Article

Is More Always Up? Evidence for a Preference of Hand-Based Associations over Vertical Number Mappings

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Abstract

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.

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... Number-space associations along the vertical axis are much less investigated than the ones along the horizontal axis. Among studies comparing SNARC effects across different axes, some have reported stronger vertical compared to horizontal number-space associations (Sixtus et al., 2019;Winter & Matlock, 2013); others have provided inconsistent results: vertical SNARC during parity judgments but not during number comparison (Ito & Hatta, 2004), vertical SNARC only in an experimental setting where the horizontal spatial representation was inhibited (Wiemers, Bekkering, & Lindemann, 2017), or even a reversed vertical SNARC with combined hand and foot response effectors (Hartmann, Gashaj, Stahnke, & Mast, 2014). In a recent pre-registered study with a within-subject design, Aleotti, Di Girolamo, Massaccesi, and Priftis (2020) compared horizontal, vertical and sagittal SNARC effect, and found that SNARC was present in each condition with equal strength and equal costs (in terms of response latencies); nonetheless, the results suggested independence of number space-associations among the three axes. ...
... Consequently, the tendency to map numbers along the vertical axis might be mainly determined by grounded aspects, while number-space associations along the horizontal axis might be mainly determined by embodied aspects (learning-related), such as reading direction and finger counting habits (e.g., Fischer & Brugger, 2011;Göbel, McCrink, Fischer, & Shaki, 2018). We suggest that both egocentric (in relation to the own body) and geocentric (in relation to the ground) reference frames contribute to the development of mental representation of numbers (Wiemers et al., 2017). An intriguing hypothesis to probe with future studies postulates that grounded factors (e. g., gravity law leading to vertical mapping) might characterize the impact of space on numbers, while in the case of numbers acting on space this link would be less systematic (e.g., Aleotti et al., 2020). ...
Article
Previous studies suggest that associations between numbers and space are mediated by shifts of visuospatial attention along the horizontal axis. In this study, we investigated the effect of vertical shifts of overt attention, induced by optokinetic stimulation (OKS) and monitored through eye-tracking, in two tasks requiring explicit (number comparison) or implicit (parity judgment) processing of number magnitude. Participants were exposed to black-and-white stripes (OKS) that moved vertically (upward or downward) or remained static (control condition). During the OKS, participants were asked to verbally classify auditory one-digit numbers as larger/smaller than 5 (comparison task; Exp. 1) or as odd/even (parity task; Exp. 2). OKS modulated response times in both experiments. In Exp.1, upward attentional displacement decreased the Magnitude effect (slower responses for large numbers) and increased the Distance effect (slower responses for numbers close to the reference). In Exp.2, we observed a complex interaction between parity, magnitude, and OKS, indicating that downward attentional displacement slowed down responses for large odd numbers. Moreover, eye tracking analyses revealed an influence of number processing on eye movements both in Exp. 1, with eye gaze shifting downwards during the processing of small numbers as compared to large ones; and in Exp. 2, with leftward shifts after large even numbers (6,8) and rightward shifts after large odd numbers (7,9). These results provide evidence of bidirectional links between number and space and extend them to the vertical dimension. Moreover, they document the influence of visuo-spatial attention on processing of numerical magnitude, numerical distance, and parity. Together, our findings are in line with grounded and embodied accounts of numerical cognition.
... We used saccadic responses because they allow to separate the responses along the true horizontal and vertical spatial axes by placing gaze trigger keys to the left and right, and also below and above the centre of the screen. Moreover, saccadic responses do not induce a near-far dimension (as it is the case for manual responses along the sagittal axis, or for up/down keys located below the screen), and they do not induce a left/right hand confound for the up/down responses, all of which can bias spatial associations (Chen et al., 2015;Hartmann, Gashaj, et al., 2014;Santens & Gevers, 2008;Wiemers et al., 2017;Zhou et al., 2019Zhou et al., , 2020. Thus, saccadic responses overcome critical issues that were observed in previous studies that used manual responses. ...
