Contents of Chapter
1. Moving Objects That Appear Stationery
2. More Movement That We Do Not See. Observations Made on Phonograph Records and Telegraph Wires
3. Again the Law of Proximity and the Law of Minimum Change
4. Further Observations on Perceived Direction; Movement Seen Through Apertures
5. Perceived Velocity: The Perambulator Races the Express Train
6. Perceived Movement Where There is No Motion: The Principles of the Motion Picture
7. Apparent and Real Movement
8. The Replicated Rider and the Question of Optimum Exposure Times
9. Modes of Appearance of Movement
10. A Car Departs: The Law of Proximity and the Objective Set
11. The Law of Similarity Becomes a Law of Minimum Change; The Role of Parts in the Whole
12. The Law of Total Absorption
13. Non-Intersecting and Smoothly Continuing Movement
14. The Significance of the Overall Properties of the Course of Movement Itself
15. The Effect of Figural Properties and of the Surrounding Field
16. Natural Components of Motion: The Secret of the Rolling Wheel
17. Independent and Dependent Movements. The Perception of Causality

1. Moving Objects That Appear Stationery

When do we see movement? The answer seems obvious: when something moves before our eyes. Yet quite frequently a moving object appears at rest, or a stationary one seems to move. These phenomena are not restricted to instances where movement and rest are interchanged, as when the moon appears to drift through the clouds; a case which we will discuss in the next chapter.

If a movement is to be seen, it must be neither too slow nor too fast. There are upper and lower 'thresholds' for movement.

If you look steadily at the hour hand of a watch for a minute or two, it ends at a place different from its starting point although it seemed to be stationary all along. Some people see it creep forward a trifle, especially just as it reaches or leaves some numeral or mark. Yet it is very obviously at rest between these movements, and then is 'suddenly' at a new position. In spite of the protests of common sense, then, we can see a change of position without movement.

The wheel of a speeding car, or a spinning top, provides the opposite case. Where the rotating spokes should be, we see only a veil lying calmly on the surface; the colored sectors of the top are replaced by a single motionless fused color. Even before the wheel attains this speed, we give up seeing its true motion. As it turns faster and faster the number of spokes or sectors begins to increase, and at the same time the smooth rotation in one direction gives way to jerks and leaps and counterrotations that make the whole process seem restless and uneven. If the speed of rotation increases further, we see only vague flecks of color, far more numerous than the spokes, which become still smaller and more numerous as we watch. As they multiply, they move less and less, until they only seem to twitch a little. The twitching then yields to stationary changes of hue or brightness, called flicker. When even this ceases, and at the same time the number of color flecks becomes infinite, the stage of full color mixture has been reached, at the so-called 'critical flicker frequency.'

Even non-cyclical motion becomes invisible if it is fast enough. A low--flying jet roaring across the window may darken the room for a moment, but no one can say if the shadow came from the right or the left.

2. More Movement That We Do Not See. Observations Made on Phonograph Records and Telegraph Wires

If you watch a phonograph record, you can see the specks of dust that may be on it go around and around in busy circles, but the grooves themselves do not seem to move. Only at the edges do you see a hurried and apparently aimless jerking back and forth. The inmost groove, in which the needle will eventually be trapped, also appears at rest if it was concentrically cut. Even if it was not, if its center lies off the axis of rotation, the inner groove doesn't seem to follow the general rotation the way the dust does. As the entire record rotates, the groove seems to be carried around in a small circle without rotating around itself. (See Fig. 460). Its apparent motion is like the actual motion of the ring around the cam at the valve of a steam engine. If the cam rotates, the ring is turned through a small circle without rotating itself.

Fig. 460 A circle, actually turning around an off-center axis, appears to remain upright and to make rotations whose radius is the distance between its two centers and the true axis.

On many records, there is a spiral groove in the inner portion that seems to leave the main mass of grooves at each rotation and shrink down steadily until it vanishes in the center. The same thing can be seen on rotating spirals, but there the movement is just as likely to proceed outwards from the center. In neither case does it follow the rotation.

The peculiar behavior of telegraph wires is a related phenomenon. If you watch them from the window of a moving train, they do not appear to lag behind, like the poles that flash by from time to time. They only rise and fall, rocking slightly. At their lowest point they move only slowly or even stand still for a moment, but they reach their peaks fleetingly and drop back down each time as if someone had slapped them.

The telegraph wire phenomena can readily be observed and studied if we have a rotating disc (Fig. 165) on which concentric circles are inscribed. One must look through a slit (Fig. 462) in a screen mounted close in front of the disc. The direction of illumination should coincide with the line of sight as much as possible. Of course, a straight line may also be moved behind the slit; this simplifies the drawing but complicates the engineering.

Fig. 461 Spirals rotated about their centers seem to expand or construct, and display no movement in the direction of rotation.
Fig. 462 Slit-screen set in front of a rotating disc, for the study of illusory directions of movement. A preliminary comment: the interior of stripes or lines being moved lengthwise appears at rest so long as one cannot see the ends. The impression of movement is transferred from the ends to the interior; another example of the law of maximum shape constancy (Ruhin).

3. Again the Law of Proximity and the Law of Minimum Change

How does the peculiar behavior of circles and spirals arise? The explana-tion is simplest for the concentric circle. If it has been well drawn, it is displaced only into itself as the disc rotates. Its retinal image is no different than if it were motionless. There is no reason why movement should be seen. The same situation obtains if a straight line or a rectangle, extending precisely in the directions of movement, is moved behind a slit (at least as long as the ends remain invisible). Movement is seen only if a discontinuity appears: an end, a corner, or some sort of irregularity. If the slit-screen is now removed, a phenomenon appears which seems quite reasonable at first, but more remarkable as we reflect upon it. When the whole rectangle or line becomes visible, all of it appears to move; not merely the ends but simultaneously also the middle, which was completely motionless as long as we looked through the slit. And yet we have no difficulty in imagining a rectangle that remained motionless while it was being increased at one end and decreased at the other. It is clear that, whenever possible, perceived movement takes place in a way that preserves the shape of the moving object. This requirement can be met only if the ends of the line or rectangle carry the middle along. The law of minimum change, which we have already met in Chapters 1 and 13, dominates the perception, of even the simplest displacements.

Fig. 463 The formation of the apparent direction of movement in the turning spiral. The component of motion along the dotted line vanishes; what remains effective is the component perpendicular to the curve at each point, directed toward the center.

Fig. 464 The apparent distortion of a rotated ellipse. (a) In the real movement point A1 moves to A2; (b) In the movement as it is perceived, point A1 remains on top and just slides up and down. The remaining points of the ellipse behave similarly (Misatti).

What about the instances where, although a movement is seen, it is quite different from the actual motion of the object? What about the spiral, the off-center circle, the telegraph wire? In all these cases the discontinuities that form the basis of the perception of real motion are absent. Even the places where the wires vanish behind the window frame do not function as endpoints (see Chapter 1). The edges of the frame (or of the slit) are boundaries only for the window-wall or the screen, not for what is seen beyond. If we look more closely at a part of the spiral it becomes clear that in the perceived movement the real motion has been 'decomposed' into its two principal components. One of them runs along the visually given line and thus vanishes, just as-the entire movement does in a concentric circle. The other component, almost perpendicular to the first, determines the motion that we see. The perpendicular is the shortest of all the possible components that do not vanish into the line itself. A movement along it is the shortest, as well as the slowest, possible under the prevailing conditions. We have, then, an unexpected instance of the law of proximity (Chapter 3) as well as a law of parsimony such as appeared in Chapter 13, Section 14: nothing takes place over and above what is absolutely necessary under prevailing conditions.

