Irrelevant digits affect feature-based attention depending on the overlap of neural circuits

Numerical values modulate size perception

The link between various codes of magnitude and their interactions has been studied extensively for many years. In the current study, we examined how the physical and numerical magnitudes of digits are mapped into a combined mental representation. In two psychophysical experiments, participants reported the physically larger digit among two digits. In the identical condition, participants compared digits of an identical value (e.g., "2" and "2"); in the different condition, participants compared digits of distinct numerical values (i.e., "2" and "5"). As anticipated, participants overestimated the physical size of a numerically larger digit and underestimated the physical size of a numerically smaller digit. Our results extend the shared-representation account of physical and numerical magnitudes.

Analogue magnitude representation of angles and its relation to geometric expertise

The distance effect (comparing objects becomes easier with increasing differences in their magnitude) is observed in tasks ranging across domains, and its existence has been interpreted as evidence for analogue magnitude representation. Similarly, associations between response side and magnitude (faster left/right-sided responses to small/large objects, respectively) are observed across domains. We investigated the analogue processing of angles and the association between angle magnitude and response side in relation to geometric expertise. We compared the behavioural pattern of two groups-architects and controls-in a direct angle magnitude classification task (i.e., judge whether a presented angle was greater or less than 90°) and in an indirect task (i.e., judge whether an angle was drawn with a dashed or continuous line). We found a robust distance effect for reaction times and accuracy at the whole sample level and in each group separately. Architects revealed a smaller distance effect for accuracy than controls. This could be interpreted as an argument for a more precise analogue representation of angles in experts compared to non-experts. However, we did not find evidence for an association between angle magnitude and response side in any group.

No conclusive evidence for number-induced attentional shifts in a temporal order judgement task

The Spatial Numerical Association of Response Codes (SNARC) effect refers to the observation that relatively small (e.g., 1) and large numbers (e.g., 9) elicit faster left- and right-sided manual responses, respectively. In a variation known as the attentional SNARC effect, merely looking at numbers caused a left- or right-ward shift in covert spatial attention, depending on the number's magnitude. In our study, we probed the notion that numbers induce shifts of spatial attention in accordance with their position on a mental number line (MNL). Critically, we removed any putative spatial response code that may contaminate the responses. We used a square and a tilted square as targets, thereby situating the decisive response dimension in the ventral, non-spatial processing stream. In two experiments where numbers were used as non-informative cues preceding a temporal order judgement (TOJ) task, we did not observe a deflection of the locus of spatial attention as a function of the numerical magnitude of the cue. In a third experiment, finding a significant modulation of TOJ performance as a function of the pointing direction of arrow cues allowed us to rule out the possibility that the absence of any significant modulation in Experiments 1 and 2 was due to a lack of sensitivity of our task set-up. We conclude from the current findings that the spatial codes that the perception and naming of numbers potentially elicit are not in and by themselves sufficient to elicit deflections of spatial attention.

Contrasting symbolic and non-symbolic numerical representations in a joint classification task

Both symbolic (digits) and non-symbolic (dots) numerals are spatially coded, with relatively small numbers being responded faster with a left key and large numbers being responded faster with a right key (spatial-numerical association of response codes [SNARC]). The idea of format independent SNARC seems to support the existence of a common system for symbolic and non-symbolic numerical representations, although evidence in the field is still mixed. The aim of the present study is to investigate whether symbolic and non-symbolic numerals interact in the SNARC effect when both information is simultaneously displayed. To do so, participants were presented with dice-like patterns, with digits being used instead of dots. In two separate magnitude classification tasks, participants had to respond either to the number of digits presented on the screen or to their numerical size. In the non-symbolic task, they had to judge whether the digits on the screen were more or less than three, irrespective of the numerical value of the digits. In the symbolic task, participants had to judge whether the digits on the screen were numerically smaller or larger than three, irrespective of the number of digits being present. The results show a consistent SNARC effect in the symbolic task and no effect in the non-symbolic one. Furthermore, congruency between symbolic and non-symbolic numerals did not modulate the response patterns, thus supporting the idea of independent representations and questioning some propositions of current theoretical accounts.

Spatial-numerical associations without a motor response? Grip force says 'Yes'

In numerical processing, the functional role of Spatial-Numerical Associations (SNAs, such as the association of smaller numbers with left space and larger numbers with right space, the Mental Number Line hypothesis) is debated. Most studies demonstrate SNAs with lateralized responses, and there is little evidence that SNAs appear when no response is required. We recorded passive holding grip forces in no-go trials during number processing. In Experiment 1, participants performed a surface numerical decision task ("Is it a number or a letter?"). In Experiment 2, we used a deeper semantic task ("Is this number larger or smaller than five?"). Despite instruction to keep their grip force constant, participants' spontaneous grip force changed in both experiments: Smaller numbers led to larger force increase in the left than in the right hand in the numerical decision task (500-700 ms after stimulus onset). In the semantic task, smaller numbers again led to larger force increase in the left hand, and larger numbers increased the right-hand holding force. This effect appeared earlier (180 ms) and lasted longer (until 580 ms after stimulus onset). This is the first demonstration of SNAs with passive holding force. Our result suggests that (1) explicit motor response is not a prerequisite for SNAs to appear, and (2) the timing and strength of SNAs are task-dependent. (216 words).

