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.     

Continuous visual properties of number influence the formation of novel symbolic representations

Numerical symbols are thought to be mapped onto preexisting nonsymbolic representations of number. A growing body of evidence suggests that nonsymbolic numerical processing is significantly influenced by the associated visual properties of continuous quantity (e.g., surface area, density), but their role in the acquisition of novel symbols is unknown. Forty undergraduate students were trained to associate novel abstract symbols with numerical magnitudes. Half of the symbols were associated with nonsymbolic arrays in which total surface area and numerosity were correlated (“congruent”), and the other symbols were associated with arrays in which total surface area was equated across numerosities (“incongruent”). As numbers are represented in multiple formats (words, digits, nonsymbolic arrays), we also tested whether providing auditory nonword labels facilitated symbol learning. Following training, participants engaged in speeded comparisons of the newly learnt symbols. Comparisons were affected by the ratio between the numerosities associated with each symbol, a characteristic marker of numerical processing. Furthermore, comparisons were hardest for large-ratio comparisons of symbols associated with incongruent area and numerosity pairing during learning. In turn, these findings call for the further investigation of visual parameters on the development of numerical cognition.     

Cross-notational semantic priming between symbolic and nonsymbolic numerosity

Symbolic and nonsymbolic numerosities produce similar behavioural effects and activate the same brain areas. These results have usually been interpreted in terms of a common, notation-independent magnitude representation. However, semantic priming between symbolic and nonsymbolic inputs has been somehow elusive (e.g., Koechlin, Naccache, Block, & Dehaene, 1999). In Experiment 1, we looked at whether cross-notational semantic priming depends on exact numerical meaning. Dice faces and digits were mixed as prime and target. Semantic priming occurred when prime and target were in the same notation as much as when they were in different notation. In Experiment 2, we found cross-notation semantic priming even when the nonsymbolic numerosity was presented as a set of random dots. Priming, however, occurred only from sets of dots to digit, not vice versa. These data support the computational model recently proposed by Verguts and Fias (2004; Verguts, Fias, & Stevens, 2005).     

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.     

SNARC效应: 现状、理论与建议

SNARC效应是当对数字进行奇偶判断时,即使数的奇偶性与数的大小无关,但右手（左手）对相对大（小）的数的反应快。首先介绍SNARC效应的起源和理论解释,然后总结SNARC效应的特性,论述SNARC效应和Simon效应以及MARC 效应的关系,并对SNARC效应的脑机制进行了概述,最后提出3个有待深入研究的问题：（1）SNARC效应的加工处理机制;（2）SANRC效应的理论探索;（3）SNARC效应的本质。     

Bad–good constraints on a polarity correspondence account for the spatial–numerical association of response codes (SNARC) and markedness association of response codes (MARC) effects

Performance in numerical classification tasks involving either parity or magnitude judgements is quicker when small numbers are mapped onto a left-sided response and large numbers onto a right-sided response than for the opposite mapping (i.e., the spatial–numerical association of response codes or SNARC effect). Recent research by Gevers et al. [Gevers, W., Santens, S., Dhooge, E., Chen, Q., Van den Bossche, L., Fias, W., & Verguts, T. (2010). Verbal-spatial and visuospatial coding of number–space interactions. Journal of Experimental Psychology: General, 139, 180–190] suggests that this effect also arises for vocal “left” and “right” responding, indicating that verbal–spatial coding has a role to play in determining it. Another presumably verbal-based, spatial–numerical mapping phenomenon is the linguistic markedness association of response codes (MARC) effect whereby responding in parity tasks is quicker when odd numbers are mapped onto left-sided responses and even numbers onto right-sided responses. A recent account of both the SNARC and MARC effects is based on the polarity correspondence principle [Proctor, R. W., & Cho, Y. S. (2006). Polarity correspondence: A general principle for performance of speeded binary classification tasks. Psychological Bulletin, 132, 416–442]. This account assumes that stimulus and response alternatives are coded along any number of dimensions in terms of – and + polarities with quicker responding when the polarity codes for the stimulus and the response correspond. In the present study, even–odd parity judgements were made using either “left” and “right” or “bad” and “good” vocal responses. Results indicated that a SNARC effect was indeed present for the former type of vocal responding, providing further evidence for the sufficiency of the verbal–spatial coding account for this effect. However, the decided lack of an analogous SNARC-like effect in the results for the latter type of vocal responding provides an important constraint on the presumed generality of the polarity correspondence account. On the other hand, the presence of robust MARC effects for “bad” and “good” but not “left” and “right” vocal responses is consistent with the view that such effects are due to conceptual associations between semantic codes for odd–even and bad–good (but not necessarily left–right).     

