Popular Science Monthly/Volume 18/February 1881/Optical Illusions of Motion
By SILVANUS P. THOMPSON, B. A., D. SC.
THERE are frequent occasions of conflict between the receptive faculties of the senses and the reflective faculties of the intellect, occasions on which the mind, prejudging of the sensation received, assigns it to a non-existent cause. Of all the senses none is more frequently the seat of such deceptive judgments than that of sight; and in the science of physiological optics a very considerable share of attention is claimed by optical illusions. For the purposes of convenience, we may draw a distinction between these illusions, which are the direct result of certain properties or imperfections of the eye as an optical instrument, and those which arise from obliquities of judgment in interpreting the sensations optically impressed upon the retina of the eye. In practice, however, it is almost impossible to draw a hard-and-fast line between the two classes of illusions, almost all partaking of both characters. Thus, for example, it has lately been shown that we habitually draw geometrical forms too large in the horizontal dimension as compared with their vertical dimension; we draw oblate ellipses where we intend to draw circles; the explanation of this being that with our two eyes we really see spheres as oblate ellipses. Here is, in fact, an illusion of pure association—yet based upon the facts of physical and physiological optics. So, again, certain inequalities in the curvature of the lenses of the eye, producing the optical defect of astigmatism, cause objects that are horizontal in position to form images at shorter (or longer as the case may be) distances from the eye than the images of vertical objects; the result being that, unless the defect is corrected by suitable lenses, vertical and horizontal objects (such as the bars of a window) do not appear to be at the same distance from the observer, though really equally remote. This would, at first sight, appear to be a purely physical illusion, and not psychological. Nevertheless, a little consideration will show that since our perception of distance is a psychological factor in the case, and that this perception is based in part upon the muscular sensations of adjustment of the lenses of the eye to exact focus, the illusion is one which has a psychological as well as a physical raison d'être. Again, take some illusions ordinarily supposed to be one purely of mental association: the common illusion of every day, that the sun or moon when a few degrees from the horizon looks larger than when high in the sky, appears at first sight to be due simply to the fact that when the orb is near the horizon the distant objects upon that horizon whose size we know, or can judge of, appear relatively small, and the sun's disk relatively large—in fact, that the illusion is one purely of association of ideas. Nevertheless, when we look a little closer into the matter, we find that our simplest conceptions of angular or apparent magnitude are very closely bound up with, if not directly due to, the sensations of muscular fatigue in moving the eyeball or head so as to bring the successive parts of the object into the center of vision.
Hence, although optical illusions are of many diverse kinds—illusions of color, illusions of form, illusions of size, illusions of distance, illusions of solidity, and illusions of motion—they have all to be considered from the twofold standpoint, the purely optical and the psychological.
For some months the writer of this article was engaged upon a study of one set of optical illusions, namely, the illusions of motion, and a number of observations, collected at intervals over several years, have been added by him to the stock of knowledge previously gleaned by Brewster, Wheatstone, Faraday, Plateau, and others. Brewster made a number of observations, in the early days of railways, on the various illusions which can be found by watching objects from a moving train; Wheatstone investigated a curious case of apparent fluttering motion at the border of two brightly illuminated colored surfaces—due probably to the attempt of the unachromatic eye to obtain fruitlessly a distinct focus of the border-line between the unequally refrangible colors—known as the illusion of the "Fluttering Hearts"; Faraday investigated the illusions produced by intermittent views of moving objects, since developed in the phenakistiscope and zoetrope, and kindred toys, and due to persistence of visual impressions. Brewster, moreover, drew attention to the existence of another class of illusions—illusions of subjective complementary—motion the typical case of which occurs also in railway-traveling. After looking out of the window at the pebbles and other objects lying beside the line, as they pass before the eyes, let the eyes be closed suddenly, when there will at once be perceived an apparent motion in the opposite sense, undistinguishable forms and patches of light seeming to rush past the blank field. This was recorded by Sir David in 1848, and the phenomenon was referred by him to a subjective complementary motion going on simultaneously, and so causing a compensation of the impressions moving over the retina. A kindred phenomenon had been even earlier noted by R. Addams, who, in 1834, narrated how, after looking for some time at a waterfall and then at the water-worn rocks immediately contiguous, he saw the rocky surface as if in motion upward with an apparent velocity equal to that of the descending water. This he ascribed to an unconscious slipping of the inferior and superior recti muscles of the eyeballs, which he thought occurred while watching the falling water, and which he supposed to continue unconsciously after the gaze had been transferred to stationary objects. This explanation differs from the one offered by Brewster, namely, that there was a subjective opposite movement going on simultaneously, so causing a compensation of the impressions moving over the retina. Brewster's hypothesis is, indeed, extremely vague, and is neither physical nor psychological in any exact sense. If understood physically, it means that there is actually motion in the retina itself, which is hardly conceivable, since the structure of the rods and cones almost precludes even any idea of vibration, or of propagation of waves of motion by vibration, much less any movements of them as a whole. And, if the explanation is intended as a psychological one, something further is needful before the principle of compensation here laid down could become intelligible.
