The Revolution in Science

I

WHAT is called the modern ‘revolution’ in science consists in the fact that the Newtonian outlook, which dominated the scientific world for nearly two hundred years, has been found insufficient. It is in process of being replaced by a different outlook, and, although the reconstruction is by no means complete, it is already apparent that the philosophical implications of the new outlook are very different from those of the old. Science has become self-conscious and comparatively humble. We are no longer taught that the scientific method of approach is the only valid method of acquiring knowledge about reality. Eminent men of science are insisting, with what seems a strange enthusiasm, on the fact that science gives us but a partial knowledge of reality, and we are no longer required to regard as illusory everything that science finds itself able to ignore.

The enthusiasm with which some men of science preach that science has limitations is not really surprising. For the universe of science, if accepted as the final reality, made of man an entirely accidental by-product of a huge mindless, purposeless, mathematical machine. And there are men of science sufficiently human to find such a conclusion disconcerting. Even the sturdy Victorians who preached this doctrine betrayed at times a despairing wish that things were not so. We need not be surprised, therefore, to find that the discovery that science no longer compels us to believe in our own essential futility is greeted with acclamation, even by some scientific men.

This change in the scientific outlook seems to have taken place suddenly. It is not yet sixty years since Tyndall, in his Belfast Address, claimed that science alone was competent to deal with all man’s major problems; and it is not yet twenty years since Bertrand Russell, contemplating the scientific answers, said that ‘only on the firm foundation of unyielding despair can the soul’s habitation henceforth be safely built.’ But, in truth, so far as these remarks sprang from the conviction that the sole reality is ‘ matter and motion,’ their foundations had already been undermined. The attempt to represent nature in terms of matter and motion was already breaking down. That attempt was at its most triumphant by the end of the eighteenth century, when Laplace was emboldened to affirm that a sufficiently great mathematician, given the distribution of the particles in the primitive nebula, could predict the whole future history of the world. The fundamental concepts isolated by Newton had proved themselves so adequate in the applications that had been made of them that they were regarded as the key to — everything.

II

The first indication that the Newtonian concepts were not all-sufficient came when men tried to fashion a mechanical theory of light. This endeavor led to the creation of the ether — the most unsatisfactory and wasteful product of human ingenuity that science has to show. For generations this monster was elaborated. Miracles of mathematical ingenuity were performed in the attempt to account for the properties of light in terms of the Newtonian concepts. The difficulties became ever more heartbreaking, until, after the publication of Maxwell’s demonstration that light is an electromagnetic phenomenon, they seemed to become insuperable.

By this time the ether had become too complicated to be credible. It was not only complicated; it was ugly, and ugliness in scientific theories is a thing no scientific man will tolerate if he can possibly help it. Copernicus, at the very beginning of the scientific movement, was a true judge of the scientific temperament when he showed himself confident that the æsthetic charm of his theory would suffice to enable it to make its way against the insufferably complicated theory of Ptolemy. Science has never lost that spirit. The construction of ethers became a decaying industry, and largely because there was so little demand for the product. For it had dawned on men of science that there was, after all, nothing sacrosanct about the entities of Newton. It might be that his list of ultimates — mass, force, and so on — was not exhaustive. Instead of reducing electricity to these terms, it might be better to add it to the list. This was done. After a certain amount of hesitation, and a few last desperate efforts to make electricity mechanical, electricity was added to the list of irreducible elements.

This may seem to have been a simple and obvious step to take, but it was, in reality, of profound significance. For the Newtonian concepts were all of a kind that one seemed to understand intimately. Thus the mass of a body was the quantity of matter in it. Inertia was that familiar property of matter which makes it offer resistance to a push. Force was a notion derived from our experience of muscular effort. Of course, all these concepts, in order to be of use to science, had to be given quantitative expression. They entered our calculations as mathematical symbols. Nevertheless, we supposed that we knew the nature of what we were talking about. But, in the case of electricity, its nature is precisely what we did not know. Attempts to represent it in familiar terms — as a condition of strain in the ether, or what not — had been given up. All that we knew about electricity was the way it affected our measuring instruments. The precise description of this behavior gave us the mathematical specification of electricity, and this, in truth, was all we knew about it.

