The analysis of matter

IN Part II., when we were considering the transition from perception to physics, we took over from common sense certain rough-and-ready approximations which, at our present stage, we must seek to replace by something more exact. We want now to make a second approximation: having inferred a certain kind of physical world from our percepts, we can use the properties of this inferred world to reinterpret the relation of percepts to the outer world, and we can consider more carefully whether any of the properties we assigned to the outer world were accepted without sufficient reason, merely because they were such as we think we find in the perceptual world. The subject is imaginatively difficult, and it is not easy to disentangle different levels of inference, but it is important to do so.

Starting from percepts, we observe that different people have similar percepts, whose differences proceed approximately according to the laws of perspective. The first picture of the physical world to be derived from a comparison of percepts (when we start with a developed logic, not with common sense) is, that there are groups of more or less similar events arranged about centres; that the first-order laws as to the differences between events in one group are spherically symmetrical with respect to the centre of the group; and that the second-order laws are obtained by combining a number of laws of "distortion," each of which has its own centre. In this picture of the world, we use a physical space which is derived from, and also correlated with, the space of percepts, in the manner explained in discussing phenomenalism in Chapter XX. I shall here repeat and amplify this construction, with a view to suggesting modifications of it derived from physics.

We cannot wholly eliminate the subjective factor in our knowledge of the world, since we cannot discover experimentally what the world looks like from a place where there is no one to see it. But we can make the subjective factor approximately constant, and thus be reasonably convinced that the differences which remain are due to causes that are not subjective. I shall therefore suppose that, at a given moment, a number of photographs are taken of some object, say a chair or a table, from different places, with cameras and plates as similar as possible. I shall suppose that the photographs are compared by a person sitting motionless, who places them successively on a fixed stand in front of him. It is then reasonable to assume that the differences between his percepts of the photographs are due to physical causes; also, within limits, that the likenesses between them are due to likenesses in the stimuli to the photographic plates. We find that the differences between the photographs proceed according to certain laws, which we call the laws of perspective; these laws are correlated with the differences between the appearances of the different cameras to an observer who sees them all at the moment when the photographs are taken, and so on. In fact, they can all be expressed as functions of the "co-ordinates" of the cameras and the parts of the table, where "co-ordinates" may be defined by relation to the single observer. E.g. he may get another man to go with one end of a stretched tape-measure to each camera in turn, while he holds the other end; he can read the length of the tape-measure, and observe, on scales, the angular co-ordinates , of the tape-measure. These facts lead us to attribute a measure of objectivity to our co-ordinates, since, although they are all observed by us from our point of view, they determine the sort of photograph that a camera will take. Further, they lead us to think that, all round the table or chair which is being photographed, there are events which are connected with each other according to the laws of perspective as stated with reference to a certain centre as defined by our polar co-ordinates. Our observer's , , are facts concerning his own percepts, yet they suffice mathematically to determine the "percepts" of the cameras; they must therefore have some significance which is not purely private to him.

This argument, elaborated and extended in obvious ways, gives the ground for supposing that our perceptual space has some objective counterpart, i.e. that there is some relation between the camera and the table corresponding to the relation between the co-ordinates of our percepts of them. (I am throughout assuming the causal theory of perception.) If we now use one camera to make one photograph containing various objects, we shall again find that the spatial relations of the representations of the objects in the photograph are such as can be calculated from the co-ordinates of the objects and the camera. We cannot know the intrinsic quality of the events at the camera which cause the photograph, but we can infer a certain similarity of structure between these events and our percept of the photograph. All this leads us to the notion of groups of events arranged about centres, the centres having to each other relations whose causal properties can be inferred from relations between certain of our percepts. That is to say, given a group , of which one member is a percept , and another group , of which one member is a percept , if , , are the co-ordinates of , and , , are the co-ordinates of , there is a relation between and which can be inferred from , , and , , . These facts give the grounds for regarding space as objective, though, even on the basis of these facts, the space which is objective will not be identical with the space of perception, but only correlated with it.

