PERCEPTION 



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Oppei 



Wundt 



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Helmholtz 



Delboeuf 



Miiller-Lyer 



Poggendorf 



Zdllner 



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Schumann 



Herlng 



fig. 34. Some of the classical optic- 

 geometric illusions. In the left section, 

 so-called illusions of extent; in the 

 right action, illusions of angles. Both 

 extent and angle are affected simul- 

 taneously in several of these patterns, 

 e.g. in the Miiller-Lyer illusion flower 

 left), and in Schumann's upright and 

 rotated squares {middle right). 



rupted vs. uninterrupted extents in his squares (fig. 

 34). The most famous illusion-, of extent, however, 

 are the circle illusions of Delboeuf (98), an illusion 

 of area (fie;. 34), and the Miiller-Lyer 'paradox' 

 (355) in which the length of a line is over- or under- 

 estimated, depending on the ancle formed In the 

 'wings'; where these wings form acute angles with 

 the main line, the line is underestimated; where the 

 angles formed are obtuse, the line is overestimated 

 (fig. 34, lower left). 



Illusions involving angles arc just as diverse as 

 those of extent, beginning in i860 with the Poggen- 

 dorff and Zollner figures, both reported by Zdllner 

 (559) in i860 [although Poggendorff's figure was not 

 named for him until much later (79)]. There were 

 many variants of these effects, such as Hering's figure 

 (199) and the numerous illusions of 'shape 1 in which a 

 simple geometric form appears distorted on super- 

 position on various repetitively patterned back- 

 grounds, as shown in figure 35 (370). 



The numerous theories that have been introduced 

 from time to time to account for these illusions have 

 been reviewed by Boring (53) and by Woodworth & 

 Schlosberg (549). Most of the theories are ad hoc, and 

 only one, the recent approach by Piaget (376), is 

 quantitative. Piaget's theory, however, seems to us 

 contradicted by the observation by Pritchard (389) 

 that the major classes of optic-geometric illusions keep 



their effects when viewed with complete stabilization 

 of the retinal image. Of great Interest, however, is 

 the recurrent notion thai most or all of the illusions 

 are, in fact, tendencies towards size or shape con- 

 stancy that are misapplied ( 46 _\ -,04), or the broader 

 but equivalent view that the illusory patterns present 

 atypical 'rigged' environments to which the perceiv er 

 adapts as he does to dioptrically induced distortions 

 Of his input (Held, unpublished observations). 



In a recent formulation of this view by Tausch 

 1 1 > _> I, illusions of extent and angles are derived from 

 size and shape constancy, as shown in figures 36 and 

 37. In the ordinary view of a rectangular table (seen 

 from the front), the far edge has to be 'enlarged 5 in 

 perception to maintain constancy of size and the 

 angles 'rectified', the angles close bv have to be 

 made less acute and the distant angles less obtuse to 

 approach rectangularity. To a perspective drawing 

 of such a table, the same rectification tendencies are 

 applied and the tendencies persist, even when rela- 

 tively isolated lines and angles arc exhibited on paper. 

 The process involved would resemble the release' of 

 particular behavioral tendencies bv schematized or 

 fragmentary dummy-stimuli, as demonstrated in 

 ethological studies of animal perception [e.g. Tinber- 

 gen (486)]. The railroad tracks that converge as they 

 stretch toward the horizon would present another 

 original situation that is schematized in a standard 