The Nature of Associations between Physical Stimulus Size and Left-Right Response Codes

In two-choice response tasks, participants respond faster and more accurate with the left hand to a small stimulus and with the right hand to a large stimulus as compared to the reverse assignment. This compatibility effect suggests the existence of associations between cognitive codes of physical stimulus size and cognitive codes of left/right responses. Here, we explore the nature of associations between stimulus-size codes and left/right response codes by using more levels of stimulus size than in our previous studies. For example, the strengths of the associations between stimulus-size codes and response codes might either change gradually when stimulus size changes, or the strength of associations might change in a more discrete fashion (i.e., associations switch at a particular size level). In Experiment 1, participants responded to stimulus color with a left/right keypress, and physical stimulus size had ten levels with 5 mm steps. Results showed correspondence effects for the smallest and the largest stimulus size only. In Experiment 2, physical stimulus size had six levels with 10 mm steps. Results showed (similar) correspondence effects for the smallest and some intermediate stimulus-size levels. In sum, the results point towards a discrete, or categorical, relationship between cognitive codes of stimulus size and left/right response codes. This pattern of results is consistent with an account of the correspondence effect in terms of the polarity correspondence principle.

Spatial-numerical associations from a novel paradigm support the mental number line account

Multiple tasks have been used to demonstrate the relation between numbers and space. The classic interpretation of these directional spatial-numerical associations (d-SNAs) is that they are the product of a mental number line (MNL), in which numerical magnitude is intrinsically associated with spatial position. The alternative account is that d-SNAs reflect task demands, such as explicit numerical judgements and/or categorical responses. In the novel "Where was The Number?" task, no explicit numerical judgements were made. Participants were simply required to reproduce the location of a numeral within a rectangular space. Using a between-subject design, we found that numbers, but not letters, biased participants' responses along the horizontal dimension, such that larger numbers were placed more rightward than smaller numbers, even when participants completed a concurrent verbal working memory task. These findings are consistent with the MNL account, such that numbers specifically are inherently left-to-right oriented in Western participants.

Multisensory Perceptual Biases for Social and Reward Associations

Linking arbitrary shapes (e.g., circles, squares, and triangles) to personal labels (e.g., self, friend, or stranger) or reward values (e.g., £18, £6, or £2) results in immediate processing benefits for those stimuli that happen to be associated with the self or high rewards in perceptual matching tasks. Here we further explored how social and reward associations interact with multisensory stimuli by pairing labels and objects with tones (low, medium, and high tones). We also investigated whether self and reward biases persist for multisensory stimuli with the label removed after an association had been made. Both high reward stimuli and those associated with the self, resulted in faster responses and improved discriminability (i.e., higher d’), which persisted for multisensory stimuli even when the labels were removed. However, these self- and reward-biases partly depended on the specific alignment between the physical tones (low, medium, and high) and the conceptual (social or reward) order. Performance for reward associations improved when the endpoints of low or high rewards were paired with low or high tones; meanwhile, for personal associations, there was a benefit when the self was paired with either low or high tones, but there was no effect when the stranger was associated with either endpoint. These results indicate that, unlike reward, social personal associations are not represented along a continuum with two marked endpoints (i.e., self and stranger) but rather with a single reference point (the self vs. other).

Automaticity in processing spatial-numerical associations: Evidence from a perceptual orientation judgment task of Arabic digits in frames

Human adults are faster to respond to small/large numerals with their left/right hand when they judge the parity of numerals, which is known as the SNARC (spatial-numerical association of response codes) effect. It has been proposed that the size of the SNARC effect depends on response latencies. The current study introduced a perceptual orientation task, where participants were asked to judge the orientation of a digit or a frame surrounding the digit. The present study first confirmed the SNARC effect with native Chinese speakers (Experiment 1) using a parity task, and then examined whether the emergence and size of the SNARC effect depended on the response latencies (Experiments 2, 3, and 4) using a perceptual orientation judgment task. Our results suggested that (a) the automatic processing of response-related numerical-spatial information occurred with Chinese-speaking participants in the parity task; (b) the SNARC effect was also found when the task did not require semantic access; and (c) the size of the effect depended on the processing speed of the task-relevant dimension. Finally, we proposed an underlying mechanism to explain the SNARC effect in the perceptual orientation judgment task.

How does number magnitude influence temporal and spatial parameters of eye movements?

The influence of numerical processing on individuals' behavior is now well documented. The spatial representation of numbers on a left-to-right mental line (i.e., SNARC effect) has been shown to have sensorimotor consequences, the majority of studies being mainly concerned with its impact on the response times. Its impact on the motor programming stage remains less documented, although swiping movement amplitudes have recently been shown to be modulated by number magnitude. Regarding saccadic eye movements, the few available studies have not provided clear-cut conclusions. They showed that spatial-numerical associations modulated ocular drifts, but not the amplitude of memory-guided saccades. Because these studies held saccadic coordinates constant, which might have masked potential numerical effects, we examined whether spontaneous saccadic eye movements (with no saccadic target) could reflect numerical effects. Participants were asked to look either to the left or to the right side of an empty screen to estimate the magnitude (< or > 5) of a centrally presented digit. Latency data confirmed the presence of the classical SNARC and distance effects. More critically, saccade amplitude reflected a numerical effect: participants' saccades were longer for digits far from the standard (1 and 9) and were shorter for digits close to it (4 and 6). Our results suggest that beyond response times, kinematic parameters also offer valuable information for the understanding of the link between numerical cognition and motor programming.

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.

