The Philosophy of the Present
Supplementary Essay 3: Scientific Objects and Experience
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The knowledge process takes a different route for the scientist from that which it takes for the epistemologist. The scientist starts with an unquestioned material world and with unquestioned objects that appear in the problem with which his research is occupied; from these he proceeds by inference to the formulation of his hypothesis and the consequences which it involves, and then on to the observation and experiment by which his hypothesis is tested. Although he criticizes his perceptual experiences and exhibits the errors and illusions of perception, his criticism is always founded on objects that are there; and his criticism does not invalidate these, since he must appeal to them as tests of the errors he discovers. In the process of thinking out the hypothesis his ideas symbolize relations in a world that is there, and he tentatively seeks to find among them such interrelations as will overcome conflicts between objects and their meanings, or between different meanings of things. He finally deduces the results that follow from his hypothetical reconstruction, and by observation and experiment in an unquestioned world finds, or fails to find, the confirmation he is seeking. His cognitive proceeding is from an accepted perceptual world through exceptional instances and conflicting meanings on to the same world, after its meanings have been reconstructed. That world itself he never questions.
The epistemologist, on the other hand, proceeds from the fact that all perceptual experiences are dependent upon the relation of the world to the organism, and makes use of such
(141) experiences as illusions and perceptual errors in order to locate percepts in a consciousness entirely separate from the world of objects to which these percepts refer. This position was strongly fortified by the doctrine of Renaissance science that secondary qualities cannot belong to the physical world with which physical science is occupied. Knowledge, as the epistemologist conceives it, undertakes to proceed from these states of consciousness, including all perceptual experience, over to an ontologically separate world to which these states of consciousness seem to refer. He is thus led to the conclusion that a cognitive reference attaches to all perceptual experience. The existence of a world to which such states of consciousness refer becomes the epistemologist's problem.
It is important to place the scientific object in its relation to the perceptual world, which is, as we have seen, presupposed both in the scientist's problem and in his experimental data. That object is an abstraction of that within experience which is subject to exact measurement. It is furthermore a physical thing, i.e., it occupies a volume of extension that could conceivably be brought within the range of a manipulatory experience. Even when we pursue de Broglie's idea and state matter in terms of wave motion, we must come back to a definable portion of space which is in so far within our field of conceivable manipulation that we could measure the waves. The ether, as long as science retained it, could be conceived of as the stuff occupying this space, and elasticity and rigidity could be ascribed to it.
If we turn to the experimental findings to which even the most abstruse hypothesis must appeal, if appeal is by any device possible, we find that the test takes place within what I have called the manipulatory area. We are here dealing with pointer readings that reflect changes lying at a distance from the changes in the apparatus. Within this
(142) manipulatory area visual perspectives disappear, and we can reach a high degree of accuracy in measurement. Its spatial structure, as we have seen, is that of the rigid body, and so far as physical tests can go it is that of Euclidean geometry. What is of peculiar importance is that it is within this field that we find, directly or indirectly, our common objects. For example, the penny with which epistemologists have been so much occupied is the same penny for different observers at different angles and at different distances in so far as these different visual pennies are recognized as appearances of one and the same penny which any of the observers, under the control of his visual experience, could touch and handle. As a result of a common method of manipulation, measurement and location, the manipulatory areas of the different observers thus become identical. It is important to recognize that while each individual will receive from the penny an experience of pressure, in a sense peculiar to himself, the method of identifying the penny that all will experience is not peculiar to himself. It is a logical procedure whose entities and relations exist only in so far as they constitute a universal factor in the experience of the individual. The individual, that is, does not first make his own measurements and reach his own identifications, and then compare these with those of others in order to reach a common object; his method of determination is rather in terms of a language that with its various symbols comes into existence only through the fact that the individual assumes the attitude common to all those involved in the common undertaking. This common penny attains the reality of experimental findings, however, only if it comes back directly or indirectly to a measurable something in the manipulatory area. At the basis of the process of measurement, of course, there lies the fundamental mechanism of perception, in which distance experiences lead to contact
(143) experiences that control the environment in the interest of the organism. The contact experiences are the reality of the distance experiences. The physical object, however, constitutes a break in the primitive biological process that finds its completion in the consummation which the biological needs of the organism call for. It is the hand under the control of the eye that is responsible for the manipulatory area. The handled object comes betwixt and between the vision of food and its eating. If the biological process, under the distance stimulation, goes through to consummation without interruption, no physical object arises in experience. In a biological sense the manipulated or physical object is thus a mediate reality. In its abstraction from consummation it is first of all an implement, and then the physical thing of a later science.
