On Iachello's model of cuprate superconductors

A U(3) model proposed by Iachello for superconductivity in cuprate materials is analyzed. The model consists of s and d pairs (approximated as bosons) in a two-dimensional Fermi system with a surface. The transition occurs between a phase in which the system is a condensate of one type of boson, and a phase which is a mixture of two types of bosons. In the current work we have investigated the validity of the Bogoliubov approximation, and we used a reduced Hamiltonian to determine a phase diagram, the symmetry of the phases, and the temperature dependence of the heat capacity.     

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.     

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.     

Rationality,sociology and the symmetry thesis

This paper attempts to clarify the debate between those philosophers who hold that the development of science is governed by objective standards of rationality and those sociologists of science who deny this. In particular it focuses on the debate over the ‘symmetry thesis’. Bloor and Barnes argue that a properly scientific approach to science itself demands that an investigator should seek the same general type of explanation for all decisions and actions by past scientists, quite independently of whether or not she or he happens to agree with those decisions or approve those actions as ‘correct’ or ‘rational’. I try to improve on previous treatments of the ‘rationalist’ position (by Lakatos, Laudan, Newton‐Smith and Brown) and clarify the exact asymmetries to which the ‘rationalist’ is, and is not, committed.     

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.     

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.     

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.     

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.     

An update on the search for symmetry in nonhumans

Sidman et al.'s (1982) failure to find evidence for symmetry (bidirectional associations between stimuli) in monkeys and baboons set the stage for decades of work on emergent relations in nonhumans. They attributed the failure to the use of procedures that did not (1) promote stimulus control based on the relation between the sample and correct comparison and (2) reduce control by irrelevant stimulus features. Previous reviews of symmetry in nonhumans indicated that multiple exemplar training and successive matching might encourage appropriate stimulus control. This review examined 16 studies that investigated symmetry in 94 subjects, including pigeons, rats, capuchin monkeys, and baboons. Several studies used alternative training procedures to minimize sources of irrelevant stimulus control, and many combined multiple exemplar training with other procedural modifications. Symmetry was observed in approximately 30% of subjects. Studies that reported the strongest evidence for symmetry used successive matching-to-sample procedures that included training on both symbolic and identity relations, and studies finding mixed evidence employed alternative methods. These studies highlight the challenge in creating training procedures that promote symmetry and the need to assess the underlying sources of control on positive demonstrations.     

Associative symmetry in the pigeon after successive matching-to-sample training

If an organism is explicitly taught an A→B association, then might it also spontaneously learn the symmetrical B→A association? Little evidence attests to such “associative symmetry” in nonhuman animals. We report for the first time a clear case of associative symmetry in the pigeon. Experiment 1 used a successive go/no go matching‐to‐sample procedure, which showed all of the training and testing stimuli in one location and intermixed arbitrary and identity matching trials. We found symmetrical responding that was as robust during testing (B→A) as during training (A→B). In Experiment 2, we trained different pigeons using only arbitrary matching trials before symmetry testing. No symmetrical responding was found. In Experiment 3, we trained other pigeons with only arbitrary matching trials and then tested for symmetry. When these pigeons, too, did not exhibit symmetrical responding, we retrained them with intermixed identity and arbitrary matching trials. Less robust symmetrical responding was obtained here than in Experiment 1. Collectively, these results suggest that identity matching may have to be learned concurrently with arbitrary matching from the outset of training for symmetry to emerge.     

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.     

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.