Deconstructing spatial-numerical associations

Spatial associations of number and pitch in human newborns

Humans use space to think, reason about, externally represent, and even talk about many dimensions (e.g., time, pitch height). One dimension that appears to exploit spatial resources is the mental representation of the numerosity of a set in the form of a mental number line. Although the horizontal number-space mapping is present from birth (small-left vs. large-right), it is unknown whether it extends to other spatial axes from birth or whether it is later acquired through development/experience. Moreover, newborns map changes in pitch height onto a vertical axis (low pitch-bottom vs. high pitch-top), but it is an open question whether it extends to other spatial axes. We presented newborns (N = 64 total, n = 16 per experiment, 0-4 days) with an auditory increase/decrease in magnitude along with a visual figure on a vertically oriented screen (bottom vs. top, change in number: Experiments 1 and 2; change in pitch: Experiment 3) or on a horizontally oriented screen (left vs. right, change in pitch: Experiment 4). Newborns associated changes in magnitude with a vertical axis only when experiencing an increase in magnitude (increase/up); however, the possibility that visuospatial biases could account for this asymmetric pattern are discussed. Newborns did not map changes in pitch horizontally (Experiment 4), in line with previous work showing that the horizontal mapping of number at birth does not generalize to other dimensions. These findings suggest that the flexible use of different spatial axes to map magnitude is not functional at birth and that the horizontal mapping of number might be privileged.

The role of cognitive control in the interaction of the SNARC and MARC effects

Many studies have identified two types of spatial congruency effects in number parity judgment tasks: the SNARC effect (Spatial-Numerical Association of Response Codes), related to numerical magnitude, and the MARC effect (Linguistic Markedness Association of Response Codes), associated with parity. Although previous work has found that these effects interact, the mechanisms underlying the interaction are unclear. Previous studies have investigated the effect of linguistic connections on the activation of the SNARC and MARC effects in right-to-left readers by manipulating the time interval between tasks. We propose that a cognitive control mechanism mediates this phenomenon, with the level of cognitive conflict induced by the MARC effect under varying conditions being a critical factor in influencing spatial-numerical associations. We first performed four behavioral experiments manipulating time intervals between parity-to-response mappings. The results demonstrate that interactions between the SNARC and MARC effects are not sensitive to changes in time intervals but are primarily influenced by the congruency between the two effects. We then performed an event related potentials study. The response patterns observed in the P300 component support the hypothesis that cognitive conflict levels influence spatial-numerical associations. In conclusion, this study highlights the essential role of cognitive control in modulating the conflict between the SNARC and MARC effects, providing a new theoretical perspective on the dynamic characteristics of spatial-numerical associations.

A SNARC-like effect for visual speed

Numerical and nonnumerical magnitudes can be represented along a hypothetical left-to-right continuum, where smaller quantities are associated with the left side and larger quantities with the right side. However, these representations are flexible, as their intensity and direction can be modulated by various contextual cues and task demands. In four experiments, we investigated the spatial representation of visual speed. Visual speed is inherently connected to physical space and spatial directions, making it distinct from other magnitudes. With this in mind, we explored whether the spatial representation of visual speed aligns with the typical left-to-right orientation or is influenced dynamically by the movement direction of the stimuli. Participants compared the speed of random dot kinematograms to a reference speed using lateralised response keys. On each trial, all dots moved consistently in one single direction, which varied across the experiments and could also vary from trial to trial in Experiments 2 and 4. The dot movements were left-to-right (Experiment 1), random across a 360° spectrum (Experiment 2), right-to-left (Experiment 3), and random left-to-right or right-to-left (Experiment 4). The results supported a relatively stable left-to-right spatial representation of speed (Experiments 1-3), which was compromised by mutable motion directions along the horizontal axis (Experiment 4). We suggest that representing stimuli as belonging to a single set rather than different sets, may be crucial for the emergence of spatial representations of quantities.

Vertical and horizontal space-valence associations: A meta-analysis

Previous research found associations between lower vs. upper space and negative vs. positive stimuli correspondingly (vertical Space-Valence Associations, SVAs) and between the left vs. right side and negative vs. positive stimuli correspondingly (horizontal SVAs). We conducted a comprehensive meta-analysis of SVAs for both dimensions in behavioral studies. We tested the robustness of SVAs and examined factors potentially modulating them: participants' culture, handedness, gender, age, the exact valence domain under study, the experimental task, type of stimuli, publication year, and statistics used. Articles were extracted from Web of Science, PubMed, and ScienceDirect in February 2021. Overall, 91 articles with 199 experiments and 21,951 participants were included in the final analysis. We found robust evidence of SVAs in vertical (r = .440, k = 111 experiments) and horizontal dimensions (r = .310; k = 88 experiments), with little evidence for literature biases. The distribution of effect sizes was highly heterogeneous, even after subgroup analyses, which indicates unidentified factors varying across studies. Experiments on vertical SVAs explicitly asking participants to evaluate valence showed larger effect sizes than experiments where valence remained task-irrelevant. There was a robust effect of handedness on horizontal SVAs: Participants associated positive stimuli with the side of their dominant hand. There was also some evidence of cultural influences on the horizontal SVAs. Overall, our meta-analysis revealed a hierarchy of factors modulating activation of SVAs, which includes both situated and embodied factors. It is, therefore, essential to focus on specific concept categories and contexts rather than consider abstract concepts in general. PUBLIC SIGNIFICANCE STATEMENT: This meta-analysis revealed medium effects of space-valence associations: Upper/right space is associated with positive and lower/right space with negative concepts. On the vertical dimension, this effect is modulated by valence being task-relevant, e.g., directly asking people about valence results in stronger associations. For the horizontal dimension, left-handers robustly showed a reversed effect (i.e., left is good); horizontal space-valence associations might be even stronger in non-Western countries.

