ORCID Profile
0000-0002-5435-6729
Current Organisations
University of Florence
,
Università degli Studi di Firenze
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Publisher: The Royal Society
Date: 2018
Abstract: It is now clear that most animals, including humans, possess an ability to rapidly estimate number. Some have questioned whether this ability arises from dedicated numerosity mechanisms, or is derived indirectly from judgements of density or other attributes. We describe a series of psychophysical experiments, largely using adaptation techniques, which demonstrate clearly the existence of a number sense in humans. The number sense is truly general, extending over space, time and sensory modality, and is closely linked with action. We further show that when multiple cues are present, numerosity emerges as the natural dimension for discrimination. However, when element density increases past a certain level, the elements become too crowded to parse, and the scene is perceived as a texture rather than array of elements. The two different regimes are psychophysically discriminable in that they follow distinct psychophysical laws, and show different dependencies on eccentricity, luminance levels and effects of perceptual grouping. The distinction is important, as the ability to discriminate numerosity, but not texture, correlates with formal maths skills. This article is part of the discussion meeting issue ‘The origins of numerical abilities’.
Publisher: Springer Science and Business Media LLC
Date: 19-10-2019
DOI: 10.1007/S10803-019-04241-4
Abstract: Autistic in iduals often present atypicalities in adaptation—the continuous recalibration of perceptual systems driven by recent sensory experiences. Here, we examined such atypicalities in human biological motion. We used a dual-task paradigm, including a running-speed discrimination task (‘comparing the speed of two running silhouettes’) and a change-detection task (‘detecting fixation-point shrinkages’) assessing attention. We tested 19 school-age autistic and 19 age- and ability-matched typical participants, also recording eye-movements. The two groups presented comparable speed-discrimination abilities and, unexpectedly, comparable adaptation. Accuracy in the change-detection task and the scatter of eye-fixations around the fixation point were also similar across groups. Yet, the scatter of fixations reliably predicted the magnitude of adaptation, demonstrating the importance of controlling for attention in adaptation studies.
Publisher: Frontiers Media SA
Date: 21-06-2021
DOI: 10.3389/FNHUM.2021.687321
Abstract: Groupitizing is a recently described phenomenon of numerosity perception where clustering items of a set into smaller “subitizable” groups improves discrimination. Groupitizing is thought to be rooted on the subitizing system, with which it shares several properties: both phenomena accelerate counting and decrease estimation thresholds irrespective of stimulus format (for both simultaneous and sequential numerosity perception) and both rely on attention. As previous research on groupitizing has been almost completely limited to vision, the current study investigates whether it generalizes to other sensory modalities. Participants estimated the numerosity of a series of tones clustered either by proximity in time or by similarity in frequency. We found that compared with unstructured tone sequences, grouping lowered auditory estimation thresholds by up to 20%. The groupitizing advantage was similar across different grouping conditions, temporal proximity and tone frequency similarity. These results mirror the groupitizing effect for visual stimuli, suggesting that, like subitizing, groupitizing is an a-modal phenomenon.
Publisher: Cambridge University Press (CUP)
Date: 2021
DOI: 10.1017/S0140525X21000996
Abstract: To understand the number sense, we need to understand its function. We argue that numerosity estimation is fundamental not only for perception, but also preparation and control of action. We outline experiments that link numerosity estimation with action, pointing to a generalized numerosity system that serves both perception and action preparation.
Publisher: Springer Science and Business Media LLC
Date: 10-08-2020
DOI: 10.1038/S41598-020-68111-1
Abstract: Previous work has shown that when arrays of objects are grouped within clusters, participants can enumerate their numerosity more rapidly than when objects are randomly scattered, a phenomenon termed “groupitizing”. Importantly, the magnitude of the grouping advantage correlates with math abilities in children. Here we show that sensory precision of numerosity estimation is also improved when grouping cues are available, by up to 20%. The grouping can be induced by color and/or spatial proximity, and occurs in temporal sequences as well as spatial arrays. The improvement is strongest for participants with the highest thresholds in the random, ungrouped conditions. Taken together with previous research, our data suggest that measurements correlations between numerosity estimation and formal math skills may be driven by grouping strategies, which require a minimal level of basic arithmetic.
