Symmetropy,an entropy-like measure of visual symmetry

A new objective measure of symmetry for single patterns, called symmetropy, is developed on two bases, the two-dimensional discrete Walsh transform of a pattern and the entropy concept in information theory. It is extended to a more general measure, called the symmetropy vector. In order to test the predictive power of the symmetropy vector, multiple regression analyses of judged pattern goodness and of judged pattern complexity were carried out. The analyses show that the symmetropy vector predicts pattern goodness and pattern complexity, as well as the amount of symmetry in a pattern. They also suggest that pattern goodness is a concept based on the holistic properties of a pattern, while pattern complexity (or simplicity) is a concept based on both holistic and partial properties of a pattern.     

Effects of partial symmetry, exposure time, and backward masking on judged goodness and reproduction of visual patterns

Six experiments investigated the effects of partial symmetry in visual patterns on judgement of pattern goodness, immediate memory, and learning. In Experiments 1—III pattern goodness ratings were substantially inter-correlated among a self-paced test condition and two conditions producing moderate to severe stimulus degradation (brief tachistoscopic exposure, and backward masking): the less the partial symmetry in a pattern, the lower was the judged goodness of the pattern. In Experiments IV and V immediate reproduction of patterns was observed respectively following exposures of 5-5000 ms, and backward masking. Correct reproduction improved with degree of partial symmetry. Concordant results were found in a free recall learning task (Experiment VI). Correlations between goodness and learning and memory performance for discrete patterns were always substantial. The results strongly suggest that pattern goodness can be appraised reliably and accurately with information processing times too short to permit pattern encoding in short-term visual memory. Evaluation of pattern goodness must therefore rest upon early (precategorical) processing of symmetry features.     

Social Concepts and Judgments: A Semantic Differential Analysis of the Concepts Feminist, Man, and Woman

Male and female participants  ( N = 274)  made judgments about the social concepts of feminist , man , and woman on 63 semantic differential items. Factor analysis identified three basic dimensions termed evaluative, potency, and activity as well as two secondary factors called expressiveness and sexuality. Results for the evaluative dimension showed that the concept feminist was rated negatively with male participants rating feminist more negatively than female participants. In terms of potency, feminist was judged higher than man whereas the concept woman was rated low on this dimension. Participants also judged the concept feminist as low in expressiveness and rated woman as the most expressive. Feminist received low ratings on the erotic-sexual dimension (sexuality) by female participants and negative sexuality ratings by men. These results are discussed in terms of social role theory, gender stereotypes, and the changes in women's roles and behavior.     

Perceiving the centroid of configurations on a rolling wheel

Undergraduates observed configurations of point-lights undergoing wheel-generated motions and judged how wheel-like the movement of each stimulus appeared on a 7-point scale. Viewer judgments were predicted by a metric defining the variable parameters for the motion path of each configuration’s geometric center—the centroid. The effects on judgments of eye movement and the stimulus characteristics of rotation, translation, and configuration were explored in six experiments. First, a strain operation on the dynamic stimuli did not affect the ability of the metric to predict perceptual judgments. Second, the predictive strength of the metric did not interact with the type of eye movements used in viewing the stimuli, though judged wheel-likeness was greater under pursuit vision than under static fixation. Third, variations in the extent of translation yielded little, if any, effect on observers’ judgments, nor did translation in a circular path. Finally, for stimuli having two lights extremely close together in the configuration, the metric’s predictive value was slightly lessened but only at the limits of visual acuity. Thus, within a wide range of presentation conditions, and for a wide variety of configurations, a metric that defined the variable parameters for the motion path of the centroid was an accurate predictor of observers’ judgments of goodness of perceived rotary motion.     

Moral Reasoning as Naturally Good: A Qualified Defense of Foot's Conception of Practical Rationality

Philippa Foot's version of ethical naturalism, centered on the idea of “natural goodness,” has received a good deal of critical scrutiny. One pervasive criticism contends that less than virtuous modes of conduct may be described as naturally good or, at least, not naturally defective on her account. If true, this contradicts the most ambitious aspect of Foot's naturalistic approach to ethics: to show that judgments of moral goodness are a subclass of judgments of natural goodness. But even if one finds this line of criticism convincing, there is a less ambitious aspect of Foot's project which remains, at least in a qualified way, defensible: her conception of moral reasoning as a legitimate form of practical rationality. This more modest claim turns not on the view that moral judgments are a subclass of judgments of natural goodness but merely on the idea that moral reasoning itself is naturally good for us.     

Developmental reversal in classification accuracy due to an increase with age in orientation-free judgments.

A complete developmental reversal in accuracy was obtained in Experiment I in which third graders, sixth graders, and adults judged the class membership of patterns presented in a same-different task. An examination of the task requirements and pattern classes employed led to the hypothesis that the reversal in accuracy resulted from an increase with age in orientation-free judgments. The results of Experiment II, in which adults were told to not rotate the patterns, and Experiment III, which was a replication of Experiment I using symmetric rather than areally skewed pattern classes, provided confirmation for that hypothesis.     