... This study further established that the oculomotor system is a valid alternative to manual responses when exploring the link between space and serial order (Rinaldi et al., 2015). In this study, we used saccadic responses in order to avoid problems that are typically induced by manual responses along the vertical axis, such as the closefar dimension or the left-right hand association (e.g., Chen et al., 2015;Hartmann, Gashaj, et al., 2014;Wiemers et al., 2017;Zhou et al., 2020). Besides these rather technical aspects, eye movements might generally play a special role in exploring the spatial nature of thoughts (e.g., Hartmann, 2015;Loetscher et al., 2010;Mast & Kosslyn, 2002;Rinaldi et al., 2015). ...
Article
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Maintaining serial order in working memory is crucial for cognition. Recent theories propose that serial information is achieved by positional coding of items on a spatial frame of reference. In line with this, an early-left and late-right spatial-positional association of response code (SPoARC) effect has been established. Various theoretical accounts have been put forward to explain the SPoARC effect (the mental whiteboard hypothesis, conceptual metaphor theory, polarity correspondence, or the indirect spatial-numerical association effect). Crucially, while all these accounts predict a left-to-right orientation of the SPoARC effect, they make different predictions regarding the direction of a possible vertical SPoARC effect. In this study, we therefore investigated SPoARC effects along the horizontal and vertical spatial dimension by means of saccadic responses. We replicated the left-to-right horizontal SPoARC effect and established for the first time an up-to-down vertical SPoARC effect. The direction of the vertical SPoARC effect was in contrast to that predicted by metaphor theory, polarity correspondence, or by the indirect spatial-numerical association effect. Rather, our results support the mental whiteboard-hypothesis, according to which positions can be flexibly coded on an internal space depending on the task demands. We also found that the strengths of the horizontal and vertical SPoARC effects were correlated, showing that some people are more prone than others to use spatial references for position coding. Our results therefore suggest that context templates used for position marking are not necessarily spatial in nature but depend on individual strategy preferences.
... Number-space associations along the vertical axis are much less investigated than the ones along the horizontal axis. Among studies comparing SNARC effects across different axes, some have reported stronger vertical compared to horizontal number-space associations (Sixtus, Lonnemann, Fischer & Werner, 2019;Winter & Matlock, 2013); others have provided inconsistent results: vertical SNARC during parity judgments but not during magnitude comparison (Ito & Hatta, 2004), vertical SNARC only in an experimental setting where the horizontal spatial representation was inhibited (Wiemers, Bekkering, & Lindemann, 2017), or even a reversed vertical SNARC with combined hand and foot response effectors (Hartmann, Gashaj, Stahnke, & Mast, 2014). In a recent pre-registered study with a within-subject design, Aleotti, Di Girolamo, Massaccesi, and Priftis (2020) compared horizontal, vertical and sagittal SNARC effect, and found that SNARC was present in each condition with equal strength and equal costs (in terms of response latencies); nonetheless, the results suggested independence of number space-associations among the three axes. ...
... We suggest that both egocentric (in relation to the own body) and geocentric (in relation to the ground) reference frames contribute to the development of mental representation of numbers (Wiemers et al., 2017). An intriguing hypothesis to probe with future studies postulates that grounded factors (e.g., gravity law leading to vertical mapping) might characterize the impact of space on numbers, while in the case of numbers acting on space this link would be less systematic (e.g., Aleotti et al., 2020). ...
