Spatial-numerical Association Of Response Codes Effect Research Articles

Critical Time Course of Right Frontoparietal Involvement in Mental Number Space

Neuropsychological, neurophysiological, and neuroimaging studies suggest that right frontoparietal circuits may be necessary for the processing of mental number space, also known as the mental number line (MNL). Here we sought to specify the critical time course of three nodes that have previously been related to MNL processing: right posterior parietal cortex (rPPC), right FEF (rFEF), and right inferior frontal gyrus (rIFG). The effects of single-pulse TMS delivered at 120% distance-adjusted individual motor threshold were investigated in 21 participants, within a window of 0-400 msec (sampling interval = 33 msec) from the onset of a central digit (1-9, 5 excluded). Pulses were delivered in a random order and with equal probability at each time point, intermixed with noTMS trials. To analyze whether and when TMS interfered with MNL processing, we fitted bimodal Gaussian functions to the observed data and measured effects on changes in the Spatial-Numerical Association of Response Codes (SNARC) effect (i.e., an advantage for left- over right-key responses to small numbers and right- over left-key responses to large numbers) and in overall performance efficiency. We found that, during magnitude judgment with unimanual key-press responses, TMS reduced the SNARC effect in the earlier period of the fitted functions (∼25-60 msec) when delivered over rFEF (small and large numbers) and rIFG (small numbers); TMS further reduced the SNARC effect for small numbers in a later period when delivered to rFEF (∼200 msec). In contrast, TMS of rPPC did not interfere with the SNARC effect but generally reduced performance for small numbers and enhanced it for large numbers, thus producing a pattern reminiscent of "neglect" in mental number space. Our results confirm the causal role of an intact right frontoparietal network in the processing of mental number space. They also indicate that rPPC is specifically tied to explicit number magnitude processing and that rFEF and rIFG contribute to interfacing mental visuospatial codes with lateralized response codes. Overall, our findings suggest that both ventral and dorsal frontoparietal circuits are causally involved and functionally connected in the mapping of numbers to space.

Children’s mental representation when comparing fractions with common numerators

Researchers debate whether one represents the magnitude of a fraction according to its real numerical value or just the discrete numerosity of its numerator or denominator. The present study examined three effects based on the notion that people possess a mental number line to explore how children represent fractions when they compare fractions with common numerators. Specifically, the effect of the spatial numerical association of response codes (SNARC), the distance effect and the size effect in representing fractions were examined in a sample of 72 sixth graders, who successfully solved the fraction comparison task with a real number (.2) or a fraction (1/5) as the reference. Results showed that in the fraction-reference group (1/5 as the reference), there was a significant reverse SNARC effect and a distance effect between the denominators of the target fractions and the reference fraction; in the real number-reference group, the three effects were also observed. These results revealed that both groups used the mental number line to represent fractions and did not represent their real numerical values but rather the discrete numerosities of denominators when comparing fractions with common numerators. It seems that the way people represent fractions may depend on their strategy choices.

SNARC效应形成机制的研究进展<br>Advances in Formation Mechanism of the SNARC Effect

“空间–数字的反应编码联合”效应(Spatial-Numerical Association of Response Codes, 简称SNARC效应)是指在数字判断任务中，被试按左侧键对小数的反应快于按右侧键对小数的反应，而按右侧键对大数的反应要快于按左侧键对大数的反应。SNARC效应自Dehaene等(1993)发现以来，虽已有大量证据证明其普遍存在性，但其仍存在很大的灵活性。本文主要从阅读与书写习惯、具身认知以及工作记忆三个方面对SNARC效应的形成机制进行了简单回顾，但其可能都不是SNARC效应产生的本质，SNARC效应有可能只是SQUARC (Spatial-Quantity Association of Response Codes)效应的一个特例。 Spatial-Numerical Association of Response Codes (SNARC) effect specifically relates small magnitudes to the left hand side and larger magnitudes to the right hand side. Since Dehaene (1993) found the SNARC effect, there are a large number of evidences about its universality, but the SNARC effect is very unstable. The paper is mainly from three aspects to state the formation mechanism of the SNARC effect, which are reading and writing habits, embodied cognition and working memory. However, all of these may be not the nature of the SNARC effect. The SNARC effect is only a special case of the SQUARC (Spatial-Quantity Association of Response Codes) effect.

