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Is More Always Up? Evidence for a Preference of Hand-Based Associations over Vertical Number Mappings
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.
... Nevertheless, the SNARC effect does not always occur on the dimension along which the response buttons are arranged. For example, Wiemers et al. (2017) arranged response buttons on the vertical axis (one button was placed below and one on a tabletop). They found no vertical SNARC effect when the hand-to-button mapping changed only once, no matter whether the participants were standing or sitting. ...
... Accordingly, we expected to find a sagittal SNARC effect (see also Gronau et al., 2017). Meanwhile, we expected an SNARC effect along the horizontal axis, as it was shown to be robust even if the effectors were arranged on another axis Wiemers et al., 2017). Given the background described above, we developed the following hypotheses: ...
Magnitude information, for instance, regarding weight, distance, or velocity, is crucial for planning goal-directed interactions. Accordingly, magnitude information, including numerical magnitude, can affect actions: Responses to small numbers are faster with the left hand than the right and vice versa (hand-based SNARC effect). Previous experiments found an influence of effector placements on the SNARC effect but also an influence of the mere distance between effectors and numbers. This indicates a sensorimotor grounding of space-number processing. In the current study, we investigated this grounding by probing the SNARC effect close to and far from the hands. We used a magnitude comparison task with a fixed standard of 5 (smaller numbers 1, 2, 3, 4; larger numbers 6, 7, 8, 9) and a sagittal response arrangement to measure hand-based and sagittal SNARC effects for digits presented at different sagittal distances to the hands, i.e., in peripersonal and extrapersonal space. A significant sagittal SNARC effect was found, with the largest effect size in extrapersonal space. Meanwhile, the hand-based SNARC effect appeared only descriptively, with the largest effect size between the hands, i.e., in peripersonal space. Additionally, a purely spatial congruency effect surfaced, prioritizing responses with the hand closer to the number. Together, these results emphasize that responses in simple decision-making tasks can be influenced interactively by a multitude of task-relevant axes and relative spatial locations, including effector placement and stimulus placement, as well as number magnitude.
... 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). ...
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). ...
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 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). ...
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. ...
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). ...
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.
... In the task with mixed magnitude comparison and orientation judgement of numbers, for example, the response mapping rule was reflected in the spatial direction of the SNARC effect in orientation judgement 60 . Additionally, frequent switching of response mapping influenced the strength of the SNARC effect by minimizing the hand-based SNARC effect 61 . To our knowledge, the response rule learned during the practice phase could reinforce the participants' spatial direction identical to the rule 62 , but no studies have shown the spatial representation opposite to the response rule in the "first block". ...
The possibility that risks interact with spatial information (such as the SNARC effect) has been explored but studies did not demonstrate a consistent left-to-right representation of risks. This is probably due to the perception of risk being different in each individual experience. The present study aimed to clarify the spatial characteristics of acute deterioration risks perceived from illnesses. Registered nurses and general students participated in the present experiment. They were instructed to judge, by pressing one of the left/right response buttons, whether the risk of a given target (illness name) presented on a computer screen was higher or lower compared to that of a standard stimulus. Reaction times to the target were measured. No spatial-risk association was observed in the comprehensive analysis, but further inspection revealed that approximately half of the participants have a left-to-right representation and the other half have a right-to-left representation. Moreover, participants’ responses appeared to be faster when the target was representationally farther away from the standard stimulus (i.e., distance effect). These findings therefore suggest a spatially aligned magnitude representation of acute deterioration risk (i.e., mental risk line) but this horizontal risk orientation is likely to be dichotomous depending on the individuals and/or given situations.
... Hartmann et al., (2014;Experiment 1) reported that smaller numbers were processed faster through down-sided responses, whereas larger numbers were processed faster through up-sided responses. On the contrary, Wiemers et al. (2017) did not replicate the results of Hartmann et al. Furthermore, Wiemers et al. reported evidence for an anatomical vertical SNARC effect. ...
