Chapter III: Part 3

Many investigations of the Zoellner 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 space 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_.

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 space intervening. This deviation from the true continuation may then be readily determined.

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.

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 illustrations. In this manner striking illusions are built up.

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.

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.

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.

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 circumference. The cord appears to form a spiral or a helix seen in perspective.

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 classified under those of "contrast" and others. In fact, it has been stated that classification 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 classification presented in the preceding chapters.

In Fig. 53 the three horizontal lines are of equal length but they appear unequal. This must be due primarily to the size of the angles made by the lines at the ends. Within certain limits, the greater the angle the greater is the apparent elongation of the central horizontal portion. This generalization appears to apply even when the angle is less than a right angle, although there appears to be less strength to the illusions with these smaller angles than with the larger angles. Other factors which contribute to the extent of the illusion are the positions of the figures, the distance between them, and the juxtaposition of certain lines. The illusion still exists if the horizontal lines are removed and also if the figures are cut out of paper after joining the lower ends of the short lines in each case.

In Fig. 54 the horizontal straight line appears to consist of two lines tilting slightly upward toward the center. This will be seen to be in agreement with the general proposition that the sides of an angle are deviated in the direction of the angle. In this case it should be noted that one of the obtuse angles to be considered is _ABC_ and that the effect of this is to tilt the line _BD_ downward from the center. In Fig. 55 the horizontal line appears to tilt upward toward its extremities or to sag in the middle. The explanation in order to harmonize with the foregoing must be based upon the assumption that our judgments may be influenced by things not present but imagined. In this case only one side of each obtuse angle is present, the other side being formed by continuing the horizontal line both ways by means of the imagination. That we do this unconsciously is attested to by many experiences. For example, we often find ourselves imagining a horizontal, a vertical, or a center upon which to base a pending judgment.

A discussion of the influence of angles must include a reference to the well-known Mueller-Lyer illusion presented in Fig. 56. It is obvious in _a_ that the horizontal part on the left appears considerably longer than that part in the right half of the diagram. The influence of angles in this illusion can be easily tested by varying the direction of the lines at the ends of the two portions.

In all these figures the influence of angles is obvious. This does not mean that they are always solely or even primarily responsible for the illusion. In fact, the illusion of Poggendorff (Fig. 46) may be due to the incorrect estimation of certain linear distances, but the angles make this erroneous judgment possible, or at least contribute toward it. Many discussions of the theories or explanations of these figures are available in scientific literature of which one by Judd[2] may be taken as representative. He holds that the false estimation of angles in the Poggendorff figure is merely a secondary effect, not always present, and in no case the source of the illusion; furthermore, that the illusion may be explained as due to the incorrect linear distances, and may be reduced to the type of illusion found in the Mueller-Lyer figure. Certainly there are grave dangers in explaining an illusion on the basis of an apparently simple operation.

In Fig. 56, _b_ is made up of the two parts of the Mueller-Lyer illusion. A small dot may be placed equally distant from the inside extremities of the horizontal lines. It is interesting to note that overestimation of distance within the figure is accompanied with underestimation outside the figure and, conversely, overestimation within the figure is accompanied by underestimation in the neighboring space. If the small dot is objected to as providing an additional Mueller-Lyer figure of the empty space, this dot may be omitted. As a substitute an observer may try to locate a point midway between the inside extremities of the horizontal lines. The error in locating this point will show that the illusion is present in this empty space.

In this connection it is interesting to note some other illusions. In Fig. 57 the influence of several factors are evident. Two obviously important ones are (1) the angles made by the short lines at the extremities of the exterior lines parallel to the sides of the large triangle, and (2) the influence of contrast of the pairs of adjacent parallel lines. The effect shown in Fig. 53 is seen to be augmented by the addition of contrast of adjacent lines of unequal length.

An interesting variation of the effect of the presence of angles is seen in Fig. 58. The two lines forming angles with the horizontal are of equal length but due to their relative positions, they do not appear so. It would be quite misleading to say that this illusion is merely due to angles. Obviously, it is due to the presence of the two oblique lines. It is of interest to turn to Figs. 25, 26 and various illusions of perspective.

