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.     

Geometrical haptic illusions revisited: Haptic illusions compared with visual illusions

Révész (1934) reported that haptic illusions were observed in almost all of the geometrical optical illusion figures. The present study reexamined seven geometrical illusions in both haptic and visual modes. In the Müller-Lyer, Ponzo, and vertical-horizontal figures, haptic illusions equivalent to the visual illusions were observed. In the Oppel-Kundt figure, a haptic illusion similar to the visual one was obtained. In the haptic Delboeuf stimuli, the size illusion of the outer circle occurred, whereas that of the inner circle did not. No haptic illusion was obtained in the Poggendorff figure. In the Zöllner figure, a haptic illusion directionally opposite to the visual one was obtained. These results show that haptic illusions do not occur in all of the geometrical illusion figures. They also suggest that haptic illusions are not necessarily mediated by visualization and that haptic processing of the figures often occurs in a manner different from vision.     

Geometrical haptic illusions revisited: haptic illusions compared with visual illusions.

Révész (1934) reported that haptic illusions were observed in almost all of the geometrical optical illusion figures. The present study reexamined seven geometrical illusions in both haptic and visual modes. In the Müller-Lyer, Ponzo, and vertical-horizontal figures, haptic illusions equivalent to the visual illusions were observed. In the Oppel-Kundt figure, a haptic illusion similar to the visual one was obtained. In the haptic Delboeuf stimuli, the size illusion of the outer circle occurred, whereas that of the inner circle did not. No haptic illusion was obtained in the Poggendorff figure. In the Z?llner figure, a haptic illusion directionally opposite to the visual one was obtained. These results show that haptic illusions do not occur in all of the geometrical illusion figures. They also suggest that haptic illusions are not necessarily mediated by visualization and that haptic processing of the figures often occurs in a manner different from vision.     

Illusory illusions: the significance of fixation on the perception of geometrical illusions

Some well-known geometrical illusions disappear when the eyes are fixating and saccades are suppressed for a period of time. This disappearance is not accompanied by fading due to stabilisation of the retinal image. Any saccade made on purpose restores the illusion immediately. The fixation time after which some illusions disappeared was measured for four illusions and four subjects each. Effects of practice have been observed after measurements were repeated on successive days. Present theories of vision cannot readily explain the effect.     

The Relationship Between Visual Illusion and Aesthetic Preference – an Attempt to Unify Experimental Phenomenology and Empirical Aesthetics

Experimental phenomenology has demonstrated that perception is much richer than stimulus. As is seen in color perception, one and the same stimulus provides more than several modes of appearance or perceptual dimensions. Similarly, there are various perceptual dimensions in form perception. Even a simple geometrical figure inducing visual illusion gives not only perceptual impressions of size, shape, slant, depth, and orientation, but also affective or aesthetic impressions. The present study reviews our experimental phenomenological work on visual illusion and experimental aesthetics, and examines how aesthetic preference is influenced by stimulus factors determining visual illusions including anomalous surface and transparency as well as geometrical illusion. Along with line figures producing geometrical illusions, illusory surface figures inducing neon color spreading and transparency effects were used as test patterns. Participants made both of psychophysical judgments and of aesthetic judgments for the same test pattern. Both of geometrical illusions and aesthetic preferences were found to change similarly as a function of stimulus variables such as the number of filling lines and the size ratio of the inner and outer figural components. Also, following specific stimulus variables such as lightness contrast ratio and spatial interval between inducing figural elements (so called ``packmen''), strong effects of color spreading and transparency were accompanied with strong preferences. It seems that the paradigm to investigate aesthetic phenomena along with perceptual dimensions is useful to bridge the gap between experimental phenomenology and experimental aesthetics.     

Why do animals differ in their susceptibility to geometrical illusions?

In humans, geometrical illusions are thought to reflect mechanisms that are usually helpful for seeing the world in a predictable manner. These mechanisms deceive us given the right set of circumstances, correcting visual input where a correction is not necessary. Investigations of non-human animals’ susceptibility to geometrical illusions have yielded contradictory results, suggesting that the underlying mechanisms with which animals see the world may differ across species. In this review, we first collate studies showing that different species are susceptible to specific illusions in the same or reverse direction as humans. Based on a careful assessment of these findings, we then propose several ecological and anatomical factors that may affect how a species perceives illusory stimuli. We also consider the usefulness of this information for determining whether sight in different species might be more similar to human sight, being influenced by contextual information, or to how machines process and transmit information as programmed. Future testing in animals could provide new theoretical insights by focusing on establishing dissociations between stimuli that may or may not alter perception in a particular species. This information could improve our understanding of the mechanisms behind illusions, but also provide insight into how sight is subjectively experienced by different animals, and the degree to which vision is innate versus acquired, which is difficult to examine in humans.     

