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

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.

Colours + Numbers differs from colours of numbers: cognitive and visual illusions in grapheme-colour synaesthesia

This study investigates the bi-directionality of synaestesic experience by means of a flanked bisection paradigm in TT, a number-colour synaesthete. Previous studies have shown that bisection is shifted towards the larger digit flanker (e.g., Ranzini & Girelli, 2012). TT and controls performed line bisections with lines flanked by black digits (experiment 1), by TT's photism colours (experiment 2), and by congruently (experiment 3), or incongruently coloured digits (experiment 4). While the results of the control group mainly replicated previous findings, only the colour-digit congruence elicited in TT the larger-digit bias. TT's absence of effects in the other conditions was not due to reduced sensitivity to luminance effects (experiment 5), or to mathematical expertise (experiment 6). We suggest that grapheme-colour synaesthesia might be characterised by a rigid access to semantic representation when the inducer is task-irrelevant.

Mapping of non-numerical domains on space: a systematic review and meta-analysis

The spatial numerical association of response code (SNARC) effect is characterized by low numbers mapped to the left side of space and high numbers mapped to the right side of space. In addition to numbers, SNARC-like effects have been found in non-numerical magnitude domains such as time, size, letters, luminance, and more, whereby the smaller/earlier and larger/later magnitudes are typically mapped to the left and right of space, respectively. The purpose of this systematic and meta-analytic review was to identify and summarise all empirical papers that have investigated horizontal (left-right) SNARC-like mappings using non-numerical stimuli. A systematic search was conducted using EMBASE, Medline, and PsycINFO, where 2216 publications were identified, with 57 papers meeting the inclusion criteria (representing 112 experiments). Ninety-five of these experiments were included in a meta-analysis, resulting in an overall effect size of d = .488 for a SNARC-like effect. Additional analyses revealed a significant effect size advantage for explicit instruction tasks compared with implicit instructions, yet yielded no difference for the role of expertise on SNARC-like effects. There was clear evidence for a publication bias in the field, but the impact of this bias is likely to be modest, and it is unlikely that the SNARC-like effect is a pure artefact of this bias. The similarities in the response properties for the spatial mappings of numerical and non-numerical domains support the concept of a general higher order magnitude system. Yet, further research will need to be conducted to identify all the factors modulating the strength of the spatial associations.

Order Information in Verbal Working Memory Shifts the Subjective Midpoint in Both the Line Bisection and the Landmark Tasks

A largely substantiated view in the domain of working memory is that the maintenance of serial order is achieved by generating associations of each item with an independent representation of its position, so-called position markers. Recent studies reported that the ordinal position of an item in verbal working memory interacts with spatial processing. This suggests that position markers might be spatial in nature. However, these interactions were so far observed in tasks implying a clear binary categorization of space (i.e., with left and right responses or targets). Such binary categorizations leave room for alternative interpretations, such as congruency between non-spatial categorical codes for ordinal position (e.g., begin and end) and spatial categorical codes for response (e.g., left and right). Here we discard this interpretation by providing evidence that this interaction can also be observed in a task that draws upon a continuous processing of space, the line bisection task. Specifically, bisections are modulated by ordinal position in verbal working memory, with lines bisected more towards the right after retrieving items from the end compared to the beginning of the memorized sequence. This supports the idea that position markers are intrinsically spatial in nature.

Cognitive Mechanisms Underlying Directional and Non-directional Spatial-Numerical Associations across the Lifespan

There is accumulating evidence suggesting an association of numbers with physical space. However, the origin of such spatial-numerical associations (SNAs) is still debated. In the present study we investigated the development of two SNAs in a cross-sectional study involving children, young and middle-aged adults as well as the elderly: (1) the SNARC (spatial-numerical association of response codes) effect, reflecting a directional SNA; and (2) the numerical bisection bias in a line bisection task with numerical flankers. Results revealed a consistent SNARC effect in all age groups that continuously increased with age. In contrast, a numerical bisection bias was only observed for children and elderly participants, implying an U-shaped distribution of this bias across age groups. Additionally, individual SNARC effects and numerical bisection biases did not correlate significantly. We argue that the SNARC effect seems to be influenced by longer-lasting experiences of cultural constraints such as reading and writing direction and may thus reflect embodied representations. Contrarily, the numerical bisection bias may originate from insufficient inhibition of the semantic influence of irrelevant numerical flankers, which should be more pronounced in children and elderly people due to development and decline of cognitive control, respectively. As there is an ongoing debate on the origins of SNAs in general and the SNARC effect in particular, the present results are discussed in light of these differing accounts in an integrative approach. However, taken together, the present pattern of results suggests that different cognitive mechanisms underlie the SNARC effect and the numerical bisection bias.