The same principles apply to the off-center circle. One component of the real motion, simple rotation, vanishes into its circumference. There remains the displacement of the circle as a whole, along a locus whose radius is the distance from the center of the circle to the axis of rotation. The circle continuously provides points of reference for this displacement, since some portion of its circumference is always perpendicular to the direction of movement.

In a closed or apparently endless curve, like the spiral, which is rela-tively free of inhomogeneities, one component of motion will tend to vanish along its length. This holds even if its orientation diverges substantially from the true direction of movement. Here is the reason why ellipses, as well as circles, behave as in our experiments of Chapter 13 (Fig. 464). If they are not too eccentric they circle around without changing their orientation, instead of simply rotating with the disc. As a result, they must undergo continuous distortion, unless they leave the plane of the disc altogether and take up an illusory position in three-dimensional space.

4. Further Observations on Perceived Direction; Movement Seen Through Apertures

At first glance the behavior of the telegraph wires seem to follow directly from the law of the shortest path. They move primarily at right angles to their length. This interpretation seems to be strengthened by the result of moving diagonal, lines behind as aperture in a screen - provided the aperture itself is square or circular (Fig. 465). If we introduce an extended rectangular window, however, the real movement reappears. The question then arises whether this movement is seen precisely because it is the objective one, or whether another factor is at work which merely happens, in this instance, to produce an apparent movement coincident with the real.

Figs. 465 and 466 The apparent directions of movement of diagonal lines behind apertures of various shapes. The objective movement is always from top to bottom (H. Wallach).

Fig. 465 Behind circular, square, or diamond-shaped windows the lines appear to move on a diagonal precisely at right angles to their length.
Fig. 466a If the aperture is narrow and its length coincides with the direction of movement, the apparent and real directions are identical.
Fig. 466b If the narrow aperture extends at right angles to the real movement, the apparent movement is likewise at right angles.
Fig. 466c Behind an appropriately angular aperture the diagonal lines change direction at the corners.

The answer is given as soon as we set the long edge of the rectangle at right angles to the objective motion, as in Fig. 466b (taken from Wallach, as is the rest of this discussion). Again the diagonal line seems to move along the length of the rectangle, this time perpendicular to the objective direction. If one designs an aperture of appropriate shape (Fig. 466c) the diagonal line can easily be seen turning a corner. It is evident that, behind extended apertures, the line simply moves along the long edges. It is as if the line genuinely ended at the points where it was merely concealed by the edges of the screen. The effect is that the portion of the line which you see seems to neither increase nor decrease; it changes its shape as little as possible. The discrepancies which can occur between real and. apparent directions of movement are astonishing. They far exceed the familiar 'optical illusions' of stationary configurations, both in their extent and their impressiveness.

5. Perceived Velocity: The Perambulator Races the Express Train

What determines the apparent speed of a perceived movement? The basic factor is certainly the velocity with which the inhomogeneities of the stimulus pattern move across the retina, together with the speed with which the eyes turn to keep the moving object in focus. If the image is simply displaced across the retina, the same objective movement appears almost twice as fast as when the eyes move to follow it. Furthermore, if the eye is not moved, a motion in the periphery of the retina seems slower than one which falls near the fovea (Fleischl 2882 and Tschermak 1857).

Figs. 467 and 468 The two principal bases of perceived movement.

Fig. 467 The eye is stationary, and the image moves across the retina.
Fig. 468 The eye follows the object, whose image remains on the same retinal region.
The same movement appears faster in the first case than in the second.

But other factors affect perceived speed as well. We hardly need to set up the race between time perambulator and the express train. We know already that the train seems to start out quite comfortably and gradually, while the pram may race furiously after it and still not catch up. The first thought is of 'normal speeds' and familiarity, but the same experiment can be performed with unfamiliar objects. One my use simple dots, or rows of dots, moved behind appropriate apertures on, two independent paper tapes, as in Fig. 469 (after J. F. Brown, like the rest of this discussion). The two tapes must be placed so that they cannot be seen simultaneously. Otherwise one would not be observing apparent speed but change of relative position (approaching, overtaking, separating) which is something quite different.

Fig. 469 Experimental setup for the comparison of perceived velocities (after J. F. Brown). If one moving object, together with its path, is twice as large as another, then its velocity must also be doubled if the two are to appear equally fast.

Fig. 470 Stroboscopic Apparent Movement. If one rapidly alternates the two windows of the "stroboscopic viewer" (in pocket at rear of book), the disc can be clearly seen moving back and forth. (Close the left eye and move the viewer to and fro jerkily before the right eye.)
Fig. 471 The stroboscopic movement can be clearly seen even with increased separation of the discs and no overlap.

If you increase the size of the moving point and its aperture the movement appears much slower, although it is objectively unchanged. If the size is doubled, in a carefully performed experiment, the objective velocity must also be. doubled if it is to appear the same. In general, two moving figures appear equally fast if their real velocities are in equal relationships to their sizes and backgrounds.

The perceived speed is reduced if only one of the magnitudes is altered: the object alone, or its frame, or even only one dimension of the frame. The reduction in speed is less in these cases than when everything is magnified. Thus it is that the speed with a bird skims the rooftops can compare, in our eyes, with that of the soaring jet.

This helps to clarify many other observations that never cease to astonish us as we travel. You can drive on a parkway fully convinced that you are doing 50, and the speedometer points to an astonishing 75 miles per hour. If you avoid a narrow traffic tunnel to take a wide highway, you hardly seem to be moving. There is an old story about two hoboes. One says that, as the crow flies, the next town is four miles away. The other replies that there must be a shorter way through the fields. The retort is not as stupid as it sounds. A narrow path, that leads us to our goal along many twists and turns, seems shorter than a broad straight highway. This is not merely because the varied scenery along the path is 'diverting' while the highway is 'monotonous.' It is also because the changing contours, the widths and lengths, which confront us at every moment much more insistently on the path than on the highway, give us the immediate impression of continuous progress.

6. Perceived Movement Where There is No Motion: The Principles of the Motion Picture

We have seen that movement can occur in reality and go unseen. It is equaIly possible to see movement where none exists. Nowadays, when moving pictures are commonplace, this is nothing new. But one tends to forget that actually there is not the slightest movement on the screen, but only one stationary picture after another. To be sure, the succession is rapid; 24 frames per second have been conventional since the introduction of sound films. In the theory of perception this type of perceived movement has come to be called 'stroboscopic' apparent movement, after the old-fashioned toy on which it could be seen long before movies were invented.

In real movement the object actually - and usually in appearance as well - proceeds through a sequence of spatial positions. One might think that the succession of stationary pictures in a film appears as uninterrupted movement because each differs but little from its predecessor. This is by no means necessary, however. The two pictures need not even overlap, as they do in Fig. 470. They may be separated by a substantial distance (Fig. 471; cf. also Figs. 203, 382, and 288-391).

The basic two-picture experiment can be performed in many ways; for example, two alternately lighting lamps may be used to cast the shadow of a stick on the wall. With practice in the alternate closing and opening of the two eyes, you can see the monocular images of objects leap back and forth (see Chapter 10 for the basis of the images). In a darkroom, two alternately lighting lamps may be viewed directly, and various observations are easily made if the lamps are set in lightboxes. Figures may be cut from the fronts of the boxes and covered with transparent paper of any desired colors. Unless you have bulbs with extremely rapid rise and decay of illumination, it is better to cover and uncover them than to turn them on and off. For simple preliminary experiments one may use a paper slider (Fig. 473, after Wertheimer). It can be held up to the light, or, for group experiments, a slide projector may be used. An occasional toy store still carries the stroboscope, or 'wheel of life' into which strips of pictures can be inserted and viewed through slits in the sides. Since the slits and the drawings are turning in opposite directions, the latter succeed one another almost instantaneously, and you see a smooth sequence of clear picture.