Small numbers are processed faster through left-sided than right-sided responses, whereas large numbers are processed faster through right-sided than left-sided responses [i.e., the Spatial–Numerical Association of Response Codes (SNARC) effect]. This effect suggests that small numbers are mentally represented on the left side of space, whereas large numbers are mentally represented on the right side of space, along a mental number line. The SNARC effect has been widely investigated along the horizontal Cartesian axis (i.e., left–right). Aleotti et al. (Cognition 195:104111, 2020), however, have shown that the SNARC effect could also be observed along the vertical (i.e., small numbers-down side vs. large numbers-up side) and the sagittal axis (i.e., small numbers-near side vs. large numbers-far side). Here, we investigated whether the three Cartesian axes could interact to elicit the SNARC effect. Participants were asked to decide whether a centrally presented Arabic digit was odd or even. Responses were collected through an ad hoc-made response box on which the SNARC effect could be compatible for one, two, or three Cartesian axes. The results showed that the higher the number of SNARC-compatible Cartesian axes, the stronger the SNARC effect. We suggest that numbers are represented in a three-dimensional number space defined by interacting Cartesian axes.
... 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. ...
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. ...
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.
When participants decide whether a presented tone is loud or soft they react faster to loud tones with a top-sided response key in comparison to a bottom-sided response key and vice versa for soft tones. This effect is comparable to the well-established horizontal Spatial-Numerical Association of Response Codes (SNARC) effect and is often referred to as Spatial-Musical Association of Response Codes (SMARC) effect for loudness. The SMARC effect for loudness is typically explained by the assumption of a spatial representation or by the polarity correspondence principle. Crucially, both theories differ in the prediction of the SMARC effect when loudness is task-irrelevant. Therefore, we investigated whether the SMARC effect still occurs in a timbre discrimination task: Participants ( N = 36) heard a single tone and classified its timbre with vertically arranged response keys. Additionally, the tone's loudness level varied in six levels. In case of a spatial representation, the SMARC effect should still occur while in case of polarity corresponding principle, the effect should be absent. Results showed that the SMARC effect was still present and that the differences between top-sided and bottom-sided responses were a linear function of loudness level indicating a continuous spatial representation of loudness.
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.
Tight cognitive links between space and number processing exist. Usually, Spatial-Numerical Associations (SNAs) are interpreted causally: spatial capabilities are a cornerstone of math skill. We question this seemingly ubiquitous assumption. After presenting SNA taxonomy, we show that only some SNAs correlate with math skill. These correlations are not conclusive: (1) Their directions vary (stronger SNA relates sometimes to better, sometimes to poorer skill), (2) the correlations might be explained by mediator variables (e.g., SNA tasks involve cognitive control or reasoning), (3) the hypothetical course of causality is not resolved: For instance, contrary to conventional theories, arithmetic skills can underlie performance in some SNA tasks. However, benefits of SNA trainings on math skills seem to reinforce the claim of primary SNA role. Nevertheless, tasks used in such trainings may tap cognitive operations required in arithmetic, but not SNA representations themselves. Therefore, using space is a powerful tool rather than a cornerstone for math.
Undoubtedly, tight links between space and number processing exist. Usually, findings of Spatial-Numerical Associations (SNA) are interpreted causally, i.e., that spatial capabilities aid or are even a fundamental cornerstone of mathematical skill. In this book chapter, we question this seemingly ubiquitous assumption.To start with, there is no robust and prevalent correlation between SNA in general and math abilities. After presenting an extended taxonomy for different SNA subtypes, we show that only some SNA subtypes correlate with math abilities, whereas others do not. We argue that these correlations are not conclusive for several reasons. (i) Their correlations vary (i.e., stronger SNA sometimes is related to better math ability, and sometimes to poorer math ability). (ii) The correlations might not show a genuine relation between space and number; rather mediator variables might explain the correlations. For instance, SNA tasks often involve an interference component tapping cognitive control functions (as in multi-digit number processing) or some relatively advanced reasoning skills or strategies. (iii) Finally, the direction of causality (if it exists) is far from resolved. While conventional theories suggest that spatial-numerical abilities underlie arithmetic skill, we argue that vice versa arithmetic abilities instead underlie performance in some spatial-numerical tasks used to assess spatial-numerical representations.On the other hand, benefits conferred by SNA trainings on math abilities seem to reinforce the claim that SNA underlies math abilities. We contend that tasks used in such trainings may tap several cognitive operations required in arithmetic, but not built-up fixed SNAs themselves. Therefore, we argue that using space is a powerful tool, especially for instructing and learning multi-digit numbers; however, this does not necessarily imply an internalized fixed mental number line.