SNARC struggles: Instant control over spatial–numerical associations.

[Correction Notice: An Erratum for this article was reported in Vol 39(6) of Journal of Experimental Psychology: Learning, Memory, and Cognition (see record 2013-39107-001). In the article, incorrect values appeared for the number of trials in the experiment (section: Procedure) and for the intercepts of four regression lines (section: Regression Coefficient Analysis). The correct number of trials in the experiment is 16 trials in a training block followed by 10 blocks of 128 trials each. The intercepts for response repetitions amounted to 0.72 ms for the SNARC effect following incongruent trials, and to 51.55ms following congruent trials. For response alternations, the intercepts amounted to 35.39 ms for the SNARC effect following incongruent trials and to 50.88 ms following congruent trials. The conclusions presented in the article are not affected by these mistakes.] Numbers and space are tightly linked-a phenomenon that is referred to as the spatial-numerical association of response codes (SNARC) effect (Dehaene, Bossini, & Giraux, 1993). The present study investigates how quickly and flexibly the behavioral impact of such spatial-numerical associations can be controlled. Participants performed a parity judgment task, and we examined how the SNARC effect is influenced by the preceding congruency between the required response and the target number's spatial association. Results indicate that the SNARC effect is reduced instantly after having experienced a number's spatial association to interfere with responding. This sequential modulation indicates a pronounced flexibility of spatial-numerical associations driven by cognitive control mechanisms.

On a generalized magnitude system in the brain: an integrative perspective

Research in the field of cognitive neuroscience has provided extensive evidence in support of a strong relationship between time, space, and number in the human brain. In 1993, Dehaene et al. discovered the SNARC (spatial-numerical association of response codes) effect and suggested that numbers may be internally represented along a spatial dimension, with low numbers on the left of a mental number line, and high numbers on the right. The investigation of this effect has been studied through the use of different methodologies and recent insights have extent this effect also to decisional processes (Daar and Pratt, 2008; Loetscher et al., 2008; Vicario, 2012, 2013). Similar relationships were also documented in research investigating link between space and time (DeLong, 1981; Vicario et al., 2007, 2009, 2011a,b; Ishihara et al., 2008; Vallesi et al., 2008; Fabbri et al., 2013) as well as between time and numbers (for instance see Dormal et al., 2006; Vicario et al., 2008; Lu et al., 2009; Vicario, 2011). This literature corroborates the suggestion of common cortical metrics for space time and numbers (Walsh, 2003). However, despite the 10 years that have elapsed since Walsh (2003) published his theoretical work, the debate about “A theory of Magnitude” (ATOM) is still object of discussion. This research topic entitled “On a generalized magnitude system in the brain: insights from experimental evidence” contains 10 state-of-the-art original research articles exploring the relationships between time, space and number. These research articles provide original contributions about the representation of magnitude in different research fields including childhood participants (Bottini and Casasanto, 2013; Lonnemann et al., 2013; Tokita and Ishiguchi, 2013), genetic polymorphism (Julio-Costa et al., 2013), clinical populations such as schizophrenia (Martinez-Cascales et al., 2013) and right brain damaged patients (Ishihara et al., 2013), investigations on healthy adults (Baker et al., 2013; Blini et al., 2013; Crollen et al., 2013; Viarouge and de Hevia, 2013). A lively contribute to this debate is also provided by the mini-review of Leibovich and Henik (2013) and six opinion articles (Agrillo and Miletto Petrazzini, 2013; Arzy et al., 2013; De Simone, 2013; Tzelgov et al., 2013; Van Opstal and Verguts, 2013; Vicario et al., 2013). These theoretical contributions address ATOM from different perspectives, revealing the strengths but also the weaknesses of this model. Much more work needs to be done and many issues remain to be addressed before we fully understand the brain mechanisms underlying the existence of analogies (Vicario and Martino, 2010) between magnitudes. It has been a great pleasure and honor to be involved in this Research Topic. I would like to thank all of the authors, reviewers, and Frontiers staff for helping to make this Research Topic possible and I look forward to further explorations of the brain mechanisms underlying ATOM.