A left-to-right bias in number-space mapping across ages and cultures

Number and space are inherently related. Previous research has provided evidence that numbers are aligned to a so-called "mental number line", which is malleable and affected by cultural factors mostly linked to literacy-related habits. However, preverbal humans and non-human animals also map numerosities into space, in a consistent left-to-right direction. These contrasting findings raise the question of whether Spatial Numerical Associations (SNA) are culturally or biologically determined. Here, we investigated Italian adults, Italian preschoolers, and Himba adults (an indigenous population with an oral cultural system) to examine whether cultural influences are necessary for SNA to emerge. We found that, when explicitly asked to order numerosities, only Italian adults showed a consistent left-to-right preference, while preschoolers and Himba adults did not have a consistent preference for one direction or the other. On the other hand, in a numerosity comparison task, all groups performed better when small numerosities were presented in the left hemispace. These results suggest that humans may display two forms of SNAs, one that emerges mostly in implicit tasks and is biologically determined, and one that emerges in explicit ordering tasks and is determined by cultural habits.

Changes in Brain Functional Connectivity Underlying the Space-Number Association

Whether small number magnitudes are inherently represented as lying to the left of larger ones, the space-number association (SNA), is an important issue in mathematical cognition. In this fMRI study, we used a go/no-go implicit association task to investigate the brain activity and functional connectivity underlying the SNA. Arabic digits lower or higher than 5 and left- or right-pointing arrows were alternated as central targets. In a single-code task condition, participants responded to a specific number magnitude and to all arrows or to a specific arrow direction and to all number magnitudes. In a joint-code (JC) condition, responses were provided after congruent, for example, "go when a number is lower than 5 or an arrow points left," or incongruent, for example, "go when a number is lower than 5 or an arrow points right," SNAs. The SNA was only found in the JC condition, where responses were faster with congruent instructions. Analyses of fMRI functional connectivity showed that the SNA was matched with enhanced excitatory inputs from ACC, the left TPJ, and the left inferior frontal gyrus to the left and right intraparietal sulcus (IPS). Incongruent JC trials were associated with enhanced excitatory modulation from ACC to the left and right IPS. These results show that the SNA is associated with enhanced activation of top-down brain control and changes in the functional interaction between the left and right IPS. We conclude that the SNA does not depend on an inherent and bottom-up spatial coding of number magnitudes.

Linguistic markedness and body specificity in parity judgments: evidence from a go/no-go task

In two experiments we tested the contribution of linguistic markedness and affective evaluation (i.e., body specificity) to the representation of abstract numerical concepts, such as parity. To this end, we employed speeded parity judgments of digits (Exp 1) or number words (Exp 2) in a go/no-go task. Fifty right-handed participants completed four blocks of trials in each experiment. In two blocks, they responded to even numbers (2, 4, 6, or 8) and in the other two blocks they responded to odd numbers (1, 3, 7, or 9). In each pair of blocks, they responded once with their right hand and once with their left hand. Results revealed faster right-hand responses to even than to odd digits (Exp 1), and faster left-hand response to odd than to even number words (Exp 2). In addition, in both experiments, we found faster responses to small-odd than large-odd digits and number words. The results support the conclusion that the affective evaluation of parity and linguistic markedness makes independent contributions to the representation of parity.

Effect of egocentric and allocentric reference frames on spatial-numerical associations

From an embodied view of cognition, sensorimotor mechanisms are strongly involved in abstract processing, such as Arabic number meanings. For example, spatial cognition can influence number processing. These spatial-numerical associations (SNAs) have been deeply explored since the seminal SNAs of response code (SNARC) effect (i.e., faster left/right sided responses to small/large magnitude numbers, respectively). Although these SNAs along the transverse plane (left-to-right axis) have been extensively studied in cognitive sciences, no systematic assessment of other planes of the tridimensional space has been afforded. Moreover, there is no evidence of how SNAs organise themselves throughout the changes in spatial body-reference frames (egocentric and allocentric). Hence, this study aimed to explore how SNAs organise themselves along the transverse and sagittal planes when egocentric and allocentric changes are processed during body displacements in the environment. In the first experiment, the results revealed that, when the participants used an egocentric reference, SNAs were observed only along the sagittal plane. In a second experiment that used an allocentric reference, the reversed pattern of results was observed: SNAs were present only along the transverse plane of the body. Overall, these findings suggest that, depending on the spatial reference frames of the body, SNAs are strongly flexible.

