Part 8

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