High-definition turns timing-dependent: Different behavioural consequences during and following cathodal high-definition transcranial direct current stimulation (HD tDCS) in a magnitude classification task.

Neuromodulation with transcranial direct current stimulation (tDCS) can transiently alter neural activity, but its spatial precision is low. High-definition (HD) tDCS was introduced to increase spatial precision by placing additional electrodes over the scalp. Initial evaluations of HD tDCS indicated polarity-specific neurophysiological effects-similar to conventional tDCS albeit with greater spatial precision. Here, we compared the effects of cathodal tDCS or HD tDCS in a 4 × 1 configuration over prefrontal cortex (PFC) regions on behavioural outcomes in a magnitude classification task. We report results on overall performance, on the numerical distance effect as a measure of numerical processing, and on the spatial-numerical associations of response codes (SNARC) effect, which was previously affected by prefrontal tDCS. Healthy volunteers (n = 68) received sham or cathodal HD tDCS at 1 mA over the left dorsolateral prefrontal cortex (DLPFC) or the left inferior frontal gyrus (IFG). Results were compared to an identical protocol with conventional cathodal tDCS to the left PFC versus sham (n = 64). Mixed effects models showed performance gains relative to sham tDCS in all conditions after tDCS (i.e. 'offline'), whereas montages over PFC and DLPFC already showed performance gains during tDCS (i.e. 'online'). In contrast to conventional tDCS, HD tDCS did not reduce the SNARC effect. Neither condition affected numerical processing, as expected. The results suggest that HD tDCS with cathodal polarity might require further adjustments (i.e. regarding tDCS intensity) for effective modulations of cognitive-behavioural performance, which could be achieved by individualised current density in electric field modelling.

Practice-induced SNARC: evidence from a null-SNARC sample.

The mental representation of numbers inherently involves a spatial organization, often positioning smaller numbers to the left and larger numbers to the right. The SNARC effect, characterized by faster responses to small numbers using the left hand and vice versa for large numbers, is typically attributed to this left-to-right oriented mental number line (MNL). However, the direction of the SNARC effect seems to rely on reading direction, with most research exploring these mechanisms conducted within left-to-right reading cultures where the SNARC effect is prevalent. This study takes advantage of a sample from a left-to-right reading culture that does not exhibit the SNARC effect, allowing us to isolate and elucidate the stand-alone effects of recent experiences on SNARC. Therefore, the current study aims to investigate how MNL-compatible and MNL-incompatible practices induce an effect within a sample lacking the SNARC effect. To accomplish this, we reinvited the individuals from the sample which had previously shown no SNARC, and retested those who agreed to take part in the current study after an MNL-compatible or MNL-incompatible practice manipulation. The findings revealed an absence of the SNARC effect with MNL-compatible practices. Conversely, MNL-incompatible practices yielded a reverse SNARC effect. These results prompt a discussion on SNARC mechanisms within the framework of practice effects.

Non-symbolic and symbolic number lines are dissociated.

People use mental number lines for both symbolic numerals and numerosity, but little is known about how these two mental number lines are related. The current study investigated the association in effect size, directionality of the mental number line, and development between symbolic and non-symbolic mental number lines to determine if they were related to or independent from each other. We collected data from numerosity- and digit-matching tasks that used the following numbers: 11, 14, 17, 20, 23, 26, and 29. Tasks were performed by college undergraduates and the fifth-grade primary school students. The results showed that none of the effects for non-symbolic numbers was related to any of the effects for symbolic numbers, and vice versa, in both adults and children. Another notable finding was that the correlation between the SNARC (spatial-numerical association of response code) effect size and mathematical ability was negative in the adult group. These results are consistent with the dissociated processes hypothesis and suggest that mental number lines are notation-dependent. As shown by the SNARC effect, the mental number line might result in interference in the current task by an automatically activated spatial notation-dependent representation of numbers.

Multiple left-to-right spatial representations of number magnitudes? Evidence from left spatial neglect.