Preprint
Previous studies suggest that associations between numbers and space are mediated by shifts of visuospatial attention along the horizontal axis. In this study, we investigated the effect of vertical shifts of overt attention, induced by optokinetic stimulation (OKS) and monitored through eye-tracking, in two tasks requiring explicit (number comparison) or implicit (parity judgment) processing of number magnitude. Participants were exposed to black-and-white stripes (OKS) that moved vertically (upward or downward) or remained static (control condition). During the OKS, participants were asked to verbally classify auditory one-digit numbers as larger/smaller than 5 (comparison task; Exp. 1) or as odd/even (parity task; Exp. 2). OKS modulated response times in both experiments. In Exp.1, downward attentional displacement increased the Magnitude effect (slower responses for large numbers) and reduced the Distance effect (slower responses for numbers close to the reference). In Exp.2, we observed a parity by magnitude interaction that was amplified by downward OKS. Moreover, eye tracking analyses revealed an influence of number processing on eye movements both in Exp. 1, with eye gaze shifting downwards during the processing of numbers 1-2 as compared to 8-9; and in Exp. 2, with leftward shifts after large even numbers (6,8) and rightward shifts after large odd numbers (7,9). These results provide evidence of bidirectional links between number and space and extend them to the vertical dimension. Moreover, they document the influence of visuo-spatial attention on processing of numerical magnitude, numerical distance and parity. Together, our findings are in line with grounded and embodied accounts of numerical cognition.
... Although some authors therefore concluded that the numbers are spontaneously mapped onto all dimensions in space, there is only little evidence for the existence of real egocentric vertical SNARC effects from number classification tasks with manual responses (Wiemers, Bekkering, & Lindemann, 2014). Several studies have been reported that failed to find vertical number-space compatibility effects (Holmes & Lourenco, 2012;Wiemers, Bekkering, & Lindemann, 2017). For instance, Hartmann, Gashaj, Stahnke and Mast (2014) examined vertical SNARC effects and found a significant up-to-down mapping only in one of their four experiments. ...
... For instance, Hartmann, Gashaj, Stahnke and Mast (2014) examined vertical SNARC effects and found a significant up-to-down mapping only in one of their four experiments. Wiemers et al. (2017) recently reviewed the literature and showed that most evidence incorrectly interpreted as support for vertical SNARC effects are based on studies using responses arranged on the sagittal axis or on studies that confound vertical positions with horizontal anatomical hand mappings. However, in a recent study, Aleotti et al. (2020) were able to show SNARC effects for all three dimensions, including a vertical effect. ...
Article
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When we interact with other people or avatars, they often provide an alternative spatial frame of reference compared to our own. Previous studies introduced avatars into stimulus-response compatibility tasks and demonstrated compatibility effects as if the participant was viewing the task from the avatar's point of view. However, the origin of this effect of perspective taking remained unclear. To distinguish changes in stimulus coding from changes in response coding, caused by the avatar, two experiments were conducted that combined a SNARC task and a spontaneous visual perspective taking task to specify the role of response coding. We observed compatibility effects that were based on the avatar's perspective rather than the participants' own. Because number magnitude was independent of the avatar's perspective, the observed changes in compatibility caused by different perspectives indicate changes in response coding. These changes in response coding are only significant when they are accompanied by visual action effects.
... Some studies have suggested the presence of a SNARC effect over the vertical (i.e., down vs. up) and the sagittal (i.e., near vs. far) axes (Chen et al., 2015;Hartmann et al., 2014;Holmes & Lourenco, 2012). In other studies, a SNARC-like effect was present along the vertical axis (Wiemers et al., 2014;Wiemers, Bekkering, & Lindemann, 2017;Winter & Matlock, 2013). ...
... RTs from saccadic responses were compared to RTs from normal manual responses: two equally-sized SNARC effects were found. In summary, the results of the abovementioned studies have suggested that the SNARC effect is determined by the space of response execution/direction, rather than by the specific effectors (Fias & Fischer, 2005; but see Wiemers et al., 2017). ...
... However, to date, only relatively few studies have tested other spatial directions than the horizontal left-to-right plane, or even tested combinatory-factorial experimental designs to investigate interactions between the potentially available horizontal, vertical, or radial (distance-based or sagittal) SNARC effects (for an exhaustive review, see Winter et al., 2015). When studied in isolation, spatial-numerical associations were observed (at least in Western cultures and besides the left-to-right direction) for lower-hand vs. upperhand (but not feet) responses from bottom-to-top (Hartmann et al., 2012;Wiemers et al., 2017) and also when responses were mapped from back-to-front (i.e., vertical in the sense of close/far from the body; Ito and Hatta, 2004;Shaki and Fischer, 2012). However, in traditional setups using frontoparallel two-dimensional computer monitors for presentation of stimuli, the metaphorical and literal interpretation of close/far (along with the linguistic declaration thereof) are not necessarily distinct. ...