At this point a digression appears to be necessary and, therefore, Fig. 59 is introduced. Here the areas of the two figures are equal. The judgment of area is likely to be influenced by juxtaposed lines and therefore, as in this case, the lower appears larger than the upper one. Similarly two trapezoids of equal dimensions and areas may be constructed. If each is constructed so that it rests upon its longer parallel and one figure is above the other and only slightly separated, the mind is tempted to be influenced by comparing the juxtaposed base of the upper with the top of the lower trapezoid. The former dimension being greater than the latter, the lower figure appears smaller than the upper one. Angles must necessarily play a part in these illusions, although it is admitted that other factors may be prominent or even dominant.

This appears to be a convenient place to insert an illusion of area based, doubtless, upon form, but angles must play a part in the illusions; at least they are responsible for the form. In Fig. 60 the five figures are constructed so as to be approximately equal in area. However, they appear unequal in this respect. In comparing areas, we cannot escape the influence of the length and directions of lines which bound these areas, and also, the effect of contrasts in lengths and directions. Angles play a part in all these, although very indirectly in some cases.

To some extent the foregoing is a digression from the main intent of this chapter, but it appears worth while to introduce these indirect effects of the presence of angles (real or imaginary) in order to emphasize the complexity of influences and their subtleness. Direction is in the last analysis an effect of angle; that is, the direction of a line is measured by the angle it makes with some reference line, the latter being real or imaginary. In Fig. 61, the effect of diverting or directing attention by some subtle force, such as suggestion, is demonstrated. This "force" appears to contract or expand an area. The circle on the left appears smaller than the other. Of course there is the effect of empty space compared with partially filled space, but this cannot be avoided in this case. However, it can be shown that the suggestions produced by the arrows tend to produce apparent reduction or expansion of areas. Note the use of arrows in advertisements.

Although theory is subordinated to facts in this book, a glimpse here and there should be interesting and helpful. After having been introduced to various types and influences, perhaps the reader may better grasp the trend of theories. The perspective theory assumes, and correctly so, that simple diagrams often suggest objects in three dimensions, and that the introduction of an imaginary third dimension effects changes in the appearance of lines and angles. That is, lengths and directions of lines are apparently altered by the influence of lines and angles, which do not actually exist. That this is true may be proved in various cases. In fact the reader has doubtless been convinced of this in connection with some of the illusions already discussed. Vertical lines often represent lines extending away from the observer, who sees them foreshortened and therefore they may seem longer than horizontal lines of equal length, which are not subject to foreshortening. This could explain such illusions as seen in Figs. 4 and 5. However this theory is not as easily applied to many illusions.

According to Thiery's perspective theory a line that appears nearer is seen as smaller and a line that seems to be further away is perceived as longer. If the left portion of _b_, Fig. 56, be reproduced with longer oblique lines at the ends but with the same length of horizontal lines, it will appear closer and the horizontal lines will be judged as shorter. The reader will find it interesting to draw a number of these portions of the Mueller-Lyer figure with the horizontal line in each case of the same length but with longer and longer obliques at the ends.

The dynamic theory of Lipps gives an important role to the inner activity of the observer, which is not necessarily separated from the objects viewed, but may be felt as being in the objects. That is, in viewing a figure the observer unconsciously separates it from surrounding space and therefore creates something definite in the latter, as a limiting activity. These two things, one real (the object) and one imaginary, are balanced against each other. A vertical line may suggest a necessary resistance against gravitational force, with the result that the line appears longer than a horizontal one resting in peace. The difficulty with this theory is that it allows too much opportunity for purely philosophical explanations, which are likely to run to the fanciful. It has the doubtful advantage of being able to explain illusions equally well if they are actually reversed from what they are. For example, gravity could either contract or elongate the vertical line, depending upon the choice of viewpoint.