Publisher: Frontiers Media SA
Date: 2011
Publisher: American Psychological Association (APA)
Date: 07-2020
DOI: 10.1037/XGE0000709
Abstract: As perception of time is fundamental for action planning and execution, we investigated how action distorts the perception of visual duration. Participants adapted to tapping in midair for a few seconds, either slowly or quickly, then judged the relative duration of 2 drifting gratings, 1 spatially coincident with the tapped region and the other in the opposite field. Fast tapping decreased apparent duration in the tapping region while slow tapping increased it. The effect was spatially specific in external (not body-centered) coordinates, occurring within a 10° region centered on the tapping hand. Within this space, motor adaptation similarly distorts visual numerosity, suggesting common mechanisms for number and time. However, motor adaptation did not affect the perception of speed, a lower level visual property, suggesting that the interactions were at a high level of processing. These results reinforce studies that suggest that visual time perception is coupled with action and suggest the existence of multiple local visuomotor clocks. (PsycInfo Database Record (c) 2020 APA, all rights reserved).
Publisher: eLife Sciences Publications, Ltd
Date: 10-06-2016
Publisher: Association for Research in Vision and Ophthalmology (ARVO)
Date: 04-2009
DOI: 10.1167/9.4.25
Publisher: eLife Sciences Publications, Ltd
Date: 09-08-2016
DOI: 10.7554/ELIFE.16161
Abstract: Humans and other species have perceptual mechanisms dedicated to estimating approximate quantity: a sense of number. Here we show a clear interaction between self-produced actions and the perceived numerosity of subsequent visual stimuli. A short period of rapid finger-tapping (without sensory feedback) caused subjects to underestimate the number of visual stimuli presented near the tapping region and a period of slow tapping caused overestimation. The distortions occurred both for stimuli presented sequentially (series of flashes) and simultaneously (clouds of dots) both for magnitude estimation and forced-choice comparison. The adaptation was spatially selective, primarily in external, real-world coordinates. Our results sit well with studies reporting links between perception and action, showing that vision and action share mechanisms that encode numbers: a generalized number sense, which estimates the number of self-generated as well as external events.
Publisher: Elsevier BV
Date: 2021
Publisher: The Royal Society
Date: 22-12-2014
Abstract: Much evidence has accumulated to suggest that many animals, including young human infants, possess an abstract sense of approximate quantity, a number sense . Most research has concentrated on apparent numerosity of spatial arrays of dots or other objects, but a truly abstract sense of number should be capable of encoding the numerosity of any set of discrete elements, however displayed and in whatever sensory modality. Here, we use the psychophysical technique of adaptation to study the sense of number for serially presented items. We show that numerosity of both auditory and visual sequences is greatly affected by prior adaptation to slow or rapid sequences of events. The adaptation to visual stimuli was spatially selective (in external, not retinal coordinates), pointing to a sensory rather than cognitive process. However, adaptation generalized across modalities, from auditory to visual and vice versa. Adaptation also generalized across formats : adapting to sequential streams of flashes affected the perceived numerosity of spatial arrays. All these results point to a perceptual system that transcends vision and audition to encode an abstract sense of number in space and in time.
Publisher: Springer Science and Business Media LLC
Date: 22-03-2016
DOI: 10.1038/SREP23341
Abstract: Adaptation to fast motion reduces the perceived duration of stimuli displayed at the same location as the adapting stimuli. Here we show that the adaptation-induced compression of time is specific for translational motion. Adaptation to complex motion, either circular or radial, did not affect perceived duration of subsequently viewed stimuli. Adaptation with multiple patches of translating motion caused compression of duration only when the motion of all patches was in the same direction. These results show that adaptation-induced compression of event-time occurs only for uni-directional translational motion, ruling out the possibility that the neural mechanisms of the adaptation occur at early levels of visual processing.
