Charles E. Wright

The idea of an exact number: children's understanding of cardinality and equinumerosity.

Understanding what numbers are means knowing several things. It means knowing how counting relates to numbers (called the cardinal principle or cardinality); it means knowing that each number is generated by adding one to the previous number (called the successor function or succession), and it means knowing that all and only sets whose members can be placed in one-to-one correspondence have the same number of items (called exact equality or equinumerosity). A previous study (Sarnecka & Carey, 2008) linked childrens understanding of cardinality to their understanding of succession for the numbers five and six. This study investigates the link between cardinality and equinumerosity for these numbers, finding that children either understand both cardinality and equinumerosity or they understand neither. This suggests that cardinality and equinumerosity (along with succession) are interrelated facets of the concepts five and six, the acquisition of which is an important conceptual achievement of early childhood.

Visually guided, aimed movements can be unaffected by stimulus-response uncertainty

Response times generally increase linearly with the logarithm of the number of potential stimulus–response alternatives (e.g., Hick’s law). The ubiquity and theoretical importance of this generalization make exceptions particularly interesting. Recently, Kveraga et al. (Exp Brain Res 146:307, 2002) added a third to the two previously known exceptions, demonstrating that saccade latencies were unaffected by stimulus–response uncertainty. They suggest that visually guided saccades are exceptional, because these movements can be automatically selected using a privileged pathway: the topographically organized regions in superior colliculus that convert spatially coded visual activity into spatially coded motor commands. We report that visually guided, aimed hand movements also are unaffected by both stimulus–response uncertainty and stimulus–response repetition. A second experiment demonstrated that this lack of an uncertainty effect persists for equiluminant stimuli. This result suggests that posterior parietal cortex is not the privileged pathway eliminating stimulus–response uncertainty for hand movements. Because hand movements are not guided by mechanisms in the superior colliculus, our results cast doubt on the privileged-pathway hypothesis, at least for hand movements. Instead, the absence of stimulus–response uncertainty may occur only in tasks that do not require the stimulus to be associated with a response effector and that have high stimulus–response compatibility.

Issues Related to HCI Application of Fitts's Law

Taking Fittss law as a premise—that is, movement time is a linear function of an appropriate index of difficulty—we explore three issues related to the collection and reporting of these data from the perspective of application within human–computer interaction. The central question involved two design choices. Whether results obtained using blocked target conditions are representative of performance in situations in which, as is often the case, target conditions vary from movement to movement and how this difference depends on whether discrete or serial (continuous) movements are studied. Although varied target conditions led to longer movement times, the effect was additive, was surprisingly small, and did not depend on whether the movements were discrete or serial. This suggests that evaluating devices or designs using blocked data may be acceptable. With Zhai (2004) we argue against the practice of reporting throughput as a one-dimensional summary for published comparisons of devices or designs. Also questioned is whether analyses using an accuracy-adjusted index of difficulty are appropriate in all design applications.

Top-down influences mediate hand bias in spatial attention

Spatial attention can be biased to locations near the hand. Some studies have found facilitated processing of targets appearing within hand-grasping space. In this study, we investigated how changing top-down task priorities alters hand bias during visual processing. In Experiment 1, we used a covert orienting paradigm with nonpredictive cues and emphasized the location of the hand relative to the target. Hands or visual anchors (boards) were placed next to potential target locations, and responses were made with the contralateral hand. Results indicated a hand-specific processing bias: Hand location, but not board location, speeded responses to targets near the hand. This pattern of results replicated previous studies using covert orienting paradigms with highly predictive cues. In Experiment 2, we used the same basic paradigm but emphasized the location of the response hand. Results now showed speeded responses to targets near response locations. Together these experiments demonstrated that top-down instructional sets (i.e., what is considered to be most relevant to task performance) can change the processing priority of hand location by influencing the strength of top-down, as compared with bottom-up, inputs competing for attention resources.

Coherent plaids are preattentively more than the sum of their parts

We investigated whether plaids activate preattentive mechanisms that are distinct from those activated by their component gratings. Observers searched for a target plaid, the sum of two perpendicular components in a circular window (radius = 0.65°). The target was present on half the trials. On all trials, half of the distractors had the same frequency and orientation as one component of the plaid, and the rest were the same as the other component. The target and the distractors were arrayed evenly on a circle (radius = 2.36°) around fixation. Target and distractor contrasts were randomly perturbed up to ±30%. The following results held for each of the 6 participants tested. (1) When F1 = 2 c/deg and F2 = 5.25 c/deg, response times (RTs) increased significantly when set size (number of distractors plus target, if present) was increased from four to eight. (2) When the spatial frequencies of both plaid components were the same (i.e., both 2 c/deg or both 5.25 c/deg), RTs increased very slightly, if at all, when set size was increased from four to eight. These results suggest the existence of a preattentive, plaid-sensitive mechanism with band-limited input that does not respond to individual grating components.

Evidence against global attention filters selective for absolute bar-orientation in human vision.