It is only now, in retrospect, that we can see how very significant a step this was. An entity had been admitted into physics of which we knew nothing but its mathematical structure. Since then other entities have been admitted on the same terms, and it is found that they play precisely the same rôle in the formation of scientific theories as do the old entities. It has become evident that, so far as the science of physics is concerned, we do not require to know the nature of the entities we discuss, but only their mathematical structure. And, in truth, that is all we do know. It is not realized that this is all the scientific knowledge we have, even of the familiar Newtonian entities. Our persuasion that we knew them in some exceptionally intimate manner was an illusion. So far as the science of physics is concerned, the old entities and the new are on the same footing: the only aspects of them with which we are concerned are their mathematical aspects.

III

With this realization, it is no long step to Eddington’s position that a knowledge of mathematical structure is the only knowledge that the science of physics can give us. Of all the philosophical speculations which have been hung on to the new physics, this seems to me the most illuminating and

the best-founded. It seems to be true that ‘exact’ science is a knowledge of what Eddington calls ‘ pointer-readings ’ — the readings on an instrument of some kind. We assume, of course, that these readings refer to various qualities of the external world, but all we actually know about these qualities, for the purposes of exact science, is the way they affect our measuring instruments.

As Eddington says in ‘The Domain of Physical Science,’ an essay in Science, Religion and Reality, ‘Leaving out all æsthetic, ethical, or spiritual aspects of our environment, we are faced with qualities such as massiveness, substantiality, extension, duration, which are supposed to belong to the domain of physics. In a sense they do belong; but physics is not in a position to handle them directly. The essence of their nature is inscrutable; we may use mental pictures to aid calculations, but no image in the mind can be a replica of that which is not in the mind. And so in its actual procedure physics studies not these inscrutable qualities, but pointer-readings which we can observe. The readings, it is true, reflect the fluctuations of the world-qualities; but our exact knowledge is of the readings, not of the qualities. The former have as much resemblance to the latter as a telephone number has to a subscriber.’

Eddington has given a very remarkable illustration of this point of view in his extension of Einstein’s Relativity Theory, in The Mathematical Theory of Relativity. Eddington starts with undefinable ‘point-events.’ We do not know, and we do not require to know, what point-events are. All we know is that it takes four numbers to indicate a point-event uniquely — as it takes two numbers, the number of the street and the number of the house, to indicate a house in New York uniquely. Between neighboring pairs of point-events is a relation called the ‘interval.’ Again we do not know the nature of this relation, but it has a mathematical aspect, and this is all we require to know.

From this primitive material Eddington manages to derive, by mathematical analysis, the world of physics, matter and its laws. It is true that the derivation is not complete. The atomic constitution of matter, all the quantum phenomena, are left on one side. But all the field phenomena of physics, the conservation of mass and energy, the laws of gravitation and electricity, emerge as necessary consequences of the elementary structural relations assumed in the beginning.

Whether or not this derivation of field physics — we know that Einstein prefers a different derivation — is of permanent, scientific importance, it is obviously a very convincing illustration of Eddington’s contention that exact science deals wholly with structure. For his derivation is not affected whatever nature we attribute to the point-events that constitute all phenomena. It could even be maintained that they are happenings in the mind of God if, like Newton, we supposed space to be God’s ’sensorium.’ Science throws no light on such questions. It would be confined to remarking, of the Big Four at Versailles, that they numbered four, to use one of Eddington’s illustrations.

The fact that science is confined to a knowledge of structure is obviously of great ‘humanistic’ importance. For it means that the problem of the nature of reality is not prejudged. We are no longer required to believe that our response to beauty, and the mystic’s sense of communion with God, have no objective counterpart. It is perfectly possible that they are, what they have so often been taken to be, clues to the nature of reality. Thus our various experiences are put on a more equal fooling, as it were. Our religious aspirations, our perceptions of beauty, may not be the essentially illusory phenomena they were supposed to be. In this new scientific universe even mystics have a right to exist.

IV

The outlook just described may fairly be said to be a result of the newscientific self-consciousness. It is more than a mere speculation. But some of the other views that have been put forth by our scientific philosophers seem a good deal less secure. We have, for instance, Sir James Jeans’s view that the universe is a thought in the mind of a Supreme Mathematician. His reason for thinking this seems to be that ’all the pictures which science now draws of nature, and which alone seem capable of according with observational fact, are mathematical pictures’ (The Mysterious Universe).