The role of pattern goodness in the reproduction of backward masked patterns.

Four experiments investigated the role of pattern goodness in backward masking using five- and four-dot patterns constructed by placing dots in the cells of a 3 x 3 matrix. In Experiment 1, subjects rated the goodness of these patterns and the results replicated previous work showing that good patterns had few alternatives. In Experiment 2, the dot patterns were the target stimuli in a backward masking task using a variety of masking stimuli. For all masking, good patterns were reproduced more accurately than poor patterns. In Experiment 3, the goodness of the masking stimulus was varied. The results indicated that good patterns were reproduced more accurately (replicating Experiment 2) and that good patterns were less effective as stimulus than were poor patterns. In Experiment 4, a long interstimulus interval which precluded masking was used to determine whether goodness affected encoding or memory. At these intervals, there were no differences among patterns, suggesting that the effect of pattern goodness was on rate of encoding. These results demonstrate the importance of configural properties in pattern perception.     

Judgments of similarity and spatial models

Ss judged the similarity between all pairs of stimulus objects under 3 conditions: when the objects were (a) Munsell 5R color patches varying in value and chroma; (b) parallelorams varying in size and tilt; and (c) circles-with-radius varying in diameter and angle of radius. For each set of judgments, the pattern of deviations from the Euclidean model was used to diagnose the most appropriate spatial model. The results confirm previous findings that the Euclidean space is appropriate for judgments of color patches, but that the city block space is appropriate for judgments of geometrie forms which vary on perceptually distinct dimensions.     

The perception of length on curved and flat surfaces

In three experiments, observers judged the apparent extents of spatial intervals along the surface of a curved cylinder or a flat plane that was binocularly viewed in a natural, indoor environment. The observers' judgments of surface lengths were precise and reliable but were also inaccurate and subject to relatively large constant errors. These distortions differed among the observers, but they tended to perceive lengths oriented along the curved dimension of the cylinder as being longer than physically equivalent lengths in the noncurved dimension. This phenomenon did not occur when the observers judged curved and noncurved paths on the flat surface. In addition, some observers' judgments of length were affected by changes in the distance to the cylinder, whereas others were affected by the cylinder's orientation in space. These results demonstrate that the perception of length on surfaces is highly dependent on the particular context in which the length occurs.     

What's in a face: Individual differences in face perception

White and black females judged the similarity of all pairs of white and black male faces. An individual difference multidimensional scaling analysis of the similarity judgments indicated that most of the dimensions underlying the perceptions of male faces involved affective (honest, tense, attractive) characteristics rather than simple physical features (eye width, mouth height). The major physical dimension was face shape (long vs. wide). The dimensions were similar for black and white subjects. An individual difference hypothesis that we pay attention to those characteristics that we possess was partially confirmed.     

The trajectory effect in intermodal temporal order judgments

Subjects judged which one of two patterns, a visual or a tactile pattern, had been presented first. The visual and tactile displays were placed in close spatial proximity. The patterns appeared to move across their respective displays. Although irrelevant to the temporal order judgment (TOJ), the direction of motion of the patterns--the trajectory--affected the judgments. When the leading pattern was moving towards the trailing pattern (consistent movement), subjects tended to judge it, correctly, as leading. When the leading pattern was moving away from the trailing pattern (inconsistent movement), subjects tended to judge it, incorrectly, as trailing. Changing the spatial position of the arrays such that the pattern trajectories were no longer towards one another eliminated the effect of movement on TOJs. Although there was a substantial difference in performance on consistent and inconsistent trials, there were no differences in subjects' ratings of their performances. The results demonstrate that the trajectory effect can be obtained multimodally. The issues whether the effect of motion alters the perceived temporal separation between the visual and tactile patterns, and whether the visual and tactile patterns are represented by a common framework, are discussed.     

The effect of hand position and pattern motion on temporal order judgments

Subjects made temporal order judgments (TOJs) of tactile stimuli presented to the fingerpads. The subjects judged which one of two locations had been stimulated first. The tactile stimuli were patterns that simulated movement across the fingerpads. Although irrelevant to the task, the direction of movement of the patterns biased the TOJs. If the pattern at one location moved in the direction of the second location, the subjects tended to judge the first location as leading the second location. If the pattern moved in the opposite direction, that location was judged as trailing. In a series of experiments, the effect of the spatial position of the hands and fingers on TOJs and the perception of the direction of pattern movement were examined. Changing the position of the hands so that the patterns no longer moved directly toward each other reduced or eliminated the effect of motion on TOJs. In a variation of Aristotle's illusion, the moving patterns were presented to crossed and uncrossed fingers. The results indicated that, contrary to Aristotle's illusion, the subjects processed the moving patterns relative to an environmental framework, rather than to the local direction of motion on the fingerpads. Presenting the patterns to crossed hands produced results similar to those obtained with crossed fingers: The subjects processed the patterns according to an environmental framework.     

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.     