The finding that an item of type A pops out from an array of distractors of type B typically is taken to support the inference that human vision contains a neural mechanism that is activated by items of type A but not by items of type B. Such a mechanism might be expected to yield a neural image in which items of type A produce high activation and items of type B low (or zero) activation. Access to such a neural image might further be expected to enable accurate estimation of the centroid of an ensemble of items of type A intermixed with to-be-ignored items of type B. Here, it is shown that as the number of items in stimulus displays is increased, performance in estimating the centroids of horizontal (vertical) items amid vertical (horizontal) distractors degrades much more quickly and dramatically than does performance in estimating the centroids of white (black) items among black (white) distractors. Together with previous findings, these results suggest that, although human vision does possess bottom-up neural mechanisms sensitive to abrupt local changes in bar-orientation, and although human vision does possess and utilize top-down global attention filters capable of selecting multiple items of one brightness or of one color from among others, it cannot use a top-down global attention filter capable of selecting multiple bars of a given absolute orientation and filtering bars of the opposite orientation in a centroid task.

The centroid paradigm: Quantifying feature-based attention in terms of attention filters

This paper elaborates a recent conceptualization of feature-based attention in terms of attention filters (Drew et al., Journal of Vision, 10(10:20), 1–16, 2010) into a general purpose centroid-estimation paradigm for studying feature-based attention. An attention filter is a brain process, initiated by a participant in the context of a task requiring feature-based attention, which operates broadly across space to modulate the relative effectiveness with which different features in the retinal input influence performance. This paper describes an empirical method for quantitatively measuring attention filters. The method uses a “statistical summary representation” (SSR) task in which the participant strives to mouse-click the centroid of a briefly flashed cloud composed of items of different types (e.g., dots of different luminances or sizes), weighting some types of items more strongly than others. In different attention conditions, the target weights for different item types in the centroid task are varied. The actual weights exerted on the participant’s responses by different item types in any given attention condition are derived by simple linear regression. Because, on each trial, the centroid paradigm obtains information about the relative effectiveness of all the features in the display, both target and distractor features, and because the participant’s response is a continuous variable in each of two dimensions (versus a simple binary choice as in most previous paradigms), it is remarkably powerful. The number of trials required to estimate an attention filter is an order of magnitude fewer than the number required to investigate much simpler concepts in typical psychophysical attention paradigms.

Bimodal distribution of performance in discriminating major/minor modes

This study investigated the abilities of listeners to classify various sorts of musical stimuli as major vs minor. All stimuli combined four pure tones: low and high tonics (G5 and G6), dominant (D), and either a major third (B) or a minor third (B[symbol: see text]). Especially interesting results were obtained using tone-scrambles, randomly ordered sequences of pure tones presented at ≈15 per second. All tone-scrambles tested comprised 16 Gs (G5s + G6s), 8 Ds, and either 8 Bs or 8 B[symbol: see text]s. The distribution of proportion correct across 275 listeners tested over the course of three experiments was strikingly bimodal, with one mode very close to chance performance, and the other very close to perfect performance. Testing with tone-scrambles thus sorts listeners fairly cleanly into two subpopulations. Listeners in subpopulation 1 are sufficiently sensitive to major vs minor to classify tone-scrambles nearly perfectly; listeners in subpopulation 2 (comprising roughly 70% of the population) have very little sensitivity to major vs minor. Skill in classifying major vs minor tone-scrambles shows a modest correlation of around 0.5 with years of musical training.

Exploring attention-based explanations for some violations of Hick’s law for aimed movements

Choice reaction time generally increases linearly with the logarithm of the number of potential stimulus–response alternatives, a regularity known as Hick’s law. Two apparent violations of this generalization, which have been reported for aimed eye movements (Kveraga, Boucher, & Hughes, Experimental Brain Research, 146, 307–314, 2002), and arm movements (Wright, Marino, Belovsky, & Chubb, Experimental Brain Research, 179, 475–496, 2007), occurred when the indicator stimulus was an abrupt change at the location that was the target of the to-be-made movement. We report two experiments that examined and rejected the hypothesis that these abrupt-onset indicator stimuli triggered a shift in exogenous attention and that this led to unusually small uncertainty effects. Each experiment compared this indicator stimulus with a single alternative: Experiment 1 tested an indicator stimulus at all locations other than the target; Experiment 2 tested a central pointer to the target. Neither alternative led to an uncertainty effect for pointing responses that was of the size typically observed for other responses using the same stimuli.

Interplay of biomechanical constraints and kinematic strategies in selecting arm postures.

Abstract In this study, the authors examined the interplay between biomechanics and control strategies in the resolution of excess degrees of freedom at the joint level. Seven participants made aimed arm movements from 30 starting points and several starting postures to targets. Final arm postures for movements to a target exhibited substantial joint angle variation. Through regression modeling and by comparing observed final arm postures with biomechanically plausible postures, the authors identified 3 kinematic strategies: (a) Maintain deviations from the average angle at the starting point to the joints final posture; (b) make torso rotations that are a fixed proportion of shoulder rotations; and (c) adopt a characteristic combination of 4 wrist-positioning approaches. The results demonstrated that kinematic strategies can account for substantial variance in final arm postures, if one takes into account 2 types of individual differences—those that arise inevitably from biomechanical constraints and those that reflect choices in movement strategy.