Moreover, these mathematical pictures are not pictures of anything that we can imagine. On the wave theory of matter, for example, an electron is a system of weaves in a three-dimensional space. This sounds intelligible. We can identify this space with the physical space of our perceptions, and imagine the waves as being waves in some kind of ether. But we find that two electrons require a six-dimensional space, three electrons nine dimensions, and so on. It is evident that the space being talked of can have nothing to do with the space of perception. Also, we find that the waves being talked of are extremely elusive. It is suggested that they may be waves of probability, with no material existence whatever. It is obvious that the wave theory of matter is a description of something which is utterly unimaginable. From this, and similar instances. Sir James Jeans concludes that the universe is more like a thought than it is like anything else. He concludes, indeed, that it is a thought in the mind of a Supreme Mathematical Thinker.

To this argument one objects, in the first place, that the universe possesses aspects other than its mathematical aspects. The artist and the mystic are concerned with aspects of the world which are not mathematical. Even the sciences, excepting physics and its allies, are dealing with phenomena which are certainly not obviously mathematical. Adopting Jeans’s line of argument, we should have to say that the Creator is thinking of a great many things besides pure mathematics.

It might be said, of course, that all aspects of nature, except its mathematical aspects, are contributed wholly by our minds, and so are entirely subjective. This was very much the outlook of the early scientific creators, Galileo and Kepler. But, if we adopt this way of reasoning, it is not at all obvious that nature’s mathematical characteristics are not also subjective. Mathematical characteristics, it may be argued, are put into nature by us. We inevitably arrange phenomena in a mathematical framework because of the structure of our minds. This was Kant’s view, and it is also Eddington’s view, when he says, ‘We have found that where science has progressed the farthest, the mind has but regained from nature that which the mind has put into nature.’ Jeans, too, believes that our minds think mathematically from their very construction, but he regards it as a significant coincidence that nature should also behave mathematically, and finds in that coincidence evidence that nature has a mathematical Designer. But if Kant’s view be correct, there is no coincidence, and the fact that we arrange nature in a mathematical framework tells us nothing at all about its Designer.

Another point of view, which also has a respectable philosophic pedigree, maintains that mathematics is not a priori, is not an inescapable activity of the mind. These philosophers maintain that the laws of mathematics are derived from experience. Mathematical thinking, they assert, has resulted from our observation of the actual laws obeyed by phenomena. Thus the fact that we think mathematically, and that nature works mathematically, is not an extraordinary coincidence, but simply an example of adaptation. Indeed, Mr. Bertrand Russell tells us that it can be shown that a mathematical web of some kind can be woven about any universe containing several objects. If this be so, then the fact that our universe lends itself to mathematical treatment is not a fact of any great philosophic significance.

But even if we agree that the universe has a mathematical Designer, the next step, that the universe is a thought in a mathematical Mind, seems a very long one. Sir James Jeans appears to have been led to this conclusion by the difficulty of imagining anything material behaving in accordance with the equations that modern physicists have found. He says: ‘The concepts which now prove to be fundamental to our understanding of nature — a space which is finite; a space which is empty, so that one point differs from another solely in the properties of the space itself; four-dimensional, seven and more dimensional spaces; a space which forever expands; a sequence of events which follows the laws of probability instead of the laws of causation — or, alternatively, a sequence of events which can only be fully and consistently described by going outside space and time, all these concepts seem to my mind to be structures of pure thought. incapable of realization in any sense which would properly be described as material.’

The state of affairs described by Jeans certainly makes it likely that whatever it is that behaves in this extraordinary way is not something which we can represent to ourselves in terms of familiar concepts. The ' atom ’ of Victorian science could be pictured as a tiny grain of sand. The ‘electron’ of modern physics certainly cannot be pictured as an even tinier grain of sand. But surely this is not surprising? Why should not the intimate workings of nature outrun our capacity for pictorial representation? Lord Kelvin said that he could understand nothing of which he could not make a mechanical model, and for that reason he never accepted Maxwell’s Electromagnetic Theory of Light. That seems to us now a strange criterion. Why should a man suppose that nature must be the kind of thing that a nineteenthcentury engineer can reproduce in his workshop? What degree of unfamiliarity will Sir James Jeans permit before he declares that nothing material could act so oddly, and that the universe must be pure thought? It is also possible, we must remember, that some of these amazing mathematical webs which have been woven testify to the inefficiency of the mathematicians. It is perfectly possible that some of their paradoxes arise from the fact that they are using inappropriate concepts, and that the subject will take on a much more coherent form when new concepts are introduced.