The confusion theory depends upon attention and begins with the difficulty of isolating from illusory figures the portions to be judged. Amid the complexity of the figure the attention cannot easily be fixed on the portions to be judged. This results in confusion. For example, if areas of different shapes such as those in Fig. 60 are to be compared, it is difficult to become oblivious of form or of compactness. In trying to see the two chief parallel lines in Fig. 38, in their true parallelism the attention is being subjected to diversion, by the short oblique parallels with a compromising result. Surely this theory explains some illusions successfully, but it is not so successful with some of the illusions of contrast. The fact that practice in making judgments in such cases as Figs. 45 and 56 reduces the illusion even to ultimate disappearance, argues in favor of the confusion theory. Perhaps the observer devotes himself more or less consciously to isolating the particular feature to be judged and finally attains the ability to do so. According to Auerbach's indirect-vision theory the eyes in judging the two halves of the horizontal line in _a_, Fig. 56, involuntarily draw imaginary lines parallel to this line but above or below it. Obviously the two parts of such lines are unequal in the same manner as the horizontal line in the Mueller-Lyer figure appears divided into two unequal parts.

Somewhat analogous to this in some cases is Brunot's mean-distance theory. According to this we establish "centers of gravity" in figures and these influence our judgments.

These are glimpses of certain trends of theories. None is a complete success or failure. Each explains some illusions satisfactorily, but not necessarily exclusively. For the present, we will be content with these glimpses of the purely theoretical aspects of visual illusions.

VII

ILLUSIONS OF DEPTH AND OF DISTANCE

Besides the so-called geometrical illusions discussed in the preceding chapters, there is an interesting group in which the perception of the third dimension is in error. When any of the ordinary criteria of relief or of distance are apparently modified, illusions of this kind are possible. There are many illusions of this sort, such as the looming of objects in a fog; the apparent enlargement of the sun and moon near the horizon; the flattening of the "vault" of the sky; the intaglio seen as relief; the alteration of relief with lighting; and various changes in the landscape when regarded with the head inverted.

Although some of the criteria for the perception of depth or of distance have already been pointed out, especially in Chapter III, these will be mentioned again. Distance or depth is indicated by the distribution of light and shade, and an unusual object like an intaglio is likely to be mistaken for relief which is more common. An analysis of the lighting will usually reveal the real form of the object. (See Figs. 70, 71, 72, 73, 76 and 77.) In this connection it is interesting to compare photographic negatives with their corresponding positive prints.

Distance is often estimated by the definition and color of objects seen through great depths of air (aerial perspective). These distant objects are "blurred" by the irregular refraction of the light-rays through non-homogeneous atmosphere. They are obscured to some degree by the veil of brightness due to the illuminated dust, smoke, etc., in the atmosphere. They are also tinted (apparently) by the superposition of a tinted atmosphere. Thus we have "dim distance," "blue peaks," "azure depths of sky," etc., represented in photographs, paintings, and writings. Incidentally, the sky above is blue for the same general reasons that the atmosphere, intervening between the observer and a distant horizon, is bluish. The ludicrous errors made in estimating distances in such regions as the Rockies is usually accounted for by the rare clearness and homogeneity of the atmosphere. However, is the latter a full explanation? To some extent we judge unknown size by estimated distance, and unknown distance by estimated size. When a person is viewing a great mountain peak for the first time, is he not likely to assume it to be comparable in size to the hills with which he has been familiar? Even by allowing considerable, is he not likely to greatly underestimate the size of the mountain and, as a direct consequence, to underestimate the distance proportionately? This incorrect judgment would naturally be facilitated by the absence of "dimness" and "blueness" due to the atmospheric haze.

Angular perspective, which apparently varies the forms of angles and produces the divergence of lines, contributes much information in regard to relative and absolute distances from the eye of the various objects or the parts of an object. For example, a rectangle may appear as a rhomboid. It is obvious that certain data pertaining to the objects viewed must be assumed, and if the assumptions are incorrect, illusions will result. These judgments also involve, as most judgments do, other data external to the objects viewed. Perhaps these incorrect judgments are delusions rather than illusions, because visual perception has been deluded by misinformation supplied by the intellect.

Size or linear perspective is a factor in the perception of depth or of distance. As has been stated, if we know the size experience determines the distance; and conversely, if we know the distance we may estimate the size. Obviously estimates are involved and these when incorrect lead to false perception or interpretation.

