporadic phenomena. The situation is made worse by the fact that there has undoubtedly been a great deal of fraud in connection with spiritualist phenomena. Eusapia Palladino, for instance, undoubtedly practised deception, “but that is not the last word.” Telepathy puzzles him. If there is such a means of communication, why should Nature have adopted the laborious method of building up our very complicated senses? An antelope in danger from a lion, for instance, depends on his senses and speed. “But would it not be simpler if he could know something telepathically of the lion’s intention, even if it were no more than vague apprehension warning him to be on the move?” He advises the society to continue their investigations, and mentions that it is quality, not quantity, that is so desirable in evidence. He concludes by saying that he fears his attitude, or want of attitude, will be disappointing to some members of the society. He suggests that after forty-five years of hesitation “it may require some personal experience of a compelling kind to break the crust.” He apologises for this. “Some of those who know me best think that I ought to be more convinced than I am. Perhaps they are right.”

There he leaves us. We do not believe more or disbelieve less, yet we are completely satisfied. His massive sincerity, his obvious competence and, above all, that impression of exquisite balance, have charmed us. So far as present evidence is concerned we feel that while he has said nothing he has also said the last word. That is the function of the sceptic.

THE SCIENTIFIC MIND

It is quite common, in reading and in conversation, to find references to the “scientific mind,” but it is difficult to ascertain precisely how this mental structure is supposed to differ from other sorts of mind. The difficulty of defining an object does not, perhaps, affect the probability of the existence of the object; although it is difficult for some people to refrain from concluding that because a man cannot define what he means he does not mean anything. We must suppose that there is some particular kind of mind called the scientific mind, in spite of the fact that the numerous references to it tell us little about it except that it is somewhat extensively disliked. So far as can be judged from a superficial comparison of different references, the “scientific mind” is characterised by an inordinate appetite for facts and an absence of generosity in drawing conclusions from facts. In ordinary times this absence of generosity is dismissed by most people as quibbling, while in time of war it becomes unpatriotic. During the war every Englishman was supposed to believe a great number of things on very slender evidence or even on no evidence. It was considered that a right patriotic feeling not only could, but should, supply the place of evidence, and lead to correct conclusions. The majority of people in every class of the community found themselves able to adopt this method of thought without discomfort, and it became evident that the scientific mind is as rare amongst scientific men as amongst any other men, while those who could not give this supreme proof of patriotism were found pretty evenly distributed amongst the different classes. As a type of mind, therefore, it is not peculiar to scientific men nor do they all possess it. It cannot be regarded as a distinguishing mark of this class. But while a just, cautious temperament need not belong to the man of science as a human being, it might be thought that, as a mental habit, it is necessary to his work. There is much truth in this, although it is not wholly true. Alternative explanations are not always explored by scientists, and if, as sometimes happens, the alternative explanations are wrong, the scientific man may have reached a correct result although he worked in a partisan spirit.

But while the characteristics of what is popularly known as the scientific mind are not peculiar to scientific men, it is true that, in their actual scientific work, these characteristics have a greater survival value than they possess in almost any other kind of work. The extent to which mental habits may be local, confined to some only of a man’s mental activities, has been made apparent by the war. The majority of men’s minds are split up into water-tight compartments in a way truly astonishing, and the various eloquent addresses on the moral value of scientific studies now make melancholy reading. We must assume of scientific men, as of any other class, that such qualities of fairness and deliberation as they exhibit in their work are imposed upon them as conditions of success, and are not, in general, the natural manifestations of an exceptionally delicate moral sensibility. If we adopt William James’ classification of human beings into tender-minded and tough-minded the dividing line runs through the scientific camp as through any other. We see this most clearly in the case of mathematicians, for idealist or empiricist assumptions seem to be equally reconcilable with the results. Such sciences as physics and chemistry seem, at first glance, to be given over to the tough-minded; the official language, as it were, is the language of the tough-minded, but directly controversy arises on a point having philosophical bearings we see the dichotomy establish itself.

Nevertheless, it remains true that while scientific men, as human beings, are of all sorts, they do exhibit, in their own work, a degree of mental honesty which is unusual. It is easy to see that this virtue, at any rate, has a strictly utilitarian basis. A scientific man is honest because he cannot succeed on any other terms in the long run. The experimental verification always looms ahead. He cannot, like the mystic who maintains his opinion in face of the world, take refuge in the deeper insight. His results are communicable and verifiable or they are not science. Philosophies may be constructed which no man can verify and no man can refute. Their authors may, with complete assurance, remain satisfied of their truth and lament the universal blindness of mankind, just as a poet may present a front of unconquerable self-esteem to the ignorant derision of the world. But the whole claim of science is that it is communicable and capable of verification. It is found, as a matter of experience, that results of this kind are not usually obtained unless a certain mental habit is first acquired. It is this mental habit which is usually called the scientific mind. Where it is the outcome of a natural predisposition it may be classed as a moral quality, and, as such, is not peculiar to, or widely distributed amongst, scientific men. But as a tool, as a kind of technique, it is of more obvious value and is more extensively employed in the sciences than in any other human activities.