Compatibility between response position and either object typical size or semantic category: SNARC- and MARC-like effects in primary school children

In two experiments, we administered two binary classification tasks to third- to fifth-grade students and found that either the conceptual size (Experiment 1) or semantic category (Experiment 2) of the target picture interacted with response position: Participants emitted faster and/or more accurate right- and left-side responses to stimuli referring to typically large and small objects (i.e., a SNARC [spatial-numerical association of response codes]-like effect) or to living and nonliving objects (i.e., a MARC [markedness association of response codes]-like effect), respectively. The effect of either stimulus dimension was present only when this dimension was the task-relevant one. These findings may be accounted for by the polarity compatibility principle. In binary classification tasks, one of the two relevant stimulus values (i.e., the dominant one) and one of the two response values would be coded as having a positive polarity, whereas the other would be coded as having a negative polarity. Response selection would be faster and/or more accurate when stimulus and response polarities are compatible. According to a less parsimonious hypothesis, the polarity principle would only explain the effect of the stimulus semantic category in Experiment 2, whereas the effect of stimulus conceptual size in Experiment 1 might be traced back to the fact that children spatially code the typical size of stimulus referents (even if only when the task requires accessing this stimulus dimension). Small and large objects would be represented relatively on the left and right, respectively, which would result in faster and/or more accurate responses when response position is compatible with the stimulus referent's position in this spatial representation.

Non-symbolic numerosities do not automatically activate spatial-numerical associations: Evidence from the SNARC effect

The SNARC (spatial-numerical association of response codes) effect is the finding that people are generally faster to respond to smaller numbers with left-sided responses and larger numbers with right-sided responses. The SNARC effect has been widely reported for responses to symbolic representations of number such as digits. However, there is mixed evidence as to whether it occurs for non-symbolic representations of number, particularly when magnitude is irrelevant to the task. Mitchell et al. reported a SNARC effect when participants were asked to make orientation decisions to arrays of one-to-nine triangles (pointing upwards vs. pointing downwards) and concluded that SNARC effects occur for non-symbolic, non-canonical representations of number. They additionally reported that this effect was stronger in the subitising range. However, here we report four experiments that do not replicate either of these findings. Participants made upwards/inverted decisions to one-to-nine triangles where total surface area was either controlled across numerosities (Experiments 1, 2, and 4) or increased congruently with numerosity (Experiment 3). There was no evidence of a SNARC effect either across the full range or within the subset of the subitising range. The results of Experiment 4 (in which we presented the original stimuli of Mitchell et al.) suggested that visual properties of non-symbolic displays can prompt SNARC-like effects driven by visual cues rather than numerosity. Taken in the context of other recent findings, we argue that non-symbolic representations of number do not offer a direct and automatic route to numerical-spatial associations.

Spatial-numerical associations: Shared symbolic and non-symbolic numerical representations

During the last decades, there have been a large number of studies into the number-related abilities of humans. As a result, we know that humans and non-human animals have a system known as the approximate number system that allows them to distinguish between collections based on their number of items, separately from any counting procedures. Dehaene and others have argued for a model on which this system uses representations for numbers that are spatial in nature and are shared by our symbolic and non-symbolic processing of numbers. However, there is a conflicting theoretical perspective in which there are no representations of numbers underlying the approximate number system, but only quantity-related representations. This perspective would then suggest that there are no shared representations between symbolic and non-symbolic processing. We review the evidence on spatial biases resulting from the activation of numerical representations, for both non-symbolic and symbolic tests. These biases may help decide between the theoretical differences; shared representations are expected to lead to similar biases regardless of the format, whereas different representations more naturally explain differences in biases, and thus behaviour. The evidence is not yet decisive, as the behavioural evidence is split: we expect bisection tasks to eventually favour shared representations, whereas studies on the spatial-numerical association of response codes (SNARC) effect currently favour different representations. We discuss how this impasse may be resolved, in particular, by combining these behavioural studies with relevant neuroimaging data. If this approach is carried forward, then it may help decide which of these two theoretical perspectives on number representations is correct.

Response-irrelevant number, duration, and extent information triggers the SQARC effect: Evidence from an implicit paradigm

Spatial-Numerical Association of Response Codes (SNARC) and Spatial-Quantity Association of Response Codes (SQARC) effects are evident when people produce faster left-sided responses to smaller numbers, sizes, and durations and faster right-sided responses to larger numbers, sizes, and durations. SQARC effects have typically been demonstrated in paradigms where the explicit processing of quantity information is required for successful task completion. The current study tested whether the implicit presentation of task-irrelevant magnitude information could trigger a SQARC effect as has been demonstrated previously when task-irrelevant information triggers a SNARC effect. In Experiment 1, participants (n = 20) made orientation judgements for triangles varying in numerosity and physical extent. In Experiment 2, participants (n = 20) made orientation judgements for triangles varying in numerosity and for a triangle preceded by a delay of varying duration. SNARC effects were observed for the numerosity conditions of Experiments 1 and 2 replicating Mitchell et al. SQARC effects were also demonstrated for physical extent and for duration. These findings demonstrate that SQARC effects can be implicitly triggered by the presentation of the task-irrelevant magnitude.