As an object approaches, the axes of the eyes converge more and more and the eye-lens must be thickened more and more to keep the object in focus. As stated in Chapter III, we have learned to interpret these accompanying sensations of muscular adjustment. This may be demonstrated by holding an object at an arm's length and then bringing it rapidly toward the eyes, keeping it in focus all the time. The sensations of convergence and accommodation are quite intense.

The two eyes look at a scene from two different points of view respectively and their images do not perfectly agree, as has been shown in Figs. 2 and 3. This binocular disparity is responsible to some degree for the perception of depth, as the stereoscope has demonstrated. If two spheres of the same size are suspended on invisible strings, one at six feet, the other at seven feet away, one eye sees the two balls in the same plane, but one appears larger than the other. With binocular vision the balls appear at different distances, but judgment appraises them as of approximately equal size. At that distance the focal adjustment is not much different for both balls, so that the muscular movement, due to focusing the eye, plays a small part in the estimation of the relative distance. Binocular disparity and convergence are the primary factors.

Some have held that the perception of depth, that is, of a relative distance, arises from the process of unconsciously running the point of sight back and forth. However, this view, unmodified, appears untenable when it is considered that a scene illuminated by a lightning flash (of the order of magnitude of a thousandth of a second) is seen even in this brief moment to have depth. Objects are seen in relief, in actual relation as to distance and in normal perspective, even under the extremely brief illumination of an electric spark (of the order of magnitude of one twenty-thousandth of a second). This can also be demonstrated by viewing stereoscopic pictures with a stereoscope, the illumination being furnished by an electric spark. Under these circumstances relief and perspective are quite satisfactory. Surely in these brief intervals the point of sight cannot do much surveying of a scene.

Parallax aids in the perception of depth or distance. If the head be moved laterally the view or scene changes slightly. Objects or portions of objects previously hidden by others may now become visible. Objects at various distances appear to move nearer or further apart. We have come to interpret these apparent movements of objects in a scene in terms of relative distances; that is, the relative amount of parallactic displacement is a measure of the relative distances of the objects.

The relative distances or depth locations of different parts of an object can be perceived as fluctuating or even reversing. This is due to fluctuations in attention, and illusions of reversible perspective are of this class. It is quite impossible for one to fix his attention in perfect continuity upon any object. There are many involuntary eye-movements which cannot be overcome and under normal conditions certain details are likely to occupy the focus of attention alternately or successively. This applies equally well to the auditory sense and perhaps to the other senses. Emotional coloring has much to do with the fixation of attention; that which we admire, desire, love, hate, etc., is likely to dwell more in the focus of attention than that which stirs our emotions less.

A slight suggestion of forward and backward movements can be produced by successively intercepting the vision of one eye by an opaque card or other convenient object. It has been suggested that the illusion is due to the consequent variations in the tension of convergence. Third dimensional movements may be produced for binocular or monocular vision during eye-closure. They are also produced by opening the eyes as widely as possible, by pressure on the eye-balls, and by stressing the eyelids. However, these are not important and are merely mentioned in passing.

An increase in the brightness of an object is accompanied by an apparent movement toward the observer, and conversely a decrease in brightness produces an apparent movement in the opposite direction. These effects may be witnessed upon viewing the glowing end of a cigar which is being smoked by some one a few yards away in the darkness. Rapidly moving thin clouds may produce such an effect by varying the brightness of the moon. Some peculiar impressions of this nature may be felt while watching the flashing light of some light-houses or of other signaling stations. It has been suggested that we naturally appraise brighter objects as nearer than objects less bright. However, is it not interesting to attribute the apparent movement to irradiation? (See Chapter VIII.) A bright object appears larger than a dark object of the same size and at the same distance. When the same object varies in brightness it remains in consciousness the same object and therefore of constant size; however, the apparent increase in size as it becomes brighter must be accounted for in some manner and there is only one way open. It must be attributed a lesser distance than formerly and therefore the sudden increase in brightness mediates a consciousness of a movement forward, that is, toward the observer.

