Tactile numerosity is coded in external space

Humans, and several non-human species, possess the ability to make approximate but reliable estimates of the number of objects around them. Alike other perceptual features, numerosity perception is susceptible to adaptation: exposure to a high number of items causes underestimation of the numerosity of a subsequent set of items, and vice versa. Several studies have investigated adaptation in the auditory and visual modality, whereby stimuli are preferentially encoded in an external coordinate system. As tactile stimuli are primarily coded in an internal (body-centered) reference frame, here we ask whether tactile numerosity adaptation operates based on internal or external spatial coordinates as it occurs in vision or audition. Twenty participants performed an adaptation task with their right hand located either in the right (uncrossed) or left (crossed) hemispace. Tactile adaptor and test stimuli were passively delivered either to the same (adapted) or different (non-adapted) hands. Our results show a pattern of over- and under-estimation according to the rate of adaptation (low and high, respectively). In the uncrossed position, we observed stronger adaptation effects when adaptor and test stimuli were delivered to the “adapted” hand. However, when both hands were aligned in the same spatial position (crossed condition), the magnitude of adaptation was similar irrespective of which hand received adaptor and test stimuli. These results demonstrate that numerosity information is automatically coded in external coordinates even in the tactile modality, suggesting that such a spatial reference frame is an intrinsic property of numerosity processing irrespective of the sensory modality

Fast saccadic eye-movements in humans suggest that numerosity perception is automatic and direct

Fast saccades are rapid automatic oculomotor responses to salient and ecologically important visual stimuli such as animals and faces. Discriminating the number of friends, foe, or prey may also have an evolutionary advantage. In this study, participants were asked to saccade rapidly towards the more numerous of two arrays. Participants could discriminate numerosities with high accuracy and great speed, as fast as 190 ms. Intermediate numerosities were more likely to elicit fast saccades than very low or very high numerosities. Reaction-times for vocal responses (collected in a separate experiment) were slower, did not depend on numerical range, and correlated only with the slow not the fast saccades, pointing to different systems. The short saccadic reaction-times we observe are surprising given that discrimination using numerosity estimation is thought to require a relatively complex neural circuit, with several relays of information through the parietal and prefrontal cortex. Our results suggest that fast numerosity-driven saccades may be generated on a single feed-forward pass of information recruiting a primitive system that cuts through the cortical hierarchy and rapidly transforms the numerosity information into a saccade command

Visual sense of number vs. sense of magnitude in humans and machines

Numerosity perception is thought to be foundational to mathematical learning, but its computational bases are strongly debated. Some investigators argue that humans are endowed with a specialized system supporting numerical representations; others argue that visual numerosity is estimated using continuous magnitudes, such as density or area, which usually co-vary with number. Here we reconcile these contrasting perspectives by testing deep neural networks on the same numerosity comparison task that was administered to human participants, using a stimulus space that allows the precise measurement of the contribution of non-numerical features. Our model accurately simulates the psychophysics of numerosity perception and the associated developmental changes: discrimination is driven by numerosity, but non-numerical features also have a significant impact, especially early during development. Representational similarity analysis further highlights that both numerosity and continuous magnitudes are spontaneously encoded in deep networks even when no task has to be carried out, suggesting that numerosity is a major, salient property of our visual environment

Estimation of magnitudes and numerosity in different formats of stimulus presentation: the numerical ratio effect

Introduction. Several researchers discuss the possibility of existence of a common mental system responsible for the estimation of both discrete numerosities and continuous magnitudes. The numerical ratio effect observed during comparison tasks is one of the evidences of an existence of such system. It manifests itself in an increase in response time and a decrease in accuracy as the numerical proportion between the compared arrays of objects or magnitudes increases. This study investigated the numerical ratio effect for different types of tests and stimulus presentation formats in order to explore the interrelationships between systems of magnitude and numerosity estimation. Methods. The sample consisted of 83 students (20% were men, the average age was 20.34 years). The participants of the study performed nonsymbolic comparison tasks, arears comparison task and comparison of nonsymbolic quantity with symbolic numbers task (nonsymbolic – symbolic comparison test). Two formats of stimulus presentation were used during the nonsymbolic comparison test: separate/homogeneous and mixed/heterogeneous. The accuracy of estimation and numerical ratio effect were calculated for each test. Results. The numerical ratio effect was significant in the nonsymbolic comparison tests (for both formats of stimulus presentation) and in the nonsymbolic-symbolic comparison test, but was not significant in the areas comparison test. Numerical ratio effects for different tests do not correlate with each other. It was also shown that the accuracy of the estimation of magnitudes correlates with the results of the nonsymbolic comparison test, and this relationship was stronger for the mixed/ heterogeneous format. Discussion. Results of this study demonstrated that the relationship between magnitude and discrete numerosity estimation systems can vary under different conditions of stimulus presentation. It makes possible to refine the existing theoretical models describing functioning of the Approximate Number System. The obtained results cannot be fully explained by the theory of a unified numerosity/magnitude estimation system. It was shown, however, that the magnitude estimation system does in fact contribute to the estimation of discrete numerosity

Seven reasons to (still) doubt the existence of number adaptation: A rebuttal to Burr et al. and Durgin

Does the visual system adapt to number? For more than fifteen years, most have assumed that the answer is an unambiguous “yes”. Against this prevailing orthodoxy, we recently took a critical look at the phenomenon, questioning its existence on both empirical and theoretical grounds, and providing an alternative explanation for extant results (the old news hypothesis). We subsequently received two critical responses. Burr, Anobile, and Arrighi rejected our critiques wholesale, arguing that the evidence for number adaptation remains overwhelming. Durgin questioned our old news hypothesis — preferring instead a theory about density adaptation he has championed for decades — but also highlighted several ways in which our arguments do pose serious challenges for proponents of number adaptation. Here, we reply to both. We first clarify our position regarding number adaptation. Then, we respond to our critics’ concerns, highlighting seven reasons why we remain skeptical about number adaptation. We conclude with some thoughts about where the debate may head from here

