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.     

In defense of the assimilation theory of visual illusions

It is argued that, contrary to Schiano's view (1986), assimilation theory does explain the nonmonotonic relationship between degree of distortion and size of context.     

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.     

The distribution postulate in Bohm's theory

On Bohm's formulation of quantum mechanics particles always have determinate positions and follow continuous trajectories. Bohm's theory, however, requires a postulate that says that particles are initially distributed in a special way: particles are randomly distributed so that the probability of their positions being represented by a point in any regionR in configuration space is equal to the square of the wave-function integrated overR. If the distribution postulate were false, then the theory would generally fail to make the right statistical predictions. Further, if it were false, then there would at least in principle be situations where a particle would approach an eigenstate of having one position but in fact always be somewhere very different. Indeed, we will see how this might happen even if the distribution postulate were true. This will help to show how loose the connection is between the wave-function and the positions of particles in Bohm's theory and what the precise role of the distribution postulate is. Finally, we will briefly consider two attempts to formulate a version of Bohm's theory without the distribution postulate.     

The tilt-constancy theory of visual illusions

The authors argue that changes in the perception of vertical and horizontal caused by local visual cues can account for many classical visual illusions. Because the perception of orientation is influenced more by visual cues than gravity-based cues when the observer is tilted (e.g., S. E. Asch & H. A. Witkin, 1948), the authors predicted that the strength of many visual illusions would increase when observers were tilted 30 degrees. The magnitude of Z?llner, Poggendorff, and Ponzo illusions and the tilt-induction effect substantially increased when observers were tilted. In contrast, the Müller-Lyer illusion and a size constancy illusion, which are not related to orientation perception, were not affected by body orientation. Other theoretical approaches do not predict the obtained pattern of results.     

Autokinetic movement in geometric illusions: a note.

Four static geometrical illusions were presented in an autokinetic movement situation. 50 Ss saw each form four times. Of the total responses, 36% were no-movement responses while 37% of the time the total figure was seen as moving. The meaning 27% of the responses involved apparent movement in only a part of the figure. In general, the elements seen as moving are the parts misperceived in the static geometrical illusion.     

The effects of display and observer strategy variables on Bourdon assimilation illusions

When a solid (filled-in) triangle is mirror-reflected about its vertex such that one angle arm and its reflection form a straight edge, this straight edge appears as a chevron bent in the direction of the other sides of the triangles, an effect directionally opposite to the well-known tilt illusion that occurs with outline angles. It has been proposed that these negative solid-angle illusions (assimilation effects) which occur in dual-angle (Bourdon-type) displays result from a failure to discriminate between the test (judged) edges and the bisectors of the solid angles. In dual-angle outline displays, near-zero effects have been attributed to the availability of collinearity cues. These hypotheses were tested in two experiments in which cues to collinearity were reduced by inserting gaps between the angles and in which collinearity information was increased by adding thick 'necks' to the displays. The results are consistent with predictions and implicate not only the nature of the angle display, but also the way in which observers perform the matching task in the production of assimilation effects.     

The effect of movement velocity on form perception: geometric illusions in dynamic displays

We investigated the effects of movement velocity on the perception of simple geometric trajectories. We show that when an ellipse is traced by the continuous displacement of a spot against an empty background, the subjective aspect ratio (R = vertical axis/horizontal axis) of the figure depends on the law of motion of the spot. If the tangential velocity of the spot is constant, very large and subject-specific biases emerge in the perception of the aspect ratio. If the tangential velocity of the spot is made equal to that of an elliptic motion with aspect ratio R less than 1, and resulting from the vectorial composition of two harmonic functions (Lissajous motion) there is a general trend to perceive the ellipse as being flatter than in reality. The effect, however, is not symmetric: when the velocity follows a Lissajous modulation with R greater than 1, highly significant biases are still present in most subjects, but no common trend emerges from the experimental population. The results are discussed in the context of recent findings on the relationship between form and kinematics in spontaneous human movements.     