THE SCIENTIFIC CONTRIBUTION

For something like seventy years science has been the dominant intellectual activity of the Western world. During that period the range of its material has greatly increased until now the scientific method is regarded as the method proper to almost any investigation. Philosophy is still a partial exception, but there is a strong tendency to regard such philosophic problems as are not susceptible to the application of the scientific method as being essentially incapable of solution, or else as incorrectly stated. But although the prestige of science is so great, and the general attitude towards it so reverential, there is still much confusion respecting its function and achievement. Its relations to other human interests and activities are not yet clearly defined. The attempts to define them by allotting to science its “sphere” have proved, in the result, to be so ill-judged that it is now considered safer to waive the question of limitations altogether. The question is not settled. Everything is left open, but it is not therefore assumed that science contains or will contain all we know or all we need to know. Science is not yet the one object of our contemplation: we have a number of interests which still lead separate lives. The separation is not complete. Science, if not openly, then indirectly, has invaded every province of the mind, and even a modern musical composition counts Copernicus as well as Beethoven amongst its ancestors. But it is admitted, of course, that we are not usually reminded of astronomy in listening to music; there is a sense in which music, and many other things, are autonomous. But it is interesting to notice that science, to a greater extent than any other pursuit, can be isolated, although its historical direction has been influenced, of course, by social and political accidents. Science has given generously, but has taken comparatively little, and its few borrowings are in process of being handed back with regret as being, after all, unsuitable.

What, then, is the precise nature and extent of the contribution of science to our total stock? Although we do not intend its practical applications by this question, we cannot wholly ignore them. It is impossible completely to separate the “material” and “spiritual” aspects of life, and the sum of the practical applications of science has even profoundly affected much of our abstract thinking. Where it has not originated questions it has at least made them acute, if by no other process than by creating or transforming social conditions. It is easy to trace the ancestry of whole schools of social philosophy to the steam engine and the dynamo, and it is probable that the influence of future applications will be even more extensive. The morality, art and philosophy of, for example, a disease-less world, where the average span of human life was two or three times its present value, would certainly differ greatly from our own. We cannot, then, ignore the practical applications of science, although they are not, in themselves, pertinent to our question. But when we turn to consider the direct spiritual value of science we are conscious, at the outset, of some hesitation.

It was a common article of the Victorian scientist’s creed that scientific study was, in itself, an “ennobling” and purifying influence. He stressed the complete detachment required, in scientific research, from all prepossessions; the man of science was completely candid, completely docile in face of the facts. Until one became as a little child it was no use entering a laboratory. We have realised since then that scientific men are human, and have their full share of the unfortunate characteristics proper to that state. But it remains true that the scientific ideal of detachment and the scientific ideal of evidence are higher than the corresponding ideals elsewhere. In spite of the evidence furnished by our newspapers we may, if we are optimists, believe that science is gradually infecting the whole community with its conception of these ideals. If this is indeed the case it must be counted a direct and very important moral gain, as an indisputably valuable contribution which may be set over against those somewhat ambiguous practical applications.

A third contribution is to be found in the large store of æsthetic objects provided by science. Many of its theories are objects of surpassing beauty. This is particularly true of the mathematical sciences--indeed, there are a number of mathematicians who have felt impelled to write of their science in a kind of prose-poetry--but it is almost equally true of such a science as Geology. We can contemplate schemes which, in their own way, are as all-embracing as that of the _Divina Commedia_, and it does not detract from their æsthetic charm to know that they are also true. The processes by which the theories are obtained are often as æsthetically important as the theories themselves. A subtle, elaborate and economical piece of reasoning often affords great æsthetic pleasure, none the less real because comparatively few people enjoy it. The fact that the history of a big scientific investigation, such as the Electromagnetic Theory or Einstein’s Theory of Relativity, is not generally regarded as a poem is due merely to an accident of language and education. But we have to admit that most people are affected by these accidents, and that the æsthetic objects provided by science count almost as few admirers as do the “beauties” of chess. If we may judge from the number of popular books and articles dealing with science, there is some hope, however, that this particular contribution is receiving more attention. The results of such increased attention will not be simple, but if it did no more than add fresh æsthetic objects, the contribution would be important.

