The Attentional-SNARC effect 16 years later: no automatic space–number association (taking into account finger counting style, imagery vividness, and learning style in 174 participants)

How time gets spatial: factors determining the stability and instability of the mental time line

Left-to-right readers classify faster past events with motor responses on the left side of space and future events with responses on the right side. This suggests a left-to-right spatial organization in the mental representation of time. Here, we show that the significance and reliability of this representation are linked to the joint use of temporal and spatial codes in the task at hand. In a first unimanual Go/No-Go Implicit Association Test (IAT), attending selectively to "past" or to "future" words did not activate corresponding "left" or "right" spatial concepts and vice versa. In a second IAT, attending to both temporal (i.e., "past" and "future") words and spatial targets (i.e., "left" and "right") pointing arrows produced faster responses for congruent rather than incongruent combinations of temporal and spatial concepts in task instructions (e.g., congruent = "Go with past words and left-pointing arrows"; incongruent = "Go with past words and right-pointing arrows"). This effect increased markedly in a STEARC task where spatial codes defined the selection between "left-side" and "right-side" button presses that were associated with "past" and "future" words. Two control experiments showed only partial or unreliable space-time congruency effects when (a) participants attended to superordinate semantic codes that included both spatial "left"/"right" or temporal "past/future" subordinate codes; (b) a primary speeded response was assigned to one dimension (e.g., "past vs. future") and a nonspeeded one to the other dimension (e.g., "left" vs. "right"). These results help to define the conditions that trigger a stable and reliable spatial representation of time-related concepts.

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 Impact of Coding Levels of Magnitude and of Spatial-Direction on the Spatial-Numerical Association of Response Codes Effect of Negative Numbers

Whether negative numbers have a fixed spatial–numerical association of response codes effect (SNARC effect), and (if they have) whether the spatial representation of negative numbers is associated with negative numbers’ absolute or signed values remains controversial. In this study, through three experiments, the coding level of the magnitude and the spatial-direction is manipulated. In the first experiment, participants are required to code the magnitude and spatial-direction explicitly by using a magnitude classification task. In the second experiment, participants are forced to code the magnitude implicitly as well as to code the spatial-direction explicitly by utilizing a cuing task. In the third experiment, participants are obliged to code the magnitude explicitly as well as to code the spatial-direction implicitly by adopting a magnitude and arrow-direction classification tasks with Go/No-Go responses. The results show that (1) the absolute value of negative numbers associates with space when the magnitude of negative numbers is explicitly coded, no matter employing the explicit or implicit spatial-direction; (2) the signed value of negative numbers associates with space under the condition of implicit magnitude as well as explicit spatial-direction. In conclusion, the current study indicates that the SNARC effect of negative numbers is variable in different conditions, and the type of SNARC effect about negative numbers is modulated by the joint coding level of the magnitude and spatial-direction.

The Effect of Verbal Task Instruction on Spatial-Numerical Associations of Response Codes Effect Coding of Spatial-Numerical Associations: Evidence From Event-Related Potential

The spatial-numerical associations of response codes (SNARC) effect reveals that individuals can represent numbers spatially. In this study, event-related potential (ERP) technology was used to probe the effect of verbal-spatial task instructions on spatial-numerical association coding by using digit parity and magnitude judgment tasks, with the numbers 1–9 (except 5) and Chinese word labels (“left” and “right”) as experimental materials. The behavioral results of Experiment 1 showed that the SNARC effect was mainly based on verbal-spatial coding and appeared when the stimulus onset asynchrony (SOA) between the presentation of the verbal labels and the target digit was 0 ms. ERP results did not reveal any significant SNARC-related effects in either the N1 or P3 components. The behavioral results of Experiment 2 again showed that the SNARC effect was dominated by verbal-spatial coding. ERP results showed that significant effects related to verbal-spatial coding were found in both the early positive deflection of the stimulus-locked lateralized readiness potential (S-LRP) and the latency of the response-locked LRP (R-LRP). Hence, in this study, the nature of the spatial coding of the digit magnitudes was influenced by the processing of the word labels and affected both the response selection and response preparation stages.

Systematic spatial distortion of quantitative estimates

Magnitude estimation has been studied since the beginnings of scientific psychology and constitutes a fundamental aspect of human behavior. Yet, it has apparently never been noticed that estimates depend on the spatial arrangement used. We tested 167 adults in three experiments to show that the spatial layout of stimuli and responses systematically distorts number estimation, length production, and weight reproduction performance. The direction of distortion depends on the observer's counting habits, but does not seem to reflect the use of spatially associated number concepts. Our results imply that all quantitative estimates are contaminated by a "spell of space" whenever stimuli or responses are spatially distributed.

