Apparent reversal frequencies in squares and trapezia: the effect of invariant and variant information

Three studies of apparent reversals (ARs) in rotating rectangular and trapezoid arrays are reported, together with a mathematical analysis. Study 1 explores the effect of different degrees of outline suppression on the frequency and distribution of ARs in squares and trapezia. Study 2 examines how modifications in both types of array reduce AR frequency, demonstrates a manipulation whereby ARs in rotating squares are eliminated, and suggests that ARs in squares and trapezia are of different origins. In the mathematical analysis, an invariant characteristic of the transformations of rotating rectangles is reported, and from this a numerical index is developed that expresses the extent to which a rotating trapezium may appear to pause just before each point of oscillation. In study 3 it is shown that this measure is a better predictor of AR frequencies than the heuristic proposed by Braunstein.     

Apparent reversals in trapezia: confirmation of the 'tan apex ratio' heuristic

A new model for predicting the frequencies of apparent reversals in rotating trapezia, proposed by the authors in 1983, is validated and extended in two studies. Experiment 1 showed that the model retained its predictive efficiency over an increased range of shapes and viewing distances, and with trapezia made of sheet metal and not, as previously, of wire. Experiment 2 was designed to investigate an unexpected effect, in which the specificity of prediction was found to decrease as the corners of the stimulus objects were slightly rounded.     

The spread of attention to hidden portions of occluded surfaces

We report two experiments in which the two-rectangles method of Egly, Driver, and Rafal (1994) was used to test whether object-specific attentional cuing advantages can spread to hidden portions of occluded objects. Displays began with portions of two rectangles hidden by a third, occluding object. One end of one of the two rectangles was cued, after which the occluder rotated around its center point and target stimuli were presented. In one condition, the occluder was removed from in front of the other objects, either by rotating away from them (Experiment 1B) or by rotating and then slipping behind them (Experiment 1B). In another condition, the occluder first rotated away but then returned to its original position. In both experiments, an object-specific cuing advantage occurred in the occluderremoved condition for targets that appeared in what had been hidden locations of the cued object. No analogous advantage occurred in the occluder-returned condition.     

Information integration study of Metelli's and Morinaga's theories of achromatic transparency

Information integration methodology was used to test Metelli's and Morinaga's theories of achromatic transparency. Stimuli were transparent achromatic disks on a background formed by two adjacent horizontal rectangles. The common border of these rectangles divided each disk in two halves. Let P and Q be the luminances of the left and right halves of a disk and let A and B be those of the left and right rectangles, respectively. Transparency is given by the ratio (P – Q)/(A – B) in Metelli's theory and is given by a weighted average of the ratios (P – Q)/(A – Q) and (P – Q)/(P – B) in Morinaga's theory. Participants rated the transparency of disks with A and B fixed and P and Q combined factorially. Morinaga's theory closely predicted the resulting pattern of curves and Metelli's theory predicted it incorrectly. Morinaga's theory could also account well for individual differences in the ratings of transparency. The results support the general idea that transparency depends on the integration of photometric luminance information rather than on the integration of perceived lightness information.     

‘Numerical trap’. A new look at outcome representation in studies on choice behaviour

In almost all experimental studies on choice behaviour the consequences of choices are limited to denumerable goods (usually money) and represented in a numerical way. It is argued that a different way of representing consequences would cause differences in social orientations. In an exploratory study (1) the kind of consequences (money, satisfaction with money and satisfaction with the situation) and (2) the way of representing consequences (numbers, rectangles, and faces) were varied. No differences were found between the three kinds of consequences represented by rectangles. Representation of money by numbers did not differ from representation of money by rectangles. However, subjects in the condition in which satisfaction with money was represented by faces were more cooperative and altruistic and less equality-oriented than subjects in the corresponding condition in which satisfaction with money was represented by rectangles. Additional correlational analyses showed differences between ways of representing consequences. It was concluded that both for theory and for future research it is important to consider how consequences are represented.     

Are children with autistic spectrum disorders susceptible to contour illusions?

