Interactions between area and numerosity

Summary The concept of filled area, i.e. the impressionistic ensemble of parts of a stimulus field occupied by dots, is used to account for various kinds of numerosity illusions due to perceptual interaction between a number of dots and their spatial arrangement. A measure of filled area is derived from a model for the perceptual clustering of dots on the basis of relative proximity. It is shown that the quantified concept of filled area successfully predicts illusion data from earlier studies. Subsequently, a two-alternatives forced-choice numerosity experiment is reported, the data of which gave further evidence of the predictive power of the filled-area hypothesis. Our approach is discussed with respect to spatial features of dot stimuli that might be in rivalry with the filled-area factor in numerosity-estimation tasks.     

The perception of continuous curves in dot stimuli

Two categorisation experiments are reported in which the perceptual phenomenon that some simple arrays of discrete dots appear as a continuous curve whereas others are perceived as an angular contour or as consisting of separate groups of dots was investigated. Triplets of dots were presented in the first experiment, and complete or incomplete regular dot polygons (ie dots positioned on the vertices of imaginary regular polygons) in the second. In both experiments the perception of a curve versus an angle was determined mainly by the relative orientations of the dots, ie by the angles between successive virtual lines, whereas the lengths of the virtual lines had relatively little influence. In experiment 2 the number of displayed dots was shown to be a second independent factor for perceiving continuity. These results are in agreement with results from experiments on dipole textures discrimination, and suggest the psychological existence and importance of virtual lines in the visual processing of dot stimuli.     

A compensatory approach to optimal selection with mastery scores

A Bayesian approach for simultaneous optimization of test-based decisions is presented using the example of a selection decision for a treatment followed by a mastery decision. A distinction is made between weak and strong rules where, as opposed to strong rules, weak rules use prior test scores as collateral data. Conditions for monotonicity of optimal weak and strong rules are presented. It is shown that under mild conditions on the test score distributions and utility functions, weak rules are always compensatory by nature. The authors are indebted to Wilbert Kallenberg for his valuable comments and to Jan Gulmans for providing the data for the empirical example. The names of the authors are alphabetical; they are equally responsible for the contents of this paper.     

Attention switching is not a fatigable process: methodological comments on Axelrod and Guzy (1972)

Guzy and Axelrod investigated auditory attention switching by means of the click-counting paradigm and concluded that attention switching is a fatigable process. In the present comment it is shown that this conclusion is based on a faulty analysis of the data: The scores subjected to the analysis of variance were transformed such that they were no longer linear combinations of the factorial effects. Reanalyzing the data in the correct way renders perfectly linear conting functions that deviate from theoretical fatigue functions. It is concluded that the attention-switching mechanism is not fatigable.     

The perceptual onset of musical tones

The perceptual onset of a musical tone can be defined as the moment in time at which the stimulus is first perceived. In the present experiments, a simple threshold model for the perceptual onset was applied. A paradigm was used in which a sequence of tones had to be adjusted in such a way that the onsets were perceived at equally spaced moments in time. In Experiment 1, the threshold model was applied in a design in which the rise times of the tones were varied. We concluded that the perceptual onsets of the tones can, indeed, be defined as the times at which the envelopes pass a relative threshold of 15 dB below the maximum level of the tones (82 dB). In Experiment 2, the maximum levels of the tones were varied from 37 to 77 dB. The results show that there is a shift in the relative threshold, but that this shift is small relative to the shift in the stimulus level. In Experiment 3, the effect of level above masked threshold on the perceptual onset was investigated in more detail by varying the level of a background noise. The results show that the relative threshold decreases with increasing level above masked threshold. The results from our experiments strongly suggest that the relative threshold is linearly dependent on the level above masked or absolute threshold and that a 7-dB increment of this level results in a 1-dB relative threshold decrement. The threshold model is compared with a current temporal integration model for the perceptual onset of tones. It is shown that our data cannot be adequately explained by temporal integration. Our experimental results suggest that adaptation of the hearing mechanism to a certain relative stimulus level is responsible for perceptual onset. The applicability of our threshold model in various realistic musical situations is discussed.     

