The Principles of Psychology, Vols. 1-2

direction to that in which, a moment previously, we had been seeing the water move, whilst on either side of this band another band of planks will move as the water did. Looking at a waterfall, or at the road from out of a carwindow in a moving tram, produces the same illusion, which may be easily verified in the laboratory by a simple piece of apparatus. A board with a window five or six inches wide and of any convenient length is supported upright on two feet. On the back side of the board, above and below the window, are two rollers, one of which is provided with a crank. An endless band of any figured stuff is passed over these rollers (one of which can be so adjusted on its bearings as to keep the stuff always taut and not liable to slip), and the surface of the front board is also covered with stuff or paper of a nature to catch the eye. Turning the crank now sets the central band in continuous motion, whilst the margins of the field remain really at rest, but after a while appear moving in the contrary way. Stopping the crank results in an illusory appearance of motion in reverse directions all over the field.

A disk with an Archimedean spiral drawn upon it, whirled round on an ordinary rotating machine, produces still more startling effects. "If the revolution is in the direction in which the spiral iin« approaches the centre of the disk the entire surface of the latter seemg to expand during revolution and to contract after it has ceased; and vice versd if the movement of revolution is in the opposite direction. If in the former case the eyes of the observers are turned from the rotating disk towards any familiar object — e.g. the face of a friend — the latter seems to contract or recede in a somewhat striking manner, and to expand or approach after the opposite motion of the spiral." *

An elementary form of these motor illusions seems to be the one described by Helmholtz on pp. 568-571 of his Optik, The motion of anything in the field of vision along an acute angle towards a straight line sensibly distorts that line, "^hus in Fig. 66 : Let AB be a line drawn on paper, CDE the tracing made over this line by the point of a compass steadily followed by the eye, as it moves. As the compass-point passes from C to D, the line appears to move downwards ; as it passes from D to E, the line appears to move upwards ; at the same time the whole line seems to incline itself in the direction FG during the first half of the compass's movement ; and in the direction HI during its last half ; the change from one inclination to another being quite distinct as the compass-point passes over D.

Any line across which we draw a pencil-point appears to be animated by a rapid movement of its own towards the pencil-point. This apparent movement of both of two things in relative motion to each other, even when one of them is absolutely still, reminds us of the instances quoted * Bowditch and Hall, in Journal of Physiology, vol. iii. p. 299. Helmholtz tries to explain this phenomenon by unconscious rotations of the eyeball. But movements of the eyeball can only explain such appearances of movements as are the same over the whole field. In the windowed board one part of the field seems to move in one way, another part in another. The same is true when we turn from the spiral to look at the wall — the centre of the field alone swells out or contracts, the margin does the reverse or remains at rest. Mach and Dvorak have beautifully proved the impossibility of eye-rotations in this case (Sitzungsber. d. Wiener Akad., Bd. LXi.). See also Bowditch and Hall's pa^er as above, p. 300.

from Vierordt on page 188, and seems to take us back to a primitive stage of perception, in which the discriminations we now make when we feel a movement have not yet been made. If w© draw the point of a pencil through * Zollner's pattern' (Fig. 60, p. 232), and follow it with the eye, the whole figure becomes the scene of the most singular apparent unrest, of which Helmholtz has very carefully noted the conditions. The illusion of Zollner's figure vanishes entirely, or almost so, with most people, if they steadily look at one point of it with an unmoving eye ; and the same is the case with many other illusions.

Now aU these facts taken together seem to show — vaguely it is true, but certainly — that present excitements and aftereffects of former excitements may alter the resvlt of processes occurring simultaneously at a distance from them in the retina or other portions of the apparatus for optical sensation. In the cases last considered, the moving eye, as it sweeps the fovea over certain parts of the figure, seems thereby to determine a modification in the feeling which the other parts confer, which modification is the figure's * distortion.' It is true that this statement explains nothing. It only keeps the cases to which it applies from being explained spuriously. The spurious account of these illusions is that they are intellectual, not sensational, that they are secondary, not primary, mental facts. The distorted figure is said to be one which the mind is led to imagine, by falsely drawing an unconscious inference from certain premises of which it is not distinctly aware. And the imagined figure is supposed to be strong enough to suppress the perception of whatever real sensations there may be. But Helmholtz, Wundt, Delbceuf, ZoUner, and all the advocates of unconscious in-- ference are at variance with each other when it comes to the question what these unconscious premises and inferences may be.