A descriptive model for perception of optical illusions

The apparent curves of stable geometrical illusions of angle are modeled by a first-order differential equation depending on a single parameter, called the strength of the illusion. The model is based on Brentano's theory that the human visual system tends to overestimate acute angles. It is mathematically equivalent to Hoffman's Lie-theoretic model (SIAM Review, 13 (1971), pp. 169–184) except for some deficiencies of detail in Hoffman's approach which are noted and corrected. By reversing the sign of the strength parameter, “correction” curves may be plotted which cause the illusion to “disappear,” thereby demonstrating the effectiveness and accuracy of the model. The method is illustrated with the classical illusions of Poggendorff, Zöllner, Hering, Orbison, Ponzo, and Müller-Lyer.     

The type I/type II perceptual dichotomy: a reanalysis for the illusions of extent

The categorization of geometrical illusions of extent as Type I or Type II phenomena based on variation in magnitude with age is critically examined. Methodological shortcomings and the failure of contemporary findings to show matching age trends for components of a single illusion are presented as factors undermining the usefulness of this perceptual dichotomy. Finally, it is shown that a new Type I/Type II dichotomy based on changes in perceived size rather than amount of illusion indicates a developmental commonality among most of the illusions of extent.     

Illusions prepared as stereograms

The loci of organization and the modes of operation of certain perceptual mechanisms may be determined by presenting appropriate stimuli independently to each eye in such a way that they become superimposed in stereoscopic vision. It is possible that understanding of the mechanisms responsible for the appearance of certain “geometrical illusions” may be furthered by adopting this procedure. The two functional components of a sample of illusions are distinguished and illustrated in the form of stereograms.     

Visual illusions viewed as stabilized retinal images

Some well-known visual illusions have been examined under conditions which remove the effect of eye movements so that the image on the retina is stationary. Under these conditions the simple geometrical illusions are perceived in the normal way. Ambiguous perceptive figures show the reversals at about the usual rate provided that the subject is able to direct his attention to a salient point of the pattern. Certain regular stationary patterns produce illusory shadows which appear to move across the pattern in normal vision. These shadows are not seen when the effect of eye movements is removed.     

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.     

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.     

Visual illusions and direct perception: Elaborating on Gibson's insights

Gibson argued that illusory pictorial displays contain “inadequate” information (1966, p. 288) but also that a “very special kind of selective attention” (p. 313) can dispel the illusion–suggesting that adequate perceptual information could in fact be potentially available to observers. The present paper describes Gibson's treatment of geometrical illusions and reviews pertinent empirical evidence. Interestingly, Gibson's insights have been corroborated by recent findings of inter- and intra-observer variability in susceptibility to visual illusions as a function of culture, learning and task. It is argued that these findings require a modification of the general Gibsonian principle of perception as the detection of specifying information. Withagen and Chemero's (2009) evolutionary motivated reconceptualization of perception predicts observers' use of both specifying and non-specifying information and inter- and intra-observer variability therein. Based on this reconceptualization we develop an ecological approach to visual illusions that explains differential illusion effects in terms of the optical variable(s) detected.     

Latency correction explains the classical geometrical illusions

There is a significant delay between the time when light hits the retina and the time of the consequent percept. It has been hypothesized that the visual system attempts to correct for this latency by generating a percept representative of the way the world probably is at the time the percept is elicited, rather than a percept of the recent past. Here we show that such a 'perceiving the present' hypothesis explains a number of classical geometrical illusions: the Hering, Orbison, Müller-Lyer, Double Judd, Poggendorff, Corner, and Upside-down-T illusions. Each stimulus is perceived as it would project in the next moment were the observer moving through the scene the stimulus probably represents. We also examine one general class of predictions made by the hypothesis, and report psychophysical experiments confirming the predictions.     