The events which cause a photograph obviously take place at the surface of the photographic plate; what happens between this and the object photographed consists of causal antecedents, not of the immediate cause. And the resulting photograph is in the plate, not in the object. Similarly the events which are the immediate causal antecedents of our percept are in the eye and optic nerve, and the percept is in us, not in the outer world, when we are speaking of physical space. The whole of our perceptual world is, for physics, in our heads, since otherwise there would be a spatio-temporal jump between stimulus and percept which would be quite unintelligible. Any two events which we experience together—e.g. a noise and a colour which we perceive to be simultaneous—are "compresent." I should not say, however, that two percepts which are not both "conscious" must be compresent. Two events are compresent when they form together one causal unit or part of one—this is a sufficient, but perhaps not a necessary, condition. When two percepts are experienced together, they are thus causally conjoined; but when either is "unconscious" they may not be, and therefore we cannot be sure that they are compresent. It is not necessary, consequently, to suppose that the mind occupies a mere point in physical space.

It is now necessary to point out the limitations to the accuracy of the above account. In the first place, there are departures from the laws of perspective which can be easily fitted in—opaque bodies, prisms, looking-glasses, echoes, etc. These cases are easy because the departure from regularity as regards one sense is accompanied by evidence, from another sense, of the existence of a physical object at the centre of the disturbance, or at the apex if the disturbance is conical, like a shadow. Then there are the cases where a physical object is inferred from the disturbance, although there is no direct evidence of its existence. But none of these are really important. The two important matters are: (1) The difficulties about measurement; (2) the difference between a percept as it seems and a stimulus as it is inferred.

(1) The difficulties about measurement have already been discussed, but we must now endeavour to reach conclusions about them. As already pointed out, every measurement, however inaccurate, records a fact, though not always the fact which it is intended to record. We saw a moment ago that, if we measure the co-ordinates , , of an object to be photographed and of a number of cameras, we can make inferences as to the pictures which the various cameras will make of the object. We inferred that the co-ordinates represented relations to our body which have certain peculiar properties of the sort called geometrical, in the sense that when we know the co-ordinates of two bodies relatively to ourselves, we can infer their co-ordinates relatively to each other. All this is only roughly true if our measurements are careless: in that case, when we mean to discover intrinsic relations, we are only discovering very complicated relations involving our sense-organs and perhaps even our desires. We seek a technique for eliminating all circumstances except those with which we wish to be concerned, and to a great extent we are successful. But relativity informs us that there is a residue of variability in measures which cannot be eliminated, because, in fact, the relations we try to measure are partially non-existent. Or, more correctly, they are relations involving more terms than we thought they did. We supposed that co-ordinates represented relations to the axes. But if we had two sets of axes momentarily coinciding, while one was moving relatively to the other, the co-ordinates of an event would not in general be the same with respect to both. And we cannot even, in any strict sense, discover any exact relation between distant points such as could give physical significance to co-ordinates. The appearance to the contrary is only an approximate truth, which cannot be made precise.

All this represents a failure of correspondence between physical space-time and perpetual space and time. If we assume that the human body moves in a geodesic, perceptual time may be identified with the integral of ds taken along that geodesic, while perceptual space consists of certain relations between simultaneous percepts (the word "simultaneous" raises no difficulties, since all percepts are in our heads), partly themselves perceptual, partly inferred, but all just what they are, whatever physics may say. There are certain respects in which we can modify perceptual space to suit physics, and certain others in which we cannot. We can, for example, infer that percepts consist of imperceptible parts, if physics gives us ground for thinking so. But where we perceive some relation between percepts, we cannot deny that there is such a relation, however little physics may allow it to subsist between the objects said to be perceived. The rule is: We can infer extra complexity of structure in percepts if physics requires it, but, however much physics may require it, we cannot infer a smaller complexity than is demanded by the study of percepts on their own account. In the world of percepts, the distinction between space and time does really exist, and space does really have certain properties which relativity denies to physical space. Thus to this extent the correspondence between perceptual and physical space breaks down, and measurement, which has to do primarily with percepts, fails to give us quite such good data as we hoped to obtain for inferences as to the physical world.

