What makes different number-space mappings interact?

Models of numerical cognition consider a visuo-spatial representation to be at the core of numerical processing, the 'mental number line'. Two main interference effects between number and space have been described: the SNARC effect reflects a small number/left side and large number/right side association (number-location mapping); the size-congruity effect (SCE) reflects a small number/small size and large number/large size association (number-size mapping). Critically, a thorough investigation on the representational source for these two number-space mappings is lacking, leaving open the question of whether the same representation underlies both phenomena. Here, we build on a recent study (Viarouge and de Hevia in Front Hum Neurosci 15:750964, 2021) in order to address this question in three experiments, by systematically manipulating the presence of the two conditions that might elicit an interaction between SNARC and SCE: (i) an implicit task whereby numerical and spatial information are task-irrelevant, (ii) a design in which the number-space congruency relative to both mappings vary at the same level -either both within or between blocks. Experiment 1 replicated the interaction between the two mappings when both factors were present. Experiments 2 and 3 dissociated the two factors by varying the two mappings at the same level but using an explicit comparison task (Experiment 2), or by using an implicit task but with mappings varying at different levels (Experiment 3). We found that both factors, either in combination or used in isolation, drive the interaction between the two number-space mappings. These findings are discussed in terms of the weight given to each mapping, suggesting that a single representation encompassing both number-space mappings is therefore activated whenever both mappings are given equal weight through task requirements.

How do human newborns come to understand the multimodal environment?

For a long time, newborns were considered as human beings devoid of perceptual abilities who had to learn with effort everything about their physical and social environment. Extensive empirical evidence gathered in the last decades has systematically invalidated this notion. Despite the relatively immature state of their sensory modalities, newborns have perceptions that are acquired, and are triggered by, their contact with the environment. More recently, the study of the fetal origins of the sensory modes has revealed that in utero all the senses prepare to operate, except for the vision mode, which is only functional starting from the first minutes after birth. This discrepancy between the maturation of the different senses leads to the question of how human newborns come to understand our multimodal and complex environment. More precisely, how the visual mode interacts with the tactile and auditory modes from birth. After having defined the tools that newborns use to interact with other sensory modalities, we review studies across different fields of research such as the intermodal transfer between touch and vision, auditory-visual speech perception, and the existence of links between the dimensions of space, time, and number. Overall, evidence from these studies supports the idea that human newborns are spontaneously driven, and cognitively equipped, to link information collected by the different sensory modes in order to create a representation of a stable world.

Spatio-Numerical Mapping in 3D.

The close link between number and space is illustrated by the Spatial Numerical Association of Response Codes (SNARC) effect. The current research focuses on the flexibility of the SNARC across three dimensions. Shaki and Fischer (2018) pointed out that spatial attributes of stimuli and response effectors can favor an ad hoc spatial representation. In this paper, we aimed to broaden this perspective using two Go/NoGo experiments with digits being presented at two spatial locations while a central response was required. In Experiment 1, stimuli appeared either to the left or right (horizontal) and below or above fixation (vertical). In Experiment 2, as the monitor was laying down flat on the desk, stimuli appeared either to the left or right (horizontal) and either close or far from the observer (midsagittal). The results of Experiment 1 show significant effects for the two dimensions (horizontal, vertical), while in Experiment 2, we observe only a barely significant effect for the sagittal axis. We interpret these findings as showing (1) the importance of motor response spatialization in eliciting the SNAs and (2) the dominance of the vertical axis over the horizontal when the spatial component of the motor response is removed.

Electrophysiological Evidence for A Number-Action Mapping in Infancy.

In the last decades, a growing body of literature has focused on the link between number and action. Many studies conducted on adult participants have provided evidence for a bidirectional influence between numerosity processing and grasping or reaching actions. However, it is not yet clear whether this link is functional in early infancy. Here, we used the event-related potential (ERP) technique to record electrical activity of the brain in response to number-hand pairings. We implemented a cueing paradigm where 3- to 4-month-old infants observed images showing either congruency (e.g., a large numerosity primed by a large hand opening) or incongruency (e.g., a large numerosity primed by a small hand opening). Infants' brain activity was modulated by the congruency of the pairings: amplitudes recorded over frontal and parietal-occipital scalp positions differed for congruent versus incongruent pairings. These findings suggest that the association between number and hand action processing is already functional early in life.

Abstract representations of small sets in newborns.

