数形联觉——数字空间表征研究“新”取向

数字空间表征是人类对数字进行表征的重要方式。数形联觉（number-form synesthesia）是一种数字可以有意识地引起空间知觉的独特现象,与此类似的是非联觉者中广泛存在的无意识的心理数字线（mental number line）现象。两者在行为和脑机制上存在着很多重叠,也存在着值得思考的差异。数形联觉的研究能够提供实质性的行为和脑机制数据,用以解决数字空间表征研究中出现的问题,加强对于数字空间表征的理解;也为更加全面深入地开展进一步研究提供了新的启示,成为数字空间表征研究中值得推崇的新取向。     

When 9 is not on the right: Implications from number-form synesthesia

Number-form synesthetes consciously experience numbers in spatially-defined locations. For non-synesthete individuals, a similar association of numbers and space appears in the form of an implicit mental number line as signified by the distance effect–reaction time decreases as the numerical distance between compared numbers increases. In the current experiment, three number-form synesthetes and two different non-synesthete control groups (Hebrew speaking and English speaking) performed a number comparison task. Synesthete participants exhibited a sizeable distance effect only when presented numbers were congruent with their number-form. In contrast, the controls exhibited a distance effect regardless of congruency or presentation type. The findings suggest that: (a) number-form synesthesia impairs the ability to represent numbers in a flexible manner according to task demands; (b) number-form synesthesia is a genuine tangible experience, triggered involuntarily; and (c) the classic mental number line can be more pliable than previously thought and appears to be independent of cultural-lingo direction.     

Expanding on the mental number line: Zero is perceived as the "smallest"

The representation of 0 in healthy adults was studied with the physical comparison task. Automatic processing of numbers, as indicated by the size congruity effect, was used for detecting the basic numerical representations stored in long-term memory. The size congruity effect usually increases with numerical distance between the physically compared numbers. This increase was attenuated for comparisons to 0 or 1 (but not to 2) when they were perceived as the smallest number in the set. Furthermore, the size congruity effect was enlarged in these cases. These results indicate an end effect in automatic processing of numbers and suggest that 0, or 1 in the absence of 0, is perceived as the smallest entity on the mental number line. The implications of these findings are discussed with regard to models of number representation. (PsycINFO Database Record (c) 2012 APA, all rights reserved).     

Gaze orientation interferes with mental numerical representation

Number comparison tasks are characterized by distance and size effects. The distance effect reveals that the higher the distance is between two numbers, the easier their magnitude comparison is. Accordingly, people are thought to represent numbers on a spatial dimension, the mental number line, on which any given number corresponds to a location on the line. The size effect, instead, states that at any given distance, comparing two small numbers is easier than comparing two large numbers, thus suggesting that larger numbers are more vaguely represented than smaller ones. In the present work we first tested whether the participants were adopting a spatial strategy to solve a very simple numbers comparison task, by assessing the presence of the distance and the magnitude effect. Secondarily, we focused on the influence of gaze position on their performance. The present results provide evidence that gaze direction interferes with number comparisons, worsening the vague representation of larger numbers and further supporting the hypothesis of the overlapping between physical and mental spaces.     

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.     

负数的空间表征机制

本研究采用快速数字大小分类范式,每次试验呈现一个数字,要求被试快速判断即时呈现的数字大于或小于-5（或5）,探讨负数在心理数字线上的表征方向问题。实验一将负数（-1～-9）和正数（1～9）分两组分别呈现;实验二将正负数混合呈现,仅对负数进行反应。结果表明,负数按照其绝对值大小表征在心理数字线上,绝对值小的负数表征在心理数字线的左侧,绝对值大的负数表征在心理数字线的右侧。该结果支持系统进化论假说     

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。     

Holistic or compositional representation of two-digit numbers? Evidence from the distance, magnitude, and SNARC effects in a number-matching task

Whether two-digit numbers are represented holistically (each digit pair processed as one number) or compositionally (each digit pair processed separately as a decade digit and a unit digit) remains unresolved. Two experiments were conducted to examine the distance, magnitude, and SNARC effects in a number-matching task involving two-digit numbers. Forty undergraduates were asked to judge whether two two-digit numbers (presented serially in Experiment 1 and simultaneously in Experiment 2) were the same or not. Results showed that, when numbers were presented serially, unit digits did not make unique contributions to the magnitude and distance effects, supporting the holistic model. When numbers were presented simultaneously, unit digits made unique contributions, supporting the compositional model. The SNARC (Spatial-Numerical Association of Response Codes) effect was evident for the whole numbers and the decade digits, but not for the unit digits in both experiments, which indicates that two-digit numbers are represented on one mental number line. Taken together, these results suggested that the representation of two-digit numbers is on a single mental number line, but it depends on the stage of processing whether they are processed holistically or compositionally.     

