The Philosophy of the Act
Essay 12 The Relativity of Objects
IN A passing world objects do not pass. In so far as the object is spatially defined, it does not pass if it keeps the same spatial content, as determined by its reference to some percipient event, or individual, in a consentient set,' or if it retains the same form with a different spatial content, as in the case of a wave. If a like spatial form is continually occupied by characters that do not pass, such as hardness or color, we conceive of it as occupied by a something, a matter. The form within a consentient set is determined by reference to a percipient individual. This determination takes place through the sensuous experience of the individual. The physical object is one that retains the same character of the effective occupation of space within the range of manipulation. This involves a sphere of distance from the individual which is within the range of continual contact. The hand is the organ which is the determining factor within this sphere. Through vision there arises an experience of form that varies but slightly within this sphere, or, if it does vary, the implications of the variation in terms of contact are readily perceived. A certain form, such as the circular form which is revealed by contact, is always to be secured by giving the object a certain set of positions. The perspectives of vision can always be reduced to a standard set by movements of the object. The object appears most fully in experience when the contacts of all its surfaces enter into experience at once, as in manipulation. Our distance experience of physical things implies a constant perception of the distant object in its reference to the experience of it in this position of normal manipulation.
(167) This implies the plotting of the space of a consentient set in terms of the co-ordinates of this normal manipulatory area.
The plotting of the object in terms of the co-ordinates of the manipulatory sphere may lead to objects which are largely identical for individuals whose spheres are at varying distances from the object. The spatial perspectives will vary greatly in vision, but their perceptual reduction to the co-ordinates of these manipulatory spheres will yield a uniformity of outline and surface. This is also true if we assume that the individuals are moving with reference to one another with anything but great velocities. That is, the object which one person in a train sees and the same object as seen by one outside the train may be identical for the two individuals when seen in terms of their manipulation of the objects. They see the same trees and stones. What will not be the same for the two individuals will be the motion and rest of the objects. All the bodies at rest for the man outside the train will be in motion for the man within the train, and vice versa. And objects moving for the man outside the train will be objects moving at different velocities, in some cases with different directions, and in the case of the same velocity and direction, at rest for the man in the train. If the velocity should approach that of light, the object seen by the two individuals would vary in diameter in the direction of the motion. That is, events which are contemporaneous for one individual will not be contemporaneous for the other. Two events, one at each end of the car, happening contemporaneously for the traveler, would not be absolutely contemporaneous for the observer outside the train. if we recognize the finite velocity of light and assume a power of discrimination equal to distinguishing the differences involved. If the velocity of light were infinite, these differences would not appear. As the velocity of light is finite, the wave which leaves one object falling at one end of the train would reach the outside observer sooner or later than the light wave from the object at the other end of the car because the distance will be shorter or longer between his eye and the object in question than it will be for the man in the
(168) train, where the distance between the object and the traveler does not change. As the light waves from the two objects, which fall simultaneously for the man in the train, have to travel over distances which, when they reach his eyes, will have been rendered different by the movement of the train for the man outside the train, the fall of the two objects will not be simultaneous for this man. The perception of objects at a distance would then be of objects of manipulation which would vary for the two individuals if they were moving with reference to each other at very high velocities. It is also evident that, if contemporaneities varied in extents of time, time intervals would also differ. While these differences would be perceptible only in case of high velocities, they are involved in any case of the movement of what may be called the consentient sets of two individuals with reference to each other. While we are able to perceive objects differing in spatial perspectives as identical in size if they are so identical in the manipulatory spheres, we would not be able so to see them under the same temporal perspectives if our perceptions were quick enough to catch the variations which temporal perspectives introduce.
This fact is of importance in making evident that the spatiotemporal dimensions of objects in one consentient set are not the same as in another, the assumption being that different consentient sets are moving with reference to one another. As a consentient set is determined only by the persistent relation of here and there with reference to a percipient individual, we see that the outlines and physical characters of objects vary with reference to the individual and that these differences belong to the physical worlds within which the individuals exist, not to an experience which can be abstracted from this world. The physical objects are determined in their objective character in the character with which science deals, by their relations percipient individual. For the differences of temporal perspective affect not only the outlines and surfaces of objects and the intervals between their happenings but also their mass or inertia. There exist, then, objective worlds which are relative
(169) to individuals, if we are willing to recognize temporal perspectives owing to movement of different consentient sets with reference to one another. If we assume an absolute space, with, say, the co-ordinates of the so-called fixed stars, these different worlds will be reduced to a real world with identical objects and identical time intervals, of which these different worlds will be but subjective pictures. Abandoning an absolute space, there are no absolute dimensions and physical characters of objects. In an absolute space it would be obviously impossible that an object should have different dimensions simply because it has that appearance to observers who observe it under different conditions of motion and rest. Its real dimensions would be those which it had in an absolute space, and the intervals which lay between its changes would be those which the absolute distances between objects in that space measured. The rising of the sun and the going-down thereof could be but the mistaken perception of the motion of the earth. These two sets cannot both be real in the same absolute space. If, however, there is no such absolute space and time, but only the spaces and times of different consentient sets answering to the percipients who determine these, then these different worlds can be no longer referred to an absolute world.
