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.

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.

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.

Representations of space, time, and number in neonates.

A rich concept of magnitude--in its numerical, spatial, and temporal forms--is a central foundation of mathematics, science, and technology, but the origins and developmental relations among the abstract concepts of number, space, and time are debated. Are the representations of these dimensions and their links tuned by extensive experience, or are they readily available from birth? Here, we show that, at the beginning of postnatal life, 0- to 3-d-old neonates reacted to a simultaneous increase (or decrease) in spatial extent and in duration or numerical quantity, but they did not react when the magnitudes varied in opposite directions. The findings provide evidence that representations of space, time, and number are systematically interrelated at the start of postnatal life, before acquisition of language and cultural metaphors, and before extensive experience with the natural correlations between these dimensions.

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.

Small on the left, large on the right: numbers orient visual attention onto space in preverbal infants.

Numbers are represented as ordered magnitudes along a spatially oriented number line. While culture and formal education modulate the direction of this number-space mapping, it is a matter of debate whether its emergence is entirely driven by cultural experience. By registering 8-9-month-old infants' eye movements, this study shows that numerical cues are critical in orienting infants' visual attention towards a peripheral region of space that is congruent with the number's relative position on a left-to-right oriented representational continuum. This finding provides the first direct evidence that, in humans, the association between numbers and oriented spatial codes occurs before the acquisition of symbols or exposure to formal education, suggesting that the number line is not merely a product of human invention.

Operational momentum and size ordering in preverbal infants.

Recent evidence has shown that, like adults and children, 9-month-old infants manifest an operational momentum (OM) effect during non-symbolic arithmetic, whereby they overestimate the outcomes to addition problems, and underestimate the outcomes to subtraction problems. Here we provide the first evidence that OM occurs for transformations of non-numerical magnitudes (i.e., spatial extent) during ordering operations. Twelve-month-old infants were tested in an ordinal task in which they detected and represented ascension or descension in physical size, and then responded to ordinal sequences that exhibited greater or lesser sizes. Infants displayed longer looking time to the size change whose direction violated the operational momentum experienced during habituation (i.e., the smaller sequence in the ascension condition and the larger sequence in the descension condition). The presence of momentum for ordering size during infancy suggests that continuous quantities are represented spatially during the first year of life.

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.

Finding the spatial-numerical association of response codes (SNARC) in signed numbers: notational effects in accessing number representation.

The present study investigates basic numerical processing in deaf signers and hearing individuals by evaluating notational effects (Arabic digits vs Italian sign language number signs) and response modality (manual vs pedal) in a parity judgment task. Overall, a standard SNARC effect emerged in both groups, suggesting similar numerical representation in hearing and deaf individuals. With the exception of Italian sign language stimuli in the hearing group, this effect applied to all stimuli notations and to both response modalities. In line with the special status of signs, the visuospatial complexity of finger configurations (i.e. number of extended fingers) affected the performance of the hearing group to a greater extent. Finally, the SNARC effect emerged systematically across lateralized effectors(manual/pedal response), challenging the hypothesis that the stimulus-response compatibility effect is specific to the effectors associated with the production of written and sign language. As for parity processing, both groups were similarly influenced by the parity information conveyed by the dominant hand, indicating the compositional nature of number signs irrespective of the preferred language modality.

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.

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.

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.

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.

Number-space mapping in human infants.

Mature representations of number are built on a core system of numerical representation that connects to spatial representations in the form of a mental number line. The core number system is functional in early infancy, but little is known about the origins of the mapping of numbers onto space. In this article, we show that preverbal infants transfer the discrimination of an ordered series of numerosities to the discrimination of an ordered series of line lengths. Moreover, infants construct relationships between numbers and line lengths when they are habituated to unordered pairings that vary positively, but not when they are habituated to unordered pairings that vary inversely. These findings provide evidence that a predisposition to relate representations of numerical magnitude to spatial length develops early in life. A central foundation of mathematics, science, and technology therefore emerges prior to experience with language, symbol systems, or measurement devices.

Placing order in space: the SNARC effect in serial learning.

The SNARC effect, consisting of a systematic association between numbers and lateralized response, reflects the mental representation of magnitude along a left-to-right mental number line (Dehaene et al. in J Exp Psychol 122:371-396, 1993). Critically, this effect has been reported in the classification of overlearned non-numerical sequences such as letters, days and months (Gevers et al. in Cognition 87:B87-B95, 2003 and Cortex 40:171-172, 2004) suggesting that ordinal, rather than magnitude information, is critical for spatial coding. This study tests the hypothesis of an oriented spatial representation as the privileged way of mentally organizing serial information, by looking for stimulus-response compatibility effects in the processing of a newly acquired arbitrary sequence. Here we report an association between ordinal position of the items and spatial response preference for both order-relevant and order-irrelevant tasks. These results suggest that any ordered information, even when order is not intrinsically relevant to it, is spontaneously mapped in the representational space. This spatial representation is likely to acquire a left-to-right orientation, at least in western cultures.

Numbers can move our hands: a spatial representation effect in digits handwriting.

The interaction between numbers and action-related processes is currently one of the most investigated topics in numerical cognition. The present study contributes to this line of research by investigating, for the first time, the effects of number on an overlearned complex motor plan that does not require explicit lateralised movements or strict spatial constrains: spontaneous handwriting. In particular, we investigated whether the spatial mapping of numbers interferes with the motor planning involved in writing. To this aim, participants' spontaneous handwriting of single digits (Exp. 1) and letters (Exp. 2) was recorded with a digitising tablet. We show that the writing of numbers is characterised by a spatial dislocation of the digits as a function of their magnitude, i.e., small numbers were written leftwards relative to large numbers. In contrast, the writing of letters showed a null or marginal effect with respect to their dislocation on the writing area. These findings show that the automatic mapping of numbers into space interacts with action planning by modulating specific motor parameters in spontaneous handwriting.

Seven-month-olds detect ordinal numerical relationships within temporal sequences.

Previous evidence has shown that 11-month-olds represent ordinal relations between purely numerical values, whereas younger infants require a confluence of numerical and non-numerical cues. In this study, we show that when multiple featural cues (i.e., color and shape) are provided, 7-month-olds detect reversals in the ordinal direction of numerical sequences relying solely on number when non-numerical quantitative cues are controlled. These results provide evidence for the influence of featural information and multiple cue integration on infants' proneness to detect ordinal numerical information.

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.