Effect on numerosity judgment of grouping of tones by auditory channels

Previous research suggests that numerosity judgments for sequences of tones improve when the sequence is structured such that equal and small groups of tones alternate between the ears. The present. study systematically investigates the effects of the structure of tone sequences on number judgment. Tone frequency is chosen as the grouping principle instead of spatial location. In the first experiment, sequences with equal groups of 2, 3, 4, 5, 6, or 7 tones (groups alternating between 800 and 1, 250 Hz) were compared with monotonous sequences. At a slow repetition rate of the tones (280 msec onset to onset), grouping the sequence deteriorated the numerosity judgment. At II fast repetition rate of the tones (100 msec onset to onset) grouping improved numerosity judgment, but only if the group size did not exceed 4 to 5 tones. In the second experiment, the equality of group size in the sequence as a necessary condition for the improvement was investigated. It was found that tone sequences comprised of equal groups were judged more accurately in number than sequences comprised of unequal groups. These results seem to give support for the existence of an auditory subitizing process. The results of this study are also compared with the results of studies in which sequences of tones, alternating one by om! between locations or frequencies, had to be judged in number.     

The perception of pure and mistuned musical fifths and major thirds: Thresholds for discrimination,beats, and identification

In Experiment 1, the discriminability of pure and mistuned musical intervals consisting of simultaneously presented complex tones was investigated. Because of the interference of nearby harmonics, two features of beats were varied independently: (1) beat frequency, and (2) the depth of the level variation. Discrimination thresholds (DTs) were expressed as differences in level (AL) between the two tones. DTs were determined for musical fifths and major thirds, at tone durations of 250, 500, and 1,000 msec, and for beat frequencies within a range of .5 to 32 Hz. The results showed that DTs were higher (smaller values of ΔL) for major thirds than for fifths, were highest for the lowest beat frequencies, and decreased with increasing tone duration. Interaction of tone duration and beat frequency showed that DTs were higher for short tones than for sustained tones only when the mistuning was not too large. It was concluded that, at higher beat frequencies, DTs could be based more on the perception of interval width than on the perception of beats or roughness. Experiments 2 and 3 were designed to ascertain to what extent this was true. In Experiment 2, beat thresholds (BTs) for a large number of different beat frequencies were determined. In Experiment 3, DTs, BTs, and thresholds for the identification of the direction of mistuning (ITs) were determined. For mistuned fifths and major thirds, sensitivity to beats was about the same. ITs for fifths and major thirds were not significantly different; deviations from perfect at threshold ranged from about 20 to 30 cents. Comparison of the different thresholds revealed that DTs are mainly determined by sensitivity to beats. Detailed analysis, however, indicated that perception of interval width is a relevant aspect in discrimination, especially for the fifths.     

Learning from exemplars: emulation,character formation and the complexities of ordinary life

In the field of character education role-modelling is advocated as an important pedagogical strategy. It is supposed that students learn from ‘significant others’ who exemplify important virtues and values. However, in these strategies it is not clear what and how students precisely can and should learn from exemplars and how the following of exemplars relates to the educational aim of ‘becoming a self.’ In this article, it is argued that modelling is only a relevant pedagogical strategy if moral exemplars are somehow related to life in its full extent, including its moral complexities and ambiguities. Understanding moral exemplarity demands not only the reappropriation of an Aristotelian conception of emulation but also an understanding of the typical modern relocation of moral exemplarity in the fullness of life, importantly originating from what Charles Taylor calls the Protestant ‘affirmation of ordinary life.’ In addition, a distinction is introduced between ‘role exemplarity’ and ‘existential exemplarity.’ Based on this distinction it is argued that emulation should not be limited to learning from role models, but should also include something that runs deeper, to the depth of our own subjectivity or self.