When the Michelson-Morley experiment and the difficulties brought to light by the lack of invariance in the Maxwell equations of electro-magnetism had ejected ether as a physical thing, the ether of "stuff," or, to use Whitehead's term, the event, was substituted for it, and time entered as a dimension of the physical thing. We have already seen that in the perceptual world space and time are inevitably separated. Motion involves a something that moves which is irrelevant to the temporal process. An event always happens to something. A striking result of recent changes in physical science, and of the new theories to which these changes have given rise, is that the event has taken the place of the physical thing. In the perceptual world and in the world of masses in motion events happen to things. Over against change there are unchanged things which are the conditions of change. That is, in the perceptual world space and time are necessarily separate. Space-time cannot be the form of perceptual experience. We can shift from one perspective to another, and realize that what from one stand-
(144) -point is rest, from another is motion; but in each perspective there are permanent things, irrelevant to time, that give meaning to the changes that go on within time. If perspectives can be reduced to diverse appearances of things that have remained the same during all changes, relativity will not bite into the nature of the things; but if the nature of things is found in process, in a system of changes, the different values which this process takes on from the various standpoints of different but related observers must affect the natures of the things themselves. Yet we cannot really reduce things to processes, for it is not possible that processes should go on that are not processes of things, and measurements can only be made in a situation within which something abides irrelevant to time.
While the event is taking place we watch it or listen to it or feel it; but if we can complete the behavior it initiates, we isolate the thing to which the event is happening. But from the standpoint of relativity no physical object can be isolated from what is happening to it. If it is at rest in one consentient set under the measurement of a scientist, it is moving in another set; and not only are its measurements in time and space shifting with the relative velocities of the sets, but its inner content of mass varies also. There is nothing that can be laid hold of except the transformations of these measurements from one set to another and the coincidences of events in an absolute space. Now what this amounts to is that we have no sooner got hold of the thing in a permanent space within which we can measure it and determine its inner mass-content than we must put ourselves at a distance from it in another space and determine its changes due to the relative velocities of these two spaces and their consentient sets.
We have thus reversed the fundamental order of our behavior and have made the "what a thing is" a distance
(145) experience instead of a contact experience. The reason for this shifting is evident. The object in the manipulatory area belongs to the perspective of the individual, and, in so far as this manipulatory area can be determined by measurements which are common to all members of the community to which he belongs, to the space and time of the consentient set of which his organism as a physical thing is a member. It is only by putting ourselves in the distant consentient set that we can realize that the distortions the objects of that set suffer are the same as those our set undergoes when seen from that standpoint. Since there is no absolute space to which these differing standpoints can be referred, as the perspectives of vision can be referred to a common manipulatory area, there can be no manipulatory area to which these perspectives or frames of reference may be referred. The measuring-rod and the clock that gives the local time belong to the manipulatory area, and the quantities they measure will vary from one set to another. There is no common measuring rod, and no common clock, that all can accept. The different observers can only make use of formulae of transformation by which measurements made in one set can be read into those of another. We are left therefore with a language of distance light-signals which can refer to no object common to the experience of all. It is true that by application of the formulae we can isolate a constant value for the interval between the coincidences of events in a Minkowski space-time, and that this constant value may be regarded as the common reality to which all the different measurements, made from the standpoints of various perspectives, ultimately refer. This space-time, however, abstracts from every character in the distance experience whose meaning lies in its reference to a common physical object. Only those character-, in the distance experience are left that refer to a single form of calculation
(146) common to all the different perspectives. It is this abstraction that makes it possible to assimilate time to space as a fourth dimension. For this calculation what is a timeinterval in one perspective is a space-interval in another. It would, however, be a mistake to assume that we have thus passed into a field of communication in which our symbols have lost all significance except that of reference to a common referent. In fact we are still in a visual world, with a finite value for the velocity of light; only the physical thing to which that visual experience refers is stated in terms of a calculation-value common to an indefinite number of diverse visual experiences.