Simultaneous but independent spatial associations for pitch and loudness

For the auditory dimensions loudness and pitch a vertical SARC effect (Spatial Association of Response Codes) exists: When responding to loud (high) tones, participants are faster with top-sided responses compared to bottom-sided responses and vice versa for soft (low) tones. These effects are typically explained by two different spatial representations for both dimensions with pitch being represented on a helix structure and loudness being represented as spatially associated magnitude. Prior studies show incoherent results with regard to the question whether two SARC effects can occur at the same time as well as whether SARC effects interact with each other. Therefore, this study aimed to investigate the interrelation between the SARC effect for pitch and the SARC effect for loudness in a timbre discrimination task. Participants (N = 36) heard one tone per trial and had to decide whether the presented tone was a violin tone or an organ tone by pressing a top-sided or bottom-sided response key. Loudness and pitch were varied orthogonally. We tested the occurrence of SARC effects for pitch and loudness as well as their potential interaction by conducting a multiple linear regression with difference of reaction time (dRT) as dependent variable, and loudness and pitch as predictors. Frequentist and Bayesian analyses revealed that the regression coefficients of pitch and loudness were smaller than zero indicating the simultaneous occurrence of a SARC effects for both dimensions. In contrast, the interaction coefficient was not different from zero indicating an additive effect of both predictors.

On the embodied nature of knowledge: From neurons to numbers

Interdisciplinary investigations of the human mind through the cognitive sciences have identified a key role of the body in representing knowledge. After characterizing knowledge at grounded, embodied, and situated levels, number knowledge is analyzed from this hierarchical perspective. Lateralized cortical processing of coarse versus fine detail is identified as a grounding substrate for the population stereotype few/left, many/right, which then contributes to number-related sensory and motor biases at the embodied and situated levels. Implications of this perspective for education and rehabilitation are discussed.

Similarities of SNARC, cognitive Simon, and visuomotor Simon effects in terms of response time distributions, hand-stimulus proximity, and temporal dynamics

The spatial-numerical association of response codes (SNARC) and Simon effects are attributed to the same type of conflict according to dimensional overlap (DO) theory: the congruency of task-irrelevant spatial information and the selected response (e.g., left or right). However, previous studies have yielded inconsistent results regarding the relationship between the two effects, with some studies reporting an interaction while others did not. This discrepancy may be attributed to the use of different types of Simon effects (visuomotor and cognitive Simon effects) in these studies, as the spatial codes associated with these two types of Simon effects are distinct (exogenous and endogenous, respectively). The aim of this study was to address these inconsistencies and gain a better understanding of the similarities and differences in spatial representations generated by spatial location, semantic information, and numerical information. We attempted to classify the relationships among the SNARC and Simon effects. Specifically, the visuomotor Simon, cognitive Simon, and SNARC effects were compared from three perspectives: the response time (RT) distribution, hand-stimulus proximity, and temporal dynamics (with the drift diffusion model; DDM). Regarding RTs, the results showed that the visuomotor Simon effect decreased with increased values of RT bins, while the cognitive Simon and SNARC effects increased. Additionally, the visuomotor Simon effect was the only effect influenced by hand-stimulus proximity, with a stronger effect observed in the hand-proximal condition than in the hand-distal condition. Regarding the DDM results, only the visuomotor Simon effect exhibited a higher drift rate and longer non-decision time in the incompatible condition than in the compatible condition. Conversely, both the SNARC and cognitive Simon effects exhibited an inverse pattern regarding the drift rate and no significant difference in non-decision time between the two conditions. These findings suggest that the SNARC effect is more similar to the cognitive Simon effect than the visuomotor Simon effect, indicating that the endogenous spatial-numerical representation of the SNARC effect might share an underlying processing mechanism with the endogenous spatial-semantic representation of the cognitive Simon effect but not with the exogenous location representation of the visuomotor Simon effect. Our results further demonstrate that the origin of spatial information could impact the classification of conflicts and supplement DO theory.

Language directs spatial attention differently in explicit and implicit tasks

How do words with either explicit or implicit spatial meanings (e.g., DOWN, BOOT) shift our attention? Recent studies, presenting prime words followed by probe targets, suggested that, for implicit spatial words, both the spatial meaning of prime words and the target locations must be processed to induce congruency benefits. Here we examined the functional necessity of the latter location component. 91 healthy adults discriminated target letters that followed explicit or implicit spatial words. Words either did or did not have to be semantically processed. Target discrimination speed was used to compute congruency benefits. With explicit prime words, spatial congruency effects emerged without semantic processing instructions. In contrast, with implicit prime words, only instructing their semantic processing ensured a congruency benefit. This shows that, for implicit spatial words, spatial processing of target locations is not necessary; instead, processing the spatial connotation of the prime, together with the identity of the target, can induce congruency benefits. Our results help to understand previous conflicting findings.

