In reality time, in the sense of the astronomer’s time, does not enter into the methods of the mathematical physicist. Let us suppose that he is investigating the change that occurs in a material system between the two moments of time t1 and t2, these moments being separated from each other by a period of duration that we can feel. Let the system be, say, the earth and moon; the first body being supposed to be motionless, and the second being supposed to have a certain tangential velocity of movement. If the interval t1 to t2 is really an interval of astronomical time, the problem, what is the difference of position of the moon owing to the gravitation of the earth, is incapable of solution, and even if we reduce the interval of time indefinitely while still supposing that it is a finite interval, the mathematical difficulty remains. We then replace the finite interval t1 to t2 by the differential dt, which means that the two phases of the system, motionless earth and moving moon at the time t1, and motionless earth and moving moon at the time t2, are separated by an interval of time dt, which is smaller than any finite interval that we can conceive. We must then integrate the differential of the position difference so as to obtain the real difference in the condition of the system after the finite interval of time t1 to t2 has elapsed. Thus mathematics, incapable of dealing with real intervals of time, evades this difficulty by considering tendencies, not real occurrences.
Things that happen in a part of inorganic nature arbitrarily detached from the rest, and investigated by the methods of mathematical physics, do not endure. Let us suppose that we take some silver and add nitric acid to it: the metal dissolves. We can then add hydrochloric acid to the solution and precipitate the metal in the form of chloride; and we can then fuse this chloride with carbonate of soda, or some other substance, and so obtain the metal again. If we work carefully enough we can repeat this series of operations again and again and the original portion of silver will remain unchanged both in nature and in mass. All the chemical reactions into which it has entered have not affected it in any way; that is to say, these reactions have not endured.
If we inject a serum, containing a toxin, into the blood stream of a susceptible animal, certain things happen. The animal will become ill, but, provided that the amount of serum which has been injected was not too great, it will recover. If the toxin be again injected a reaction occurs, but the animal does not become so ill as on the first occasion, and after a number of injections the dose administered may be so great as to kill a susceptible animal but may yet produce no effect on the animal which is the subject of the process of immunisation: immunity has been conferred on it. Now can we compare the two operations, that of the solution and precipitation of the metal and that of the immunisation of the animal? We can to some extent, but the analogy soon fails, and indeed we should not attempt to formulate a theory of immunity on a physico-chemical basis if we did not start with the assumption that the series of operations was one in which only physico-chemical reactions were involved, that is to say, there is nothing in the phenomena of immunisation that suggests that what occurs in the animal body is similar to what we can cause to occur in inorganic materials outside the tissues of the living organism. We start with the assumption that the administration of the toxin causes the formation of an antitoxin in very much the same sort of way as the administration of hydrochloric acid to a solution of nitrate of silver causes the formation of chloride of silver. This antitoxin then neutralises the dose of toxin which may be administered after the process of immunisation has been effected, very much in the same sort of way as a certain amount of some acid can be neutralised by an equivalent amount of some base with which the acid can combine. If the reader will analyse any of the theories of immunisation current at the present day he will find that these are the physical ideas that are involved in it.[4] But physiological science has the much more formidable task of explaining the persistence of the immunity. The animal rendered immune to the toxins produced by certain species of bacteria may remain so for many years, that is, for a very long time after the antitoxins originally produced by the reaction of the tissues to the toxins first administered have disappeared. We must imagine, therefore, that the anti-substances produced originally by the reaction of the toxin are produced again and again by the tissues of the susceptible animal, for the latter may resist repeated infections, that is, repeated doses of toxin, without illness. But then the tissues of the animal body are transitory substances and they do not persist unchanged. Muscles, glands, connective tissues, even nerve-fibres and nerve-cells undergo metabolism, and the chemical substances of which they are composed break down into the excretory products, pass out into the blood stream, and are eliminated from the body; while at the same time these tissues are continually being renewed from the nutritive substances in the blood and lymph. It is the organisation of the tissues—their form and modes of reaction—that endure, but the material substances of which they are composed are in a state of continual flux. Yet the organisation of these tissues does not persist unchanged, for it is continually responding to new conditions experienced by it. The reactions that occur when a toxin is administered to a susceptible animal affect the organisation of its tissues in such a way that the latter acquire the capability of producing antitoxins which may—if we like to say so—neutralise the toxins that enter into them when they become infected. The reaction endures. But this is a different thing from saying that the process is a physico-chemical one alone.
This is what we must understand by the duration of the organism. Everything that it experiences for the first time persists in its organisation. It acquires the ability of responding to some stimulus by a definite, purposeful reaction, the effect of which is to aid it in its struggle for existence; and this reaction, once carried out, becomes a “motor habit” or the basis of a reflex, or in some other way, as in the process of immunisation, remains a part of the modes of functioning of the animal. In our behaviour certain cerebral nerve tracts become laid down and continue to exist throughout life, modifying all our future experience. Our past experience accumulates. There must be direct continuity in our flux of consciousness, for no perception seems ever to fade absolutely from memory. This continual addition of perceptions to those that already exist makes our consciousness ever become more complex, so that a perception experienced for the first time is never quite the same when it is again experienced. The first time that we go up and down in an elevator, or sit on a “joy-wheel,” or ascend in a balloon or an aeroplane, or become intoxicated, constitutes an unique event in our lives, and we experience a “new sensation.” What the blasé man of the world complains of is this accumulation, or rather persistence, of his experiences. A repetition of the same stimulus never again begets the same perception. The first hearing of a modern drawing-room song may be enjoyable, but the next time we hear it we are not interested, and by-and-bye it becomes very tiresome. The first hearing of a great symphony usually perplexes us, and we are perhaps repelled by unusual harmonies, or progressions, or strange modulations, but subsequent hearings afford increasing pleasure. We say that there was “so much in it” that we did not understand it, yet precisely the same series of external stimuli affected our auditory membranes on each occasion, and the same molecular disturbances were transmitted along our afferent nerves to the central nervous system, where the same physical effects must have been produced. The difference in all these cases between the repetitions of the same stimuli was that the later ones became added to the earlier ones, so that the state of consciousness produced by, or which was concomitant with, these external stimuli was a different state in each case.
