Gerbino, Walter and Ventimiglia, Fabrizio and Fantoni, Carlo (2005) The Tangent illusion. Perception, Vol. 34 (Suppl.), p. 45. eISSN 1468-4233. Article.
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Here is a new geometrical illusion. Draw three disks of increasing size, all tangent to a pair of non-parallel straight lines. Ask observers (or yourself) to visually extrapolate the tangents to the two smaller disks and to evaluate whether the largest disk is also tangent or, if not, whether it is too large or too small. Surprisingly, perception of common tangency fails to occur. The largest disk appears too large, relative to the extrapolated tangents. A similar illusion is obtained if observers are asked to visually extrapolate the tangents to the two larger disks and evaluate the smallest disk. In this case, the smallest disk appears too small: observers perceive the three disks as having common tangents when the smallest disk is larger than the objectively tangent disk. Several hypotheses may account for the effect. According to the categorical hypothesis, the largest disk is overestimated and the smallest disk is underestimated, as an effect of induced categorisation. Asking observers to visualise the tangents to two disks would favour their grouping and the consequent differentiation of the third disk (in the direction of either an expansion or a shrinkage), with a paradoxical loss of collinearity. According to a distortion-based hypothesis, the illusion depends on the underestimation of the angle between the two tangents; ie on the tendency to perceive the two tangents as if they were closer to parallelism than they actually are. A more general hypothesis derives from the nonlinear shrinkage of interfigural distances, demonstrated in other visual phenomena. We ran a parametric study of the tangent illusion and varied the rate of growth of the three disks (ie the size of the angle between the two geometrical tangents) and the relative distance between their centres. Using the method of constant stimuli, we obtained data supporting the categorical hypothesis.
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