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.

Implicit response-irrelevant number information triggers the SNARC effect: Evidence using a neural overlap paradigm

There is evidence from the SNARC (spatial-numerical association of response codes) effect and NDE (numerical distance effect) that number activates spatial representations. Most of this evidence comes from tasks with explicit reference to number, whether through presentation of Arabic digits (SNARC) or through magnitude decisions to nonsymbolic representations (NDE). Here, we report four studies that use the neural overlap paradigm developed by Fias, Lauwereyns, and Lammertyn (2001) to examine whether the presentation of implicit and task-irrelevant numerosity information (nonsymbolic arrays and auditory numbers) is enough to activate a spatial representation of number. Participants were presented with either numerosity arrays (1-9 circles or triangles) to which they made colour (experiment 1) or orientation (experiment 2) judgements, or auditory numbers coupled with an on-screen stimulus to which they made a colour (experiment 3) or orientation (experiment 4) judgement. SNARC effects were observed only for the orientation tasks. Following the logic of Fias et al., we argue that this SNARC effect occurs as a result of overlap in parietal processing for number and orientation judgements irrespective of modality. Furthermore, we found stronger SNARC effects in the small number range (1-4) than in the larger number range (6-9) for both nonsymbolic displays and auditory numbers. These results suggest that quantity is extracted (and interferes with responses in the orientation task) but this is not exact for the entire number range. We discuss a number of alternative models and mechanisms of numerical processing that may account for such effects.

Components representation of negative numbers: Evidence from auditory stimuli detection and number classification tasks

Past research suggested that negative numbers could be represented in terms of their components in the visual modality. The present study examined the processing of negative numbers in the auditory modality and whether it is affected by context. Experiment 1 employed a stimuli detection task where only negative numbers were presented binaurally. Experiment 2 employed the same task, but both positive and negative numbers were mixed as cues. A reverse attentional spatial-numerical association of response codes (SNARC) effect for negative numbers was obtained in these two experiments. Experiment 3 employed a number classification task where only negative numbers were presented binaurally. Experiment 4 employed the same task, but both positive and negative numbers were mixed. A reverse SNARC effect for negative numbers was obtained in these two experiments. These findings suggest that negative numbers in the auditory modality are generated from the set of positive numbers, thus supporting a components representation.

Are low and high number magnitudes processed differently while resolving the conflict evoked by the SNARC effect?

In the brain, numbers are thought to be represented in a spatially organised fashion on what is known as the Mental Number Line (MNL). The SNARC (Spatial-Numerical Association of Response Codes) effect refers to the faster responses to digits when the reaction side is congruent with the digit position on the MNL (e.g. a left-handed response to a small magnitude) and the slowing down of responses (inhibition) in the case of incongruity. We examined the electrophysiological correlates of conflict, which are linked to that of inhibition, to shed light on the relationship between the SNARC effect and executive attention. Event-related potentials (ERPs) were recorded from twenty-nine participants during a parity-judgment task. The participants responded more quickly on congruent than on incongruent trials. The congruency effect was reflected in early sensory (N1, N2) components above parieto-occipital and frontal regions, as well as in the later P3 component above centro-parietal areas. Moreover, both the N1 amplitude and N2 latency were greater with high than low magnitude digit targets. P3 amplitude modulation implies that the SNARC effect is the result of first evoking the parallel processing of digit magnitude categorisation (in the occipital and central areas) and numeric conflict detection (in the parieto-occipital and frontal areas) and secondly conflict monitoring and resolution localised in the centro-parietal and frontal sites. These results also suggest that the left hemisphere specialises in conflict processing of high magnitude digit targets, while the right hemisphere of low digit magnitudes.

