Abstract
A STRIKING illusion, first described by Zöllner some thirty years ago, and usually called by his name, appears in Fig. 1. Of the four main lines each adjoining pair seems to converge at one end, and to diverge at the other, whereas in reality the lines are all parallel. The first step in an explanation of the illusion would be the determination of its essential factors, of its various forms, and of some general principle embracing under one formula its several varieties. The next step would be to correlate this formulation with some recognized psychological principle. The generalization is found in the statement, that the direction of the sides of an angle are deviated, toward the direction of the angle, and may be illustrated by reference to Fig. 2. In this figure the continuation of the left horizontal line seems to fall below the right horizontal line, and the continuation of the latter above the former; in reality the two are continuous. Similarly, if the continuations of the oblique lines be added, they will not seem continuous, but diver gent slightly to one side or the other. If now we call the direction of an angle the direction of the line that bisects it, then the deviation is what would result from a drawing up of the sides of the angle towards this central bisecting line; the left end of the left horizontal line would be drawn up, and the right end of the right horizontal line would be drawn down, and thus the two seem discontinuous. The same would happen, though to a less degree, if either oblique line were omitted. There are many other ways of illustrating this fact. Instead of drawing the right line horizontal, we may incline its right end downwards slightly, and then it will seem continuous with the left horizontal line. We may apparently incline both lines so that they would converge towards a point between and below them, as in Fig. 3 and the like. Two further points or corollaries should be noted: (1) that the larger the angle the greater the deviation. Similar figures with acute angles substituted for the obtuse ones would show a scarcely perceptible illusion. (2) When obtuse angles are combined with acute angles, the deviating effects of the former outweigh those of the latter. In Fig. 4 the effect of the angle ACD would be to make the line AB if continued fall below FG, while the effect of BCD would be to make AB fall above FG; the former outweighs the latter, and the illusion appears as directed by the angle ACD. The angle BCE reinforces ACD, while ACE reinforces BCD. Angles greater than 180° do not come into consideration. When all the angles about a point are equal, i.e., are right angles, the illusion disappears. Figs. 5 and 6 furnish other illustrations of the same principles. In Fig. 5 the line a seems continuous with c while it is so with b, and this because the obtuse angles formed by lines a and c with the vertical lines respectively, deviate the lines a and c towards the direction of the angles sufficiently to bring them in line with one another. Fig. 6 adds the further complication—explicable upon the same principles—that the line is deviated once in one direction and then in the reverse direction.
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Some Optical Illusions. Nature 46, 590–592 (1892). https://doi.org/10.1038/046590a0
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DOI: https://doi.org/10.1038/046590a0