V

Nevertheless, although they adopt very different routes, both Eddington and Jeans arrive at very much the same conclusion — namely, that the ultimate nature of the universe is mental. We have seen that Jeans has been led to this conclusion by the impossibility of conceiving anything save pure thought to which the modern mathematical description of the universe could apply. Eddington reaches his conclusion by reflecting that the only direct knowledge we possess is knowledge of mental states. All other knowledge, such as our knowledge of the material universe, is inferred knowledge — often the product of a long and complicated chain of inference. He holds the well-known theory that all our knowledge of the external world comes to us in the form of physical stimuli which travel along the nerves to the brain. Having arrived at the brain, these stimuli are somehow transformed into, or give rise to, mental states, which are apparently of an entirely different nature from the physical stimuli. But, he argues, the only link in this chain of whose nature we know anything is the last link — the mental state. Are we to suppose that this link is something absolutely different in kind from the other links?

Consider vision, for example. The process starts with the vibrating atoms of an external object. These vibrating atoms give rise to what the older physics called waves in the ether, but what the newer physics cannot yet satisfactorily describe. This physical process, whatever it may be, reaches the eye, and causes another physical process there. This, in turn, leads, presumably, to molecular movements in the brain. There then occurs the wholly dissimilar phenomenon that we call seeing a glowing red patch. This phenomenon appears so unlike those which preceded it that an absolute breach of continuity seems to have occurred. But why should we suppose this? We have seen that the only knowledge we have of the vibrating atoms, ether waves, and so on, is knowledge of their structure. This tells us nothing about their nature. May it not be, then, that their nature is the same as that of the red patch — namely, mental?

This is, in essence, what Professor Eddington asserts. He quotes with approval W. K. Clifford’s remark, ‘The succession of feelings which constitutes a man’s consciousness is the reality which produces in our minds the perception of the motions of his brain.’ Seen from the outside, as it were, a living brain is a collection of molecules in movement. Experienced from the inside, it is a collection of mental states. The first view gives us knowledge of structure. The second view gives us knowledge of nature or substance.

Thus, for Eddington, the whole of what exists, the external universe and our minds, is homogeneous in its nature. ‘The stuff of the world,’ he says, ‘is mind-stuff.’ He goes on: ‘The mind-stuff is not spread in space and time; these are part of the cyclic scheme ultimately derived out of it. But we must presume that in some other way or aspect it can be differentiated into parts. Only here and there does it rise to the level of consciousness, but from such islands proceeds all knowledge. Besides the direct knowledge contained in each self-knowing unit, there is inferential knowledge. The latter includes our knowledge of the physical world.’

It will be seen that Eddington leaves his notion of ‘mind-stuff’ very indefinite. It is not ‘stuff,’ since it is not spread in space and time; and it is not mind in the ordinary sense, since it is only here and there that it rises to the level of consciousness. It may be regarded, perhaps, as an extension of the ‘unconscious’ that psychologists talk about. Mr. C. D. Broad’s very able analysis of the ‘ unconscious ’ in his book, The Mind and Its Place in Nature, shows us the lines on which this concept could be developed. Jeans, as we have seen, goes even further, and would make the universe even more fully mental, being, indeed, a thought in the mind of God.

VI

The humanistic importance of this outlook, in the minds of its authors, seems to be that it leaves us more free to attach the traditional significance to our æsthetic, religious, or, compendiously, mystic experiences. It does not actively reënforce any particular religious interpretation of the universe, but it cuts the ground from under those arguments which were held to prove that any such interpretation is necessarily illusory. This it does by showing that science deals with but a partial aspect of reality, and that there is no faintest reason for supposing that everything science ignores is less real than what it accepts.