Yang's iris illusion: External contour causes length‐assimilation illusions1

The Delboeuf illusion and the Ebbinghaus illusion (also known as the Titchener illusion) demonstrate that an external contour can lead to size‐assimilation and size‐contrast perception. This paper explores a novel illusion, revealing that neighboring external contours can also lead to a distortion in length perception. The illusion was originally discovered from a face stimulus (Experiment 1) in which a face was depicted alongside its mirror image so as to make the four irises absolutely equidistant. The distance between the middle two irises was underestimated in Asian faces, but overestimated in Caucasian faces. The illusion was also maintained when the facial stimuli were replaced by line drawings of eyes (Experiment 2). However, the illusion vanished when the irises were presented alone. Further scrutiny of the differences in facial characteristics between Asian and Caucasian faces reveals that the illusion might be elicited by the relative position of the eye shapes. This hypothesis was confirmed in Experiment 3, in which the distances between the eye shapes and the irises were manipulated.     

Testing the tilt-constancy theory of visual illusions

Prinzmetal and Beck (2001) Journal of Experimental Psychology: Human Perception and Performance 27 206 - 217) argued that a subset of visual illusions is caused by the same mechanisms that are responsible for the perception of vertical and horizontal a theory they referred to as the tilt-constancy theory of visual illusions. They argued that these illusions should increase if the observer's head or head and body are tilted because extra reliance would then be placed on the illusion-inducing local visual context. Exactly that result had previously been reported in the case of the tilted-room and the rod-and-frame illusions. Prinzmetal and Beck reported similar increases in the tilt illusion (TI), as well as the Z?llner, Poggendorff, and Ponzo illusions. In two experiments, we re-examined the effect of head tilt on the TI. In experiment 1, we used more conventional TI stimuli, more standard experimental methods, and a more complete experimental design than Prinzmetal and Beck, and additionally extended the investigation to attraction as well as repulsion effects. Experiment 2 more closely replicated the Prinzmetal and Beck stimuli. Although we found that head tilt did increase TIs in both experiments, the increases were of the order of 1 degrees -2 degrees, more modest than the 7 degrees reported by Prinzmetal and Beck. Significantly, the TI increase was larger when inducing tilts and head tilts were in the same direction than when they were in opposite directions, suggesting that the tilt-constancy theory may be oversimplified. In addition, because previous evidence renders unlikely the claim that the Poggendorff illusion can be explained simply in terms of misperceived orientation of the transversals, the question arises whether there might be some other explanation for the increase in the Z?llner, Poggendorff, and Ponzo illusions with body tilt that Prinzmetal and Beck reported.     

Susceptibility to semantic illusions: An individual-differences perspective

When askedHow many animals of each kind did Moses take on the ark?, people frequently respond “two” even though they know it was Noah, not Moses, who took animals on the ark. We replicate previous research by showing that susceptibility to semantic illusions is influenced by the semantic relatedness of both the impostor word and the surrounding context. However, we also show that the two text manipulations make independent contributions to semantic illusions, and we propose two individual-differences mechanisms that might underlie these two effects. We propose that the ability to resist the lure of a semantically related impostor word is related to the individual’s skill at accessing and reasoning about knowledge from long-term memory. And we propose that the ability to resist the lure of the surrounding sentential context is related to the individual’s capacity to simultaneously process and store information in working memory.     

An empirical taxonomy of visual illusions

A classification system for visual-geometric illusions, based upon the interrelationships between behavioral responses to various distortions was created. Forty-five illusion configurations were presented to 221 observers. Factor analysis revealed that there are five classes of illusions. A secondorder analysis revealed that visual distortions are ultimately reducible to two global types of distortions: illlusions of extent and illusions of shape or direction.     