That small angles look proportionally larger than larger ones is, in brief, the fundamental illusion to which almost all authors would reduce the peculiarity of Fig. 67, as of Figs. 60, 61, 62 (pp. 232, 233). This peculiarity of small angles is by Wundt treated as the case of a filled space seeming larger than an empty one, as in Fig. 68 ; and this, according to both Delboeuf and Wundt, is owing to the fact that more muscular innervation is needed for the eye to traverse a filled space than an empty one, because the points and lines

in the filled space inevitably arrest and constrain the eye, and this makes us feel as if it were doing more work, i.e. traversing a longer distance.* When, however, we recollect that muscular movements are positively proved to have no share in the waterfall and revolving-spiral illusions, and that it is hard to see how Wundt's and Delboeuf 's particular form of muscle-explanation can possibly apply to the compass-point illusion considered a moment ago, we must conclude that these writers have probably exaggerated, to say the least, the reach of their muscleexplanation in the case

of the subdivided angles and lines. Never do we get such strong muscular feelings as when, against the course of nature, we oblige our eyes to be still ; but fixing the eyes on one point of the figure, so far from making that part of the latter seem larger, dispels, in most persons, the illusion of these diagrams altogether. As for Helmholtz, he invokes, to explain the enlargement of small angles,* what he calls a * laiv of contrast ' between directions and distances of lines, analogous to that between colors and intensities of light. Lines cutting another line make the latter seem more inclined away from them than it really is. Moreover, clearly recognizable magnitudes appear greater than equal magnitudes which we but vaguely apprehend. But this is surely a sensationalistic law, a native function of our seeing-apparatus. Quite as little as the negative after-image of the revolving spiral could such contrast be deduced from any association of ideas or recall of past objects. The principle of contrast is criticised by Wundt, f who says that by it small spaces ought to appear to us smaller, and not larger, than they really are. Helmholtz might have retorted (had not the retort been as fatal to the uniformity of his own principle as to Wundt's) that if the muscle-explanation were true, it ought not to give rise to just the opposite illusions in the skin. We saw on p. 141 that subdivided spaces appear shorter than empty ones upon the skin. To the instances there given add this : Divide a line on paper into equal halves, puncture the extremities, and make punctures all along one of the halves ; then, with the finger-tip on the opposite side of the paper, follow the line of punctures ; the empty half will seem much longer than the punctured half. This seems to bring things back to unanalyzable laws, by reason of which our feeling of size is determined differently in the skin and in the retina, even when the objective conditions are the same. Hering's explanation of ZoUner's figure is to be found in Hermann's Handb. d. Physiologie, lii. 1. p. 579. Lipps % gives another reason

why lines cutting another line make the latter seem to bend away from them more than is really the case. If, he says, wo draw (Fig. 69) the line pm upon the line ah, and follow the latter with our eye, we shall, on reaching the point m, tend for a moment to slip off ah and to follow mpy without distinctly realizing that we are not still on the main line. This makes us feel as if the remainder mh of the main line were bent a little away from its original direction. The illusion is apparent in the shape of a seeming

approach of the ends &, &, of the two main lines. This to my mind would be a more satisfactory explanation of this class of illusions than any of those given by previous authors, were it not again for what happens in the skin. Considering all the circumstances j I feel justified in discarding his entire hatch of illusions as irrelevant to our present inquiry. Whatever they may prove, they do not prove that our visual percepts of form and movement may not be sensations strictly so called. They much more probably fall into line with the phenomena of irradiation and of color-contrast, and with Yierordt's primitive illusions of movement. They show us, if anything, a realm of sensations in which our habitual experience has not yet made traces, and which persist in spite of our better knowledge, t^nsuggestive of those other space-sensations which we all the time know from extrinsic evidence to constitute the real spacedeterminations of the diagram. Yery likely, if these sensations were as frequent and as practically important as they now are insignificant and rare, we should end by substituting their significates — the real space-values of the diagrams — for them. These latter we should then seem to

see directly, and the illusions would disappear like that of the size of a tooth-socket when the tooth has been out 9 week. (6) Another hatch of cases which we may discard is that of dovhle images. A thoroughgoing anti-sensationalist ought to deny all native tendency to see double images when disparate retinal points are stimulated, because, he should say, most people never get them, but see all things single which experience has led them to believe to be single. " Can a doubleness, so easily neutralized by our knowledge, ever be a datum of sensation at all ? " such an anti-sensationalist might ask.