... This is problematic because also vertical labels and horizontal response arrangements can produce spatial-numerical associations (Holmes and Lourenco, 2011). Since spatial associations in different spatial dimensions could have different cognitive origins (Winter et al., 2015;Wiemers et al., 2017), it is not clear whether which dimensions would produce an effect or how the different spatial and numerical magnitudes would interact. Nevertheless, at least semantically, there seems to be an association between close-small and far-large (Santens and Gevers, 2008). ...
Article
Full-text available
Spatial, physical, and semantic magnitude dimensions can influence action decisions in human cognitive processing and interact with each other. For example, in the spatial-numerical associations of response code (SNARC) effect, semantic numerical magnitude facilitates left-hand or right-hand responding dependent on the small or large magnitude of number symbols. SNARC-like interactions of numerical magnitudes with the radial spatial dimension (depth) were postulated from early on. Usually, the SNARC effect in any direction is investigated using fronto-parallel computer monitors for presentation of stimuli. In such 2D setups, however, the metaphorical and literal interpretation of the radial depth axis with seemingly close/far stimuli or responses are not distinct. Hence, it is difficult to draw clear conclusions with respect to the contribution of different spatial mappings to the SNARC effect. In order to disentangle the different mappings in a natural way, we studied parametrical interactions between semantic numerical magnitude, horizontal directional responses, and perceptual distance by means of stereoscopic depth in an immersive virtual reality (VR). Two VR experiments show horizontal SNARC effects across all spatial displacements in traditional latency measures and kinematic response parameters. No indications of a SNARC effect along the depth axis, as it would be predicted by a direct mapping account, were observed, but the results show a non-linear relationship between horizontal SNARC slopes and physical distance. Steepest SNARC slopes were observed for digits presented close to the hands. We conclude that spatial-numerical processing is susceptible to effector-based processes but relatively resilient to task-irrelevant variations of radial-spatial magnitudes.
... Please note that a study byWood, Nuerk, and Willmes (2006) failed to replicate the described primacy of space-over hand-based associations in the SNARC paradigm. Moreover, a study byWiemers, Bekkering, and Lindemann (2017) gives evidence for a primacy of hand-based associations over space-based number mappings in the vertical dimension. By contrast, an experiment by Brozzoli and colleagues(Brozzoli, Ishihara, Göbel, Salemme, Rossetti, & Farnè, 2008) found evidence for both space-and body-based associations, but a preference for spatial-numerical associations in case of competition. ...