A mathematical theory of optical illusions and figural aftereffects

If it is assumed that spurious enhancement of receptive field excitations near the intersection of image lines on the retina contributes to the cortical determination of the geometry of two-dimensional figures, an equation based on the least-squares fit of data points to a straight line-can be obtained to represent theapparent line. Such a fit serves as anextreemum on the precision with which a data set can be represented by a straight line. The disparity between theapparent line and the actual line that occurs in the case of peripheral (and to a lesser degree in more central regions of the retina) vision is sufficient to produce the perceptual errors that occur in the Poggendorff, Hering, and Mueller-Lyer illusions. The magnitude of the Poggendorff illusion as a function of the line angle is derived and experimentally tested. Blakemore, Carpenter, and Georgeson’s (1970) experimental data on angle perception are shown to fit this same function. Theapparent curve is derived for the Hering illusion. The Mueller-Lyer illusion is found to be a variation of the Poggendorff illusion. The equations are further developed and used to derive Pollack’s (1958) experimental results on figural aftereffects. The results involve onlyone experimentally determined coefficient that can be evaluated, within the limits of experimental error, in terms of physiological data. The use of these concepts provides a foundation for the abstract modeling of the initial phases of the central nervous system data reduction processes, including receptive field structure, that is consistent with the physiological limitations of the retina as a source of visual data, as well as with the findings of Hubel and Wiesel (1962).     

The social postulate of theoretical ethics

Conclusion Kant believed all and only the guilty should be punished. Other retributivists believed that only guilt should bring punishment down on a person. In neither way is the retributive theory sufficiently distinguished from utilitarianism for, on contingent grounds, the utilitarian may agree with either of these theses. The advantage of PRJ is that it brings out the difference between retributivism and utilitarianism more sharply while at the same time it manages to be a less stern and unyielding view than traditional retributivism. The retributivist need not deny the core of good sense in utilitarianism, and he certainly need not deny the connection between morality and happiness. His view is that punishment does not have to produce good consequences in order to be justified. It suffices that it be deserved and that it not produce a set of clearly bad consequences. If it is true that punishment generally does have bad consequences which more than outweigh its good consequences then retributivists and utilitarians should join hands in their condemnation of punishment. The heart of the difference between the retributivist and the utilitarian is that the latter counts punishment itself as an evil but believes that, generally speaking, it is an evil which is instrumental in the production of enough good to out-weigh its intrinsic demerit. The retributivist does not regard punishment as an evil. The pain of punishment is not by itself a reason for not punishing (so long as it is not excessive). Insofar as utilitarianism is the view that no considerations but those of utility should justify punishment, it is only one side of that counterfeit coin the other side of which is Kant's dictum: ...Woe to him who creeps through the serpent-windings of Utilitarianism to discover some advantage that may discharge him from the Justice of Punishment, or even from the due measure of it.... It is irrational for Kant to rule out concern for utility but it is also irrational for the utilitarian to rule out concern for retribution.I have tried to show in this paper that the two main aspects of a plausible theory of retribution - PRJ and that the punishment should fit the crime - can be vindicated in terms of acceptable beliefs one of which is incompatible with utilitarianism (PRJ), and one of which does not derive the respect we accord it from any connection with utilitarianism. I emphasize, however, what I previously stated, that the retributivist does not have to believe that retributive justice must prevail at all costs. What is asked for is the recognition that one purpose of punishment (and not the one purpose) can justifiably have nothing to do with utility. The sensible retributivist will concede, and gladly, that there are more things in heaven and earth than retribution.     

A criticism of the diffraction theory of some geometrical illusions

Chung Chiang (1968) invoked diffraction in the eye to explain Poggendorff’s illusion and extended the discussion to account for other geometrical illusions produced by intersecting lines. But diffraction in the eye cannot account for the displacement and rotation of lines assumed by Chung to produce Poggendorff’s illusion. And even if displacement and rotation do occur, the theory does not account for all illusions of the type considered. I am grateful to R. H. Day and M. Coltheart for critically reading a draft of this paper.