Decade breaks in the mental number line? Putting the tens and units back in different bins.

Most models of number recognition agree that among other number representations there is a central semantic magnitude representation which may be conceptualized as a logarithmically compressed mental number line. Whether or not this number line is decomposed into different representations for tens and units is, however, controversial. We investigated this issue in German participants in a magnitude comparison (selection) task in which the larger of two visually presented Arabic two-digit numbers had to be selected. Most importantly, we varied unit-decade-compatibility: a number pair was defined as compatible if the decade magnitude comparison and the unit magnitude comparison of the two numbers would lead to the same response (e.g. 52 and 67) and as incompatible if this was not the case (e.g. 47 and 62). While controlling for overall numerical distance, size and other variables, we consistently found compatibility effects. A control experiment showed that this compatibility effect was not due to perceptual presentation characteristics. We conclude that the idea of one single number line representation that does not additionally assume different magnitude representations for tens and units is not sufficient to account for the data. Finally, we discuss why decade effects were not found in other experimental settings.     

The representation of negative numbers: exploring the effects of mode of processing and notation

The representation of negative numbers was explored during intentional processing (i.e., when participants performed a numerical comparison task) and during automatic processing (i.e., when participants performed a physical comparison task). Performance in both cases suggested that negative numbers were not represented as a whole but rather their polarity and numerical magnitudes were represented separately. To explore whether this was due to the fact that polarity and magnitude are marked by two spatially separated symbols, participants were trained to mark polarity by colour. In this case there was still evidence for a separate representation of polarity and magnitude. However, when a different set of stimuli was used to refer to positive and negative numbers, and polarity was not marked separately, participants were able to represent polarity and magnitude together when numerical processing was performed intentionally but not when it was conducted automatically. These results suggest that notation is only partly responsible for the components representation of negative numbers and that the concept of negative numbers can be grasped only through that of positive numbers.     

Interactions between perceptual and numerical space

Interactions between numbers and space have become a major issue in numerical cognition. Neuropsychological studies suggest that the interactions occur, before response selection, at a spatially organized representation of numbers (the mental number line). Reaction time (RT) studies, on the other hand, usually point to associations between response codes that do not necessarily imply a number line. There is only one such study that has found a spationumerical interaction between perception and semantics (SNIPS) effect before response selection. Here, in Experiment 1, we isolated the SNIPS effect from other numerical effects and corroborated the prediction that it can be induced by both left and right spatial cues. In Experiment 2, we isolated the peak of the time course of the SNIPS effect and corroborated the prediction that it occurs when a cue follows a target, and not when both appear simultaneously. The results reconcile neuropsychological and RT studies and support the hypothesis that numbers are represented along a left-to-right spatially organized mental number line. [corrected]     

Number-space associations without language: Evidence from preverbal human infants and non-human animal species

It is well known that humans describe and think of numbers as being represented in a spatial configuration, known as the ‘mental number line’. The orientation of this representation appears to depend on the direction of writing and reading habits present in a given culture (e.g., left-to-right oriented in Western cultures), which makes this factor an ideal candidate to account for the origins of the spatial representation of numbers. However, a growing number of studies have demonstrated that non-verbal subjects (preverbal infants and non-human animals) spontaneously associate numbers and space. In this review, we discuss evidence showing that pre-verbal infants and non-human animals associate small numerical magnitudes with short spatial extents and left-sided space, and large numerical magnitudes with long spatial extents and right-sided space. Together this evidence supports the idea that a more biologically oriented view can account for the origins of the ‘mental number line’. In this paper, we discuss this alternative view and elaborate on how culture can shape a core, fundamental, number–space association.     