One of the frequent questions by users of the mixed model function lmer of the lme4 package has been: How can I get p values for the F and t tests for objects returned by lmer? The lmerTest package extends the 'lmerMod' class of the lme4 package, by overloading the anova and summary functions by providing p values for tests for fixed effects. We have implemented the Satterthwaite's method for approximating degrees of freedom for the t and F tests. We have also implemented the construction of Type I - III ANOVA tables. Furthermore, one may also obtain the summary as well as the anova table using the Kenward-Roger approximation for denominator degrees of freedom (based on the KRmodcomp function from the pbkrtest package). Some other convenient mixed model analysis tools such as a step method, that performs backward elimination of nonsignificant effects - both random and fixed, calculation of population means and multiple comparison tests together with plot facilities are provided by the package as well.
Journal of Cognitive Psychology Publication details, including instructions for authors and subscription information:
Maximum likelihood or restricted maximum likelihood (REML) estimates of the
parameters in linear mixed-effects models can be determined using the lmer
function in the lme4 package for R. As for most model-fitting functions in R,
the model is described in an lmer call by a formula, in this case including
both fixed- and random-effects terms. The formula and data together determine a
numerical representation of the model from which the profiled deviance or the
profiled REML criterion can be evaluated as a function of some of the model
parameters. The appropriate criterion is optimized, using one of the
constrained optimization functions in R, to provide the parameter estimates. We
describe the structure of the model, the steps in evaluating the profiled
deviance or REML criterion, and the structure of classes or types that
represents such a model. Sufficient detail is included to allow specialization
of these structures by users who wish to write functions to fit specialized
linear mixed models, such as models incorporating pedigrees or smoothing
splines, that are not easily expressible in the formula language used by lmer.
Recent research in cognitive sciences shows a growing interest in spatial-numerical associations. The horizontal SNARC (spatial-numerical association of response codes) effect is defined by faster left-sided responses to small numbers and faster right-sided responses to large numbers in a parity judgment task. In this study we investigated whether there is also a SNARC effect for upper and lower responses. The grounded cognition approach suggests that the universal experience of "more is up" serves as a robust frame of reference for vertical number representation. In line with this view, lower hand responses to small numbers were faster than to large numbers (Experiment 1). Interestingly, the vertical SNARC effect reversed when the lower responses were given by foot instead of the hand (Experiments 2, 3, and 4). We found faster upper (hand) responses to small numbers and faster lower (foot) responses to large numbers. Additional experiments showed that spatial factors cannot account for the reversal of the vertical SNARC effect (Experiments 4 and 5). Our results question the view of "more is up" as a robust frame of reference for spatial-numerical associations. We discuss our results within a hierarchical framework of numerical cognition and point to a possible link between effectors and number representation. (PsycINFO Database Record (c) 2014 APA, all rights reserved).
Abstract The SNARC effect refers to faster reaction times for larger numbers with right-sided responses, and for smaller numbers with left-sided responses (Dehaene et al., 1993), even when numerical magnitude is irrelevant. Although the SNARC is generally thought to reflect a mapping between numbers and space, the question of which spatial reference frame(s) are critical for the effect has not been systematically explored. We propose a dynamic hierarchical organization of the reference frames (from a global left-right frame to body- and object-related frames), where the influence of each frame can be modulated by experimental context. We conducted two experiments based on predictions derived from this organizational system. Experiment 1 compared instructions that differed only in focusing participants' attention on either the response buttons or the hands. Instructions focusing on a hand-based reference frame eliminated the SNARC. Experiment 2 provided the opportunity for an object-centered reference frame to manifest itself in the SNARC. Although we did not observe an effect of an object-centered reference frame, we observed the influence of other reference frames in a context where an object-centered reference frame was emphasized. Altogether, these results support the proposed organization of the reference frames.