Ecological Meanings: A Consensus Paper on Individual Differences and Contextual Influences in Embodied Language

Embodied theories of cognition consider many aspects of language and other cognitive domains as the result of sensory and motor processes. In this view, the appraisal and the use of concepts are based on mechanisms of simulation grounded on prior sensorimotor experiences. Even though these theories continue receiving attention and support, increasing evidence indicates the need to consider the flexible nature of the simulation process, and to accordingly refine embodied accounts. In this consensus paper, we discuss two potential sources of variability in experimental studies on embodiment of language: individual differences and context. Specifically, we show how factors contributing to individual differences may explain inconsistent findings in embodied language phenomena. These factors include sensorimotor or cultural experiences, imagery, context-related factors, and cognitive strategies. We also analyze the different contextual modulations, from single words to sentences and narratives, as well as the top-down and bottom-up influences. Similarly, we review recent efforts to include cultural and language diversity, aging, neurodegenerative diseases, and brain disorders, as well as bilingual evidence into the embodiment framework. We address the importance of considering individual differences and context in clinical studies to drive translational research more efficiently, and we indicate recommendations on how to correctly address these issues in future research. Systematically investigating individual differences and context may contribute to understanding the dynamic nature of simulation in language processes, refining embodied theories of cognition, and ultimately filling the gap between cognition in artificial experimental settings and cognition in the wild (i.e., in everyday life).

How time gets spatial: factors determining the stability and instability of the mental time line

Left-to-right readers classify faster past events with motor responses on the left side of space and future events with responses on the right side. This suggests a left-to-right spatial organization in the mental representation of time. Here, we show that the significance and reliability of this representation are linked to the joint use of temporal and spatial codes in the task at hand. In a first unimanual Go/No-Go Implicit Association Test (IAT), attending selectively to "past" or to "future" words did not activate corresponding "left" or "right" spatial concepts and vice versa. In a second IAT, attending to both temporal (i.e., "past" and "future") words and spatial targets (i.e., "left" and "right") pointing arrows produced faster responses for congruent rather than incongruent combinations of temporal and spatial concepts in task instructions (e.g., congruent = "Go with past words and left-pointing arrows"; incongruent = "Go with past words and right-pointing arrows"). This effect increased markedly in a STEARC task where spatial codes defined the selection between "left-side" and "right-side" button presses that were associated with "past" and "future" words. Two control experiments showed only partial or unreliable space-time congruency effects when (a) participants attended to superordinate semantic codes that included both spatial "left"/"right" or temporal "past/future" subordinate codes; (b) a primary speeded response was assigned to one dimension (e.g., "past vs. future") and a nonspeeded one to the other dimension (e.g., "left" vs. "right"). These results help to define the conditions that trigger a stable and reliable spatial representation of time-related concepts.

How to not induce SNAs: The insufficiency of directional force

People respond faster to smaller numbers in their left space and to larger numbers in their right space. Here we argue that movements in space contribute to the formation of spatial-numerical associations (SNAs). We studied the impact of continuous isometric forces along the horizontal or vertical cardinal axes on SNAs while participants performed random number production and arithmetic verification tasks. Our results suggest that such isometric directional force do not suffice to induce SNAs.

When time stands upright: STEARC effects along the vertical axis

According to the spatial-temporal association of response codes (STEARC) effect, time can be spatially represented from left to right. However, exploration of a possible STEARC effect along the vertical axis has yielded mixed results. Here, in six experiments based on a novel paradigm, we systematically explored whether a STEARC effect could emerge when participants were asked to classify the actual temporal duration of a visual stimulus. Speeded manual responses were provided using a vertically oriented response box. Interestingly, although a top-to-bottom time representation emerged when only two temporal durations were employed, an inverted bottom-to-top time representation emerged when a denser set of temporal durations, arranged along a continuum, was used. Moreover, no STEARC effects emerged when participants classified the shapes of visual stimuli rather than their temporal duration. Finally, three additional experiments explored the STEARC effect along the horizontal axis, confirming that the paradigm we devised successfully replicated the standard left-to-right representation of time. These results provide supporting evidence for the notion that temporal durations can be mapped along the vertical axis, and that such mapping appears to be relatively flexible.

Spatio-Numerical Mapping in 3D

The close link between number and space is illustrated by the Spatial Numerical Association of Response Codes (SNARC) effect. The current research focuses on the flexibility of the SNARC across three dimensions. Shaki and Fischer (2018) pointed out that spatial attributes of stimuli and response effectors can favor an ad hoc spatial representation. In this paper, we aimed to broaden this perspective using two Go/NoGo experiments with digits being presented at two spatial locations while a central response was required. In Experiment 1, stimuli appeared either to the left or right (horizontal) and below or above fixation (vertical). In Experiment 2, as the monitor was laying down flat on the desk, stimuli appeared either to the left or right (horizontal) and either close or far from the observer (midsagittal). The results of Experiment 1 show significant effects for the two dimensions (horizontal, vertical), while in Experiment 2, we observe only a barely significant effect for the sagittal axis. We interpret these findings as showing (1) the importance of motor response spatialization in eliciting the SNAs and (2) the dominance of the vertical axis over the horizontal when the spatial component of the motor response is removed.