(2) I come now to the difference between a percept as it seems and a stimulus as it is inferred. But this is not the whole scope of the problem to be discussed. The word "perception" implies relation to a physical object; we are supposed to "perceive" a chair or a table or a person. If physics is correct, the relation of a percept to a physical object is very remote and curious. In ordinary cases, we see objects by means of light which is reflected or scattered, which increases the complication. To take the simplest possible case, let us suppose that we are seeing a glowing gas. The percept seems to be a patch of bright colour of a certain shape, sensibly continuous in perceptual space, and approximately constant in perceptual time. Perception gives knowledge only in so far as this percept corresponds to what is really taking place in the gas. Now if physics is true, there are great differences between the apparent structure of the percept and the real structure of what is taking place in the gas. (Differences other than structural may be ignored.) Instead of something steady and continuous, such as the percept seems to be, the process in the gas is supposed to be a large number of separated sudden discrete upheavals. It is true that there are important similarities between the percept and the physical event. The shape of the percept corresponds to the shape of the region in which the upheavals are taking place, with the limitations mentioned just now in connection with measurement. The colour of the percept corresponds to the amount of energy lost by each atom in an upheaval. The constancy of the percept corresponds to the statistical constancy in the rate at which upheavals occur in any not too small portion of the gas. Thus everything in the percept represents a statistical fact about the gas, with the exception of the colour, which is supposed to represent a fact about each atom. This, by the way, is an odd reversal of Locke's dictum about secondary qualities: the colour is the most nearly objective of all the elements in the percept.

These differences are all of one kind in a certain respect: they attribute more structure to the physical occurrence than to the percept. This is in line with the general principle that the relation of distant to near appearances is one-many, so that differences in the percept imply differences in the object, but not vice versa. The finer structure of the object is all, in the last analysis, inferred from the grosser structure of percepts, but it involves the comparison of many percepts and the search for invariable causal laws, in the manner which we considered in Part II. There is therefore no inconsistency in the view that the physical event differs from the percept in the way suggested by physics, since the difference consists in attributing more structure to the physical event, not in denying to it those elements of structure which are possessed by the percept.

It is possible, if we choose, to attribute to the percept the same structure as that possessed by the physical occurrence, or rather the same structure as that possessed by the immediate external stimulus. It cannot be proved that this hypothesis is untrue, but it is less useful than it might be supposed to be, because only what is known about percepts is epistemologically important, and such structure, if it exists, is certainly unperceived. What we only discover about percepts by means of inference does not belong to the part which affords premisses for science, but is, from the standpoint of theory of knowledge, in the same position as events in the external world. Therefore, although percepts may have an unperceived structure, this does not diminish the significance of the fact that the structure we perceive in percepts has only a one-many relation to that of their stimuli.

The question must be faced: Is physical space-time perhaps much more unlike the space and time of perception than we have supposed? Have we been victims of imaginative laziness in our merely piecemeal modifications of common-sense prejudices? Dr Whitehead, most emphatically, is not open to such a charge; his "fallacy of simple location," when avoided, leads to a world-structure quite different from that of common sense and early science. But his structure depends upon a logic which I am unable to accept, namely the logic which supposes that "aspects" may be not quite alike, and yet may be in some sense numerically one. To my mind, such a view, if taken seriously, is incompatible with science, and involves a mystic pantheism. But I shall not pursue this topic here, having treated it on former occasions. The question I wish to ask is: Without adopting heroic measures, what could we suppose about physical space-time, if we were anxious to preserve what is probably true in physics, but not anxious to keep as near as possible to common sense? In particular, can space-time itself be atomic, as the existence of the unit of action seems to suggest? And first, how are we to conceive "action"?

Action is usually defined as the time-integral of energy; since energy can be identified with mass, "action" may also be defined as mass multiplied by time. Gravitational mass is a length; e.g. the mass of the sun is 1·47 kilometres.[69] Since gravitational and inertial mass are equal, we might regard action as length multiplied by time. Dr Jeans (Atomicity and Quanta, p. 8) says:

In this passage, the "high confidence" seems to me to go beyond what is warranted. If there were a scientific gain in conceiving the space-time structure atomically, I do not believe that any theoretical arguments to the contrary could interpose a veto. Arguments from dimensions, such as Dr Jeans employs, have no longer the definiteness that they had before the introduction of relativity. As we have just seen, we could define "action" so that its dimensions would be length multiplied by time. Now there is a universal constant of action, namely . Perhaps, if we were to take action as one of the basic conceptions of physics, we might be able to construct a physics which would be atomistic all through, and yet would contain all that is verifiable. I do not "proclaim with high confidence" that this is possible; I only invite attention to the hypothesis, as worth investigating on the chance of its affording a simplification of the conceptual apparatus of physics. In the following chapters, this hypothesis is to be borne in mind.