The shared numerical representation for action and perception develops independently from vision

The role of motor effort on the sensorimotor number system

The integration of numerical information with motor processes has emerged as a fascinating area of investigation in both animal and human cognition. The interest in a sensorimotor number system has recently generated neurophysiological and psychophysical evidence which combine to highlight the importance of motor functions in the encoding of numerical information. Nevertheless, several key questions remain, such as the influence of non-numerical motor parameters over numerical perception. Here we tested the role of physical effort, a parameter positively correlated with the number of actions, in modulating the link between hand-actions and visual numerosity perception. Effort was manipulated during sensorimotor adaptation as well as during a new actions-estimation paradigm. The results of Experiment 1 shows that physical effort in the absence of actions (passive effort) is not sufficient to activate the sensorimotor number system, indicating that self-produced actions are instead necessary. Further experiments demonstrated that effort is marginally integrated during motor adaptation (Experiment 2) but discarded when estimating the number of self-produced hand actions (Experiment 3). Overall, the results indicate that the sensorimotor number system is largely fed by the number of discrete actions rather than the amount of effort but also indicates that effort (under specific circumstances) might be integrated. These findings provide novel insights into the sensorimotor numerical integration, paving the way for future investigations, such as on its functional role.

Sensorimotor mechanisms selective to numerosity derived from individual differences

We have previously shown that after few seconds of adaptation by finger-tapping, the perceived numerosity of spatial arrays and temporal sequences of visual objects displayed near the tapping region is increased or decreased, implying the existence of a sensorimotor numerosity system (Anobile et al., 2016). To date, this mechanism has been evidenced only by adaptation. Here, we extend our finding by leveraging on a well-established covariance technique, used to unveil and characterize 'channels' for basic visual features such as colour, motion, contrast, and spatial frequency. Participants were required to press rapidly a key a specific number of times, without counting. We then correlated the precision of reproduction for various target number presses between participants. The results showed high positive correlations for nearby target numbers, scaling down with numerical distance, implying tuning selectivity. Factor analysis identified two factors, one for low and the other for higher numbers. Principal component analysis revealed two bell-shaped covariance channels, peaking at different numerical values. Two control experiments ruled out the role of non-numerical strategies based on tapping frequency and response duration. These results reinforce our previous reports based on adaptation, and further suggest the existence of at least two sensorimotor number channels responsible for translating symbolic numbers into action sequences.

The interplay of motor adaptation and groupitizing in numerosity perception: Insights from visual motion adaptation and proprioceptive motor adaptation

Groupitizing is a well-established strategy in numerosity perception that enhances speed and sensory precision. Building on the ATOM theory, Anobile proposed the sensorimotor numerosity system, which posits a strong link between number and action. Previous studies using motor adaptation technology have shown that high-frequency motor adaptation leads to underestimation of numerosity perception, while low-frequency adaptation leads to overestimation. However, the impact of motor adaptation on groupitizing, and whether visual motion adaptation produces similar effects, remain unclear. In this study, we investigate the persistence of the advantage of groupitizing after motor adaptation and explore the effects of visual motion adaptation. Surprisingly, our findings reveal that proprioceptive motor adaptation weakens the advantage of groupitizing, indicating a robust effect of motor adaptation even when groupitizing is employed. Moreover, we observe a bidirectional relationship, as groupitizing also weakens the adaptation effect. These results highlight the complex interplay between motor adaptation and groupitizing in numerosity perception. Furthermore, our study provides evidence that visual motion adaptation also has an adaptation effect, but does not fully replicate the effects of proprioceptive motor adaptation on groupitizing. In conclusion, our research underscores the importance of groupitizing as a valuable strategy in numerosity perception, and sheds light on the influence of motion adaptation on this strategy.

Numerical Representation for Action in Crows Obeys the Weber-Fechner Law

The psychophysical laws governing the judgment of perceived numbers of objects or events, called the number sense, have been studied in detail. However, the behavioral principles of equally important numerical representations for action are largely unexplored in both humans and animals. We trained two male carrion crows (Corvus corone) to judge numerical values of instruction stimuli from one to five and to flexibly perform a matching number of pecks. Our quantitative analysis of the crows' number production performance shows the same behavioral regularities that have previously been demonstrated for the judgment of sensory numerosity, such as the numerical distance effect, the numerical magnitude effect, and the logarithmical compression of the number line. The presence of these psychophysical phenomena in crows producing number of pecks suggests a unified sensorimotor number representation system underlying the judgment of the number of external stimuli and internally generated actions.

