Cross-dimensional mapping of number, length and brightness by preschool children

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.

No intrinsic number bias: Evaluating the role of perceptual discriminability in magnitude categorization

Accumulating evidence suggests that there is a spontaneous preference for numerical, compared to non-numerical (e.g., cumulative surface area), information. However, given a paucity of research on the perception of non-numerical magnitudes, it is unclear whether this preference reflects a specific bias towards number, or a general bias towards the more perceptually discriminable dimension (i.e., number). Here, we found that when the number and area of visual dot displays were matched in mathematical ratio, number was more perceptually discriminable than area in both adults and children. Moreover, both adults and children preferentially categorized these ratio-matched stimuli based on number, consistent with previous work. However, when number and area were matched in perceptual discriminability, a different pattern of results emerged. In particular, children preferentially categorized stimuli based on area, suggesting that children's previously observed number bias may be due to a mismatch in the perceptual discriminability of number and area, not an intrinsic salience of number. Interestingly, adults continued to categorize the displays on the basis of number. Altogether, these findings suggest a dominant role for area during childhood, refuting the claim that number is inherently and uniquely salient. Yet they also reveal an increased salience of number that emerges over development. Potential explanations for this developmental shift are discussed. RESEARCH HIGHLIGHTS: Previous work found that children and adults spontaneously categorized dot array stimuli by number, over other magnitudes (e.g., area), suggesting number is uniquely salient. However, here we found that when number and area were matched by ratio, as in prior work, number was significantly more perceptually discriminable than area. When number and area were made equally discriminable ('perceptually-matched'), children, contra adults, spontaneously categorized stimuli by area over number (and other non-numerical magnitudes). These findings suggest that area may be uniquely salient early in childhood, with the previously-observed number bias not emerging until later in development.

Real models: The limits of behavioural evidence for understanding the ANS

Clarke and Beck use behavioural evidence to argue that (1) approximate ratio computations are sufficient for claiming that the approximate number system (ANS) represents the rationals, and (2) the ANS does not represent the reals. We argue that pure behaviour is a poor litmus test for this problem, and that we should trust the psychophysical models that place ANS representations within the reals.

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.

Evidence for a visuospatial bias in decimal number comparison in adolescents and in adults

There is a close relation between spatial and numerical representations which can lead to interference as in Piaget's number conservation task or in the numerical Stroop task. Using a negative priming (NP) paradigm, we investigated whether the interference between spatial and numerical processing extends to more complex arithmetic processing by asking 12 year olds and adults to compare the magnitude of decimal numbers (i.e., the prime) and, subsequently, the length of two lines or the luminance of two circles (i.e., the probe). We found NP effects when participants compare length but not luminance. Our finding suggests that decimal comparison is impacted by a visuospatial bias due to the interference between the magnitude of the numbers to be compared and their physical length. We discuss the educational implications of these findings.

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.

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.

Spatial metaphor and the development of cross-domain mappings in early childhood

Spatial language is often used metaphorically to describe other domains, including time (long sound) and pitch (high sound). How does experience with these metaphors shape the ability to associate space with other domains? Here, we tested 3- to 6-year-old English-speaking children and adults with a cross-domain matching task. We probed cross-domain relations that are expressed in English metaphors for time and pitch (length-time and height-pitch) as well as relations that are unconventional in English but expressed in other languages (size-time and thickness-pitch). Participants were tested with a perceptual matching task, in which they matched between spatial stimuli and sounds of different durations or pitches, and a linguistic matching task, in which they matched between a label denoting a spatial attribute, duration, or pitch and a picture or sound representing another dimension. Contrary to previous claims that experience with linguistic metaphors is necessary for children to make cross-domain mappings, children performed above chance for both familiar and unfamiliar relations in both tasks, as did adults. Children's performance was also better when a label was provided for one of the dimensions, but only when making length-time, size-time, and height-pitch mappings (not thickness-pitch mappings). These findings suggest that although experience with metaphorical language is not necessary to make cross-domain mappings, labels can promote these mappings, both when they have familiar metaphorical uses (e.g., English long denotes both length and duration) and when they describe dimensions that share a common ordinal reference frame (e.g., size and duration but not thickness and pitch). (PsycINFO Database Record