The SNARC effect reflects the observation that when healthy observers with left-to-right reading habits are asked to compare the magnitude or to judge the parity of numbers, they provide faster reaction times (RT) to small numbers with left-sided responses and faster RTs to large numbers with right-sided responses. In magnitude comparison (MC), right brain damaged patients with left-sided neglect typically show a pathologically enlarged SNARC for large numbers and selective slowing to numbers that are immediately lower than the numerical reference (e.g. 4 for reference 5). This asymmetry has been taken as evidence that small numbers are mentally positioned to the left of the reference and, therefore, are processed less efficiently by patients neglecting the left side of space. In parity judgement (PJ), on the other hand, the size of the SNARC effect is unaffected by neglect. This dissociation is typically attributed to the disturbed explicit processing of number magnitude in MC and preserved implicit processing of magnitude in PJ. Before accepting this interpretation, however, it remains to be investigated whether neglect patients show the same RT pattern that characterizes the performance of healthy participants (i.e. left-side RTs that increase linearly as a function of number magnitude and right-side RTs that decrease linearly as a function of magnitude). Clarifying this point is crucial, because an equally sized SNARC can originate from different RT patterns. Here we demonstrate that the RT pattern of neglect patients during PJ is entirely comparable to those of patients without neglect and healthy controls, while the same neglect patients show selective slowing to numbers that are immediately lower than the numerical reference in MC. These findings suggest the existence of multiple left-to-right spatial representations of number magnitude and provides an explanation of the functional dissociation between MC and PJ tasks.

Spatial-numerical association of response code effect as a window to mental representation of magnitude in long-term memory among Hebrew-speaking children.

The well-known spatial-numerical association of response code (SNARC) effect supports the idea that the mental number line (MNL) is organized from left to right in participants writing from left to right. In Arabic speakers writing from right to left, the direction of the SNARC effect is reversed. Until recently, no consistent numerical-spatial associations were reported in Hebrew speakers, who write letters from right to left and write numbers from left to right. However, a left-to-right SNARC effect was recently demonstrated in adult Hebrew readers by reducing the markedness association of response code (MARC) effect, which masks the SNARC effect. Adult Hebrew speakers (especially university students) are skilled English readers and writers, supporting the claim that the direction of reading is not the sole factor contributing to direction of the emergence of the left-to-right organization of the MNL. Thus, to understand the effect of reading habits on the SNARC effect, here we demonstrate the SNARC in young Hebrew-speaking children who read Hebrew letters from right to left, read numbers from left to right, and had little experience in writing English letters from left to right. Our findings, therefore, are innovative in providing supporting evidence for the claim that the direction of reading is not the sole factor contributing to direction of the emergence of the left-to-right organization of the MNL.

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.

Embodied Interaction Priority: Other's Body Part Affects Numeral-Space Mappings.

Traditionally, the spatial-numerical association of response codes (SNARC) effect was presented in two-choice condition, in which only one individual reacted to both even (small) and odd (large) numbers. Few studies explored SNARC effect in a social situation. Moreover, there are many reference frames involved in SNARC effect, and it has not yet been investigated which reference frame is dominated when two participants perform the go-nogo task together. In the present study, we investigated which reference frame plays a primary role in SNARC effect when allocentric and egocentric reference frames were consistent or inconsistent in social settings. Furthermore, we explored how two actors corepresent number-space mapping interactively. Results of the two experiments demonstrated that egocentric reference frame was at work primarily when two reference frames were consistent and inconsistent. This shows that body-centered coordinate frames influence number-space mapping in social settings, and one actor may represent another actor's action and tasks.

Mathematical abilities in elementary school: Do they relate to number-space associations?

Considering the importance of mathematics in Western societies, it is crucial to understand the cognitive processes involved in the acquisition of more complex mathematical skills. The current study, therefore, investigated how the quality of number-space mappings on the mental number line, as indexed by the parity SNARC (spatial-numerical association of response codes) effect, relates to mathematical performances in third- and fourth-grade elementary school children. Mathematical competencies were determined using the "Heidelberger Rechentest," a standardized German math test assessing both arithmetical and visuospatial math components. Stronger parity SNARC effects significantly related to better arithmetical but not visuospatial math abilities, albeit only in the relatively younger children. These findings highlight the importance of spatial-numerical interactions for arithmetical (as opposed to visuospatial) math skills at the fairly early stages of mathematical development. Differential relations might be explained by the reliance on problem-solving strategies involving number-space mappings only for arithmetic tasks mainly in younger children.