A similar criticism may be made of the view that would regard energy as constituting the nature of the physical thing. For the perceptual world there must be a system of things, and energy is the measure of the changes brought about in this system when a force is brought to bear upon it from without. Experiments, and the mathematical formulation in which thermodynamics has clothed the results of these experiments, however, have justified the conclusion that such measurement reveals only the potential energy within the system. How widely we are justified in spreading the generalization of the conservation of energy has been made the subject of dispute, though, as Poincaré has pointed out, we can always assume potential energy to keep the doctrine intact. When, however, we make this energy the nature of the thing, we are as necessarily passing out of the perceptual world as when we substitute space-time for space and time.
Energy, like space-time, is a transformation value. We select a process in the manipulatory field-the amount of work done-as the measure of energy; but what is measured is not stated as a function of the mass of the body, on the contrary mass itself is stated in terms of energy. Thus,
(147) when we reduce physical things either to space-time or to energy, we are in either case utilizing a process of measurement in a perceptual, manipulatory area to give the nature of the physical thing, while the nature thus ascribed to the physical thing does not belong to the field of the measurement. In the one case instead of the thing we set up an event located in a space-time that lies outside of experience; in the other, we appeal, as in Ostwald's view, to a metaphysical field equally remote from experience.
Reduction of mass to electro-magnetism. would provide us with a further illustration, for electro-magnetism and light have thus been brought back to the same process, viz., that which relates an organism to distant objects. If mass could be stated in electro-magnetic terms we should have substituted the distance-value of the object for its manipulatory value. That it should be so stated, however, presupposes that we are using the wave formulation and not the corpuscular formulation for electro-magnetism, and that we are not driven to introduce the corpuscular concept - the photon, into the theory of light.
This brings us to Professor Bridgman's program of rigidly reducing all our physical concepts to the operations we make use of in measurement.[1] His proposal seems to amount to an undertaking to bring the object back to the manipulatory area, but not to interpret the physical thing as a volume of mass in motion, but rather to redefine the physical thing of the manipulatory area in terms of its uses in scientific measurement. The simple Newtonian doctrine interpreted the light and heat of the sun as evidence of molecules of massive elements in violent motions; but the elements have now become particles of electricity that can conceivably be defined entirely in electro-magnetic terms, and this means
(148) that we can define them only in terms of mathematical formulations whose constants are certain pointer-readings. The mathematical formulations fix as exactly as possible the conditions under which we can obtain these pointer readings. We are thus getting a picture, not of the movements of manipulatory things, which, within the realm of our observations, are the conditions of our distance experiences, but of ideal conditions of control of manipulatory situations in which these distance experiences can be reproduced. If we conceive the sun as made up of electrons and protons, we can present in an imagined manipulatory area the movements of these particles, with their distances from each other and their velocities. We can present the electron and the proton as pressing toward each other and as held apart by the centrifugal force of the incredible velocity with which the electron revolves about the proton. But if we go on to picture the electron and proton as crushed together in the center of the sun, thus setting free, in the form of radiation, the electro-magnetic energy, including that of mass, which is the "what it is" of these electrical particles, we have transformed the stuff or manipulatory content of the thing into distance experience. The indestructibility of Newtonian mass reflected our fundamental attitude that what we get hold of is the permanent reality of what we see, hear and otherwise sense at a distance. If this permanent reality disappears in radiation, and this comes to us, say, in heat and light, or in the form of cosmic rays, it is no longer a distance experience of anything. The same is true of fields of force. We may say that they are events but there are no things to which the events happen at the location where they are.