Reading/writing direction as a source of directional bias in spatial cognition: Possible mechanisms and scope

Becoming literate has been argued to have a range of social, economic and psychological effects. Less examined is the extent to which repercussions of becoming literate may vary as a function of writing system variation. A salient way in which writing systems differ is in their directionality. Recent studies have claimed that directional biases in a variety of spatial domains are attributable to reading and writing direction. This claim is the focus of the present paper, which considers the scope and possible mechanisms underlying script directionality effects in spatial cognition, with particular attention to domains with real-world relevance. Three questions are addressed: (1) What are possible mediating and moderator variables relevant to script directionality effects in spatial cognition? (2) Does script directionality exert a fixed or a malleable effect? and (3) How can script directionality effects be appropriately tested? After discussing these questions in the context of specific studies, we highlight general methodological issues in this literature and provide recommendations for the design of future research.

Processing stage flexibility of the SNARC effect: Task relevance or magnitude relevance?

Previous studies have shown that the processing stage of the spatial-numerical association of response codes (SNARC) effect is flexible. Two recent studies used the same experimental paradigm to check whether the SNARC effect occurred in the semantic-representation stage but reached contradictory conclusions, showing that the SNARC effect was influenced by a magnitude Stroop effect in a magnitude comparison task but not by a parity Stroop effect in a parity judgment task. Those two studies had two distinct operational factors: the task type (magnitude comparison task or parity judgment task, with the numerical magnitude information task-relevant or task-irrelevant) and the semantic representation stage-related interference information (magnitude or parity Stroop effect, with the interference information magnitude-relevant or magnitude-irrelevant). To determine which factor influenced the SNARC effect, in the present study, the Stroop effect was switched in the two tasks based on the previous studies. The findings of four experiments consistently showed that the SNARC effect was not influenced by the parity Stroop effect in the magnitude comparison task but was influenced by the magnitude Stroop effect in the parity judgment task. Combined with the results of those two contradictory studies, the findings indicated that regardless of the task type or the task relevance of numerical magnitude information, magnitude-relevant interference information was the primary factor to affect the SNARC effect. Furthermore, a two-stage processing model that explained the observed flexibility of the SNARC effect was proposed and discussed.

Spatial-numerical associations without a motor response? Grip force says 'Yes'

In numerical processing, the functional role of Spatial-Numerical Associations (SNAs, such as the association of smaller numbers with left space and larger numbers with right space, the Mental Number Line hypothesis) is debated. Most studies demonstrate SNAs with lateralized responses, and there is little evidence that SNAs appear when no response is required. We recorded passive holding grip forces in no-go trials during number processing. In Experiment 1, participants performed a surface numerical decision task ("Is it a number or a letter?"). In Experiment 2, we used a deeper semantic task ("Is this number larger or smaller than five?"). Despite instruction to keep their grip force constant, participants' spontaneous grip force changed in both experiments: Smaller numbers led to larger force increase in the left than in the right hand in the numerical decision task (500-700 ms after stimulus onset). In the semantic task, smaller numbers again led to larger force increase in the left hand, and larger numbers increased the right-hand holding force. This effect appeared earlier (180 ms) and lasted longer (until 580 ms after stimulus onset). This is the first demonstration of SNAs with passive holding force. Our result suggests that (1) explicit motor response is not a prerequisite for SNAs to appear, and (2) the timing and strength of SNAs are task-dependent. (216 words).

Vertical versus horizontal Spatial-Numerical Associations (SNA): A processing advantage for the vertical dimension

Humans have associations between numbers and physical space on both horizontal and vertical dimensions, called Spatial-Numerical Associations (SNAs). Several studies have considered the hypothesis of there being a dominant orientation by examining on which dimension people are more accurate and efficient at responding during various directional SNA tasks. However, these studies have difficulty differentiating between a person’s efficiency at accessing mental representations of numbers in space, and the efficiency at which they exercise motor control functions, particularly bilateral ones, when manifesting a response during an explicit directional SNA task. In this study we use a conflict test employing combined explicit magnitude and spatial directional processing in which pairs of numbers are placed along the diagonal axes and response accuracy/efficiency are considered across the horizontal and vertical dimensions simultaneously. Participants indicated which number in each pair was largest using a joystick that only required unilateral input. The experiment was run in English using Arabic numerals. Results showed that directional SNAs have a vertical rather than horizontal dominance. A moderating factor was also found during post-hoc analysis, where response efficiency, but not accuracy, is conditional on a person’s native language being oriented the same as the language of the experiment, left to right. The dominance of the vertical orientation suggests adopting more vertical display formats for numbers may provide situational advantages, particularly for explicit magnitude comparisons, with some domains like flight controls and the stock market already using these in some cases.

