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Seeing is deceiving. Thus a familiar epigram may be challenged in order to indicate the trend of this book which aims to treat certain phases of visual illusions. In general, we do not see things as they are or as they are related to each other; that is, the intellect does not correctly interpret the deliverances of the visual sense, although sometimes the optical mechanism of the eyes is directly responsible for the illusion. In other words, none of our conceptions and perceptions are quite adequate, but fortunately most of them are satisfactory for practical purposes. Only a part of what is perceived comes through the senses from the object; the remainder always comes from within. In fact, it is the visual sense or the intellect which is responsible for illusions of the various types to be discussed in the following chapters. Our past experiences, associations, desires, demands, imaginings, and other more or less obscure influences create illusions.

An illusion does not generally exist physically but it is difficult in some cases to explain the cause. Certainly there are many cases of errors of judgment. A mistaken estimate of the distance of a mountain is due to an error of judgment but the perception of a piece of white paper as pink on a green background is an error of sense. It is realized that the foregoing comparison leads directly to one of the most controversial questions in psychology, but there is no intention on the author’s part to cling dogmatically to the opinions expressed. In fact, discussions of the psychological judgment involved in the presentations of the visual sense are not introduced with the hope of stating the final word but to give the reader an idea of the inner process of perception. The final word will be left to the psychologists but it appears possible that it may never be formulated.

In general, a tree appears of greater length when standing than when lying upon the ground. Lines, areas, and masses are not perceived in their actual physical relations. The appearance of a colored object varies considerably with its environment. The sky is not perceived as infinite space nor as a hemispherical dome, but as a flattened vault. The moon apparently diminishes in size as it rises toward the zenith. A bright object appears larger than a dark object of the same physical dimensions. Flat areas may appear to have a third dimension of depth. And so on.

Illusions are so numerous and varied that they have long challenged the interest of the scientist. They may be so useful or even so disastrous that they have been utilized or counteracted by the skilled artist or artisan. The architect and painter have used or avoided them. The stage-artist employs them to carry the audience in its imagination to other environments or to far countries. The magician has employed them in his entertainments and the camoufleur used them to advantage in the practice of deception during the recent war. They are vastly entertaining, useful, deceiving, or disastrous, depending upon the viewpoint.

Incidentally, a few so-called illusions will be discussed which are not due strictly to errors of the visual sense or of the intellect. Examples of these are the mirage and certain optical effects employed by the magician. In such cases neither the visual sense nor the intellect errs. In the case of the mirage rays of light coming from the object to the eye are bent from their usual straight-line course and the object appears to be where it really is not. However, with these few exceptions, which are introduced for their specific interest and for the emphasis they give to the “true” illusion, it will be understood that illusions in general as hereinafter discussed will mean those due to the visual mechanism or to errors of judgment or intellect. For the sake of brevity we might say that they are those due to errors of visual perception. Furthermore, only those of a “static” type will be considered; that is, the vast complexities due to motion are not of interest from the viewpoint of the aims of this book.

There are two well-known types of misleading perceptions, namely illusions and hallucinations. If, for example, two lines appear of equal length and are not, the error in judgment is responsible for what is termed an “illusion.” If the perceptual consciousness of an object appears although the object is not present, the result is termed an “hallucination.” For example, if something is seen which does not exist, the essential factors are supplied by the imagination. Shadows are often wrought by the imagination into animals and even human beings bent upon evil purpose. Ghosts are created in this manner. Hallucinations depend largely upon the recency, frequency, and vividness of past experience. A consideration of this type of misleading perception does not advance the aims of this book and therefore will be omitted.

The connection between the material and mental in vision is incomprehensible and apparently must ever remain so. Objects emit or reflect light and the optical mechanism known as the eye focuses images of the objects upon the retina. Messages are then carried to the brain where certain molecular vibrations take place. The physiologist records certain physical and chemical effects in the muscles, nerves, and brain and behold! there appears consciousness, sensations, thoughts, desires, and volitions. How? and, Why? are questions which may never be answered.

It is dangerous to use the word never, but the ultimate answers to those questions appear to be so remote that it discourages one from proceeding far over the hazy course which leads toward them. In fact, it does not appreciably further the aims of this book to devote much space to efforts toward explanation. In covering this vast and complex field there are multitudes of facts, many hypotheses, and numerous theories from which to choose. Judgment dictates that of the limited space most of it be given to the presentation of representative facts. This is the reasoning which led to the formulation of the outline of chapters.