From the very first days of life, newborns are not tied to represent narrow, modality- and object-specific aspects of their environment. Rather, they sometimes react to abstract properties shared by stimuli of very different nature, such as approximate numerosity or magnitude. As of now, however, there is no evidence that newborns possess abstract representations that apply to small sets: in particular, while newborns can match large approximate numerosities across senses, this ability does not extend to small numerosities. In two experiments, we presented newborn infants (N = 64, age 17 to 98 h) with patterned sets AB or ABB simultaneously in the auditory and visual modalities. Auditory patterns were presented as periodic sequences of sounds (AB: triangle-drum-triangle-drum-triangle-drum …; ABB: triangle-drum-drum-triangle-drum-drum-triangle-drum-drum …), and visual patterns as arrays of 2 or 3 shapes (AB: circle-diamond; ABB: circle-diamond-diamond). In both experiments, we found that participants reacted and looked longer when the patterns matched across the auditory and visual modalities - provided that the first stimulus they received was congruent. These findings uncover the existence of yet another type of abstract representations at birth, applying to small sets. As such, they bolster the hypothesis that newborns are endowed with the capacity to represent their environment in broad strokes, in terms of its most abstract properties. This capacity for abstraction could later serve as a scaffold for infants to learn about the particular entities surrounding them.

The link between number and action in human infants.

Humans' inborn ability to represent and manipulate numerical quantities is supported by the parietal cortex, which is also involved in a variety of spatial and motor abilities. While the behavioral links between numerical and spatial information have been extensively studied, little is known about the connection between number and action. Some studies in adults have shown a series of interference effects when simultaneously processing numerical and action information. We investigated the origins of this link by testing forty infants (7- to 9-month-old) in one of two experimental conditions: one group was habituated to congruent number-hand pairings, where the larger the number, the more open the hand-shape associated; the second group was habituated to incongruent number-hand pairings, where the larger the number, the more close the hand-shape associated. In test trials, both groups of infants were presented with congruent and incongruent pairings. We found that only infants habituated to congruency showed a significantly higher looking time to the test trial depicting incongruent pairings. These findings show for the first time that infants spontaneously associate magnitude-related changes across the dimensions of number and action-related information, thus offering support to the existence of an early, preverbal number-action link in the human mind.

Space modulates cross-domain transfer of abstract rules in infants.

Developmental studies have shown that infants exploit ordinal information to extract and generalize repetition-based rules from a sequence of items. Within the visual modality, this ability is constrained by the spatial layout within which items are delivered given that a left-to-right orientation boosts infants' rule learning, whereas a right-to-left orientation hinders this ability. Infants' rule learning operates across different domains and can also be transferred across modalities when learning is triggered by speech. However, no studies have investigated whether the transfer of rule learning occurs across different domains when language is not involved. Using a visual habituation procedure, we tested 7-month-old infants' ability to extract rule-like patterns from numerical sequences and generalize them to non-numerical sequences of visual shapes and whether this ability is affected by the spatial orientation. Infants were first habituated to left-to-right or right-to-left oriented numerical sequences instantiating an ABB rule and were then tested with the familiar rule instantiated across sequences of single geometrical shapes and a novel (ABA) rule. Results showed a transfer of learning from number to visual shapes for left-to-right oriented sequences but not for right-to-left oriented ones (Experiment 1) even when the direction of the numerical change (increasing vs. decreasing) within the habituation sequences violated a small-left/large-right number-space association (Experiment 2). These results provide the first demonstration that visual rule learning mechanisms in infancy operate at a high level of abstraction and confirm earlier findings that left-to-right oriented directional cues facilitate infants' representation of order.

Signatures of functional visuospatial asymmetries in early infancy.

Adults present a large number of asymmetries in visuospatial behavior that are known to be supported by functional brain lateralization. Although there is evidence of lateralization for motor behavior and language processing in infancy, no study has explored visuospatial attention biases in the early stages of development. In this study, we tested for the presence of a leftward visuospatial bias (i.e., pseudoneglect) in 4- and 5-month-old infants using an adapted version of the line bisection task. Infants were trained to identify the center of a horizontal line (Experiment 1) while their eye gazes were monitored using a remote eye-tracking procedure to measure their potential gazing error. Infants exhibited a robust pseudoneglect, gazing leftward with respect to the veridical midpoint of the horizontal line. To investigate whether infants' pseudoneglect generalizes to any given object or is dependent on the horizontal dimension, in Experiment 2 we assessed infants' gaze deployment in vertically oriented lines. No leftward bias was found, suggesting that early visuospatial attention biases in infancy are constrained by the orientation of the visual plane in which the information is organized. The interplay between biological and cultural factors that might contribute to the early establishment of the observed leftward bias in the allocation of visuospatial attention is discussed.