Judgment stability and pseudorecognition of random and patterned configurations

Thirty six simple patterns were judged as “random” or “patterned” by adult Ss. Category judgments were consistent whether Ss were told that 1/4, 1/2, or 3/4 of the patterns were random or if no proportion was specified. In a second experiment, Ss viewed a series of slides previously judged patterned followed by a recognition series with two additional patterned slides inserted in a series of otherwise random slides. Although slides were never labeled random or patterned, Ss made the most false recognitions for the two patterned slides. In another condition where random and patterned slides were reversed, most false recognitions were made for the two random slides. Both Gamer’s notion of hypothetical set size and an analysis of balanced elements fit the results, but the adequacy of both hypotheses can be questioned when applied to previous results with more complex patterns.     

Effects of array organization on same-different judgments

Two experiments investigated the role of array organization in the simultaneous matching task. Multielement arrays of letters were arranged in either “good” or “poor” configurations and subjects were asked to determine whether all the letters were the same or if at least one was different. Correct “different” responses were slower when the letters were presented in good configurations than in poor configurations. Correct “same” responses, however, were not affected by the organizational quality (goodness) of the array. This effect of pattern goodness on matching performance was not affected by the confusability of the letters being compared, the relative eccentricity (spread) of the configuration, or the ratio of different letters present on different trials. The results suggest an encoding stage locus for the effect of pattern goodness and provide evidence supporting a two-process model of same-different judgments.     

Intergroup differentiation: stereotyping as a function of status hierarchy

The authors explored how negative intergroup comparisons affect intergroup differentiation. More specifically, they tested the prediction that the in-group's negative intergroup comparisons with a high-status group would result in more negative stereotyping of a lower status out-group. The authors elicited stereotypes of a lower status university in 2 conditions. In the 1st, the participants judged only the middle-ranking university in-group and a lower status university. In the 2nd, those judgments followed comparison with a higher status university. In the 2nd condition, there was an increased differentiation between the in-group and the lower status out-group because of the more negative stereotyping of the lower status out-group. This evidence of intergroup differentiation was found only on the dimension judged most important and along which the in-group was negatively compared with the higher status group.     

Information Redundancy and Decision Behavior: A Process Tracing Investigation

Effects of information redundancy on decision behavior were studied using a process tracing decision task. Information redundancy was defined both in terms of dimension similarity as indicated by dimension labels (expected redundancy) and as actual intercorrelations among the values on the several dimensions (actual redundancy). Time constraints on the decision task were manipulated to investigate the possible interaction between constraints and redundancy. Undergraduate students (n = 140) completed three job choice tasks on the computer, each of which involved selecting one best job from among 10 job offers. Decision behavior was studied with measures of depth, pattern, and latency of search. Subjects examined less information, but in a more interdimensional search pattern and for longer durations with the redundant information dimensions. Interactions were found between actual and expected redundancy. Although time constraints were found to limit depth and latency of information search, no interactions were observed between constraints and redundancy. Future research examining the processes by which redundancy influences search behavior is discussed.     

Temporal order and tactile patterns

Temporal order judgments (TOJs) were obtained for tactile stimuli presented to subjects' fingerpads. In one set of measurements, pairs of spatial patterns were presented successively to a single fingerpad (same-site condition), to two fingers on the same hand (ipsilateral condition), or to two fingers on opposite hands (bilateral condition). The subjects were instructed to report which one of the two patterns was presented first. TOJs were more accurate in the same-site condition than in either the ipsilateral or the bilateral conditions. In the ipsilateral and bilateral conditions, performance improved when judging which one of two locations received a stimulus first, although performance levels were still lower than in the same-site condition. Increasing the size of the pattern set from which the two patterns to be judged were drawn had only a slight effect on same-site performance and no effect on ipsilateral/bilateral performance; however, changing the nature of the patterns had a considerable effect on same-site performance and a smaller effect on ipsilateral/bilateral performance. Introducing an intensity imbalance between members of the pair of stimuli also had a large effect on same-site TOJs: a less intense stimulus tended to be judged as being presented first. In the bilateral condition, however, there was a small effect in the reverse direction: more intense stimuli tended to be judged as being presented first. The intensity imbalance had no effect in the ipsilateral condition. The results suggest that different mechanisms are responsible for TOJs for patterns presented to the same-site and to separate sites and, furthermore, that separate sites may constitute separate channels for spatial information.     

Effects of similarity and repetition on memory: registration without learning?

We investigated judgments of the frequency of test items (Y) that were highly similar to studied items (X) to test a prediction made by several memory models: that the judged frequency of Y should be proportional to the judged frequency of X. Whether stimuli were pictures or words, judged frequency of Y was bimodally distributed with 1 mode at zero, suggesting that frequency judgments involve a 2-stage process in which a zero judgment is made if there is a mismatch between retrieved information and the test item. Nonzero judgements, taken by themselves, were consistent with the prediction of proportionality. In 2 experiments, the percentage of zero judgments made to Y increased with repetition of X, but in 2 others the percentage did not change beyond frequency = 1. The percentage of "new" judgments in recognition memory followed this same pattern. Because the judged frequency of X increased even as X-Y discrimination showed no improvement, we characterize the result as "registration without learning."