Dissociation of the distance effect and size effect in one-digit numbers

Magnitude comparison of single digits is robustly characterized by a distance effect (close numbers are more difficult to compare than numbers further apart) and a size effect (for a given distance, comparison difficulty increases with increasing size). The distance effect indicates access to the mental number line (Dehaene, 1997), and the size effect is usually interpreted as indicating that the mental number line represents larger numbers more vaguely than smaller ones. In contrast, we have argued earlier (Verguts, Fias, & Stevens, 2005) that for symbolic numbers (Arabic or verbal notation), the size effect does not originate from the mental number line but, instead, originates from mappings to relevant output components that are specific for magnitude comparison. If the latter is true, it should be possible to dissociate the distance effect from the size effect in tasks other than magnitude comparison. In two experiments, we observed a robust distance effect insame/different judgments, which implies access to the mental number line. Yet the size effect was absent. Consistent with our prediction, this finding establishes a dissociation between the size effect and the distance effect.     

Moving the eyes along the mental number line: comparing SNARC effects with saccadic and manual responses

Bimanual parityjudgments about numerically small (large) digits are faster with the left (right) hand, even though parity is unrelated to numerical magnitude per se (the SNARC effect; Dehaene, Bossini, & Giraux, 1993). According to one model, this effect reflects a space-related representation of numerical magnitudes (mental number line) with a genuine left-to-right orientation. Alternatively, it may simply reflect an overlearned motor association between numbers and manual responses--as, for example, on typewriters or computer keyboards--in which case it should be weaker or absent with effectors whose horizontal response component is less systematically associated with individual numbers. Two experiments involving comparisons of saccadic and manual parity judgment tasks clearly support the first view; they also establish a vertical SNARC effect, suggesting that our magnitude representation resembles a number map, rather than a number line.     

Automatic activation of spatial-numerical association in a primed parity judgement task: Evidence from the number-line congruency effect

Using a forward masked priming paradigm, the present parity judgement experiment examines how the automatic activation of spatial-numerical associations of single-digit primes and targets has an effect on the primed Spatial-Numerical Association Response Code (SNARC) effect. Both the parity priming effect (i.e., faster and more accurate responses when the prime and target are matched in parity) and the repetition-primed SNARC effect (i.e., responses to large numbers are faster when made by right hand than when made by left hand and the reverse is true for small numbers) are replicated. The nonrepetition-primed SNARC effect is stronger when the response (e.g., made by the left hand) to the target (e.g., 4) is congruent with the position of the prime on a mental number line (e.g., 6) than when it is incongruent (e.g., 1). This number-line congruency effect reflects the notion that the coactivation of spatial-numerical association of prime and target occurs even when the prime is masked and presented so rapidly that it cannot be processed via participants’ use of strategies.     

A mere exposure effect for transformed three-dimensional objects: Effects of reflection, size, or color changes on affect and recognition

If the mere exposure effect is based on implicit memory, recognition and affect judgments should be dissociated by experimental variables in the same manner as other explicit and implicit measures. Consistent with results from recognition and picture naming or object decision priming tasks (e.g., Biederman & E. E. Cooper, 1991, 1992; L. A. Cooper, Schacter, Ballesteros, & Moore, 1992), the present research showed that recognition memory but not affective preference was impaired by reflection or size transformations of three-dimensional objects between study and test. Stimulus color transformations had no effect on either measure. These results indicate that representations that support recognition memory code spatial information about an object’s left-right orientation and size, whereas representations that underlie affective preference do not. Insensitivity to surface feature changes that do not alter object form appears to be a general characteristic of implicit memory measures, including the affective preference task.     