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。     

Differences between digit naming and number word reading in a flanker task

Numbers can be represented as number words or as digits, but are the two notations processed differently? Two experiments in which a flanker paradigm with a naming task was used were conducted, with digits and number words as targets and flankers. Reaction times were shortest when the flanker denoted the same numerical value as the target. The numerical distance between the target and a numerically different flanker modulated reaction times in all conditions, except for number word targets with digit flankers. The direction of this effect—targets were named faster when the flanker was numerically close than when it was far—indicates that the numerical magnitude representations of numbers are associatively connected. When the target and the flanker were presented in the same format, no difference was observed in the distance effects for the two formats. This indicates that number words activate the abstract representation of their numerical value in a way that is very similar to that for digits.     

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。     

The universal SNARC effect: the association between number magnitude and space is amodal

It is thought that number magnitude is represented in an abstract and amodal way on a left-to-right oriented mental number line. Major evidence for this idea has been provided by the SNARC effect (Dehaene, Bossini, & Giraux, 1993): responses to relatively larger numbers are faster for the right hand, those to smaller numbers for the left hand, even when number magnitude is irrelevant. The SNARC effect has been used to index automatic access to a central semantic and amodal magnitude representation. However, this assumption of modality independence has never been tested and it remains uncertain if the SNARC effect exists in other modalities in a similar way as in the visual modality. We have examined this question by systematically varying modality/notation (auditory number word, visual Arabic numeral, visual number word, visual dice pattern) in a within-participant design. The SNARC effect was found consistently for all modality/notation conditions, including auditory presentation. The size of the SNARC effect in the auditory condition did not differ from the SNARC effect in any visual condition. We conclude that the SNARC effect is indeed a general index of a central semantic and amodal number magnitude representation.     

Dynamic representations underlying symbolic and nonsymbolic calculation: Evidence from the operational momentum effect

When we add or subtract, do the corresponding quantities “move” along a mental number line? Does this internal movement lead to spatial biases? A new method was designed to investigate the psychophysics of approximate arithmetic. Addition and subtraction problems were presented either with sets of dots or with Arabic numerals, and subjects selected, from among seven choices, the most plausible result. In two experiments, the subjects selected larger numbers for addition than for subtraction problems, as if moving too far along the number line. This operational momentum effect was present in both notations and increased with the size of the outcome. Furthermore, we observed a new effect of spatial-numerical congruence, related to but distinct from the spatial numerical association of response codes effect: During nonsymbolic addition, the subjects preferentially selected numbers at the upper right location, whereas during subtraction, they were biased toward the upper left location. These findings suggest that approximate mental arithmetic involves dynamic shifts on a spatially organized mental representation of numbers. Supplemental materials for this study may be downloaded from app.psychonomic-journals.org/content/supplemental.     

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.     

Concept driven color experiences in digit-color synesthesia

In digit-color synesthesia, black digits elicit conscious experiences of highly specific colors (photisms). This paper describes C, an undergraduate student who experiences digit-color synesthesia. We evaluated whether C's photisms could occur even in the absence of an externally presented digit. C was shown simple arithmetic problems (e.g., 5 + 2) followed by a color patch. C was significantly faster at naming the color of the patch when it was congruent with the photism associated with the answer to the problem than when the color patch was incongruent with the answer. These results replicate previous findings (Dixon, Smilek, Cudahy, & Merikle, 2000) and strongly suggest that for C, an externally presented inducing stimulus is not necessary to trigger a photism--activating the concept of a digit is sufficient.     

The representation of negative numbers: Exploring the effects of mode of processing and notation

The representation of negative numbers was explored during intentional processing (i.e., when participants performed a numerical comparison task) and during automatic processing (i.e., when participants performed a physical comparison task). Performance in both cases suggested that negative numbers were not represented as a whole but rather their polarity and numerical magnitudes were represented separately. To explore whether this was due to the fact that polarity and magnitude are marked by two spatially separated symbols, participants were trained to mark polarity by colour. In this case there was still evidence for a separate representation of polarity and magnitude. However, when a different set of stimuli was used to refer to positive and negative numbers, and polarity was not marked separately, participants were able to represent polarity and magnitude together when numerical processing was performed intentionally but not when it was conducted automatically. These results suggest that notation is only partly responsible for the components representation of negative numbers and that the concept of negative numbers can be grasped only through that of positive numbers.