A working memory account for spatial-numerical associations

Several psychophysical and neuropsychological investigations have suggested that the mental representation of numbers takes the form of a number line along which magnitude is positioned in ascending order according to our reading habits. A longstanding debate is whether this spatial frame is triggered automatically as intrinsic part of the number semantics or whether it constitutes a short-term representation constructed during task execution. Although several observations clearly favor the working memory account, its causal involvement has not yet been demonstrated. In two experiments we show that information stored in working memory get spatially coded in function of its ordinal position in the sequence and that the spatial–numerical associations typically observed in number categorization tasks draw upon this mechanism.     

Attentional SNARC: there's something special about numbers (let us count the ways)

We report a study that examines whether the presentation of irrelevant, ordinal information at central fixation interacts with the allocation of attention beyond fixation. Previous research has demonstrated that number perception influences the allocation of spatial attention, such that the presentation of a spatially nonpredictive number at fixation results in attention being allocated to the left when the central number is low (e.g., 1), and attention being allocated to the right when the central number is high (e.g., 9). Here, we examine whether this attentional SNARC effect (spatial numerical association of response codes) generalizes to other ordinal sequences: letters, days, and months. Though we replicate the attentional SNARC we find that this effect is number-specific, unless participants are required to process the cue in an order-relevant fashion. This discovery of number-specificity has important implications both for the functional separation between SNARC and attention-SNARC effects, as well as lending support to recent theories regarding the specificity of a shared neural architecture between numbers and visuospatial attention.     

Spatial representation of pitch height: the SMARC effect

Through the preferential pairing of response positions to pitch, here we show that the internal representation of pitch height is spatial in nature and affects performance, especially in musically trained participants, when response alternatives are either vertically or horizontally aligned. The finding that our cognitive system maps pitch height onto an internal representation of space, which in turn affects motor performance even when this perceptual attribute is irrelevant to the task, extends previous studies on auditory perception and suggests an interesting analogy between music perception and mathematical cognition. Both the basic elements of mathematical cognition (i.e. numbers) and the basic elements of musical cognition (i.e. pitches), appear to be mapped onto a mental spatial representation in a way that affects motor performance.     

情境对序数的空间表征之影响

通过设置垂直维度上不同的情境,本研究采用“奇偶判断任务”探讨了情境对序数空间表征的影响。结果发现,只有序数的情况下,被试对小数的上键反应或下键反应、对大数的上键反应或下键反应都没有显著差异;在楼层情境下,被试对小数的下键反应更快,对大数的上键反应更快;在家谱情境下,被试对小数的上键反应更快,对大数的下键反应更快。以上结果表明,垂直维度上序数的空间表征受到情境的影响,这说明在垂直维度上数字的空间表征具有动态性,且受到具体和情境的调节。     

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.     

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.     

数字SNARC效应中大小和顺序信息的分离*

分别以经度数和语言等级数为材料,采用快速刺激分类范式,通过两个实验试图分离出SNARC效应中的数字大小和顺序信息。结果发现,被试在对东经经度数的加工中存在SNARC效应,对西经经度数的加工出现反转的SNARC效应;正数组被试在汉语等级数加工中出现反转的SNARC效应,在日语等级数加工中出现SNARC效应,而负数组恰好相反。本研究表明,数字SNARC效应在大小信息和顺序信息中出现了分离,相较数字的大小信息而言,数字的顺序信息对SNARC效应影响更大。     

Is Emotional Magnitude Spatialized? A Further Investigation

Accumulating evidence suggests that different magnitudes (e.g., number, size, and duration) are spatialized in the mind according to a common left–right metric, consistent with a generalized system for representing magnitude. A previous study conducted by two of us (Holmes & Lourenco, 2011 ) provided evidence that this metric extends to the processing of emotional magnitude, or the intensity of emotion expressed in faces. Recently, however, Pitt and Casasanto ( 2018 ) showed that the earlier effects may have been driven by a left–right mapping of mouth size rather than emotional magnitude, and they found no evidence for an emotional magnitude mapping when using words as stimuli. Here, we report two new experiments that further examine these conclusions. In Experiment 1, using face stimuli with mouths occluded, we replicate the original finding: Less emotional faces were associated with the left and more emotional faces with the right. However, we also find that people can reliably infer the sizes of the occluded mouths, and that these inferred mouth sizes can explain the observed left–right mapping. In Experiment 2, we show that comparative judgments of emotional words yield a left–right mapping of emotional magnitude not attributable to stimulus confounds. Based on these findings, we concur with Pitt and Casasanto that faces pose challenges for isolating the forces driving spatialization, but we suggest that emotional magnitude, when assessed using unconfounded stimuli in a sufficiently sensitive task, may indeed be spatialized as originally proposed. Suggestions for further research on the spatialization of emotional magnitude are discussed.     

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.     

The mental representation of ordinal sequences is spatially organized

In the domain of numbers the existence of spatial components in the representation of numerical magnitude has been convincingly demonstrated by an association between number magnitude and response preference with faster left- than right-hand responses for small numbers and faster right- than left-hand responses for large numbers (Dehaene, S., Bossini, S., & Giraux, P. (1993) The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122, 371-396). Because numbers convey not only real or integer meaning but also ordinal meaning, the question of whether non-numerical ordinal information is spatially coded naturally follows. While previous research failed to show an association between ordinal position and spatial response preference, we present two experiments involving months (Experiment 1) and letters (Experiment 2) in which spatial coding is demonstrated. Furthermore, the response-side effect was obtained with two different stimulus-response mappings. The association occurred both when ordinal information was relevant and when it was irrelevant to the task, showing that the spatial component of the ordinal representation can be automatically activated.     

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.     

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。     

The development of ordinal numerical knowledge in infancy

A critical question in cognitive science concerns how numerical knowledge develops. One essential component of an adult concept of number is ordinality: the greater than and less than relationships between numbers. Here it is shown in two experiments that 11-month-old infants successfully discriminated, whereas 9-month-old infants failed to discriminate, sequences of numerosities that descended in numerical value from sequences that increased in numerical value. These results suggest that by 11 months of age infants possess the ability to appreciate the greater than and less than relations between numerical values but that this ability develops between 9 and 11 months of age. In an additional experiment 9-month-old infants succeeded at discriminating the ordinal direction of sequences that varied in the size of a single square rather than in number, suggesting that a capacity for non-numerical ordinal judgments may develop before a capacity for ordinal numerical judgments. These data raise many questions about how infants represent number and what happens between 9 and 11 months to support ordinal numerical judgments.     

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     

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.