To which the answer is that it is a datum of sensation, but a datum which, like many other data, must first be discriminated. As a rule, no sensible qualities are dis^ criminated without a motive.^ And those that later we learn to discriminate were originally felt confused. As well pretend that a voice, or an odor, which we have learned to pick out, is no sensation now. One may easily acquire skill in discriminating double images, though, as Hering somewhere says, it is an art of which one cannot become master in one year or in two. For masters like Hering himself, or Le Conte, the ordinary stereoscopic diagrams are of little use. Instead of combining into one solid appearance, they simply cross each other with their doubled

lines. Volkmann has shown a great variety of ways in which the addition of secondary lines, differing in the two fields, helps us to see the primary lines double. The effect is analogous to that shown in the cases which we despatched a moment ago, where given lines have their space-value changed by the addition of new lines, without our being able to say why, except that a certain mutual adhesion of the lines and modification of the resultant feeling takes place by psychophysiological laws. Thus, if in Fig. 70, 1 and r be crossed by an horizontal line at the same level, and viewed stereoscopically, they appear as a single pair of lines, s, in space. But if the horizontal be at different levels, as in l\ r', three lines appear, as in s',^

Let us then say no more about double images. All that the facts prove is what Volkmann says,t that, although there may be sets of retinal fibres so organized as to give an impression of two separate spots, yet the excitement of other retinal fibres may inhibit the effect of the first excitement, and prevent us from actually making the discrimination. Still farther retinal processes may, however, bring the doubleness to the eye of attention ; and, once there, it is as genuine a sensation as any that our life affords. :f

(c) These groups of iUusionsheing diminated, either as cases of defective discrimination, or as changes of one spacesensation into another when the total retinal process changes, there remain hut two other groups to puzzle us. The first is that of the after-images distorted by projection on to oblique planes ; the second relates to the instability of our judgments of relative distance and size by the eye, and includes especially what are known as pseudoscopic illusions.

X 1 pass over certain difficulties about double images, drawn from the perceptions of a few squinters (e.g. by Schweigger, Klin. Untersuch. tlbef das Schielen, Berlin, 1881 ; by Javal. Annales d'Oculistique, lxxxv. p. 217), because the facts are exceptional at best and very difficult of interpretation. In favor of the sensationalistic or nativistic view of one such case, see the important paper by Von Kries, Archiv f. Ophthalm., xxiv. 4, p. 117.

The phenomena of the first group were described on page 232. A. W. Yolkmann has studied them with his accustomed clearness and care. * Even an imaginarily inclined wall, in a picture, will, if an after-image be thrown upon it, distort the shape thereof, and make us see a form of which our after-image would be the natural projection on the retina, were that form laid upon the wall. Thus a signboard is painted in perspective on a screen, and the eye, after steadily looking at a rectangular cross, is turned to the painted signboard. The after-image appears as an oblique-legged cross upon the signboard. It is the converse phenomenon of a perspective drawing like Fig. 71, in which

really oblique-legged figures are seen as rectangular crosses. The unstable judgments of relati^^e distance and size were also mentioned on pp. 231-2. Whatever the size may be of the retinal image which an object makes, the object is seen as of its own normal size. A man moving towards us is not sensibly perceived to grow, for example ; and my finger, of which a single joint may more than conceal him from my view, is nevertheless seen as a much smaller object than the man. As for distances, it is often possible to make the farther part of an object seem near and the nearer part far. A human profile in intaglio, looked at steadily with one eye, or even both, soon appears irresistibly as a basrelief. The inside of a common pasteboard mask, painted like the outside, and viewed with one eye in a direct light, also looks convex instead of hollow. So strong is the iilu-

sion, after long fixation, that a friend who painted such a mask for me told me it soon became difficult to see how to apply the brush. Bend a visiting-card across the middle, so that its halves form an angle of 90° more or less ; set it upright on the table, as in Fig. 72, and view it with one eye. You can make it appear either as if it opened towards you or away from you. In the former case, the angle oh lies upon the table, h being nearer to you than a ; in the latter

case ab seems vertical to the table — as indeed it really is — with a nearer to you than 6.* Again, look, with either one or * Cf. E. Mach, Beitrage zur Analyse der Einpflndimgen, p. 87. two eyes, at the opening of a wine-glass or tumbler (Fig. 73), held either above or below the eye's level. The retinal image of the opening is an oval, but we can see the oval in either of two ways, — as if it were the perspective view of a circle whose edge h were farther from us than its edge a (in which case we should seem to be looking down on the circle), or as if its edge a were the more distant edge (in which case we should be looking up at it through the h side of the glass). As the manner of seeing the edge changes, the glass itself alters its form in space and looks straight or seems bent towards or from the eye,* according as the latter is placed beneath or above it.