If two similar objects, such as the points of a compass, are viewed binocularly and their lateral distance apart is altered, the observer is conscious of a third dimensional movement. Inasmuch as the accommodation is unaltered but convergence must be varied as the lateral distance between the two, the explanation of the illusion must consider the latter. The pair of compass-points are very convenient for making a demonstration of this pronounced illusion. The relation of size and distance easily accounts for the illusion.

Obviously this type of illusion cannot be illustrated effectively by means of diagrams, so the reader must be content to watch for them himself. Some persons are able voluntarily to produce illusory movements in the third dimension, but such persons are rare. Many persons have experienced involuntary illusions of depth. Carr found, in a series of classes comprising 350 students, 58 persons who had experienced involuntary depth illusions at some time in their lives. Five of these also possessed complete voluntary control over the phenomenon. The circumstances attending visual illusions of depth are not the same for various cases, and the illusions vary widely in their features.

Like other phases of the subject, this has been treated in many papers, but of these only one will be specifically mentioned, for it will suffice. Carr[3] has studied this type of illusion comparatively recently and apparently quite generally, and his work will be drawn upon for examples of this type. Apparently they may be divided into four classes: (1) Those of pure distance; that is, an object may appear to be located at varying distances from the observer, but no movement is perceived. For example, a person might be seen first at the true distance; he might be seen next very close in front of the eyes; then he might suddenly appear to be quite remote; (2) illusions of pure motion; that is, objects are perceived as moving in a certain direction without any apparent change in location. In other words, they appear to move, but they do not appear to traverse space; (3) illusions of movement which include a change in location. This appears to be the most common illusion of depth; (4) those including a combination of the first and third classes. For example, the object might first appear to move away from its true location and is perceived at some remote place. Shortly it may appear in its true original position, but this change in location does not involve any sense of motion.

These peculiar illusions of depth are not as generally experienced as those described in preceding chapters. A geometrical illusion, especially if it is pronounced, is likely to be perceived quite universally, but these illusions of depth are either more difficult to notice or more dependent upon psychological peculiarities far from universal among people. It is interesting to note the percentages computed from Carr's statistics obtained upon interrogating 350 students. Of these, 17 per cent had experienced depth-illusions and between one and two per cent had voluntary control of the phenomenon. Of the 48 who had experienced illusions of this type and were able to submit detailed descriptions, 25 per cent belonged to class (1) of those described in the preceding paragraph; 4 per cent to class (2); 52 per cent to class (3); and 17 per cent to class (4).

Usually the illusion involves all objects in the visual field but with some subjects the field is contracted or the objects in the periphery of the field are unaffected. For most persons these illusions involve normal perceptual objects, although it appears that they are phases of hallucinatory origin.

Inasmuch as these illusions cannot be illustrated diagrammatically we can do no better than to condense some of the descriptions obtained and reported by Carr.[3]

A case in which the peripheral objects remain visible and stationary at their true positions while the central portion of the field participates in the illusion is as follows:

The observer on a clear day was gazing down a street which ended a
block away, a row of houses forming the background at the end of the
street. The observer was talking to and looking directly at a
companion only a short distance away. Soon this person (apparently)
began to move down the street, until she reached the background of
houses at the end, and then slowly came back to her original position.
The movement in both directions was distinctly perceived. During the
illusory movement there was no vagueness of outline or contour, no
blurring or confusion of features; the person observed, seemed
distinct and substantial in character during the illusion. The
perceived object moved in relation to surrounding objects; there was
no movement of the visual field as a whole. The person decreased in
size during the backward movement and increased in size during the
forward return movement.

With many persons who experience illusions of depth, the objects appear to move to, or appear at, some definite position and remain there until the illusion is voluntarily overcome, or until it disappears without voluntary action. A condensation of a typical description of this general type presented by Carr is as follows:

All visual objects suddenly recede to the apparent distance of the
horizon and remain in that position several minutes, returning at the
end of this period to their original positions. This return movement
is very slow at the beginning, but the latter phase of the movement is
quite rapid. If the subject closes her eyes while the objects appear
at their distant position she cannot even _imagine_ those objects
located anywhere except at their apparent distant position.