Intuitive mapping between nonsymbolic quantity and observed action across development

Adults’ concurrent processing of numerical and action information yields bidirectional interference effects consistent with a cognitive link between these two systems of representation. This link is in place early in life: infants create expectations of congruency across numerical and action-related stimuli (i.e., a small [large] hand aperture associated with a smaller [larger] numerosity). Although these studies point to a developmental continuity of this mapping, little is known about the later development and thus how experience shapes such relationships. We explored how number–action intuitions develop across early and later childhood using the same methodology as in adults. We asked 3-, 6-, and 8-year-old children, as well as adults, to relate the magnitude of an observed action (a static hand shape, open vs. closed, in Experiment 1; a dynamic hand movement, opening vs. closing, in Experiment 2) to either a small or large nonsymbolic quantity (numerosity in Experiment 1 and numerosity and/or object size in Experiment 2). From 6 years of age, children started performing in a systematic congruent way in some conditions, but only 8-year-olds (added in Experiment 2) and adults performed reliably above chance in this task. We provide initial evidence that early intuitions guiding infants’ mapping between magnitude across nonsymbolic number and observed action are used in an explicit way only from late childhood, with a mapping between action and size possibly being the most intuitive. An initial coarse mapping between number and action is likely modulated with extensive experience with grasping and related actions directed to both arrays and individual objects.     

壮族大学生一位数字词的SNARC效应

本研究以壮族大学生为被试,要求他们对壮语、汉语听觉数字词(实验一)或汉语、英语视觉数字词(实验二)进行奇偶判断。结果发现：(1)壮族大学生对汉语、壮语听觉数字词以及汉语、英语视觉数字词都表现出了SNARC效应。(2)数字词在听觉条件下和视觉条件下产生的SNARC效应的强度相当。(3)书写习惯也影响到壮语听觉数字的SNARC效应的方向。     

Generating nonsymbolic number stimuli

Studies investigating nonsymbolic numbers (e.g., dot arrays) are confronted with the problem that changes in numerosity are always accompanied by changes in the visual properties of the stimulus. It is therefore debated whether the visual properties of the stimulus rather than number can explain the results obtained in studies investigating nonsymbolic number processing. In this report, we present a program (available at ; note that the program is designed to work with the Psychophysics Toolbox in MATLAB) that exports information about the visual properties of stimuli that co-vary with number (area extended, item size, total surface, density, and circumference). Consequently, insight into the relation between the visual properties of the stimulus and numerical distance can be achieved, and post hoc analyses can be conducted to directly reveal whether numerical distance or (some combinations of) the visual properties of a stimulus could be the most likely candidate underlying the results. Here, we report data that demonstrate the program’s usefulness for research on nonsymbolic number stimuli.     

不同加工深度非符号数量信息的SNARC效应：眼动证据

通过两项眼动实验考察了个体在水平和垂直方向上对点阵数量进行较浅(浏览)和较深(数字比较)程度加工时的数量空间表征联系。结果显示：点阵在水平方向上出现了SNARC效应, 且SNARC效应的大小不受加工深浅的影响, 而在垂直方向上没有出现SNARC效应。表明(1)点阵数量SNARC效应的稳定性不如阿拉伯数字; (2)方向对点阵SNARC效应的影响更大, 加工程度的影响则不明显。结合加工程度、空间方向和点阵数量的自身特征等对研究发现进行了讨论, 认为数字的空间表征在多个因素的共同影响下可能呈现出多样性。     

