Processing number and length in the parietal cortex: Sharing resources, not a common code

Cortical quantity representations of visual numerosity and timing overlap increasingly into superior cortices but remain distinct

Many sensory brain areas are organized as topographic maps where neural response preferences change gradually across the cortical surface. Within association cortices, 7-Tesla fMRI and neural model-based analyses have also revealed many topographic maps for quantities like numerosity and event timing, often in similar locations. Numerical and temporal quantity estimations also show behavioral similarities and even interactions. For example, the duration of high-numerosity displays is perceived as longer than that of low-numerosity displays. Such interactions are often ascribed to a generalized magnitude system with shared neural responses across quantities. Anterior quantity responses are more closely linked to behavior. Here, we investigate whether common quantity representations hierarchically emerge by asking whether numerosity and timing maps become increasingly closely related in their overlap, response preferences, and topography. While the earliest quantity maps do not overlap, more superior maps overlap increasingly. In these overlapping areas, some intraparietal maps have consistently correlated numerosity and timing preferences, and some maps have consistent angles between the topographic progressions of numerosity and timing preferences. However, neither of these relationships increases hierarchically like the amount of overlap does. Therefore, responses to different quantities are initially derived separately, then progressively brought together, without generally becoming a common representation. Bringing together distinct responses to different quantities may underlie behavioral interactions and allow shared access to comparison and action planning systems.

Network dynamics underlying alterations in apparent object size

A target circle surrounded by small circles looks larger than an identical circle surrounded by large circles (termed as the Ebbinghaus illusion). While previous research has shown that both early and high-level visual regions are involved in the generation of the illusion, it remains unclear how these regions work together to modulate the illusion effect. Here, we used functional MRI and dynamic causal modelling to investigate the neural networks underlying the illusion in conditions where the focus of attention was manipulated via participants directing their attention to and maintain fixation on only one of the two illusory configurations at a time. Behavioural findings confirmed the presence of the illusion. Accordingly, functional MRI activity in the extrastriate cortex accounted for the illusory effects: apparently larger circles elicited greater activation than apparently smaller circles. Interestingly, this spread of activity for size overestimation was accompanied by a decrease in the inhibitory self-connection in the extrastriate region, and an increase in the feedback connectivity from the precuneus to the extrastriate region. These findings demonstrate that the representation of apparent object size relies on feedback projections from higher- to lower-level visual areas, highlighting the crucial role of top-down signals in conscious visual perception.

Intuitive mapping between nonsymbolic quantity and observed action across development

Adults' concurrent processing of numerical and action information yields bidirectional interference effects consistent with a cognitive link between these two systems of representation. This link is in place early in life: infants create expectations of congruency across numerical and action-related stimuli (i.e., a small [large] hand aperture associated with a smaller [larger] numerosity). Although these studies point to a developmental continuity of this mapping, little is known about the later development and thus how experience shapes such relationships. We explored how number-action intuitions develop across early and later childhood using the same methodology as in adults. We asked 3-, 6-, and 8-year-old children, as well as adults, to relate the magnitude of an observed action (a static hand shape, open vs. closed, in Experiment 1; a dynamic hand movement, opening vs. closing, in Experiment 2) to either a small or large nonsymbolic quantity (numerosity in Experiment 1 and numerosity and/or object size in Experiment 2). From 6 years of age, children started performing in a systematic congruent way in some conditions, but only 8-year-olds (added in Experiment 2) and adults performed reliably above chance in this task. We provide initial evidence that early intuitions guiding infants' mapping between magnitude across nonsymbolic number and observed action are used in an explicit way only from late childhood, with a mapping between action and size possibly being the most intuitive. An initial coarse mapping between number and action is likely modulated with extensive experience with grasping and related actions directed to both arrays and individual objects.