Movement-related tactile gating in blindness

When we perform an action, self-elicited movement induces suppression of somatosensory information to the cortex, requiring a correct motor-sensory and inter-sensory (i.e. cutaneous senses, kinesthesia, and proprioception) integration processes to be successful. However, recent works show that blindness might impact some of these elements. The current study investigates the effect of movement on tactile perception and the role of vision in this process. We measured the velocity discrimination threshold in 18 sighted and 18 blind individuals by having them perceive a sequence of two movements and discriminate the faster one in passive and active touch conditions. Participants' Just Noticeable Difference (JND) was measured to quantify their precision. Results showed a generally worse performance during the active touch condition compared to the passive. In particular, this difference was significant in the blind group, regardless of the blindness duration, but not in the sighted one. These findings suggest that the absence of visual calibration impacts motor-sensory and inter-sensory integration required during movement, diminishing the reliability of tactile signals in blind individuals. Our work spotlights the need for intervention in this population and should be considered in the sensory substitution/reinforcement device design.

The role of non-numerical information in the perception of temporal numerosity

Numerosity perception refers to the ability to make rapid but approximate estimates of the quantity of elements in a set (spatial numerosity) or presented sequentially (temporal numerosity). Whether numerosity is directly perceived or indirectly recomputed from non-numerical features is a highly debated issue. In the spatial domain, area and density have been suggested as the main parameters through which numerosity would be recomputed. In the temporal domain, stimuli duration and temporal frequency could be similarly exploited to retrieve numerosity. By adapting a psychophysical technique previously exploited in the spatial domain, we investigated whether temporal visual numerosity is directly perceived. Adult participants observed sequences of visual impulses sampled from a stimulus space spanning several levels of temporal frequency and duration (and hence numerosity), and then reproduced the sequence as accurately as possible via a series of keypresses. Crucially, participants were not asked to reproduce any particular property (such as number of impulses) but were free to choose any available cue (such as total duration, or temporal frequency). The results indicate that while the overall sequence duration was barely considered, numerosity and temporal frequency were both spontaneously used as the main cues to reproduce the sequences, with a slight but significant dominance of numerosity. Overall, the results are in line with previous literature suggesting that numerosity is directly encoded, even for temporal sequences, but a non-numerical feature (temporal frequency) is also used in reproducing sequences.

Early visual deprivation disrupts the mental representation of numbers in visually impaired children

Several shreds of evidence indicate that visual deprivation does not alter numerical competence neither in adults nor in children. However, studies reporting non-impaired numerical abilities in the visually impaired population present some limitations: (a) they mainly assessed the ability to process numbers (e.g. mathematical competence) rather than represent numbers (e.g. mental number line); (b) they principally focused on positive rather than negative number estimates; (c) they investigated numerical abilities in adult individuals except one focusing on children (Crollen et al. in Cognition 210:104586, 2021). Overall, this could limit a comprehensive explanation of the role exerted by vision on numerical processing when vision is compromised. Here we investigated how congenital visual deprivation affects the ability to represent positive and negative numbers in horizontal and sagittal planes in visually impaired children (thirteen children with low vision, eight children with complete blindness, age range 6-15 years old). We adapted the number-to-position paradigm adopted by Crollen et al. (Cognition 210:104586, 2021), asking children to indicate the spatial position of positive and negative numbers on a graduated rule positioned horizontally or sagittally in the frontal plane. Results suggest that long-term visual deprivation alters the ability to identify the spatial position of numbers independently of the spatial plane and the number polarity. Moreover, results indicate that relying on poor visual acuity is detrimental for low vision children when asked to localize both positive and negative numbers in space, suggesting that visual experience might have a differential role in numerical processing depending on number polarity. Such findings add knowledge related to the impact of visual experience on numerical processing. Since both positive and negative numbers are fundamental aspects of learning mathematical principles, the outcomes of the present study inform about the need to implement early rehabilitation strategies to prevent the risk of numerical difficulties in visually impaired children.