The fourth contribution of science, both in itself and for its reaction on other interests, is perhaps the most important of all. This contribution is, put briefly, the light thrown by science on man’s place in the universe. Every branch of science conspires directly to this end. With some the emphasis is on the universe as distinct from man; others are concerned chiefly with man himself. To the general mind the result has been to make the universe bigger and man smaller, and this is, perhaps, no unfair summary. It is probably difficult, after hearing a duet sung by an astronomer and a psycho-analyst, not to feel depressed. But, such as it is, there can be no doubt that any conception of man’s destiny that is to command attention must conceive that destiny as played against the background of the scientific cosmos. Whether the vision be that of a prophet, philosopher or poet, it must accept those postulates. The cosmos revealed by science, both in its direct influence upon the mind and in its almost equally direct influence upon religion, philosophy and the arts, is the most important part of the scientific contribution to our spiritual life. So far as philosophers and artists are concerned, this influence is recognised. It is probably desirable that the influence upon philosophy should increase, but in the case of the artist we are faced with a special problem. Its discussion would be interesting, the more so in view of the fact that artists themselves have contributed very little that is helpful to its elucidation. We think it essential to its solution to remember that the artist, like the scientist, starts with facts. But the system within which the facts are related is entirely different in the two cases. The scientific scheme must, of course, be accepted by the artist _en bloc_ if his work is to be more than a pure fantasy. But this is very different from identifying his own scheme with the scientific scheme. That is to fail signally to perceive the limitations of the scientific contribution. An interesting particular case of this problem is to be found in the question of the right relations of the psychological novelist to the science of psycho-analysis. A scientific investigation is often, as we have said, a work of art, but not necessarily a work of literary art. The scientific contribution is very considerable, but offerings from the older benefactors are still gratefully received.

THEORIES AND PERSONALITIES

That a scientific theory is, in some sense, a personal achievement, becomes evident when we study a number of theories lying within the same branch of science. The ordinary belief that science is completely impersonal is certainly not true. And yet it is not easy to see how a scientific theory can express the personality of its author; it is difficult, that is to say, to understand in what way a scientific theory can resemble a work of art. It seems that the fact that a scientific theory must have “objective truth” renders it an altogether different thing from a work of art. It would be more just to say that the element of objective truth radically differentiates a scientific theory from those works of art which are independent of all experience of life--as certain musical compositions may be, for instance. But it is not clear that, in general, works of art are independent of objective truth; all those works of art which assume experience claim assent--they do, in their intention, claim universal assent--to the truth of their assumptions. The serious artist believes his personal vision to be true; he will not, probably, claim “absolute” truth for it, but neither does a scientific theory profess to be absolutely true. And, further, works of art and scientific theories exist to serve the same purpose--to aid _comprehension_. An artist’s chief title to consideration is to be found in the depth and extent of his vision, in the profundity and range, that is to say, of the comprehension he makes possible. The value of a scientific theory is judged by the same criteria. So far, therefore, it would appear that the chief difference between a work of art and a scientific theory is to be found in their subject-matter. It cannot even be said that the subject-matter is arranged to serve different ends in the two cases, for in each case the end which is aimed at is æsthetic satisfaction. Comprehension is one of the elements of what is loosely termed the æsthetic emotion, and it is the most important element. Even when we descend to particulars, and study the quality of similes in poetry, and, indeed, “ornamentation” generally, we shall find the criterion we employ is still the degree of comprehension afforded by the device. But we cannot here work out the analogy in detail. It is sufficient to show that works of art that have a reference to experience, to an external world, in short, are, in important respects, similar to scientific theories.

Since, then, a work of art, although conditioned by experience, may nevertheless be a personal achievement, we need have no _a priori_ objection to conceding personality to a scientific theory. In each case it is the method of transformation from what we may call the raw material to the finished product which is the personal thing. The artist’s raw material, whether it be the Thames in a fog, a number of incidents from Holinshed, or the lives of the inhabitants of a Russian village, is no more and no less common property than are the _données_ from which a scientific man constructs a theory; the end product, also, in each case, claims universal assent and bestows comprehension. What is personal is the law of transformation by which the one objective thing is changed into the other objective thing. The law of transformation is different for each individual mind, and this is as true of scientific men as of any other sort of men. In this sense, then, both works of art and scientific theories are personal achievements. A history of science written from this point of view would be instructive. It would be interesting to trace the personal element in each great scientific achievement, to show what kinds of personalities have dominated us, to see what meaning _eccentricity_ can have as applied to the thought of a scientific man. But although a detailed history of this kind has not yet been written, certain _national_ differences have long been recognised.