Development of a Possible General Magnitude System for Number and Space

There is strong evidence for a link between numerical and spatial processing. However, whether this association is based on a common general magnitude system is far from conclusive and the impact of development is not yet known. Hence, the present study aimed to investigate the association between discrete non-symbolic number processing (comparison of dot arrays) and continuous spatial processing (comparison of angle sizes) in children between the third and sixth grade (N = 367). Present findings suggest that the processing of comparisons of number of dots or angle are related to each other, but with angle processing developing earlier and being more easily comparable than discrete number representations for children of this age range. Accordingly, results favor the existence of a more complex underlying magnitude system consisting of dissociated but closely interacting representations for continuous and discrete magnitudes.

Numerical Affordance Influences Action Execution: A Kinematic Study of Finger Movement

Humans represent symbolic numbers as oriented from left to right: the mental number line (MNL). Up to now, scientific studies have mainly investigated the MNL by means of response times. However, the existing knowledge on the MNL can be advantaged by studies on motor patterns while responding to a number. Cognitive representations, in fact, cannot be fully understood without considering their impact on actions. Here we investigated whether a motor response can be influenced by number processing. Participants seated in front of a little soccer goal. On each trial they were visually presented with a numerical (2, 5, 8) or a non-numerical ($) stimulus. They were instructed to kick a small ball with their right index toward a frontal soccer goal as soon as a stimulus appeared on a screen. However, they had to refrain from kicking when number five was presented (no-go signal). Our main finding is that performing a kicking action after observation of the larger digit proved to be more efficient: the trajectory path was shorter and lower on the surface, velocity peak was anticipated. The smaller number, instead, specifically altered the temporal and spatial aspects of trajectories, leading to more prolonged left deviations. This is the first experimental demonstration that the reaching component of a movement is influenced by number magnitude. Since this paradigm does not require any verbal skill and non-symbolic stimuli (array of dots) can be used, it could be fruitfully adopted to evaluate number abilities in children and even preschoolers. Notably, this is a self-motivating and engaging task, which might help children to get involved and to reduce potential arousal connected to institutional paper-and-pencil examinations.

Effect of perceived length on numerosity estimation: Evidence from the Müller-Lyer illusion

Previous studies showed that the magnitude information conveyed by sensory cues, such as length or surface, influences the ability to compare the numerosity of sets of objects. However, the perceptual nature of this representation and how it interacts with the processes involved in numerical judgements remain unclear. This study aims to address these issues by studying the interference of length on numerosity under different perceptual and response conditions. The first experiment shows that the influence of length does not depend on the actual length but on subjective values reflecting the way length is perceived in a given visual context. The Müller-Lyer illusion was used to manipulate the perceived length of two dot arrays independently of their actual length. When the length of two dot arrays was equal but perceived as different due to the illusion, participants erroneously reported differences in the number of dots contained in each array, evidencing a similar effect of Müller-Lyer illusion on length and numerosity comparison. This finding was replicated in a second experiment where participants had to give a verbal estimate of the number of dots contained in a given array, thereby eliminating the choice between a small or large response. Compared with a neutral condition, estimations were systematically larger than the actual number of dots as the illusory length increased. These results demonstrate that the illusory-induced experience of length influences numerosity estimation over and beyond objective cues and that this influence is not a response selection bias.

Number prompts left-to-right spatial mapping in toddlerhood

Toddlers performed a spatial mapping task in which they were required to learn the location of a hidden object in a vertical array and then transpose this location information 90° to a horizontal array. During the vertical training, they were given (a) no labels, (b) alphabetical labels, or (c) numerical labels for each potential spatial location. After the array was transposed to become a horizontal continuum, the children who were provided with numerical labels during training and those who heard alphabetical labels and formed a strong memory for the vertical location, selectively chose the location corresponding to a left-to-right mapping bias. Children who received no concurrent ordinal labels during training were not able to transpose the array, and did not exhibit any spatial directionality bias after transposition. These results indicate that children exhibit more flexible spatial mapping than other animals, and this mapping is modulated depending on the type of concurrent ordinal information the child receives. (PsycINFO Database Record

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.