Abstract Recent research on spatial number representations suggest that the number space is not necessarily horizontally organized and might also be affected by acquired associations between magnitude and sensory experiences in vertical space. Evidence for this claim is however controversial. The present study now aims to compare vertical and horizontal spatial associations in mental arithmetic. In Experiment 1, participants solved addition and subtraction problems and indicated the result verbally while moving their outstretched right arm continuously either left-, right-, up- or downwards. The analysis of the problem solving performances revealed a motion-arithmetic compatibility effect for spatial actions along both the horizontal and vertical axes. Performances in additions was impaired while making downward compared to upward movements as well as when moving left compared to right and vice versa in subtractions. In Experiment 2, instead of instructing to perform active body movements, participants calculated while the problems moved in one of the four relative directions on the screen. For visual motions, only the motion-arithmetic compatibility effect for the vertical dimension could be replicated. Taken together, our findings provide first evidence for an impact of spatial processing on mental arithmetic. Moreover, the stronger effect of the vertical dimension supports the idea that mental calculations operate on representations of numerical magnitude that are grounded in a vertically organized mental number space.
Expyriment is an open-source and platform-independent lightweight Python library for designing and conducting timing-critical behavioral and neuroimaging experiments. The major goal is to provide a well-structured Python library for script-based experiment development, with a high priority being the readability of the resulting program code. Expyriment has been tested extensively under Linux and Windows and is an all-in-one solution, as it handles stimulus presentation, the recording of input/output events, communication with other devices, and the collection and preprocessing of data. Furthermore, it offers a hierarchical design structure, which allows for an intuitive transition from the experimental design to a running program. It is therefore also suited for students, as well as for experimental psychologists and neuroscientists with little programming experience.
Several studies suggest that numerical and spatial representations are intrinsically linked. Recent findings demonstrate that also motor actions interact with number magnitude processing, showing a motor-to-semantic effect. The current study assesses whether calculation processes can be modulated by motions performed with the whole body. Participants were required to make additions or subtractions while performing (on-line condition) or after having experienced (off-line condition) an ascending or descending motion through a passive (i.e., taking the elevator) or an active (i.e., taking the stairs) mode. Results show a congruency effect between the type of calculation and the direction of the motion depending on: a) the off-line or on-line condition, b) the passive or active mode and c) the real or imagined task. Implications of the results for an embodied and grounded perspective view will be discussed.
Linear mixed-effects models (LMEMs) have become increasingly prominent in psycholinguistics and related areas. However, many researchers do not seem to appreciate how random effects structures affect the generalizability of an analysis. Here, we argue that researchers using LMEMs for confirmatory hypothesis testing should minimally adhere to the standards that have been in place for many decades. Through theoretical arguments and Monte Carlo simulation, we show that LMEMs generalize best when they include the maximal random effects structure justified by the design. The generalization performance of LMEMs including data-driven random effects structures strongly depends upon modeling criteria and sample size, yielding reasonable results on moderately-sized samples when conservative criteria are used, but with little or no power advantage over maximal models. Finally, random-intercepts-only LMEMs used on within-subjects and/or within-items data from populations where subjects and/or items vary in their sensitivity to experimental manipulations always generalize worse than separate F1 and F2 tests, and in many cases, even worse than F1 alone. Maximal LMEMs should be the ‘gold standard’ for confirmatory hypothesis testing in psycholinguistics and beyond.
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)
Converging evidence suggests that visuospatial attention plays a pivotal role in numerical processing, especially when the task involves the manipulation of numerical magnitudes. Visuospatial neglect impairs contralesional attentional orienting not only in perceptual but also in numerical space. Indeed, patients with left neglect show a bias toward larger numbers when mentally bisecting a numerical interval, as if they were neglecting its leftmost part. In contrast, their performance in parity judgments is unbiased, suggesting a dissociation between explicit and implicit processing of numerical magnitude. Here we further investigate the consequences of these visuospatial attention impairments on numerical processing and their interaction with task demands. Patients with right hemisphere damage, with and without left neglect, were administered both a number comparison and a parity judgment task that had identical stimuli and response requirements. Neglect patients’ performance was normal in the parity task, when processing of numerical magnitude was implicit, whereas they showed characteristic biases in the number comparison task, when access to numerical magnitude was explicit. Compared to patients without neglect, they showed an asymmetric distance effect, with slowing of the number immediately smaller than (i.e., to the left of) the reference and a stronger SNARC effect, particularly for large numbers. The latter might index an exaggerated effect of number-space compatibility after ipsilesional (i.e., rightward) orienting in number space. Thus, the effect of neglect on the explicit processing of numerical magnitude can be understood in terms of both a failure to orient to smaller (i.e., contralesional) magnitudes and a difficulty to disengage from larger (i.e., ipsilesional) magnitudes on the number line, which resembles the disrupted pattern of attention orienting in visual space.