I am not voicing a hankering after the fleshpots of what Whitehead has called the materialism of the Newtonian period. That view was afflicted by the bifurcation that
(149) Whitehead deplored, and harbored the whole nest of epistemological problems that Lovejoy has extensively spread before us.[2] I am only insisting that whatever view we may take of the momentous changes that science has brought in its wake since electro-magnetism. began to dominate its research and doctrine, we cannot get away from the perceptual findings that all science accepts as its most fundamental criterion of reality. The appeal of science to its perceptual findings as its criterion evidently involves more than any mere confirmation of distance experience by contact experience; the appeal is rather to the perceptual occurrence of events predicted on the basis of an hypothesis, in order to confirm that hypothesis. The importance of the perceptually real thing of the manipulatory area appears when an object of this sort can be identified under observation and experiment in an exceptional instance; consider, for example, the radiation of black bodies where the reality of the object as a perceptual thing must be accepted, wholly in advance of any further interpretation of it that a later hypothesis may give. Here we reach a something that maintains itself as an object that can be felt as seen. It is further evident that the reliability of measurements-of pointer readings-must be assured within this same perceptual field. Even if we can neither spread out the space and time of this area into the Euclidean space of the Newtonian doctrine, nor subdivide its perceptual things into Newtonian mass-particles, we nevertheless in some fashion relate the assumed reality of a universe that goes way beyond the boundaries of our perceptual experience to the decisive reality of the scientist's findings.
Even if we reduce our physical concepts to operational processes, we must confess that our physical things belong
(150) to the field of our control-the field of measurement of changes in our experience. The causal antecedents of these changes can no longer be stated in terms of physical things, in the sense that they are conceivable permanent contactexperiences referred to by distance-experiences; but our relevant measurements must still take place by means of physical things. The causal antecedent may, for example, be both physical and mental. It may be an event with adjectives supplied by ingression from a world of eternal objects or universals. Or the expression for it may be an elaborate mathematical apparatus for carrying out exact measurements within the field of experiment and observation, as in Bridgman's Logic of the Physical Sciences. Or again it may be a logical pattern corresponding to some structure in a metaphysical world beyond experience-an absolute world of space-time whose coincidences of events and the intervals between them cannot appear in our relative spaces and times. But in no case can the nature of these elements of the subatomic, electro-magnetic world take the place of the physical mass-particles of Newtonian doctrine which could be conceived of as subdivisions of the massive objects that come under our own hands.
The breakdown of the Newtonian mechanical system was reached when, with the development of the laws of thermodynamics and of the theory of electro-magnetism, that meaning of physical things which fits our perceptual experience could no longer be applied to the so-called material universe. We now find that exactly determined distance-experiences occur, which answer to something going on-something, however, that cannot be stated in terms of changes among manipulatory things. In fact, we now postulate in our physical hypotheses, as the inner nature of the things referred to by the earlier distance experiences, other distance experiences, such as energies, or radiations. In the account
(151) given of the pressure of gases, on the other hand, we present to ourselves a picture of mass-particles bombarding each other and the walls of the container. Here the ultimate elements are physical things conceived in perceptual terms. But when we speak of the content of the electrons and protons as an energy which may take the form of radiation, we are describing them in terms of another distance experience-one which, moreover, can refer to no conceivable contact-experience. We cannot however simply brush to one side the whole of perceptual experience with the claim that we are dealing rather with the conceptual objects of science, for both our problems and our observations and experiments are stated in perceptual experience.