Children with autism have been shown to be less susceptible to Kanisza type contour illusions than children without autism ( Happé, 1996 ). Other authors have suggested that this finding could be explained by the fact that participants with autism were required to make a potentially ambiguous verbal response which may have masked whether or not they actually perceived the illusory contours ( Ropar & Mitchell, 1999 ). The present study tested perception of illusory contours in children with autism using a paradigm that requires participants to make a forced choice about the dimensions of a shape defined by illusory contours. It was reasoned that accuracy of the participant on this task would indicate whether or not children with autism could perceive illusory contours. A total of 18 children with autistic spectrum disorder, 16 children with special educational needs not including autism and 20 typically developing children completed an experimental task which assessed perception of Kanisza‐style rectangles defined by illusory contours. There were no significant differences between the performance of the children with autism and either of the two control groups, suggesting that perception of illusory contours is intact in autism.     

The discrimination of structure: III. Representation of spatial relationships

Pigeons received a discrimination in which the spatial relationship between 2 adjacent rectangles filled with different colors signaled the trial outcome. Test trials then involved the same rectangles separated horizontally by a gap. The tests in Experiment 1 disrupted the discrimination more when the rectangles were tall and thin than when they were short and wide. Experiment 2 revealed that the width of the rectangles rather than their height determined the extent to which separating them would disrupt the original discrimination. The results are explained in terms of a template-matching account of pattern recognition with the additional assumption, supported by Experiment 3, that the size of a template can be altered to improve its match with a test pattern.     

The 'golden rectangle': some new data.

From two different series of dimensions were generated six ranges of nine rectangles each. Each range was presented to a different group of 15 men and 15 women, and a novel measure was used to assess aesthetic preference for each rectangle. The ratios between the lengths of the sides of the rectangles were the same in both series, but in one series the size of the rectangles covaried with the ratio between length and width, as in Godkewitsch's 1974 study, and in the other series the rectangles were of equal area. The subjects tended to prefer large to small rectangles in the former series and rectangles in the vicinity of the 'golden section' in the latter.     

Simulation (mostly) rules: A commentary

I consider three issues: children's attribution of belief‐based emotions, the contribution of language input to children's developing theory of mind, and the default settings we assume in our dealings with the world. I ask whether the proposals made by Mitchell, Currie and Ziegler can help throw light on each issue ( Mitchell, Currie, & Ziegler, 2009 ).     

Gestalts are more closely associated with performance on a discrimination task than are component stimuli

Distance, similarity, and other components of the physical stimulus but also gestalts are associated with the ability to discriminate between two objects. The present research bears on this confound. Identical lines were added to the opening and closing bracket of a pair of brackets to form two identical rectangles. A stimulus consisted of either one or two of these brackets, lines, or rectangles. Subjects indicated as quickly as possible whether one or two objects occurred. The discriminations between two near brackets and two near lines were more difficult than the discrimination between two near rectangles. A large distance between two objects improved the bracket and line discriminations more than the rectangle discrimination. Single brackets and lines did not result in poorer performance than did single rectangles. These results disconfirm the distance, similarity (including relational similarity), good continuation, location of geometric centers, size, closedness, symmetry, spatial frequency, redundancy, and number of lines component stimulus predictions at least twice. Both the two near brackets and the two near lines produce single gestalts, whereas each remaining 2-object stimulus results in two gestalts. Therefore, gestalts predicted performance better than did component stimuli. Another result was that the 2-object responses were faster than the 1-object responses for far objects.     

Shape discrimination for motion-defined and contrast-defined form: squareness in special.