The question as to why science can afford to ignore these other elements has also been answered by Eddington. Why is it that science forms a closed system? Why is it that the elements of reality it ignores never come in to disturb it? The reason is that all the terms of physics are defined in terms of one another. The abstractions with which physics begins are all it ever has to do with. By starting with ‘pointevents,’ for instance, we can, mathematically, grind out one expression after another, until we come to the mathematical specification of ‘matter.’ From this specification we can continue until we arrive back at our starting point. We are doing what the dictionary compiler did when he defined a violin as a small violoncello, and a violoncello as a large violin. But what we have left out of this description is the process by which the mind of the scientist makes contact with one of the ent ities — namely, matter — which appear in this mathematical chain. It is in virtue of his recognition of this entity that the cycle of definitions has a meaning for him, and gives him genuine information. Similarly, to one who has seen either a violin or a violoncello, the dictionary definition gives information. But as long as the abstractions of physics form a closed cycle, it is obviously immune from all disturbance from factors it has neglected.

It is not quite clear that this immunity will endure. The above analysis applies only to ‘field physics, which, as we have mentioned, covers a very large part of physics. But it does not cover the whole of physics, and the hope that it could be made to do so grows steadily less. In atomic and subatomic phenomena we seem to be faced by a state of affairs that lies right outside the cyclic scheme. The most disconcerting characteristic of this region is that strict causality, a cardinal assumption in science, does not seem to apply. In the motions of individual atoms and electrons there seems to be an element of free will. Determinism has broken down, and the Principle of Indeterminacy has taken its place.

There is great difference of opinion at present as to whether this is a genuine discovery or whether it is a merely temporary technical device. Einstein, Max Planck, and others think that strict causality will ultimately be restored in physics, while such men as Eddington and Schrödinger think that determinism must be definitely abandoned. If the principle of indeterminacy comes to be definitely established, it will obviously have important philosophic consequences. It will make it easier to believe that our intuition of free will is not an illusion. Moreover, instead of regarding the course of nature as the mere unrolling of a vast machine where every product is predetermined, we shall be freer to attribute to nature a genuine creative advance. And the distinction between the natural and the supernatural, as Eddington has pointed out, would be appreciably diminished. Indeed, if this principle is definitely admitted, it will lead to the greatest revolution in scientific thought, and in the philosophy based on it, that has yet occurred.

VII

So far we have dealt with the limitations of science as a method of acquiring knowledge about reality. We have seen that the new self-consciousness of science has resulted in the recognition that its claims were greatly exaggerated. The philosophy based on science had made ‘matter and motion’ the sole reality. In doing so, it had dismissed other elements of our experience — those that seemed to us to have the greatest significance and which, finally, made life worth living — as illusory. Science, in spite of all its practical benefits, had seemed to many thoughtful men, perhaps to the majority, to have darkened life. That the new attitude of science, as explained by such men as Eddington and Jeans, has obtained such widespread attention is not, therefore, surprising. It was the metaphysical doctrines which accompanied science that were found so depressing. This is a striking testimonial to the fact that man is, after all, a philosophizing animal, for the purely practical aspects of science met with almost universal acclamation. And the wonderful vistas opened up by science seem to have been sufficient, in themselves, to inspire many men with optimism and a sense of freedom.

Professor Millikan, an eminent man of science, has eloquently expressed this outlook. He points out that our civilization is the first one in history that has not been based on slave labor. This is unquestionably a great gain. Also the amenities of life are now more numerous and more widely distributed than they have ever been before. And we may have every confidence that this advancement will continue. The sciences of geology, palæontology, and biology have revealed an orderly development of living forms from the lower to the higher which has been going on for many millions of years. We may well suppose that it is part of the order of nature that such development should continue. Millikan quotes, —

and comments, ‘That sort of sentiment is the gift of modern science to the world.’ And the fact that we ourselves are playing a part, a conscious part, in this evolutionary process is, he thinks, of ‘tremendous inspirational appeal.’

But it may justly be objected that all this is consistent with the old scientific philosophy which made man a purely accidental outcome of matter and motion, and which presented the universe, large and magnificent as it is, as entirely purposeless. The doctrine of progress, seen against that background, loses a good deal of its inspirational appeal unless we are content to find the whole meaning of life in the rearing of better and better human beings until, with the final death of the physical universe, the whole irrelevant human adventure comes to an end. The matter is not much better if we suppose the physical universe to be continually renewed. Our religious impulses cannot be satisfied with anything less than a belief that life has a transcendental significance. And it is precisely this belief that the old philosophy of science made impossible.

We conclude, therefore, that the truly significant change in modern science is not to be found in its increased powers to aid man’s progress, but in the change in its metaphysical foundations.