The development of the SNARC effect: Evidence for early verbal coding

In a recent study, Gevers and colleagues (2010, Journal of Experimental Psychology: General, Vol. 139, pp. 180–190) showed that the SNARC (spatial numerical association of response codes) effect in adults results not only from spatial coding of magnitude (e.g., mental number line hypothesis) but also from verbal coding. Because children are surrounded by rulers, number lines, and the like in the classroom, it is intuitively appealing to assume that they first use their mental number line to represent numbers and that only later in development a verbal recoding of magnitude information takes place. However, this hypothesis has never been tested. The goal of the current study was to define the developmental pattern of both accounts (spatial and verbal) in explaining the SNARC effect. To this end, 9- and 11-year-olds were tested in a magnitude comparison task. Surprisingly, clear and robust evidence for verbal coding of magnitude information was observed in both age groups. Our results imply that the ability to use verbal coding of magnitude information is robustly present early in formal schooling.

Repetition and the SNARC effect with one- and two-digit numbers.

The SNARC (Spatial Numerical Association of Response Codes) effect is the finding that small numbers elicit faster left than right responses and large numbers elicit faster right than left responses. This effect suggests that numbers activate left-right magnitude-laterality codes and that these codes interact with the selection of left-right responses. In the present research, subjects made parity decisions for one-digit numbers (in Experiment 1) and two-digit numbers (in Experiment 2), and we examined the effect of stimulus repetition on the SNARC effect. With single-digit stimuli, responses were faster and the SNARC effect was eliminated when stimuli were identical on successive trials. With two-digit stimuli, responses were faster when the ones digit was repeated, but the SNARC effect was found regardless of whether the digit was repeated or not. We argue that magnitude-laterality codes are activated in the process of accessing number information in memory and that this process can be short circuited if the visual stimulus matches that on the previous trial. Thus, no SNARC effect is found in Experiment 1 when identical stimuli are presented on successive trials. However, this result is not found in Experiment 2 because successive stimuli do not match even if the ones digit is repeated.

Unimanual SNARC Effect: Hand Matters

A structural representation of the hand embedding information about the identity and relative position of fingers is necessary to counting routines. It may also support associations between numbers and allocentric spatial codes that predictably interact with other known numerical spatial representations, such as the mental number line (MNL). In this study, 48 Western participants whose typical counting routine proceeded from thumb-to-little on both hands performed magnitude and parity binary judgments. Response keys were pressed either with the right index and middle fingers or with the left index and middle fingers in separate blocks. 24 participants responded with either hands in prone posture (i.e., palm down) and 24 participants responded with either hands in supine (i.e., palm up) posture. When hands were in prone posture, the counting direction of the left hand conflicted with the direction of the left–right MNL, whereas the counting direction of the right hand was consistent with it. When hands were in supine posture, the opposite was true. If systematic associations existed between relative number magnitude and an allocentric spatial representation of the finger series within each hand, as predicted on the basis of counting habits, interactions would be expected between hand posture and a unimanual version of the spatial–numerical association of response codes (SNARC) effect. Data revealed that with hands in prone posture a unimanual SNARC effect was present for the right hand, and with hands in supine posture a unimanual SNARC effect was present for the left hand. We propose that a posture-invariant body structural representation of the finger series provides a relevant frame of reference, a within-hand directional vector, that is associated to simple number processing. Such frame of reference can significantly interact with stimulus–response correspondence effects, like the SNARC, that have been typically attributed to the mapping of numbers on a left-to-right mental line.