Fig. 472 to Fig. 474 Simple devices for the production of stroboscogic apparent movement.

Fig. 472 Two lightboxes, alternately switched on or uncovered.
Fig. 473 Wertheimer's sliding stroboscopic frame. The fixed part, to which the alternately appearing pictures are fastened, is folded over the edges of the moving part and taped together. The moving part uncovers one picture as it conceals the other.
Fig. 474 The old stroboscope or "wheel of life," from which the name "stroboscopic movement" is taken. Details in the text.

Apparent movement also occurs between sounds, as well as between touches that succeed one another at different places and at appropriate time intervals. For example, it may be clearly experienced between two light touches of a mallet, on the palms of the hands held next to each other. Of course, the eyes must be closed, and it is best if the palms are slightly tilted toward one another. The observer is asked whether he experienced one hammer-stroke or two. If he replies 'one,' he may be asked to trace the path which it took. It is remarkable how precisely he can do this, and how little he can deliberately alter it (Benussi, Schnehage).

Actually, two successive images are not necessary to elicit the experience of movement where there is none in reality. In principle, one is enough. It is only necessary to observe what happens when a common light bulb is turned on. The velocity of light is so great that to all intents and purposes the entire area of the bulb is simultaneously illuminated. Nevertheless it appears just as if the brilliance spread out from the center to the edges, and contracted to the center again when the bulb was turned off. The effect remains even if you use a bulbous milk-glass shade, whose surface is equally bright everywhere, so that highlights cannot move toward the edges as the bulb lights up fully. The term 'gamma-movement' (due to Koffka) has been generally used for this phenomenon.

If one figure appears and disappears, near a second figure which is continuously visible, then again no other alternately exposed stimulus is needed for the appearance of stroboscopic movement. The sporadically visible figure seems to leap out of the stationary one and then to retreat back into it.

A more protracted apparent movement of stationary objects occurs as the after-effect of real movement that has been viewed with ocular fixation. As a boy I once stood on the rear platform of a train and watched the countryside roll back into the distance. Turning around, I sawn to my astonishment that the rear wall of the railway car was creeping toward me. The effect was all the more confusing because it did not become twisted or distorted in its progress. A rotating spiral is particularly welt suited to the production of these 'negative after-images of movement' because the eyes automatically fixate the center and are held there. If after some time the wheel is suddenly halted, it will appear to turn in the opposite direction, and the previously contracting spiral will expand. Its behavior is the counterpart to that of the hour hand in our first paragraph. In that case we had displacement without movement, while here you see clearly directed movement although no point changes its position.

Fig. 475 Apparent movement with a single alternately appearing and disappearing object. The dot seems to leap out of the rectangle and withdraw back into it.

The after-image of movement, like colored after-images, appears at whatever point the eyes happen to be directed. It follows that it is based on some change is the affected region of the retina and/or the rest of the visual nervous system, created by the previously viewed movement.

7. Apparent and Real Movement

Are real and apparent movement Identical? One can check with the aid of Wertheimer's sliding frame, by shoving a good apparent movement together with a real one and asking the subject to distinguish them. One must be skilled in the operation of the slider so that it does not stick halfway across. If good abrupt movements are produced, no one who does not know the answer in advance can tell the two apart. This is a fundamental datum for the theory of perceived movement, since it forces us to explain real and apparent movement on the same basis. It follows that everything discovered in the study of apparent movement contributes also to our understanding of the ability to perceive actual movement.

Fig. 476 Setup on the sliding frame for the simultaneous presentation of real and apparent movement.

Is it possible that in stroboscopic movement (e.g. in Fig. 471) the two stationary endpoints are 'really' seen first and the movement itself is added later as a reasonable intermediary? (At one time there was a whole host of theories of this sort, according to which eye movements, shifts of attention, etc., were to supply the missing link. It is no longer profitable to discuss them in detail.) Or, on the other hand, is the perception of movement the eye's direct response to the rapid succession of neighboring stimuli? If the former were true, the endpoints would always have to remain distinct from the region between them. This question cannot be settled with back-and-forth movement, since there the endpoints are figurally distinct, as places where the movement changes direction. A steady continuous movement is needed, like that of a pointer on a dial. This can be readily produced in the stroboscope itself. One may compare the movement of the pointer is Fig. 477a with that in Fig. 477b. According to the hypothesis we are now considering, the vertical position should be outstanding in (a), the horizontal in (b). If the experiment is well performed, no such distinction appears. The pointer traverses its path with smooth and steady motion, and looks no different at the stimulating points. The issue is thus decided, if we are not to recur to the impossible and unnecessary assumption of 'unnoticed sensations' (cf. Chapter 7).

Fig. 477 In well-developed and smooth apparent movement in the stroboscope, it makes no difference whether the pointer is circling on the basis of the successive stimuli in (a) or those in (b). The stimulated points are in no way distinct from the unstimulated ones - a fact with which the movies have already made us thoroughly familiar.

8. The Replicated Rider and the Question of Optimum Exposure Times

An unfortunate flaw occurred quite regularly in the old silent movies when a sudden quick movement was shown, as for example when a horse and rider jumped a hurdle. Instead of one rider jumping, a whole sequence of replicated riders hovered for a moment in the successive positions of the leap. The explanation is not difficult. If, in the experiment of Fig. 477, we let the stroboscope turn more and more quickly, we eventually see the pointer in several of its positions at once, and ultimately at rest in all of them. Even in the red-green demonstration (Fig. 471) you occasionally succeed in changing colors so rapidly that the figure is seen at both positions at once; that is, two stationary figures appear ('simultaneous phase'). On the other hand, if the alternation is too slow and the interval too great, you again see two stationary figures, each in its own position ('successive phase').

Between these two phases lies a particular rate of presentation, varying from one situation to the next but fairly well determined for any particular set of conditions, in which you see a single object move from one position to the other, or through the appropriate sequence of positions. At the transitions between the three main phases all sorts of transitory effects appear. You may see two figures, of which only one or the other moves, or both successively, or both simultaneously ('single' and 'double' part-motion).

If the individual figures are exposed only very briefly, for small fractions of a second, the time interval necessary for optimal movement depends very precisely on various properties of the figures themselves: their size, their brightness, the distance between them. For example, greater distances require longer time intervals. (The critical factor here is the apparent distance and not the retinal distance, as in the types of functional dependence discussed in Chapter 9.) The fact that apparent movement depends not only on the attitude and condition of the observer but also on certain exact conditions of presentation, not noticeable in themselves, is of great importance. It provides further support for the assumption that the perception of movement is an immediate response of the eye to a particular type of stimulus con-figuration.

From this point of view apparent movement has acquired a certain historical importance. Until Wertheimer's experiments it had been taken for granted that two successive stimuli falling on two well-separated points could elicit only two successive 'sensations,' experienced at their respective positions. Wertheimer grasped for the first time, clearly and with full realization of the consequences, that the excitations produced by such a stimulus complex could work together to produce something very different. The result of the stimulus complex was a unified whole, not only in consciousness but perhaps also in the corresponding events at the visual cortex. This realization was the core of the whole dynamic theory of perception and of psychological phenomena generally which has became known as Gestalt Theory; a theory which has proven its value astonishingly and repeatedly in these sixteen chapters. The many objections which were originally raised against Wertheimer's interpretation of apparent movement prove something else: no psychologist then suspected that, from the point of view of physics, this assumption would turn out to be far more reasonable than its contrary when the properties of the receptor system were considered (W. Köhler).