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。     

Cross-notation number priming investigated at different stimulus onset asynchronies in parity and naming tasks

In this paper, a parity judgment task and a number naming task were used to investigate cross-notational number priming. Primes and targets could be verbal (e.g., seven) or Arabic numbers (e.g., 7), and were always presented in a different notation within the same trial (either a verbal prime and an Arabic target or an Arabic prime and a verbal target). Previous experiments showed that response latencies increase when the distance between prime and target increases (for example, in a naming task, seven is pronounced faster after 6 than after 5). This semantic distance priming effect was the same for Arabic and verbal targets and was the same for within-notation trials as for cross-notation trials. In the present experiments, we wanted to investigate whether the cross-notational priming effect also occurs at SOAs shorter than the ones used in previous experiments. Therefore, we used SOAs of 43, 57, 86, and 115 ms. Semantic distance effects were indeed present at these shorter SOAs: Processing times in the semantic parity judgment task and in the non-semantic naming task increased when the distance between prime and target increased. The results are discussed and integrated within an interactive dual-route model of number processing that postulates that the impact of the semantic and the non-semantic route depends on the task and the notation of the stimuli.     

Further evidence that the SNARC effect is processed along a dual-route architecture: Evidence from the lateralized readiness potential

In a binary response setting, it has been frequently observed that small numbers are reacted to faster with the left hand and large numbers with the right hand (i. e., the SNARC-effect) which reflects the spatial left-right orientation of the mental number line (Dehaene, Bossini, & Giraux, 1993). In line with the work of Keus and Schwarz (in press), we investigated the locus of the conflict in the SNARC effect in a parity judgment task with the Arabic numerals 1, 2, 8, or 9. Differences between compatible (left-hand response to 1 or 2 and right-hand response to 8 and 9) and incompatible SNARC conditions (left-hand response to 8 or 9 and right-hand response to 1 or 2) were observed in the lateralized readiness potential (LRP) but not in the peak latency of the P300. In accordance with Keus and colleagues (Keus, Jenks, & Schwarz, 2005), we argue that the locus of the conflict is situated at intermediate response-related stages. However, instead of adopting a single-route processing architecture, a dual route account is proposed as the underlying processing architecture explaining the SNARC effect.     

Spatial structure of quantitative representation of numbers: Evidence from the SNARC effect

Dehaene, Bossini, and Giraux (1993) revealed that subjects responded to large numbers faster with the choice on the right than with the choice on the left, whereas the reverse held true for small numbers (SNARC effect). According to Dehaene et al. (1993), the SNARC effect depends on the quantitative representation of number, such as a left-to-right-oriented analog number line. The main goal of the present study was twofold: first, to investigate whether the vertical SNARC effect could be observed, and, second, to verify whether Dehaene et al.'s (1993) explanation of the SNARC effect is correct. Experiments 2A and 2B showed the vertical SNARC effect in a parity judgment task. Subjects responded to large numbers faster with the top choice than with the bottom choice, whereas the reverse held true for small numbers. However, Experiment 3 failed to show the SNARC effect in a number magnitude judgment task, suggesting that the quantitative representation could be dissociated from the spatial code that produces the SNARC effect.     

Unconscious task application

The nature of unconscious information processing is a heavily debated issue in cognitive science (e.g., Kouider & Dehaene, 2007), and neuroscience (e.g., Crick & Koch, 1998). Traditionally, it has been thought that unconscious cognitive processing is restricted to knowledge that is strongly prepared by conscious processes (e.g., Dehaene et al., 1998). In three experiments, we show that the task that is performed consciously can also be applied unconsciously to items outside the current task set. We found that a same–different judgment of two target stimuli was also performed on two subliminally presented prime stimuli. This was true for target and prime stimuli from entirely different categories, as well as for prime and target stimuli at different levels of abstraction. These results reveal that unconscious processing can generalize more widely than previously accepted.     

Single-digit and two-digit Arabic numerals address the same semantic number line.

