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。     

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。     

The A Theory Of Magnitude (ATOM) model in temporal perception and reproduction tasks

According to the A Theory of Magnitude (ATOM) model, time, numbers and space are processed by a common analog magnitude system. The model proposes that time, numbers and space are influenced by each other. Indeed, spatial-temporal (STEARC effect), spatial-numerical (SNARC effect) and temporal-numerical (TiNARC effect) interactions have been observed. However, the processing of time, numbers and space has not yet been studied within the same experimental procedure. The goal of this study is to test the ATOM model using a procedure in which time, numbers and space are all present. The participants were asked to perform temporal estimation (Experiment 1) and reproduction (Experiment 2) tasks in two different conditions, with either numbers or letters as stimuli. In Experiment 1, significant STEARC, SNARC and TiNARC effects were found in general and when numbers were presented. Moreover, a significant triple interaction between space, time and magnitude was observed, indicating associations between the left key, short duration and small magnitudes, as well as between the right key, long duration and large magnitudes. These results were similar in reaction times and accuracy. In Experiment 2, the results of reproduction times mirrored the previous data but the triple interaction was not found on reproduction times. Considering the temporal accuracy, the STEARC, SNARC and TiNARC effects as well as triple interaction were found. The results seem to partially confirm the ATOM model, even if differences between temporal tasks should be posited.     

Spatializing Emotion: No Evidence for a Domain‐General Magnitude System

People implicitly associate different emotions with different locations in left‐right space. Which aspects of emotion do they spatialize, and why? Across many studies people spatialize emotional valence, mapping positive emotions onto their dominant side of space and negative emotions onto their non‐dominant side, consistent with theories of metaphorical mental representation. Yet other results suggest a conflicting mapping of emotional intensity (a.k.a., emotional magnitude), according to which people associate more intense emotions with the right and less intense emotions with the left — regardless of their valence; this pattern has been interpreted as support for a domain‐general system for representing magnitudes. To resolve the apparent contradiction between these mappings, we first tested whether people implicitly map either valence or intensity onto left‐right space, depending on which dimension of emotion they attend to (Experiments 1a, b). When asked to judge emotional valence, participants showed the predicted valence mapping. However, when asked to judge emotional intensity, participants showed no systematic intensity mapping. We then tested an alternative explanation of findings previously interpreted as evidence for an intensity mapping (Experiments 2a, b). These results suggest that previous findings may reflect a left‐right mapping of spatial magnitude (i.e., the size of a salient feature of the stimuli) rather than emotion. People implicitly spatialize emotional valence, but, at present, there is no clear evidence for an implicit lateral mapping of emotional intensity. These findings support metaphor theory and challenge the proposal that mental magnitudes are represented by a domain‐general metric that extends to the domain of emotion.     

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。     

Magnitude and Order are Both Relevant in SNARC and SNARC-like Effects: A Commentary on Casasanto and Pitt (2019)

In a recent paper by Casasanto and Pitt (2019), the authors addressed a debate regarding the role of order and magnitude in SNARC and SNARC-like effects. Their position is that all these effects can be explained by order, while magnitude could only account for a subset of evidence. Although we agree that order can probably explain the majority of these effects, in this commentary we argue that magnitude is still relevant, since there is evidence that cannot be explained based on ordinality alone. We argue that SNARC-like effects can occur for magnitudes not clearly characterized by overlearned ordinality and that magnitude can prevail on order, when the two are pitted against each other. Finally, we propose that different interpretations of the role of order and magnitude depend on the interaction of stimulus properties and task demands.     

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.     

SNARC for numerosities is modulated by comparative instruction (and resembles some non-numerical effects)

The spatial–numerical association of response codes (SNARC) effect is observed for both numerical (Arabic digits) and non-numerical stimuli (size, duration, height). However, in a context of comparative judgment, Arabic numbers are mapped onto space differently from sizes and heights: SNARC for Arabic digits is formed consistently in a certain cultural reading direction, whereas SNARC for sizes and heights is additionally modulated by comparative instruction (it reverses when participants choose larger magnitudes). In the present study, we test whether the spatial characteristic of magnitude processing revealed in a context of comparison is determined by a presence or lack of numerical content of the processed information, or it depends on specific directional experience (e.g., left-to-right ordering) associated with the processed magnitude format. We examine the SNARC effect with the pairwise comparison design, by using non-symbolic numerical stimuli (objects’ collections), for which the left-to-right spatial structure is not as exceedingly overlearned as for Arabic numbers. We asked participants from two reading cultures (left-to-right vs. mixed reading culture) to compare numerosities of two sets, choosing either a larger or smaller one. SNARC emerged in both groups. Additionally, it was modulated by comparative instruction: It appeared in a left-to-right direction when participants selected a smaller set, but it tended to reverse when participants selected a larger set. We conclude that spatial processing of numerosities is dissociated from spatial processing of Arabic numbers, at least in a context of comparative judgment. This dissociation could reflect differences in spatial ordering experience specific to a certain numerical input.     