9. Modes of Appearance of Movement

Apparent movement is particularly vivid and impressive if you present the individual figures for a considerable time, say half a second or a full second, and keep the time interval between them short or omit it altogether. These intervals are also appropriate for viewing the red-green illustrations in this book. In this connection certain variations in the mode of appearance of the movement are worthy of note. If the distance between the figures is small compared with their size, you see them shift 'bag and baggage' from one place to the other. Everything - color, form, structure - is as clearly visible in transit as at the endpoints. This has been called 'optimal' movement; 'full' movement would be another good term. If a large intervening distance is used (Fig. 478b) you still see a single object shift from one place to the next, but it becomes hard to say how it looked while it was moving. Although it has brought all of its properties with it to the other end of the path, it was almost without properties as it went. Only the movement itself is clearly visible, nothing else. This is what is called 'pure' movement. If, under these conditions, a third stationary object (a screen works best, see fig. 479) is placed between the other two, 'tunnel movement' appears. The motion goes behind the screen so that the moving object is temporarily invisible; nevertheless, it remains present throughout, as in interposition.

Fig. 478 Modes of appearance of movement. (a) "Optimal" or "full" movement, with vivid presentation of the figures themselves and little distance between them; (b) "pure" or "empty" movement, with weak figures and considerable distance intervening.
Fig. 479 "Tunnel movement." The movement seems go behind the intervening objects and to be concealed by them.

Fig. 480 Setup for producing concealed continuous movement with pre-arranged longer path (after Michotte). As the spiral turns one can see the dot move along the slit, vanish behind the small screen, and appear again on the other side.

If the latter experiment is done with lamps, and the room is darkened so that the screen becomes invisible, the tunnel movement remains as before. The movement is thus rendered invisible by something which itself cannot be seen. The situation is unchanged if the screen is secretly removed. If the illumination of the room is then gradually restored, the observer is startled to notice that the screen is no longer there. In that instant, the tunnel movement is transformed into ordinary pure movement (Erismann-Lehmann). Concealed movement of this kind can also be obtained with the rotating spiral and slit-screen of Fig. 461, if you cover part of the slit with a second screen (Fig. 480). The observer can describe the invisible portion of the path in astonishing detail, and is remarkably unable to alter it intentionally (Michotte, Burke).

10. A Car Departs: The Law of Proximity and the Objective Set

Remarkable things happen in the movies if a car drives off or an airplane propeller begins to turn. In reality wheels and propellers turn first slowly and then faster and faster in the same direction, but in the film they reverse their rotation several times with increasing rapidity. It can easily happen that when the car finally attains a steady speed the wheels happen to be turning in the wrong direction, and the whole car drives away with its wheels going backward.

Fig. 481 Explanation of reversals of rotation in moving pictures. The movement tends to proceed along the shortest available path between two successive phases (law of proximity, Chapter 3).

Fig. 482 Illustration of the law of proximity in stroboscopic apparent movement. The cross rotates along the shorter route.

No simple photographic error is involved here, but a fundamental limitation on the reproduction of movement by successive stationary pictures. A fundamental law of movement perception is playing a part. Consider the sequence of images at the retina (Fig. 481). The faster the wheel turns, the further the spokes travel between successive exposures. As a result, each succeeding spoke is brought progressively nearer to the point where its predecessor was in the previous frame. If the spokes are identical, the eye does not care which spoke, in the second frame, is nearest the position of a particular spoke in the first frame. The movement goes over the shortest route to the nearest spoke-image, whether it lies ahead or behind, often in contradiction to both experience and expectation (see also fig. 482). The law of proximity is therefore valid here, just as it is for the coherence of stationary wholes (Chapters 2 & 3) and for the continuous movement of the spiral in Section 3 of this chapter.

If you gradually alter the distances in an experiment like that of Fig. 482, the movement can usually be observed to continue for a while along its first path, even after the latter has become substantially longer than its (originally longer) alternate. Then, suddenly, it leaps backward and proceeds along the shorter route. The tendency for movement to continue in an accustomed way, even one which does not correspond to the momentarily given gestalt--properties of the stimulus, has been called the 'objective set.' The term 'objective' is used because the set is not assumed deliberately but is directly elicited by the sequence of stimulus events. In experiments like those described here and subsequently, this effect must be suitably controlled by variations in the order of presentation if it is not to bias the results.

11. The Law of Similarity Becomes a Law of Minimum Change; The Role of Parts in the Whole

Are the other Gestalt laws as valid for movement as for the figure-ground relationship (Chapter 1) and coherence (Chapters 2 and 3)? The law of similarity, like the law of proximity, can be checked with stroboscopic rotation. The question is whether a configuration like those of Fig. 481 rotates to the right or to the left, into a similar or a dissimilar element. We can employ the first and third positions in Fig. 481 for this purpose, where the distances are equal so that proximity is controlled. For the sake of simplicity, only a pair of oppositely oriented configurations is used in each case (Figs. 483 to 486). In almost every case, the movement takes place between identical or similar members, provided that the differences are sufficiently pronounced. The law of similarity again turns into a law of minimum change, like that of Chapters 1 and 13 and of the third section of this chapter. It asserts that perceived objects tend to change as little as possible.

Fig. 483 to 486 The law of similarity, or minimum change, in apparent movement (after P. v. Schiller ).

Fig. 483 The diameter rotates so that its thick end stays thick and its thin end thin.
Fig. 484 The cross moves to keep its thick line thick and its thin line thin.
Fig. 485 Movement proceeds from circle to circle and cross to cross.
Fig. 486The Movement is such as to keep the large dot large and the small dot small.

Fig. 487 Clarification of the concept of "similarity" in apparent movement. It is not "excitations" which are primarily involved; if they were, the cross would not move since it is white in both exposures.

Of the many properties that a visual configuration may possess, which are the most important in this respect? In the traditional terminology, apparent movement occurs when two 'excitations' succeed one another at disparate points. In Fig. 487 you see, among other things, a cross which jumps back and forth. Upon more careful inspection it becomes clear that there has been no change of stimulation within the cross at all; the region in question is of equal brightness on both sides. It is not 'the white area' which moves to the other 'white area' but the cross which moves to the other cross: figure to figure. We are reminded of the black dot, which does not arise from an 'excitation' but from an absence of excitation in an otherwise excited field. It follows that not 'excitations' but singularities in the structure of the field are important, as they develop on the basis of the extended stimulus manifold.

Fig. 488 Two configurations which move in such a way that certain components undergo no perceptual displacement in the shift from one exposure to the other. The sufficient condition is not the absence of real stimulus displacement, but the unchanged role of the component in its supraordinate whole. (a) The two side points of the hexagon become "hinges" around which the whole figure turns; (b) If the vertical row of three dots acts as the axis of rotation, all three remain stationery; if the whole figure rotates in its plane, at least the middle dot does not move (after J. Ternus).

This becomes even more obvious in more extensive well-structured groups. Here, as already in Fig. 487, steady stimulation produces a stationary effect only if, in this way, the role of the part in its supraordinated whole (Chapter 2, Section 5) is preserved unchanged (see fig. 488). If a stationary state could be preserved only at the expense of changing the role played by the part, then the fact that the 'stimulation' might be unaltered would be of no significance. (See Figs. 489-493. In principle Fig. 470 belongs here as well.) In such a case, movement takes place between those parts that have equivalent roles in their respective configurations. In other words, it is the role itself which persists. What moves is not 'a line' or 'a point,' let alone 'a sensation,' but rather 'the midpoint,' 'the left corner,' 'the right edge,' etc. (Wertheimer, Ternus).

In Chapter 3, when we first discussed the roles which parts play, the reader may have wondered whether, in our enthusiasm for a new discovery, we were not overestimating its importance. Already there we saw that this class of properties, which so readily escapes the casual glance, was of fundamental importance for the reproduction of memory traces. It appears now that it is equally basic to all the phenomena which occur in our visual environment. The scope of this book does not extend to the critical role which changes in these role-attributes play in productive thinking (Wertheimer). But we are no longer surprised that Wertheimer referred to them as the 'real flesh and blood' of every articulated form that we see.