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.
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 (SNARC) 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.
Active head turns to the left and right have recently been shown to influence numerical cognition by shifting attention along the mental number line. In the present study, we found that passive whole-body motion influences numerical cognition. In a random-number generation task (Experiment 1), leftward and downward displacement of participants facilitated small number generation, whereas rightward and upward displacement facilitated the generation of large numbers. Influences of leftward and rightward motion were also found for the processing of auditorily presented numbers in a magnitude-judgment task (Experiment 2). Additionally, we investigated the reverse effect of the number-space association (Experiment 3). Participants were displaced leftward or rightward and asked to detect motion direction as fast as possible while small or large numbers were auditorily presented. When motion detection was difficult, leftward motion was detected faster when hearing small number and rightward motion when hearing large number. We provide new evidence that bottom-up vestibular activation is sufficient to interact with the higher-order spatial representation underlying numerical cognition. The results show that action planning or motor activity is not necessary to influence spatial attention. Moreover, our results suggest that self-motion perception and numerical cognition can mutually influence each other. (PsycINFO Database Record (c) 2011 APA, all rights reserved).
Spatial–numerical associations (SNAs) are prevalent yet their origin is poorly understood. We first consider the possible prime role of reading habits in shaping SNAs and list three observations that argue against a prominent influence of this role: (1) directional reading habits for numbers may conflict with those for non-numerical symbols, (2) short-term experimental manipulations can overrule the impact of decades of reading experience, (3) SNAs predate the acquisition of reading. As a promising alternative, we discuss behavioral, neuroscientific, and neuropsychological evidence in support of finger counting as the most likely initial determinant of SNAs. Implications of this “manumerical cognition” stance for the distinction between grounded, embodied, and situated cognition are discussed.
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.
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.
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.
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.
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.
Since the time of Pythagoras, numerical and spatial representations have been inextricably linked. We suggest that the relationship between the two is deeply rooted in the brain's organization for these capacities. Many behavioural and patient studies have shown that numerical-spatial interactions run far deeper than simply cultural constructions, and, instead, influence behaviour at several levels. By combining two previously independent lines of research, neuroimaging studies of numerical cognition in humans, and physiological studies of spatial cognition in monkeys, we propose that these numerical-spatial interactions arise from common parietal circuits for attention to external space and internal representations of numbers.
Differences in performance with various stimulus-response mappings are among the most prevalent findings for binary choice reaction tasks. The authors show that perceptual or conceptual similarity is not necessary to obtain mapping effects; a type of structural similarity is sufficient. Specifically, stimulus and response alternatives are coded as positive and negative polarity along several dimensions, and polarity correspondence is sufficient to produce mapping effects. The authors make the case for this polarity correspondence principle using the literature on word-picture verification and then provide evidence that polarity correspondence is a determinant of mapping effects in orthogonal stimulus-response compatibility, numerical judgment, and implicit association tasks. The authors conclude by discussing implications of this principle for interpretation of results from binary choice tasks and future model development.