Near-optimal integration of the magnitude information of time and numerosity

Magnitude information is often correlated in the external world, providing complementary information about the environment. As if to reflect this relationship, the perceptions of different magnitudes (e.g. time and numerosity) are known to influence one another. Recent studies suggest that such magnitude interaction is similar to cue integration, such as multisensory integration. Here, we tested whether human observers could integrate the magnitudes of two quantities with distinct physical units (i.e. time and numerosity) as abstract magnitude information. The participants compared the magnitudes of two visual stimuli based on time, numerosity, or both. Consistent with the predictions of the maximum-likelihood estimation model, the participants integrated time and numerosity in a near-optimal manner; the weight of each dimension was proportional to their relative reliability, and the integrated estimate was more reliable than either the time or numerosity estimate. Furthermore, the integration approached a statistical optimum as the temporal discrepancy of the acquisition of each piece of information became smaller. These results suggest that magnitude interaction arises through a similar computational mechanism to cue integration. They are also consistent with the idea that different magnitudes are processed by a generalized magnitude system.

Spontaneous supra-modal encoding of number in the infant brain

The core knowledge hypothesis postulates that infants automatically analyze their environment along abstract dimensions, including numbers. According to this view, approximate numbers should be encoded quickly, pre-attentively, and in a supra-modal manner by the infant brain. Here, we directly tested this idea by submitting the neural responses of sleeping 3-month-old infants, measured with high-density electroencephalography (EEG), to decoders designed to disentangle numerical and non-numerical information. The results show the emergence, in approximately 400 ms, of a decodable number representation, independent of physical parameters, that separates auditory sequences of 4 vs. 12 tones and generalizes to visual arrays of 4 vs. 12 objects. Thus, the infant brain contains a number code that transcends sensory modality, sequential or simultaneous presentation, and arousal state.

Neural Basis of Social Influence of Observing Other's Perception in Dot-Number Estimation

Our perceptions and decisions are often implicitly influenced by observing another's actions. However, it is unclear how observing other people's perceptual decisions without interacting with them can engage the processing of self-other discrepancies and change the observer's decisions. In this study, we employed functional magnetic resonance imaging and a computational model to investigate the neural basis of how unilaterally observing the other's perceptual decisions modulated one's own decisions. The experimental task was to discriminate whether the number of presented dots was higher or lower than a reference number. The participants performed the task solely while unilaterally observing the performance of another "participant," who produced overestimations and underestimations in the same task in separate sessions. Results of the behavioral analysis showed that the participants' decisions were modulated to resemble those of the other. Image analysis based on computational model revealed that the activation in the medial prefrontal cortex was associated with the discrepancy between the inferred participant's and the presented other's decisions. In addition, the number-sensitive region in the superior parietal region showed altered activation patterns after observing the other's overestimations and underestimations. The activity of the superior parietal region was not involved in assessing the observation of other's perceptual decisions, but it was engaged in plain numerosity perception. These results suggest that computational modeling can capture the neuro-behavioral processing of self-other discrepancies in perception followed by the activity modulation in the number-sensitive region in the task of dot-number estimation.

Event-Related Potentials Reveal the Impact of Conflict Strength in a Numerical Stroop Paradigm

Numerical cognition provides an opportunity to study the underlying processes of selective attention to numerical information in the face of conflicting, non-numerical, information of different magnitudes. For instance, in the numerical Stroop paradigm, participants are asked to judge pairs of Arabic digits whose physical size can either be congruent (e.g., 3 vs. 5) or incongruent (e.g., 3 vs. 5) with numerical value. Congruency effects when deciding which of the two digits is numerically larger are thought to reflect the inhibition of the irrelevant physical size. However, few studies have investigated the impact of the salience of the irrelevant non-numerical information on these congruency effects and their neural substrates. EEG was recorded in 32 adults during a numerical Stroop task with two levels of salience (low, high) of the irrelevant size dimension. At the behavioral level, we observed larger congruency effects in the high salience condition (i.e., when the difference in size between the two digits is larger). At the neural level, at centro-parietal electrodes, we replicated previous studies showing a main effect of congruency on event-related potential (ERP) amplitudes between 280 and 370 ms post-stimulus, as well as a main effect of salience around 200 ms post-stimulus. Crucially, congruency and salience interacted both between 230 and 250 ms (P2), and between 290 and 340 ms (P3). These results provide support for separate processes underlying the increase in congruency effect, which can be attributed to higher demands in both the inhibition of the irrelevant dimension, and the attention to the relevant numerical information.

