Spatial structure of quantitative representation of numbers: Evidence from the SNARC effect

Dehaene, Bossini, and Giraux (1993) revealed that subjects responded to large numbers faster with the choice on the right than with the choice on the left, whereas the reverse held true for small numbers (SNARC effect). According to Dehaene et al. (1993), the SNARC effect depends on the quantitative representation of number, such as a left-to-right-oriented analog number line. The main goal of the present study was twofold: first, to investigate whether the vertical SNARC effect could be observed, and, second, to verify whether Dehaene et al.'s (1993) explanation of the SNARC effect is correct. Experiments 2A and 2B showed the vertical SNARC effect in a parity judgment task. Subjects responded to large numbers faster with the top choice than with the bottom choice, whereas the reverse held true for small numbers. However, Experiment 3 failed to show the SNARC effect in a number magnitude judgment task, suggesting that the quantitative representation could be dissociated from the spatial code that produces the SNARC effect.     

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.     

符号数量和非符号数量的空间表征:5岁儿童的SNARC效应和距离效应

对物理刺激的数量信息表征是符号数字表征的前提和基础,据此假设在儿童的SNARC效应发生的时序问题上,非符号数量(如面积)的空间表征早于符号数量(如阿拉伯数字)的空间表征。本研究邀请5岁幼儿完成数字比较和面积比较两类任务,结果发现在数字比较任务中没有出现SNARC效应,但却存在距离效应;在面积比较任务中出现了SNARC效应和距离效应。可以推断,在阿拉伯数字的空间表征出现之前,儿童已经能够对非符号数量信息进行空间表征。     

Comparing implicit and synaesthetic number–space associations: Visuospatial and verbal spatial–numerical associations of response codes

In the theory of the mental number line, number, and space are implicitly associated, giving rise to the spatial–numerical association of response codes (SNARC) effect, in which smaller numbers are more readily associated with the left side of space and larger numbers with the right, during a parity judgement task. Others, however, have argued that the SNARC effect is flexible and better explained by verbal rather than spatial associations. A few single-case studies on the SNARC effect have tested number–space synaesthetes, who make explicit associations between number and space. Here, we present data from experiments conducted on groups of synaesthetes and nonsynaesthetes on the classic SNARC parity judgement task with lateralized response keys and a modified version in which they responded to labels appearing on screen. Synaesthetes' behaviour was expected to differ from nonsynaesthetes' behaviour due to the explicit, fixed nature of their number–space associations, but both experiments show the two groups behaving in the same way, indicating that parity judgement tasks may not be tapping the same representation of number that gives rise to synaesthetic number–space experiences.     

The SNARC effect in the processing of second-language number words: Further evidence for strong lexico-semantic connections

We present new evidence that word translation involves semantic mediation. It has been shown that participants react faster to small numbers with their left hand and to large numbers with their right hand. This SNARC (spatial-numerical association of response codes) effect is due to the fact that in Western cultures the semantic number line is oriented from left (small) to right (large). We obtained a SNARC effect when participants had to indicate the parity of second-language (L2) number words, but not when they had to indicate whether L2 number words contained a particular sound. Crucially, the SNARC effect was also obtained in a translation verification task, indicating that this task involved the activation of number magnitude.     

Developing number–space associations: SNARC effects using a color discrimination task in 5-year-olds

Human adults’ numerical representation is spatially oriented; consequently, participants are faster to respond to small/large numerals with their left/right hand, respectively, when doing a binary classification judgment on numbers, known as the SNARC (spatial–numerical association of response codes) effect. Studies on the emergence and development of the SNARC effect remain scarce. The current study introduces an innovative new paradigm based on a simple color judgment of Arabic digits. Using this task, we found a SNARC effect in children as young as 5.5 years. In contrast, when preschool children needed to perform a magnitude judgment task necessitating exact number knowledge, the SNARC effect started to emerge only at 5.8 years. Moreover, the emergence of a magnitude SNARC but not a color SNARC was linked to proficiency with Arabic digits. Our results suggest that access to a spatially oriented approximate magnitude representation from symbolic digits emerges early in ontogenetic development. Exact magnitude judgments, on the other hand, rely on experience with Arabic digits and, thus, necessitate formal or informal schooling to give access to a spatially oriented numerical representation.     

