Visual Illusions Part 4

Perhaps the reader has often witnessed the striking illusion of some portraits which were made of subjects looking directly at the camera or painter. Regardless of the position of the observer the eyes of the portrait appear to be directed toward him. In fact, as the observer moves, the eyes in the picture follow him so relentlessly as to provoke even a feeling of uncanniness. This fact is accounted for by the absence of a third dimension, for a sculptured model of a head does not exhibit this feature. Perspective plays a part in some manner, but no attempt toward explanation will be made.

In Fig. 36 are two sketches of a face. One appears to be looking at the observer, but the other does not. If the reader will cover the lower parts of the two figures, leaving only the two pairs of eyes showing, both pairs will eventually appear to be looking at the observer. Perhaps the reader will be conscious of mental effort and the lapse of a few moments before the eyes on the left are made to appear to be looking directly at him.

Although it is not claimed that this illusion is caused by the same conditions as those immediately preceding, it involves attention. At least, it is fluctuating in appearance and therefore is equivocal. It is interesting to note the influence of the other features (below the eyes).

The perspective of these is a powerful influence in "directing" the eyes of the sketch.

In the foregoing only definite illusions have been presented which are universally witnessed by normal persons. There are no hallucinatory phases in the conditions or causes. It is difficult to divide these with definiteness from certain illusions of depth as discussed in Chapter VII.

The latter undoubtedly are sometimes entwined to some extent with hallucinatory phases; in fact, it is doubtful if they are not always hallucinations to some degree. Hallucinations are not of interest from the viewpoint of this book, but illusions of depth are treated because they are of interest. They are either hallucinations or are on the border-line between hallucinations and those illusions which are almost universally experienced by normal persons under similar conditions. The latter statement does not hold for illusions of depth in which objects may be seen alternately near and far, large and small, etc., although they are not necessarily pure hallucinations as distinguished from the types of illusions regarding which there is general perceptual agreement.

[Ill.u.s.tration: Fig. 36.--Ill.u.s.trating certain influences upon the apparent direction of vision. By covering all but the eyes the latter appear to be drawn alike in both sketches.]

In explanation of the illusory phenomena pertaining to such geometrical figures as are discussed in the foregoing paragraphs, chiefly two different kinds of hypotheses have been offered. They are respectively psychological and physiological, although there is more or less of a mixture of the two in most attempts toward explanation. The psychological hypotheses introduce such factors as attention, imagination, judgment, and will. Hering and also Helmholtz claim that the kind of inversion which occurs is largely a matter of chance or of volition. The latter holds that the perception of perspective figures is influenced by imagination or the images of memory. That is, if one form of the figure is vividly imagined the perception of it is imminent. Helmholtz has stated that, "Glancing at a figure we observe spontaneously one or the other form of perspective and usually the one that is a.s.sociated in our memory with the greatest number of images."

The physiological hypotheses depend largely upon such factors as accommodation and eye-movement. Necker held to the former as the chief cause. He has stated that the part of the figure whose image lies near the fovea is estimated as nearer than those portions in the peripheral regions of the visual field. This hypothesis is open to serious objections. Wundt contends that the inversion is caused by changes in the points and lines of fixation. He says, "The image of the retina ought to have a determined position if a perspective illusion is to appear; but the form of this illusion is entirely dependent on motion and direction." Some hypotheses interweave the known facts of the nervous system with psychological facts but some of these are examples of a common anomaly in theorization, for facts plus facts do not necessarily result in a correct theory. That is, two sets of facts interwoven do not necessarily yield an explanation which is correct.

VI

THE INFLUENCE OF ANGLES

As previously stated, no satisfactory cla.s.sification of visual illusions exists, but in order to cover the subject, divisions are necessary. For this reason the reader is introduced in this chapter to the effects attending the presence of angles. By no means does it follow that this group represents another type, for it really includes many illusions of several types. The reason for this grouping is that angles play an important part, directly or indirectly, in the production of illusions.

For a long time many geometrical illusions were accounted for by "overestimation" or "underestimation" of angles, but this view has often been found to be inadequate. However, it cannot be denied that many illusions are due at least to the presence of angles.