In all cases (encountered by Carr) the motion in both directions is an
actual experience reality and the subject was helpless as to
initiating, stopping, or modifying the course of the illusion in any
way. Objects and even visual images (which are subject to the same
illusions) decrease in size in proportion to the amount of backward
movement and grow larger again on their return movement. The objects
are always clearly defined as if in good focus. In this particular
case the illusion occurred about twice a year, under a variety of
conditions of illumination, at various times of the day, but
apparently under conditions of a rather pronounced fatigue.

In regard to the variation in the size of objects, many who have experienced these illusions of depth testify that the size seems to change in proportion to the apparent distance, according to the law of perspective. Some persons appear in doubt as to this change and a few have experienced the peculiar anomaly of decreasing size as the objects apparently approached.

Many persons who have experienced these peculiar illusions report no change in the distinctness of objects; almost as many are uncertain regarding this point; and as many report a change in distinctness. Apparently there are phases of hallucinatory origin so that there is a wide variety of experiences among those subject to this type of illusion.

According to Carr's investigation internal conditions alone are responsible for the illusion with more persons than those due to external conditions alone. With some persons a combination of internal and external conditions seem to be a necessity. Fixation of vision appears to be an essential objective condition for many observers. That is, the illusion appeared while fixating a speaker or singer in a church or a theater. With others the illusion occurs while reading. Some reported that fixation upon checkered or other regularly patterned objects was an essential condition. Among the subjective conditions reported as essential are steady fixation, concentration of attention, complete mental absorption, dreamy mental abstraction, and fatigue.

Ocular defects do not appear to be essential, for the illusions have been experienced by many whose eyes were known to be free from any abnormalities.

Period of life does not appear to have any primary influence, for those who are subject to these peculiar illusions often have experienced them throughout many years. In some cases it is evident that the illusions occur during a constrained eye position, while lying down, immediately upon arising from bed in the morning, and upon opening the eyes after having had them closed for some time. However, the necessity for these conditions are exceptional.

The control of these illusions of depth, that is, the ability to create or to destroy them, appears to be totally lacking for most of those who have experienced them. Some can influence them, a few can destroy them, a few can indirectly initiate them, but those who can both create and destroy them appear to be rare.

It may seem to the reader that the latter part of this chapter departs from the main trend of this book, for most of these illusions of depth are to a degree of hallucinatory origin. Furthermore it has been the intention to discuss only those types of illusions which are experienced quite uniformly and universally. The digression of this chapter is excused on the basis of affording a glimpse along the borderland of those groups of illusions which are nearly universally experienced. Many other phases of depth illusions have been recorded in scientific literature. The excellent records presented by Carr could be drawn upon for further glimpses, but it appears that no more space should be given to this exceptional type. The reader should be sufficiently forewarned of this type and should be able to take it into account if peculiarities in other types appear to be explainable in this manner. However, in closing it is well to emphasize the fact that the hallucinatory aspect of depth illusions is practically absent in types of illusions to which attention is confined in other chapters.

VIII

IRRADIATION AND BRIGHTNESS-CONTRAST

Many interesting and striking illusions owe their existence to contrasts in brightness. The visual phenomenon of irradiation does not strictly belong to this group, but it is so closely related to it and so dependent upon brightness-contrast that it is included. A dark line or spot will appear darker in general as the brightness of its environment is increased; or conversely, a white spot surrounded by a dark environment will appear brighter as the latter is darkened. In other words, black and white, when juxtaposed, mutually reinforce each other. Black print on a white page appears much darker than it really is. This may be proved by punching a hole in a black velvet cloth and laying this hole over a "black" portion of a large letter. The ink which appeared so black in the print, when the latter was surrounded by the white paper, now appears only a dark gray. Incidentally a hole in a box lined with black velvet is much darker than a piece of the black velvet surrounding the hole.