Plane diagrams also can be conceived as solids, and that in more than one way. Figs. 74, 75, 76, for example, are ambiguous perspective projections, and may each of them remind us of two different natural objects. Whichever of these * Cf. V. Egger, Revue Philos., xx. 488. objects we conceive clearly at the moment of looking at the figure, we seem to see in all its solidity before us. A little practice will enable us to flap the figures, so to speak, backwards and forwards from one object to the other at will. We need only attend to one of the angles represented, and imagine it either solid or hollow — pulled towards us out of the plane of the paper, or pushed back behind the same — and the whole figure obeys the cue and is instantaneously transformed beneath our gaze.*

The peculiarity of all these cases is the ambiguity of the perception to which the fixed retinal impression gives rise. With our retina excited in exactly the same way, whether by after-image, mask or diagram, we see now this object and now that, as if the retinal image per se had no essential space-import. Surely if form and length were originally retinal sensations, retinal rectangles ought not to become acute or obtuse, and lines ought not to alter their relative lengths as they do. If relief were an optical feeling, it ought not to flap to and fro, with every optical condition unchanged. Here, if anywhere, the deniers of spacesensation ought to be able to make their final stand.f

It must be confessed that their plea is plausible at first sight. But it is one thing to throw out retinal sensibility altogether as a space-yielding function the moment we find an ambiguity in its deliverances, and another thing to examine candidly the conditions which may have brought the ambiguity about. The former way is cheap, wholesale, shallow; the latter difficult and complicated, but full of instruction in the end. Let us try it for ourselves.

In the case of the diagrams 72, 73, 74, 75, 76, the real object, lines meeting or crossing each other on a plane, is * Loeb (Pflilger's Archiv, xl. 274) has proved that muscular changes of adaptation in the eye for near and far distance are what determine the form of the relief. f The strongest passage in Helmholtz's argument against sensations of space is relative to these fluctuations of seen relief: "Ought one not to conclude that if sensations of relief exist at all, they must be so faint and vague as to have no influence compared with that of past experience? Ought we not to believe that the perception of the third dimension may have arisen without them, since we now see it taking place as well against them as with them ?" (Physiol. Optik, p. 817.)

replaced by an imagined solid which loe describe as seen. Really it, is not seen but only so vividly conceived as to approach a vision of reality. We feel all the while, however, that the solid suggested is not solidly there. The reason why one solid may seem more easily suggested than another, and ivhy it is easier in general to perceive the diagram solid than flat, seems due to probability.^ Those lines have countless times in our past experience been drawn on our retina by solids for once that we have seen them flat on paper. And hundreds of times we have looked down upon the upper surface of parallelopipeds, stairs and glasses, for once that we have looked upwards at their bottom— hence we see the solids easiest as if from above.

Habit or probability seems also to govern the illusion of the intaglio profile, and of the hollow mask. We have never seen a human face except in relief — hence the case with which the present sensation is overpowered. Hence, too, the obstinacy with which human faces and forms, and other extremely familiar convex objects, refuse to appear hollow when viewed through Wheatstone's pseudoscope. Our perception seems wedded to certain total ways of seeing certain objects. The moment the object is suggested at all, it takes possession of the mind in the fulness of its stereotyped habitual form. This explains the suddenness of the transformations when the perceptions change. The object shoots back and forth completely from this to that familiar thing, and doubtful, indeterminate, and composite things are excluded, apparently because we are unused to their existence.

W^hen we turn from the diagrams to the actual folded visiting-card and to the real glass, the imagined form seems fully as real as the correct one. The card flaps over ; the glass rim tilts this way or that, as if some inward spring suddenly became released in our eye. In these changes the actual retinal image receives different complements from the mind. But the remarkable thing is that the complement and the image combine so completely that the twain are one flesh, as it were, and cannot be discriminated in the result If the complement be, as we have called it (on pp. 237-8), a set of imaginary absent eye-sensations, they seem no whit less vividly there than the sensation which the eye now receives from without.

The case of the after-images distorted by projection upon an oblique plane is even more strange, for the imagined perspective figure, lying in the plane, seems less to combine with the one a moment previously seen by the eye than to suppress it and take its place.^ The point needing explanation, then, in all this, is how it comes to pass that, when imagined sensations are usually so inferior in vivacity to real ones, they should in these few experiences prove to bo almost or quite their match.

The mystery is solved when we note the class to which all these experiences belong. They are 'perceptions' of definite * things,' definitely situated in tridimensional space. The mind uniformly uses its sensations to identify things by. The sensation is invariably apperceived by the idea, name, or ' normal ' aspect (p. 238) of the thing. The peculiarity of the optical signs of things is their extraordinary mutability. A * thing ' which we follow with the eye, never doubting of its physical identity, will change its retinal image incessantly. A cross, a ring, waved about in the air, will pass through every conceivable angular and elliptical form. All the while, however, as we look at them, we hold fast to the perception of their ' real ' shape, by mentally combining the pictures momentarily received with the notion of peculiar positions in space. It is not the cross and ring pure and simple which we perceive, but the cross so hdd, the ring so hdd. From the day of our birth we have sought every hour of our lives to correct the apparent form of things, and trans-