There is almost as marked a difference between English and French science as between English and French literature. The English scientific mind is, on the whole, intuitive, mobile, illogical, and very prone to imagery of a curiously practical kind. The French scientific mind, on the other hand, likes to simplify the complicated reality to as few terms as possible, and then to build up an impeccable logical edifice. Maxwell was a very fine type of the great English man of science, but we have Poincaré’s authority for saying that the great _Treatise on Electricity and Magnetism_ awakens in the French reader feelings of distrust. So far from finding an impeccable logical structure, he finds that different parts of the book are written from different points of view, and that these points of view are even irreconcilable with one another. Maxwell’s liking for immensely complicated mechanical models, designed to illustrate some abstruse equation, is also a stumbling-block to the French reader. What are such models supposed to prove? Surely Maxwell did not suppose that the æther contained trains of geared wheels with “idle wheels” in between? What mysterious satisfaction did he derive from such unnecessary and irrelevant pictures? But this curious liking for models is characteristic of the English school, and it is a characteristic that Continental physicists have never been able to understand. It is doubtless a manifestation of the English reluctance to get out of touch with experience. The English man of science trusts logic much less than he trusts experience. The Frenchman has much less respect for experience. He is willing to simplify in a way which, to the English mind, is almost outrageous--to see the Universe as a collection of little billiard balls with forces varying inversely as the square of the distance. And on such assumptions he is willing to proceed as far as logic can take him. There is, indeed, a school in France which asserts that all we can ever know of the Universe is its equations; we can never know what they “mean” in the English sense. From the æsthetic point of view there is no doubt that the French method is to be preferred. We can all share Lagrange’s satisfaction when he says, in the Avertissement to his _Mécanique Analytique_: “Je me suis proposé de réduire la théorie de cette Science, et l’art de résoudre les problèmes qui s’y rapportent, à des formules générales, dont le simple développement donne toutes les équations nécessaires pour la solution de chaque problème.” But we must remember that when the interest is chiefly in the “développement” the assumptions may remain uncriticised. The English way is to hold the assumptions tentatively, and to be always open to the suggestions of experience. The German way, which, if we are to judge by the work of Riemann and Einstein, seems to be to concentrate an immense critical apparatus on the assumptions, is equally interesting. The “philosophic” tendency which is supposed to characterise German thought in other departments, is certainly apparent in its science. The three tendencies are sufficiently marked to constitute national differences and suggest that a detailed analysis of individual achievements would yield equally interesting results.

THE IDEAL SCIENTIFIC MAN

Is the scientific man really a distinct kind of man, or is it merely that science is a distinct occupation? To answer the question we must make the elementary distinction between the scientific man and the man who practises science, and when we do that the answer is obvious. There is as certainly the “born” scientific man as there is the born artist. But in saying this we are referring to ideals. Perhaps there has never been a perfect man of science, and perhaps there has never been a perfect artist. But in order to understand the distinction between one kind of man and another it is helpful to construct ideals--extreme cases which may be used as measuring rods. What, then, are the characteristics of the ideal man of science? We may approach the solution by trying to make precise the characteristics which have led us, vaguely, to construct the hierarchy we already possess. We _feel_, for instance, that Henry Cavendish, that passionless recluse, was a much more “purely scientific” man than, say, Thomas Henry Huxley. If we examine this conviction of ours we make the interesting discovery that it is chiefly for his negative characteristics that we assign this greater purity to Cavendish. Huxley was passionately interested in the questions which concern every good citizen, in politics, in social reform, in religion; he took sides on these questions and fought for his side. Of Cavendish we can only say that it is inconceivable that he would have taken sides on these questions, and very difficult to believe that he was even remotely interested in them. Take another point. Huxley abounded in ordinary human affections. He was a devoted husband, a good father, a faithful friend, a resolute opponent. Cavendish never manifested a vestige of any of these qualities. He had no wife, no children, no friends, and never showed the faintest dislike of anybody. Huxley was a champion of what he thought the truth, and strained every nerve to enable it to prevail. Cavendish, who was one of the greatest investigators, one of the clearest and most subtle minds, in the history of science, kept his discoveries to himself. For years Huxley bore the brunt of the attacks on Darwin’s theory. Cavendish blandly watched the growth in popularity of theories he had privately demonstrated to be wrong, and never stirred a finger to rebut them. And finally, Huxley was a man who suffered his alternations of high spirits and despondency, hope and despair, while Cavendish, from the evidence we have, was imperturbably serene.