This is the duration of the intelligently acting animal: it is not merely memory, but memory and the accumulation of all its past modes of responding to changes in its environment, whether these modes of response were conscious ones (as in the case of an intelligently performed or “learned” action), or unconscious ones (as, for instance, in the case of the acquirement of immunity by an animal which had become able to resist disease). It is not merely the experience of the individual organism, but also all the experience of those things which were done or experienced by the ancestry of the organism, and which were transmitted by heredity to the progeny. Motor habits are formed, so that much the same series of muscular actions are carried out when a stimulus formerly experienced is again experienced. Pure memory remains, so that the images of past things and actions somehow persist in our consciousness. Physical analogy suggests that these images are inscribed on the substance of the brain or are stored away in some manner; but, apart from the incredible difficulty of imagining a mechanism competent for this purpose, it is obvious that we thus apply to the investigation of our consciousness (which is an intensive multiplicity), the concept of extension which can only apply in all its strictness to the things outside ourselves on which we are able to act. All these motor habits, functional reactions, and memory images are our duration or accumulated experience. The motor habits and those functional habitual reactions of other parts of the body than the sensori-motor system are the basis of our actions, but the memory images are, so to speak, pressed back into that part of our organisation which does not emerge into consciousness. Only so much of them as bear on the situation in which we, for the moment, find ourselves and which may therefore influence our actions, flash out into consciousness. As “dreamers” we indulge ourselves in the luxury of becoming conscious of these memory images, but as “men of action” we sternly repress them, or so much of them as do not assist us in the actions that we are performing. Yet it is in the experience of each of us that, in spite of this continual inhibition, parts of our memories slip through the barriers of utility and surreptitiously remind us of all that we have been and thought.
Thus we simplify the stream of our consciousness. That of which we are conscious at any time is never more than a part of our crude sensation: we never perceive more than a small part of all that our organs of sense transmit to our central nervous system. But even these chosen perceptions of the external world are so rich, so chaotic and confused, that we are unable to attend to them all at once and we therefore “skeletonise” the contents of our consciousness. We think about it a bit at a time. It is an unitary thing, unable to be broken up, but we look at it from a great number of different points of view, so to speak; and then, fixing our attention on some aspect of it, we agree to ignore all the rest. We thus detach parts of it from the rest and, having thus arbitrarily decomposed it, we call these separate aspects the elements of our perceptions, and confer upon them separate existence in space and time. We remember and classify things and group together all those that seem to resemble each other. We form genera, agreeing to ignore all but the most general characteristics of the things which we try to conceptualise. We do not think separately about all the dogs or horses or fishes that we have ever seen, but we group all these animals into species, and it is usually the species that we think about when the idea of a dog or a horse or a herring emerges into our consciousness. When we think about a tramcar we do not think about all the separate vehicles that we have seen, nor about their colours, nor the advertisements on the boards outside, nor the people hanging on to the straps inside. Just so much of the experience of what is relevant to the purpose of our thought enters into our idea of the tramcar: it is a conceptual vehicle that we think about. Such is the nature of the concepts that form the basis of our reasoning: they are generalised aspects of our experience of nature, usually poorer in content than were the actually perceived things, except when it is necessary that some individual thing seen or otherwise experienced should be investigated or reasoned about. All our descriptions of nature are conceptual schemes. The world of perception, says William James, is too rich to be attended to all at once, but in conceptualising it we spread it out and make it thinner, and we mark out boundaries and division lines in it that do not really exist. It is this generalised nature that is the subject matter of our reasoning of pure science; and it is these concepts that form the matter of all our descriptions. We do not describe nature “as we see it,” it is our conceptions that we write about. Genera and species and varieties do not really exist in the animate world: all these are logical categories generated by our thought, concepts that facilitate our descriptions. When an anatomist gives an account of the structure of an animal he does not say what it looks like, nor as a rule does he content himself by making a photograph of his dissections. For him the animal is a complex of muscles, skeleton, nerves, glands, and so on, and in his drawings all these things are given an individuality that they do not really possess. In the living creature there were no such sharply-distinguished organs as a good drawing represents: all are bound together and are continuous. But for practical convenience in description—that is, in the long run, that we may act upon these things, we isolate from each other aspects that are in reality one unitary whole.
The universe, that is, all that is given to us, presents itself as immediately perceived phenomena which are then conceptually transformed. It is an aggregate of things—gross matter, particles, molecules, atoms, and electrons. These things have separate existence and shape, so that each of them lies outside all other things—we apply to them the category of extension. They possess properties—that is, they are hard, or heavy, or hot, or cold, or they are coloured, or they smell, and so on—we thus apply to them the category of inherence. They are not things that are immutable, for they change in place, or are transformed in other ways, that is, they are acted upon by energies. But beneath the properties of the things, or the transformations that they undergo, we imagine something that has properties and which transforms: it is not convenient that we speak solely of attributes or transformations as entities in themselves, for we think of things as having properties and being subject to transformations. Thus we apply the category of substance.
Has this universe that we construct from the data of sensation objective reality? We are led quite naturally by our study of physiology to the notion of idealism. We see that our perception of things, that is, our knowledge of the universe, depends on the integrity of functioning of certain bodily structures, and upon the condition that in men in general this integrity of functioning is normal, that is, common to the great majority of mankind.