The numerosity of small numbers of objects, up to about four, can be rapidly appraised without error, a phenomenon known as subitizing. Larger numbers can either be counted, accurately but slowly, or estimated, rapidly but with errors. There has been some debate as to whether subitizing uses the same or different mechanisms than those of higher numerical ranges and whether it requires attentional resources. We measure subjects' accuracy and precision in making rapid judgments of numerosity for target numbers spanning the subitizing and estimation ranges while manipulating the attentional load, both with a spatial dual task and the "attentional blink" dual-task paradigm. The results of both attentional manipulations were similar. In the high-load attentional condition, Weber fractions were similar in the subitizing (2-4) and estimation (5-7) ranges (10-15%). In the low-load and single-task condition, Weber fractions substantially improved in the subitizing range, becoming nearly error-free, while the estimation range was relatively unaffected. The results show that the mechanisms operating over the subitizing and estimation ranges are not identical. We suggest that pre-attentive estimation mechanisms works at all ranges, but in the subitizing range, attentive mechanisms also come into play.

We have recently provided evidence that the perception of number and texture density is mediated by two independent mechanisms: numerosity mechanisms at relatively low numbers, obeying Weber's law, and texture-density mechanisms at higher numerosities, following a square root law. In this study we investigated whether the switch between the two mechanisms depends on the capacity to segregate individual dots, and therefore follows similar laws to those governing visual crowding. We measured numerosity discrimination for a wide range of numerosities at three eccentricities. We found that the point where the numerosity regime (Weber's law) gave way to the density regime (square root law) depended on eccentricity. In central vision, the regime changed at 2.3 dots/°2, while at 15° eccentricity, it changed at 0.5 dots/°2, three times less dense. As a consequence, thresholds for low numerosities increased with eccentricity, while at higher numerosities thresholds remained constant. We further showed that like crowding, the regime change was independent of dot size, depending on distance between dot centers, not distance between dot edges or ink coverage. Performance was not affected by stimulus contrast or blur, indicating that the transition does not depend on low-level stimulus properties. Our results reinforce the notion that numerosity and texture are mediated by two distinct processes, depending on whether the individual elements are perceptually segregable. Which mechanism is engaged follows laws that determine crowding.

Autism is known to be associated with major perceptual atypicalities. We have recently proposed a general model to account for these atypicalities in Bayesian terms, suggesting that autistic individuals underuse predictive information or priors. We tested this idea by measuring adaptation to numerosity stimuli in children diagnosed with autism spectrum disorder (ASD). After exposure to large numbers of items, stimuli with fewer items appear to be less numerous (and vice versa). We found that children with ASD adapted much less to numerosity than typically developing children, although their precision for numerosity discrimination was similar to that of the typical group. This result reinforces recent findings showing reduced adaptation to facial identity in ASD and goes on to show that reduced adaptation is not unique to faces (social stimuli with special significance in autism), but occurs more generally, for both parietal and temporal functions, probably reflecting inefficiencies in the adaptive interpretation of sensory signals. These results provide strong support for the Bayesian theories of autism.utism is a heritable, lifelong neurodevelopmental condition with striking effects on social communication. The condition, however, is also associated with a range of nonsocial symptoms, including both hypersensitivity and hyposensitivity to perceptual stimuli, and sensory-seeking behaviors such as attraction to light, intense looking at objects, and fascination with brightly colored objects. These sensory atypicalities, which now form part of the diagnostic criteria for autism (1), can have debilitating effects on the lives of autistic people (2) and their families (3).We have recently proposed a Bayesian account of autism (4), suggesting that it is not sensory processing itself that is disrupted in individuals with autism, but the interpretation of the sensory input. The Bayesian class of theories, including predictive coding and other generative models (5-7), assumes that perception is an optimized combination of external sensory data (the likelihood) and an internal model (the prior). We suggested that this process may be atypical in autism, in that the internal priors are underweighted and less used than in typical individuals. Our theory has been followed by several others along similar lines (8-11).The suggestion of underutilization of priors leads to several specific predictions. One strong prediction is that autistic individuals should show reduced adaptation aftereffects. Adaptation, which occurs throughout sensory systems, represents a form of experience-dependent plasticity in which our current sensory experience is intimately affected by how we viewed the world only moments before. It is widely held to pose numerous functional advantages (12-16), including serving to autocalibrate perceptual systems to their environment by dynamically tuning its responses to match the distribution of stimuli to make maximal use of the limited working range of the system (12-16). It achieves this by reducing the transm...

