Visual Illusions Part 3

Fig. 16 might be considered to be an illusion of contour, but the length of the top horizontal line of the lower figure being apparently less than that of the top line of the upper figure is due largely to contrasting the two figures. Incidentally, it is difficult to believe that the maximum horizontal width of the lower figure is as great as the maximum height of the figure. At this point it is of interest to refer to other contrast illusions such as Figs. 20, 57, and 59.

[Ill.u.s.tration: Fig. 16.--An illusion of contrast.]

A striking illusion of contrast is shown in Fig. 17, where the central circles of the two figures are equal, although the one surrounded by the large circles appears much smaller than the other. Similarly, in Fig. 18 the inner circles of _b_ and _c_ are equal but that of _b_ appears the larger. The inner circle of _a_ appears larger than the outer circle of _b_, despite their actual equality.

[Ill.u.s.tration: Fig. 17.--Equal circles which appear unequal due to contrast (Ebbinghaus' figure).]

[Ill.u.s.tration: Fig. 18.--Equal circles appearing unequal owing to contrasting concentric circles.]

In Fig. 19 the circle nearer the apex of the angle appears larger than the other. This has been presented as one reason why the sun and moon appear larger at the horizon than when at higher alt.i.tudes. This explanation must be based upon the a.s.sumption that we interpret the "vault" of the sky to meet at the horizon in a manner somewhat similar to the angle but it is difficult to imagine such an angle made by the vault of the sky and the earth's horizon. If there were one in reality, it would not be seen in profile.

[Ill.u.s.tration: Fig. 19.--Circles influenced by position within an angle.]

[Ill.u.s.tration: Fig. 20.--Contrasting angles.]

If two angles of equal size are bounded by small and large angles respectively, the apex in each case being common to the inner and two bounding angles, the effect of contrast is very apparent, as seen in Fig.

20. In Fig. 57 are found examples of effects of lines contrasted as to length.

[Ill.u.s.tration: Fig. 21.--Owing to perspective the right angles appear oblique and vice versa.]

The reader may readily construct an extensive variety of illusions of contrast; in fact, contrast plays a part in most geometrical-optical illusions. The contrasts may be between existing lines, areas, etc., or the imagination may supply some of them.

[Ill.u.s.tration: Fig. 22.--Two equal diagonals which appear unequal.]

_Illusions of Perspective._--As the complexity of figures is increased the number of possible illusions is multiplied. In perspective we have the influences of various factors such as lines, angles, and sometimes contour and contrast. In Fig. 21 the suggestion due to the perspective of the cube causes right angles to appear oblique and oblique angles to appear to be right angles. This figure is particularly illusive. It is interesting to note that even an after-image of a right-angle cross when projected upon a wall drawn in perspective in a painting will appear oblique.

[Ill.u.s.tration: Fig. 23.--Apparent variations in the distance between two parallel lines.]

A striking illusion involving perspective, or at least the influence of angles, is shown in Fig. 22. Here the diagonals of the two parallelograms are of equal length but the one on the right appears much smaller. That _AX_ is equal in length to _AY_ is readily demonstrated by describing a circle from the center _A_ and with a radius equal to _AX_. It will be found to pa.s.s through the point _Y_. Obviously, geometry abounds in geometrical-optical illusions.

[Ill.u.s.tration: Fig. 24.--A striking illusion of perspective.]

The effect of contrast is seen in _a_ in Fig. 23; that is, the short parallel lines appear further apart than the pair of long ones. By adding the oblique lines at the ends of the lower pair in _b_, these parallel lines now appear further apart than the horizontal parallel lines of the small rectangle.

The influence of perspective is particularly apparent in Fig. 24, where natural perspective lines are drawn to suggest a scene. The square columns are of the same size but the further one, for example, being apparently the most distant and of the same physical dimensions, actually appears much larger. Here is a case where experience, allowing for a diminution of size with increasing distance, actually causes the column on the right to appear larger than it really is. The artist will find this illusion even more striking if he draws three human figures of the same size but similarly disposed in respect to perspective lines. Apparently converging lines influence these equal figures in proportion as they suggest perspective.

[Ill.u.s.tration: Fig. 25.--Distortion of a square due to superposed lines.]

Although they are not necessarily illusions of perspective, Figs. 25 and 26 are presented here because they involve similar influences. In Fig. 25 the hollow square is superposed upon groups of oblique lines so arranged as to apparently distort the square. In Fig. 26 distortions of the circ.u.mference of a circle are obtained in a similar manner.

[Ill.u.s.tration: Fig. 26.--Distortion of a circle due to superposed lines.]

It is interesting to note that we are not particularly conscious of perspective, but it is seen that it has been a factor in the development of our visual perception. In proof of this we might recall the first time as children we were asked to draw a railroad track trailing off in the distance. Doubtless, most of us drew two parallel lines instead of converging ones. A person approaching us is not sensibly perceived to grow. He is more likely to be perceived all the time as of normal size.

The finger held at some distance may more than cover the object such as a distant person, but the finger is not ordinarily perceived as larger than the person. Of course, when we think of it we are conscious of perspective and of the increase in size of an approaching object. When a locomotive or automobile approaches very rapidly, this "growth" is likely to be so striking as to be generally noticeable. The reader may find it of interest at this point to turn to ill.u.s.trations in other chapters.

The foregoing are a few geometrical illusions of representative types.

