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.
Fig. 8.—This drawing may be viewed as the representation of a book standing on its half-opened covers as seen from the back of the book; or as the inside view of an open book showing the pages.
Fig. 9.—When this figure is viewed as an arrow, the upper or feathered end seems flat; when the rest of the arrow is covered, the feathered end may be made to project or recede like the book cover in Fig. 8.
A good example to begin with is Fig. 8. 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 toward 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. 9 is practically the same as Fig. 8, 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. 10), 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. 13) 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. 10.—The smaller square may be regarded as either the nearer face of a projecting figure or as the more distant face of a hollow figure.
Fig. 11.—This represents an ordinary table-glass, the bottom of the glass and the entire rear side, except the upper portion, being seen through the transparent nearer side, and the rear apparently projecting above the front. But it fluctuates in appearance between this and a view of the glass in which the bottom is seen directly, partly from underneath, the whole of the rear side is seen through the transparent front, and the front projects above the back.