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。     

The role of working memory in the association between number magnitude and space

In two experiments, participants performed a magnitude comparison task in single and dual-task conditions. In the dual conditions, the comparison task was accomplished while phonological or visuospatial information had to be maintained for a later recall test. The results showed that the requirement of maintaining visuospatial information produced the lack of spatial-numerical association of response codes (SNARC) effect. The SNARC effect was not found even when the performance in the comparison task did not decline, as indicated by a similar distance effect in all conditions. These results show a special role for the visuospatial component of working memory in the processing of spatial representation of numbers and an interesting dissociation between SNARC and distance effects.     

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。     

The SNARC effect: an instance of the Simon effect?

Our aim was to investigate the relations between the Spatial-Numerical Association of Response Codes (SNARC) effect and the Simon effect. In Experiment 1 participants were required to make a parity judgment to numbers from 1 to 9 (without 5), by pressing a left or a right key. The numbers were presented to either the left or right side of fixation. Results showed the Simon effect (left-side stimuli were responded to faster with the left hand than with the right hand whereas right-side stimuli were responded to faster with the right hand), and the SNARC effect (smaller numbers were responded to faster with the left hand than with the right hand, whereas larger numbers were responded to faster with the right hand). No interaction was found between the Simon and SNARC effects, suggesting that they combine additively. In Experiment 2 the temporal distance between formation of the task-relevant non-spatial stimulus code and the task-irrelevant stimulus spatial code was increased. As in Experiment 1, results showed the presence of the Simon and SNARC effects but no interaction between them. Moreover, we found a regular Simon effect for faster RTs, and a reversed Simon effect for longer RTs. In contrast, the SNARC effect did not vary as a function of RT. Taken together, the results of the two experiments show that the SNARC effect does not simply constitute a variant of the Simon effect. This is considered to be evidence that number representation and space representation rest on different neural (likely parietal) circuits.     

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.     

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.     

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.     

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。     

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。     

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.     

Implicit and explicit spatial-numerical representations diverge in number-form synesthetes

In number-form (NF) synesthesia—a condition in which people report vivid, automatic and consistent mental layouts for numerical sequences—numbers and space are closely linked. These explicit associations are similar to the implicit associations demonstrated by the Spatial-Numerical Association of Response Codes (SNARC) effect. Thus, NF synesthesia offers a unique opportunity to investigate spatial-numerical associations. We tested implicit and explicit representations in NF synesthetes using a multiple case-study design. Over two sessions, synesthetes participated in a semi-structured interview focusing on the nature of their associations, as well as SNARC and number line estimation tasks. Contrary to our hypotheses, only one synesthete demonstrated SNARC effects congruent with her reported form, whereas two others exhibited SNARC effects that were the opposite of their explicit NFs. While this inconsistency between implicit and explicit representations may indicate separate underlying cognitive mechanisms, factors such as task-specific constraints and strategic variability must also be considered.     

The impact of inhibition capacities and age on number–space associations

Numerical and spatial representations are tightly linked, i.e., when doing a binary classification judgment on Arabic digits, participants are faster to respond with their left/right hand to small/large numbers, respectively (Spatial-Numerical Association of Response Codes, SNARC effect, Dehaene et al. in J Exp Psychol Gen 122:371–396, 1993). To understand the underlying mechanisms of the well-established SNARC effect, it seems essential to explore the considerable inter-individual variability characterizing it. The present study assesses the respective roles of inhibition, age, working memory (WM) and response speed. Whereas these non-numerical factors have been proposed as potentially important factors to explain individual differences in SNARC effects, none (except response speed) has so far been explored directly. Confirming our hypotheses, the results show that the SNARC effect was stronger in participants that had weaker inhibition abilities (as assessed by the Stroop task), were relatively older and had longer response times. Interestingly, whereas a significant part of the age influence was mediated by cognitive inhibition, age also directly impacted the SNARC effect. Similarly, cognitive inhibition abilities explained inter-individual variability in number–space associations over and above the factors age, WM capacity and response speed. Taken together our results provide new insights into the nature of number–space associations by describing how these are influenced by the non-numerical factors age and inhibition.     

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.     

Spatial representation of magnitude in humans (<Emphasis Type="Italic">Homo sapiens</Emphasis>), Western lowland gorillas (<Emphasis Type="Italic">Gorilla gorilla gorilla</Emphasis>), and American black bears (<Emphasis Type="Italic">Ursus americanus</Emphasis>)

The spatial-numerical association of response codes (SNARC) effect is the tendency for humans to respond faster to relatively larger numbers on the left or right (or with the left or right hand) and faster to relatively smaller numbers on the other side. This effect seems to occur due to a spatial representation of magnitude either in occurrence with a number line (wherein participants respond to relatively larger numbers faster on the right), other representations such as clock faces (responses are reversed from number lines), or culturally specific reading directions, begging the question as to whether the effect may be limited to humans. Given that a SNARC effect has emerged via a quantity judgement task in Western lowland gorillas and orangutans (Gazes et al., Cog 168:312–319, 2017), we examined patterns of response on a quantity discrimination task in American black bears, Western lowland gorillas, and humans for evidence of a SNARC effect. We found limited evidence for SNARC effect in American black bears and Western lowland gorillas. Furthermore, humans were inconsistent in direction and strength of effects, emphasizing the importance of standardizing methodology and analyses when comparing SNARC effects between species. These data reveal the importance of collecting data with humans in analogous procedures when testing nonhumans for effects assumed to bepresent in humans.     

The SNARC effect is not a unitary phenomenon

Models of the spatial–numerical association of response codes (SNARC) effect—faster responses to small numbers using left effectors, and the converse for large numbers—diverge substantially in localizing the root cause of this effect along the numbers’ processing chain. One class of models ascribes the cause of the SNARC effect to the inherently spatial nature of the semantic representation of numerical magnitude. A different class of models ascribes the effect’s cause to the processing dynamics taking place during response selection. To disentangle these opposing views, we devised a paradigm combining magnitude comparison and stimulus–response switching in order to monitor modulations of the SNARC effect while concurrently tapping both semantic and response-related processing stages. We observed that the SNARC effect varied nonlinearly as a function of both manipulated factors, a result that can hardly be reconciled with a unitary cause of the SNARC effect.     

Spatial associations in number-related tasks: A comparison of manual and pedal responses

Bimanual parity judgments of numerically small (large) digits are faster with the left (right) hand (the SNARC effect; Dehaene, Bossini, & Giraux, 1993). According to one explanation, this effect is culturally derived and reflects ontogenetic influences such as the direction of written language; it might therefore be limited to, or at least be larger with, pairs of lateralized effectors which are instrumental to the production and comprehension of written language. We report two experiments which test for SNARC effects with pedal responses, and compare these effects to manual results. Pedal responses yielded highly systematic SNARC effects; furthermore, these effects did not differ from manual SNARC effects. These results argue against accounts in which the SNARC effect is specific for effectors that are habitually associated with the production or comprehension of written language.     

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.     

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.