Shape discrimination was measured for: (i) two-dimensional rectangular targets that were perfectly camouflaged within a stationary pattern of random dots and rendered visible by relative motion of the dots, and (ii) similar dotted rectangles that were rendered visible by luminance contrast. Shape discrimination was disconfounded from size discrimination by requiring subjects to discriminate the aspect ratios of rectangles whose areas were altered independently of aspect ratio. When dot speed and contrast were both high, the aspect-ratio discrimination threshold was as acute for motion-defined (MD) rectangles as for contrast-defined (CD) rectangles and, at 2-3%, corresponded to a change of side length of about 24 s arc compared to a mean dot separation of 360 s arc. Discrimination of MD rectangles collapsed at low dot speeds and could not be measured at speeds less than about 0.03-0.08 deg s-1, but discrimination of CD rectangles was almost unaffected by dot speed. The aspect-ratio discrimination threshold was lowest for a square and progressively increased as the rectangle became more asymmetric. It is suggested that the visual system contains a mechanism that compares the separations of pairs of contours along different azimuths, and that, during visual development, this shape-discrimination processing of MD and CD targets is driven by the same environmental and behavioural pressures towards a common end point. The human equivalent of a pathway that includes the cortical area MT is thought to be important for shape discrimination of MD forms.     

Aspects of Psychosomatic Orchidalgia

Children aged 5 to 9 years matched the shape of (a) small squares embedded in large rectangles and (b) small rectangles embedded in large squares. Predictions made were that (a) the influence of the whole on the perception of the part would be greatest at the 5-year-old level and (b) this effect of the whole would make the parts look to the child somewhat like the whole figure of which the part is a member. Both predictions were supported by the data. The 5-year-olds perceived the small squares as more rectangular, and the small rectangles as more square-like, significantly more than the older age groups, each result representing a shift towards the shape of the whole configuration.     

Lexical- and perceptual-based object effects in the two-rectangle cueing paradigm

Previous studies demonstrate that attentional selection can be object-based, in which the object is defined in terms of Gestalt principles or lexical organizations. Here we investigate how attentional selection functions when the two types of objects are manipulated jointly. Experiment 1 replicated Li and Logan (2008) by showing that attentional shift between two Chinese characters is more efficient when they form a compound word than when they form a nonword. Experiment 2A presented characters either alone or within rectangles (Egly, Driver, & Rafal, 1994) and the characters in a rectangle formed either a word or a nonword. Experiment 2B differed from Experiment 2A in that the two characters forming a word were in different rectangles. Experiment 3A presented the two characters of a word either within a rectangle or in different rectangles. Experiment 3B used the same design as Experiment 3A but presented stimuli of different types in random orders, rather than in blocks as in Experiments 2A, 2B and 3A. In blocked presentation, detection responses to the target color on a character were faster when this character and the cue character formed a word than when they did not, and the size of this lexical-based object effect did not vary according to whether the two characters were presented alone or within or between rectangles. In random presentation, however, the lexical-based object effect was diminished when the two characters of a word were presented in different rectangles. Overall, these findings suggest that the processes that constrain attention deployment over conjoined objects can be strategically adjusted.     

T-junctions and perceived slant of partially occluded surfaces

H?kkinen and Nyman (1997 Perception 26 29-38) reported that perceived slant is reduced when occlusion is a possible interpretation for the visual system. We present data from three experiments that confirm and expand on their finding. Our stimuli consisted of four types of stereograms depicting white central rectangles flanked on either side by two grey rectangles. The central white rectangles varied in height, thus manipulating the polarity of the T-junction information between the central and flanking rectangles. Perceived slant was smallest or not apparent when T-junction information indicated the central rectangles were nearer than the flanking rectangles and greatest when T-junction information indicated a farther central rectangle. Slant estimates for a stimulus containing a subjective pacmen-induced central rectangle were biased towards a depth step when an occlusion interpretation was possible.     

Retention of shape discrimination after regeneration of the optic nerves in the toad

Using a method of successive discrimination previously described by the author eight toads (Bufo bufo), were trained to discriminate first between horizontal and vertical rectangles, each 3.5 ± 7.5 cm., and second between horizontal and vertical rectangles each 5.0 ± 7.5 cm. Immediately after training, both optic nerves were severed in four animals and allowed to regenerate. After a period of 10 weeks without training both the operated and non-operated animals retained the capacity to discriminate both the large and the small rectangles at a level either not significantly different from training or significantly better than training.     