Many theories about human number representation stress the importance of a central semantic representation that includes the magnitude information of small integer numbers, and that is conceived as an abstract, compressed number line. However, thus far there has been little or no direct evidence that units and teens are represented on the same number line. In two masked priming experiments, we show that single-digit and two-digit Arabic numerals are equally well primed by an Arabic numeral with the same number of digits as by an equally distant Arabic numeral with a different number of digits (e.g. the priming effect of 7 on the target 9 is the same as the priming effect of 11 on the target 9). The finding was obtained both with a number naming task and with a parity judgement task. This is in line with the hypothesis that units and teens are part of a continuous number line.     

Mental number line disruption in a right-neglect patient after a left-hemisphere stroke

A right-neglect patient with focal left-hemisphere damage to the posterior superior parietal lobe was assessed for numerical knowledge and tested on the bisection of numerical intervals and visual lines. The semantic and verbal knowledge of numbers was preserved, whereas the performance in numerical tasks that strongly emphasize the visuo-spatial layout of numbers (e.g. number bisection) was impaired. The behavioral pattern of error in the two bisection tasks mirrored the one previously described in left-neglect patients. In other words, our patient misplaced the subjective midpoint (numerical or visual) to the left as function of the interval size. These data, paired with the patient's lesion site are strictly consistent with the tripartite organization of number-related processes in the parietal lobes as proposed by Dehaene and colleagues. According to these authors, the posterior superior parietal lobe on both hemispheres underpins the attentional orientation on the putative mental number line, the horizontal segment of the intraparietal sulcus is bilaterally related to the semantic of the numerical domain, whereas the left angular gyrus subserves the verbal knowledge of numbers. In summary, our results suggest that the processes involved in the navigation along the mental number line, which are related to the parietal mechanisms for spatial attention, and the processes involved in the semantic and verbal knowledge of numbers, are dissociable.     

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。     

The representational space of numerical magnitude: illusions of length

In recent years, a growing amount of evidence concerning the relationships between numerical and spatial representations has been interpreted, by and large, in favour of the mental number line hypothesis--namely, the analogue continuum where numbers are spatially represented (Dehaene, 1992; Dehaene, Piazza, Pinel, & Cohen, 2003). This numerical representation is considered the core of number meaning and, accordingly, needs to be accessed whenever numbers are semantically processed. The present study explored, by means of a length reproduction task, whether besides the activation of lateralized spatial codes, numerical processing modulates the mental representation of a horizontal spatial extension. Mis-estimations of length induced by Arabic numbers are interpreted in terms of a cognitive illusion, according to which the elaboration of magnitude information brings about an expansion or compression of the mental representation of spatial extension. These results support the hypothesis that visuo-spatial resources are involved in the representation of numerical magnitude.     

Beyond the mental number line: A neural network model of number–space interactions

It is commonly assumed that there is an interaction between the representations of number and space (e.g., Dehaene et al., 1993, Walsh, 2003), typically ascribed to a mental number line. The exact nature of this interaction has remained elusive, however. Here we propose that spatial aspects are not inherent to number representations, but that instead spatial and numerical representations are separate. However, cultural factors establish ties between them. By extending earlier models (Gevers et al., 2006, Verguts et al., 2005) based on this hypothesis, the authors present computer simulations showing that a model incorporating this idea can account for data from a series of studies. These results suggest that number–space interactions are emergent properties resulting from the interaction between different brain areas.     

A colorful walk on the mental number line: Striving for the right direction

Verguts and Van Opstal [Verguts, T., & Van Opstal, F. (2008). A colorful walk, but is it on the mental number line? Reply to Cohen Kadosh, Tzelgov, and Henik, Cognition, 106, 558-563] cleverly explained the results of Cohen Kadosh, Tzelgov, and Henik [Cohen Kadosh, R., Tzelgov, J., & Henik, A. (2008). A synesthetic walk on the mental number line: The size effect, Cognition, 106, 548-557] as a result of different association strength between the size of a number and its color in synesthesia. Here we present three challenges to their alternative explanation, and support our original suggestion.     