Thesis
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In many parts of the modern world, numbers are used as tools to describe spatial relationships, be it heights, latitudes, or distances. However, this connection goes deeper as a myriad of studies showed that number representations are rooted in space (vertical, horizontal, and/or radial). For instance, numbers were shown to affect spatial perception and, conversely, perceptions or movements in space were shown to affect number estimations. This bidirectional link has already found didactic application in the classroom when children are taught the meaning of numbers. However, our knowledge about the cognitive (and neuropsychological) processes underlying the numerical magnitude operations is still very limited. Several authors indicated that the processing within peripersonal space (i.e. the space surrounding the body in reaching distance) and numerical magnitude operations are functionally equivalent. This assumption has several implications that the present work aims at describing. For instance, vision and visuospatial attention orienting play a prominent role for processing within peripersonal space. Indeed, both neuropsychological and behavioral studies also suggested a similar role of vision and visuospatial attention orienting for number processing. Moreover, social cognition research showed that movements, posture and gestures affect not only the representation of one's own peripersonal space, but also the visuospatial attention behavior of an observer. Against this background, the current work tests the specific implication of the functional equivalence assumption that the spatial attention response to an observed person’s posture should extend to the observer’s numerical magnitude operations. The empirical part of the present work tests the spatial attention response of observers to vertical head postures (with continuing eye contact to the observer) in both perceptual and numerical space. Two experimental series are presented that follow both steps from the observation of another person’s vertical head orientation (within his/her peripersonal space) to the observer’s attention orienting response (Experimental series A) as well as from there to the observer’s magnitude operations with numbers (Experimental Series B). Results show that the observation of a movement from a neutral to a vertical head orientation (Experiment 1) as well as the observation of the vertical head orientation alone (Experiment 3) shifted the observer’s spatial attention in correspondence with the direction information of the observed head (up vs. down). Movement from a vertical to a neutral end position, however, had no effect on the observer's spatial attention orienting response (Experiment 2). Furthermore, following down-tilted head posture (relative to up- or non-tilted head orientation), observers generated smaller numbers in a random number generation task (range 1- 9, Experiment 4), gave smaller estimates to numerical trivia questions (mostly multi-digit numbers, Experiment 5) and chose response keys less frequently in a free choice task that was associated with larger numerical magnitude in a intermixed numerical magnitude task. Experimental Series A served as groundwork for Experimental Series B, as it demonstrated that observing another person’s head orientation indeed triggered the expected directional attention orienting response in the observer. Based on this preliminary work, the results of Experimental Series B lend support to the assumption that numerical magnitude operations are grounded in visuospatial processing of peripersonal space. Thus, the present studies brought together numerical and social cognition as well as peripersonal space research. Moreover, the Empirical Part of the present work provides the basis for elaborating on the role of processing within peripersonal space in terms of Walsh’s (2003, 2013) Theory of Magnitude. In this context, a specification of the Theory of Magnitude was staked out in a processing model that stresses the pivotal role of spatial attention orienting. Implications for mental magnitude operations are discussed. Possible applications in the classroom and beyond are described.
... This SNARC-like effect points at a congruency relation between left responses and small and right responses and large magnitude (see Wood et al. 2006), which could be explained with an anatomical (i.e. hand-based) association between numbers and (internal) space (e.g., Wiemers et al. 2017) or correspondence between numerical and spatial polarity (Proctor and Cho 2006). Crucially, however, the mapping effect did not interact with the head orientation effect, which means that both effects were unrelated. ...
Article
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The present research shows effects of observed vertical head orientation of another person on numerical cognition in the observer. Participants saw portrait-like photographs of persons from a frontal view with gaze being directed at the camera and the head being tilted up or down (vs. not tilted). The photograph appeared immediately before each trial in different numerical cognition tasks. In Experiment 1, participants produced smaller numbers in a random number generation task after having viewed persons with a down-tilted head orientation relative to up-tilted and non-tilted head orientations. In Experiment 2, numerical estimates in an anchoring-like trivia question task were smaller following presentations of persons with a down-tilted head orientation relative to a non-tilted head orientation. In Experiment 3, a response key that was associated with larger numbers in a numerical magnitude task was pressed less frequently in a randomly intermixed free choice task when the photograph showed a person with a down-tilted relative to an up-tilted head orientation. These findings consistently show that social displays can influence numerical cognition across a variety of task settings.
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Multiple tasks have been used to demonstrate the relation between numbers and space. The classic interpretation of these directional spatial-numerical associations (d-SNAs) is that they are the product of a mental number line (MNL), in which numerical magnitude is intrinsically associated with spatial position. The alternative account is that d-SNAs reflect task demands, such as explicit numerical judgments and/or categorical responses. In the novel ‘Where was The Number?’ task, no explicit numerical judgments were made. Participants were simply required to reproduce the location of a numeral within a rectangular space. Using a between-subject design, we found that numbers, but not letters, biased participants’ responses along the horizontal dimension, such that larger numbers were placed more rightward than smaller numbers, even when participants completed a concurrent verbal working memory task. These findings are consistent with the MNL account, such that numbers specifically are inherently left-to-right oriented in Western participants.