Culturally inconsistent spatial structure reduces learning

Human adults tend to use a spatial continuum to organize any information they consider to be well-ordered, with a sense of initial and final position. The directionality of this spatial mapping is mediated by the culture of the subject, largely as a function of the prevailing reading and writing habits (for example, from left-to-right for English speakers or right-to-left for Hebrew speakers). In the current study, we tasked American and Israeli subjects with encoding and recalling a set of arbitrary pairings, consisting of frequently ordered stimuli (letters with shapes: Experiment 1) or infrequently ordered stimuli (color terms with shapes: Experiment 2), that were serially presented in a left-to-right, right-to-left, or central-only manner. The subjects were better at recalling information that contained ordinal stimuli if the spatial flow of presentation during encoding matched the dominant directionality of the subjects' culture, compared to information encoded in the non-dominant direction. This phenomenon did not extend to infrequently ordered stimuli (e.g., color terms). These findings suggest that adults implicitly harness spatial organization to support memory, and this harnessing process is culturally mediated in tandem with our spatial biases.

Core mathematical abilities in infants: Number and much more

Adults' ability to process numerical information can be traced back to the first days of life. The cognitive mechanisms underlying numerical representations are functional in preverbal infants, who are able to both track a small number of individuals and to estimate the numerosity of large sets across different modalities. This ability is closely linked to their ability to compute other quantitative dimensions such as spatial extent and temporal duration. In fact, the human mind establishes, early in life, spontaneous links between number, space, and time, which are privileged relative to links with other continuous dimensions (like loudness and brightness). Finally, preverbal infants do not only associate numbers to corresponding spatial extents but also to different spatial positions along a spatial axis. It is argued that these number-space mappings are at the origins of the "mental number line" representation, which is already functional in the first year of life.

Where music meets space: Children's sensitivity to pitch intervals is related to their mental spatial transformation skills

Relations have been found among various continuous dimensions, including space and musical pitch. To probe the nature and development of space-pitch mappings, we tested 5- to 7-year-olds and adults (N=69), who heard pitch intervals and were asked to choose the corresponding spatial representation. Results showed that children and adults both mapped pitches continuously onto space, although effects were stronger in older than younger children. Additionally, children's spatial and numerical skills were tested, showing a relation between children's spatial and pitch-matching skills, and between their spatial and numerical skills. However, pitch and number were not related, suggesting spatial underpinnings for pitch and number.

Thinking about quantity: the intertwined development of spatial and numerical cognition

There are many continuous quantitative dimensions in the physical world. Philosophical, psychological, and neural work has focused mostly on space and number. However, there are other important continuous dimensions (e.g., time and mass). Moreover, space can be broken down into more specific dimensions (e.g., length, area, and density) and number can be conceptualized discretely or continuously (i.e., natural vs real numbers). Variation on these quantitative dimensions is typically correlated, e.g., larger objects often weigh more than smaller ones. Number is a distinctive continuous dimension because the natural numbers (i.e., positive integers) are used to quantify collections of discrete objects. This aspect of number is emphasized by teaching of the count word sequence and arithmetic during the early school years. We review research on spatial and numerical estimation, and argue that a generalized magnitude system is the starting point for development in both domains. Development occurs along several lines: (1) changes in capacity, durability, and precision, (2) differentiation of the generalized magnitude system into separable dimensions, (3) formation of a discrete number system, i.e., the positive integers, (4) mapping the positive integers onto the continuous number line, and (5) acquiring abstract knowledge of the relations between pairs of systems. We discuss implications of this approach for teaching various topics in mathematics, including scaling, measurement, proportional reasoning, and fractions.

Development of Spatial-Numerical Associations

Links between spatial and numerical thinking are well established in studies of adult cognition. Here, we review recent research on the origins and development of these links, with an emphasis on the formative role of experience in typical development and on the theoretical insights to be gained from infant cognition. This research points to three important influences on the development of spatial-numerical associations: innate mechanisms linking space and nonsymbolic number, gross and fine motor activity that couples spatial location to both symbolic and nonsymbolic number, and culturally bound activities (e.g., reading, writing, and counting) that shape the relationship between spatial direction and symbolic number.