Now, the interesting point that emerges from this comparison is that Cavendish, in virtue of his scientific purity, _could not_ have exhibited those qualities which allied Huxley to the ordinary run of men. A man’s characteristics are not disconnected. Cavendish’s cold passion for knowledge required for its gratification qualities of the spirit as well as of the mind. No man was ever more single in his desire to _know_; no man ever was so little hindered by having other interests to serve; no man, therefore, had a greater measure of the purely scientific spirit. This is the important point for our question; it is comparatively irrelevant that very few men have ever had so great a mind to place at the service of their passion. That his actual scientific standing should be so much greater than Huxley’s is an accident; he would still have been more purely scientific than Huxley had his ability been less than Huxley’s. Cavendish is all of a piece. His very perfection as a recording and measuring instrument tended to deprive him of “personality.” The less personal he was, in fact, the more dispassionately open he could be. Other passions were incompatible with his perfection; they would derange this exquisite instrument. Judgments of good and evil would not have been natural to him. His reaction to anything was exhausted in the act of _understanding_ that thing.

So far as we have gone, it would seem that Nietzsche’s description of what he calls the “objective man” is exactly what we mean by the ideal man of science. “The objective man is in truth a mirror: accustomed to prostration before everything that wants to be known, with such desires only as knowing or ‘reflecting’ implies ...” he will regard such personality as he has, Nietzsche goes on to say, as accidental and arbitrary. He cannot take himself seriously and devote time to himself. His love is constrained, his hate artificial. He is only genuine so far as he can be objective; he is unable to say either “Yea” or “Nay” to life; he is concerned solely to understand, to “reflect.” He says, with Leibniz: “Je ne méprise presque rien.” This description is undoubtedly the result of genuine psychological insight. When we try to disentangle the purely scientific element in a man of science we find that, so far as he is scientific, he approximates to Nietzsche’s objective man. If this, then, is the ideal scientific man, what place does he occupy? Where does he stand in relation to the rest of mankind? According to Nietzsche he is merely an instrument; “he is an instrument, something of a slave, though certainly the sublimest sort of slave, but nothing in himself.” He is no goal, no termination, no complementary man in whom the rest of creation justifies itself. As compared with the _true_ philosopher, the philosopher in Nietzsche’s sense, the man who gives a new direction to life, the ideal man of science is merely the most costly, the most easily tarnished, the most exquisite of instruments.

We need not quarrel with this valuation, but we would point out that there is an omission in it. The scientific man is an instrument, but he is an indispensable instrument. The human race has endured all the different “new directions” given to it by the “true” philosophers of the past without any marked increase in its spiritual stature. The philosopher, however commanding, who would really lead us in any but a circular direction must have _knowledge_. This knowledge, to be valuable, must be clear and trustworthy; it must be scientific. And if the inspirations and impulses of our leaders should prove to be incompatible with deductions from scientific knowledge, then we may be sure that the Promised Land does not lie their way. The scientific man is merely an instrument. But it is this instrument alone that can show to mankind which, of all the goals it desires, are possible goals, and which, of all the leaders it trusts, are trustworthy leaders. The scientific man is an instrument, but it is by this instrument that those who would use it are first tested. Scientific knowledge is, if you like, as dispassionate and inhuman as is the universe with which it concerns itself--and it can as little be ignored.

PARALLEL STRAIGHT LINES

Geometry, it has been satisfactorily shown, had a purely empirical origin. It appears that the earliest geometrical formulæ which have been discovered belong to ancient Egypt, and that all these formulæ served a useful purpose. The oldest of them are concerned with the measurements of areas, a class of problem which the yearly sinking of the Nile rendered of great importance. The formulæ obtained by the ancient Egyptians were usually wrong, although they were approximately correct; they evidently rested on no theoretical basis, but were compendious statements of the results of somewhat rough measurements, a point of view which is borne out by the fact that no proof, nor even an attempt at a proof, is anywhere hinted at. So far as the evidence goes, it seems to be established that geometry, as consisting of logical deductions from stated premises, began with the Greeks. A number of theorems of a fair degree of complexity had been developed before they were reduced to a system; before, that is, the assumptions on which they were based were made explicit. The task of discovering the necessary and sufficient assumptions on which a system of geometry rests is one of the greatest difficulty; the necessary combination of subtlety and rigour is rare. The great systematisation of Greek geometry was effected, of course, by Euclid, and although his reduction of the system to its essential assumptions was not final, his performance was such as to awaken the admiration of great mathematicians in every succeeding century. But there is one point in which this great reduction is notably imperfect--the so-called parallel axiom. It says, essentially, that through a given point only one line can be drawn parallel to a given straight line. It was felt, even by the earliest commentators on Euclid, that this postulate did not possess quite the same degree of self-evidence as was manifested by the others. It was necessary, they felt, to give a proof of this postulate; they attempted to improve on Euclid’s work in a number of minor ways, but it was the parallel axiom which they were most concerned to revise; the proof of this postulate should be contained, they thought, in the other postulates. The attempts to supply this proof were all fruitless, and the sixth century was reached with this nine-hundred-years-old disfigurement still persisting. For some time after the sixth century the world rested from Euclid’s parallel axiom; indeed, it rested from geometry altogether, and the old empirical outlook of the Egyptians, and even their formulæ, again became current. But the Greek culture penetrated to the Arabs, and with the Greek culture came the riddle of Euclid’s axiom. Again proofs were attempted; a famous attempt is that of Nasir Eddin, who flourished in the thirteenth century. In 1663 John Wallis made the important discovery that unless the parallel axiom be assumed, similar figures of different sizes are not possible, that is to say, that if we are to assume that _shape_ is independent of _size_, then we must assume Euclid’s parallel axiom. Many of these attempts brought out points of interest, but none of them were successful. In the year 1733, however, the whole research took on a new complexion with the publication of Girolamo Saccheri’s _Euclides ab omni naevo vindicatus_. The importance of this work consists in the fact that, although it was written to vindicate Euclid’s parallel axiom once for all, it contains the first real outline of a non-Euclidean geometry.

