On the use of symmetry in the Rorschach Test.

Rorschach's justifications for the use of symmetry in his inkblots are evaluated in the light of recent empirical research concerning the perception of symmetry. The role of symmetry in response facilitation, in the production of whole and movement responses, in the creation of similar conditions for left- and right-handers, and as a response determinant, is discussed and re-evaluated.     

Perception of symmetry in infancy: the salience of vertical symmetry and the perception of pattern wholes

Four experiments were conducted to assess converging aspects of 4-month-old infants' perception of symmetry in visual patterns. Experiments 1 and 2 manipulated the structure and orientation of comparable patterns in order to evaluate the specialty of vertical symmetry. Infants showed no preference among vertically symmetrical, vertically repeated, and obliquely symmetrical patterns, but they processed vertically symmetrical patterns more efficiently than either vertically repeated patterns or obliquely symmetrical patterns. Experiment 3 manipulated the spatial separation of pattern components in order to determine the ability of young infants to integrate and coalesce information in visual patterns that is distributed in space. Infants processed vertically symmetrical patterns whose components were contiguous or nearly contiguous about the vertical axis (0 to 2.5 degrees separations) more efficiently than discontiguous patterns (5 and 10 degrees separations). Thus, extreme spatial separation about the vertical meridian caused infants to lose the advantage for vertical symmetry, and by inference their holistic perception of the visual pattern. Experiment 4 manipulated the organization of individual components of a vertical pattern in order to examine further infants' sensitivity to perceptual organization and synthesis of pattern form. Infants discriminated vertically symmetrical patterns from asymmetrical patterns with a vertical organization, thereby demonstrating sensitivity to the symmetrical organization of the pattern above their perception of components in the pattern. The results of these four experiments together corroborate and extend previous findings that vertical symmetry has a special status in early perceptual development and that infants can perceive pattern wholes.     

Facial symmetry and the perception of beauty

Evolutionary, as well as cultural, pressures may contribute to our perceptions of facial attractiveness. Biologists predict that facial symmetry should be attractive, because it may signal mate quality. We tested the prediction that facial symmetry is attractive by manipulating the symmetry of individual faces and observing the effect on attractiveness, and by examining whether natural variations in symmetry (between faces) correlated with perceived attractiveness. Attractiveness increased when we increased symmetry, and decreased when we reduced symmetry, in individual faces (Experiment 1), and natural variations in symmetry correlated significantly with attractiveness (Experiments 1 and 1A). Perfectly symmetric versions, made by blending the normal and mirror images of each face, were preferred to less symmetric versions of the same faces (even when those versions were also blends) (Experiments 1 and 2). Similar results were found when subjects judged the faces on appeal as a potential life partner, suggesting that facial symmetry may affect human mate choice. We conclude that facial symmetry is attractive and discuss the possibility that this preference for symmetry may be biologically based.     

On the relation between indistinguishability of identical particles and (anti)symmetry of the wave function in quantum mechanics

Two different concepts of distinguishability are often mixed up in attempts to derive in quantum mechanics the (anti)symmetry of the wave function from indistinguishability of identical particles. Some of these attempts are analyzed and shown to be defective. It is argued that, although identical particles should be considered as observationally indistinguishable in (anti)symmetric states, they may be considered to be conceptually distinguishable. These two notions of (in)distinguishability have quite different physical origins, the former one being related to observations while the latter has to do with the preparation of the system.     

Effects of pattern orientation and number of symmetry axes on the detection of mirror symmetry in dot and solid patterns

It has been postulated that as the number of axes of symmetry in a pattern increases, so pattern 'goodness' increases. Recently, a distinction was made between two different theoretical accounts of regularity or 'goodness' in relation to patterns with mirror symmetry: the 'transformational' and the 'holographic' models. It was argued that the former predicts a 'goodness' ordering of four > three > two > one whereas the latter predicts four > two > three > one, where '>' means greater regularity or goodness. In three experiments, we have tested these predictions. In experiment 1, we measured percentage correct and reaction time to dot patterns which had one, two, three, or four axes of symmetry and were flashed for 150 ms. Experiment 2 was identical except that patterns were presented for 2000 ms. In experiment 3, dot patterns were replaced by solid shapes which also had one, two, three, or four axes of symmetry. Although it was found that stimuli with four axes clearly allowed superior performance to that of stimuli with one axis, results obtained with stimuli with two and three axes were almost identical and in between those obtained with one and four axes. The data thus support the suggestion that extra axes add 'goodness' to symmetrical patterns but not in a monotonic fashion.     