Intrinsic excitability of human right parietal cortex shapes the experienced visual size illusions

Converging evidence has found that the perceived visual size illusions are heritable, raising the possibility that visual size illusions might be predicted by intrinsic brain activity without external stimuli. Here we measured resting-state brain activity and 2 classic visual size illusions (i.e. the Ebbinghaus and the Ponzo illusions) in succession, and conducted spectral dynamic causal modeling analysis among relevant cortical regions. Results revealed that forward connection from right V1 to superior parietal lobule (SPL) was predictive of the Ebbinghaus illusion, and self-connection in the right SPL predicted the Ponzo illusion. Moreover, disruption of intrinsic activity in the right SPL by repetitive transcranial magnetic stimulation (TMS) temporally increased the Ebbinghaus rather than the Ponzo illusion. These findings provide a better mechanistic understanding of visual size illusions by showing the causal and distinct contributions of right parietal cortex to them, and suggest that spontaneous fluctuations in intrinsic brain activity are relevant to individual difference in behavior.

The nature of magnitude integration: Contextual interference versus active magnitude binding

Magnitude dimensions such as duration and numerosity have been shown to systematically interact, biasing each other in a congruent fashion: the more numerous a set of items is, the longer it is perceived to last in time. This integration between dimensions plays an important role in defining how we perceive magnitude. So far, however, the nature of magnitude integration remains unclear. Is magnitude integration a contextual interference, occurring whenever different types of information are concurrently available in the visual field, or does it involve an active “binding” of the different dimensions of the same object? To address these possibilities, we measured the integration bias induced by numerosity on perceived duration, in two cases: with duration and numerosity conveyed by distinct stimuli, or by the same stimulus. We show that a congruent integration effect can be observed only when the two magnitudes belong to the same stimulus. Instead, when the two magnitudes are conveyed by distinct stimuli, we observed an opposite effect. These findings demonstrate for the first time that a congruent integration occurs only between the dimensions of the same stimulus, suggesting the involvement of an active mechanism integrating the different dimensions of the same object in a unified percept.

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.

Neural basis of approximate number in congenital blindness

Although humans are unique among animals in their ability to manipulate symbolic numbers, we share with other species an approximate number sense that allows us to estimate and compare the number of objects or events in a set, such as the number of apples in a tree. Our ability to discriminate the numerosity of two sets decreases as the ratio between them becomes smaller (e.g., 8 vs 16 items is harder to discriminate than 8 vs 32 items). The intraparietal sulcus (IPS) plays a key role in this numerical approximation. Neuronal populations within the IPS code for numerosity, with stimuli of different numerosities eliciting discriminable spatial patterns of activity. The developmental origins of these IPS number representations are not known. Here, we tested the hypothesis that representations of number in the IPS require visual experience with object sets, by working with individuals blind from birth. While undergoing fMRI, congenitally blind (n = 17) and blindfolded sighted (n = 25) participants judged which of two sequences of beeps was more numerous. In both sighted and blind individuals, patterns of activity in the IPS discriminated among different numerosities (4, 8, 16 vs 32), with better discrimination in the IPS of the blind group. In both groups, decoding performance decreased as the ratio between numerosities decreased (e.g., 8 vs 16 was less discriminable than 8 vs 32). These findings suggest that number representations in the IPS either have innate precursors, or that auditory or tactile experience with sets is sufficient for typical development.

