Geometrical Visual Illusions Revisited: The Curse of Symmetry, the Cure of Sighting, and Taxing Task Demands

For nine popular geometrical visual-illusion figures, a mathematical analysis is provided along with a characterization of the figures’ psychological effectiveness. Supported by graphical illustrations, for the L and the T, it is shown how mathematical singularities of these figures can be isolated, and the illusions annihilated. For the Poggendorff, the Hering, and the Zöllner figures, building on observations from Kennedy and Portal (1990), sighting the figures from specific vantage points at a shallow angle is proposed as a means to overcome these illusions. For the T, the Oppel–Kundt, the Müller–Lyer, and the Ebbinghaus figures, a new experiment demonstrated that observers were able to find a slant of the stimuli at which the illusory impressions vanished. Task demands on part of the beholders comprise discrimination and identification. The observed independence of response bias and sensitivity in psychometric functions can possibly be explained by the intrusion of identifying responses into discrimination tasks.