These are not all the types of illusions by any means and they are only a few of an almost numberless host. These have been presented in a brief cla.s.sification in order that the reader might not be overwhelmed by the apparent chaos. Various special and miscellaneous geometrical illusions are presented in later chapters.

V

EQUIVOCAL FIGURES

Many figures apparently change in appearance owing to fluctuations in attention and in a.s.sociations. A human profile in intaglio (Figs. 72 and 73) may appear as a bas-relief. Crease a card in the middle to form an angle and hold it at an arm's length. When viewed with one eye it can be made to appear open in one way or the other; that is, the angle may be made to appear pointing toward the observer or away from him. The more distant part of an object may be made to appear nearer than the remaining part. Plane diagrams may seem to be solids. Deception of this character is quite easy if the light-source and other extraneous factors are concealed from the observer. It is very interesting to study these fluctuating figures and to note the various extraneous data which lead us to judge correctly. Furthermore, it becomes obvious that often we see what we expect to see. For example, we more commonly encounter relief than intaglio; therefore, we are likely to think that we are looking at the former.

Proper consideration of the position of the dominant light-source and of the shadows will usually provide the data for a correct conclusion.

However, habit and probability are factors whose influence is difficult to overcome. Our perception is strongly a.s.sociated with accustomed ways of seeing objects and when the object is once suggested it grasps our mind completely in its stereotyped form. Stairs, gla.s.ses, rings, cubes, and intaglios are among the objects commonly used to ill.u.s.trate this type of illusion. In connection with this type, it is well to realize how tenaciously we cling to our perception of the real shapes of objects. For example, a cube thrown into the air in such a manner that it presents many aspects toward us is throughout its course a cube.

[Ill.u.s.tration: Fig. 27.--Ill.u.s.trating fluctuation of attention.]

The figures which exhibit these illusions are obviously those which are capable of two or more spatial relations. The double interpretation is more readily accomplished by monocular than by binocular vision. Fig. 27 consists of identical patterns in black and white. By gazing upon this steadily it will appear to fluctuate in appearance from a white pattern upon a black background to a black pattern upon a white background.

Sometimes fluctuation of attention apparently accounts for the change and, in fact, this can be tested by willfully altering the attention from a white pattern to a black one. Incidentally one investigator found that the maximum rate of fluctuation was approximately equal to the pulse rate, although no connection between the two was claimed. It has also been found that inversion is accompanied by a change in refraction of the eye.

[Ill.u.s.tration: Fig. 28.--The grouping of the circles fluctuates.]

Another example is shown in Fig. 28. This may appear to be white circles upon a black background or a black mesh upon a white background. However, the more striking phenomenon is the change in the grouping of the circles as attention fluctuates. We may be conscious of hollow diamonds of circles, one inside the other, and then suddenly the pattern may change to groups of diamonds consisting of four circles each. Perhaps we may be momentarily conscious of individual circles; then the pattern may change to a hexagonal one, each "hexagon" consisting of seven circles--six surrounding a central one. The pattern also changes into parallel strings of circles, triangles, etc.

[Ill.u.s.tration: Fig. 29.--Crossed lines which may be interpreted in two ways.]

The crossed lines in Fig. 29 can be seen as right angles in perspective with two different spatial arrangements of one or both lines. In fact there is quite a tendency to see such crossed lines as right angles in perspective. The two groups on the right represent a simplified Zollner's illusion (Fig. 37). The reader may find it interesting to spend some time viewing these figures and in exercising his ability to fluctuate his attention. In fact, he must call upon his imagination in these cases.

Sometimes the changes are rapid and easy to bring about. At other moments he will encounter an aggravating stubbornness. Occasionally there may appear a conflict of two appearances simultaneously in the same figure.

The latter may be observed occasionally in Fig. 30. Eye-movements are brought forward by some to aid in explaining the changes.

[Ill.u.s.tration: Fig. 30.--Reversible cubes.]

In Fig. 30 a reversal of the aspect of the individual cubes or of their perspective is very apparent. At rare moments the effect of perspective may be completely vanquished and the figure be made to appear as a plane crossed by strings of white diamonds and zigzag black strips.

The illusion of the bent card or partially open book is seen in Fig. 31.

The tetrahedron in Fig. 32 may appear either as erect on its base or as leaning backward with its base seen from underneath.

[Ill.u.s.tration: Fig. 31.--The reversible "open book" (after Mach).]

[Ill.u.s.tration: Fig. 32.--A reversible tetrahedron.]

The series of rings in Fig. 33 may be imagined to form a tube such as a sheet-metal pipe with its axis lying in either of two directions.

Sometimes by closing one eye the two changes in this type of illusion are more readily brought about. It is also interesting to close and open each eye alternately, at the same time trying to note just where the attention is fixed.

The familiar staircase is represented in Fig. 34. It is likely to appear in its usual position and then suddenly to invert. It may aid in bringing about the reversal to insist that one end of a step is first nearer than the other and then farther away. By focusing the attention in this manner the fluctuation becomes an easy matter to obtain.

[Ill.u.s.tration: Fig. 33.--Reversible perspective of a group of rings or of a tube.]

[Ill.u.s.tration: Fig. 34.--Schroder's reversible staircase.]

In Fig. 35 is a similar example. First one part will appear solid and the other an empty corner, then suddenly both are reversed. However, it is striking to note one half changes while the other remains unchanged, thus producing momentarily a rather peculiar figure consisting of two solids, for example, attached by necessarily warped surfaces.

[Ill.u.s.tration: Fig. 35.--Thiery's figure.]