Goodness of regularity in dot patterns: global symmetry, local symmetry, and their interactions

Goodness is a classic Gestalt notion defined as salience or perceptual strength of a given pattern. All operational models of goodness have assigned a central role to mirror symmetry but not much attention has been paid to the distinction between global and local mirror symmetry, and their possible interactions. We designed eight different types of dot patterns (all consisting of 80 dots), combining different numbers (0, 1, and 2) and relative orientations (parallel or orthogonal to each other) of local and global axes of symmetry (affecting 50% or 100% of the dots, respectively) at different absolute orientations (vertical and horizontal). Each of 640 trials consisted of a short presentation of a new dot pattern, which subjects had to classify as regular or random. We hypothesised that the overall goodness of patterns is not the simple sum of the amount of regularity present in them but depends on the cooperation and competition between symmetries. The results confirmed our hypothesis, showing that performance in this regularity-detection task did not increase in a linear way when some symmetries were added to other symmetries.     

Uniqueness and symmetry in bargaining theories of justice

For contractarians, justice is the result of a rational bargain. The goal is to show that the rules of justice are consistent with rationality. The two most important bargaining theories of justice are David Gauthier’s and those that use the Nash’s bargaining solution. I argue that both of these approaches are fatally undermined by their reliance on a symmetry condition. Symmetry is a substantive constraint, not an implication of rationality. I argue that using symmetry to generate uniqueness undermines the goal of bargaining theories of justice.     

Fluctuations and phase symmetry in coordinated rhythmic movements

Pendular, clocking movements typify mammalian terrestrial locomotion. They can be investigated with a procedure in which people swing hand-held pendulums at the wrists, comfortably and rhythmically. Pendular, clocking behavior was examined for in-phase and out-of-phase coordinations. The periodic timing and powering of rhythmic movements in the comfort state follow from different laws (Kugler & Turvey, 1986). One law guides the assembling of the reference frame for "clocking." Another law guides the assembling of the muscular, escapement processes determining the cycle energy. Wing and Kristofferson's (1973) method for parsing periodic-timing variance into independent "clock" and "motor" sources was applied. Mean periodicity was unaffected by phase. "Clock" fluctuations, however, were larger out of phase than in phase. "Motor" fluctuations were indifferent to phase but reflected the departures of individual wrist-pendulum systems from their preferred periods. It appears that an intended phase relation is realized as a constraint on "clock" states. These states are more stable under the in-phase constraint than under the out-of-phase constraint.     

Redundancy in the perception of bilateral symmetry in dot textures

Redundancy in the perception of bilateral symmetry in dynamic dot textures was investigated using two-alternative forced-choice techniques. It was found that the symmetry information utilized by the visual system fell within a strip approximately 1 deg wide about the central axis of symmetry, irrespective of the size of the texture at the retina. Outside this strip, the symmetry information was found to be completely redundant.     

Visual and haptic discrimination of symmetry in unfamiliar displays extended in the z-axis

We investigated, in two experiments, the discrimination of bilateral symmetry in vision and touch using four sets of unfamiliar displays. They varied in complexity from 3 to 30 turns. Two sets were 2-D flat forms (raised-line shapes and raised surfaces) while the other two were 3-D objects constructed by extending the 2-D shapes in height (short and tall objects). Experiment 1 showed that visual accuracy was excellent but latencies increased for raised-line shapes compared with 3-D objects. Experiment 2 showed that unimanual exploration was more accurate for asymmetric than for symmetric judgments, but only for 2-D shapes and short objects. Bimanual exploration at the body midline facilitated the discrimination of symmetric shapes without changing performance with asymmetric ones. Accuracy for haptically explored symmetric stimuli improved as the stimuli were extended in the third dimension, while no such a trend appeared for asymmetric stimuli. Unlike vision, haptic response latency decreased for 2-D shapes compared with 3-D objects. The present results are relevant to the understanding of symmetry discrimination in vision and touch.     

On the detection of time-reversal symmetry breaking by photoemission with circularly polarized light in the high- T c superconductor Bi2212

We argue that that in their recent experiment in which they claim to have found evidence for a time-reversal symmetry broken state, Kaminski et al. () (Nature, 416, p. 610) overlooked small temperature-dependent changes in the superstructure of Bi2212. These subtle changes may manifest themselves by changing the final state configurations of the photoemission process and thus invalidate their ultimate conclusions.     