Saccheri was a Jesuit, and it was in 1690, while he was teaching grammar in Milan, that he first studied the _Elements_ of Euclid. He was a man of very great acumen, and when he, in turn, succumbed to the spell of the parallel postulate, he brought to bear on it a more subtle and rigorous logic than had yet been applied to it. Thirty-six years before he published his treatise on Euclid he had published a book on logic which gives him a high place as a logician. In it he is particularly concerned with investigating the compatibility of different assumptions or postulates. His method was to determine whether a member of a group of postulates is independent of the others by finding a particular case in which the postulate in question is not true while all the others remain true. If such a case can be found, it is obvious that the postulate in question cannot be deduced from the others, else it would be true whenever they were true. This was the method he applied to the parallel postulate of Euclid. He showed that the parallel postulate is equivalent to saying that the three interior angles of a triangle are equal to two right angles. He proceeds, therefore, in accordance with his method, to develop the consequences of supposing them less than, or greater than, two right angles. In the latter case he succeeds in showing that we are led to impossible conclusions, since he assumed, as everybody assumed for more than a century after, that the straight line is of infinite length. But in the former case, the hypothesis that the interior angles of a triangle are together less than two right angles, Saccheri, although he struggled very hard, did not succeed in falling into contradictions. He does not seem to have had the boldness necessary completely to trust his own logic, but the fact remains that, accepting the rest of Euclid’s axioms and denying the parallel axiom, he developed a logically consistent geometry.

There is reason to suppose that Saccheri’s work had some influence on subsequent thought, although its full significance was certainly not perceived. The parallel axiom continued to be investigated, and the total effect of all these efforts was to induce a doubt concerning the absolute _necessity_ of the Euclidean geometry. Such a doubt was very daring; for two thousand years the postulates of Euclid had been accepted as absolutely true; the fact of their existence had profoundly influenced philosophy, and, indeed, theology. But the doubt persisted and grew, until finally, early in the nineteenth century, a perfectly logical and consistent non-Euclidean geometry, one explicitly denying the parallel postulate, was published to the world. As so often happens, the great step was taken by two men independently of one another, Lobatschewski, a Russian, and Bolyai, a Hungarian. It appeared, however, that both had been preceded by that great mathematical genius, Gauss, although he had been too timid to publish his conclusions. The new geometry developed the consequences of that one of Saccheri’s alternatives which supposed the interior angles of a triangle to be less than two right angles. The whole outlook on geometry now assumed a new complexion. Riemann tried the effect of denying the infinity of the straight line and of developing Saccheri’s other alternative. He found he was led to no contradictions. But with Riemann’s work we come to a yet further extension of geometry--the extension to space of four, five, or any number of dimensions. And these investigations, which seemed for some time to constitute the most gratuitous, although the most profound and subtle, exercises of the mind, have now received their complete justification by flowering into the Generalised Principle of Relativity.

THE NEW SCIENTIFIC HORIZON

About current scientific speculations there is one characteristic, subtle, perhaps, but profound and far-reaching, which distinguishes them from the scientific speculations of the Victorian age. We can best isolate this characteristic by considering it as a particular manifestation of something which is met with in nearly every phase of contemporary life--something which may fairly be called the _Zeitgeist_ of our time. This spirit is chiefly a sense of unlimited possibilities, a sense that the radically new and unprecedented may be upon us; with this feeling comes a recrudescence of the spirit of adventure; there are unknown paths leading to vague but--probably--splendid goals. In the Victorian age the main lines of everything were settled; the chief features of the universe were known. There were matter and energy, and there was, of course, the æther. The astronomical and geological scales were known in broad outline, and a first survey of the march from amœba to man had been taken. The work of future ages was to fill in the details. The universe of the Victorians was a large and rather grand affair, but it was sombre. Those emotional barometers, the poets, in so far as they were aware of the scientific outlook, either “transcended” it or were crushed by it. Jules Laforge furnishes an excellent example of the effect of the Victorian scientific outlook on an intelligent and sensitive mind. His reaction was to compose funereal dirges on the death of the earth and the extinction of mankind. The universe of the Victorians was objective, indifferent, tracing a purposeless pattern in obedience to “iron” laws. It was a universe which held no great surprises.