刺激模拟量的空间表征:面积和亮度的类SNARC效应

在数字比较任务中的SNARC效应表明心理数字线具有空间上从左到右的方向性。本研究在两个实验中分别用面积和亮度作为比较刺激来探讨SNARC效应是否存在于面积比较任务和亮度比较任务中。实验结果显示,面积比较和亮度比较任务中存在类SNARC效应。     

Infants' enumeration of actions: numerical discrimination and its signature limits

Are abstract representations of number – representations that are independent of the particular type of entities that are enumerated – a product of human language or culture, or do they trace back to human infancy? To address this question, four experiments investigated whether human infants discriminate between sequences of actions (jumps of a puppet) on the basis of numerosity. At 6 months, infants successfully discriminated four‐ versus eight‐jump sequences, when the continuous variables of sequence duration, jump duration, jump rate, jump interval and duration, and extent of motion were controlled, and rhythm was eliminated. In contrast, infants failed to discriminate two‐ versus four‐jump sequences, suggesting that infants fail to form cardinal number representations of small numbers of actions. Infants also failed to discriminate between sequences of four versus six jumps at 6 months, and succeeded at 9 months, suggesting that infants’ number representations are imprecise and increase in precision with age. All of these findings agree with those of studies using visual–spatial arrays and auditory sequences, providing evidence that a single, abstract system of number representation is present and functional in infancy.     

Grammatical number elicits SNARC and MARC effects as a function of task demands

Despite the robustness of the spatial–numerical association of response codes (SNARC) and linguistic markedness of response codes (MARC) effect, the mechanisms that underlie these effects are still under debate. In this paper, we investigate the extraction of quantity information from German number words and nouns inflected for singular and plural using two alternative forced choice paradigms. These paradigms are applied to different tasks to investigate how access to quantity representation is modulated by task demands. In Experiment 1, we replicated previous SNARC findings for number words—that is, a relative left-hand advantage for words denoting small numbers and a right-hand advantage for words denoting large numbers in semantic tasks (parity decision and quantity comparison). No SNARC effect was obtained for surface or lexical processing tasks (font categorization and lexical decision). In Experiment 2, we found that German words inflected for singular had a relative left-hand advantage, and German words inflected for plural a relative right-hand advantage, showing a SNARC-like effect for grammatical number. The effect interfered, however, with a MARC-like effect based on the markedness asymmetry of singulars and plurals. These two effects appear to be dissociated by response latency rather than task demands, with MARC being more pronounced in early responses and SNARC being more pronounced in late responses. The present findings shed light on the relationship of conceptual number and grammatical number and constrain current accounts of the SNARC and MARC effects.     

数量空间表征的特点:跨视听通道下的SNARC效应

从跨通道的角度入手,采用大小比较任务,对视听单通道及跨通道下数量空间表征的特点及表征过程中的相互影响进行探讨。结果发现,视觉通道和听觉通道均存在SNARC效应;在跨通道任务下,无论启动通道是视觉还是听觉通道,都表现出,当启动通道的数量大小信息与主通道的数量大小一致或无关时,主通道的SNARC效应没有显著变化;但当启动通道的数量大小信息与主通道不一致时,主通道的SNARC效应受到显著影响,表现为降低或消失。这进一步证明了SNARC效应受情境影响的特点,并发现在进行跨通道数量空间表征时,听觉通道的数量信息对视觉通道下的数量空间表征的影响大于视觉通道的数量信息对听觉通道下的数量空间表征的影响。     

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.     

亮度对空间-数字反应编码联合效应的影响

本研究探讨亮度对空间-数字反应编码联合效应（Spatial-Numerical Association of Response Codes,简称SNARC效应）的影响及其机制。通过三个实验设计不同的亮度对比水平,要求被试对阿拉伯数字1~9（5除外）进行奇偶判断。实验一将数字亮度设为最高值255时,结果出现了数字的SNARC效应。实验二将数字的亮度值分别设为255和213时,结果仍存在SNARC效应。实验三将亮度值分别设置为213和42时,数字的SNARC效应却消失了。这些结果表明亮度会激活或抑制数字的空间表征,可能与亮度对比值的高低及所消耗认知资源的多少有关。     

How do people apprehend large numerosities?