Development of spatial preferences for counting and picture naming

The direction of object enumeration reflects children's enculturation but previous work on the development of such spatial preferences has been inconsistent. Therefore, we documented directional preferences in finger counting, object counting, and picture naming for children (4 groups from 3 to 6 years, N = 104) and adults (N = 56). We found a right-side preference for finger counting in 3- to 6-year-olds and a left-side preference for counting objects and naming pictures by 6 years of age. Children were consistent in their special preferences when comparing object counting and picture naming, but not in other task pairings. Finally, spatial preferences were not related to cardinality comprehension. These results, together with other recent work, suggest a gradual development of spatial-numerical associations from early non-directional mappings into culturally constrained directional mappings.

Are numbers, size and brightness equally efficient in orienting visual attention? Evidence from an eye-tracking study

A number of studies have shown strong relations between numbers and oriented spatial codes. For example, perceiving numbers causes spatial shifts of attention depending upon numbers' magnitude, in a way suggestive of a spatially oriented, mental representation of numbers. Here, we investigated whether this phenomenon extends to non-symbolic numbers, as well as to the processing of the continuous dimensions of size and brightness, exploring whether different quantitative dimensions are equally mapped onto space. After a numerical (symbolic Arabic digits or non-symbolic arrays of dots; Experiment 1) or a non-numerical cue (shapes of different size or brightness level; Experiment 2) was presented, participants' saccadic response to a target that could appear either on the left or the right side of the screen was registered using an automated eye-tracker system. Experiment 1 showed that, both in the case of Arabic digits and dot arrays, right targets were detected faster when preceded by large numbers, and left targets were detected faster when preceded by small numbers. Participants in Experiment 2 were faster at detecting right targets when cued by large-sized shapes and left targets when cued by small-sized shapes, whereas brightness cues did not modulate the detection of peripheral targets. These findings indicate that looking at a symbolic or a non-symbolic number induces attentional shifts to a peripheral region of space that is congruent with the numbers' relative position on a mental number line, and that a similar shift in visual attention is induced by looking at shapes of different size. More specifically, results suggest that, while the dimensions of number and size spontaneously map onto an oriented space, the dimension of brightness seems to be independent at a certain level of magnitude elaboration from the dimensions of spatial extent and number, indicating that not all continuous dimensions are equally mapped onto space.

How number-space relationships are assessed before formal schooling: A taxonomy proposal

The last years of research on numerical development have provided evidence that spatial-numerical associations (SNA) can be formed independent of formal school training. However, most of these studies used various experimental paradigms that referred to slightly different aspects of number and space processing. This poses a question of whether all SNAs described in the developmental literature can be interpreted as a unitary construct, or whether they are rather examples of different, but related phenomena. Our review aims to provide a starting point for a systematic classification of SNA measures used from infancy to late preschool years, and their underlying representations. We propose to distinguish among four basic SNA categories: (i) cross-dimensional magnitude processing, (ii) associations between spatial and numerical intervals, (iii) associations between cardinalities and spatial directions, (iv) associations between ordinalities and spatial directions. Such systematization allows for identifying similarities and differences between processes and representations that underlie the described measures, and also for assessing the adequacy of using different SNA tasks at different developmental stages.

A cross-sectional developmental examination of the SNARC effect in a visually-guided grasping task

The present study documents the influence of numerical processing on hand and space use during a reach-to-grasp task. Three questions regarding the SNARC (spatial-numerical association of response codes) effect were asked: (1) would the SNARC effect influence hand and/or space preference for grasping?; (2) would the SNARC effect be demonstrated during the processing of one-digit numbers, two-digit numbers, or both?; and (3) would developmental age influence the strength of the SNARC effect? A total of 84 participants in three age/school level groups (Primary, Secondary, and Post-secondary) took part in the study. Two identical sets of small wooden blocks numbered from 0 to 19 were used. Each set was presented to the right and to the left of each participant. A number was called and participants were asked to find and grasp a block with the corresponding number as fast and accurately as possible. Hand and space used (L/R) was recorded for each grasp. Number magnitude was shown to influence the selection of hand and hemi-space in accordance with the SNARC effect. In the small percentage of trials where the left hand was used, it was more commonly recruited to grasp blocks displaying low numbers than high numbers. Participants grasped blocks from left and right space with equal frequency, but respectively left/right space was accessed more often for blocks displaying low/high numbers. Regression analyses revealed that developmental age is a powerful predictor of the SNARC effect on hand and space selection for grasping. This study provides the first description of the SNARC effect on hand and space preference for the reach-to-grasp action. Results are discussed with relevant literature of numerical processing in the human brain.