The role of cognitive control in the SNARC effect: A review

The spatial-numerical association of response codes (SNARC) effect, in which people respond to small numbers faster with the left hand and to large numbers faster with the right hand, is a popular topic in cognitive psychology. Some well-known theoretical accounts explaining this effect include the mental number line model, polarity correspondence principle, dual-route model, and working memory account. However, these fail to explain the finding that the size of the SNARC effect is modulated by cognitive control. Here, we propose a new account-a cognitive control-based view of the SNARC effect. This view argues that the SNARC effect is fundamentally determined by cognitive control in resolving conflicts during stimulus-response mapping. Several subcomponents of cognitive control, such as working memory, mental or task set shifting, inhibition control, and conflict adaptation, can easily modulate the SNARC effect. The cognitive control-based view can account for the flexible SNARC effect observed in diverse task situations while providing new insight into its mechanism.

The SNARC effect: a preregistered study on the interaction of horizontal, vertical, and sagittal spatial-numerical associations

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.

Catch the star! Spatial information activates the manual motor system

Previous research demonstrated a close bidirectional relationship between spatial attention and the manual motor system. However, it is unclear whether an explicit hand movement is necessary for this relationship to appear. A novel method with high temporal resolution–bimanual grip force registration–sheds light on this issue. Participants held two grip force sensors while being presented with lateralized stimuli (exogenous attentional shifts, Experiment 1), left- or right-pointing central arrows (endogenous attentional shifts, Experiment 2), or the words "left" or "right" (endogenous attentional shifts, Experiment 3). There was an early interaction between the presentation side or arrow direction and grip force: lateralized objects and central arrows led to a larger increase of the ipsilateral force and a smaller increase of the contralateral force. Surprisingly, words led to the opposite pattern: larger force increase in the contralateral hand and smaller force increase in the ipsilateral hand. The effect was stronger and appeared earlier for lateralized objects (60 ms after stimulus presentation) than for arrows (100 ms) or words (250 ms). Thus, processing visuospatial information automatically activates the manual motor system, but the timing and direction of this effect vary depending on the type of stimulus.

The Impact of Coding Levels of Magnitude and of Spatial-Direction on the Spatial-Numerical Association of Response Codes Effect of Negative Numbers

Whether negative numbers have a fixed spatial–numerical association of response codes effect (SNARC effect), and (if they have) whether the spatial representation of negative numbers is associated with negative numbers’ absolute or signed values remains controversial. In this study, through three experiments, the coding level of the magnitude and the spatial-direction is manipulated. In the first experiment, participants are required to code the magnitude and spatial-direction explicitly by using a magnitude classification task. In the second experiment, participants are forced to code the magnitude implicitly as well as to code the spatial-direction explicitly by utilizing a cuing task. In the third experiment, participants are obliged to code the magnitude explicitly as well as to code the spatial-direction implicitly by adopting a magnitude and arrow-direction classification tasks with Go/No-Go responses. The results show that (1) the absolute value of negative numbers associates with space when the magnitude of negative numbers is explicitly coded, no matter employing the explicit or implicit spatial-direction; (2) the signed value of negative numbers associates with space under the condition of implicit magnitude as well as explicit spatial-direction. In conclusion, the current study indicates that the SNARC effect of negative numbers is variable in different conditions, and the type of SNARC effect about negative numbers is modulated by the joint coding level of the magnitude and spatial-direction.

Number to me, space to you: Joint representation of spatial-numerical associations

Recent work has shown that number concepts activate both spatial and magnitude representations. According to the social co-representation literature which has shown that participants typically represent task components assigned to others together with their own, we asked whether explicit magnitude meaning and explicit spatial coding must be present in a single mind, or can be distributed across two minds, to generate a spatial-numerical congruency effect. In a shared go/no-go task that eliminated peripheral spatial codes, we assigned explicit magnitude processing to participants and spatial processing to either human or non-human co-agents. The spatial-numerical congruency effect emerged only with human co-agents. We demonstrate an inter-personal level of conceptual congruency between space and number that arises from a shared conceptual representation not contaminated by peripheral spatial codes. Theoretical implications of this finding for numerical cognition are discussed.

The vertical space-time association

The space-time interaction suggests a left-to-right directionality in the mind's representation of elapsing time. However, studies showing a possible vertical time representation are scarce and contradictory. In Experiment 1, 32 participants had to judge the duration (200, 300, 500, or 600 ms) of the target stimulus that appeared at the top, centre, or bottom of the screen, compared with a reference stimulus (400 ms) that always appeared in the centre of the screen. In Experiment 2, 32 participants were administered the same procedure, but the reference stimulus appeared at the top, centre, or bottom of the screen and the target stimulus was fixed in the centre location. In both experiments, a space-time interaction was found with an association between short durations and bottom response key as well as between long durations and top key. The evidence of a vertical mental timeline was further confirmed by the distance effect with a lower level of performance for durations close to that of the reference stimulus. The results suggest a bottom-to-top mapping of time representation, more in line with the metaphor "more is up."