Owing to the vast complex beyond the physical phenomena, physical measurements upon objects and space which have done so much toward building a solid foundation for scientific knowledge fail ultimately to provide an exact mathematical picture of that which is perceived. Much of the author’s previous work has been devoted to the physical realities but the ever-present differences between physical and perceptive realities have emphasized the need for considering the latter as well.

Illusions are legion. They greet the careful observer on every hand. They play a prominent part in our appreciation of the physical world. Sometimes they must be avoided, but often they may be put to work in various arts. Their widespread existence and their forcefulness make visual perception the final judge in decoration, in painting, in architecture, in landscaping, in lighting, and in other activities. The ultimate limitation of measurements with physical instruments leaves this responsibility to the intellect. The mental being is impressed with things as perceived, not with things as they are. It is believed that this intellectual or judiciary phase which plays such a part in visual perception will be best brought out by examples of various types of static illusions coupled with certain facts pertaining to the eye and to the visual process as a whole.

In special simple cases it is not difficult to determine when or how nearly a perception is true but in general, agreement among normal persons is necessary owing to the absence of any definite measuring device which will span the gap between the perception and the objective reality. Illusions are sometimes called “errors of sense” and some of them are such, but often they are errors of the intellect. The senses may deliver correctly but error may arise from imagination, inexperience, false assumptions, and incorrect associations, and the recency, frequency, and vividness of past experience. The gifts of sight are augmented by the mind with judgments based upon experience with these gifts.

The direct data delivered by the visual sense are light, intensity, color, direction. These may be considered as simple or elemental sensations because they cannot be further simplified or analyzed. At this point it is hoped that no controversy with the psychologist will be provoked. In the space available it appears unfruitful to introduce the many qualifications necessary to satisfy the, as yet uncertain or at least conflicting, definitions and theories underlying the science of psychology. If it is necessary to add darkness to the foregoing group of elemental visual sensations, this will gladly be agreed to.

The perceptions of outline-form and surface-contents perhaps rank next in simplicity; however, they may be analyzed into directions. The perception of these is so direct and so certain that it may be considered to be immediate. A ring of points is apparently very simple and it might be considered a direct sense-perception, but it consists of a number of elemental directions.

The perception of solid-form is far more complex than outline-form and therefore more liable to error. It is judged partially by binocular vision or perspective and partly by the distribution of light and shade. Colors may help to mold form and even to give depth to flat surfaces. For example, it is well known that some colors are “advancing” and others are “retiring.”

Perhaps of still greater complexity are the judgments of size and of distance. Many comparisons enter such judgments. The unconscious acts of the muscles of the eye and various external conditions such as the clearness of the atmosphere play prominent parts in influencing judgment. Upon these are superposed the numerous psycho-physiological phenomena of color, irradiation, etc.

In vision judgments are quickly made and the process apparently is largely outside of consciousness. Higher and more complex visual judgments pass into still higher and more complex intellectual judgments. All these may appear to be primary, immediate, innate, or instinctive and therefore, certain, but the fruits of studies of the psychology of vision have shown that these visual judgments may be analyzed into simpler elements. Therefore, they are liable to error.

That the ancients sensed the existence or possibility of illusions is evidenced by the fact that they tried to draw and to paint although their inability to observe carefully is indicated by the absence of true shading. The architecture of ancient Greece reveals a knowledge of certain illusions in the efforts to overcome them. However, the study of illusions did not engage the attention of scientists until a comparatively recent period. Notwithstanding this belated attention there is a vast scientific literature pertaining to the multitudinous phases of the subject; however, most of it is fragmentary and much of it is controversial. Some of it deals with theory for a particular and often a very simple case. In life complex illusions are met but at present it would be futile to attempt to explain them in detail. Furthermore, there have been few attempts to generalize and to group examples of typical phenomena in such a manner as to enable a general reader to see the complex fabric as a whole. Finally, the occurrence and application of illusions in various arts and the prominence of illusions on every hand have not been especially treated. It is the hope that this will be realized in the following chapters in so far as brevity of treatment makes this possible.

Doubtless thoughtful observers ages ago noticed visual illusions, especially those found in nature and in architecture. When it is considered that geometrical figures are very commonly of an illusory character it appears improbable that optical illusions could have escaped the keenness of Euclid. The apparent enlargement of the moon near the horizon and the apparent flattened vault of the sky were noticed at least a thousand years ago and literature yields several hundred memoirs on these subjects. One of the oldest dissertations upon the apparent form of the sky was published by Alhazen, an Arab astronomer of the tenth century. Kepler in 1618 wrote upon the subject.