The effect of working memory load on the SNARC effect: Maybe tasks have a word to say

We investigated the effect of working memory load on the SNARC (spatial–numerical association of response codes) effect under different number judgment tasks (parity judgment and magnitude comparison), using a novel dual task. Instead of exerting load over the whole block of number judgment trials, in this dual task, number judgment trials were inserted into each interstimulus interval of an n-back task, which served as the working memory load. We varied both load type (verbal and spatial) and amount (1-load, 2-load, and 3-load). The results indicated that the SNARC effect disappeared even under the 1-load condition for a parity judgment, regardless of the type of load. However, during the magnitude comparison task, the SNARC effect increased with increasing load amounts under spatial load conditions; under verbal load conditions, the SNARC effect decreased with increasing amounts of load, and disappeared during the 3-load task. The difference between the parity and magnitude tasks was not attributable to the interval stimuli or task switching. These findings confirm that different spatial–numerical associations for comparing numerical magnitudes and judgments of parity have different needs with respect to working memory resources.     

Syllabic priming effects in picture naming in French: lost in the sea!

Ferrand, Segui, and Grainger (1996) found robust syllable priming effects in picture naming latencies: Pictures primed with their initial syllable (e.g., ba for baleine [whale]) were processed faster than pictures primed with a string of letters shorter or longer than their initial syllable (e.g., bal for baleine). However, in several studies, these priming effects have not been replicated in word naming or in picture naming either in Dutch or in English (Schiller, 1998, 1999, 2000). The present study was aimed at replicating syllable priming effects in picture naming in French using a masked priming paradigm. The study employed a larger number of participants and items than were used in the Ferrand et al. (1996) study. The syllable priming effect in picture naming latencies was not replicated. Subsampling procedures were then used to examine the stability of the Ferrand et al. (1996) pattern of results in picture naming in greater detail. The syllabic priming effect in picture naming turned out to be an extremely rare event.     

Hemispheric asymmetries in semantic processing: evidence from false memories for ambiguous words

We used fMRI to investigate competition during language production in two word production tasks: object naming and color naming of achromatic line drawings. Generally, fMRI activation was higher for color naming. The line drawings were followed by a word (the distractor word) that referred to either the object, a related object, or an unrelated object. The effect of the distractor word on the BOLD response was qualitatively different for the two tasks. The activation pattern suggests two different kinds of competition during lexical retrieval: (1) Task-relevant responses (e.g., red in color naming) compete with task-irrelevant responses (i.e., the object’s name). This competition effect was dominant in prefrontal cortex. (2) Multiple task-relevant responses (i.e., target word and distractor word) compete for selection. This competition effect was dominant in ventral temporal cortex. This study provides further evidence for the distinct roles of frontal and temporal cortex in language production, while highlighting the effects of competition, albeit from different sources, in both regions.     

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.     

Dimensional complexity and power spectral measures of the EEG during functional versus predicative problem solving

Electroencephalograms were recorded in 22 men while solving tasks of visual-pattern completion and during mental relaxation. They were primed (by foregoing trials) to solve these tasks either in a predicative or functional mode of thinking. Predicative thinking required that in order to complete the pattern the subject had to get involved with the logic of the static structure of the pattern and therefore had to recognize the recurrence of certain features of the elements (e.g., shape, color, and size). Functional thinking required involvement in a dynamic reading of the logic of the pattern and therefore to search for operations and actions to be performed on the pattern elements (e.g., pushing, mirroring, and rotating). The EEG complexity during predicative thinking decreased in comparison to functional thinking and mental relaxation, with this reduction being most pronounced over the right parietal cortex. A reduction in dimensional complexity during functional thinking as compared to mental relaxation, which was concentrated over the left central cortex, although significant, was less clear. The reduced EEG complexity during predicative thought, dominant over the right hemisphere, could reflect increased competitive inhibition among respective cortical neuron assemblies in association with the visual analysis of static element features, converging upon those predicates relevant for the solution.