Autism spectrum disorders (ASD) are characterized by difficulties in social cognition, but are also associated with atypicalities in sensory and perceptual processing. Several groups have reported that autistic individuals show reduced integration of socially relevant audiovisual signals, which may contribute to the higher-order social and cognitive difficulties observed in autism. Here we use a newly devised technique to study instantaneous adaptation to audiovisual asynchrony in autism. Autistic and typical participants were presented with sequences of brief visual and auditory stimuli, varying in asynchrony over a wide range, from 512 ms auditory-lead to 512 ms auditory-lag, and judged whether they seemed to be synchronous. Typical adults showed strong adaptation effects, with trials proceeded by an auditory-lead needing more auditory-lead to seem simultaneous, and vice versa. However, autistic observers showed little or no adaptation, although their simultaneity curves were as narrow as the typical adults. This result supports recent Bayesian models that predict reduced adaptation effects in autism. As rapid audiovisual recalibration may be fundamental for the optimisation of speech comprehension, recalibration problems could render language processing more difficult in autistic individuals, hindering social communication.

How our perceptual experience of the world remains stable and continuous despite the frequent repositioning eye movements remains very much a mystery. One possibility is that our brain actively constructs a spatiotopic representation of the world, which is anchored in external—or at least head-centred—coordinates. In this study, we show that the positional motion aftereffect (the change in apparent position after adaptation to motion) is spatially selective in external rather than retinal coordinates, whereas the classic motion aftereffect (the illusion of motion after prolonged inspection of a moving source) is selective in retinotopic coordinates. The results provide clear evidence for a spatiotopic map in humans: one which can be influenced by image motion.

Considerable recent work suggests that mathematical abilities in children correlate with the ability to estimate numerosity. Does math correlate only with numerosity estimation, or also with other similar tasks? We measured discrimination thresholds of school-age (6- to 12.5-years-old) children in 3 tasks: numerosity of patterns of relatively sparse, segregatable items (24 dots); numerosity of very dense textured patterns (250 dots); and discrimination of direction of motion. Thresholds in all tasks improved with age, but at different rates, implying the action of different mechanisms: In particular, in young children, thresholds were lower for sparse than textured patterns (the opposite of adults), suggesting earlier maturation of numerosity mechanisms. Importantly, numerosity thresholds for sparse stimuli correlated strongly with math skills, even after controlling for the influence of age, gender and nonverbal IQ. However, neither motion-direction discrimination nor numerosity discrimination of texture patterns showed a significant correlation with math abilities. These results provide further evidence that numerosity and texture-density are perceived by independent neural mechanisms, which develop at different rates; and importantly, only numerosity mechanisms are related to math. As developmental dyscalculia is characterized by a profound deficit in discriminating numerosity, it is fundamental to understand the mechanism behind the discrimination. (PsycINFO Database Record

The pupil is primarily regulated by prevailing light levels but is also modulated by perceptual and attentional factors. We measured pupil-size in typical adult humans viewing a bistable-rotating cylinder, constructed so the luminance of the front surface changes with perceived direction of rotation. In some participants, pupil diameter oscillated in phase with the ambiguous perception, more dilated when the black surface was in front. Importantly, the magnitude of oscillation predicts autistic traits of participants, assessed by the Autism-Spectrum Quotient AQ. Further experiments suggest that these results are driven by differences in perceptual styles: high AQ participants focus on the front surface of the rotating cylinder, while those with low AQ distribute attention to both surfaces in a more global, holistic style. This is the first evidence that pupillometry reliably tracks inter-individual differences in perceptual styles; it does so quickly and objectively, without interfering with spontaneous perceptual strategies.

Various aspects of numerosity judgments, especially subitizing and the mapping of number onto space, depend strongly on attentional resources. Here we use a dual-task paradigm to investigate the effects of cross-sensory attentional demands on visual subitizing and spatial mapping. The results show that subitizing is strongly dependent on attentional resources, far more so than is estimation of higher numerosities. But unlike many other sensory tasks, visual subitizing is equally affected by concurrent attentionally demanding auditory and tactile tasks as it is by visual tasks, suggesting that subitizing may be amodal. Mapping number onto space was also strongly affected by attention, but only when the dual-task was in the visual modality. The non-linearities in numberline mapping under attentional load are well explained by a Bayesian model of central tendency.