Temporal Coordination in Piano Duet Networked Music Performance (NMP): Interactions Between Acoustic Transmission Latency and Musical Role Asymmetries

Today’s audio, visual, and internet technologies allow people to interact despite physical distances, for casual conversation, group workouts, or musical performance. Musical ensemble performance is unique because interaction integrity critically depends on the timing between each performer’s actions and when their acoustic outcomes arrive. Acoustic transmission latency (ATL) between players is substantially longer for networked music performance (NMP) compared to traditional in-person spaces where musicians can easily adapt. Previous work has shown that longer ATLs slow the average tempo in ensemble performance, and that asymmetric co-actor roles and empathy-related traits affect coordination patterns in joint action. Thus, we are interested in how musicians collectively adapt to a given latency and how such adaptation patterns vary with their task-related and person-related asymmetries. Here, we examined how two pianists performed duets while hearing each other’s auditory outcomes with an ATL of 10, 20, or 40 ms. To test the hypotheses regarding task-related asymmetries, we designed duets such that pianists had: (1) a starting or joining role and (2) a similar or dissimilar musical part compared to their co-performer, with respect to pitch range and melodic contour. Results replicated previous clapping-duet findings showing that longer ATLs are associated with greater temporal asynchrony between partners and increased average tempo slowing. While co-performer asynchronies were not affected by performer role or part similarity, at the longer ATLs starting performers displayed slower tempos and smaller tempo variability than joining performers. This asymmetry of stability vs. flexibility between starters and joiners may sustain coordination, consistent with recent joint action findings. Our data also suggest that relative independence in musical parts may mitigate ATL-related challenges. Additionally, there may be a relationship between co-performer differences in empathy-related personality traits such as locus of control and coordination during performance under the influence of ATL. Incorporating the emergent coordinative dynamics between performers could help further innovation of music technologies and composition techniques for NMP.

From Affordances to Abstract Words: The Flexibility of Sensorimotor Grounding

The sensorimotor system plays a critical role in several cognitive processes. Here, we review recent studies documenting this interplay at different levels. First, we concentrate on studies that have shown how the sensorimotor system is flexibly involved in interactions with objects. We report evidence demonstrating how social context and situations influence affordance activation, and then focus on tactile and kinesthetic components in body-object interactions. Then, we turn to word use, and review studies that have shown that not only concrete words, but also abstract words are grounded in the sensorimotor system. We report evidence that abstract concepts activate the mouth effector more than concrete concepts, and discuss this effect in light of studies on adults, children, and infants. Finally, we pinpoint possible sensorimotor mechanisms at play in the acquisition and use of abstract concepts. Overall, we show that the involvement of the sensorimotor system is flexibly modulated by context, and that its role can be integrated and flanked by that of other systems such as the linguistic system. We suggest that to unravel the role of the sensorimotor system in cognition, future research should fully explore the complexity of this intricate, and sometimes slippery, relation.

Systematic spatial distortion of quantitative estimates

Magnitude estimation has been studied since the beginnings of scientific psychology and constitutes a fundamental aspect of human behavior. Yet, it has apparently never been noticed that estimates depend on the spatial arrangement used. We tested 167 adults in three experiments to show that the spatial layout of stimuli and responses systematically distorts number estimation, length production, and weight reproduction performance. The direction of distortion depends on the observer's counting habits, but does not seem to reflect the use of spatially associated number concepts. Our results imply that all quantitative estimates are contaminated by a "spell of space" whenever stimuli or responses are spatially distributed.

Is the attentional SNARC effect truly attentional? Using temporal order judgements to differentiate attention from response

The spatial–numerical association of response codes (SNARC) effect reflects the phenomenon that low digits are responded to faster with the left hand and high digits with the right. Recently, a particular variant of the SNARC effect known as the attentional SNARC (which reflects that attention can be shifted in a similar manner) has had notable replicability issues. However, a potentially useful method for measuring it was revealed by Casarotti et al. using a temporal order judgement (TOJ) task. Accordingly, the present study evaluated whether Casarotti et al.’s results were reproducible by presenting a low (1) or high (9) digit prior to a TOJ task where participants had to indicate which of two peripherally presented targets appeared first (Experiment 1) or second (Experiment 2). In Experiment 1, it was revealed that the findings of Casarotti et al.’s were indeed observable upon replication. In Experiment 2, when attention and response dimensions were put in opposition, the SNARC effect corresponded to the side of response rather than attention. Taken together, the present study confirms the robustness of the attentional SNARC in TOJ tasks, but that it is not likely due to shifts in attention.