Figs. 489 to 493 Five figures in which unchanged stimulus positions have no significance for the behavior of the corresponding parts. The movement takes place compellingly in a way determined by the roles which the parts play in the whole (from Ternus).

Fig. 489 Three points are stimulated identically in both exposures the lower right corner, the midpoint of the base, and the midpoint of the right side. Nevertheless one does not see them stand still.. Everything slides to the right, so that the triangle as a whole is preserved. The lower right corner becomes the midpoint of the base; the midpoint becomes the left corner, the center of the right side becomes the center of the left.

Fig. 490 The same effect with unaltered stimulis positions for two points, which do not remain at rest perceptually because the whole triangle moves up to the right. The second point of the right side becomes the midpoint of the left; the fourth point of the right side becomes the center of the base.

Fig. 491 The same effect with four points coincident. They act as the upper four points of the right side in the first exposure and as the lower four of the left side in the second, if the triangle is seen rotating around its highest point as it slides down one space. It may also be seen rotating around its right side through the third dimension, but even in this case the unchanged points do not remain identical: point 2 becomes the peak, point 3 becomes point2, etc., as the triangle slides down.

Fig. 492 The original outer edge of the picture frame undergoes no actual displacement; the inner edge vanishes and another appears further out. The phenomenon cannot be seen in this way, however. The whole frame expands, so that what was formerly the outer edge becomes the inner.

Fig. 493 If a gestalt moves as a whole from one place to another with a single form-preserving movement, it can readily undergo a certain amount of distortion provided that its overall structure remains unchanged. In this case it is again irrelevant that local stimulation may be unaltered. Perceptually, midpoint moves smoothly to midpoint and corner to corner, although the stimulus that was the midpoint before has become the left base-point while what was the upper right corner now serves as the center.

12. The Law of Total Absorption

We tested the law of similarity with the direction of rotation of a wheel. Could one not simply make the second figure less and less similar to the first, and wait to see if the movement would eventually fail to take place? Such a test would be fruitless, because the desired degree of dissimilarity would never be attained. Movement will take place even though it must change black into white (Fig. 494) or fish into fowl (Fig. 495). Even the sensory modality can be altered. If a flash and a bang, or a sound and a touch, or a touch and a point of light succeed one another at neighboring points with the appropriate time intervals, you can still experience the same labile 'something' jumping from one place to the other. One is reminded of that law of grouping, according to which almost arbitrarily different figures will group themselves together in an unstructured environment.

Figs. 494 and 495 For movement, the law of total absorption (Chapter 1) becomes a law demanding that, if possible, nothing be destroyed and nothing created except out of what is already present. As a result, stroboscopic movement can accompany some rather absurd transformations.

Fig. 494 Black turns to white, white to black.

Fig. 495a Fish into fowl, fowl into fish.

Fig. 495b An alarm clock becomes a hammer, and vice versa.

What happens if, after a first exposure of a single figure, a similar and a dissimilar one are shown simultaneously (Fig. 496) or a whole set of dissimilar ones are available to choose from (Fig. 497)? Here also, the outcome is not what one might predict in advance. Rather than move to its similar mate, the first figure 'bursts' and becomes, as it were, the parent of the entire group. If the sequence is reversed the group as a whole contracts back into the single figure. What is the explanation? If the predicted movement had occurred, all of the dissimilar figures would have arisen 'from nowhere' in the first case and vanished 'into nothingness' in the second. It is apparent that in perception the law of similarity is subordinate to the need that nothing be destroyed and nothing arbitrarily created. This is precisely the principle of grouping which we called the law of total absorption (Chapters 1 end 2), transferred to the case of temporal persistence or 'identity.'

Figs. 496 and 497 Two demonstrations which do not prove the Law of Similarity, because of the law that nothing shall be arbitrarily created and nothing destroyed.

Fig. 496 If the pair on the right come after the single element on the left, the latter is seen to split and both members of the pair emerge from it. With the opposite order of presentation the two members unite into the single cross.

Fig. 497 For the same reason as before, the single element "bursts" into the entire group, or the group retreats into the one.

13. Non-Intersecting and Smoothly Continuing Movement

If pairs of similar figures are so arranged in a stroboscopic experiment that their movement paths ought to cross (Fig. 498) the result is frequently that, instead, they move to their dissimilar neighbors and undergo the resultant transformations. Non-intersecting movement is preferred. But if the figures are made sufficiently dissimilar, it is also possible to see intersecting movement without difficulty (Fig. 499). Two oppositely directed movements in the same region are even possible (Fig. 500). Non-intersecting movement is preferred to movement which crosses only if, as here, it can occur with equal smoothness. If the uncrossed path can only be obtained at the expense of some discontinuity of motion, the other, steadier, movement generally has the advantage. It is irrelevant whether the discontinuity is of directions or of speed.

Fig. 498 With this configuration an occasional transformation of shape may be observed in opposition to the law of similarity; non-intersecting movement is favored.
Fig. 499 If the moving figures are sufficiently unlike, so that the effect of similarity is strengthened, intersecting movement is altogether possible.

Fig. 500 Even precisely opposite movements within the same field can occur. The large figures move to the right while the small ones go to the left, or vice versa. These peculiar forms are used to reduce the tendency of the whole structure to rotate through the third dimension.

A sliding arrangement with two screens can serve to demonstrate the effect of sudden changes in direction. On one screen the paths of the several movements are cut as sequences of tiny holes. The other, which is slid along behind the first, contains a single slit. If the screens are held up to the light, the paths are not visible. Only where the slit crosses them do points of light appear in the evenly darkened field. These coincide as a single point wherever the paths cross (Fig. 501). If the paths are arranged as in the figure, crossed, smoothly interpenetrating movement is usually seen. But this may readily be altered if the law of similarity or minimum change comes into action. If the upper half of the main screen is covered with red cellophane and the lower half with blue (Fig. 502), you see a red dot and a blue dot rushing toward one another, colliding, and again recoiling away. If the movements were to interpenetrate in this case, the points would have to exchange colors at the intersection. This would amount to exchanging real 'properties,' and would clearly go deeper than the mere exchange of 'states' created by the shift in direction.

The role of discontinuities of speed can be examined with the aid of a moving stick-shadow arrangement (Fig. 378). When the shadow of one stick over-takes that of another, they become a single shadow for the moment of coincidence. If the shadows are identical, the two segments of path which are seen as belonging together are nearly always those that succeed one another smoothly (Fig. 503). The two shadows seem to pass one another without pausing, or one seems to over-take the other. Only if the approach and separation of the shadows is so gradual that no discontinuity arises when they are interchanged (Fig. 504), can one shadow easily take over the identity of another. Under these conditions one sees a pair of shadows shift back and forth while the distance between its members slowly increases and decreases; the left member always remaining on the left, the right on the right.

Fig. 501 Arrangement for the study of preferred routes of movement. The vertical slit is moved behind the diagonals, so that in holding the whole setup against the light one sees two points of light moving along invisible paths. ln this arrangement the motion follows the law of smooth continuation: the movements cross.

Fig. 502 If the points are colored, thus invoking the law of similarity, it is easy to obtain angular movement instead of smooth interpenetration. A red and a green point approach each other diagonally, and recoil from one another at the center.

The law of the smooth course of motion is clearly the direct application of the law of smooth continuation (Chapter 2, Fig. 59) to the case of temporal persistence.

Figs. 503 and 504 (Translator's note) The lower part of each figure gives the top view of a rotating disc, on which two upright sticks are mounted. A beam of light casts the shadows of the sticks on a screen. The horizontal excursions of the stick-shadows are shown in the upper part of each figure, as functions of time (or angle of rotation of the disc).