Chapter
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Models of the numerical cognitive system differ in the importance they attach to magnitude information in numerical processing. In this paper, the necessity of addressing a central semantic number system in arabic number processing is evaluated by looking at the SNARC-effect. This effect has been interpreted as an indication of access to the semantic system. In Experiment 1, we replicated the effect in a parity judgement task. In Experiment 2, we extended the SNARC-effect to a phoneme monitoring task, showing that magnitude information was accessed during arabic-to-verbal transcoding. We conclude, therefore, that number magnitude plays a more important role than is generally accepted.
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Nine experiments of timed odd–even judgments examined how parity and number magnitude are accessed from Arabic and verbal numerals. With Arabic numerals, Ss used the rightmost digit to access a store of semantic number knowledge. Verbal numerals went through an additional stage of transcoding to base 10. Magnitude information was automatically accessed from Arabic numerals. Large numbers preferentially elicited a rightward response, and small numbers a leftward response. The Spatial–Numerical Association of Response Codes effect depended only on relative number magnitude and was weaker or absent with letters or verbal numerals. Direction did not vary with handedness or hemispheric dominance but was linked to the direction of writing, as it faded or even reversed in right-to-left writing Iranian Ss. The results supported a modular architecture for number processing, with distinct but interconnected Arabic, verbal, and magnitude representations. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
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While research on the spatial representation of number has provided substantial evidence for a horizontally oriented mental number line, recent studies suggest vertical organization as well. Directly comparing the relative strength of horizontal and vertical organization, however, we found no evidence of spontaneous vertical orientation (upward or downward), and horizontal trumped vertical when pitted against each other (Experiment 1). Only when numbers were conceptualized as magnitudes (as opposed to nonmagnitude ordinal sequences) did reliable vertical organization emerge, with upward orientation preferred (Experiment 2). Altogether, these findings suggest that horizontal representations predominate, and that vertical representations, when elicited, may be relatively inflexible. Implications for spatial organization beyond number, and its ontogenetic basis, are discussed.
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Spatial stimulus—response (S-R) compatibility designates the observation that speeded reactions to unilateral stimuli are faster for the hand ipsilateral than for the hand contralateral to the sensory hemifield containing the stimulus. In two experiments involving presentation of the numbers 1 to 11 in the center of the visual field we show (1) a left-hand reaction time (RT) advantage for numerals <6 and a right-hand advantage for those >6 for subjects who conceive of the numbers as distances on a ruler, and (2) a reversal of this RT advantage for subjects who conceive of them as hours on a clock face. While the results in the first task (RULER) replicate a robust finding from the neuropsychology of number processing (the ‘‘SNARC effect’’) those in the second task (CLOCK) show that extension of the number scale from left to right in representational space cannot be the decisive factor for the observed interaction between hand and number size. Taken together, the findings in the two tasks are best accounted for in terms of an interaction between lateralized mental representations and lateralized motor outputs (i.e. an analog of traditional spatial S-R compatibility effects in representational space). We discuss potential clinical applications of the two tasks in patients with neglect of representational space.
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This paper provides an introduction to mixed-effects models for the analysis of repeated measurement data with subjects and items as crossed random effects. A worked-out example of how to use recent software for mixed-effects modeling is provided. Simulation studies illustrate the advantages offered by mixed-effects analyses compared to traditional analyses based on quasi-F tests, by-subjects analyses, combined by-subjects and by-items analyses, and random regression. Applications and possibilities across a range of domains of inquiry are discussed.
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A recent cross-cultural comparison (Shaki, Fischer, & Petrusic, 2009) suggested that spatially consistent processing habits for words and numbers are a necessary condition for the spatial representation of numbers (Spatial-Numerical Association of Response Codes; SNARC effect). Here we reexamine the SNARC in Israelis who read text from right to left but numbers from left to right. We show that, despite these spatially inconsistent processing habits, a SNARC effect still emerges when the response dimension is spatially orthogonal to the conflicting processing dimension. These results clarify the cognitive conditions for spatial-numerical mappings.