Publisher: American Psychological Association (APA)
Date: 03-2018
DOI: 10.1037/DEV0000448
Abstract: Humans and other animals are able to make rough estimations of quantities using what has been termed the approximate number system (ANS). Much evidence suggests that sensitivity to numerosity correlates with symbolic math capacity, leading to the suggestion that the ANS may serve as a start-up tool to develop symbolic math. Many experiments have demonstrated that numerosity perception transcends the sensory modality of stimuli and their presentation format (sequential or simultaneous), but it remains an open question whether the relationship between numerosity and math generalizes over stimulus format and modality. Here we measured precision for estimating the numerosity of clouds of dots and sequences of flashes or clicks, as well as for paired comparisons of the numerosity of clouds of dots. Our results show that in children, formal math abilities correlate positively with sensitivity for estimation and paired-comparisons of the numerosity of visual arrays of dots. However, precision of numerosity estimation for sequences of flashes or sounds did not correlate with math, although sensitivities in all estimations tasks (for sequential or simultaneous stimuli) were strongly correlated with each other. In adults, we found no significant correlations between math scores and sensitivity to any of the psychophysical tasks. Taken together these results support the existence of a generalized number sense, and go on to demonstrate an intrinsic link between mathematics and perception of spatial, but not temporal numerosity. (PsycINFO Database Record
Publisher: Frontiers Media SA
Date: 03-06-2020
Publisher: SAGE Publications
Date: 22-12-2021
DOI: 10.1177/09567976211034501
Abstract: Mapping number to space is natural and spontaneous but often nonveridical, showing a clear compressive nonlinearity that is thought to reflect intrinsic logarithmic encoding of numerical values. We asked 78 adult participants to map dot arrays onto a number line across nine trials. Combining participant data, we confirmed that on the first trial, mapping was heavily compressed along the number line, but it became more linear across trials. Responses were well described by logarithmic compression but also by a parameter-free Bayesian model of central tendency, which quantitatively predicted the relationship between nonlinearity and number acuity. To experimentally test the Bayesian hypothesis, we asked 90 new participants to complete a color-line task in which they mapped noise-perturbed color patches to a “color line.” When there was more noise at the high end of the color line, the mapping was logarithmic, but it became exponential with noise at the low end. We conclude that the nonlinearity of both number and color mapping reflects contextual Bayesian inference processes rather than intrinsic logarithmic encoding.
Publisher: Springer Science and Business Media LLC
Date: 09-07-2021
DOI: 10.1038/S41598-021-93710-X
Abstract: While most animals have a sense of number, only humans have developed symbolic systems to describe and organize mathematical knowledge. Some studies suggest that human arithmetical knowledge may be rooted in an ancient mechanism dedicated to perceiving numerosity, but it is not known if formal geometry also relies on basic, non-symbolic mechanisms. Here we show that primary-school children who spontaneously detect and predict geometrical sequences (non-symbolic geometry) perform better in school-based geometry tests indexing formal geometric knowledge. Interestingly, numerosity discrimination thresholds also predicted and explained a specific portion of variance of formal geometrical scores. The relation between these two non-symbolic systems and formal geometry was not explained by age or verbal reasoning skills. Overall, the results are in line with the hypothesis that some human-specific, symbolic systems are rooted in non-symbolic mechanisms.
Publisher: Association for Research in Vision and Ophthalmology (ARVO)
Date: 16-03-2006
DOI: 10.1167/6.3.6
Publisher: Elsevier BV
Date: 11-2011
Publisher: Elsevier BV
Date: 11-2005
DOI: 10.1016/J.VISRES.2004.09.020
Abstract: A brief flash presented physically aligned with a moving stimulus is perceived to lag behind, a well studied phenomenon termed the Flash-Lag Effect (FLE). It has been recently shown that the FLE also occurs in audition, as well as cross-modally between vision and audition. The present study has two goals: to investigate the acoustic and cross-modal FLE using a random motion technique and to investigate whether neural latencies may account for the FLE in general. The random motion technique revealed a strong cross-modal FLE for visual motion stimuli and auditory probes, but not for the other conditions. Visual and auditory latencies for stimulus appearance and for motion were measured with three techniques: integration, temporal alignment and reaction times. All three techniques showed that a brief static acoustic stimulus is perceived more rapidly than a brief static visual stimulus, while a sound source in motion is perceived more slowly than a comparable visual stimulus. While the results of these three techniques agreed closely with each other, they were exactly opposite that required to account for the FLE by neural latencies. We conclude that neural latencies do not, in general, explain the flash-lag effect. Rather, our data suggest that neural integration times are more important.