People discriminate remarkably well among large numerosities. These discriminations, however, need not entail numerical representation of the quantities being compared. This research evaluated the role of both non-numerical and numerical information in adult judgments of relative numerosity for large-numerosity spatial arrays. Results of Experiment 1 indicated that judgments of relative numerosity were affected by the amount of open space in the arrays being compared. Further, the accuracy of verbal estimates of the numerosities of the arrays made upon completion of the comparison task bore little relation to performance on that task. Experiment 2, however, showed that numerical estimates for individually presented arrays were affected in much the same way by open space within or around the edges of the array as were the comparative judgments examined in Experiment 1. The findings suggest that adults heuristically utilize non-numerical cues as well as numerical information in apprehending large numerosities.     

The influence of time units on the flexibility of the spatial numerical association of response codes effect

The Spatial Numerical/Temporal Association of Response Codes (SNARC/STEARC) effects are considered evidence of the association between number or time and space, respectively. As the SNARC effect was proposed by Dehaene, Bossini, and Giraux in 1993, several studies have suggested that different tasks and cultural factors can affect the flexibility of the SNARC effect. This study explored the influence of time units on the flexibility of the SNARC effect via materials with Arabic numbers, which were suffixed with time units and subjected to magnitude comparison tasks. Experiment 1 replicated the SNARC effect for numbers and the STEARC effect for time units. Experiment 2 explored the flexibility of the SNARC effect when numbers were attached to time units, which either conflicted with the numerical magnitude or in which the time units were the same or different. Experiment 3 explored whether the SNARC effect of numbers was stable when numbers were near the transition of two adjacent time units. The results indicate that the SNARC effect was flexible when the numbers were suffixed with time units: Time units influenced the direction of the SNARC effect in a way which could not be accounted for by the mathematical differences between the time units and numbers. This suggests that the SNARC effect is not obligatory and can be easily adapted or inhibited based on the current context.     

SNARC effects with numerical and non-numerical symbolic comparative judgments: instructional and cultural dependencies

With English-language readers in an experiment requiring pairwise comparative judgments of the sizes of animals, the nature of the association between the magnitudes of the animal pairs and the left or right sides of response (i.e., the SNARC effect) was reversed depending on whether the participants had to choose either the smaller or the larger member of the pair. In contrast, such a dependence of the direction of the SNARC effect on the form of the comparative instructions was not evident for pairwise comparisons of numerical magnitude made by a similar group of participants. Furthermore, exactly the same configuration of findings was obtained for a single group of Israeli-Palestinian right-to-left reading and writing participants, except that the spatial direction of the SNARC effects for both the animal-size and number comparisons were completely reversed. In a final experiment with English readers, SNARC effects paralleling those for the animal-size comparisons were obtained for pairwise comparative judgments involving the just-learned height relations between 6 imaginary individuals. As will be discussed, such results serve to extend the generality of the SNARC effect far beyond the current modal view that it simply reflects culturally influenced, long-term learned associations between numerical magnitudes and the locations on a fixed mental number line. The implications that these results have for both the Proctor and Cho (2006) polarity correspondence view and the Gevers, Verguts, Reynvoet, Caessens, and Fias (2006) computational model of the SNARC effect will also discussed.     

Calibrating the mental number line

Human adults are thought to possess two dissociable systems to represent numbers: an approximate quantity system akin to a mental number line, and a verbal system capable of representing numbers exactly. Here, we study the interface between these two systems using an estimation task. Observers were asked to estimate the approximate numerosity of dot arrays. We show that, in the absence of calibration, estimates are largely inaccurate: responses increase monotonically with numerosity, but underestimate the actual numerosity. However, insertion of a few inducer trials, in which participants are explicitly (and sometimes misleadingly) told that a given display contains 30 dots, is sufficient to calibrate their estimates on the whole range of stimuli. Based on these empirical results, we develop a model of the mapping between the numerical symbols and the representations of numerosity on the number line.