Chapter 6 - The Influence of Angles:
Muller-Lyer Optical Illusion

A discussion of the influence of angles must include a reference to the well-known Muller-Lyer optical illusion presented in Fig. 56. It is obvious in a that the horizontal part on the left appears considerably longer than that part in the right half of the diagram. The influence of angles in this optical illusion can be easily tested by varying the direction of the lines at the ends of the two portions.

Fig. 56. - The Muller-Lyer optical illusion.

In all these figures the influence of angles is obvious. This does not mean that they are always solely or even primarily responsible for the optical illusion. In fact, the optical illusion of Poggendorff (Fig. 46) may be due to the incorrect estimation of certain linear distances, but the angles make this erroneous judgment possible, or at least contribute toward it. Many discussions of the theories or explanations of these figures are available in scientific literature of which one by Judd [A Study of Geometrical Illusions, C. H. Judd, Psych. Rev. 1899, 6, p. 241.] may be taken as representative. He holds that the false estimation of angles in the Poggendorff figure is merely a secondary effect, not always present, and in no case the source of the optical illusion; furthermore, that the illusion may be explained as due to the incorrect linear distances, and may be reduced to the type of optical illusion found in the Muller-Lyer figure. Certainly there are grave dangers in explaining an optical illusion on the basis of an apparently simple operation.

In Fig. 56, b is made up of the two parts of the Muller-Lyer optical illusion. A small dot may be placed equally distant from the inside extremities of the horizontal lines. It is interesting to note that overestimation of distance within the figure is accompanied with underestimation outside the figure and, conversely, overestimation within the figure is accompanied by underestimation in the neighboring space. If the small dot is objected to as providing an additional Muller-Lyer figure of the empty space, the dot may be left out. Instead, the observer may attempt to locate a point which is midway between the inside extremities of the horizontal lines. The error in locating this point will show that the optical illusion is present in this empty space.

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