A. W. Pressey

An extension of assimilation theory to illusions of size, area, and direction

Two postulates, one concerning assimilation and the other concerning attentive fields, are employed to explain the Ponzo, Poggendorff, Wundt, and Hering illusions. Several new configurations are predicted from the theory. In addition, changes in the magnitude or direction of illusion which result from alterations of the basic illusion are explained.

A theory of the Mueller-Lyer illusion.

The Mueller-Lyer illusion is explained on the basis of the central tendency effect which refers to errors of overestimation and underestimation that occur whenever repeated judgments of a series of stimuli are made. It was noted that the theory could be extended to explain some, but not all, other types of geometrical illusions.

Further developments in the assimilation theory of geometric illusions: The adjacency ,principle

It is argued that the parallel lines illusion is the basic model for many visual distortions that are produced by geometric patterns. An experiment assessed the effect of moving the contextual contour away from the standard contour in two directions—away from the center of the attentive field and toward the center of the attentive field. The degree of illusion declined as the contextual magnitude moved away from the standard magnitude, but the rate of decline was more rapid when the contextual stimulus was moved away from the center of the attentive field. The results necessitated the addition of a new postulate for the assimilation theory of geometric illusions. This postulate states that the effectiveness of a contextual magnitude decreases as the distance between the contextual magnitude and the standard magnitude increases. The postulate was translated into a mathematical form in a manner analogous to the way in which the “attentive field” postulate was quantified. The new formula was successful in predicting both the pattern of means and the pattern of variances found in this study. The formula was cross-validated with data from the Ponzo and reversed Mueller-Lyer illusions.

The assimilation theory of geometric illusions: An additional postulate

The assimilation theory of geometric illusions is extended to include an additional postulate which states that “assimilative effects increase with an increase in the range of contextual magnitudes”. The effects of several stimulus variables on the Müller-Lyer and Poggendorff illusions are explained on the basis of this postulate.

Effects of distance between standard and comparison lines on the Müller-Lyer illusion

The Müller-Lyer illusion was measured as a joint function of gap between fins and shaft and distance between standard and comparison lines. The results showed that the traditional function relating illusion to gap was present, but that the shape of the function was greatly influenced by the distance between standard and comparison lines. The mathematical formulation of assimilation theory provided adequate predictions under the assumption that the attentive field changes as a constant ratio of target size.

Evidence for the role of attentive fields in the perception of illusions.

On the basis of the concept of attentive fields, it was predicted that the position of the comparison line would systematically affect the amount of illusion displayed in the Ponzo configuration and in two impoverished forms of the Müller-Lyer illusion. Ten of 12 predictions which seemed to be unique to assimilation theory were verified statistically and the remaining two predictions were in the correct direction. A reversed Ponzo illusion which was expected from the concept of attentive fields was not exhibited. This latter result was explained on the basis of the fact that the Müller-Lyer illusion of elongation is normally greater than the Müller-Lyer illusion of shrinkage.

A VARIATION OF THE POGGENDORFF ILLUSION

A variation of the Poggendorff illusion in which there were no closed angles was found to correlate highly with the classical Poggendorff figure. In addition, repeated trials had a similar effect on both illusions. It was concluded that explanations of the Poggendorff illusion which focus on the presence of closed acute angles are probably incorrect.

Assimilation Theory and the Reversed Müller—Lyer Illusion

The assimilation theory of geometric illusions was employed to explain the reversed ingoing form of the Müller–Lyer illusion. The mathematical formula which was used previously to predict changes in the Ponzo and Poggendorff illusions was employed in simulated experiments on the reversed Müller–Lyer illusion. It correctly predicted the form of the function, relating illusion to size of gap, that was found previously by Fellows (1967). In addition it correctly predicted the effects of increasing the length of the fins on the form of the function. Finally a reversed outgoing Müller–Lyer illusion was found when the outgoing fins were moved towards the center of the shaft.

The assimilation theory applied to a modification of the Müller-Lyer illusion

The assimilation theory of illusions, which utilizes the principle that large magnitudes in a series are underestimated and small magnitudes are overestimated, was applied to a modification of the Müller-Lyer illusion. A close link was shown to exist between the Müller-Lyer illusion, a modification of the Müller-Lyer illusion, and the Sander parallelogram. In addition, a new illusory target was predicted.

Some puzzling results on the Poggendorff illusion

Results obtained by Weintraub and Krantz on the Poggendorff illusion were critically evaluated. It was also shown that the assimilation theory of the Poggendorff illusion adequately predicted the form of the function that results from rotating one of the oblique arms.