Number selective sensorimotor neurons in the crow translate perceived numerosity into number of actions

Translating a perceived number into a matching number of self-generated actions is a hallmark of numerical reasoning in humans and animals alike. To explore this sensorimotor transformation, we trained crows to judge numerical values in displays and to flexibly plan and perform a matching number of pecks. We report number selective sensorimotor neurons in the crow telencephalon that signaled the impending number of self-generated actions. Neuronal population activity during the sensorimotor transformation period predicted whether the crows mistakenly planned fewer or more pecks than instructed. During sensorimotor transformation, both a static neuronal code characterized by persistently number-selective neurons and a dynamic code originating from neurons carrying rapidly changing numerical information emerged. The findings indicate there are distinct functions of abstract neuronal codes supporting the sensorimotor number system.

Numbers in action

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.

Evidence for an A-Modal Number Sense: Numerosity Adaptation Generalizes Across Visual, Auditory, and Tactile Stimuli

Humans and other species share a perceptual mechanism dedicated to the representation of approximate quantities that allows to rapidly and reliably estimate the numerosity of a set of objects: an Approximate Number System (ANS). Numerosity perception shows a characteristic shared by all primary visual features: it is susceptible to adaptation. As a consequence of prolonged exposure to a large/small quantity (“adaptor”), the apparent numerosity of a subsequent (“test”) stimulus is distorted yielding a robust under- or over-estimation, respectively. Even if numerosity adaptation has been reported across several sensory modalities (vision, audition, and touch), suggesting the idea of a central and a-modal numerosity processing system, evidence for cross-modal effects are limited to vision and audition, two modalities that are known to preferentially encode sensory stimuli in an external coordinate system. Here we test whether numerosity adaptation for visual and auditory stimuli also distorts the perceived numerosity of tactile stimuli (and vice-versa) despite touch being a modality primarily coded in an internal (body-centered) reference frame. We measured numerosity discrimination of stimuli presented sequentially after adaptation to series of either few (around 2 Hz; low adaptation) or numerous (around 8 Hz; high adaptation) impulses for all possible combinations of visual, auditory, or tactile adapting and test stimuli. In all cases, adapting to few impulses yielded a significant overestimation of the test numerosity with the opposite occurring as a consequence of adaptation to numerous stimuli. The overall magnitude of adaptation was robust (around 30%) and rather similar for all sensory modality combinations. Overall, these findings support the idea of a truly generalized and a-modal mechanism for numerosity representation aimed to process numerical information independently from the sensory modality of the incoming signals.

Geometry intuitions without vision? A study in blind children and adults

Geometry intuitions seem to be rooted in a non-verbal system that humans possess since early age. However, the mechanisms underlying the comprehension of basic geometric concepts remain elusive. Some authors have suggested that the starting point of geometry development could be found in the visual perception of specific features in our environment, thus conferring to vision a foundational role in the acquisition of geometric skills. To examine this assumption, a test probing intuitive understanding of basic geometric concepts was presented to congenitally blind children and adults. Participants had to detect the intruder among four different shapes, from which three instantiated a specific geometrical concept and one (the intruder) violated it. Although they performed above the chance level, the blind presented poorer performance than the sighted participants who did the task in the visual modality (i.e., with the eyes open), but performed equally well than the sighted who did the task in the tactile modality (i.e., with a blindfold). We therefore provide evidence that geometric abilities are impacted by the lack of vision.

Serial dependence in time and numerosity perception is dimension-specific

The perception of a visual event (e.g., a flock of birds) at the present moment can be biased by a previous perceptual experience (e.g., the perception of an earlier flock). Serial dependence is a perceptual bias whereby a current stimulus appears more similar to a previous one than it actually is. Whereas serial dependence emerges within several visual stimulus dimensions, whether it could simultaneously operate across different dimensions of the same stimulus (e.g., the numerosity and the duration of a visual pattern) remains unclear. Here we address this question by assessing the presence of serial dependence across duration and numerosity, two stimulus dimensions that are often associated and can bias each other. Participants performed either a duration or a numerosity discrimination task, in which they compared a constant reference with a variable test stimulus, varying along the task-relevant dimension (either duration or numerosity). Serial dependence was induced by a task-irrelevant inducer, that is, a stimulus presented before the reference and always varying in both duration and numerosity. The results show systematic serial dependencies only within the task-relevant stimulus dimension, that is, stimulus numerosity affects numerosity perception only, and duration affects duration perception only. Additionally, at least in the numerosity condition, the task-irrelevant dimension of the inducer (duration) had an opposite, repulsive effect. These findings thus show that attractive serial dependence operates in a highly specific fashion and does not transfer across different stimulus dimensions. Instead, the repulsive influence, possibly reflecting perceptual adaptation, can transfer from one dimension to another.

