Towards a common processing architecture underlying Simon and SNARC effects

It has been shown repeatedly that relatively small numbers are responded to faster with the left hand and relatively large numbers are responded to faster with the right hand. This so-called SNARC effect (Dehaene, Bossini, & Giraux, 1993) is thought to arise through activation of irrelevant spatial codes associated with the magnitude of the number. This conflict between irrelevant magnitude information and the response is conceptually similar to the well-known Simon effect. Recently, both Mapelli, Rusconi, and Umiltà (2003) and Keus and Schwarz (in press) directly compared both effects in a single task within the framework of the additive factor method (Sternberg, 1969). While Mapelli et al. found additive effects of SNARC and Simon levels, suggesting different processing stages, Keus and Schwarz found that the SNARC effect depended on the compatibility level of the Simon task leading them to propose a common origin at the response selection stage. In the present study we demonstrate in 2 experiments that the relationship between Simon and SNARC depends on the relevance of the magnitude code, thereby violating one of the core assumptions of the AFM. Instead we propose a temporal overlap model to interpret the relationship between these effects which allows to commensurate apparently divergent outcomes.     

数字的空间特性

当要求被试对数字进行奇偶判断时,左手对小数的反应较快,而右手对大数的反应较快,该现象被称为空间数字反应编码联合效应（SNARC效应）。大量研究证实了SNARC效应的存在,该效应表明人类对数字的加工受空间表征和空间注意的影响。该文系统地回顾了SNARC效应存在及其发生阶段的证据,对比了Simon效应与SNARC效应,最后尝试着从空间注意的角度挖掘数字和空间的本质联     

Language statistics explain the spatial–numerical association of response codes

The spatial–numerical association of response codes (SNARC) has shown that parity judgments with participants’ left hands yield faster response times (RTs) for smaller numbers than for larger numbers, with the opposite result for right-hand responses. These findings have been explained by participants perceptually simulating magnitude on a mental number line. In three RT experiments, we showed that the SNARC effect can also be explained by language statistics. Participants made parity judgments of number words (Exp. 1) and Arabic numerals (Exp. 2). Linguistic frequencies of the number words and numbers mirrored the SNARC effect, explaining aspects of processing that a perceptual simulation account could not. In Experiment 3, we investigated whether high- and low-frequency nonnumerical words would also elicit a SNARC-like effect. Again, RTs were faster for high-frequency words for left-hand responses, with the opposite result for right-hand responses. These results demonstrate that what has only been attributed to perceptual simulation should also be attributed to language statistics.     

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.     

贵州少数民族儿童青少年SNARC效应的发展

采用奇偶判断任务,考察二年级至大学阶段贵州民族儿童青少年SNARC效应的发展状况。结果显示：三年级开始出现SNARC效应（包括正确率SNARC效应）;各阶段SNARC效应无显著差异;高、低年级正确率存在显著差异,六年级以后各阶段正确率无显著差异。结论：民族儿童三年级开始形成数字的空间表征。SNARC效应的大小不因年龄而发生变化;被试对奇偶知识的掌握存在发展过程,三年级可能基本理解奇偶信息,六年级后熟练掌握奇偶信息。     

Visuospatial priming of the mental number line

It has been argued that numbers are spatially organized along a "mental number line" that facilitates left-hand responses to small numbers, and right-hand responses to large numbers. We hypothesized that whenever the representations of visual and numerical space are concurrently activated, interactions can occur between them, before response selection. A spatial prime is processed faster than a numerical target, and consistent with our hypothesis, we found that such a spatial prime affects non-spatial, verbal responses more when the prime follows a numerical target (backward priming) then when it precedes it (forward priming). This finding emerged both in a number-comparison and a parity judgment task, and cannot be ascribed to a "Spatial-Numerical Association of Response Codes" (SNARC). Contrary to some earlier claims, we therefore conclude that visuospatial-numerical interactions do occur, even before response selection.     

Searching for the functional locus of the SNARC effect: Evidence for a response-related origin

Dehaene, Bossini, and Giraux (1993) showed that when participants make parity judgments, responses to numerically small numbers are made faster with the left hand, whereas responses to large numbers are made faster with the right hand (the SNARC [spatial-numerical association of response codes] effect). According to one view, the SNARC effect arises at an early processing stage due to (in)congruencies between the digit's side of presentation and its representation on the mental number line, independently of response effector(s). Alternatively, the SNARC effect might arise at a later response-related stage due to (in)congruencies between the digit's representation on the mental number line and the side of response, independently of the side of presentation. The results of three experiments, using central and lateralized stimuli, and vocal and manual responses, clearly support the view that the SNARC effect arises at a relatively late response-related stage, without substantive contributions from earlier processing stages.     