The effects of brightness-contrast are particularly striking when demonstrated by means of lighting, a simple apparatus being illustrated diagrammatically in Fig. 62. For example, if a hole _H_ is cut in an opaque white blotting paper and a large piece of the white blotting paper is placed at _C_, the eye when placed before the opening at the right will see the opening at _H_ filled with the background _C_. The hole _H_ may be cut in thin metal, painted a dull white, and may be of the shape of a star. This shape provides an intimacy between the hole and its environment which tends to augment the effects of contrasts. _R_ and _F_ are respectively the rear and front lamps. That is, the lamps _R_ illuminate _C_, which "fills" the hole and apparently is the hole; and the lamps _F_ illuminate the diffusing white environment _E_. The two sets of lamps may be controlled by separate rheostats, but if the latter are unavailable the lamps (several in each set) may be arranged so that by turning each one off or on, a range of contrasts in brightness between _E_ and _H_ (in reality _C_) may be obtained. (By using colored lamps and colored papers as discussed in Chapter IX the marvelous effects of color-contrast may be superposed upon those of brightness-contrast.)

If, for example, _C_ is very feebly illuminated and _E_ is very bright, _C_ will be pronounced black; but when the lamps _F_ are extinguished and no light is permitted to reach _E_, the contrast is reversed, and _C_ may actually appear "white." Of course, it is obvious that white and black are relative terms as encountered in such a case. In fact in brightness-contrasts relative and not absolute values of brightness are usually the more important. In order to minimize the stray light which emerges from _H_, it is well to paint the inside of both compartments black with the exception of sufficiently large areas of _C_ and _E_. The use of black velvet instead of black paint is sometimes advisable. It is also well to screen the lamps as suggested in the diagram. This simple apparatus will demonstrate some very striking effects of contrasts in brightness and will serve, also, to demonstrate even more interesting effects of contrasts in color.

Two opposite contrasts obtainable by means of a simple apparatus illustrated in Fig. 62 may be shown simultaneously by means of white, black, and gray papers arranged as in Fig. 63. In this figure the gray is represented by the partially black _V_s, each of which contains equal amounts of black and of white. When held at some distance this serves as a gray and the same effect is apparent as is described for the case of actually gray _V_s. An excellent demonstration may be made by the reader by using two _V_s, cut from the same sheet of gray paper, and pasted respectively upon white and black backgrounds, as in Fig. 63. It will be apparent that the one amid the black environment appears much brighter than the one (same gray) amid the white environment. This can be demonstrated easily to an audience by means of a figure two feet long. It is interesting to carry the experiment further and place a _V_ of much darker gray on the black background than the _V_ on the white background. The persistency of the illusion is found to be remarkable, for it will exist even when the one _V_ is actually a much darker gray than the other. To become convinced that the two grays are of the same brightness in Fig. 63, it is only necessary to punch two holes in a white or gray card at such a distance apart that they will lie respectively over portions of the two _V_s when the card is laid upon Fig. 63. The grays in the holes should now appear alike because their environments are similar.

The importance of contrasts in brightness and in color cannot be overemphasized, and it appears certain that no one can fully realize their effectiveness without witnessing it in a manner similar to that suggested in Fig. 62.

Many illusions of brightness-contrast are visible on every hand. For example, the point at which the mullions of a window cross will be seen to appear brighter than the remaining portions of them when viewed against a bright sky. Conversely, in Fig. 64, dark spots appear where the white bars cross. This is purely an illusion and the same type may be witnessed by the observant many times a day. In Fig. 64 it is of interest to note that the illusion is weak for the crossing upon which the point of sight rests, but by averted vision the illusion is prominent for the other crossings. This is one of the effects which depends upon the location in the visual field.

No brightness-contrasts are seen correctly and often the illusions are very striking. If a series of gray papers is arranged from black to white, with the successive pieces overlapped or otherwise juxtaposed, a series of steps of uniform brightness is not seen. An instrument would determine the brightness of each as uniform, but to the eye the series would appear somewhat "fluted." That is, where a light gray joined a darker gray the edge of the former would appear lighter than its actual brightness, and the edge of the darker gray would appear darker than it should. This may also be demonstrated by laying a dozen pieces of white tissue paper in a pile in such a manner that a series of 1, 2, 3, 4, etc., thickness would be produced. On viewing this by transmitted light a series of grays is seen, and the effect of contrast is quite apparent. Such a pattern can be made photographically by rotating before a photographic plate a disk with openings arranged properly in steps.