Core knowledge of geometry can develop independently of visual experience

Geometrical intuitions spontaneously drive visuo-spatial reasoning in human adults, children and animals. Is their emergence intrinsically linked to visual experience, or does it reflect a core property of cognition shared across sensory modalities? To address this question, we tested the sensitivity of blind-from-birth adults to geometrical-invariants using a haptic deviant-figure detection task. Blind participants spontaneously used many geometric concepts such as parallelism, right angles and geometrical shapes to detect intruders in haptic displays, but experienced difficulties with symmetry and complex spatial transformations. Across items, their performance was highly correlated with that of sighted adults performing the same task in touch (blindfolded) and in vision, as well as with the performances of uneducated preschoolers and Amazonian adults. Our results support the existence of an amodal core-system of geometry that arises independently of visual experience. However, performance at selecting geometric intruders was generally higher in the visual compared to the haptic modality, suggesting that sensory-specific spatial experience may play a role in refining the properties of this core-system of geometry.

Disentangling feedforward versus feedback processing in numerosity representation

Numerosity is a fundamental aspect of the external environment, needed to guide our behavior in an effective manner. Previous studies show that numerosity processing involves at least two temporal stages (~100 and ~150 msec after stimulus onset) in early visual cortex. One possibility is that the two stages reflect an initial feedforward processing followed by feedback signals from higher-order cortical areas that underlie segmentation of visual inputs into perceptual units that define numerosity. Alternatively, multiple stages of feedforward processing might progressively refine the input leading to the segmented representation. Here, we distinguish these two hypotheses by exploiting the connectedness illusion (i.e., the systematic underestimation of pairwise-connected dots), backward masking (to suppress feedback signals), and serial dependence (i.e., a perceptual bias making a stimulus appear to be more similar to its preceding one). Our results show that a connected dot array biases the numerosity representation of the subsequent dot array based on its illusory perception, irrespective of whether it is visible or suppressed by masking. These findings demonstrate that feedback processing is not strictly necessary for the perceptual segmentation that gives rise to perceived numerosity, and instead suggest that different stages of feedforward activity presumably carrying low and high spatial frequency information are sufficient to create a numerosity representation in early visual areas.

A Sensorimotor Numerosity System

Incoming sensory input provides information for the planning and execution of actions, which yield motor outcomes that are themselves sensory inputs. One dimension where action and perception strongly interact is numerosity perception. Many non-human animals can estimate approximately the number of external elements as well as their own actions, and neurons have been identified that respond to both. Recent psychophysical adaptation studies on humans also provide evidence for neural mechanisms responding to both the number of externally generated events and self-produced actions. Here we advance the idea that these strong connections may arise from dedicated sensorimotor mechanisms in the brain, part of a more generalized system interfacing action with the processing of other quantitative magnitudes such as space and time.

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, in order for the two hands to occupy either two completely different positions, or the same position in space, respectively. Tactile adaptor and test stimuli were passively delivered either to the same (adapted) or different (non-adapted) hands. Our results show a clear signature of tactile numerosity adaptation aftereffects with a pattern of over- and under-estimation according to the adaptation rate (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.

How visual is the « number sense »? Insights from the blind

Is vision a necessary building block for the foundations of mathematical cognition? A straightforward model to test the causal role visual experience plays in the development of numerical abilities is to study people born without sight. In this review we will demonstrate that congenitally blind people can develop numerical abilities that equal or even surpass those of sighted individuals, despite representing numbers using a qualitatively different representational format. We will also show that numerical thinking in blind people maps onto regions typically involved in visuo-spatial processing in the sighted, highlighting how intrinsic computational biases may constrain the reorganization of numerical networks in case of early visual deprivation. More generally, we will illustrate how the study of arithmetic abilities in congenitally blind people represents a compelling model to understand how sensory experience scaffolds the development of higher-level cognitive representations.