正负数混合呈现对负数SNARC效应的影响

采用数字大小判断任务,探讨正负数混合呈现对负数SNARC效应的影响。结果发现,负数单独呈现条件下,负数出现反转的SNARC效应;负数和无加号正数混合呈现,且只对负数作反应条件下,负数有反转SNARC效应;负数和有加号正数混合呈现,且只对负数作反应条件下,负数出现反转SNARC效应;负数和无加号正数混合呈现,并对正负数分别作反应的条件下,负数有反转SNARC效应出现,而正数出现SNARC效应。说明负数空间表征受其绝对值大小的影响,绝对值较小的负数(-1、-2)表征在心理数字线的左侧,绝对值较大的负数(-8、-9)表征在数字线的右侧,且不能延伸至心理数字线左侧。     

正负数混合呈现对负数SNARC效应的影响

采用数字大小判断任务,探讨正负数混合呈现对负数SNARC效应的影响。结果发现,负数单独呈现条件下,负数出现反转的SNARC效应;负数和无加号正数混合呈现,且只对负数作反应条件下,负数有反转SNARC效应;负数和有加号正数混合呈现,且只对负数作反应条件下,负数出现反转SNARC效应;负数和无加号正数混合呈现,并对正负数分别作反应的条件下,负数有反转SNARC效应出现,而正数出现SNARC效应。说明负数空间表征受其绝对值大小的影响,绝对值较小的负数(-1、-2)表征在心理数字线的左侧,绝对值较大的负数(-8、-9)表征在数字线的右侧,且不能延伸至心理数字线左侧。     

Two routes for the processing of verbal numbers: evidence from the SNARC effect

The functional locus of the semantic system is an important issue in number processing. In the present article, the necessity of addressing a central semantic magnitude system in the processing of printed verbal number words is evaluated by looking at the presence of a spatial-numerical association of response codes or SNARC effect. This effect consists of an association of number magnitude and response-preference (preferred responses to small numbers with the left hand and to large numbers with the right hand) and reflects semantic access. Two experiments were run. In Experiment 1, participants performed a parity judgment task which requires access to number semantics. A SNARC effect was observed. In Experiment 2 a phoneme monitoring task was used, which can, in principle, be performed through direct asemantic transcoding. No SNARC effect occurred. Apparently, written number words access the semantic system only if this is necessary for correct task completion. Hence, a semantic and an asemantic route can be postulated for the processing of word numerals. These observations contrast with the processing of Arabic numerals for which semantic effects are omnipresent. Implications of this explicit demonstration of a dissimilarity between the processing of digits and of number words are discussed. Received: 25 October 2000 / Accepted: 21 May 2001     

The SNARC effect in the processing of second-language number words: further evidence for strong lexico-semantic connections

We present new evidence that word translation involves semantic mediation. It has been shown that participants react faster to small numbers with their left hand and to large numbers with their right hand. This SNARC (spatial-numerical association of response codes) effect is due to the fact that in Western cultures the semantic number line is oriented from left (small) to right (large). We obtained a SNARC effect when participants had to indicate the parity of second-language (L2) number words, but not when they had to indicate whether L2 number words contained a particular sound. Crucially, the SNARC effect was also obtained in a translation verification task, indicating that this task involved the activation of number magnitude.     

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.     

Moving the eyes along the mental number line: comparing SNARC effects with saccadic and manual responses

Bimanual parityjudgments about numerically small (large) digits are faster with the left (right) hand, even though parity is unrelated to numerical magnitude per se (the SNARC effect; Dehaene, Bossini, & Giraux, 1993). According to one model, this effect reflects a space-related representation of numerical magnitudes (mental number line) with a genuine left-to-right orientation. Alternatively, it may simply reflect an overlearned motor association between numbers and manual responses--as, for example, on typewriters or computer keyboards--in which case it should be weaker or absent with effectors whose horizontal response component is less systematically associated with individual numbers. Two experiments involving comparisons of saccadic and manual parity judgment tasks clearly support the first view; they also establish a vertical SNARC effect, suggesting that our magnitude representation resembles a number map, rather than a number line.     

Look,no hands: A perceptual task shows that number magnitude induces shifts of attention

The mental representation of numbers along a line oriented left to right affects spatial cognition, facilitating responses in the ipsilateral hemispace (the spatial-numerical association of response codes [SNARC] effect). We investigated whether the number/space association is the result of an attentional shift or response selection. Previous research has often introduced covert left/right response cues by presenting targets to the left or the right. The present study avoided left/right cues by requiring forced choice upper/lower luminance discriminations to two mirror-reversed luminance gradients (the grayscale task). The grayscale stimuli were overlaid with strings of (1) low numbers, (2) high numbers, and (3) nonnumerical characters. In Experiment 1, 20 dextrals judged the number’s magnitude and then indicated whether the upper/lower grayscale was darker. Results showed leftward and rightward attentional biases for low and high numbers, respectively. Demands to process numbers along a left/right line were made less explicit in Experiment 2 (N=8 dextrals), using (1) a parity judgment and (2) arbitrary linguistic labels for top/bottom. Once again, a spatial congruency effect was observed. Because the response (up/down) was orthogonal to the dimension of interest (left/right), the effect of number cannot be attributed to late-stage response congruencies. This study required unspeeded responses to stimuli presented in free vision, whereas other experiments have used speeded responses. Understanding the time course of number-space effects may, therefore, be important to the debate associated with response selection.     