The effect of working memory load on the SNARC effect: Maybe tasks have a word to say.

We investigated the effect of working memory load on the SNARC (spatial-numerical association of response codes) effect under different number judgment tasks (parity judgment and magnitude comparison), using a novel dual task. Instead of exerting load over the whole block of number judgment trials, in this dual task, number judgment trials were inserted into each interstimulus interval of an n-back task, which served as the working memory load. We varied both load type (verbal and spatial) and amount (1-load, 2-load, and 3-load). The results indicated that the SNARC effect disappeared even under the 1-load condition for a parity judgment, regardless of the type of load. However, during the magnitude comparison task, the SNARC effect increased with increasing load amounts under spatial load conditions; under verbal load conditions, the SNARC effect decreased with increasing amounts of load, and disappeared during the 3-load task. The difference between the parity and magnitude tasks was not attributable to the interval stimuli or task switching. These findings confirm that different spatial-numerical associations for comparing numerical magnitudes and judgments of parity have different needs with respect to working memory resources.

The associations between space and order in numerical and non-numerical sequences.

Spatial-numerical associations have been found across different studies, yet the basis for these associations remains debated. The current study employed an order judgment task to adjudicate between two competing accounts of such associations, namely the Mental Number Line (MNL) and Working Memory (WM) models. On this task, participants judged whether number pairs were in ascending or descending order. Whereas the MNL model predicts that ascending and descending orders should map onto opposite sides of space, the WM model predicts no such mapping. Moreover, we compared the spatial-order mapping for numerical and non-numerical sequences because the WM model predicts no difference in mapping. Across two experiments, we found consistent spatial mappings for numerical order along both horizontal and vertical axes, consistent with a MNL model. In contrast, we found no consistent mappings for letter sequences. These findings are discussed in the context of conflicting extant data related to these two models.

Development of SNARC and distance effects and their relation to mathematical and visuospatial abilities.

The current experiment measured symbolic SNARC (Spatial-Numeric Association of Response Codes) and distance effects in school-aged children and investigated the relation between these measures and visuospatial skills and mathematics ability. In the experiment, 6-, 7-, and 8-year-olds performed a magnitude-relevant SNARC task, in which they indicated whether a target number was less or greater than 5, as well as standardized tests of visuospatial skills (Developmental Test of Visual Perception-Second Edition, DTVP-2) and mathematics ability (Test of Early Mathematics Ability-Third Edition, TEMA-3). Consistent with previous research using numerical SNARC tasks with Western children, all age groups exhibited robust distance effects, and SNARC effects were observed only in 7- and 8-year-olds. Distance effects, but not SNARC effects, were moderately but significantly correlated with a subtest of the DTVP-2 measuring the ability to mentally manipulate objects in space but no other subtest. These data suggest that mental orientation abilities, but perhaps not visuospatial skills involved in visual perception and visuomotor coordination, are related to some aspects of mental number line development. Nevertheless, no relation was observed between SNARC or distance effects and mathematics ability. This result is consistent with previous developmental studies investigating the association between SNARC and math skill. However, these data are inconsistent with most experiments assessing the relationship between distance effect strength and math-a difference that can likely be attributed to the fact that a magnitude-relevant SNARC task was employed as opposed to a traditional SNARC parity task.

Number-space interactions in the human parietal cortex: Enlightening the SNARC effect with functional near-infrared spectroscopy.

Interactions between numbers and space have become a major issue in cognitive neuroscience, because they suggest that numerical representations might be deeply rooted in cortical networks that also subserve spatial cognition. The spatial-numerical association of response codes (SNARC) is the most robust and widely replicated demonstration of the link between numbers and space: in magnitude comparison or parity judgments, participants' reaction times to small numbers are faster with left than right effectors, whereas the converse is found for large numbers. However, despite the massive body of research on number-space interactions, the nature of the SNARC effect remains controversial and no study to date has identified its hemodynamic correlates. Using functional near-infrared spectroscopy, we found a hemodynamic signature of the SNARC effect in the bilateral intraparietal sulcus, a core region for numerical magnitude representation, and left angular gyrus (ANG), a region implicated in verbal number processing. Activation of intraparietal sulcus was also modulated by numerical distance. Our findings point to number semantics as cognitive locus of number-space interactions, thereby revealing the intrinsic spatial nature of numerical magnitude representation. Moreover, the involvement of left ANG is consistent with the mediating role of verbal/cultural factors in shaping interactions between numbers and space.