Complexity and goodness of dot patterns varying in symmetry

Summary Two experiments were performed to specify stimulus determinants of pattern complexity and pattern goodness. Dot patterns distributed in 3×3 and 4×4 matrices with a rectilinear frame were used in Experiment 1, and dot patterns in hexagonal frameworks with a circular frame were used in Experiment 2. The patterns were invariant for transformations of rotation or reflection, and formed symmetry groups of different orders, i.e., cyclic and dihedral groups. The complexity and goodness of the patterns depended upon such stimulus variables as follows: (1) complexity decreased with the order of symmetry groups with equal weights for cyclic and dihedral groups, whereas goodness increased with the order of both symmetry groups with different weights; (2) the simplicity and goodness of patterns with a vertical axis were greater than those with a horizontal axis and those with an oblique one; (3) the complexity of the patterns that had collinear elements with equal length was rated the simplest; (4) pattern goodness increased as a function of the number of dots and the concentrations of dot to rotation/reflection axis in 3×3 and 4 × 4 matrices. Thus, complexity and goodness of pattern differed with respect to these stimulus variables.     

On the utility of looking in the “wrong” direction1

In his reply to Lamiell, Foss, and Cavenee (1980), Shweder (1980) fails to address an important question: Did the behavior report task used by Lamiell et al. meet his requirements for a “diffieult memory condition,” or did it not? In light of the nature of the illusory correlation hypothesis and Lamiell et al.'s findings, it is explained that for any of three possible answers to this question (yes, no, or maybe) the integrity of the illusory correlation hypothesis in its present form is compromised. It is also explained that further research on the hypothesis is likely to be pointless, because Lamiell et al.'s findings suggest that it is not salvageable in any form. Finally, it is explained that the incompatibility between lay persons' usage of personality concepts and the study of individual differences does not lead inextricably to the conclusion that the former have no legitimate role to play in a science of personality.     

Arm coordination symmetry and breathing effect in front crawl

This study analysed the relationships among arm coordination symmetry, motor laterality and breathing laterality during a 100-m front crawl, as a function of expertise. Ten elite swimmers (G1), 10 mid-level swimmers (G2), and 8 non-expert swimmers (G3) composed three skill groups, which were distinguished by velocity, stroke rate, stroke length, breathing frequency (BF) and the mean number of strokes between two breaths - the stroke breath (SB) - over a 100-m front crawl. Four stroke phases were identified by video analysis (catch, pull, push and recovery) and the index of coordination (IdC) measured the lag time between the propulsive phases of the two arms. The three modes of coordination are catch-up (IdC<0%), opposition (IdC=0%) and superposition (IdC>0%). The IdC was established as the mean of IdC1 and IdC2, which measured the lag time between the propulsive phases of the left and right arms, respectively. The coordination symmetry was analysed by comparing IdC1 and IdC2, and the breathing effect was studied by distinguishing IdC1 (and IdC2) with and without breathing. Motor laterality was determined by an adaptation of the Edinburgh Handedness Inventory. Breathing laterality was determined by a questionnaire and observation during the 100-m trial. Most of the front crawl swimmers showed asymmetric arm coordination, with propulsive discontinuity on one side and propulsive superposition on the other. This asymmetry was most often related to breathing laterality (a preferential breathing side for a unilateral breathing pattern) and motor laterality (arm dominance), with different profiles noted. More than the breathing laterality itself, the breathing actions of the non-expert swimmers amplified their asymmetric coordination on the breathing side. Conversely, the elite swimmers, who had higher and more stable spatial-temporal parameters (velocity and stroke lengths), a high coordination value (IdC) and lower breathing frequency (BF), managed their race better than the less proficient swimmers and their asymmetric arm coordination was not disturbed by breathing actions. By determining the dominant arm and the preferential breathing side, the coach can obtain a swimmer profile that allows both coach and swimmer to better understand and respond to excessive coordination asymmetry.     

Lack of symmetry in employees' perceptions of the psychological contract

Despite debate on the nature of employees' perceptions of their psychological contract, little research has compared employees' and employers' sides of the psychological contract. All 80 items from both scales in the Psychological Contract Inventory were used in a survey of 436 currently working, non-student respondents. Structural equation modeling yielded nonsymmetrical perspectives on promises and obligations, highlighting the validity of approaching the issues via individual perceptions.     

The role of ON- and OFF-channel processing in the detection of bilateral symmetry

We present evidence that grouping for luminance does not take precedence over the detection of bilaterally symmetrical patterns. Using single-axis and double-axis images, we found that element pairs within which luminance is held constant drive symmetry-detection mechanisms more effectively than pairs within which luminance varies. Moreover, the performance decrement observed for patterns defined by element pairs within which luminance varies is not specific to interchannel variation. Luminance variation within the ON and OFF channels has the same effect as variation between the channels on the performance of axis-orientation identification tasks. It is argued that this constitutes possible evidence for subchannels within the ON and OFF channels. One of the characteristics of the subchannels is that each processes only a limited range of luminance steps. The implications of this type of luminance processing for the detection of symmetry in the visual scene are discussed.