Can a Single Representational Object Account for Different Number-Space Mappings?

Numbers are mapped onto space from birth on, as evidenced by a variety of interactions between the processing of numerical and spatial information. In particular, larger numbers are associated to larger spatial extents (number/spatial extent mapping) and to rightward spatial locations (number/location mapping), and smaller numbers are associated to smaller spatial extents and leftward spatial locations. These two main types of number/space mappings (number/spatial extent and number/location mappings) are usually assumed to reflect the fact that numbers are represented on an internal continuum: the mental number line. However, to date there is very little evidence that these two mappings actually reflect a single representational object. Across two experiments in adults, we investigated the interaction between number/location and number/spatial extent congruency effects, both when numbers were presented in a non-symbolic and in a symbolic format. We observed a significant interaction between the two mappings, but only in the context of an implicit numerical task. The results were unaffected by the format of presentation of numbers. We conclude that the number/location and the number/spatial extent mappings can stem from the activation of a single representational object, but only in specific experimental contexts.

A left visual advantage for quantity processing in neonates.

Forty-eight newborn infants were tested in one of three multimodal stimulus conditions, in which auditory quantities were presented alongside visual object arrays in two test trials. These tests varied with respect to which side (either left or right) numerically matched the auditory number. The infants looked longer to the test trials in which the left side of the visual display exhibited a quantity that matched the presented auditory quantity. This study provides the first evidence for an untrained, innate bias for humans to preferentially process quantity information presented in the left field of vision.

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.

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.

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

A current intense discussion in numerical cognition concerns the relationship between the processing of numerosity and other non-numerical quantities. In particular, it is a matter of debate whether number and other quantities (e.g., size, length) are represented separately in the brain or whether they share a common generalized magnitude representation. We acquired high-resolution functional MRI data while adult subjects engaged in a magnitude comparison task involving either numerosity (i.e., which of the two sets has more elements?) or line length (i.e., which of the two lines is longer?). We compared the activation evoked by the two different types of quantity and observed a common recruitment of a vast portion of occipital and parietal cortices. Using MVPA, we demonstrated that some of the commonly activated regions represented the discrete and continuous quantities via a similar distance-dependent magnitude code. However, we found no effect of distance across the two quantity representations, failing to support the existence of a common, dimension invariant, generalized quantity code. Taken together, these findings indicate that although the processing of number and length is supported by partially overlapping neural resources, representations within these regions do not appear to be based on a common neural code.

Operational momentum for magnitude ordering in preschool children and adults.

When adding or subtracting quantities, adults tend to overestimate addition outcomes and underestimate subtraction outcomes. They also shift visuospatial attention to the right when adding and to the left when subtracting. These operational momentum phenomena are thought to reflect an underlying representation in which small magnitudes are associated with the left side of space and large magnitudes with the right side of space. Currently, there is limited research on operational momentum in early childhood or for operations other than addition and subtraction. The current study tested whether English-speaking 3- and 4-year-old children and college-aged adults exhibit operational momentum when ordering quantities. Participants were presented with two experimental blocks. In one block of trials, they were tasked with choosing the same quantity they had previously seen three times; in the other block, they were asked to generate the next quantity in a doubling sequence composed of three ascending quantities. A bias to shift attention to the right after an ascending operation was found in both age groups, and a bias to overestimate the next sequential quantity during an ascending ordering operation was found in adults under conditions of uncertainty. These data suggest that, for children, the spatial biases during operating are more pronounced than the mis-estimation biases. These findings highlight the spatial underpinnings of operational momentum and suggest that both very young children and adults conceptualize quantity along a horizontal continuum during ordering operations, even before formal schooling.

At Birth, Humans Associate "Few" with Left and "Many" with Right.

