Chapter III

There is a further interesting class of illustrations in which a single outward impression changes its character according as it is viewed as representing one thing or another. In a general way we see the same thing all the time, and the image on the retina does not change. But as we shift the attention from one portion of the view to another, or as we view it with a different mental conception of what the figure represents, it assumes a different aspect, and to our mental eye becomes quite a different thing. A slight but interesting change takes place if we view Fig. 4 first with the conception that the black is the pattern to be seen and the white the background, and again try to see the white as the pattern against a black background. I give a further illustration of such a change in Fig. 5. In our first and natural view of this we focus the attention upon the black lines and observe the familiar illusion, that the four vertical black bands seem far from parallel. That they are parallel can be verified by measurement, or by covering up all of the diagram except the four main bands. But if the white part of the diagram be conceived as the design against a black background, then the design is no longer the same, and with this change the illusion disappears, and the four bands seem parallel, as they really are. It may require a little effort to bring about this change, but it is marked when once realized.

A curious optical effect, which in part illustrates the change in appearance under different aspects, is reproduced in Fig. 6. In this case the enchantment of distance is necessary to produce the transformation. Viewed at the usual reading distance, we see nothing but an irregular and meaningless assemblage of black and white blotches. At a distance of not less than fifteen to eighteen feet, however, a man's head appears quite clearly. Also observe that after the head has once been realized it becomes possible to obtain suggestions of it at nearer distances.

A much larger class of ambiguous diagrams consists of those which represent by simple outlines familiar geometrical forms or objects. We cultivate such a use of our eyes, as indeed of all our faculties, as will on the whole lead to the most profitable results. As a rule, the particular impression is not so important as what it represents. Sense-impressions are simply the symbols or signs of things or ideas, and the thing or the idea is more important than the sign. Accordingly, we are accustomed to interpret lines, whenever we can, as the representations of objects. We are well aware that the canvas or the etching or the photograph before us is a flat surface in two dimensions, but we see the picture as the representation of solid objects in three dimensions. This is the illusion of pictorial art. So strong is this tendency to view lines as the symbols of things, that if there is the slightest chance of so viewing them, we invariably do so; for we have a great deal of experience with things that present their contours as lines, and very little with mere lines or surfaces. If we view outlines only, without shading or perspective or anything to definitely suggest what is foreground and what background, it becomes possible for the mind to supply these details and see foreground as background, and _vice versa_.

A good example to begin with is Fig. 7. These outlines will probably suggest at first view a book, or better a book-cover, seen with its back toward you and its sides sloping away from you; but it may also be viewed as a book opened out towards you and presenting to you an inside view of its contents. Should the change not come readily, it may be facilitated by thinking persistently of the appearance of an open book in this position. The upper portion of Fig. 8 is practically the same as Fig. 7, and if the rest of the figure be covered up, it will change as did the book cover; when, however, the whole figure is viewed as an arrow, a new conception enters, and the apparently solid book cover becomes the _flat_ feathered part of the arrow. Look at the next figure (Fig. 9), which represents in outline a truncated pyramid with a square base. Is the smaller square nearer to you, and are the sides of the pyramid sloping away from you toward the larger square in the rear? Or are you looking into the hollow of a truncated pyramid with the smaller square in the background? Or is it now one and now the other, according as you decide to see it? Here (Fig. 12) is a skeleton box which you may conceive as made of wires outlining the sides. Now the front, or side nearest to me, seems directed downward and to the left; again, it has shifted its position and is no longer the front, and the side which appears to be the front seems directed upward and to the right. The presence of the diagonal line makes the change more striking: in one position it runs from the left-hand _rear_ upper corner to the right-hand _front_ lower corner; while in the other it connects the left-hand _front_ upper corner with the right-hand _rear_ lower corner.

FIG. 12_a_.

FIG. 12_b_.

FIGS. 12, 12_a_, 12_b_.--The two methods of viewing Fig.
12 are described in the text. Figs. 12_a_ and 12_b_
are added to make clearer the two methods of viewing
Fig. 12. The heavier lines seem to represent the nearer
surface. Fig. 12_a_ more naturally suggests the nearer
surface of the box in a position downward and to the
left, and Fig. 12_b_ makes the nearer side seem to be
upward and to the right. But in spite of the heavier
outlines of the one surface, it may be made to shift
positions from foreground to background, although not
so readily as in Fig. 12.]

Fig. 14 will probably seem at first glimpse to be the view of a flight of steps which one is about to ascend from right to left. Imagine it, however, to be a view of the under side of a series of steps; the view representing the structure of overhanging solid masonwork seen from underneath. At first it may be difficult to see it thus, because the view of steps which we are about to mount is a more natural and frequent experience than the other; but by staring at it with the intention of seeing it differently the transition will come, and often quite unexpectedly.

FIG. 14_a_.

FIG. 14_b_.

FIGS. 14, 14_a_, and 14_b_.--The two views of Fig. 14
described in the text are brought out more clearly in
Figs. 14_a_ and 14_b_. The shaded portion tends to
be regarded as the nearer face. Fig. 14_a_ is more
apt to suggest the steps seen as we ascend them. Fig.
14_b_ seems to represent the hollowed-out structure
underneath the steps. But even with the shading the
dual interpretation is possible, though less obvious.]

The blocks in Fig. 15 are subject to a marked fluctuation. Now the black surfaces represent the bottoms of the blocks, all pointing downward and to the left, and now the black surfaces have changed and have become the tops, pointing upward and to the right. For some the changes come at will; for others they seem to come unexpectedly, but all are aided by anticipating mentally the nature of the transformation. The effect here is quite striking, the blocks seeming almost animated and moving through space. In Fig. 16 a similar arrangement serves to create an illusion as to the real number of blocks present. If viewed in one way--the black surface forming the tops of the blocks--there seem to be six, arranged as in Fig. 17; but when the transformation has taken place and the black surfaces have become the overhanging bottoms of the boxes, there are seven, arranged as in Fig. 18. Somewhat different, but still belonging to the group of ambiguous figures, is the ingenious conceit of the duck-rabbit shown in Fig. 19. When it is a rabbit, the face looks to the right and a pair of ears are conspicuous behind; when it is a duck, the face looks to the left and the ears have been changed into the bill. Most observers find it difficult to hold either interpretation steadily, the fluctuations being frequent, and coming as a surprise.

FIG. 16_a_.

FIG. 16_b_.

FIGS. 16, 16_a_, and 16_b_.--How many blocks are
there in this pile? Six or seven? Note the change in
arrangement of the blocks as they change in number
from six to seven. This change is described in the
text. Figs. 16_a_ and 16_b_ show the two phases of a
group of any three of the blocks. The arrangement of
a pyramid of six blocks seems the more stable and is
usually first suggested; but hold the page inverted,
and you will probably see the alternate arrangement
(with, however, the black surfaces still forming the
tops). And once knowing what to look for, you will very
likely be able to see either arrangement, whether the
diagram be held inverted or not. This method of viewing
the figures upside down and in other positions is also
suggested to bring out the changes indicated in Figs.
12, 12_a_, 12_b_, and in Figs. 14, 14_a_, 14_b_.]