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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.
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Despite the apparent simplicity of picking numbers at random, it is virtually impossible to produce a sequence of truly random numbers. Although numbers seem to pop-up spontaneously in one's mind, their choice is invariably influenced by previously generated numbers [1 • Knoch D. • Brugger P. • Regard M. Suppressing versus releasing a habit: frequency-dependent effects of prefrontal transcranial magnetic stimulation.Cerebr. Cortex. 2005; 15: 885-887 • Crossref • PubMed • Scopus (47) • Google Scholar ]. Here, we demonstrate how the eyes and their position give an insight into the nature of the systematic choices made by the brain's ‘random number generator’. By measuring a person's vertical and horizontal eye position, we were able to predict with reliable confidence the size of the next number — before it was spoken. Specifically, a leftward and downward change in eye position announced that the next number would be smaller than the last. Correspondingly, if the eyes changed position to the right and upward, it forecast that the next number would be larger. Apart from supporting the old wisdom that it is often the eyes that betray the mind, the findings highlight the intricate links between supposedly abstract thought processes, the body's actions and the world around us.
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Li and Gleitman (Turning the tables: language and spatial reasoning. Cognition, in press) seek to undermine a large-scale cross-cultural comparison of spatial language and cognition which claims to have demonstrated that language and conceptual coding in the spatial domain covary (see, for example, Space in language and cognition: explorations in linguistic diversity. Cambridge: Cambridge University Press, in press; Language 74 (1998) 557): the most plausible interpretation is that different languages induce distinct conceptual codings. Arguing against this, Li and Gleitman attempt to show that in an American student population they can obtain any of the relevant conceptual codings just by varying spatial cues, holding language constant. They then argue that our findings are better interpreted in terms of ecologically-induced distinct cognitive styles reflected in language. Linguistic coding, they argue, has no causal effects on non-linguistic thinking--it simply reflects antecedently existing conceptual distinctions. We here show that Li and Gleitman did not make a crucial distinction between frames of spatial reference relevant to our line of research. We report a series of experiments designed to show that they have, as a consequence, misinterpreted the results of their own experiments, which are in fact in line with our hypothesis. Their attempts to reinterpret the large cross-cultural study, and to enlist support from animal and infant studies, fail for the same reasons. We further try to discern exactly what theory drives their presumption that language can have no cognitive efficacy, and conclude that their position is undermined by a wide range of considerations.
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In the present paper, we focus on how irrelevant implicit spatial information is processed. By irrelevant we mean information that is not required to fulfill the task and by implicit we mean information that is not directly available in the external stimulus. A good example of a task in which such information exists is the SNARC task [Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122, 371-396]. The SNARC effect shows that the magnitude of a number, although irrelevant to the task, activates spatial codes that may interfere with the task-related response. These spatial associations exist both for the horizontal and the vertical direction. In Experiment 1, response keys were discriminating in the vertical or the horizontal direction. It is shown that the impact of the numerical spatial codes on overt behavior, although automatic, depends on the response discrimination of the horizontal or the vertical dimension. In Experiment 2, response keys were assigned such that both the horizontal and the vertical direction of the response were discriminating. In this case, the horizontal and the vertical dimension of the irrelevant numerical spatial codes were shown to interact. In general, the results are in line with the response-discrimination account [Ansorge, U., & Wühr, P. (2004). A response-discrimination account of the Simon effect. Journal of Experimental Psychology: Human Perception and Performance, 30, 365-377].