The Relationality of Everyday Life: The Unfinished Journey of Relational Psychoanalysis

Building on the insights embodied in Stephen Mitchell’s critiques of the developmental tilt and the metaphor of the baby, this paper aims to further illuminate the limitations of theoretical models rooted in infantile prototypes and to point relational theory toward a more thoroughgoing understanding of the contextuality and relationality of every facet of our lives. In its examinations of both the mother–infant interaction and the intricacies of the analytic relationship, the relational turn has yielded deep insights into the reciprocal, two-person causal sequences that characterize the development and dynamics of personality. But in the massive zone of living that occurs outside the nursery or the consulting room—the countless interactions and experiences of everyday life—relational theory has made less of a contribution, implicitly relying on an older psychoanalytic model in which these events of daily life reflect or express inner dynamics, rather than highlighting how daily life experiences continue to shape the inner world even as the inner world gives meaning and shape to those ongoing experiences. Drawing on both parallels and differences between Mitchell’s seminal contributions and the theoretical perspective known as cyclical psychodynamics, the paper aims to extend relational advances in understanding the mother–infant matrix and the dynamic structure of the analytic relationship to the everyday events that constitute the vast majority of our waking hours. In doing so, it points to a consequentiality to everyday life that, when appreciated and taken seriously, opens new pathways for therapeutic advance and provides a more solid and comprehensive foundation for relational theory.     

Perceptual encoding and decision strategies for integral dimensions

These three experiments employed rectangles in stimulus identification tasks. Consistent with the stimulus set used by Weintraub, the rectangles were generated by modifying a square. Across experiments, the number of stimulus/response alternatives was varied (two-, three-, and four-choice tasks). In the two-choice task, redundancy gain for the positively correlated set was just as large as for the negatively correlated set. In contrast, reaction time ws faster for the negatively correlated set than for the positively correlated set in the three-choice task (after extended practice) and in the four-choice task. Considered in the context of previous research, the data support two conclusions. First, the initial perceptual processing of rectangles is accomplished by separate dimensional analyzers operating in parallel. Second, observers adopt a different decision strategy for the negatively correlated set than for the positively correlated and the single dimension sets when the number of stimulus/response alternatives is increased.     

Extent,multiplying, and proportionality rules in children's judgments of area

The study examined children's use of multiplying and proportionality rules in judgments of area. In two experiments children judged the area of rectangles. Seven-year-olds used linear extent as an index of area. Eight- and nine-year-olds replaced the extent rule with the height × width rule. In a third experiment 8-through 11-year-olds were presented with a rectangle and a horizontal line representing the width of a second rectangle. Children were asked to indicate the height that would make the second rectangle equal in area to the first. The correct response was proportional to the product of the ratio of the widths of the two rectangles and the height of the first rectangle. Graphical and statistical analyses indicated that children applied the ratio rule to these judgments. The implications for Piaget's theory of cognitive development were discussed.     

The Apollonian Eye and the Dionysian Ear

A comparison of the aesthetic underpinnings of psychoanalytic praxis is undertaken using Nietzsche's distinction between Apollonian and Dionysian tendencies. Drawing from Nietzsche, Freud, Lacan, Jung, and Stephen Mitchell as well as research and theory from the study of infant–parent interaction, the author offers a clinical case to illustrate a perspective that gives more emphasis to Dionysian forces in psychoanalytic activity than in traditional case reporting, thus illustrating the utility of such an expansion of underlying assumptions for psychoanalytic praxis. The perspective highlights the importance of attention to “faintly conscious stimuli” on nonsymbolized embodied registers of interaction for their significance in the communication of affective meanings.     

Figural preference and the visual field

Three experiments tested a hypothesis that the shape and relative dimensions of the binocular visual field determine a preference for rectangles possessing dimensions similar to those of the golden section. The results were that Ss horizontally oriented the rectangles they had drawn in correspondence with the shape of the binocular visual field but when Ss chose the most pleasing rectangles there was no significant preference for rectangles whose long side was horizontal. For all experiments there was little preference for rectangles whose ratio of short to long side approximated the golden section. There was some evidence that the placement of the rectangles with respect to the background affects preference.