There are two sides to the question. I think we must admit that the distance-experience does and must imply that what is going on there would be responsible for contact-experiences if the organism could be at the place where the process responsible for the distance experience is going on, and were provided with the appropriate sensitivity. The other side of the question is, why do we state the nature of the object not in these terms but in terms of distance-experience? I assume that the reason for this is that the scientist is seeking for what is permanent, that he finds this in the uniformities of the processes, that it is in terms of these uniformities that he defines his objects, and that this therefore is what he means when he speaks of conceptual objects. The scientist seems thus to have transcended the perceptual field. He seems to be dealing no longer either with distance-or with contact-experience, but rather with an organized system of changes which may in perceptual experience reflect themselves in either of these categories, but which is really entirely independent of such experience. The door thus is thrown open to the representative theory of perception. The perceptual content of the object comes
(152) to be defined in terms of sense-data, which are correlated with scientific objects, but have their proper locus in a consciousness, or else lie somewhere between the mind and nature.
There are two reasons why the scientist does not make use of this realm of consciousness, either in terms of consciousness or in terms of sense data. The first is that the world which is out there in his observations and experiments is the world of reality. No satisfactory line can be drawn that will leave what is real for him on one side and sense-data on the other. This fact becomes particularly evident when we consider what we term the meanings of things. These are inextricably interwoven with what must be termed consciousness; yet these meanings are the very nature of the scientific objects. The other reason is that so-called consciousness has now been brought within the range of biologic science. Mind can no longer be put outside of nature.
As long as the scientist could be at home in a world of Newtonian mechanics, before the atom disintegrated into particles of electricity, he could look with Du Bois-Reymond's telescopic eye through the masses of things down to ultimate particles whose motions followed relatively simple laws. The connection of scientific with perceptual objects was close enough to make him feel that his observations and experiments were in the same world with the objects of his science. It is true that the so-called sensory qualities, whether secondary or primary, could not be the actual characters of the object; but the agreement between the Euclidean space of science and that of perception was adequate, and the correlation of weight with mass was so complete that the imaginary subdivision of the matter of sense-perception still paralleled the analyses of physics. The scientist was compelled, of course, so far as he considered the matter, to locate all secondary qualities in consciousness,
(153) since the mechanical universe consisted simply of mass-particles in motion, and of ether waves. In the physical world it was types of motion that corresponded to color, sound, taste, odor and temperature. If the scientist had been consistent he would have had to relegate to consciousness the resistances of things as well; but as a matter of fact nothing interfered with his building up mechanical models of mass-particles in his perceptual imagination of what was going on in nature. Lord Kelvin is an excellent example of the scientist of the period that had come to terms with thermo-dynamics and electro-magnetism, yet still sought to preserve in the vortices and stresses of the ether a mechanical picture of the anatomy of the universe within which the perceptual imagination could be at home. Millikan's oil-drops, Rutherford's photographs of the bombardment of atoms by alpha-particles, and the models of the Bohr atom, seemed to connect the galaxies of the submicroscopical world with those of stellar space. As long as pushing and resistant things with calculable velocities could be located in space, scientific imagination did not leave the world of perception.
It is relativity that changed all this. In the geometry of a Minkowski space-time perceptual motion disappears. The ether has vanished, and events take the place of physical things. Time is assimilated to space, and the mind with its own spatial frame of reference adventures into this space-time whose curvature corresponds to the gravitational constant. The result is to carry the whole world of perception and perceptual imagination into perspectives that exhibit only a logical correlation between patterns affected with transformation formulae and events in a four dimensional time-space and intervals between them. By definition both events and intervals here lie outside of any experience. We reach them by way of the reference in the knowledge process
(154) to something beyond itself, and by a theory of probability. In our mathematical formulations of scientific experience we have come upon a cipher that seems to refer to inexperiencable entities and their mutual relations; and this hypostasized structure of logical entities satisfies our desire for an absolute reality to which our confessedly relative experience shall refer.