If we recognize that, instead of space being static, what we call the space of our world is passing as well as its events, then the seeming impossibility of the same things belonging to two different spatial orders disappears. What is meant by space passing is that its points are recognized as routes which from the standpoint of another consentient set become lines in that set. From the standpoint of the co-ordinates of the fixed stars, every point which is determined on the surface of the earth is a route which has become a line, and lines have become surfaces, and surfaces volumes. When it is recognized that there is no system of co-ordinates which is absolute, then there is no point that is anything more than the assembling of a series of positions which from one standpoint may all be regarded as one position, while from any one of an indefinite number of standpoints they
(170) may be regarded as lying differently in one of the three-way spreads of extension. Adopting for the moment the conception of instantaneousness, and considering simply spatial perspectives, the line between the individual and a distant point is itself a point. The line may be conceived of as the locus of an infinite number of events stretching from the individual to the point in question. The perspective reduces them to a single event-particle. If the perspective is shifted, and one stands to one side, the point becomes a line of varying extent as one comes to take a position that is closer and closer to that of perpendicularity to the line.
If one moves about in a circle from the original position of the. individual to the point which was the object of vision, the line in question would not only increase in length up to a maximum at the point of perpendicularity, and then would decrease again in length, reaching a point again when the individual occupied what had been the point of vision and envisaged the point which he had occupied at first, but also the line would be at an angle which would vary through all the 180 degrees. It would also be on the left of the individual if he were moving to the right, while the line would have been on the right if he had moved to the left about the same circle. If we assume that the up-and-down coordinate is determined by the longitudinal axis of the individual in question, then a movement in a circle in the plane of that axis of the organism would give to the line every possible degree of angularity to the co-ordinate, from horizontality to uprightness. As the assumption is that of instantaneity, the presentation of motion is paradoxical. What is involved, however, is merely that one should conceive of one's self at the instant as being at any one of the points which such a motion is conceived as passing through.
It is obvious that a visual, or distant, object, which is made up of visual elements, may be indefinitely distorted by the occupation of these different positions in an instantaneous space. It is, however, the nature of our percepts that they can exist with the values of the manipulatory sphere, that is, that we can see
(171) them with the dimensions they would have if they were brought within the field in which we could both handle and see them. In this sphere it is the manipulatory experience that determines the dimensions, and we see those visual characters as the real characters of the object which we see when we are manipulating the object. The laws of projective geometry express the rational character of space, which makes this translation of the distant dimensions into those of the manipulatory sphere possible. These so-called distortions are only distortions in so far as we have present the visual form both at a distance and in the manipulatory sphere. Otherwise the visual form at a distance is the percept at a distance and would be a distortion if seen with the values of the manipulatory sphere, e.g., if we see a distant object through a telescope. The location of objects seen in a mirror and their forms seen through refracting mediums are instances of the so-called errors of perception, which involve the comparison of the visual, or distance, form with that of the manipulatory sphere. When, then, we state that we see objects as having the forms of the manipulatory sphere, we imply such a comparison, unless we are referring to the attitudes which we take toward the distant objects. These attitudes are those which, if carried out into overt action, would lead to movements which, if persevered in, would overcome the distances and bring the objects into the manipulatory sphere. The result of the act implied in the attitude is compared with the immediate experience. This may take place in experience, but it is not necessary to perception, nor does it ordinarily characterize our perception. What is characteristic of ordinary perception is the adjustment of the organism with reference to the distance field, which makes normal conduct in that field possible. This adjustment leads in conduct to the results to which I have referred. They need not be in experience in this form of imagery, though they can appear at any instant in which they become of assistance in controlling conduct.
What is of importance, in considering the situation, is the fact that, in bringing in this actual or possible comparison, we
(172) are deserting our instantaneous space, for it is only in the actual, or imagined, or conceived accomplishment of the act that the comparison can take place. When we do this, we prolong the instantaneous space beyond the hypothetical instant. In the instantaneous space there is and can be no error, for even the presence of the imagery of the distant object at the instant in the experience implies the completion of the act, and this involves time. Imagery is, of course, present in perception, but in so far as the immediate attitude is concerned it lies in the distant object with its appropriate perspective. The object filled out with imagery is still a distant object. In correcting the perception of the object seen in a mirror, or when partially immersed in water, we make a comparison. We do not immediately see the object behind us, nor do we see a straight stick. It is the assumption of such a comparison that the instantaneous space persists, or, at least, if the space of the instant has passed on, that those which succeed it are identical with it in respect to their relations to the individual and the objects in his perception.
This assumption not only is borne out in our everyday conduct but also has been borne out in scientific observation up to a relatively recent period. As I pointed out earlier, it would not be borne out in immediate experience if we were moving relatively to other things and their consentient sets with high velocities and were able to perceive objects passing us with these enormous velocities. The situation would be analogous to that of the mirror object or of that of the stick partially immersed in water. We would see one thing and have to correct the perception by past experience to get the other, i.e., the object as it would exist in our manipulatory sphere; and, when we so corrected it, we would he obliged to recognize that the spatiotemporal relations of the objects moving with the high velocity were not identical with those of our so-called instantaneous space. That is, we would see things with dimensions which would have a meaning for our manipulatory spheres which would not be borne out by the experience of getting them into those spheres. And we could not translate these errors into laws
(173) of reflection and refraction which implied a static space within which the mirror and the water image exist. We can get these images and the objects in their proper places into the same space; we could not do this with the objects observed moving at these high velocities. With the proper Lorentz transformations, we could translate from the one situation to the other, but they would remain objects in different time-space systems. We would never be able to get them into the same perceptual world as we understand this in the case of the so-called errors of perception.