Spatial and numerical processing in children with high and low visuospatial abilities.

In the literature on numerical cognition, a strong association between numbers and space has been repeatedly demonstrated. However, only a few recent studies have been devoted to examine the consequences of low visuospatial abilities on calculation processing. In this study, we wanted to investigate whether visuospatial weakness may affect pure spatial processing as well as basic numerical reasoning. To do so, the performances of children with high and low visuospatial abilities were directly compared on different spatial tasks (the line bisection and Simon tasks) and numerical tasks (the number bisection, number-to-position, and numerical comparison tasks). Children from the low visuospatial group presented the classic Simon and SNARC (spatial numerical association of response codes) effects but showed larger deviation errors as compared with the high visuospatial group. Our results, therefore, demonstrated that low visuospatial abilities did not change the nature of the mental number line but rather led to a decrease in its accuracy.

Development of spatial representation of numbers: a study of the SNARC effect in Chinese children.

Using the standard parity judgment task, this study investigated the development of numerical-spatial representation. Participants were 314 healthy right-handed Chinese children (from kindergarteners to sixth graders) and adults. The results revealed that all age groups showed a significant (or marginally significant in the case of first graders) SNARC (spatial-numerical association of response codes) effect, indicating that Chinese children as young as kindergarteners already had developed automatic spatial representations of numbers (or the mental number line). Surprisingly, however, the size of the SNARC effect did not show much developmental change. These results are discussed in the context of the literature on spatial representations of numbers and on cross-cultural differences in early development of number cognition.

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

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

Don't SNARC me now! Intraindividual variability of cognitive phenomena - Insights from the Ironman paradigm.

Two implicit generalizations are often made from group-level studies in cognitive experimental psychology and their common statistical analysis in the general linear model: (1) Group-level phenomena are assumed to be present in every participant with variations between participants being often treated as random error in data analyses; (2) phenomena are assumed to be stable over time. In this preregistered study, we investigated the validity of these generalizations in the commonly used parity judgment task. In the proposed Ironman paradigm, the intraindividual presence and stability of three popular numerical cognition effects were tested in 10 participants on 30 days: the SNARC (Spatial-Numerical Association of Response Codes, i.e., faster left-/right-sided responses to small/large magnitude numbers, respectively; Dehaene, Bossini, & Giraux, 1993), MARC (Linguistic Markedness of Response Codes; i.e., faster left-/right-sided responses to odd/even numbers, respectively; Nuerk, Iversen, & Willmes, 2004), and Odd (i.e., faster responses to even numbers; Hines, 1990) effects. We replicated the group-level effects; however, they were reliably present in only four to five (SNARC), six (MARC) or five (Odd) of 10 participants. Fluctuations seemed unsystematic, although the SNARC effect decreased over time along with reaction times. No correlation between the SNARC and MARC effects and sleep duration, tiredness, daytime, and consumption of stimulants were detected in most participants. These results challenge the frequent generalizations from group-level phenomena to individual participants and from single sessions to typical behavior. The innovative Ironman paradigm combined with bootstrap analyses permits unique insights into the intraindividual presence and stability of cognitive phenomena.

Separating spatial representations from polarity encoding in the processing of number and sequence stimuli in a four-way classification task.