Representation of visual numerosity information during working memory in humans: An fMRI decoding study

Both animal and human studies on numerosity have shown the importance of the parietal cortex for numerosity processing. However, most studies have focused on the perceptual processing of numerosity. Still, it is unclear how and where numerosity information is coded when this information is retained during a working memory delay phase. Such temporal storage could be realized by the same structures as perceptual processes, or be transformed to a more abstract representation, potentially involving prefrontal regions. FMRI decoding studies allow the identification of brain areas that exhibit multi‐voxel activation patterns specific to the content of working memory. Here, we used an assumption‐free searchlight‐decoding approach to test where numerosity‐specific codes can be found during a 12 s retention period. Participants (n = 24) performed a retro‐cue delayed match‐to‐sample task, in which numerosity information was presented as visual dot arrays. We found mnemonic numerosity‐specific activation in the right lateral portion of the intraparietal sulcus; an area well‐known for perceptual processing of numerosity. The applied retro‐cue design dissociated working memory delay activity from perceptual processes and showed that the intraparietal sulcus also maintained working memory representation independent of perception.

Grid-like and distance codes for representing word meaning in the human brain

Relational information about items in memory is thought to be represented in our brain thanks to an internal comprehensive model, also referred to as a "cognitive map". In the human neuroimaging literature, two signatures of bi-dimensional cognitive maps have been reported: the grid-like code and the distance-dependent code. While these kinds of representation were previously observed during spatial navigation and, more recently, during processing of perceptual stimuli, it is still an open question whether they also underlie the representation of the most basic items of language: words. Here we taught human participants the meaning of novel words as arbitrary labels for a set of audiovisual objects varying orthogonally in size and sound. The novel words were therefore conceivable as points in a navigable 2D map of meaning. While subjects performed a word comparison task, we recorded their brain activity using functional magnetic resonance imaging (fMRI). By applying a combination of representational similarity and fMRI-adaptation analyses, we found evidence of (i) a grid-like code, in the right postero-medial entorhinal cortex, representing the relative angular positions of words in the word space, and (ii) a distance-dependent code, in medial prefrontal, orbitofrontal, and mid-cingulate cortices, representing the Euclidean distance between words. Additionally, we found evidence that the brain also separately represents the single dimensions of word meaning: their implied size, encoded in visual areas, and their implied sound, in Heschl's gyrus/Insula. These results support the idea that the meaning of words, when they are organized along two dimensions, is represented in the human brain across multiple maps of different dimensionality. SIGNIFICANT STATEMENT: How do we represent the meaning of words and perform comparative judgements on them in our brain? According to influential theories, concepts are conceivable as points of an internal map (where distance represents similarity) that, as the physical space, can be mentally navigated. Here we use fMRI to show that when humans compare newly learnt words, they recruit a grid-like and a distance code, the same types of neural codes that, in mammals, represent relations between locations in the environment and support physical navigation between them.

Visual similarity and psychological closeness are neurally dissociable in the brain response to vicarious pain

Personal and vicarious experience of pain activate partially overlapping brain networks. This brain activity is further modulated by low- and high-order factors, e.g., the perceived intensity of the model's pain and the model's similarity with the onlooker, respectively. We investigated which specific aspect of similarity modulates such empathic reactivity, focusing on the potential differentiation between visual similarity and psychological closeness between the onlooker and different types of models. To this aim, we recorded fMRI data in neurotypical participants who observed painful and tactile stimuli delivered to an adult human hand, a baby human hand, a puppy dog paw, and an anthropomorphic robotic hand. The interaction between type of vicarious experience (pain, touch) and nature of model (adult, baby, dog, robot) showed that the right supramarginal gyrus (rSMG) was selectively active for visual similarity (more active during vicarious pain for the adult and baby models), while the anterior cingulate cortex (ACC) was more sensitive to psychological closeness (specifically linked to vicarious pain for the baby model). These findings indicate that visual similarity and psychological closeness between onlooker and model differentially affect the activity of brain regions specifically implied in encoding interindividual sharing of sensorimotor and affective aspects of vicarious pain, respectively.