Many demonstrations of the chief illusion of brightness-contrast are visible at night under glaring lighting conditions. It is difficult or impossible to see objects beyond automobile headlights, and adjacent to them, in the visual field. Objects similarly located in respect to any surface sufficiently bright are more or less obscured. Characters written upon a blackboard, placed between two windows, may be invisible if the surfaces seen through the window are quite bright, unless a sufficient quantity of light reaches the blackboard from other sources. Stage-settings have been changed in perfect obscurity before an audience by turning on a row of bright lights at the edge of the stage-opening. The term "blinding light" owes its origin to this effect of brightness-contrast.

The line of juncture between a bright and a dark surface may not be seen as a sharp line, but as a narrow band of gray. When this is true it is possible that an undue amount of area is credited to the white. In preceding paragraphs we have seen the peculiar effect at the border-lines of a series of grays. This may have something to do with the estimate; however, irradiation may be due to excitation of retinal rods and cones adjacent to, but not actually within the bright image.

A remarkable effect which may be partially attributable to irradiation can be produced by crossing a grating of parallel black lines with an oblique black line. At the actual crossings the black appears to run up the narrow angle somewhat like ink would under the influence of surface tension. This is particularly striking when two gratings or even two ordinary fly-screens are superposed. The effect is visible when passing two picket-fences, one beyond the other. If a dark object is held so that a straight edge appears to cross a candle-flame or other light-source, at this portion the straight edge will appear to have a notch in it.

Irradiation in general has been defined as the lateral diffusion of nervous stimuli beyond the actual stimulus. It is not confined to the visual sense but irradiation for this sense is a term applied to the apparent enlargement of bright surfaces at the expense of adjacent darker surfaces. The crescent of the new moon appears larger in radius than the faint outline of the darker portion which is feebly illuminated chiefly by light reflected from the earth's surface. A filament of a lamp appears to grow in size as the current through it is slowly increased from a zero value; that is, as it increases in brightness. In Fig. 65 the small inner squares are of the same size but the white square appears larger than the black one. It seems that this apparent increase is made at the expense of the adjacent dark area. This phenomenon or illusion is strongest when the brightness is most intense, and is said to be greatest when the accommodation is imperfect. A very intense light-source may appear many times larger than its actual physical size.

Doubtless a number of factors may play a part in this phenomenon. It appears possible that there is a rapid spreading of the excitation over the retina extending quite beyond the border of the more intensely stimulated region, but this must be practically instantaneous in order to satisfy results of experiments. Eye-movements may play some part for, despite the most serious efforts to fixate the point of sight, a fringe will appear on the borders of images which is certainly due to involuntary eye-movements.

Irradiation has also been ascribed to spherical aberration in the eye-lens and to diffraction of light at the pupil. Printed type appears considerably reduced in size when the pupil is dilated with atropin and is restored to normal appearance when a small artificial pupil is placed before the dilated pupil. It has been suggested that chromatic aberration in the eye-lens is a contributory cause, but this cannot be very important, for the illusion is visible with monochromatic light which eliminates chromatic aberration. The experimental evidence appears to indicate that the phenomenon is of a physical nature.

There are variations in the effects attributable to radiation, and it is difficult to reduce them to simple terms. Perhaps it may aid the reader to have before him the classification presented by Boswell.[4] He describes the varieties of irradiation as follows:

1. Very rapid spreading of the excitation over the retina extending
far beyond the border of the stimulated region and occurring
immediately upon impact of the stimulating light.

2. Irradiation within the stimulated portion of the retina after the
form of a figure becomes distinctly perceptible.

3. Emanations of decreasing intensity extend themselves outward and
backward from a moving image until lost in the darkness of the
background.

4. A well known form of irradiation which occurs when a surface of
greater intensity enlarges itself at the expense of one of less
intensity.

5. A form having many of the characteristics of the first type, but
occurring only after long periods of stimulation, of the magnitude of
30 to 60 seconds or more.

IX

COLOR