Fig. 503 Again the law of smooth continuation. When the stick-shadows cross, in the experimental setup of Fig. 376, the lines which one sees as temporally "the same" before and after the mcnent of intersection are those whose movement proceeds without discontinuity, and without change (for example, in thickness).
Fig. 504 If the meeting and separation of the shadows occurs without discontinuity in either case, "false" shadows may continue for one another. With this arrangement you see the pair of lines swim back and forth, and simultaneously become wider and narrower, without exchanging sides.

14. The Significance of the Overall Properties of the Course of Movement Itself

Even in cases where the course of movement does not follow from the law of similarity or minimum change, as in Figs. 483-486, a rather discontinuous movement can sometimes occur, as an alternative to smooth interpenetration or perhaps as the preferred form. This happens first of all if several simultaneous movements form a symmetrical group of paths (Fig. 505). It also occurs if smooth continuation would require the movements to interchange their whole--properties. If both before and after the point of contact there is a steadily progressive movement and a movement which swings jerkily back and forth, there is a strong tendency to see one movement which is steady from start to finish and another which is jerky, regardless of whether this results in intersection or in shift of direction at the contact point. (Figs. 506 & 507).

Overall paths of motion whose character remains unchanged from start to finish are thus preferred to those which change their nature as they go (cf. also Figs. 59a and 66, Chapter 2). In all likelihood the aftereffects called 'objective set' (Section 10) are related to these phenomena. Continuation of an accustomed type of movement leads to a substantially simpler and more unified spatio-temporal configuration than does change (Fig. 508).

We have rediscovered all of the laws of stationary grouping here (appropriately altered) as laws of persistence through time, with the exception of the laws of closure and of the common center (Figs. 18, 61, 113, 118b, 120b and 122b). It is not yet known whether these Laws can also be applied to movement; i.e. whether movements which return to their starting point after circling a particular area are preferred to other movements.1 The question will probably be decided only with the help of trick photography.

Fig. 505 Where the overall course of the movement is rhythmic and symmetrical, discontinuous movements can occur. The "accordion movement" of the even row of stick-shadows in Fig. 379a belongs here as well. (Translator's note: Fig. 505 is to be interpreted like the preceding two figures, except that the time function is now given below rather than above.)

Figs. 506 and 507 Two paths of movement may proceed discontinuously after they meet, if they would otherwise have to exchange their overall character (cf. the stationary curves of Figs. 59a and 112).

Fig. 506 Here the movement alters course sharply at the meeting point.
Fig. 507 Here smooth intersection occurs. In each of these figures, one overall event is a zig-zag motion, the other a steadily progressive one.

To test the law of closure, paths like those of Fig. 509 would be necessary. Single points should be moving simultaneously along all the segments of these paths in such a way that they regularly meet at the intersections. If the law of smooth continuation were to dominate, one would see intersecting paths a-e-c and d-b-f. If the law of closure prevails, three recursive non-intersecting movements should appear in a-f, e-b, and c-d, the middle one running oppositely from the other two. To avoid conflict with the law of smooth continuation, one would have to have the points move to the right in the upper half and to the left in the lower half of every loop, so that a right-angle turn would be required at each point of contact no matter which of the two motions was seen. If closure is effective, a series of small clockwise rotations should appear at a-n, b-m, c-l, etc. If it is not, the points should move in short regular leaps: to the right on top and to the left below (Fig. 510). The law of the common center could be tested in a similar way (Fig. 511).

Fig. 508 The "objective set" itself (Wertheimer) is ultimately based on greater simplicity and unity in the overall spatio-temporal configuration. If two points appear alternately at positions a,a and b,b, the observer sees an up-and-doom movement in accordance with the law of proximity. If the vertical distance is increased until it exceeds the horizontal, a movement to and fro should take over immediately (as in A). This does not occur. Continuation of the up-and-down motion leads to the more unified spatio-temporal configuration in B.

Figs. 509 and 510 Arrangwent for testing the law of closure in the case of movement. Single points of light move simultaneously along all of the (invisible) sectors of the curves, and meet one another at the "intersections."

Fig. 509 Movement along smooth continuous curves is in opposition to movement along closed (recursive) curves.
Fig. 510 Controlled conditions: both closed and "open" paths of movement involve sharp turns at the points of contact, and smooth continuation is avoided.

Fig. 511 Arrangement for testing the law of the common center in the case of movement. A radial slit is rotated in front of the two circular ones. If the law of the common center holds here also, the overall movement ought to separate into an inner and an outer path.

15. The Effect of Figural Properties and of the Surrounding Field

It is known that the formation of stationary groups can be forced by enclosure (Fig. 512). Particular directions of movement can also be more or less effectively determined in this way (v. Schiller). The vertical and horizontal distances are the same in Fig. 513, but the movement is primarily up and down, so that the figures remain within their boundaries (cf. also section 6). It is possible to control the path even more precisely: in Fig. 514, most observers see movement along the prescribed curves (Wittman, Koffka).

Fig. 512 Grouping of stationary points by means of enclosure (after G. E. Muller).

Fig. 513 According to v. Schiller, stroboscopic movement also prefers to remain within an enclosure, and is reluctant to cross boundaries. The movement should proceed up and down more readily than to and fro in this case. With many observers, however, the difference is slight if it exists at all.
Fig. 514 Effect of field conditions on the course of movement. Stroboscopic movement mostly follows prescribed paths, curvilinear in this case. This happens even in 514b, where the direct route between the endpoints is open (after Wittman and Koffka).

We have already encountered several impressive examples of the effect of the forms of the moving objects themselves (e.g. Fig. 394; cf. also Van Der Mullen and Dooremall's experiment, Chapter 11, sections 6 and. 13 and page 283). Motion takes place most readily along the long axis of the figure, somewhat less easily at right angles to it, and least of all diagona11y. If two luminous lines approach one another very slowly along a diagonal, as in Fig. 515, the vertical line looks clearly as if it were moving down, the horizontal one as if moving to the left. The result is rather peculiar, since they do not end up at all where they should.

The sense of a rotation can also be influenced by figural factors. In Fig. 516 the arrowheads move in the direction in which they point. (To be sure, this applies only under good conditions. In the red-green illustrations used here, the back-and-forth movement of the observer's hand tends to force a perceived movement to and fro as well. As a result, it is difficult to see the continuous rotary motion of the arrowheads. This factor suggests another, self-evident, law of movement.) Furthermore, those rotations are, clearly pre-ferred whose axes are marked or suggested in the figure. Thus the trapezoids in Fig. 517 turn through the third dimension, but in Fig. 518 the rotation is equally or more often around the mid-point and within the plane of the paper. The latter tendency is strengthened further if, as in Fig. 519, the direction of rotation is indicated by small protuberances on the figures themselves. The motion of the arcs across the enclosed regions in Fig. 520 corresponds to that of the trapezoids in Fig. 517; movement through the 'outside' regions would fit the figure less well, and would itself be less simple and go further from the plane of the paper.

Contractions and expansions are particularly under the control of figural factors. In symmetrical figures they always proceed from the center. In Fig. 521a, the second exposure can be formed from the first by adding to the right side of the small diamond, as in 521b. But in fact, the diamond appears to grow from its center, not toward the right; at the same time it moves a step toward the right as a whole. Meanwhile the left corner is not standing still, but makes two opposite motions at once, and only 'coincidentally' remains in the same place because the shift to the right and the expansion to the left 'happen to be equal.' The movement falls apart into its natural components, a phenomenon we must consider further later on.