Is the attentional SNARC effect truly attentional? Using temporal order judgements to differentiate attention from response

The spatial–numerical association of response codes (SNARC) effect reflects the phenomenon that low digits are responded to faster with the left hand and high digits with the right. Recently, a particular variant of the SNARC effect known as the attentional SNARC (which reflects that attention can be shifted in a similar manner) has had notable replicability issues. However, a potentially useful method for measuring it was revealed by Casarotti et al. using a temporal order judgement (TOJ) task. Accordingly, the present study evaluated whether Casarotti et al.’s results were reproducible by presenting a low (1) or high (9) digit prior to a TOJ task where participants had to indicate which of two peripherally presented targets appeared first (Experiment 1) or second (Experiment 2). In Experiment 1, it was revealed that the findings of Casarotti et al.’s were indeed observable upon replication. In Experiment 2, when attention and response dimensions were put in opposition, the SNARC effect corresponded to the side of response rather than attention. Taken together, the present study confirms the robustness of the attentional SNARC in TOJ tasks, but that it is not likely due to shifts in attention.

Perceiving numerosity does not cause automatic shifts of spatial attention

It is debated whether the representation of numbers is endowed with a directional-spatial component so that perceiving small-magnitude numbers triggers leftward shifts of attention and perceiving large-magnitude numbers rightward shifts. Contrary to initial findings, recent investigations have demonstrated that centrally presented small-magnitude and large-magnitude Arabic numbers do not cause leftward and rightward shifts of attention, respectively. Here we verified whether perceiving small or large non-symbolic numerosities (i.e., clouds of dots) drives attention to the left or the right side of space, respectively. In experiment 1, participants were presented with central small (1, 2) vs large-numerosity (8, 9) clouds of dots followed by an imperative target in the left or right side of space. In experiment 2, a central cloud of dots (i.e., five dots) was followed by the simultaneous presentation of two identical dot-clouds, one on the left and one on the right side of space. Lateral clouds were both lower (1, 2) or higher in numerosity (8, 9) than the central cloud. After a variable delay, one of the two lateral clouds turned red and participants had to signal the colour change through a unimanual response. We found that (a) in Experiment 1, the small vs large numerosity of the central cloud of dots did not speed up the detection of left vs right targets, respectively, (b) in Experiment 2, the detection of colour change was not faster in the left side of space when lateral clouds were smaller in numerosity than the central reference and in the right side when clouds were larger in numerosity. These findings show that perceiving non-symbolic numerosity does not cause automatic shifts of spatial attention and suggests no inherent association between the representation of numerosity and that of directional space.

Number space is made by response space: Evidence from left spatial neglect

Whether the semantic representation of numbers is endowed with an intrinsic spatial component, so that smaller numbers are inherently represented to the left of larger ones on a Mental Number Line (MNL), is a central matter of debate in numerical cognition. To gain an insight into this issue, we investigated the performance of right brain damaged patients with left spatial neglect (N+) in a bimanual Magnitude Comparison SNARC task and in a uni-manual Magnitude Comparison Go/No-Go task (i.e. "is the number smaller or larger than 5?"). While the first task requires the use of contrasting left/right spatial codes for response selection, the second task does not require the use of these codes. In line with previous evidence, in the SNARC task N+ patients displayed a significant asymmetry in Reaction Times (RTs), with slower RTs to number "4", that was immediately precedent to the numerical reference "5", with respect to the number "6", that immediately followed the same reference. This RTs asymmetry was correlated with lesion of white matter tracts, i.e. Fronto-Occipital-Fasciculus, that allows prefrontal Ba 8 and 46 to regulate the distribution of attention on sensory and memory traces in posterior occipital, temporal and parietal areas. In contrast, no similar RTs asymmetry was found in the Go/No-Go task. These findings suggest that while in the SNARC task numbers get mentally organised from left-to-right as a function of their increasing magnitude, so that N+ patients display a delay in the processing of number-magnitudes that are immediately smaller than a given numerical reference, in the Go/No-Go task no left-to-right organization is activated. These results support the idea that it is the use of contrasting left/right spatial codes, whether motor or conceptual, that triggers the generation of a spatially left-to-right organised MNL and that the representation of number magnitude is not endowed with an inherent spatial component.