Philosophers of the past centuries prepared the way toward an understanding of many complexities of today. They molded thought into correct form and established fundamental concepts and principles. Their chief tool was philosophy, the experimental attack being left to the scientists of the modern age. However, they established philosophically such principles as “space and time are not realities of the phenomenal world but the modes under which we see things apart.” As science became organized during the present experimental era, measurements were applied and there began to appear analytical discussions of various subjects including optical illusions. One of the earliest investigations of the modern type was made by Oppel, an account of which appeared in 1854. Since that time scientific literature has received thousands of worthy contributions dealing with visual illusions.

There are many facts affecting vision regarding which no theory is necessary. They speak for themselves. There are many equally obvious facts which are not satisfactorily explained but the lack of explanation does not prevent their recognition. In fact, only the scientist needs to worry over systematic explanations and theoretical generalizations. He needs these in order to invade and to explore the other unknowns where he will add to his storehouse of knowledge. A long step toward understanding is made by becoming acquainted with certain physical, physiological, and psychological facts of light, color, and lighting. Furthermore, acquaintance with the visual process and with the structure of the eye aids materially. For this reason the next two chapters have been added even at the risk of discouraging some readers.

In a broad sense, any visual perception which does not harmonize with physical measurements may be termed an “illusion.” Therefore, the term could include those physical illusions obtained by means of prisms, lenses, and mirrors and such illusions as the mirage. It could also include the physiological illusions of light and color such as after-images, irradiation, and contrast, and the psycho-physiological illusions of space and the character of objects. In fact, the scope of the following chapters is arbitrarily extended to include all these aspects, but confines consideration only to “static” illusions.

In a more common sense attention is usually restricted to the last group; that is, to the psycho-physiological illusions attending the perception of space and the character of objects although motion is often included. It should be obvious that no simple or even single theory can cover the vast range of illusions considered in the broad sense because there are so many different kinds of factors involved. For this reason explanations will be presented wherever feasible in connection with specific illusions. However, in closing this chapter it appears of interest to touch upon the more generally exploited theories of illusions of the type considered in the foregoing restricted sense. Hypotheses pertaining to illusions are generally lacking in agreement, but for the special case of what might be more safely termed “geometrical-optical illusions” two different theories, by Lipps and by Wundt respectively, are conspicuous. In fact, most theories are variants of these two systematic “explanations” of illusions (in the restricted sense).

Lipps proposed the principle of mechanical-esthetic unity, according to which we unconsciously give to every space-form a living personality and unconsciously consider certain mechanical forces acting. Our judgments are therefore modified by this anthropomorphic attitude. For example, we regard the circle as being the result of the action of tangential and radial forces in which the latter appear to triumph. According to Lipps’ theory the circle has a centripetal character and these radial forces toward the center, which apparently have overcome the tangential forces during the process of creating the circle, lead to underestimation of its size as compared with a square of the same height and breadth. By drawing a circle and square side by side, with the diameter of the former equal to the length of a side of the latter, this illusion is readily demonstrated. Of course, the square has a greater area than the circle and it is difficult to determine the effect of this disparity in area. Figure 60 where the areas of the circle and square are equal and consequently the height of the former is considerably greater than the latter, is of interest in this connection. By experimenting with a series of pairs consisting of a circle and a square, varying in dimensions from equal heights to equal areas, an idea of the “shrinking” character of the circle becomes quite apparent.

Wundt does not attribute the illusion to a deception or error of judgment but to direct perception. According to his explanation, the laws of retinal image (fixation) and eye-movement are responsible. For example, vertical distances appear greater than horizontal ones because the effort or expenditure of energy is greater in raising the eyes than in turning them through an equal angle in a horizontal plane. Unconscious or involuntary eye-movements also appear to play a part in many linear or more accurately, angular illusions, but certainly Wundt’s explanation does not suffice for all illusions although it may explain many geometrical illusions. It may be said to be of the “perceptive” class and Lipps’ theory to be of the “judgment” or “higher-process” class. As already stated, most of the other proposed explanations of geometrical illusions may be regarded as being related to one of these two theories. There is the “indistinct vision” theory of Einthoven; the “perspective” theory of Hering, Guye, Thiéry, and others; the “contrast” theory of Helmholtz, Loeb, and Heyman; and the “contrast-confluxion” theory of Müller-Lyer. In order not to discourage the reader at the outset, theories as such will be passed by with this brief glimpse. However, more or less qualified explanations are presented occasionally in some of the chapters which follow in order to indicate or to suggest a train of thought should the reader desire to attempt to understand some of the numerous interesting illusions.