The SNARC and MARC effects measured online: Large-scale assessment methods in flexible cognitive effects

The Spatial-Numerical Association of Response Codes (SNARC) effect (i.e., faster reactions to small/large numbers on the left-/right-hand side) is usually observed along with the linguistic Markedness of Response Codes (MARC) effect-that is, faster left-/right-hand responses to odd/even numbers. The SNARC effect is one of the most thoroughly investigated phenomena in numerical cognition. However, almost all SNARC and MARC studies to date were conducted with sample sizes smaller than 100. Here we report on a study with 1,156 participants from various linguistic and cultural backgrounds performing a typical parity judgment task. We investigated whether (1) the SNARC and MARC effects can be observed in an online setup, (2) the properties of these effects observed online are similar to those observed in laboratory setups, (3) the effects are reliable, and (4) they are valid. We found robust SNARC and MARC effects. Their magnitude and reliabilities were comparable to values previously reported in in-lab studies. Furthermore, we reproduced commonly observed validity correlations of the SNARC and MARC effects. Namely, SNARC and MARC correlated with mean reaction times and intraindividual variability in reaction times. Additionally, we found interindividual differences in the SNARC and MARC effects (e.g., finger-counting routines for the SNARC and handedness for the MARC). Large-scale testing via web-based data acquisition not only produces SNARC and MARC effects and validity correlations similar to those from small, in-lab studies, but also reveals substantial insights with regard to interindividual differences that usually cannot be revealed in the offline laboratory, due to power considerations.

Automatic and intentional processing of numerical order and its relationship to arithmetic performance

Recent findings have demonstrated that numerical order processing (i.e., the application of knowledge that numbers are organized in a sequence) constitutes a unique and reliable predictor of arithmetic performance. The present work investigated two central questions to further our understanding of numerical order processing and its relationship to arithmetic. First, are numerical order sequences processed without conscious monitoring (i.e., automatically)? Second, are automatic and intentional ordinal processing differentially related to arithmetic performance? In the first experiment, adults completed a novel ordinal congruity task. Participants had to evaluate whether number triplets were arranged in a correct (e.g., ) physical order or not (e.g., ). Results of this experiment showed that participants were faster to decide that the physical size of ascending numbers was in-order when the physical and numerical values were congruent compared to when they were incongruent (i.e., congruency effect). In the second experiment, a new group of participants was asked to complete an ordinal congruity task, an ordinal verification task (i.e., are the number triplets in a correct order or not) and an arithmetic fluency test. Results of this experiment revealed that the automatic processing of ascending numerical order is influenced by the numerical distance of the numbers. Correlation analysis further showed that only reaction time measures of the intentional ordinal verification task were associated with arithmetic performance. While the findings of the present work suggest that ascending numerical order is processed automatically, the relationship between numerical order processing and arithmetic appears to be limited to the intentional manipulation of numbers. The present findings show that the mental engagement of verifying the order of numbers is a crucial factor for explaining the link between numerical order processing and arithmetic performance.

SNARC-like compatibility effects for physical and phenomenal magnitudes: a study on visual illusions

Both numerical and non-numerical magnitudes elicit similar Spatial-Numerical Association of Response Codes (SNARC) effects, with small magnitudes associated with left hand responses and large magnitudes associated with right hand responses (Dehaene et al., J Exp Psychol Gen 122(3), 371, 1993). In the present study, we investigated whether the phenomenal size of visual illusions elicits the same SNARC-like effect revealed for the physical size of pictorial surfaces. Four experiments were conducted by using the Delboeuf illusion (Experiment 1) and the Kanizsa triangle illusion (Experiments 2, 3 and 4). Experiment 1 suggests the presence of a SNARC-like compatibility effect for the physical size of the inducers, while this effect was not revealed for the phenomenal size of the induced elements, possibly masked by a stronger effect of the inducers. A SNARC-like effect for the phenomenal size of the Kanizsa triangle was revealed when participants directly compared the size of the triangles (Experiment 4). Conversely, when participants performed an indirect task (orientation judgment), the SNARC-like effect was present neither for the illusory nor for the physical displays (Experiments 2 and 3). The effect revealed for the size of illusory triangles was comparable to that of real triangles with physical contours, suggesting that both phenomenal and physical magnitudes similarly elicit SNARC-like effects.

Compatibility between object size and response side in grasping: the left hand prefers smaller objects, the right hand prefers larger objects

It has been proposed that the brain processes quantities such as space, size, number, and other magnitudes using a common neural metric, and that this common representation system reflects a direct link to motor control, because the integration of spatial, temporal, and other quantity-related information is fundamental for sensorimotor transformation processes. In the present study, we examined compatibility effects between physical stimulus size and spatial (response) location during a sensorimotor task. Participants reached and grasped for a small or large object with either their non-dominant left or their dominant right hand. Our results revealed that participants initiated left hand movements faster when grasping the small cube compared to the large cube, whereas they initiated right hand movements faster when grasping the large cube compared to the small cube. Moreover, the compatibility effect influenced the timing of grip aperture kinematics. These findings indicate that the interaction between object size and response hand affects the planning of grasping movements and supports the notion of a strong link between the cognitive representation of (object) size, spatial (response) parameters, and sensorimotor control.

Does the spatial-numerical association of response codes effect depend on digits' relative or absolute magnitude? Evidence from a perceptual orientation judgment task

Many previous studies have demonstrated the SNARC effect-i.e., participants are faster to respond with their left/right hand to small/large numbers. However, there is a debate on whether it is based on working or long-term memory (i.e., relative or absolute magnitude). Here, we examined the flexibility of the spatial-numerical associations using orientation judgment tasks. Participants were asked to judge the orientation of a rotated frame surrounding an Arabic digit under numerical ranges 1-6, 4-9 (Experiment 1), and 1-9 (Experiment 2). The task difficulty was manipulated by rotating stimuli. We observed a significant SNARC effect for range 1-6 and a reversed SNARC effect for 4-9, regardless of the total numerical range presented in the task. Furthermore, the SNARC effect became more salient with increasing task difficulty. Our results suggest that the SNARC effect is based on the absolute magnitude of digits, supporting the long-term memory explanation.