It is obvious that a very different spirit is abroad to-day. At the present time the general consciousness seems to hold that almost anything is possible. In part this may be accounted for, as in other ages, by credulity based on ignorance, but there is also a credulity based on knowledge, and it is this aspect of the general attitude which deserves attention. The two kinds of credulity may be observed in different believers of the same statements. Spiritualism, for instance, has its followers amongst those who are unfamiliar with investigations in the subject and amongst those whose belief has been compelled by their very knowledge of the investigations. And disbelievers form two exactly similar classes. There is also a credulity--the most common kind--based on neither ignorance nor knowledge, but on partial knowledge. Thus knowledge, but incomplete knowledge, of such phenomena as wireless telegraphy or telephony, seems to predispose many people to believe “wonders” which have no real connection with those phenomena, but which are merely as inexplicable by partial knowledge. Undoubtedly the recent developments in science are responsible for much of this kind of credulity. But the new indulgence of possibilities, as exhibited by the man of science, is dependent on quite different considerations. To the student of physics, at any rate, the work of the last two or three decades has been peculiarly disturbing. He has been called upon, not merely to revise and extend his knowledge, but to alter his assumptions. It is in this respect that the physics of our own day chiefly differs from Victorian physics.

The distinctively modern epoch began with the promulgation of the Electron Theory. That “matter” could be “electrified” was easily granted. The fact that the famous question, What is electricity? could not be answered was no difficulty in admitting the fact that, as a result of certain processes, matter could be made to exhibit certain phenomena which could conveniently be referred to the fact that it possessed an “electric charge.” And the discovery of particles very much smaller than a hydrogen atom presented no conceptual difficulties. The fact that the ultimate particles of matter were smaller than had been supposed could easily be granted; the new assumption was of the same kind as the old one. And, further, to admit that each of these particles possessed an electric charge made no unfamiliar demands on the imagination. But the next step, that these particles consisted of nothing but an electric charge--that was a very different thing. The early popularisations of the idea show something of the mental confusion it caused. “Disembodied charges of electricity” was a favourite descriptive phrase; many physicists fought hard to retain even a nucleus of “ordinary matter” on which this charge could be supposed to be lodged. That an electric charge could exist apart from matter seemed to many people as difficult to conceive as motion without anything which moved. But the conception speedily became familiar; that useful entity, the æther, soon made things easier. For the disembodied charge, the electron, could be conceived as a local distortion of some kind in the æther, and, by endowing the æther with some sort of substantiality, the hypothesis that matter was in some way built up out of this primitive substance could be tolerated. But the general effect of the theory was to give a more philosophical tinge to science. The gross, easy assumptions of everyday thinking about “matter” had to be revised; articles were written showing that matter was really immaterial, and materialism was conjectured to have received a severe set-back.

The mind had barely become accustomed to the new assumptions before it was again profoundly disturbed by the publication of Planck’s Quantum Theory. The theory, which was invented to explain certain radiation phenomena, asserted, briefly, that energy was atomic. One’s most intimate assumptions were disturbed. Men of science are not usually accustomed to philosophic exercises, and the idea that energy, which they regarded as necessarily continuous, had an atomic structure seemed at first almost meaningless. If we consider, for instance, the energy possessed by a moving body, it seems natural to suppose that this energy can be increased or diminished in a continuous manner; the idea that its energy can only increase or decrease by finite jumps was a very strange idea, and led again to a scrutiny of assumptions which had appeared fundamental in science. Here, again, objections to the new theory were sometimes the outcome purely of mental inertia, of an inability to examine and discard a way of thinking which seemed almost a necessary consequence of the structure of the mind. The last great _bouleversement_ of one’s fundamental assumptions has been, of course, Einstein’s generalised theory of relativity. Here we are asked to revise our most deep-rooted assumptions--so deep-rooted that we are, for the most part, unconscious of them--our assumptions regarding space and time.