Manual actions cover symbolic distances at different speed

A privileged way of representing numbers in the human mind is along an oriented mental number line. Activation of this representation has been proposed to account for the impact of numbers on motor tasks, such as on grasping, pointing, and eye movements. Here we evaluated the impact of numbers on motor control, by exploiting the evidence that the speed reached by the manual connection of two points is correlated with their physical distance. We reasoned that, if irrelevant numbers induce a mis-perception of the distance between two points, this should be reflected in the movement speed. Results showed a speed difference in the manual connection of two numerically close numbers (i.e., connected slower) and two numerically distant numbers (i.e., connected faster), placed at equal physical distance. This representational length effect indicates not only that symbolic distance modulates speed movement as physical distance does, but suggests that the impact of numbers on action planning does not only involve action initiation but it extends to the definition of kinematic parameters. More generally, the reported findings show that the representation of numbers along a mental space affects our behaviour in the physical space.

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.

The Spatial Representation of Numerical and Non-Numerical Ordered Sequences: Insights from a Random Generation Task

It is widely believed that numbers are spatially represented from left to right on the mental number line. Whether this spatial format of representation is specific to numbers or is shared by non-numerical ordered sequences remains controversial. When healthy participants are asked to randomly generate digits they show a systematic small-number bias that has been interpreted in terms of “pseudoneglect in number space”. Here we used a random generation task to compare numerical and non-numerical order. Participants performed the task at three different pacing rates and with three types of stimuli (numbers, letters, and months). In addition to a small-number bias for numbers, we observed a bias towards “early” items for letters and no bias for months. The spatial biases for numbers and letters were rate independent and similar in size, but they did not correlate across participants. Moreover, letter generation was qualified by a systematic forward direction along the sequence, suggesting that the ordinal dimension was more salient for letters than for numbers in a task that did not require its explicit processing. The dissociation between numerical and non-numerical orders is consistent with electrophysiological and neuroimaging studies and suggests that they rely on at least partially different mechanisms.

Gaining the upper hand: comparison of alphabetic and keyboard positions as spatial features of letters producing distinct S-R compatibility effects

The present study explored which stimulus feature, alphabetic or keyboard position, primarily influences letter processing in different task settings. In Experiment 1 (alphabetic position judgment) a response side effect (faster responses when the location of letters within the alphabet or on the keyboard maps onto the response hand) could be observed for alphabetic position as task-relevant stimulus feature. In Experiments 2 and 3 participants responded to a non-spatial stimulus feature (uppercase-lowercase classification) so that both attributes can be characterized as task-irrelevant. The pattern indicated that a keyboard position-hand correspondence effect emerged independent of the time window (after stimulus onset) in which the response was given. However, an alphabetic position-hand correspondence effect only emerged when participants were forced to delay their responses by 450ms. The overall pattern indicated that although both features were processed and translated into a spatial code reflecting their position within the alphabet vs. on the keyboard, the relevance of these features to the task as well as the time that elapsed since stimulus onset determined which attribute of the letters was effective in yielding a stimulus-response compatibility effect.

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.

Different effects of numerical magnitude on visual and proprioceptive reference frames

This study assessed whether numerical magnitude affects the setting of basic spatial coordinates and reference frames, namely the subjective straight ahead. Three tasks were given to 24 right-handed healthy participants: a proprioceptive and a visuo-proprioceptive task, requiring pointing to the subjective straight ahead, and a visual task, requiring a perceptual judgment about the straight ahead position of a light moving left-to-right, or right-to-left. A control task, requiring the bisection of rods of different lengths, was also given. The four tasks were performed under conditions of passive auditory numerical (i.e., listening to small, “2,” and large, “8,” numbers), and neutral auditory-verbal (“blah”) stimulation. Numerical magnitude modulated the participants’ deviations in the visual straight ahead task, when the movement of the light was from left-to-right, with the small number bringing about a leftward deviation, the large number a rightward deviation. A similar directional modulation was found in the rod bisection task, in line with previous evidence. No effects of numerical magnitude were found on the proprioceptive and visuo-proprioceptive straight ahead tasks. These results suggest that the spatial effects induced by the activation of the mental number line extend to an egocentric frame of reference but only when a portion of horizontal space has to be “actively” explored.