Yet, however far the scientists' procedure may go it never reaches any situation except one in which a transformation , or a possible transformation, takes place. If we ask for what lies back of all transformations, we are asking for something outside of any experience, whether actual or imaginary. We do, for example, postulate stages of development of the universe which antedate any possible human experience, but in imagination these are spread before an inner eye, or at least before a mind. If we exclude the imagination, we have the abstractions of symbolic analysis, which are of the same logical character as the transformation formulae to which I have referred. If I say that this is a color, and hold this color in its universality before my mind, I am isolating that which enables me to reduce any other visual experience to the present experience in so far as this is occupied with visual as distinct from auditory or sensuous qualities of things. There is a common way of acting toward all qualities that exist for the eye, as there is another way of acting toward those that exist for the ear; and the isolation of this typical reaction enables me to "transform" my conduct toward red into that toward blue, in so far as I am able to react to color by one response and to sound by another.
What we designate as "mental" is this attitude of isolation of common features that call out identical responses provided that we have symbols by which we refer to them. To set up a world of essences or universals or eternal objects within
(155) which these entities subsist or exist is parallel to the procedure of setting up a Minkowski space-time or a four dimensional aggregate of events. Presumably objects in motion with reference to us have different values spatially, temporally and in terms of mass from those at rest; and if we are to measure them as we measure objects at rest about us we must isolate the common feature-viz., the relational character of space and time common to the two situations of rest and motion. The expression of this common feature in the transformation formulae that Larmor and Lorentz worked out in order to give invariance to the Maxwell equations carries with it most interesting implications, especially with reference to the constant velocity of light; but it does not change the fact that what is going on is measurement in one situation of something whose measurable characters are partly dependent upon the fact that it is in another situation as well. It does not carry with it the necessity of setting up a space-time realm. The postulation of such a realm rests upon the assumption that because the same object may be dealt with either as at rest or in motion, it must therefore be affected with the coordinate of time in the same fashion in each situation. This assumption consequently wipes out motion and substitutes for it geometrical determination in a four dimensional realm outside of any possible experience.
It all comes back to this; the separation of space and time is essential to the perceptual fact of motion. There must be a timeless space within which motion takes place. But timeless spaces differ according as the individual or "percipient event" is in motion or at rest. If, as in the example of the railway train, we transfer ourselves from the space of the compartment within the train to that of the landscape, then the space of the compartment within the train is in motion, and that space, if measured, will be measured in units- differing from those of the space of the
(156) landscape. The same is true of the times. Given the relational character of space and time, their structural characters differ according to what may be called the temporal perspective of the individual. And, as Whitehead insists, these differences belong to nature. They are not subjective. But the scientist is satisfied with the transformation from one situation to another. Whether he accepts a geometry of space-time or not, his operation is occupied only with the transformation and does not require the assumption of a transcendent space-time. The physicist's aim is an invariant set of equations that will formulate the conditions under which we may control our physical conduct. In order to reach an invariance for the Maxwell equations, and to interpret the Michelson-Morley experiment, it became necessary to work out transformations from one temporal perspective to another. The possibility of successful formulae of transformation involves numerical statements identical for all different perspectives. These can be expressed in terms of intersections of events, and intervals between them, in an absolute space-time; but such a formulation is not made use of in the physicist's transformations. In every instance the physicist is in a perceptual world, transforming, so far as may be necessary, one perceptual perspective into another. Nor is the situation changed when we pass from the special to the general principle of relativity. In the application of the special theory the coordinates have immediate physical significance, denoting measures expressed in terms of standard measuring-rods and clocks, while in the general theory the numbers refer to a continuum lying, as we have seen, outside of any possible experience. The constants remain therefore mere numbers in terms of which natural laws can be so expressed that they hold in any frame of reference, that a transformation of axes of coordinate systems may be substituted for a field of gravita-
(157) -tional force, and, in general, that the metrical properties of space are wholly determined by the masses of bodies. Einstein's genius has on the basis of these principles elaborated a physical theory which not only carries through to logical completeness the relativity of space and time, but also gives a more perfect and accurate formulation of physical processes--one, moreover, that has stood the test of observation and experiment at those points at which it could be brought to the test. In the special theory we are formulating measurable values-in terms of different systems of coordinates -- for one perceptual perspective in terms of another perceptual perspective, i.e., we are dealing with local times and local measuring rods. The numbers have physical significance. In the general theory we obtain equations that are covariant, i.e., we do not transform from one set of coordinates to another, but obtain expressions that hold for all possible sets of coordinates. The numbers evidently cannot express the measures of time and space in any one coordinate system, as distinct from another. They arise out of the possibility of transformation from any possible set to any other possible set. They are reached by the use of a Riemannian geometry of a four-dimensional manifold, and tensor mathematics. These provide the mathematical apparatus for the measurement of the intervals in a continuum however it may be deformed -- a continuum, in this case, of space-time, and determine the form which equations that express natural laws must have if they are to hold for every set of coordinates.