The first experiments made by the writer of this article upon illusions of motion arose from a casual observation in 1876. He had been preparing, for the purpose of testing astigmatism, a set of concentric circles in black and white, such as those shown in Fig. 1. Happening
to shake the sheet on which the circles were drawn, he noticed an apparent motion of rotation to be set up. The illusion is easily produced by imparting to the pattern a slight motion of the same character as that adopted in rinsing out a pail, but with a very minute radius of motion. All the circles will appear to rotate with the same angular velocity as that imparted. Now, undoubtedly the persistence of visual impressions has a good deal to do with the production of this illusion, which, by the way, succeeds best when the circles make from two to four turns in a second, and when the radius of the imparted motion is equal to the thickness of one ring, so that each black or white band is displaced through a distance equal to its own width in all directions successively. Nevertheless, the persistence of visual impressions will not explain all the facts of this curious illusion: for, in the first place, it is found that for increasing distances from the eye the concentric rings must be made wider if the illusion is to succeed; there being apparently one particular magnitude of their images on the retinæ which favors the production of the illusion. Again, if two such "strobic circles" (as I have called them) are printed side by side on one card, that set of circles seems to turn most effectively at which the eye is not looking. On stopping the "rinsing motion" suddenly, there appears to be, for an instant, a reverse motion. Finally, if a set of circles is "rotated" while another set lies motionless within the field of view, the second set will appear to rotate when the first are "rotated" in the manner described above. It is possible, also, to have a number of such apparent motions going on at once independently in one field of view. Fig. 2 shows a compound pattern, containing an
interior set of concentric circles and six internally-toothed wheels. When a very minute "rinsing" motion is imparted to this figure, the circles appear to whirl round while the toothed-wheels work slowly backward, moving through one tooth while the circles whirl round once. Here, again, persistence of vision is concerned—but not exclusively.
Dr. Emile Javal, the able director of the Ophthalmological Laboratory of the Sorbonne, has recently advanced an explanation of these illusions different from that adopted by the writer, and in substance identical with that advanced by R. Addams in the case of the water-fall illusion. He avers that the eye, in order to observe a movement, follows the moving body for an instant and then suddenly slips back; that this oscillation, frequently repeated, is associated with a sensation of motion in the particular direction in question; and that when the eye is subsequently directed to a stationary object it continues the habit of thus oscillating, causing the observer to attribute to the object a velocity of opposite sign to that just observed. M. Javal alleges in support of this view the appearance presented in the ophthalmoscope of the retina of a person affected with nystagmus. This affection consists in continual rapid involuntary movements to and fro of the eye. The retina, under these circumstances, appears to be animated with a vibratory motion which M. Javal declares to be identical in character with the apparent movements of the circles. In another place, M. Javal has endeavored to prove that the interior and exterior recti muscles of the eyeball are more prone to this slipping than are the superior and inferior recti, and that these illusions of complementary motion succeed better for motions in an horizontal sense than for vertical and oblique motions. My own experience, and that of other observers, admits of no such conclusion being drawn.
An experiment of Brewster's, which the writer tried without knowing at the time that Brewster had employed it, has an important bearing on the muscular-slipping theory. A disk marked out into black and white sectors, as in Fig. 3, was caused to rotate at about one revolution per second, so that the separate sensations of black and white were not confused. The eye was steadily directed for twenty or thirty seconds at the central point, and then the gaze was suddenly turned upon some fixed objects, or at a distant landscape. For two
or three seconds a hazy rotation is noticed at the center of the field of vision. Now, if the muscular-slipping theory holds good, the complementary movement of rotation must be due to a slipping of the whole of the muscles of the eyeball, and would affect objects all over the field of vision with an equal angular velocity. This is not the case, the apparent complementary rotation being confined to the central field, and with apparent angular velocities increasing toward the center of vision. Furthermore, I have arranged two such disks so that they could be simultaneously in the field of view while rotating in opposite directions. When the gaze was directed first at a point between them and then at fixed objects, there appeared to be two portions of the field of view rotating, and animated with rotations in opposed senses. Clearly, the eye can not slip round in opposite directions at the same time. In all these illusions, moreover, it is found that this illusory complementary motion only occurs over limited parts of the field of view—namely, those which correspond to the portions of the retina which previously received the moving images. Thus, if a waterfall be looked at—as in Addams's observation—the upward illusory after-motion is confined to a vertical streak across the field of vision. This fact alone is sufficient to negative the theory of muscular slip.