The tendency to respond faster with the left hand to relatively small numbers and faster with the right hand to relatively large numbers (spatial numerical association of response codes, SNARC effect) has been interpreted as an automatic association of spatial and numerical information. We investigated in two experiments the impact of task-irrelevant memory representations on this effect. Participants memorized three Arabic digits describing a left-to-right ascending number sequence (e.g., 3-4-5), a descending sequence (e.g., 5-4-3), or a disordered sequence (e.g., 5-3-4) and indicated afterwards the parity status of a centrally presented digit (i.e., 1, 2, 8, or 9) with a left/right keypress response. As indicated by the reaction times, the SNARC effect in the parity task was mediated by the coding requirements of the memory tasks. That is, a SNARC effect was only present after memorizing ascending or disordered number sequences but disappeared after processing descending sequences. Interestingly, the effects of the second task were only present if all sequences within one experimental block had the same type of order. Taken together, our findings are inconsistent with the idea that spatial-numerical associations are the result of an automatic and obligatory cognitive process but do suggest that coding strategies might be responsible for the cognitive link between numbers and space.
Reproducibility is a defining feature of science, but the extent to which it characterizes current research is unknown. We conducted replications of 100 experimental and correlational studies published in three psychology journals using high-powered designs and original materials when available. Replication effects were half the magnitude of original effects, representing a substantial decline. Ninety-seven percent of original studies had statistically significant results. Thirty-six percent of replications had statistically significant results; 47% of original effect sizes were in the 95% confidence interval of the replication effect size; 39% of effects were subjectively rated to have replicated the original result; and if no bias in original results is assumed, combining original and replication results left 68% with statistically significant effects. Correlational tests suggest that replication success was better predicted by the strength of original evidence than by characteristics of the original and replication teams.
Linear mixed-effects models (LMEMs) have become increasingly prominent in psycholin-guistics and related areas. However, many researchers do not seem to appreciate how random effects structures affect the generalizability of an analysis. Here, we argue that researchers using LMEMs for confirmatory hypothesis testing should minimally adhere to the standards that have been in place for many decades. Through theoretical arguments and Monte Carlo simulation, we show that LMEMs generalize best when they include the maximal random effects structure justified by the design. The generalization performance of LMEMs including data-driven random effects structures strongly depends upon modeling criteria and sample size, yielding reasonable results on moderately-sized samples when conservative criteria are used, but with little or no power advantage over maximal models. Finally, random-intercepts-only LMEMs used on within-subjects and/or within-items data from populations where subjects and/or items vary in their sensitivity to experimental manipulations always generalize worse than separate F 1 and F 2 tests, and in many cases, even worse than F 1 alone. Maximal LMEMs should be the 'gold standard' for confirmatory hypothesis testing in psycholinguistics and beyond.
A large number of experimental findings from neuroscience and experimental psychology demonstrated interactions between spatial cognition and numerical cognition. In particular, many researchers posited a horizontal mental number line, where small numbers are thought of as being to the left of larger numbers. This review synthesizes work on the mental association between space and number, indicating the existence of multiple spatial mappings: Recent research has found associations between number and vertical space, as well as associations between number and near/far space. We discuss number space in three dimensions with an eye on potential origins of the different number mappings, and how these number mappings fit in with our current knowledge of brain organization and brain-culture interactions. We derive novel predictions and show how this research fits into a general view of cognition as embodied, grounded and situated.
Discusses man's capabilities and limitations as an element in a closed loop control system under normal environmental conditions. Factors considered include the nature of manual control, modes of tracking, mathematical models of human operators, and characteristics of controls and displays in tracking tasks. (21/2 p ref) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
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.
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.
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.
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.
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]. 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.
The space around us is represented not once but many times in parietal cortex. These multiple representations encode locations and objects of interest in several egocentric reference frames. Stimulus representations are transformed from the coordinates of receptor surfaces, such as the retina or the cochlea, into the coordinates of effectors, such as the eye, head, or hand. The transformation is accomplished by dynamic updating of spatial representations in conjunction with voluntary movements. This direct sensory-to-motor coordinate transformation obviates the need for a single representation of space in environmental coordinates. In addition to representing object locations in motoric coordinates, parietal neurons exhibit strong modulation by attention. Both top-down and bottom-up mechanisms of attention contribute to the enhancement of visual responses. The saliance of a stimulus is the primary factor in determining the neural response to it. Although parietal neurons represent objects in motor coordinates, visual responses are independent of the intention to perform specific motor acts.
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.
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].
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.
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.
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.
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.
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