It is as if we should take the formula by which we transform the value of the dollar in 1913 into that of 1930, and into that of any other possible date in human history, and should pass over from the constants of food, clothing and the like and what they will exchange for, to a generalized economic field in which the distances between the exchange-
(158) -able goods we possess and those we want could be expressed in a certain formula which would serve in any possible situation. If we should set up such a world of determined intervals between abstract values, and if in our effort to give our economic laws such a formulation that they would obtain in any possible situation, we should state the values in terms of their scarcity, i.e., in terms of the intervals-if we succeeded in this undertaking, we might conceive of this abstract economic world as the world of real valuation, of which our experienced economic situations were subjective reflections. The orthodox school of economics did in a manner thus reduce all values to the work necessary for their production, that is, to the economic interval between the raw material and the finished product, and sought thus within an economic process to obtain more exact laws of exchange such as should be capable of universal application within all economic situations. The Austrian school, however, brought out the unique character of the want that lies behind the valuation, which therefore could not be dissolved into the abstract formulae of exchange.
I do not wish to pursue too far a somewhat far-fetched analogy; yet it may serve to bring out the fallacy of reference common to both cases. The constants that appear in formulae of exchange or transformation refer not to entities that can be defined in terms of symbols of exchange or transformation, but to such uniformities in these processes as enable us to give them the widest generalization. I make bold to say that the successful development of the theory of general relativity, with its seeming reference beyond experience, is due to the power of its mathematical apparatus, which has exploited the conception of the "field," taken from electro-magnetism and carried over to gravitation. The generalization belonging to the, Riemannian geometry, the Gaussian coordinates, and the Tensor Mathematics, ap-
(159) -plied to the field of physics, introduce a new entity only in so far as their application presupposes a four-dimensional manifold within which time is one dimension. The assimilation of time to space, as we have seen, divests reality of the character of novelty inherent in change. It relegates change, including motion, to subjective experience, and substitutes for it a geometry of space-time within which every event is inexorably charted. In the Newtonian mechanics, given uniformities of nature such as the law of gravitation, a like determination of physical events was involved; but the determination did not flow from formal characters in which a lapse of time could be equated with a spatial extent, or in which spatial and temporal extents fell together as predetermined numbers in the determination of an interval. Space, whether Euclidean or non-Euclidean, was a necessary frame-work within which change must take place, and the changes that had taken place could be spatially charted and geometrically described; but none of this necessity spread over into the causes of motion. The mind might be wholly possessed by a faith that the laws of change were as inexorable as were the structural characters of space; but it was a faith, resting at best upon an induction that could never go beyond a presumption. A change might always conceivably be other than it is. A geometrical structure and what follows from that structure can never conceivably be other than it is. In a space-time whose structure is once given nothing could conceivably be other than it is. As long, then, as nature appears in experience with the brute constants we discover, which change under our further investigation, the reference of formulae such as those of generalized relativity will always be to a situation that may conceivably be other than it is. They can never disappear, in our thinking of the world, into the geometry of a space-time. For example, it will always be conceivable that the
(160) constant of gravitation will prove to be such as not to resolve itself into curvatures of space-time. I recur to the statement I made earlier, that the reference of general relativity as well as that of special relativity is to the field of experience within which scientific problems, observations and experiments lie.