Publisher: Springer Science and Business Media LLC
Date: 11-09-2020
DOI: 10.1038/S41598-020-71871-5
Abstract: When asked to estimate the number of items in a visual array, educated adults and children are more precise and rapid if the items are clustered into small subgroups rather than randomly distributed. This phenomenon, termed “groupitizing”, is thought to rely on the recruitment of the subitizing system (dedicated to the perception of very small numbers), with the aid of simple arithmetical calculations. The aim of current study is to verify whether the advantage for clustered stimuli does rely on subitizing, by manipulating attention, known to strongly affect attention. Participants estimated the numerosity of grouped or ungrouped arrays in condition of full attention or while attention was erted with a dual-task. Depriving visual attention strongly decreased estimation precision of grouped but not of ungrouped arrays, as well as increasing the tendency for numerosity estimation to regress towards the mean. Additional explorative analyses suggested that calculation skills correlated with the estimation precision of grouped, but not of ungrouped, arrays. The results suggest that groupitizing is an attention-based process that leverages on the subitizing system. They also suggest that measuring numerosity estimation thresholds with grouped stimuli may be a sensitive correlate of math abilities.
Publisher: Elsevier BV
Date: 02-2019
DOI: 10.1016/J.JECP.2018.09.017
Abstract: Small quantities of visual objects can be rapidly estimated without error, a phenomenon known as subitizing. Larger quantities can also be rapidly estimated, but with error, and the error rate predicts math abilities. This study addressed two issues: (a) whether subitizing generalizes over modalities and stimulus formats and (b) whether subitizing correlates with math abilities. We measured subitizing limits in primary school children and adults for visual and auditory stimuli presented either sequentially (sequences of flashes or sounds) or simultaneously (visual presentations, dot arrays). The results show that (a) subitizing limits for adults were one item larger than those for primary school children across all conditions (b) subitizing for simultaneous visual stimuli (dots) was better than that for sequential stimuli (c) subitizing limits for dots do not correlate with subitizing limits for either flashes or sounds (d) subitizing of sequences of flashes and subitizing of sequences of sounds are strongly correlated with each other in children and (e) regardless of stimuli sensory modality and format, subitizing limits do not correlate with mental calculation or digit magnitude knowledge proficiency. These results suggest that although children can subitize sequential numerosity, simultaneous and temporal subitizing may be subserved by separate systems. Furthermore, subitizing does not seem to be related to numerical abilities.
Publisher: Society for Neuroscience
Date: 18-01-2012
DOI: 10.1523/JNEUROSCI.3411-11.2012
Abstract: We measured temporal reproduction in human subjects with various levels of musical expertise: expert drummers, string musicians, and non-musicians. While duration reproduction of the non-percussionists showed a characteristic central tendency or regression to the mean, drummers responded veridically. Furthermore, when the stimuli were auditory tones rather than flashes, all subjects responded veridically. The behavior of all three groups in both modalities is well explained by a Bayesian model that seeks to minimize reproduction errors by incorporating a central tendency prior, a probability density function centered at the mean duration of the s le. We measured separately temporal precision thresholds with a bisection task thresholds were twice as low in drummers as in the other two groups. These estimates of temporal precision, together with an adaptable Bayesian prior, predict well the reproduction results and the central tendency strategy under all conditions and for all subject groups. These results highlight the efficiency and flexibility of sensorimotor mechanisms estimating temporal duration.