Attention allows the SNARC effect to operate on multiple number lines

To investigate whether participants can activate only one spatially oriented number line at a time or multiple number lines simultaneously, they were asked to solve a unit magnitude comparison task (unit smaller/larger than 5) and a parity judgment task (even/odd) on two-digit numbers. In both these primary tasks, decades were irrelevant. After some of the primary task trials (randomly), participants were asked to additionally solve a secondary task based on the previously presented number. In Experiment 1, they had to decide whether the two-digit number presented for the primary task was larger or smaller than 50. Thus, for the secondary task decades were relevant. In contrast, in Experiment 2, the secondary task was a color judgment task, which means decades were irrelevant. In Experiment 1, decades' and units' magnitudes influenced the spatial association of numbers separately. In contrast, in Experiment 2, only the units were spatially associated with magnitude. It was concluded that multiple number lines (one for units and one for decades) can be activated if attention is focused on multiple, separate magnitude attributes.

On the genesis of spatial-numerical associations: Evolutionary and cultural factors co-construct the mental number line

Mapping numbers onto space is a common cognitive representation that has been explored in both behavioral and neuroimaging contexts. Empirical work probing the diverse nature of these spatial-numerical associations (SNAs) has led researchers to question 1) how the human brain links numbers with space, and 2) whether this link is biologically vs. culturally determined. We review the existing literature on the development of SNAs and situate that empirical work within cognitive and neuroscientific theoretical frameworks. We propose that an evolutionarily-ancient frontal-parietal circuit broadly tuned to multiple magnitude dimensions provides the phylogenetic substrate for SNAs, while enculturation and sensorimotor experience shape their specific profiles. We then use this perspective to discuss educational implications and highlight promising avenues for future research.

How Deep Is Your SNARC? Interactions Between Numerical Magnitude, Response Hands, and Reachability in Peripersonal Space

Spatial, physical, and semantic magnitude dimensions can influence action decisions in human cognitive processing and interact with each other. For example, in the spatial-numerical associations of response code (SNARC) effect, semantic numerical magnitude facilitates left-hand or right-hand responding dependent on the small or large magnitude of number symbols. SNARC-like interactions of numerical magnitudes with the radial spatial dimension (depth) were postulated from early on. Usually, the SNARC effect in any direction is investigated using fronto-parallel computer monitors for presentation of stimuli. In such 2D setups, however, the metaphorical and literal interpretation of the radial depth axis with seemingly close/far stimuli or responses are not distinct. Hence, it is difficult to draw clear conclusions with respect to the contribution of different spatial mappings to the SNARC effect. In order to disentangle the different mappings in a natural way, we studied parametrical interactions between semantic numerical magnitude, horizontal directional responses, and perceptual distance by means of stereoscopic depth in an immersive virtual reality (VR). Two VR experiments show horizontal SNARC effects across all spatial displacements in traditional latency measures and kinematic response parameters. No indications of a SNARC effect along the depth axis, as it would be predicted by a direct mapping account, were observed, but the results show a non-linear relationship between horizontal SNARC slopes and physical distance. Steepest SNARC slopes were observed for digits presented close to the hands. We conclude that spatial-numerical processing is susceptible to effector-based processes but relatively resilient to task-irrelevant variations of radial-spatial magnitudes.

Finger–digit compatibility in Arabic numeral processing

Finger–digit response compatibility was tested by asking participants to identify Arabic digits by pressing 1 of 10 keys with all 10 fingers. The direction of the finger–digit mapping was varied by manipulating the global direction of the hand–digit mapping as well as the direction of the finger–digit mapping within each hand (in each case, from small to large digits, or the reverse). The hypothesis of a left-to-right mental number line predicted that a complete left-to-right mapping should be easier whereas the hypothesis of a representation based on finger counting predicted that a counting-congruent mapping should be easier. The results show that when all 10 fingers are used to answer, a mapping congruent with the prototypical finger-counting strategy reported by the participants leads to better performance than does a mapping congruent with a left-to-right oriented mental number line, both in palm-down and palm-up postures of the hands, and they demonstrate that finger-counting strategies influence the way that numerical information is mentally represented and processed.

Notational Modulation of the SNARC and the MARC (Linguistic Markedness of Response Codes) Effect

Number magnitude and number parity representation are fundamental number representations. However, the representation of parity is much less understood than that of magnitude: Therefore, we investigated it by examining the (new) Linguistic Markedness of Response Codes (MARC) effect: Responses are facilitated if stimuli and response codes both have the same (congruent) linguistic markedness (even–right, odd–left) while incongruent conditions (even–left, odd–right) lead to interference. We examined systematically the MARC (for parity) and the Spatial Numerical Association of Response Codes (SNARC; for magnitude) effect for different number notations (positive Arabic, negative Arabic, number words) and with different methods of data analysis. In a parity judgement task, the SNARCeffect indicating a magnitude representation was replicated for all notations except for negative numerals. The MARCeffect was found for number words in all analyses, but less consistently for the other notations. In contrast, a correlational analysis of the reaction time (RT) data, as suggested by Sternberg (1969) using a nonmetric multi–dimensional scaling (MDS) procedure, produced a clear association of parity and response code for all notations (MARCeffect), but little evidence of the SNARCeffect. We discuss the extent to which these notation–specific MARC and SNARC effects constrain current models of number processing and elaborate on the possible functional locus of the MARC effect.