Geometrical haptic illusions: The role of exploration in the Müller-Lyer,vertical-horizontal,and Delboeuf illusions

This article surveys studies of the occurrence, in the haptic modality, of three geometrical illusions well known in vision, and it discusses the nature of the processes underlying these haptic illusions.We argue that the apparently contradictory results found in the literature concerning them may be explained, at least partially, by the characteristics of manual exploratory movements. The Müller-Lyer illusion is present in vision and in haptics and seems to be the result of similar processes in the two modalities. The vertical-horizontal illusion also exists in vision and haptics but is due partly to similar processes (bisection) and partly to processes specific to each modality (anisotropy of the visual field and overestimation of radial vs. tangential manual exploratory movements). The Delboeuf illusion seems to occur only in vision, probably because exploration by the index finger may exclude the misleading context from tactile perception. The role of these haptic exploratory movements may explain why haptics is as sensitive as vision to certain illusions and less sensitive to others.     

The Clinical Challenges of Assimilative Integration

S. B. Messer (1992) introduced the notion of assimilative integration in psychotherapy, theorizing that integrative practitioners adhere to their preferred theoretical paradigms while judiciously blending aspects from other models. His assimilative approach offers a conceptual and clinical middle ground between technical eclecticism and a grand, unified theory of psychotherapy. However, the practice of competent assimilative integration is fraught with many challenges, both theoretical and clinical. The goal of the present paper is to explore the challenges of implementing assimilative integration. First, the theoretical and clinical barriers to assimilative approaches are considered. Second, the use of assimilative integration to avoid therapeutic failures is discussed. Finally, a case example is presented to illustrate the author's attempt to assimilate narrative, interpretive interventions within his preferred cognitive–behavioral treatment paradigm.     

Assimilation and contrast illusions: Differences in plasticity

Three experiments show differences in the plasticity of the contrast and assimilation portions of the Delboeuf, Ebbinghaus, and Ponzo illusions. Contrast illusions show decrement in illusion magnitude with free inspection, whereas assimilation illusions do not. A model to explain both the original distortion and the differential susceptibility of the two classes of illusion to decrement is offered.     

What is the End Point of Psychotherapy Integration? A Commentary

This commentary on six papers about assimilative integration considers the place assimilative integration, as defined by Messer, ought to have in the discussion on psychotherapy integration. After briefly summarizing the contribution of each paper, with particular attention to whether the paper takes a position on the end point of psychotherapy integration, the author compares the relative benefits of assimilative integration to those of a unified grand theory. He argues that assimilative integration, as an end point, is preferable to a unified grand theory because it has a more generative influence on both theory evolution and clinical practice.     

Are size illusions in simple line drawings affected by shading?

In a number of simple line drawings, such as the Müller-Lyer or Judd figures, we can experience strong distortions of perceived space-geometric illusions. One way of explaining these effects is based on the perspective information that can be read from the line drawings. For instance, the 'inappropriate constancy scaling' theory advocates that the inferred three-dimensional structure of the pictured object is used by the perceptual system to adjust the size of line-drawing components. Such a theory would predict that additional depth cues, for instance shading added to line drawings, should affect these illusions because they influence the three-dimensional appearance. We present here systematic measurements of the magnitude of length misjudgments in horizontal Müller-Lyer and Judd figures for three configurations: (i) pure line drawings, and with shading attached to (ii) the top, and (iii) the bottom of the figures. The latter two configurations are unambiguously interpreted as 'folded' structures with a horizontal edge behind the image plane or protruding from it, respectively. While we could not find any effect of shading in our experimental data, we did observe a length misjudgment in Judd figures that corresponds precisely to the asymmetry that can be observed in the Müller-Lyer illusion for inward and outward fins. This pattern of results is not consistent with notions of inappropriate constancy scaling but is fully coherent with the view that neural filtering mechanisms, which are affecting the perceived position of line intersections, are responsible for this type of geometrical illusions.     

Positive Illusions in Parenting: Every Child Is Above Average

This study examined the paradox between the difficulties of parenting and the high levels of parenting satisfaction in terms of positive illusions. Results were consistent with a positive illusions model, as biological parents with a child between the ages of 2 and 5 reported unrealistically positive views of their children. They rated their own children as possessing more positive and less negative attributes than the average child. The more positively parents rated themselves, the more positively they rated their children. Parents' self-esteem scores, unrealistically positive ratings of the child, and positive illusions of parenting were related to 3 aspects of the parenting experience. This study extends the literature on positive illusions to encompass parents' positive illusions about their young children.