The final test to which I have appealed is, if possible, even more conclusive. It is probably a familiar observation that the end of the last carriage of a retreating railway-train appears to shrink down smaller and smaller as it subtends a decreasing angular magnitude in the field of view. After looking at this motion for a sufficient number of seconds to fatigue the eye, stationary objects appear to be expanding. To produce this illusion more effectually, I take a disk like that shown in Fig. 4 (the figure is quarter actual size), marked out in spirals of white and black. If this is slowly rotated—say at about one revolution in two seconds—the whole pattern appears either to be running into, or running out of, the center of the disk: there is a motion of convergence or divergence, according to the sense of the rotation. Let the disk be turned so as to cause an apparent convergence from all sides to the center, and let the eye steadily watch the center for about a minute, or until the fatigue becomes almost unendurable. Then look at any fixed object—the pattern of the wall-paper, or the dial of a clock—the object so regarded will for some two, or three, or more seconds, appear to be expanding from the center outward. The effect is still more startling if the object thus viewed be the face of a familiar friend. It is quite evident that the eyeball can not slip in all directions at once.
I have, therefore, somewhat reluctantly been led to propound an explanation for these illusions, embodying the theory of them in an empirical law based upon the physical fact of retinal fatigue, and on the psychological fact of association of contrasts. It is as follows: The retina ceases to perceive as a motion a steady succession of images that pass over a particular region for a sufficient time to induce fatigue; and, on a portion of the retina so affected, the image of a body not in motion appears by contrast to be moving in a complementary direction. This law is precisely similar to that of the complementary subjective colors seen after fatiguing the retina by the image of a colored body. Similar laws of physico-psychological after-effects are abundant. A steady sound of one constant pitch ceases to be heard until we become aware of it by its cessation. A steady light of one color, such as the yellow light of gas-flames, ceases to be noticed as a yellow light until some other color-sensation break the illusion. The same is true of smells, of tastes, of the sensations of temperature, of the sensation of rotation after a waltz, and of many others. All these are probably only different instances of the operation of some much more general physico-psychological law. It is quite consonant with these kindred phenomena that, when any region of the retina is affected by an image of objects moving steadily across the corresponding portion of the field of view in any given direction, that portion of the retina gradually loses consciousness of the motion, and perceives it only as a steady sensation, or as one of approximate rest. When, however, an object really at rest is looked at, the associative faculty seizes upon the contrast in the sensations affecting that region, and interprets the new sensation by imputing a motion in the opposite sense to the objects occupying the corresponding portion of the field of vision. I have proposed to give to the empirical law expressing these matters the name of the law of subjective complementary motion.
It is impossible to quit the subject without pointing out two lines of thought suggested by that which has been advanced.
Firstly, it is conceivable that the explanation here propounded may at some future time be superseded by a better hypothesis of a more purely physical character. Suppose, for example, that it could be shown—what I have reason to suspect, but have been foiled in all attempts to prove in any experimental fashion—that the eye has the power of altering at will the actual size of the retinal images by a double muscular adjustment between the magnifying power of the lenses of the eye and the distance of their equivalent optical center from the surface of the retina, such a fact, once established, would entirely cut away the significance of my crucial test with the rotating spirals; and the apparent expansions and contractions of objects would be merely due to the continuous attempts of the eye to retain the retinal images of one constant size. If this were so (though I have failed in every kind of attempt to devise some satisfactory test), it might also explain one little matter that is still very mysterious and unexplainable, namely, that in these illusions of expansion and contraction the changes of apparent magnitude often appear to take place by discontinuous jumps rather than by steady motions.
Secondly, it is found that these different illusions affect different individuals with very different degrees of success, some persons being much more sensitive than others to the after-workings of the subjective motion; and, indeed, there are individuals in whose case it is almost impossible to produce the illusions. Doubtless some of these differences may be accounted for by defects of vision, astigmatism, achromatopsy, myopy, and the like. But there is also a time-element in the case which varies very greatly with individuals, and even varies with the nervous states of the same individual. And this suggests the further thought that a careful comparison of individuals relatively to their illusion-capacity might elicit some interesting and perhaps valuable facts concerning the relation between the states of brain-organization and the sensations of the more highly specialized organs of sense.—Brain.