Apparently Zollner was the first to describe an illusion which is ill.u.s.trated in simple form in Fig. 29 and more elaborately in Figs. 37 to 40. The two figures at the right of Fig. 29 were drawn for another purpose and are not designed favorably for the effect, although it may be detected when the figure is held at a distance. Zollner accidentally noticed the illusion on a pattern designed for a print for dress-goods. The illusion is but slightly noticeable in Fig. 29, but by multiplying the number of lines (and angles) the long parallel lines appear to diverge in the direction that the crossing lines converge. Zollner studied the case thoroughly and established various facts. He found that the illusion is greatest when the long parallel lines are inclined about 45 degrees to the horizontal. This may be accomplished for Fig. 37, by turning the page (held in a vertical plane) through an angle of 45 degrees from normal. The illusion vanishes when held too far from the eye to distinguish the short crossing lines, and its strength varies with the inclination of the oblique lines to the main parallels. The most effective angle between the short crossing lines and the main parallels appears to be approximately 30 degrees. In Fig. 37 there are two illusions of direction. The parallel vertical strips appear unparallel and the right and left portions of the oblique cross-lines appear to be shifted vertically. It is interesting to note that steady fixation diminishes and even destroys the illusion.

[Ill.u.s.tration: Fig. 37.--Zollner's illusion of direction.]

The maximum effectiveness of the illusion, when the figure is held so that the main parallel lines are at an inclination of about 45 degrees to the horizontal was accounted for by Zollner as the result of less visual experience in oblique directions. He insisted that it takes less time and is easier to infer divergence or convergence than parallelism. This explanation appears to be disproved by a figure in which slightly divergent lines are used instead of parallel ones. Owing to the effect of the oblique crossing lines, the diverging lines may be made to appear parallel. Furthermore it is difficult to attach much importance to Zollner's explanation because the illusion is visible under the extremely brief illumination provided by one electric spark. Of course, the duration of the physiological reaction is doubtless greater than that of the spark, but at best the time is very short. Hering explained the Zollner illusion as due to the curvature of the retina, and the resulting difference in the retinal images, and held that acute angles appear relatively too large and obtuse ones too small. The latter has been found to have limitations in the explanation of certain illusions.

This Zollner illusion is very striking and may be constructed in a variety of forms. In Fig. 37 the effect is quite apparent and it is interesting to view the figure at various angles. For example, hold the figure so that the broad parallel lines are vertical. The illusion is very p.r.o.nounced in this position; however, on tilting the page backward the illusion finally disappears. In Fig. 38 the short oblique lines do not cross the long parallel lines and to make the illusion more striking, the obliquity of the short lines is reversed at the middle of the long parallel lines.

Variations of this figure are presented in Figs. 39 and 40. In this case by steady fixation the perspective effect is increased but there is a tendency for the parallel lines to appear more nearly truly parallel than when the point of sight is permitted to roam over the figures.

[Ill.u.s.tration: Fig. 38.--Parallel lines which do not appear so.]

[Ill.u.s.tration: Fig. 39.--Wundt's illusion of direction.]

[Ill.u.s.tration: Fig. 40.--Hering's illusion of direction.]

Many investigations of the Zollner illusion are recorded in the literature. From these it is obvious that the result is due to the additive effects of many simple illusions of angle. In order to give an idea of the manner in which such an illusion may be built up the reasoning of Jastrow[1] will be presented in condensed form. When two straight lines such as _A_ and _B_ in Fig. 41 are separated by a s.p.a.ce it is usually possible to connect the two mentally and to determine whether or not, if connected, they would lie on a straight line. However, if another line is connected to one, thus forming an angle as _C_ does with _A_, the lines which appeared to be continuous (as _A_ and _B_ originally) no longer appear so. The converse is also true, for lines which are not in the same straight line may be made to appear to be by the addition of another line forming a proper angle. All these variations cannot be shown in a single figure, but the reader will find it interesting to draw them. Furthermore, the letters used on the diagram in order to make the description clearer may be confusing and these can be eliminated by redrawing the figure. In Fig. 41 the obtuse angle _AC_ tends to tilt _A_ downward, so apparently if _A_ were prolonged it would fall below _B_. Similarly, _C_ appears to fall to the right of _D_.