身体形式和社会环境对SNARC效应的影响:基于具身认知观的理解

目前SNARC效应在认知心理学领域得到了广泛研究,然而较少有研究考察身体形式和社会环境对SNARC效应的影响.研究以127名在校大学生为被试,使用奇偶判断任务、Go/No-go任务以及合作情境下的Go/No-go任务依次展开了三个研究,拟揭示身体形式和社会环境对SNARC效应的影响.实验一要求被试双手完成奇偶判断任务,结果出现了经典的SNARC效应.实验二要求被试完成Go/No-go任务,并让被试单手(左手或右手)对奇数或偶数进行反应,结果SNARC效应没有出现,这表明认知主体的身体形式对SNARC效应产生了影响.实验三要求被试合作完成Go/No-go任务,该实验按照被试所坐的位置(左边和右边)和反应手(左手和右手),设计了四个条件,结果只有身体位置和反应手完全一致时出现了 SNARC 效应.以上结果一方面表明了具身认知观的合理性,另外一方面扩展了以往对SNARC效应本质的理解.     

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 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.     

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。     

数字空间联结的灵活性及其内在机制

数字空间联结一直是认知心理学领域研究的热点之一。探索数字空间联结的一个重要指标为空间-数字反应联合编码(spatial-numerical association of response codes, SNARC)效应(左/右手对小/大数反应更快更准确)。以往研究已验证SNARC效应的普遍性及其在方向上的灵活性, 并提出多种理论解释。此外, SNARC效应在加工阶段上也具有灵活性, 其原因可能有：(1)加因素法则的理解偏差; (2)观察的角度单一; (3)观察效标的差异; (4)使用任务的差异。结合以上因素, 提出双阶段(数量信息的空间表征、空间表征到反应选择)加工模型, 不同的操控因素分别作用于两个阶段可能是引起SNARC效应灵活变化的核心原因。未来研究可从对比任务差异、引入不同干扰因素等方面进一步验证双阶段加工模型, 并结合认知神经科学技术揭示数字空间联结灵活性的内在神经机制。     

Left hemisphere specialization for response to positive emotional expressions: a divided output methodology

An extensive literature credits the right hemisphere with dominance for processing emotion. Conflicting literature finds left hemisphere dominance for positive emotions. This conflict may be resolved by attending to processing stage. A divided output (bimanual) reaction time paradigm in which response hand was varied for emotion (angry; happy) in Experiments 1 and 2 and for gender (male; female) in Experiment 3 focused on response to emotion rather than perception. In Experiments 1 and 2, reaction time was shorter when right-hand responses indicated a happy face and left-hand responses an angry face, as compared to reversed assignment. This dissociation did not obtain with incidental emotion (Experiment 3). Results support the view that response preparation to positive emotional stimuli is left lateralized.     

Spatial representations in number processing--evidence from a pointing task

This study investigated cognitive interactions between visuo-motor processing and numerical cognition. In a pointing task healthy participants moved their hand to a left or right target, depending on the parity of small or large digits (1, 2, 8, or 9) shown at central fixation. Movement execution was faster when left-responses were made to small digits and right-responses to large digits. These results extend the SNARC effect (spatial-numerical association of response codes) to manual pointing and support the notion of a spatially oriented mental number line.     

大小判断任务中正负号及其异同对SNARC效应的影响

SNARC效应(Spatial-Numerical Association of Response Codes)是指被试对数字做按键反应时,对于较小的数字,按左键的速度快于按右键;对于较大的数字,按右键的速度快于按左键。本研究以ERP作为测量手段,采用修正的大小判断任务,旨在探究数字正负号及其异同对SNARC效应的影响。行为结果发现,在反应时上,当目标数字与基线数字正负号相同且基线数字为+5时,一致条件显著快于不一致条件。ERP结果发现,当目标数字与基线数字正负号相同时,无论基线数字为+5还是–5,在反应选择阶段,不一致都比一致条件更负且均诱发了P3。当目标数字与基线数字正负号相异时,若基线数字为+5,一致比不一致条件在刺激呈现阶段诱发了波幅显著更小的N300;若基线数字为–5,一致比不一致条件在反应执行阶段诱发了更正的LPP。无论目标数字与基线数字正负号相同还是相异,在反应选择阶段,不一致都比一致条件更负且均诱发了P3,表明出现了SNARC效应。同时,SNARC效应的出现激活了额叶头皮位置,负数加工伴随左额叶的激活,而正数加工伴随右额叶的激活,溯源分析结果进一步表明SNARC效应定位于额叶与顶叶。这些结果说明负数按实际大小表征在心理数字线上,支持了负数空间表征的个体发展论假说;表明符号捷径机制会改变SNARC效应的发生时间;同时证明了负数与正数的空间表征具有不同的优势半球。     

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。     

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.     

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.     

Numbers and space: a computational model of the SNARC effect

The SNARC (spatial numerical associations of response codes) effect reflects the tendency to respond faster with the left hand to relatively small numbers and with the right hand to relatively large numbers (S. Dehaene, S. Bossini, & P. Giraux, 1993). Using computational modeling, the present article aims to provide a framework for conceptualizing the SNARC effect. In line with models of spatial stimulus-response congruency, the authors modeled the SNARC effect as the result of parallel activation of preexisting links between magnitude and spatial representation and short-term links created on the basis of task instructions. This basic dual-route model simulated all characteristics associated with the SNARC effect. In addition, 2 experiments tested and confirmed new predictions derived from the model.