Humans use spatial representations to structure abstract concepts [1]. One of the most well-known examples is the "mental number line"-the propensity to imagine numbers oriented in space [2, 3]. Human infants [4, 5], children [6, 7], adults [8], and nonhuman animals [9, 10] associate small numbers with the left side of space and large numbers with the right. In humans, cultural artifacts, such as the direction of reading and writing, modulate the directionality of this representation, with right-to-left reading cultures associating small numbers with right and large numbers with left [11], whereas the opposite association permeates left-to-right reading cultures [8]. Number-space mapping plays a central role in human mathematical concepts [12], but its origins remain unclear: is it the result of an innate bias or does it develop after birth? Infant humans are passively exposed to a spatially coded environment, so experience and culture could underlie the mental number line. To rule out this possibility, we tested neonates' responses to small or large auditory quantities paired with geometric figures presented on either the left or right sides of the screen. We show that 0- to 3-day-old neonates associate a small quantity with the left and a large quantity with the right when the multidimensional stimulus contains discrete numerical information, providing evidence that representations of number are associated to an oriented space at the start of postnatal life, prior to experience with language, culture, or with culture-specific biases.

Infants learn better from left to right: a directional bias in infants' sequence learning.

A wealth of studies show that human adults map ordered information onto a directional spatial continuum. We asked whether mapping ordinal information into a directional space constitutes an early predisposition, already functional prior to the acquisition of symbolic knowledge and language. While it is known that preverbal infants represent numerical order along a left-to-right spatial continuum, no studies have investigated yet whether infants, like adults, organize any kind of ordinal information onto a directional space. We investigated whether 7-month-olds' ability to learn high-order rule-like patterns from visual sequences of geometric shapes was affected by the spatial orientation of the sequences (left-to-right vs. right-to-left). Results showed that infants readily learn rule-like patterns when visual sequences were presented from left to right, but not when presented from right to left. This result provides evidence that spatial orientation critically determines preverbal infants' ability to perceive and learn ordered information in visual sequences, opening to the idea that a left-to-right spatially organized mental representation of ordered dimensions might be rooted in biologically-determined constraints on human brain development.

Perceiving numerosity from birth.

Leibovich et al. opened up an important discussion on the nature and origins of numerosity perception. The authors rightly point out that non-numerical features of stimuli influence this ability. Despite these biases, there is evidence that from birth, humans perceive and represent numerosities, and not just non-numerical quantitative features such as item size, density, and convex hull.

Infants' detection of increasing numerical order comes before detection of decreasing number.

Ordinality is a fundamental aspect of numerical cognition. However, preverbal infants' ability to represent numerical order is poorly understood. In the present study we extended the evidence provided by Macchi Cassia, Picozzi, Girelli, and de Hevia (2012), showing that 4-month-old infants detect ordinal relationships within size-based sequences, to numerical sequences. In three experiments, we showed that at 4months of age infants fail to represent increasing and decreasing numerical order when numerosities differ by a 1:2 ratio (Experiment 1), but they succeed when numerosities differ by a 1:3 ratio (Experiments 2 and 3). Critically, infants showed the same behavioral signature (i.e., asymmetry) described by Macchi Cassia et al. for discrimination of ordinal changes in area: they succeed at detecting increasing but not decreasing order (Experiments 2 and 3). These results support the idea of a common (or at least parallel) development of ordinal representation for the two quantitative dimensions of size and number. Moreover, the finding that the asymmetry signature, previously reported for size-based sequences, extends to numerosity, points to the existence of a common constraint in ordinal magnitude processing in the first months of life. The present findings are discussed in the context of possible evolutionary and developmental sources of the ordinal asymmetry, as well as their implication for other related cognitive abilities.

Number-space associations without language: Evidence from preverbal human infants and non-human animal species.

It is well known that humans describe and think of numbers as being represented in a spatial configuration, known as the 'mental number line'. The orientation of this representation appears to depend on the direction of writing and reading habits present in a given culture (e.g., left-to-right oriented in Western cultures), which makes this factor an ideal candidate to account for the origins of the spatial representation of numbers. However, a growing number of studies have demonstrated that non-verbal subjects (preverbal infants and non-human animals) spontaneously associate numbers and space. In this review, we discuss evidence showing that pre-verbal infants and non-human animals associate small numerical magnitudes with short spatial extents and left-sided space, and large numerical magnitudes with long spatial extents and right-sided space. Together this evidence supports the idea that a more biologically oriented view can account for the origins of the 'mental number line'. In this paper, we discuss this alternative view and elaborate on how culture can shape a core, fundamental, number-space association.