Semantic congruity effects in judgments of loudness

This research uses comparative judgments of the relative loudness of sounds to make a critical test of one theory of the mental representation of continuous physical attributes. The first two experiments find a semantic congruity effect, which is an interaction such that subjects can pick the louder of two loud sounds faster than the softer, and the softer of two quiet sounds faster than the louder. According to the theory under test, physical quantities are stored as points on a representational continuum, with a variance as well as a mean placement on it. The theory predicts the semantic congruity effect by assuming that the variance of placement of intensities on the representational continuum is a function of the direction of judgment: a soft sound will have less variance than a loud one when judged for softness and more when judged for loudness. Since the speed of making a judgment increases as variance decreases, the theory predicts a semantic congruity effect. However, for loudness, it can be shown that variance does not change in the manner assumed. The finding of a semantic congruity effect therefore disconfirms the theory. Alternative models are discussed. This research was supported by NSF Grant BNS 78-17442.     

SNARC (spatial–numerical association of response codes) meets SPARC (spatial–pitch association of response codes): Automaticity and interdependency in compatibility effects

Concepts, including the mental number line, or addressing pitch as high and low, suggest that the spatial–numerical and spatial–pitch association of response codes (SNARC and SPARC) effects are domain-specific and thus independent. Alternatively, there may be dependencies between these effects, because they share common automatic or controlled decision mechanisms. In two experiments, participants were presented with spoken numbers in different pitches; their numerical value, pitch, and response compatibility were varied systematically. This allowed us to study SNARC and SPARC effects in a factorial design (see also Fischer, Riello, Giordano, &; Rusconi, 2013 Fischer, M. H., Riello, M., Giordano, B. L., &; Rusconi, E. (2013). Singing numbers?…?in cognitive space--a dual-task study of the link between pitch, space, and numbers. Topics in Cognitive Science, 5(2), 354–366. Retrieved from http://doi.org/10.1111/tops.12017[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Participants judged the stimuli on numerical magnitude, pitch, or parity (odd–even). In all tasks, the SNARC and SPARC effects had superadditive interactions. These were interpreted as both effects sharing a common mechanism. The task variation probes the mechanism: In the magnitude judgement task, numerical magnitude was explicit, whereas pitch was implicit; in the pitch judgement task, it was vice versa. In the parity judgement task, both dimensions were implicit. Regardless of whether they were implicit or explicit, both SNARC and SPARC effects occurred in all tasks. We concluded that by not requiring focal attention the common mechanism operates automatically.     

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.     

空间-数字反应编码联合效应下冲突适应过程的ERP研究

为了考察被试在不能意识到任务中包含冲突的情况下的认知控制过程,将产生SNARC效应的奇偶判断任务看作是一种潜在的冲突任务。大小与反应手一致的视为一致的试次,大小与反应手不一致的视为不一致的试次。根据不一致试次之前一个试次的类型将其划分为iI(不一致—不一致,incongruent-incongruent)试次和cI(一致—不一致,congruent-incongruent)试次两种类型。对冲突适应过程的分析表明iI试次的反应时显著快于cI试次,iI试次和cI试次相比,两者的脑电在大约260~300ms的时间段内在FCz位置上差异最大。偶极子分析表明差异波的产生源定位于背侧前扣带回(dorsal anterior cingulate cortex),这些结果与前扣带回的意识监测理论并不一致。最后结合冲突监测理论和其他解释前扣带回功能的理论对研究结果做了相应的解释,认为冲突适应可以是一个无意识的过程     

Developing access to number magnitude: a study of the SNARC effect in 7- to 9-year-olds

The SNARC (spatial-numerical association of response codes) effect refers to the finding that small numbers facilitate left responses, whereas larger numbers facilitate right responses. The development of this spatial association was studied in 7-, 8-, and 9-year-olds, as well as in adults, using a task where number magnitude was essential to perform the task and another task where number magnitude was irrelevant. When number magnitude was essential, a SNARC effect was found in all age groups. But when number magnitude was irrelevant, a SNARC effect was found only in 9-year-olds and adults. These results are taken to suggest that (a) 7-year-olds represent number magnitudes in a way similar to that of adults and that (b) when perceiving Arabic numerals, children have developed automatic access to magnitude information by around 9 years of age.     

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.     

The role of parity, physical size, and magnitude in numerical cognition: The SNARC effect revisited

People indicate the physical size or the parity status of small numbers faster by a left-hand key and those of larger numbers by a right-hand key. Because magnitude information is not required for successful performance in these tasks, the presence of a number-space association (the SNARC effect) has been taken to indicate the automatic activation of numerical magnitude in all tasks with numerals. In order to test this account, in a series of five experiments, we derived two consensual markers of automatic activation of irrelevant numerical magnitude, the size congruity effect (for judgments of physical size), and the Garner effect (for judgments of parity). Both markers were found independent of the SNARC effect. Consequently, we question the traditional explanation of the SNARC effect and offer an alternative account in terms of a highly overlearned stimulus-response loop.