[Ill.u.s.tration: Fig. 41.--Simple effect of angles.]

This illusion apparently is due to the presence of the angle and the effect is produced by the presence of right and acute angles to a less degree. The illusion decreases or increases in general as the angle decreases or increases respectively.

Although it is not safe to present simple statements in a field so complex as that of visual illusion where explanations are still controversial, it is perhaps possible to generalize as Jastrow did in the foregoing case as follows: If the direction of an angle is that of the line bisecting it and pointing toward the apex, the direction of the sides of an angle will apparently be deviated toward the direction of the angle. The deviation apparently is greater with obtuse than with acute angles, and when obtuse and acute angles are so placed in a figure as to give rise to opposite deviations, the greater angle will be the dominant influence.

Although the illusion in such simple cases as Fig. 41 is slight, it is quite noticeable. The effect of the addition of many of these slight individual influences is obvious in accompanying figures of greater complexity. These individual effects can be so multiplied and combined that many illusory figures may be devised.

In Fig. 42 the oblique lines are added to both horizontal lines in such a manner that _A_ is tilted downward at the angle and _B_ is tilted upward at the angle (the letters corresponding to similar lines in Fig. 41). In this manner they appear to be deviated considerably out of their true straight line. If the reader will draw a straight line nearly parallel to _D_ in Fig. 41 and to the right, he will find it helpful. This line should be drawn to appear to be a continuation of _C_ when the page is held so _D_ is approximately horizontal. This is a simple and effective means of testing the magnitude of the illusion, for it is measured by the degree of apparent deviation between _D_ and the line drawn adjacent to it, which the eye will tolerate. Another method of obtaining such a measurement is to begin with only the angle and to draw the apparent continuation of one of its lines with a s.p.a.ce intervening. This deviation from the true continuation may then be readily determined.

[Ill.u.s.tration: Fig. 42. The effect of two angles in tilting the horizontal lines.]

[Ill.u.s.tration: Fig. 43. The effect of crossed lines upon their respective apparent directions.]

A more complex case is found in Fig. 43 where the effect of an obtuse angle _ACD_ is to make the continuation of _AB_ apparently fall below _FG_ and the effect of the acute angle is the reverse. However, the net result is that due to the preponderance of the effect of the larger angle over that of the smaller. The line _EC_ adds nothing, for it merely introduces two angles which reinforce those above _AB_. The line _BC_ may be omitted or covered without appreciably affecting the illusion.

[Ill.u.s.tration: Fig. 44.--Another step toward the Zollner illusion.]

In Fig. 44 two obtuse angles are arranged so that their effects are additive, with the result that the horizontal lines apparently deviate maximally for such a simple case. Thus it is seen that the tendency of the sides of an angle to be apparently deviated toward the direction of the angle may result in an apparent divergence from parallelism as well as in making continuous lines appear discontinuous. The illusion in Fig. 44 may be strengthened by adding more lines parallel to the oblique lines. This is demonstrated in Fig. 38 and in other ill.u.s.trations. In this manner striking illusions are built up.

[Ill.u.s.tration: Fig. 45.--The two diagonals would meet on the left vertical line.]

[Ill.u.s.tration: Fig. 46.--Poggendorff's illusion. Which oblique line on the right is the prolongation of the oblique line on the left?]

If oblique lines are extended across vertical ones, as in Figs. 45 and 46, the illusion is seen to be very striking. In Fig. 45 the oblique line on the right if extended would meet the upper end of the oblique line on the left; however, the apparent point of intersection is somewhat lower than it is in reality. In Fig. 46 the oblique line on the left is in the same straight line with the lower oblique line on the right. The line drawn parallel to the latter furnishes an idea of the extent of the illusion.

This is the well-known Poggendorff illusion. The upper oblique line on the right actually appears to be approximately the continuation of the upper oblique line on the right. The explanation of this illusion on the simple basis of underestimation or overestimation of angles is open to criticism.