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Dehaene et al. (1993, Experiment 6) presented evidence that the mental number line is left-to-right oriented with respect to representational associations and not with respect to left and right hands. Here we tried to replicate the study of Dehaene et al. (1993) in a larger sample (n = 32) using four different stimulus notations (Arabic numbers, number words, auditory number words, and dice patterns). As in the study by Dehaene et al. (1993), the spatial numerical association of response codes (SNARC) effect was examined with an incongruent hand assignment to left/right response keys (crossed hands). In contrast to Dehaene et al. (1993), we did not observe a SNARC effect in any condition. Power analyses revealed that n = 32 should have been large enough to detect SNARC effects of usual size. Furthermore, time-course analyses revealed no SNARC slope in faster and slower responses, so that the null effect could not be due to relatively slow responses with crossed hands. Joint analyses with previous data (Nuerk et al., 2005b) revealed significantly steeper SNARC slopes with congruent hand assignment, and no interaction between hand assignment and notation. Altogether, these findings suggest that the results of Dehaene et al. (1993) only hold under specific conditions. Differences between studies are discussed. We suggest that spatial context has an influence on the SNARC effect and that hand-based associations (and not only representational associations) are relevant for the SNARC effect.
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The present study examines the functional and anatomical underpinnings of egocentric and allocentric coding of spatial coordinates. For this purpose, we set up a functional magnet resonance imaging experiment using verbal descriptions of spatial relations either with respect to the listener (egocentric) or without any body-centered relations (allocentric) to induce the two different spatial coding strategies. We aimed to identify and distinguish the neuroanatomical correlates of egocentric and allocentric spatial coding without any possible influences by visual stimulation. Results from sixteen participants show a general involvement of a bilateral fronto-parietal network associated with spatial information processing. Furthermore, the egocentric and allocentric conditions gave rise to activations in primary visual areas in both hemispheres. Moreover, data show separate neural circuits mediating different spatial coding strategies. While egocentric spatial coding mainly recruits the precuneus, allocentric coding of space activates a network comprising the right superior and inferior parietal lobe and the ventrolateral occipito-temporal cortex bilaterally. Furthermore, bilateral hippocampal involvement was observed during allocentric, but not during egocentric spatial processing. Our results demonstrate that the processing of egocentric spatial relations is mediated by medial superior-posterior areas, whereas allocentric spatial coding requires an additional involvement of right parietal cortex, the ventral visual stream and the hippocampal formation. These data suggest that a hierarchically organized processing system exists in which the egocentric spatial coding requires only a subsystem of the processing resources of the allocentric condition.
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The spatial component of numerical and ordinal information has been explored in previous research. However, how such mapping emerges and how it is affected by the learning experience are issues still under debate. In the current study, we examined the orientation of the mental number line for different numerical notations (e.g., "1", "---", "[symbol: see text]") in Chinese readers. Our data demonstrated that Arabic numbers are mentally aligned horizontally with a left-to-right directionality, while Chinese number words are aligned vertically with a top-to-bottom directionality. These findings indicate that different notations of the same concept have flexible mappings within space, which is plausibly shaped by the dominant context in which the numerical notations appear.
Article
The SNARC effect refers to the association of smaller numbers with the left and of larger numbers with the right side of extracorporal space (Dehaene, Bossini, & Giraux, 1993). We tested the assumption that, in addition to these associations, numbers are also related to participants' hands. We report two experiments with vertically arranged buttons in which the nature of the SNARC effect depended on whether the task set was button or hand related: In the first case, a vertical location-related SNARC effect occurred, whereas in the second a hand-related SNARC effect was found. Our third experiment confirmed that space-related number representations dominate the SNARC effect when the buttons are arranged horizontally. We concluded that both effector- and space-related number representations can influence and modify the SNARC effect.
Spatial cognition -An interdisciplinary approach to representation and processing of spatial knowledge
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Klatzky, R. L. (1998). Allocentric and egocentric spatial representations:Definitions, distinctions, and interconnections. In C. Freksa, C. Habel, & K. F.Wender (Eds.), Spatial cognition -An interdisciplinary approach to representation and processing of spatial knowledge (Lecture Notes in Artificial Intelligence 1404) (pp. 1-17). Berlin: Springer-Verlag.
A SNARC in the dark: Input modality affects number representation. 22nd European Workshop of
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Fischer, M.H., & Hill, R. (2004). A SNARC in the dark: Input modality affects number representation. 22nd European Workshop of Cognitive Neuropsychology, Bressanone, 26-31.