Preschoolers and multi-digit numbers: A path to mathematics through the symbols themselves

Numerous studies from developmental psychology have suggested that human symbolic representation of numbers is built upon the evolutionally old capacity for representing quantities that is shared with other species. Substantial research from mathematics education also supports the idea that mathematical concepts are best learned through their corresponding physical representations. We argue for an independent pathway to learning “big” multi-digit symbolic numbers that focuses on the symbol system itself. Across five experiments using both between- and within-subject designs, we asked preschoolers to identify written multi-digit numbers with their spoken names in a two-alternative-choice-test or to indicate the larger quantity between two written numbers. Results showed that preschoolers could reliably map spoken number names to written forms and compare the magnitudes of two written multi-digit numbers. Importantly, these abilities were not related to their non-symbolic representation of quantities. These findings have important implications for numerical cognition, symbolic development, teaching, and education

Shape facilitates number: brain potentials and microstates reveal the interplay between shape and numerosity in human vision

Recognition of simple shapes and numerosity estimation for small quantities are often studied independently of each other, but we know that these processes are both rapid and accurate, suggesting that they may be mediated by common neural mechanisms. Here we address this issue by examining how spatial configuration, shape complexity, and luminance polarity of elements affect numerosity estimation. We directly compared the Event Related Potential (ERP) time-course for numerosity estimation under shape and random configurations and found a larger N2 component for shape over lateral-occipital electrodes (250-400ms), which also increased with higher numbers. We identified a Left Mid Frontal (LMF; 400-650ms) component over left-lateralised medial frontal sites that specifically separated low and high numbers of elements, irrespective of their spatial configuration. Different luminance-polarities increased N2 amplitude only, suggesting that shape but not numerosity is selective to polarity. Functional microstates confined numerosity to a strict topographic distribution occurring within the LMF time-window, while a microstate responding only to shape-configuration was evidenced earlier, in the N2 time-window. We conclude that shape-coding precedes numerosity estimation, which can be improved when the number of elements and shape vertices are matched. Thus, numerosity estimation around the subitizing range is facilitated by a shape-template matching process

On the functional relationship between visual working memory and numerical acuity

openÈ presente nella letteratura scientifica una lunga serie di elementi coerenti con l'ipotesi di una dissociazione tra la memoria di lavoro visuo-spaziale e il sistema deputato all'elaborazione delle informazioni relative alla numerosità degli stimoli. Ciononostante, negli ultimi anni è emerso un numero crescente di evidenze a sostegno dell’ipotesi che un sistema che elabora la numerosità pura dalla nascita esista ma non sia di per sé sufficiente a generare le rappresentazioni utilizzate per guidare le risposte. Si osserva invece una sovrapposizione con la memoria di lavoro visiva in termini funzionali e di risorse legata all'integrazione di informazioni spaziali e all'interferenza delle informazioni relative alle altre caratteristiche fisiche degli stimoli. In questo studio, abbiamo replicato lo studio di Piazza et al. (2011) che costituisce il riferimento empirico a sostegno dell’ipotesi di una dissociazione tra approssimazione numerica e memoria di lavoro visuo-spaziale. La capacità di memoria di lavoro visiva è stata misurata utilizzando un recente paradigma di change-detection e sono state corrette alcune imperfezioni metodologiche dello studio di Piazza e colleghi, arrivando comunque a replicare la mancanza di correlazione originariamente osservata. La presenza di evidenze contraddittorie ha costituito quindi la base per una riflessione teorica e metodologica finalizzata a spiegare i nostri risultati allo stato dell’arte attuale e ad orientare la ricerca futura sul ruolo della memoria di lavoro nella stima numerica

Contextual modulation of visual variability: perceptual biases over time and across the visual field

The visual system extracts statistical information about the environment to manage noise, ensure perceptual stability and predict future events. These summary representations are able to inform sensory information received in subsequent times or in other regions of the visual field. This has been conceptualized in terms of Bayesian inference within the predictive coding framework. Nevertheless, contextual influence can also drive anti-Bayesian biases, as in sensory adaptation. Variance is a crucial statistical descriptor, yet relatively overlooked in ensemble vision research. We assessed the mechanisms whereby visual variability exerts and is subject to contextual modulation over time and across the visual field. Perceptual biases over time: serial dependence (SD) In a series of visual experiments, we examined SD on visual variance: the influence of the variance of previously presented ensembles in current variance judgments. We encountered two history-dependent biases: a positive bias exerted by recent presentations and a negative bias driven by less recent context. Contrary to claims that positive SD has low-level sensory origin, our experiments demonstrated a decisional bias requiring perceptual awareness and subject to time and capacity limitations. The negative bias was likely of sensory origin (adaptation). A two-layer model combining population codes and Bayesian Kalman filters replicated positive and negative effects in their approximate timescales. Perceptual biases across the visual field: Uniformity Illusion (UI) In UI, presentation of a pattern with uniform foveal components and more variable peripheral elements results in the latter taking the appearance of the foveal input. We studied the mechanistic basis of UI on orientation and determined that it arose without changes in sensory encoding at the primary visual cortex. Conclusions We studied perceptual biases on visual variability across space and time and found a combination of sensory negative and positive decisional biases, likely to handle the balance between change sensitivity and perceptual stability