Culturally-Driven Biases in Preschoolers' Spatial Search Strategies for Ordinal and Non-Ordinal Dimensions

Culturally-driven spatial biases affect the way people interact with and think about the world. We examine the ways in which spatial presentation of stimuli affects learning and memory in preschool-aged children in the USA and Israel. In Experiment 1, preschoolers in both cultures were given a spatial search task in which they were asked to utilize verbal labels (letters of the alphabet) to match the hiding locations of two monkeys. The labels were taught to the children in either a left-to-right or right-to-left fashion to assess whether performance on this task is affected by directionality of labeling. English-speaking children performed better on the spatial search task when locations were labeled in a left-to-right fashion, while Hebrew-speaking children exhibited higher performance when labels were taught in a right-to-left fashion. In Experiment 2, English-speaking preschoolers were given a modified task in which the verbal label was a non-ordinal stimulus type (colors). These children showed no subsequent advantage on the task for spatial presentations which were culturally-consistent (left-to-right) relative to culturally-inconsistent (right-to-left). These findings support the hypothesis that culturally-consistent spatial layout improves learning and memory, and that this benefit is reduced or absent when information lacks ordinal properties.

Not all continuous dimensions map equally: number-brightness mapping in human infants

Evidence for spontaneous mappings between the dimensions of number and length, time and length, and number and time, has been recently described in preverbal infants. It is unclear, however, whether these abilities reflect the existence of privileged mappings between certain quantitative dimensions, like number, space and time, or instead the existence of a magnitude system underlying the representation of any quantitative dimension, and allowing mappings across those dimensions. Four experiments, using the same methods from previous research that revealed a number-length mapping in eight-month-old infants, investigated whether infants of the same age establish mappings between number and a different, non-spatial continuous dimension: level of brightness. We show that infants are able to learn and productively use mappings between brightness and number when they are positively related, i.e., larger numbers paired with brighter or higher contrast levels, and fail when they are inversely related, i.e., smaller numbers paired with brighter or higher contrast levels, suggesting that they are able to learn this mapping in a specific direction. However, infants not only do not show any baseline preference for any direction of the number-brightness mapping, but fail at transferring the discrimination from one dimension (number) to the other (brightness). Although infants can map multiple dimensions to one another, the number-length mapping may be privileged early in development, as it is for adults.

The role of numerical magnitude and order in the illusory perception of size and brightness

Processing magnitudes constitutes a common experience across multiple dimensions, for example when one has to compare sizes, duration, numbers, sound height or loudness. From a cognitive point of view, however, it is still unclear whether all these experiences rely on a common system, or on distinct systems, with more or less strong associations. One particularly striking way of observing such interference between the spatial and numerical dimensions consists in eliciting a bias in size judgment through the mere perception of irrelevant numerical stimuli. In such experimental context though, two questions remain open. First, it is still unknown whether the direction of the bias is related to the magnitude of the number presented, or to their position in an ordinal sequence, and thus could be elicited by other non-numerical ordinal sequences such as letters of the alphabet. Second, it is still unclear whether the observed interactions generalize to other continuous dimension of magnitude such as brightness. In the study reported here, both letters and numbers were used in a size- and a brightness-reproduction task. We observed a dissociation between the two types of stimuli when reproducing size, the illusion being elicited solely by numbers. When reproducing brightness, however, neither the letters nor the numbers elicited a bias. These findings suggest that, while only numerical magnitude, and not letters, elicits a bias in size perception, the concurrent processing of magnitude and brightness does not bring about the same illusion, supporting the idea of a relative independence in the processing of these two dimensions.