How to trigger and keep stable directional Space-Number Associations (SNAs)

Humans are prone to mentally organise the ascending series of integers according to reading habits so that in western cultures small numbers are positioned to the left of larger ones on a mental number line. Despite 140 years since seminal observations by Sir Francis Galton (Galton, 1880a, b), the functional mechanisms that give rise to directional Space-Number Associations (SNAs) remain elusive. Here, we contrasted three different experimental conditions, each including a different version of a Go/No-Go task with intermixed numerical and arrow-targets (Shaki and Fischer, 2018; Pinto et al., 2019a). We show that directional SNAs are not "all or none" phenomena. We demonstrate that SNAs get progressively less noisy and more stable the more contrasting small/large magnitude-codes and contrasting left/right spatial-codes are explicitly and fully combined in the task set. The analyses of the time-course of space-number congruency effects showed that both the absence and presence of the SNA were independent of the speed of reaction times. In agreement with our original proposal (Aiello et al., 2012), these findings show that conceptualising the ascending series of integers in spatial terms depends on the use of spatial codes in the numerical task at hand rather than on the presence of an inherent spatial dimension in the semantic representation of numbers. This evidence suggests that directional SNAs, like the SNARC effect, are secondary to the primary transfer of spatial response codes to number stimuli, rather than deriving from a primary congruency or incongruence between independent spatial-response and spatial-number codes.

Shifting attention does not influence numerical processing

Many theories of numerical cognition assume that numbers and space share a common representation at the response level. For example, observers are faster to respond to small numbers with their left hand and large numbers with their right hand (the SNARC effect). There is also evidence that viewing numbers can produce spatial shifts of attention, suggesting that attention may play a role in the spatial representation of numbers. In the present study, we assessed whether shifts of attention can influence numerical processing. Participants viewed a leftward or rightward peripheral cue followed by a centrally presented number, then judged whether the number was odd or even. Participants responded faster and made fewer errors when the number magnitude and response side were compatible, revealing a response-based SNARC effect. Participants also responded faster when the cue direction and response side were compatible, revealing a Simon effect. However, participants did not respond faster when the cue direction and number magnitude were compatible. Similar findings were observed when the association between numbers and space was relatively explicit. Moreover, although we failed to observe a response-based SNARC effect when number magnitude was directly relevant to observers' task, we observed a large Simon effect. Together, these findings suggest that although numbers and space share a common representation at the response level, attention does not play a substantial role in the spatial representation of numbers.

Does Number Perception Cause Automatic Shifts of Spatial Attention? A Study of the Att-SNARC Effect in Numbers and Chinese Months

The Attentional Spatial Numerical Association of Response Codes (Att-SNARC) effect has shown that number perception induces shifts in spatial attention (Fischer et al., 2003; Dodd et al., 2008). However, many replications were attempted and they often failed. In the present study, we investigated whether the Att-SNARC effect can be found for numbers in different notations: months in Arabic form, Simplified Chinese form, Traditional Chinese form (includes numerical ordinal information) and in Chinese non-numerical form (an ordinal sequence). By varying the cognitive task, we also examined whether the effect is a consequence of automatic perceptual processing. In Experiment 1, an Att-SNARC effect was observed for numbers regardless of notation. In Experiment 2 (order-irrelevant task) and Experiment 3 (order-relevant task), the effect was also found consistently for months in Arabic form, Simplified Chinese form, and Traditional Chinese form. This effect was not observed for months in Chinese non-numerical form in Experiment 3. These results show that number and numerical sequence perception automatically causes a spatial shift of attention. Our study provides positive evidence for the Att-SNARC effect and indicates that the effect can generalize to other numerical ordinal sequences that contain numeric information.

The spatial-numerical association of response codes effect and math skills: why related?

Evidence from multiple studies conducted in the past few decades converges on the conclusion that numerical properties can be associated with specific directions in space. Such spatial-numerical associations (SNAs), as a signature of elementary number processing, seem to be a likely correlate of math skills. Nevertheless, almost three decades of research on the spatial-numerical association of response codes (SNARC) effect, the hallmark of SNAs, has not provided conclusive results on whether there is a relation with math skills. Here, going beyond reviewing the existing literature on the topic, we try to answer a more fundamental question about why the SNARC effect should (and should not) be related to math skills. We propose a multiroute model framework for a SNARC-math skills relationship. We conclude that the relationship is not straightforward and that several other factors should be considered, which under certain circumstances or in certain groups can cause effects of opposite directions. The model can account for conflicting results, and thus may be helpful for deriving predictions in future studies.