If an endless belt of diagonal lines moves behind a rectangular window, something happens which, for the sake of clarity, we omitted from the previous discussion. The lines enter the window diagonally, and then grow steadily from their center toward both ends. They do not grow only to the right from their left corner, as one might expect on the basis of their real motion. The diagonal movement does not occur simply on the basis of the Law of Proximity, as the shortest possible one. This can be demonstrated with an aperture like that of Fig. 523. In this case the Law of Proximity would require the line to move at right angles to itself, along the shortest path. On the other hand, if expansion is to take place evenly in both directions, the line as a whole must move along a curved path. And this is precisely what is seen if the movement is observed naively, with somewhat distracted attention.

Fig. 515 et seq. The movement depends on the form of the moving figures.

Fig. 515 With slow movement in a dark room, one does not see the actual diagonal motion. The vertical line seems to move vertically, the horizontal one horizontally.
Fig. 516 In the stroboscope, the arrowhead tends to move progressively with its point in front (after P. v. Schiller, as are Figs. 517-520). Unfortunately, this experiment cannot be properly performed with our little stroboscopic viewer, because the perceived configuration tends to take on the back-and-forth motion of the observer's hand. It is therefore difficult for a steadily progressive movement to occur in the visual field.

Fig. 517 The closely neighboring long edges of the alternately presented trapezoids lie near a correspondingly oriented axis of rotation. The resulting apparent movement goes through the third dimension.
Fig. 518 The tips of the alternately presented figures point at one another and lie near a center point, around which rotation takes place in the plane of the paper.
Fig. 519 Rotation of both trapezoids in the same direction and in the picture plane is supported by the protuberances on the figures.
Fig. 520 The arcs tend to move over the momentarily "enclosed" field. The reason is the same as in Fig. 517.

Fig. 521 One can imagine the expansion of the diamond (in Fig. 521a) occurring by an increment of area to the right, as in (b). But one usually has the compelling impression that the diamond is expanding from its center outwards, and simultaneously moving as a whole to the right.

Fig. 522 The diagonal lines of Fig. 465 also grow first from their centers outward, thus moving diagonally, as long as they are still bounded by one vertical and one horizontal window edge.
Fig. 523 Proof that the diagonal movement of Fig. 522 is not a simple consequence of the Law of Proximity. This window is constructed so that the lines expand or contract during their entire visible course. Their overall movement is seen as curved in such a way that in spite of the asymmetric window the expansion proceeds out from their centers and the contraction back into their centers (H. Wallach).

16. Natural Components of Motion: The Secret of the Rolling Wheel

What path is traversed by a point on the circumference of a rolling wheel? Without special consideration, no one can answer this question, although all of us see rolling wheels every day of our lives. The matter becomes clear if we reflect on it. 'Rolling' implies that the moving object proceeds in such a way that its every point is momentarily at rest, in the instant in which it touches the underlying surface. Each point must approach the surface perpendicularly, touch it, and leave perpendicularly again. This process must be repetitive, with a 'wave length' equal to the circumference of the wheel. Half-way between two points of contact, the point in question traverses the highest point in its course and is traveling with twice the linear speed of the hub. But we can see this motion only if the wheel is rolling in a darkened roam, with the point present as a feeble dot of light.

Fig. 524 The Cycloid. Every point on the rim of a rolling wheel traverses this curve. Nevertheless it is never seen, unless everything other then the point is made invisible (as, for example, if the point is given as a dot of light in a dark room).
Fig. 525 The paths traversed by a number of points on the rim of a rolling vheel, completely "visible" and yet never seen.
Fig. 526 What one actually sees as a wheel rolls. There is a displacement of the entire figure, as represented by the hub, and in addition a rotation around the hub. The two components are related in a well-defined way by contact with the underlying surface. The point which is momentarily touching the surface does not appear to stand still, but seems to undergo two opposite motions at once, like the left corner of the diamond in Fig. 521.

What do we see ordinarily? No trace of the 'cycloid' or wheel-curve traversed by the point (Fig. 524), no hint of its reversals of direction or of the regular, changes in its velocity: not even if we know precisely what to look for. And we cannot even imagine the paths taken by all the points on the circumference together, or by the several spokes (Fig. 525). If the entire wheel or major parts of it are visible, all the points seem to describe absolutely regular rotations with constant angular velocity around the hub, moving forward at the top and backward at the bottoms. At the same time the wheel as a whole moves along with a speed and in a direction that actually corresponds only to a single point, namely the hub (Fig. 526). The hub comes to represent the entire configuration in its linear movement, at the same time that it forms a point of reference for the divergent motion of the remaining points. Thus it can happen that the point which is momentarily at the bottom does not seem to stand still, but instead moves in two opposite directions simultaneously, as the left corner of the diamond did in Fig. 521. It undergoes translation forward, with the rest of the wheel, at just the rate with which it rotates backward around the hub. The motion is everywhere decomposed into its two components; the result gives an impression of constant velocity, even at the highest point.

In this phenomenon an important and very general law of perceptions is revealed. There are only two conditions in which we can directly see the paths taken by all the points of a moving object. The first case is simple translation, in which all the points on the object move with approximately equal speeds and directions. The locus of the movement must be rectilinear or at most slightly curved; that is, the radius of curvature must be large with respect to the object itself and especially with respect to its transverse axis. The second case occurs if the various points of the moving object travel with evenly varying speeds and directions, while its, anchoring point or center of gravity remains fixed in space. This occurs, for example, in simple rotation around a stationery axis lying at some figurally distinct point within the object. It also occurs in pure expansion out of, and contraction into, a fixed point of origin (Fig. 394). In these instances the axis, or the point of origin, comes to represent the spatial location of the entire figure. Perceptually it is the figure itself, not merely the axis or origin, which remains in the same place. This remains true even if the origin is quite close to the edge, as when a door turns on its hinges, or in the stick-shadow experiment of Fig. 527 where the point of the triangular solid lies at the center of the disc, or if a 'standing' object seems to grow from its base rather than its center.

In all other cases, if the various points of a perceived object travel with unequal velocities and directions, all motion except that of the axis or origin will be decomposed into its natural components. These components are determined by the structure of the whole. As a rule, they are so inaccessible to conscious intent that inexperienced observers think nothing else is possible.

Fig. 527 In this stick-shadow experiment the "triangular solid" remains in one place, as a whole. It seems to rotate without translation, in spite of the extreme position of the axis. The axis comes to represent its spatial position.

The basic component is always the translation of the entire object in space, as represented by the actual motion of its center of gravity. The other components are given by the movements of the remaining points, which are always seen only as referred to that center. The characteristic case is that of an object which undergoes translation while it simultaneous1y rotates or expands or changes its shape in some other manner, perhaps by twisting or bending. There are also perceived motions which decompose into more than two natural components. Thus a rotation may be added to a translation, and some other change or additional rotation superimposed on the first. Consider the appearance of a man's foot, or a point on the foot, if we watch him as he walks.

Fig. 528 A line standing upright on a board has its point of origin (see text) at its base, not at its center like the diamond in Fig. 521. It appears to grow upwards as it moves to the right.

We have already pointed, out that the position of the point of origin, or of the axis, is not forced from without, but is itself determined by gestalt factors. There is always a figurally distinct point or member within the figure that takes this role. In a symmetrical figure, it is the axis of rotation. In unsymmetrical ones it can be the largest part, or one at the end, or one that moves least or is stationary, or one that moves out ahead, or one that momentarily catches the eye. Whenever the axis of rotation fails to coincide with the axis of symmetry, in a symmetrical figure, the object no longer undergoes simple rotation: it shifts a little as well (Fig. 529). This decomposition remains compelling, even if the real axis of rotation is clearly visible. In Fig. 531 the wheel does not simply spin around the axis of the disc like a stone in a sling; in addition to moving around the axis, it also turns around its own hub.

Figs. 529 & 530 If the axis of rotation does not coincide with the gestalt-axis in a symmetrical figure, every simple rotation will be decomposed perceptually into a component going around the axis of rotation2 and a simultaneous rotation of the whole figure around the gestalt-axis. This can be observed with equal facility with Misatti's disc (Fig. 530) and in a stick-shadow arrangement (Fig. 529).