Number magnitude determines gaze direction: Spatial–numerical association in a free-choice task

Since Dehaene et al. (1993) reported the SNARC (Spatial–Numerical Association of Response Codes) effect, researchers have repeatedly documented an influence of number magnitude on reaction time in various motor tasks. In addition, thinking about numbers induces shifts of visuo-spatial attention ( Fischer et al., 2003). The present study examined whether number magnitude affects a person’s eye movement in a free-choice task. After the presentation of a number in the middle of the screen, two pictures of human faces were simultaneously presented on either side of the screen. Participants were asked to explore the screen after the presentation of a number. Analyses performed on first eye fixations confirmed that number magnitude affects gaze direction in this free-choice task. The present study shows that the influence of number magnitude on visuo-spatial attention affects the choice of where to look first.

Processing negative numbers by transforming negatives to positive range and by sign shortcut

Numerals are processed by a phylogenetically old analogue magnitude system. Can culturally new negative numerals be processed using this same representation? To find out whether magnitude representation could be used, we contrasted three possible processing mechanisms: an extended magnitude system for both positive and negative numbers, a mirroring mechanism that could transform negative values to the positive range to be processed on the positive magnitude system, and a sign shortcut strategy that can process the signs of numbers independently of the absolute values of numerals. To test these three hypotheses, a comparison task was used and the reaction time pattern, numerical distance, and Spatial-Numerical Association of Response Codes (SNARC) effect was analysed. The results revealed a mirroring process along with a sign shortcut mechanism. The SNARC effect was observed only when positive numbers were compared.

Negative numbers eliminate, but do not reverse, the attentional SNARC effect

Three experiments are reported examining whether the presentation of irrelevant negative numbers at central fixation interacts with attentional orienting beyond fixation. It has been previously shown that number perception influences spatial attention, with the presentation of spatially nonpredictive numbers resulting in the allocation of attention to the left when the number is low (e.g., 1 or 2) and to the right when the number is high (e.g., 8 or 9). In the present experiment, it is examined whether this attentional spatial numerical association of response codes (SNARC) effect is influenced by the presentation of negative numbers, which should have spatial properties that are in direct opposition to their positive counterparts (e.g., -1 or -2 would be considered high numbers relative to -8 or -9, which would be considered low numbers). Though the presentation of negative numbers does not lead to a reversal of the attentional SNARC effect, it does lead to an elimination of the effect, providing insight into how the attentional SNARC effect develops.

Influence on Simon and SNARC effects of a nonspatial stimulus-response mapping: Between-task logical recoding.

In 4 experiments, we intermixed trials in which the stimulus color was relevant with trials where participants had to judge the stimulus shape or parity and found that the logical-recoding rule (Hedge & Marsh, 1975) applied to the relevant dimension in a task can generalize to the irrelevant dimension of the other task. The mapping assigned to participants in color-relevant trials modulated the Simon and SNARC (spatial-numerical association of response codes) effects (Simon & Small, 1969; Dehaene, Bossini, & Giraux, 1993) observed in shape- and parity-relevant trials. Standard effects were obtained when color-relevant trials required participants to respond by pressing a key of the same color as the stimulus, whereas an alternate-color mapping caused either the disappearance or reversal of the effects. The present results demonstrate that for between-task transfer effects to occur the critical dimensions in the two alternative tasks do not have to share the same representation nor need the stimuli of the two tasks have any feature in common.

Verbal-spatial and visuospatial coding of number–space interactions.

A tight correspondence has been postulated between the representations of number and space. The spatial numerical association of response codes (SNARC) effect, which reflects the observation that people respond faster with the left-hand side to small numbers and with the right-hand side to large numbers, is regarded as strong evidence for this correspondence. The dominant explanation of the SNARC effect is that it results from visuospatial coding of magnitude (e.g., the mental number line hypothesis). In a series of experiments, we demonstrated that this is only part of the story and that verbal-spatial coding influences processes and representations that have been believed to be purely visuospatial. Additionally, when both accounts were directly contrasted, verbal-spatial coding was observed in absence of visuospatial coding. Relations to other number-space interactions and implications for other tasks are discussed.

