Maria Dolores de Hevia

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.

Representations of space, time, and number in neonates

Significance Space, time, and number are connected in the world and in the human mind. How do these connections arise? Do we learn to link larger numbers and durations to longer spatial extents because they are correlated in the world, or is the human mind built to capture these relations? We showed that neonates relate both number and duration to spatial length when these dimensions vary in the same direction (number or duration increases as length increases), but not in opposite directions (number or duration increases and length decreases). After being familiarized to a pairing between two magnitudes, newborns expect these dimensions to change in the same direction. At birth, humans are sensitive to the common structure of these fundamental magnitudes. 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.

Numbers and space: a cognitive illusion?

This study investigated the relationships between numerical and spatial representations by means of a bisection task, exploring the view that the core representation of number meaning is spatially organized as a mental number line. In Experiment nos. 1 (bisection of digit strings) and 2 (bisection of flanked lines) spatial biases towards the larger digit were found to be related only to processing of relative magnitude. Experiment nos. 3 (bisection of an unfilled space) and 4 (bisection of flanked lines/unfilled spaces) aimed at disclosing perceptual, attentional, and numerical constraints on the bias induced by the position of the larger digit. This effect is interpreted in terms of a cognitive illusion of length, whereby a spatial bias compensates for the numerical disparity. This seems to operate in a categorical fashion (“small/large”), and to be congruent with the assumption that relatively large numbers are associated with the right side of a mental representational space.

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.

Human infants' preference for left-to-right oriented increasing numerical sequences.

While associations between number and space, in the form of a spatially oriented numerical representation, have been extensively reported in human adults, the origins of this phenomenon are still poorly understood. The commonly accepted view is that this number-space association is a product of human invention, with accounts proposing that culture, symbolic knowledge, and mathematics education are at the roots of this phenomenon. Here we show that preverbal infants aged 7 months, who lack symbolic knowledge and mathematics education, show a preference for increasing magnitude displayed in a left-to-right spatial orientation. Infants habituated to left-to-right oriented increasing or decreasing numerical sequences showed an overall higher looking time to new left-to-right oriented increasing numerical sequences at test (Experiment 1). This pattern did not hold when infants were presented with the same ordinal numerical information displayed from right to left (Experiment 2). The different pattern of results was congruent with the presence of a malleable, context-dependent baseline preference for increasing, left-to-right oriented, numerosities (Experiment 3). These findings are suggestive of an early predisposition in humans to link numerical order with a left-to-right spatial orientation, which precedes the acquisition of symbolic abilities, mathematics education, and the acquisition of reading and writing skills.

The representational space of numerical magnitude: illusions of length.

In recent years, a growing amount of evidence concerning the relationships between numerical and spatial representations has been interpreted, by and large, in favour of the mental number line hypothesis—namely, the analogue continuum where numbers are spatially represented (Dehaene, 1992; Dehaene, Piazza, Pinel, & Cohen, 2003). This numerical representation is considered the core of number meaning and, accordingly, needs to be accessed whenever numbers are semantically processed. The present study explored, by means of a length reproduction task, whether besides the activation of lateralized spatial codes, numerical processing modulates the mental representation of a horizontal spatial extension. Mis-estimations of length induced by Arabic numbers are interpreted in terms of a cognitive illusion, according to which the elaboration of magnitude information brings about an expansion or compression of the mental representation of spatial extension. These results support the hypothesis that visuo-spatial resources are involved in the representation of numerical magnitude.

Minds without language represent number through space: origins of the mental number line

During the last decades, extensive research has investigated both the developmental origins and the representational format of numerical information. A crucial contribution to these issues comes from recent studies on non-verbal populations, such as non-human animals and preverbal infants, which suggest that number is intuitively and fundamentally spatial in nature, that a predisposition to relate numerical information to spatial magnitude emerges very early in life, and that the association of numbers to different spatial positions critically depends on biologically determined processing and attentional biases.

Cross-Dimensional Mapping of Number, Length and Brightness by Preschool Children

Human adults in diverse cultures, children, infants, and non-human primates relate number to space, but it is not clear whether this ability reflects a specific and privileged number-space mapping. To investigate this possibility, we tested preschool children in matching tasks where the dimensions of number and length were mapped both to one another and to a third dimension, brightness. Children detected variation on all three dimensions, and they reliably performed mappings between number and length, and partially between brightness and length, but not between number and brightness. Moreover, children showed reliably better mapping of number onto the dimension of length than onto the dimension of brightness. These findings suggest that number establishes a privileged mapping with the dimension of length, and that other dimensions, including brightness, can be mapped onto length, although less efficiently. Childrens adeptness at number-length mappings suggests that these two dimensions are intuitively related by the end of the preschool years.

What do We Know about Neonatal Cognition

Research on neonatal cognition has developed very recently in comparison with the long history of research on child behavior. The last sixty years of research have provided a great amount of evidence for infants’ numerous cognitive abilities. However, only little of this research concerns newborn infants. What do we know about neonatal cognition? Using a variety of paradigms, researchers became able to probe for what newborns know. Amongst these results, we can distinguish several levels of cognitive abilities. First, at the perceptual or sensory level, newborns are able to process information coming from the social world and the physical objects through all their senses. They are able to discriminate between object shapes and between faces; that is, they are able to detect invariants, remember and recognize them. Second, newborns are able to abstract information, to compare different inputs and to match them across different sensory modalities. We will argue that these two levels can be considered high-level cognitive abilities: they constitute the foundations of human cognition. Furthermore, while some perceptual competencies can stem from the fetal period, many of these perceptual and cognitive abilities cannot be a consequence of the environment surrounding the newborn before birth.

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.