Although the SNARC effect in the processing of most magnitude stimuli and sequence stimuli has been reported for the past 30 years, it remains unclear whether this effect is caused by the spatial representation or polarity encoding of stimuli. In the present study, we designed five experiments using a four-way classification task to evaluate the ability of spatial representation theory and polarity encoding theory to explain the SNARC effect in the processing of number and sequence stimuli. In all five experiments in the present study, stimuli (Experiments 1 and 4: four different Arabic numbers, Experiment 2: sequence stimuli, Experiment 3: ordinal sequences relevant to working memory, Experiment 5: Chinese characters without any implicit spatial information) were centrally presented. Participants were asked to respond to specific number or sequence stimuli by pressing the A, S, K, and L keys in consistent trials (or the L, K, S, and A keys in inconsistent trials). The results showed that (1) the SNARC effect occurred in the processing of number and sequence stimuli both when only one specific number was mapped to one specific key (Experiments 1, 2 and 3) and when two numbers were mapped to one specific key (Experiment 4). (2) There was not a SNARC effect when the numbers were replaced with Chinese characters without any implicit spatial information (Experiment 5). The results of these five experiments imply that the SNARC effect in the processing of magnitude stimuli, including numbers and sequences, originates from the spatial representation of stimuli, supporting spatial representation theory.

SNARC-like effect for tempo is consistent for fast and full tempo ranges but still controversial for slow tempo range.

Recent evidence suggested the existence of a spatial associations for music tempo with faster left-hand responses to relatively slow tempos and faster right-hand responses to relatively fast tempos. We refer to a study that systematically explored these spatial associations across different tempo ranges, revealed a clear effect only in the fast tempo range (DOI 10.3758/s13414-019-01945-8). The present study further investigated whether a spatial association exists across different tempo ranges (i.e., "full", "slow" or "fast" tempo range). In particular, the present study was conducted aiming (1) to test the spatial associations for tempo in the full tempo range (Experiment 1) and (2) to further investigate the occurrence of this spatial associations in the slow and fast tempo ranges (Experiment 2). Experiment 1 revealed a spatial association for tempo occurs in the full tempo range (40-200 bpm). Experiment 2 confirmed this association in the fast tempo range (133-201 bpm) but showed contradictory results in the slow tempo range (40-104 bpm). This suggests that a spatial association is plausible in the slow tempo range, although further research is needed to clarify this phenomenon.

Influence of different spatial representations on the SNARC effect for letters: Electrophysiological evidence.

Studies have previously demonstrated that different spatial representations may affect the spatial-numerical association of response codes (SNARC) effect for numbers; however, limited studies have assessed the SNARC effect for letters. In this study, event-related potentials (ERPs) were used to measure the influence of two spatial representation modes (ruler and clock) on the SNARC effect. The ruler produced a SNARC-like effect; i.e., the left hand reacted faster than the right to the letters that appeared before N in the alphabet; the right hand reacted faster than the left to the letters that appeared after N, whereas the clock produced a reverse SNARC effect. In addition, the ERP data showed that the SNARC-like effect for letters in both representations induced significant activation in the frontal and parietal regions, indicating that the same brain areas are involved in processing letters and numbers in terms of spatial dimensions. This study further identified the conditions for the SNARC effect and proved that the SNARC effect is attributed to the simultaneous participation of brain regions for sequence and spatial information processing.

Effect of egocentric and allocentric reference frames on spatial-numerical associations.

From an embodied view of cognition, sensorimotor mechanisms are strongly involved in abstract processing, such as Arabic number meanings. For example, spatial cognition can influence number processing. These spatial-numerical associations (SNAs) have been deeply explored since the seminal SNAs of response code (SNARC) effect (i.e., faster left/right sided responses to small/large magnitude numbers, respectively). Although these SNAs along the transverse plane (left-to-right axis) have been extensively studied in cognitive sciences, no systematic assessment of other planes of the tridimensional space has been afforded. Moreover, there is no evidence of how SNAs organise themselves throughout the changes in spatial body-reference frames (egocentric and allocentric). Hence, this study aimed to explore how SNAs organise themselves along the transverse and sagittal planes when egocentric and allocentric changes are processed during body displacements in the environment. In the first experiment, the results revealed that, when the participants used an egocentric reference, SNAs were observed only along the sagittal plane. In a second experiment that used an allocentric reference, the reversed pattern of results was observed: SNAs were present only along the transverse plane of the body. Overall, these findings suggest that, depending on the spatial reference frames of the body, SNAs are strongly flexible.