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。     

Loudness counts: Interactions between loudness,number magnitude,and space

ATOM (a theory of magnitude) suggests that magnitude information of different formats (numbers, space, and time) is processed within a generalized magnitude network. In this study we investigated whether loudness, as a possible indicator of intensity and magnitude, interacts with the processing of numbers. Small and large numbers, spoken in a quiet and a loud voice, were simultaneously presented to the left and right ear (Experiments 1a and 1b). Participants judged whether the number presented to the left or right ear was louder or larger. Responses were faster when the smaller number was spoken in a quiet voice, and the larger number in a loud voice. Thus, task-irrelevant numerical information influenced the processing of loudness and vice versa. This bi-directional link was also confirmed by classical SNARC paradigms (spatial–numerical association of response codes; Experiments 2a–2c) when participants again judged the magnitude or loudness of separately presented stimuli. In contrast, no loudness–number association was found in a parity judgment task. Regular SNARC effects were found in the magnitude and parity judgment task, but not in the loudness judgment task. Instead, in the latter task, response side was associated with loudness. Possible explanations for these results are discussed.     

Is more always up? Evidence for a preference of hand-based associations over vertical number mappings

It has been argued that the association of numbers and vertical space plays a fundamental role for the understanding of numerical concepts. However, convincing evidence for an association of numbers and vertical bimanual responses is still lacking. The present study tests the vertical Spatio-Numerical-Association-of-Response-Codes (SNARC) effect in a number classification task by comparing anatomical hand-based and spatial associations. A mixed effects model of linear spatial-numerical associations revealed no evidence for a vertical but clear support for an anatomical SNARC effect. Only if the task requirements prevented participants from using a number-hand association due to frequently alternating hand-to-button assignments, numbers were associated with the vertical dimension. Taken together, the present findings question the importance of vertical associations for the conceptual understanding of numerical magnitude as hypothesised by some embodied approaches to number cognition and suggest a preference for ego- over geocentric reference frames for the mapping of numbers onto space.     

基于增强现实和ERPs架构的SNARC效应展望

SNARC效应是人类空间认知的重要组成部分。限于技术手段,现有SNARC研究的理论和技术多以小尺度空间环境为基础,致使其生态效度较低。基于增强现实技术和认知神经科学范式,通过增强现实技术生成的交互情境,从核心加工系统(静态空间SNARC、动态空间SNARC、静态-动态联合SNARC)和加工特性两个方面,研究建立起基于大尺度空间环境的SNARC加工模型。为人类空间认知研究提供了更加完备的知识领域。     

Task instructions determine the visuospatial and verbal–spatial nature of number–space associations

Evidence for number–space associations comes from the spatial–numerical association of response codes (SNARC) effect, consisting in faster reaction times to small/large digits with the left/right hand, respectively. Two different proposals are commonly discussed concerning the cognitive origin of the SNARC effect: the visuospatial account and the verbal–spatial account. Recent studies have provided evidence for the relative dominance of verbal–spatial over visuospatial coding mechanisms, when both mechanisms were directly contrasted in a magnitude comparison task. However, in these studies, participants were potentially biased towards verbal–spatial number processing by task instructions based on verbal–spatial labels. To overcome this confound and to investigate whether verbal–spatial coding mechanisms are predominantly activated irrespective of task instructions, we completed the previously used paradigm by adding a spatial instruction condition. In line with earlier findings, we could confirm the predominance of verbal–spatial number coding under verbal task instructions. However, in the spatial instruction condition, both verbal–spatial and visuospatial mechanisms were activated to an equal extent. Hence, these findings clearly indicate that the cognitive origin of number–space associations does not always predominantly rely on verbal–spatial processing mechanisms, but that the spatial code associated with numbers is context dependent.     

Spatial reference frames and SNARC

In this work, the role that spatial reference frames play in determining the spatial-numerical association of response codes (SNARC) effect is examined. Participants were instructed to generate an image of the numbers 1–9 oriented spatially in either a horizontal, vertical, or proximo-distal manner. Responses to a magnitude comparison task were then provided manually using keys located either to the left and right or at the bottom and top of a computer keyboard. For conditions in which the orientation of the generated image and the response locations were orthogonally misaligned, SNARC effects were not evident. It is argued that such results imply that alignment of the spatial reference frames associated with the responses and with the representation of numerical magnitude is a necessary condition for the elicitation of the SNARC effect.     

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.     

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.     

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。     

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.     

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。