Neural representations of haptic object size in the human brain revealed by multivoxel fMRI patterns

The brain must interpret sensory input from diverse receptor systems to estimate object properties. Much has been learned about the brain mechanisms behind these processes in vision, but our understanding of haptic perception remains less clear. Here we examined haptic judgments of object size, which require integrating multiple cutaneous and proprioceptive afferent signals, as a model problem. To identify candidate human brain regions that support this process, participants (n = 16) in an event-related functional MRI experiment grasped objects to categorize them as one of four sizes. Object sizes were calibrated psychophysically to be equally distinct for each participant. We applied representational similarity logic to whole brain, multivoxel searchlight analyses to identify brain regions that exhibit size-relevant voxelwise activity patterns. Of particular interest was to identify regions for which more similar sizes produce more similar patterns of activity, which constitutes evidence of a metric size code. Regions of the intraparietal sulcus and the lateral prefrontal cortex met this criterion, both within hands and across hands. We suggest that these regions compute representations of haptic size that abstract over the specific peripheral afferent signals generated in a grasp. Results of a matched visual size task, performed by the same participants and analyzed in the same fashion, identified similar regions, indicating that these representations may be partly modality general. We consider these results with respect to perspectives on magnitude estimation in general and to computational views on perceptual signal integration.NEW & NOTEWORTHY Our understanding of the neural basis of haptics (perceiving the world through touch) remains incomplete. We used functional MRI to study human haptic judgments of object size, which require integrating multiple afferent signals. Multivoxel pattern analyses identified intraparietal and prefrontal regions that encode size haptically in a metric and hand-invariant fashion. Effector-independent haptic size estimates are useful on their own and in combination with other sensory estimates for a variety of perceptual and motor tasks.

Parametric Representation of Tactile Numerosity in Working Memory

Estimated numerosity perception is processed in an approximate number system (ANS) that resembles the perception of a continuous magnitude. The ANS consists of a right lateralized frontoparietal network comprising the lateral prefrontal cortex (LPFC) and the intraparietal sulcus. Although the ANS has been extensively investigated, only a few studies have focused on the mental representation of retained numerosity estimates. Specifically, the underlying mechanisms of estimated numerosity working memory (WM) is unclear. Besides numerosities, as another form of abstract quantity, vibrotactile WM studies provide initial evidence that the right LPFC takes a central role in maintaining magnitudes. In the present fMRI multivariate pattern analysis study, we designed a delayed match-to-numerosity paradigm to test what brain regions retain approximate numerosity memoranda. In line with parametric WM results, our study found numerosity-specific WM representations in the right LPFC as well as in the supplementary motor area and the left premotor cortex extending into the superior frontal gyrus, thus bridging the gap in abstract quantity WM literature.

Discrimination of ordinal relationships in temporal sequences by 4-month-old infants

The ability to discriminate the ordinal information embedded in magnitude-based sequences has been shown in 4-month-old infants, both for numerical and size-based sequences. At this early age, however, this ability is confined to increasing sequences, with infants failing to extract and represent decreasing order. Here we investigate whether the ability to represent order extends to duration-based sequences in 4-month-old infants, and whether it also shows the asymmetry signature previously observed for number and size. Infants were tested in an order discrimination task in which they were habituated to either increasing or decreasing variations in temporal duration, and were then tested with novel sequences composed of new temporal items whose durations varied following the familiar and the novel orders in alternation. Across three experiments, we manipulated the duration of the single temporal items and therefore of the whole sequences, which resulted in imposing more or less constraints on infants' working memory, or general processing capacities. Results showed that infants failed at discriminating the ordinal direction in temporal sequences when the sequences had an overall long duration (Experiment 1), but succeeded when the duration of the sequences was shortened (Experiments 2 and 3). Moreover, there was no sign of the asymmetry signature previously reported for number and size, as successful discrimination was present for infants habituated to both increasing and decreasing sequences. These results suggest that sensitivity to temporal order is present very early in development, and that its functional properties are not shared with other magnitude dimensions, such as size and number.