Fig. 531 Rubin's experiment with a small circle rolling inside another twice as large. One necessarily sees two ccmponents, just as when the rolling is along a flat surface. The displacement of the center (necessarily circular in this case) comprises one component, while the oppositely directed rotation around the center is the other (Fig. 531a). It is completely impossible to see that every point of the small circle executes only rectilinear motion: that they all slide back and forth, with different phases, along diameters of the larger circle (Fig. 531b).

The compelling effectiveness of these laws is illustrated in Rubin's experi-ment (Fig. 531). A small circle of points of light rolls around on the inside circumference of another circle whose diameter is twice that of the first. Elementary geometry shows that each point of the small circle moves back and forth in a perfect straight line along a diameter of the large one. The paths of the various points, taken together, form a simple star (Fig. 531b). Yet this star cannot be perceived. To be sure, you can see the rectilinear motion of a single point if it alone is illuminated in a darkroom. If a second point is illuminated, you do not see two rectilinear motions but still only one: that of whichever point momentarily catches the eye. The second point rotates compellingly around the first. Only a few more points are needed to form the circle, or parts of it. From then on the individual points are only seen rotating around the center of the small circle, which itself rolls around inside the large one (Fig. 531a). No trace of rectilinear motion remains.

The movements of perceived wholes decompose into their natural components according to Gestalt laws, just as these wholes themselves are segregated into their natural parts according to such laws. We are usually as unable to alter the former intentionally as the latter.

17. Independent and Dependent Movements. The Perception of Causality

When a stick that has been tossed into the air turns over and over, the impression is almost always that its progression and its rotation are merely added together, that they coincide by accident. The motions do not seem to be in any necessary or sensible relationship to one another. The situation is quite different when a wheel rolls. It is in the nature of rolling, in contrast to sliding or jerking, that the point of contact does not itself move along the surface. In this case, then, every displacement of the whole demands a particular rotation that 'belongs' to it, and every rotation demands a similarly related displacement. Sometimes one and sometimes the other of these components can 'take charge.' In other words, one sometimes has the impression that the wheel moves forward because it is turning, and at other times that it turns because it is being moved. Another case of such interdependence, which we may call 'dangling,' occurs when one figure seems to drag another one along behind. An example can be constructed in the stick-shadow experiment (Fig. 375) with the arrangement of Fig. 532. The movements of the member that seems to be dragged are clearly dependent on the one that is doing the dragging.

Such observations lead to a significant question. Can it happen that one movement is immediately experienced as dependent on another, even when it does not form a second natural component of the motion of one and the same figure? This question is important because, in different words, it reads: Is it possible that causality, the causation of one event by another, can be seen directly? Since Hume, modern epistemology has unanimously taken something quite different for granted. It is assumed that we can perceive individual events, but not their causal relationship. The latter can only be guessed at, or assumed. And such an assumption is only made if we see two events succeed one another often enough so that the impressions of the events become 'associated,' and as a result the perception of the first makes us expect the second.

Fig. 532 Setup for a stick-shadow experiment which produces the impression of "dragging behind" and "dangling."

Preliminary experiments on perceived causality can be carried out with a slowly turning disc, viewed through a slit in a screen, as in Fig. 461. For this purpose two lines are drawn on the disc, so that two points move simultaneously within the slit as the disc is rotated (Fig. 533). The movement can then be arranged as desired: in the same or opposite directions, successive or simultaneous; with and without brief or prolonged contact, with steady or discontinuous, increasing or decreasing velocity. Only the direction of the movement is unalterable (except by 180°). Control of direction would require complicated arrangements with coupled projectors, unless one went directly to trick photography.

Fig. 533 (a) Lines drawn on a rotating disc, to be viewed through a slit for the production of perceived causality (after Michotte, as are Figs. 534-537). (b,c) The two lines are drawn on separate, independently rotating discs to permit systematic variation of temporal conditions.

The extensive investigations of Michotte, following on haphazard isolated observations by others, have shown that causality can in fact be seen directly. It can occur without the preliminary formation of an 'association' by repeated similar presentations; it can also occur in cases where the second movement is unexpected. Causality is thus a basic sensory 'given,' like the colors, forms, sizes, and positions of objects. There are a whole host of different kinds of immediate causality-perceptions: pushing away (Fig. 534), shoving (Fig. 535), dragging, picking up (Fig. 536), throwing off, tracing (making tracks), extinguishing, pressing, ripping, slowing; halting, releasing, etc. On the other hand, the impressions of 'attraction' and of transmission of properties have not yet been demonstrated. For each of the various types of perceived causality one can specify stimulus conditions rather precisely. And, as one might expect, there are many cases where the experience is variable and can be influenced by shifts of attention.

Fig. 534 Arrangement of lines to create the impression of a "push." The moment the moving dot comes in contact with the stationary one it stops, while the one previously at rest beings to move.
Fig. 535 Arrangement of lines to create a "shoving" effect. The lines are drawn so that a moving dot encounters a stationary one, which thereafter moves in front of the first.
Fig. 536 Arrangement of lines to create the impression of "picking up." The moving dot changes direction at the moment of contact with the stationary one, which then follows behind.
Fig. 537 Arrangement of lines to create an impression of causality which contradicts our experience. Both dots are in motion. The faster one gives the slower a push from behind, and as a result makes it slow down.

One of the basic types is the push, as between billiard balls. In the simplest case the motion jumps from one ball to the other. The occurrence of such a jump is not enough, however, since it can also give rise to an 'exchange,' as in a relay race. For the experience of causality, the movement of the first figure must dominate the scene. The motion of the second figure must not seem to be its own, but rather a continuation of the first figure's motion, merely 'forced' upon it. For this to occur the two figures have to be related, just through their movements, in a manner which makes the motion appear 'toward' or 'away from.' Yet the two figures must not be so closely connected that they act as parts of a whole, or that one 'carries' the other like a crate on a wagon. In the latter case the figure which is being carried does not seem to be making any movement at all. It simply 'rests' on the first, no matter how fast the first is moving (cf. next chapter). Nothing remains of the impression of causality.

The impression of 'releasing,' by contrast, is the limiting case before the perception of completely independent simultaneous or successive individual move-ments. Here only the onset of the second object's motion seems to be caused by the first. The motion itself is not transferred and taken over, but belongs entirely to the second object from the very beginning. An example of 'releasing' occurs if, in the instant of contact with a moving object, a stationary one begins to move in a totally different direction while the originally moving object comes to rest.

In Michotte's experiments, the impression of causality is frequently in flat contradiction to our daily experience of actual causal relationships. Appropriate drawings (Fig. 537) can copy the impression that one dot overtakes another and slows the latter down by the impact, instead of speeding it up. It is possible, with suitable arrangements, to give the impression that a point of light pushes away an object, or vice versa; all are things that we would not expect.

Impressions of causality depend on certain very well-defined properties of the spatio-temporal structure of the moving objects. If they are to be genuinely compelling, a particular set of events must be realized at the critical moments: certain directions, durations, or velocities; certain changes of velocity; or certain sequences of discontinuities of motion or of spatial separation. These conditions are so completely determined, and yet comprise such an arbitrary selection from the actual instances of causation that we encounter daily, that they must be based on our own inner nature, like the conditions governing apparent movement and apparent object-formation. In other words, the experience of causality is also dependent on Gestalt Laws. This means that it depends on laws of visual perception and of perception in general which, prior to all experience, create in us the conditions under which experience is possible.

1 The phenomena described as 'closure' by P. v. Schiller are not relevant here.

2 The text here is "gestalt-axis," but I have treated this as a misprint - translator.