Increasing the difficulty of response selection does not increase the switch cost.

Several theories of task switching assume that basic task processes such as stimulus identification and response selection do not contribute to task-switch costs. This conclusion is mainly based on the finding that stimulus-identification manipulations have no influence on the size of the switch cost. The present study tested the influence of response-selection manipulations on the size of the switch cost. The authors manipulated the difficulty of response selection by using a semantically based response-side effect that is associated with numerical-judgement tasks, namely the Spatial Numerical Association of Response Codes (SNARC) effect. The authors observed a SNARC effect and a switch cost, but no interaction between the two: the task-switch cost did not differ between SNARC-compatible and -incompatible responses. The authors conclude that response selection does not contribute to the switch cost on the current trial, which provides further support for the idea that basic task processes and task-switch processes are separate.

The objectification of overlearned sequences: A new view of spatial sequence synesthesia

In the phenomenon of spatial sequence synesthesia (SSS), subjects can articulate explicit spatial locations for sequences such as numbers, letters, weekdays, months, years, and other overlearned series. Similarly, abstract sequences can take on implicit spatial representations in non-synesthetes, as evidenced by the spatial numerical association of response codes (SNARC) effect. An open question is whether the two findings represent different degrees of the same condition, or different conditions. To address this, we developed computer programs to quantify three-dimensional (3D) month-form coordinates in 571 self-reported spatial sequence synesthetes; this approach opens the door for the first time to quantified large-scale analysis. First, despite the common assumption that month-forms tend to be elliptical, we find this to be true in only a minority of cases. Second, we find that 27% of month forms are in the shape of lines, consistent with the assumed shape of implicit spatial forms in the SNARC effect. Next, we find that the majority of month forms are biased in a left-to-right direction, also consistent with the directional bias in the SNARC effect (in Western speakers). Collectively, these findings support the possibility that SSS is directly related to the sequence representations in non-synesthetes. While the search for neural correlates has concentrated on areas in the parietal lobe involved in numeric manipulation and coordinate systems, we propose that the basis of this synesthesia may be the close proximity of temporal lobe regions implicated in sequence coding and visual object representation.

What information is critical to elicit interference in number-form synaesthesia?

Numerous behavioural paradigms have demonstrated a close connection between numbers and space, suggesting that numbers may be represented on an internal mental number line. For example, in the Spatial Numerical Association of Response Codes (SNARC) effect, reaction times are faster for left-sided responses to smaller numbers and for right-sided responses to larger numbers. One valuable tool for exploring such numerical–spatial interactions is the study of number-form synaesthesia, in which participants report vivid, automatic associations of numerical and other ordinal sequences with precise, idiosyncratic, spatial layouts. Recent studies have demonstrated the influence of synaesthetic spatial experiences on behavioural number tasks. The aim of the present study is to further explore these internal spatial representations by presenting a case-study of an unusual synaesthete, DG, who reports highly detailed representations not only of numerical sequences (including representations of negative and Roman numbers), but also different representations for other ordinal sequences, such as time sequences (months, days and hours), the alphabet, financial sequences and different units of measure (e.g., kilograms, kilometres and degrees). Here, we describe DG's synaesthetic experiences and a series of behavioural experiments on numerical tasks concerning the automaticity of this phenomenon. DG's performance on number comparison and cued-detection tasks was modulated by his synaesthetic mental representation for the numerical sequence, such that his reaction times were slower when the spatial layout was incompatible with the orientation of his mental number line. We found that the spatial presentation of stimuli, rather than the implicit or explicit access to numerosity required by tasks, was essential to eliciting DG's number-forms. These results are consistent with previous studies and suggest that numerical–spatial interactions may be most strongly present in synaesthetes when both numerical and spatial information are explicitly task-relevant, consistent with a growing body of literature regarding the SNARC and other related effects.