Structure learning and the posterior parietal cortex

We propose a theory of structure learning in the primate brain. We argue that the parietal cortex is critical for learning about relations among the objects and categories that populate a visual scene. We suggest that current deep learning models exhibit poor global scene understanding because they fail to perform the relational inferences that occur in the primate dorsal stream. We review studies of neural coding in primate posterior parietal cortex (PPC), drawing the conclusion that neurons in this brain area represent potentially high-dimensional inputs on a low-dimensional manifold that encodes the relative position of objects or features in physical space, and relations among entities in abstract conceptual space. We argue that this low-dimensional code supports generalisation of relational information, even in nonspatial domains. Finally, we propose that structure learning is grounded in the actions that primates take when they reach for objects or fixate them with their eyes. We sketch a model of how this might occur in neural circuits.

The association of brightness with number/duration in human newborns

Human neonates spontaneously associate changes in magnitude across the dimensions of number, length, and duration. Do these particular associations generalize to other pairs of magnitudes in the same way at birth, or do they reflect an early predisposition to expect specific relations between spatial, temporal, and numerical representations? To begin to answer this question, we investigated how strongly newborns associated auditory sequences changing in number/duration with visual objects changing in levels of brightness. We tested forty-eight newborn infants in one of three, bimodal stimulus conditions in which auditory numbers/durations increased or decreased from a familiarization trial to the two test trials. Auditory numbers/durations were paired with visual objects in familiarization that remained the same on one test trial but changed in luminance/contrast or shape on the other. On average, results indicated that newborns looked longer when changes in brightness accompanied the number/duration change as compared to no change, a preference that was most consistent when the brightness change was congruent with the number/duration change. For incongruent changes, this preference depended on trial order. Critically, infants showed no preference for a shape change over no shape change, indicating that infants likely treated brightness differently than a generic feature. Though this performance pattern is somewhat similar to previously documented associations, these findings suggest that cross-magnitude associations among number, length, and duration may be more specialized at birth, rather than emerge gradually from postnatal experience or maturation.

Attentional amplification of neural codes for number independent of other quantities along the dorsal visual stream

Humans and other animals base important decisions on estimates of number, and intraparietal cortex is thought to provide a crucial substrate of this ability. However, it remains debated whether an independent neuronal processing mechanism underlies this ‘number sense’, or whether number is instead judged indirectly on the basis of other quantitative features. We performed high-resolution 7 Tesla fMRI while adult human volunteers attended either to the numerosity or an orthogonal dimension (average item size) of visual dot arrays. Along the dorsal visual stream, numerosity explained a significant amount of variance in activation patterns, above and beyond non-numerical dimensions. Its representation was selectively amplified and progressively enhanced across the hierarchy when task relevant. Our results reveal a sensory extraction mechanism yielding information on numerosity separable from other dimensions already at early visual stages and suggest that later regions along the dorsal stream are most important for explicit manipulation of numerical quantity.

Numbers and the ability to count and calculate are an essential part of human culture. They are part of everyday life, featuring in calendars, computers or the weekly shop, but also in some of humanity’s biggest achievements: without them the pyramids or space travel would not exist. A precursor of sophisticated mathematical skill could reside in a simpler mental ability: the capacity to assess numerical quantities at a glance. This ‘number sense’ appears in humans in early childhood and it is also present in other animals, but it is still poorly understood.

Brain imaging techniques have identified the parts of the brain that are active when perceiving numbers or making calculations. As techniques have advanced, it has become possible to resolve fine differences in brain activity that occur when people switch their attention between different visual tasks. But how exactly does the human brain process visual information to make sense of numbers? One theory suggests that humans use visual cues, such as the size of a group of objects or how densely packed objects are, to estimate numbers. On the other hand, it is also possible that humans can sense number directly, without reference to other properties of the group being observed.