Switching between Multiple Codes of SNARC-Like Associations: Two Conceptual Replication Attempts with Anodal tDCS in Sham-Controlled Cross-Over Design

In societies with left-to-right reading direction, left-side vs. right-side behavioral decisions are faster for relatively small vs. large number magnitudes, and vice versa, a phenomenon termed Spatial-Numerical Associations of Response Codes (SNARC) effect. But also for non-numerical sequential items, SNARC-like effects were observed, suggesting a common neurocognitive mechanism based on the ordinal structures of both numbers and sequences. Modulation of prefrontal networks that are involved in providing spatial associations during cognitive behavior can contribute to elaborate their neuropsychological theoretical foundations. With transcranial direct current stimulation (tDCS) directed to the left prefrontal cortex, we recently showed that (i) cathodal tDCS can block the emergence of spatial-numerical associations and that (ii) anodal tDCS can reverse spatial associations of sequential order, most likely based on markedness correspondence. Two conceptual replication attempts of the latter reversal of space-order associations are presented in the current sham-controlled experiment, using either weekdays (Monday-Friday) or month names (January-December) as stimuli in the temporal order classification task. In addition, to control for possible influences of notation, number stimuli were presented as written German names (One-Five). We report on a successful modulation of spatial-numerical associations of response codes (SNARC) effects with month stimuli induced by anodal tDCS, but failed to observe the same reversal of SNARC effects for weekday stimuli. The former stimulation effect was orthogonal to the small anodal tDCS effect on written number words, which replicates the dissociation of SNARC effects for numbers vs. non-numerical sequences. Moreover, this result reinforces the hypothesis that the ordinal item and task structure was the source of dissociation (as opposed to verbal presentation). We suggest that the diverging results can be explained by the markedness correspondence account of spatial associations in a multiple coding framework. Left-hemispheric prefrontal excitation from anodal tDCS renders verbal markedness relatively more dominant, but this effect is not absolute. We discuss task contagion, study design, and individual differences in performance measures or tDCS response as possible contributors to systematic variation of the weights of multiple coding parameters for spatial-numerical associations.

Finding the SNARC Instead of Hunting It: A 20∗20 Monte Carlo Investigation

The Spatial Numerical Association of Response Codes (SNARC) effect describes a stimulus-response association of left with small magnitude and right with large magnitude. Usually, it is estimated by means of regression slopes, where the independent variable only has a limited number of levels. Inspection of the literature reveals that it is not difficult to detect a SNARC effect within a group, but it has been quite unusual to find group differences. Is the SNARC effect as it is usually estimated using regression slopes largely insensitive to group differences, and are there design parameters necessary to increase sensitivity in group comparison analyses? Using numerical simulations, we provide evidence that both sample size and the number of stimulus repetitions, as well as intra-individual variability, contribute in a substantial way to the probability of detecting an existing SNARC effect. Our results show that the adequate choice of either sample size or number of repetitions per experimental cell does not fully compensate for a poor choice of the other parameter. Moreover, repeated failures to find significant group differences in the SNARC effect can be explained by insufficient power. Fortunately, increasing the number of repetitions to about 20 and testing at least 20 participants provides in most cases sufficient sensitivity to reliably detect the SNARC effect as well as group differences. Power plots are provided, which may help to improve both the economy and sensitivity of experimental design in future SNARC experiments, or, more generally when regression slopes are estimated intra-individually.

The Automatic Mapping of Magnitude to Temporal Order Is Space-Dependent

Past research has shown that performance in ordinal magnitude tasks is enhanced when stimuli are presented in ascending order, suggesting that magnitude is mapped to temporal order, with small magnitude associated with early and large with late presentation. The present study addresses the automaticity of this effect and its limitations. We used the "same/different" task for numbers (Experiment 1) and physical sizes of shapes (Experiment 2) as well as identity of shapes (Experiment 3). The advantage for stimuli in ascending order was found for both numbers and physical sizes of shapes. However, it was limited to specific conditions - when magnitude processing was required for the task and when a "different" response was mapped to the right hand side. Thus, it seems that the automatic mapping of magnitude to temporal order is dependent on the mapping of magnitude to space.

Perceiving Musical Note Values Causes Spatial Shift of Attention in Musicians

The Spatial-Numerical Association of Response Codes (SNARC) suggests the existence of an association between number magnitude and response position, with faster left-key responses to small numbers and faster right-key responses to large numbers. The attentional SNARC effect (Att-SNARC) suggests that perceiving numbers can also affect the allocation of spatial attention, causing a leftward (vs. rightward) target detection advantage after perceiving small (vs. large) numbers. Considering previous findings that revealed similar spatial association effects for both numbers and musical note values (i.e., the relative duration of notes), the aim of this study is to investigate whether presenting note values instead of numbers causes a spatial shift of attention in musicians. The results show an advantage in detecting a leftward (vs. rightward) target after perceiving small (vs. large) musical note values. The fact that musical note values cause a spatial shift of attention strongly suggests that musicians process numbers and note values in a similar manner.

The SNARC Effect in Number Memorization and Retrieval. What is the Impact of Congruency, Magnitude and the Exact Position of Numbers in Short-Term Memory Processing?