Publisher: eLife Sciences Publications, Ltd
Date: 2016
Publisher: Springer Science and Business Media LLC
Date: 29-09-2005
DOI: 10.1007/S00221-005-2384-9
Abstract: Simultaneous changes in visual stimulus attributes (such as motion or color) are often perceived to occur at different times, a fact usually attributed to differences in neural processing times of those attributes. However, other studies suggest that perceptual misalignments are not due to stimulus attributes, but to the type of change, first- or second-order. To test whether this idea generalizes across modalities, we studied perceptual synchrony of acoustic and of audiovisual cross-modal stimuli, which varied in a first- or second-order fashion. First-order changes were abrupt changes in tone intensity or frequency (auditory), or spatial position (visual), while second-order changes were an inversion of the direction of change, such as a turning point when a rising tone starts falling or a translating visual blob reverses. For both pure acoustic and cross-modal stimuli, first-order changes were systematically perceived before second-order changes. However, when both changes were first-order, or both were second-order, little or no difference in perceptual delay was found between them, regardless of attribute or modality. This shows that the type of attribute change, as well as latency differences, is a strong determinant of subjective temporal alignments. We also performed an analysis of reaction times (RTs) to the first- and second-order attribute changes used in these temporal alignment experiments. RT differences between these stimuli did not correspond with our temporal alignment data, suggesting that subjective alignments cannot be accounted for by a simple latency-based explanation.
Publisher: Association for Research in Vision and Ophthalmology (ARVO)
Date: 02-2011
DOI: 10.1167/11.2.1
Abstract: The ability to attend to multiple objects that move in the visual field is important for many aspects of daily functioning. The attentional capacity for such dynamic tracking, however, is highly limited and undergoes age-related decline. Several aspects of the tracking process can influence performance. Here, we investigated effects of feature-based interference from distractor objects that appear in unattended regions of the visual field with a hemifield-tracking task. Younger and older participants performed an attentional tracking task in one hemifield while distractor objects were concurrently presented in the unattended hemifield. Feature similarity between objects in the attended and unattended hemifields as well as motion speed and the number of to-be-tracked objects were parametrically manipulated. The results show that increasing feature overlap leads to greater interference from the unattended visual field. This effect of feature-based interference was only present in the slow speed condition, indicating that the interference is mainly modulated by perceptual demands. High-performing older adults showed a similar interference effect as younger adults, whereas low-performing adults showed poor tracking performance overall.
Publisher: Wiley
Date: 08-12-2021
DOI: 10.1002/HBM.25694
Abstract: Numerical estimation of arrays of objects is faster and more accurate when items can be clustered into groups, a phenomenon termed “groupitizing.” Grouping can facilitate segregation into subitizable “chunks,” each easily estimated, then summed. The current study investigates whether spatial grouping of arrays drives specific neural responses during numerical estimation, reflecting strategies such as exact calculation and fact retrieval. Fourteen adults were scanned with fMRI while estimating either the numerosity or shape of arrays of items, either randomly distributed or spatially grouped. Numerosity estimation of both classes of stimuli elicited common activation of a right lateralized frontoparietal network. Grouped stimuli additionally recruited regions in the left hemisphere and bilaterally in the angular gyrus. Multivariate pattern analysis showed that classifiers trained with the pattern of neural activations read out from parietal regions, but not from the primary visual areas, can decode different numerosities both within and across spatial arrangements. The behavioral numerical acuity correlated with the decoding performance of the parietal but not with occipital regions. Overall, this experiment suggests that the estimation of grouped stimuli relies on the approximate number system for numerosity estimation, but additionally recruits regions involved in calculation.
Publisher: The Royal Society
Date: 27-05-2020
Abstract: Like most perceptual attributes, the perception of numerosity is susceptible to adaptation, both to prolonged viewing of spatial arrays and to repeated motor actions such as hand-tapping. However, the possibility has been raised that adaptation may reflect response biases rather than modification of sensory processing. To disentangle these two possibilities, we studied visual and motor adaptation of numerosity perception while measuring confidence and reaction times. Both sensory and motor adaptation robustly distorted numerosity estimates, and these shifts in perceived numerosity were accompanied by similar shifts in confidence and reaction-time distributions. After adaptation, maximum uncertainty and slowest response-times occurred at the point of subjective (rather than physical) equality of the matching task, suggesting that adaptation acts directly on the sensory representation of numerosity, before the decisional processes. On the other hand, making reward response-contingent, which also caused robust shifts in the psychometric function, caused no significant shifts in confidence or reaction-time distributions. These results reinforce evidence for shared mechanisms that encode the quantity of both internally and externally generated events, and advance a useful general technique to test whether contextual effects like adaptation and serial dependence really affect sensory processing.
No related grants have been discovered for ROBERTO ARRIGHI.