Castaldi et al. presented twenty adult volunteers with groups of dots and asked them to focus either on the number of dots or on the size of the dots during a brain scan. This approach allowed the separation of brain signals specific to number from signals corresponding to other visual cues, such as size or density of the group. The experiment revealed that brain activity changed depending on the number of dots displayed. The signal related to number became stronger when people focused on the number of dots, while signals related to other properties of the group remained unchanged. Moreover, brain signals for number were observed at the very early stages of visual processing, in the parts of the brain that receive input from the eyes first.

These results suggest that the human visual system perceives number directly, and not by processing information about the size or density of a group of objects. This finding provides insights into how human brains encode numbers, which could be important to understand disorders where number sense can be impaired leading to difficulties learning math and operating with numbers.

Number, time, and space are not singularly represented: Evidence against a common magnitude system beyond early childhood

Our ability to represent temporal, spatial, and numerical information is critical for understanding the world around us. Given the prominence of quantitative representations in the natural world, numerous cognitive, neurobiological, and developmental models have been proposed as a means of describing how we track quantity. One prominent theory posits that time, space, and number are represented by a common magnitude system, or a common neural locus (i.e., Bonn & Cantlon in Cognitive Neuropsychology, 29(1/2), 149-173, 2012; Cantlon, Platt, & Brannon in Trends in Cognitive Sciences, 13(2), 83-91, 2009; Meck & Church in Animal Behavior Processes, 9(3), 320, 1983; Walsh in Trends in Cognitive Sciences, 7(11), 483-488, 2003). Despite numerous similarities in representations of time, space, and number, an increasing body of literature reveals striking dissociations in how each quantity is processed, particularly later in development. These findings have led many researchers to consider the possibility that separate systems may be responsible for processing each quantity. This review will analyze evidence in favor of a common magnitude system, particularly in infancy, which will be tempered by counter evidence, the majority of which comes from experiments with children and adult participants. After reviewing the current data, we argue that although the common magnitude system may account for quantity representations in infancy, the data do not provide support for this system throughout the life span. We also identify future directions for the field and discuss the likelihood of the developmental divergence model of quantity representation, like that of Newcombe (Ecological Psychology, 2, 147-157, 2014), as a more plausible account of quantity development.

Asymmetrical interference between number and item size perception provides evidence for a domain specific impairment in dyscalculia

Dyscalculia, a specific learning disability that impacts arithmetical skills, has previously been associated to a deficit in the precision of the system that estimates the approximate number of objects in visual scenes (the so called 'number sense' system). However, because in tasks involving numerosity comparisons dyscalculics' judgements appears disproportionally affected by continuous quantitative dimensions (such as the size of the items), an alternative view linked dyscalculia to a domain-general difficulty in inhibiting task-irrelevant responses. To arbitrate between these views, we evaluated the degree of reciprocal interference between numerical and non-numerical quantitative dimensions in adult dyscalculics and matched controls. We used a novel stimulus set orthogonally varying in mean item size and numerosity, putting particular attention into matching both features' perceptual discriminability. Participants compared those stimuli based on each of the two dimensions. While control subjects showed no significant size interference when judging numerosity, dyscalculics' numerosity judgments were strongly biased by the unattended size dimension. Importantly however, both groups showed the same degree of interference from the unattended dimension when judging mean size. Moreover, only the ability to discard the irrelevant size information when comparing numerosity (but not the reverse) significantly predicted calculation ability across subjects. Overall, our results show that numerosity discrimination is less prone to interference than discrimination of another quantitative feature (mean item size) when the perceptual discriminability of these features is matched, as here in control subjects. By quantifying, for the first time, dyscalculic subjects' degree of interference on another orthogonal dimension of the same stimuli, we are able to exclude a domain-general inhibition deficit as explanation for their poor / biased numerical judgement. We suggest that enhanced reliance on non-numerical cues during numerosity discrimination can represent a strategy to cope with a less precise number sense.