Mental representations of numbers are spatially organized along a Mental Number Line (MNL). One widely proven manifestation of this relationship is the Spatial Numerical Association of Response Codes (SNARC) effect. It refers to the phenomenon of faster responses to numbers when there is congruency between the reaction side and the number position on the MNL . Although long-term memory is considered to house the MNL, short-term memory (STM) load may also modulate responses to numbers and the SN ARCRC effect. Our question, however, was not how STM content modulates the SNARC effect observed in responses to digits, but rather how the MNLNL representation affects the number retrieval from ST M. Each trial began with four digits presented horizontally in a spatial sequence (prime stimuli), which were then replaced by one of the priming digits as a single target. The task required participants to recall the exact location of the target. The SN ARCRC effect occurred only in the retrieval of left-sided digits, most likely because of the generally better processing of right-sided ones, as well as in reaction to digits presented more laterally. Moreover, memory processing was more efficient with low-magnitude numbers, which may suggest that they trigger attention shifting. We conclude that the MNL affects not only the responses to numbers obtained in typical SNARC-induction tasks, such as number detection, parity judgment or magnitude comparison, but also memorization and retrieval of them. Importantly, this effect seems to be dependent on the exact position of a digit in STM.

The SNARC Effect in Chinese Numerals: Do Visual Properties of Characters and Hand Signs Influence Number Processing?

The SNARC effect refers to an association of numbers and spatial properties of responses that is commonly thought to be amodal and independent of stimulus notation. We tested for a horizontal SNARC effect using Arabic digits, simple-form Chinese characters and Chinese hand signs in participants from Mainland China. We found a horizontal SNARC effect in all notations. This is the first time that a horizontal SNARC effect has been demonstrated in Chinese characters and Chinese hand signs. We tested for the SNARC effect in two experiments (parity judgement and magnitude judgement). The parity judgement task yielded clear, consistent SNARC effects in all notations, whereas results were more mixed in magnitude judgement. Both Chinese characters and Chinese hand signs are represented non-symbolically for low numbers and symbolically for higher numbers, allowing us to contrast within the same notation the effects of heavily learned non-symbolic vs. symbolic representation on the processing of numbers. In addition to finding a horizontal SNARC effect, we also found a robust numerical distance effect in all notations. This is particularly interesting as it persisted when participants reported using purely visual features to solve the task, thereby suggesting that numbers were processed semantically even when the task could be solved without the semantic information.

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.

Loudness counts: Interactions between loudness, number magnitude, and space

ATOM (a theory of magnitude) suggests that magnitude information of different formats (numbers, space, and time) is processed within a generalized magnitude network. In this study we investigated whether loudness, as a possible indicator of intensity and magnitude, interacts with the processing of numbers. Small and large numbers, spoken in a quiet and a loud voice, were simultaneously presented to the left and right ear (Experiments 1a and 1b). Participants judged whether the number presented to the left or right ear was louder or larger. Responses were faster when the smaller number was spoken in a quiet voice, and the larger number in a loud voice. Thus, task-irrelevant numerical information influenced the processing of loudness and vice versa. This bi-directional link was also confirmed by classical SNARC paradigms (spatial-numerical association of response codes; Experiments 2a-2c) when participants again judged the magnitude or loudness of separately presented stimuli. In contrast, no loudness-number association was found in a parity judgment task. Regular SNARC effects were found in the magnitude and parity judgment task, but not in the loudness judgment task. Instead, in the latter task, response side was associated with loudness. Possible explanations for these results are discussed.

Spatial Representation of Ordinal Information

Right hand responds faster than left hand when shown larger numbers and vice-versa when shown smaller numbers (the SNARC effect). Accumulating evidence suggests that the SNARC effect may not be exclusive for numbers and can be extended to other ordinal sequences (e.g., months or letters in the alphabet) as well. In this study, we tested the SNARC effect with a non-numerically ordered sequence: the Chinese notations for the color spectrum (Red, Orange, Yellow, Green, Blue, Indigo, and Violet). Chinese color word sequence reserves relatively weak ordinal information, because each element color in the sequence normally appears in non-sequential contexts, making it ideal to test the spatial organization of sequential information that was stored in the long-term memory. This study found a reliable SNARC-like effect for Chinese color words (deciding whether the presented color word was before or after the reference color word “green”), suggesting that, without access to any quantitative information or exposure to any previous training, ordinal representation can still activate a sense of space. The results support that weak ordinal information without quantitative magnitude encoded in the long-term memory can activate spatial representation in a comparison task.

The role of numerical and non-numerical cues in nonsymbolic number processing: Evidence from the line bisection task

In line bisection tasks, adults and children bisect towards the numerically larger of two nonsymbolic numerosities [de Hevia, M. D., & Spelke, E. S. (2009). Spontaneous mapping of number and space in adults and young children. Cognition, 110, 198–207. doi:10.1016/j.cognition.2008.11.003]. However, it is not clear whether this effect is driven by number itself or rather by visual cues such as subtended area [Gebuis, T., & Gevers, W. (2011). Numbers and space: Indeed a cognitive illusion! A reply to de Hevia and Spelke (2009). Cognition, 121, 248–252. doi:10.1016/j.cognition.2010.09.008]. Furthermore, this effect has only been demonstrated with flanking displays of two and nine items. Here, we report three studies that examined whether this “spatial bias” effect occurs across a range of absolute and ratio numerosity differences; in particular, we examined whether the bias would occur when both flankers were outside the subitizing range. Additionally, we manipulated the subtended area of the stimulus and the aggregate surface area to assess the influence of visual cues. We found that the spatial bias effect occurred for a range of flanking numerosities and for ratios of 3:5 and 5:6 when subtended area was not controlled (Experiment 1). However, when subtended area and aggregate surface area were held constant, the biasing effect was reversed such that participants bisected towards the flanker with fewer items (Experiment 2). Moreover, when flankers were identical, participants bisected towards the flanker with larger subtended area or larger aggregate surface area (Experiments 2 and 3). On the basis of these studies, we conclude that the spatial bias effect for nonsymbolic numerosities is primarily driven by visual cues.