It is this thorough overhauling of primary assumptions which distinguishes the modern progress in physics from all the progress of the Victorian age. Physics has not merely been extended, it has become a radically new thing, and there are very good reasons for supposing that it is going to change still more. A certain sense of unknown possibilities is therefore natural, even if it be the product merely of bewilderment. The total effect of the new ideas is to make the universe of physics less objective; to an unsuspected extent this indifferent universe, with its iron laws, is a product of our own minds. To some extent this fact was always recognised, particularly by the Continental physicists, but as a general persuasion it is comparatively recent. We cannot escape the structure of our own minds, it is true, but we do not yet know what that structure is; we do not know what barriers are breakable; we do not know what thoughts are thinkable by man. A universe in whose construction so plastic and mysterious an entity as the mind of man collaborates, may very well hold great surprises.

THE HOPE OF SCIENCE

It is not an unfair judgment, we think, that decides, on a survey of contemporary intellectual activities, to grant science the first place. Whether we consider the quality of the work which is being done, its importance to mankind, or the spirit in which the work is done, we think science earns that place. Our age is a scientific age to an extent which is certainly not generally realised. Contemporary scientific work is of a quality fully comparable with that of the greatest periods of its history; it is inevitable that our age should emerge, in the history of the future, as an age of science. It has, indeed, already established a perspective which leads to a revaluation of the Victorian age. There have already been many writers who have thought that age more memorable for its science than for its other achievements, that its significance to humanity lay more in the work of Darwin, Faraday, and Maxwell than in that of Tennyson and Matthew Arnold, or even in that of Mr. Gladstone, but the perspective we have now obtained puts the matter almost beyond doubt. With most of us our outlook is the result of a decrepit tradition. Our orientation towards life, so far as we are conscious of having one, is based upon the values we attribute to the various objects of our thoughts, and these values are determined partly by our instinctive desires and partly by the suggestions of our education--using the term “education” to include all converse with the minds of our fellows. Education, so defined, is the result very largely of a long and widespread tradition, a general tradition of European culture. It is a curious fact that, although the history of science goes as far back as the history of the arts, science is not an integral part of this, nevertheless, very catholic culture. There are periods, it is true, when some scientific theory is sufficiently dramatic, or appears sufficiently pertinent to man’s destiny, to secure general attention; Newton’s theory of gravitation, Darwin’s theory of evolution, and Einstein’s theory of relativity have each given rise to such a period. Einstein’s theory, we are informed, is now the favourite topic of enlightened conversation in Parisian salons, as Newton’s theory once was. Some of this interest, no doubt, is the product of disinterested curiosity, and in that respect is vastly different from the once general interest in Darwin’s theory. But we fear that many of those who are curious about Einstein’s theory would, if they understood it, find it uninteresting. We dare not interpret this curiosity as a sign that people are beginning to be as naturally interested in science as they are in literature, for instance.

Nevertheless, we believe that the old culture is moribund in the sense that its particular scale of values is undergoing revision. Science is becoming less an affair for specialists; it is acquiring a “human” value. An increasing number of people are beginning to realise that a great science, such as Physics, may offer objects for contemplation which are as delicate, as subtle, as exquisitely harmonious as the dreams of Plato--and much better founded. And in relation to man, his present state and possible future, science alone, to those who are not satisfied with less than verifiable knowledge, speaks with the accent of authority. The great constructions of science are grandiose without being chimerical; they are beautiful but not deceiving. Indeed, one sometimes has the feeling that it is only in science, nowadays, that one still meets with the spirit of adventure, the sense of boundless and glorious possibilities, with an exultant hope. Our poets and men of letters generally are extraordinarily tame and disillusioned creatures compared with our romantic and daring men of science. It is refreshing to turn from the lamentations of our literary men to such a book as the _Space, Time, Matter_ of Hermann Weyl, if only for the fervour, the immense enthusiasm with which that highly accomplished mathematician writes. Einstein is his Columbus, with the difference that his America has indicated the existence of yet vaster continents. And this enthusiasm is justified by its fruits; it has inspired Herr Weyl to make what is unquestionably the greatest advance on Einstein’s own work which has yet been made. It is not in Physics alone that we find this note. To the biologists, also, the world has become young again. Should our ignorant and unimaginative politicians, and our still more ignorant and unimaginative business men, succeed in turning the whole heroic effort and age-long struggle which has produced our present culture to a mockery, they will put an end to a curiously interesting and promising transition age, to an age which is at once _fin de siècle_ and at the morning of a glorious renaissance. But if they do not succeed, if the ordinary man shows himself even a little worthy of the immense travail of his species, then we prophesy that science will become an integral part of the culture of the future. The new physics, the new biology, the new psychology, will be too obviously pertinent to all man’s chief preoccupations for us to be able to pretend that the present narrowly conceived _humaniora_ furnish a liberal education. We even believe that if the old arts are to become youthful again, it must be by a transfusion of blood. It will not be sufficient that the philosophy and literature of the future should “accommodate” themselves to the scientific outlook; they must be inspired by it.