Patricia Cain Smith

An Illusion of Parallelism

The illusion of parallelism was discovered accidentally during observations intended for another purpose. The observations were continued under the same conditions since the initial evidence of the illusion could have been attributed to the small size of the first sample of Ss. Consequently, the data to be reported are sufficient for establishing the fact of the illusion, but were not gathered to determine its psychophysics in a traditional sense. The illusion is thac the longitudinal axes of two objects may appear parallel when, in fact, they are grossly divergent. In this experiment, S was located about 12 ft. from a small replica of a cannon which he aimed at targets by remote control. Immediately to his right at about 3 ft. was a turntable atop a pedestal. One diameter of the turntable was marked by a small rod. Ss task was to cause E to rotate the turntable so that the rod would appear parallel to the direction of aim of the cannon. When rod and cannon appeared parallel, there was frequently an obvious discrepancy between their physical directions for some positions of the cannon. Insofar as we know, this illusion has not been previously reported. Illusions of direction, of which the present illusion is but one case, are common in the literature. The paper-and-pencil illusions of Poggendorf, Zoellner, Hering, and Wundt are famous (see Boring, 1742, pp. 238-243) as are the illusions of the transactionalists (see Kilpatrick, 1761). Less familiar as iilusions are the results of the alley experiments (see Boring, 1942, pp. 288-296). Perhaps most familiar is the railroad track illusion in which a pair of suaight tracks may be perceived as both converging and parallel (for discussion, see Boring, 1952a, 1952b; Gibson, 1952). The railroad track illusion and the illusion of parallelism are similar in thac: ( a ) both may be perceived binocularly in common everyday three dimensional environments, ( b ) both are illusions of parallelism since the longirudinal axes of two objeccs may not appear parallel when physically parallel, and ( c ) in both cases S is usually aware of the illusion. In this last sense both are categorically different from the other illusions noted above where the naive S is usually unaware of the illusory nature of his perceptions. However, the magnitude of the present illusion is readily measurable, unlike thar of the railroad track illusion.

SOME STIMULI AND APTITUDES DETERMINING APPARENT PARALLELISM

Apparent parallelism was studied to determine spatial relations of S, standard, and variable which might be sufficient for veridical and illusory perceptions of parallelism. Relationships between Ss aptitude for spatial visualization (paper-and-pencil tests) and the measures of parallelism were assessed. Different spatial relations of S, standard, and variable resulted in veridical and illusory perceptions of parallelism. The magnitude of the illusory effects was inversely related to Ss aptitude for spatial visualization, the highest r being –.98. The two tests correlated +.92. A theory of apparent parallelism is proposed.

A Developmental Study of the Illusion of Parallelism

An illusion of parallelism as discovered by Smith and Smith (1962) with adults was replicated with nine age groups of children, 6 through 14 yr. inclusive. The results demonstrate: (a) large errors of aiming at targets displaced from the line of regard, which diminish systematically with age; (b) an increase in the effect of the illusion with increasing age; (c) a drastic reduction of developmental effects of the illusion with a change in 5s location of observation; and (d) the comparability of the correlation matrix for children to that of adults. The effects of age were hypothesized to be due to changes in the developmental age for the aptitude of spatial visualization.

ILLUSION OF PARALLELISM IN REDUCED ILLUMINATION

A picture-plane theory of the illusion of parallelism was tested by replicating, with only standard and variable dimly visible, portions of a previous study demonstrating positive and negative directions of the illusion. The differences between means of the two studies ranged from 0.2° to 11.6°. Correlation between the matrices of the two studies was +.62, indicative of common determinants, one of which was proposed to be the aptitude of spatial visualization. The picture-plane theory remained tenable.