If Fig. 46 is held so that the intercepted line is horizontal or vertical, the illusion disappears or at least is greatly reduced. It is difficult to reconcile this disappearance of the illusion for certain positions of the figure with the theory that the illusion is due to an incorrect appraisal of the angles.

[Ill.u.s.tration: Fig. 47.--A straight line appears to sag.]

According to Judd,[2] those portions of the parallels lying on the obtuse-angle side of the intercepted line will be overestimated when horizontal or vertical distances along the parallel lines are the subjects of attention, as they are in the usual positions of the Poggendorff figure. He holds further that the overestimation of this distance along the parallels (the two vertical lines) and the underestimation of the oblique distance across the interval are sufficient to provide a full explanation of the illusion. The disappearance and appearance of the illusion, as the position of the figure is varied appears to demonstrate the fact that lines produce illusions only when they have a direct influence on the direction in which the attention is turned. That is, when this Poggendorff figure is in such a position that the intercepted line is horizontal, the incorrect estimation of distance along the parallels has no direct bearing on the distance to which the attention is directed. In this case Judd holds that the entire influence of the parallels is absorbed in aiding the intercepted line in carrying the eye across the interval. For a detailed account the reader is referred to the original paper.

Some other illusions are now presented to demonstrate further the effect of the presence of angles. Doubtless, in some of these, other causes contribute more or less to the total result. In Fig. 47 a series of concentric arcs of circles end in a straight line. The result is that the straight line appears to sag perceptibly. Incidentally, it may be interesting for the reader to ascertain whether or not there is any doubt in his mind as to the arcs appearing to belong to circles. To the author the arcs appear distorted from those of true circles.

[Ill.u.s.tration: Fig. 48.--Distortions of contour due to contact with other contours.]

In Fig. 48 the bounding figure is a true circle but it appears to be distorted or dented inward where the angles of the hexagon meet it.

Similarly, the sides of the hexagon appear to sag inward where the corners of the rectangle meet them.

The influences which have been emphasized apparently are responsible for the illusions in Figs. 49, 50 and 51. It is interesting to note the disappearance of the illusion, as the plane of Fig. 49 is varied from vertical toward the horizontal. That is, it is very apparent when viewed perpendicularly to the plane of the page, the latter being held vertically, but as the page is tilted backward the illusion decreases and finally disappears.

[Ill.u.s.tration: Fig. 49.--An illusion of direction.]

[Ill.u.s.tration: Fig. 50.--"Twisted-cord" illusion. These are straight cords.]

[Ill.u.s.tration: Fig. 51.--"Twisted-cord" illusion. These are concentric circles.]

The illusions in Figs. 50 and 51 are commonly termed "twisted cord"

effects. A cord may be made by twisting two strands which are white and black (or any dark color) respectively. This may be superposed upon various backgrounds with striking results. In Fig. 50 the straight "cords"

appear bent in the middle, owing to a reversal of the "twist." Such a figure may be easily made by using cord and a checkered cloth. In Fig. 51 it is difficult to convince the intellect that the "cords" are not arranged in the form of concentric circles, but this becomes evident when one of them is traced out. The influence of the illusion is so powerful that it is even difficult to follow one of the circles with the point of a pencil around its entire circ.u.mference. The cord appears to form a spiral or a helix seen in perspective.

[Ill.u.s.tration: Fig. 52.--A spiral when rotated appears to expand or contract, depending upon direction of rotation.]

A striking illusion is obtained by revolving the spiral shown in Fig. 52 about its center. This may be considered as an effect of angles because the curvature and consequently the angle of the spiral is continually changing. There is a peculiar movement or progression toward the center when revolved in one direction. When the direction of rotation is reversed the movement is toward the exterior of the figure; that is, there is a seeming expansion.

Angles appear to modify our judgments of the length of lines as well as of their direction. Of course, it must be admitted that some of these illusions might be cla.s.sified under those of "contrast" and others. In fact, it has been stated that cla.s.sification is difficult but it appears logical to discuss the effect of angles in this chapter apart from the divisions presented in the preceding chapters. This decision was reached because the effect of angles could be seen in many of the illusions which would more logically be grouped under the cla.s.sification presented in the preceding chapters.