Professional mathematicians differ from controls in their spatial-numerical associations

While mathematically impaired individuals have been shown to have deficits in all kinds of basic numerical representations, among them spatial-numerical associations, little is known about individuals with exceptionally high math expertise. They might have a more abstract magnitude representation or more flexible spatial associations, so that no automatic left/small and right/large spatial-numerical association is elicited. To pursue this question, we examined the Spatial Numerical Association of Response Codes (SNARC) effect in professional mathematicians which was compared to two control groups: Professionals who use advanced math in their work but are not mathematicians (mostly engineers), and matched controls. Contrarily to both control groups, Mathematicians did not reveal a SNARC effect. The group differences could not be accounted for by differences in mean response speed, response variance or intelligence or a general tendency not to show spatial-numerical associations. We propose that professional mathematicians possess more abstract and/or spatially very flexible numerical representations and therefore do not exhibit or do have a largely reduced default left-to-right spatial-numerical orientation as indexed by the SNARC effect, but we also discuss other possible accounts. We argue that this comparison with professional mathematicians also tells us about the nature of spatial-numerical associations in persons with much less mathematical expertise or knowledge.

Beyond left and right: Automaticity and flexibility of number-space associations

Close links exist between the processing of numbers and the processing of space: relatively small numbers are preferentially associated with a left-sided response while relatively large numbers are associated with a right-sided response (the SNARC effect). Previous work demonstrated that the SNARC effect is triggered in an automatic manner and is highly flexible. Besides the left-right dimension, numbers associate with other spatial response mappings such as close/far responses, where small numbers are associated with a close response and large numbers with a far response. In two experiments we investigate the nature of this association. Associations between magnitude and close/far responses were observed using a magnitude-irrelevant task (Experiment 1: automaticity) and using a variable referent task (Experiment 2: flexibility). While drawing a strong parallel between both response mappings, the present results are also informative with regard to the question about what type of processing mechanism underlies both the SNARC effect and the association between numerical magnitude and close/far response locations.

Numerosity adaptation along the Y-Axis affects numerosity perception along the X-Axis: does numerosity adaptation activate MNLs?

The current study characterized the spatial selectivity of numerosity adaptation. In Experiment 1, adaptors were arranged vertically with 8 dots at the top of the visual field and 400 dots at the bottom, and participants' perceived magnitude in the left field decreased compared to that in the right, as revealed in the numerosity comparing task after adaptation. In contrast, the perceived magnitude in the right field decreased compared to that in the left with inversed adaptors (400 dots at top, 8 at bottom). In Experiment 2, adaptors were presented horizontally, and they showed no significant effect on numerosity perception, which was tested vertically. This study demonstrated that numerosity adaptation along the vertical orientation could affect numerosity perception along the horizontal orientation, and the latter was affected by the former according to a rule of associating "top" with "right" and "bottom" with "left." The spatial selectivity of numerosity adaptation showed distinguishing features that should function to abstract spatial relationships rather than create purely retinotopic mapping. We proposed that numerosity adaptation is based on spatial-numerical-associated codes. Vertical adaptors could activate both the vertical and horizontal Mental Number Lines (MNLs) and involve an interaction between these types of MNLs. According to behavioral data, horizontal adaptors showed no significant influence on perception along the vertical orientation, which might be due to the higher threshold required to activate the vertical MNL.

Grasping numbers: evidence for automatic influence of numerical magnitude on grip aperture

Previous research has shown that the fingers' aperture during grasp is affected by the numerical values of numbers embedded in the grasped objects: Numerically larger digits lead to larger grip apertures than do numerically smaller digits during the initial stages of the grasp. The relationship between numerical magnitude and visuomotor control has been taken to support the idea of a common underlying neural system mediating the processing of magnitude and the computation of object size for motor control. The purpose of the present study was to test whether the effect of magnitude on motor preparation is automatic. During grasping, we asked participants to attend to the colors of the digit while ignoring numerical magnitude. The results showed that numerical magnitude affected grip aperture during the initial stages of the grasp, even when magnitude information was irrelevant to the task at hand. These findings suggest that magnitude affects grasping preparation in an automatic fashion.

Number-induced shifts in spatial attention: a replication study

In a spatial attention paradigm, Fischer et al. (2003) showed that merely perceiving a number shifted attention according to the magnitude of the number. Low numbers shifted attention to the left and high numbers shifted attention to the right. This suggests that numbers are represented by the mental number line – a spatial image schema that is ordered from left to right with increasing magnitude. In six experiments, we used the spatial attention paradigm of Fischer et al. (2003) to investigate if and when such mental representations are activated. Participants detected visual targets that were preceded by low and high numbers. Between experiments we manipulated how participants processed the number. Participants either merely perceived the number, as in the experiments by Fischer et al. (2003) processed the number’s parity, or processed the number’s magnitude. Our results provide little support for the idea that numbers shift spatial attention. Only in one of the two experiments in which participants processed number magnitude did participants respond faster to targets in congruent locations (left for low magnitudes and right for high magnitudes) than in incongruent locations. In the other five experiments number magnitude did not affect spatial attention. This shows, in contrast to Fischer et al.’s (2003) results, that the mental number line is not activated automatically but at best only when it is contextually relevant. Furthermore, these results suggest that image schemas in general may be context-dependent rather than fundamental to mental concepts.