Perceiving numerosity does not cause automatic shifts of spatial attention

It is debated whether the representation of numbers is endowed with a directional-spatial component so that perceiving small-magnitude numbers triggers leftward shifts of attention and perceiving large-magnitude numbers rightward shifts. Contrary to initial findings, recent investigations have demonstrated that centrally presented small-magnitude and large-magnitude Arabic numbers do not cause leftward and rightward shifts of attention, respectively. Here we verified whether perceiving small or large non-symbolic numerosities (i.e., clouds of dots) drives attention to the left or the right side of space, respectively. In experiment 1, participants were presented with central small (1, 2) vs large-numerosity (8, 9) clouds of dots followed by an imperative target in the left or right side of space. In experiment 2, a central cloud of dots (i.e., five dots) was followed by the simultaneous presentation of two identical dot-clouds, one on the left and one on the right side of space. Lateral clouds were both lower (1, 2) or higher in numerosity (8, 9) than the central cloud. After a variable delay, one of the two lateral clouds turned red and participants had to signal the colour change through a unimanual response. We found that (a) in Experiment 1, the small vs large numerosity of the central cloud of dots did not speed up the detection of left vs right targets, respectively, (b) in Experiment 2, the detection of colour change was not faster in the left side of space when lateral clouds were smaller in numerosity than the central reference and in the right side when clouds were larger in numerosity. These findings show that perceiving non-symbolic numerosity does not cause automatic shifts of spatial attention and suggests no inherent association between the representation of numerosity and that of directional space.

An implicit task reveals space-time associations along vertical and diagonal axes

In previous studies investigating the space-time compatibility effect, the experimental task always invites explicit spatial or temporal processing or both. In this study, we kept space and time irrelevant to the task. In a go/no-go task, participants (N = 50) were asked to either press a single button when they found the target or refrain from responding when there was no target in a search array. We manipulated the duration of the target-alone presentation that preceded a 7 × 7 search array consisting of either target plus distractors or distractors alone. The results revealed faster responses to shorter durations when the target appeared in the upper relative to the lower space. A similar effect also appeared along the diagonal axis with faster responses to shorter durations in upper-left relative to lower-right space. In contrast, no such difference was found along the horizontal axis. We hypothesize that vertical and diagonal space-time associations arise from the grounding of mental representation of time in physical experiences.

Children's spatial-numerical associations on horizontal, vertical, and sagittal axes

There is substantial evidence linking numerical magnitude to the physical properties of space. The most influential support for this connection comes from the SNARC effect (spatial-numerical association of response codes), in which responses to small/large numbers are faster on the left/right side of space, respectively. The SNARC effect has been extensively replicated, and is understood as horizontal mapping of numerical magnitude. However, much less is known about how numbers are represented on the vertical and sagittal axes, and whether spatial-numerical associations on different axes emerge during childhood. To that end, we tested two groups of children, aged 5-7 years and 8 and 9 years, on a single-digit magnitude comparison task with response buttons positioned either upper/lower (vertical), left/right (horizontal) or near/far (sagittal). Our results provide evidence of spatial-numerical mapping on all three axes for both age groups that are similar in strength. This indicates that, even at an early stage of formal education, children can flexibly assign numerical magnitude to any spatial dimension. To examine the contribution of extracorporeal space and spatio-anatomical mapping to the SNARC effect across axes, these sources were pitted against each other by swapping the position of the response hands in Experiment 1b. Switching hand position did not reveal convincing evidence for SNARC effects on any axis. Results are discussed with respect to the utility of three-dimensional mental number lines, and potential avenues for future research are outlined.

Spatial-numerical associations from a novel paradigm support the mental number line account

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 judgements and/or categorical responses. In the novel "Where was The Number?" task, no explicit numerical judgements 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.

Turn the beat around: Commentary on "Slow and fast beat sequences are represented differently through space" (De Tommaso & Prpic, 2020, in Attention, Perception, & Psychophysics)

There has been increasing interest in the spatial mapping of various perceptual and cognitive magnitudes, such as expanding the spatial-numerical association of response codes (SNARC) effect into domains outside of numerical cognition. Recently, De Tommaso and Prpic (Attention, Perception, & Psychophysics, 82, 2765–2773, 2020) reported in this journal that only fast tempos over 104 beats per minute have spatial associations, with more right-sided associations and faster responses for faster tempos. After discussing the role of perceived loudness and possible response strategies, we propose and recommend methodological improvements for further research.

Number space is made by response space: Evidence from left spatial neglect

Whether the semantic representation of numbers is endowed with an intrinsic spatial component, so that smaller numbers are inherently represented to the left of larger ones on a Mental Number Line (MNL), is a central matter of debate in numerical cognition. To gain an insight into this issue, we investigated the performance of right brain damaged patients with left spatial neglect (N+) in a bimanual Magnitude Comparison SNARC task and in a uni-manual Magnitude Comparison Go/No-Go task (i.e. "is the number smaller or larger than 5?"). While the first task requires the use of contrasting left/right spatial codes for response selection, the second task does not require the use of these codes. In line with previous evidence, in the SNARC task N+ patients displayed a significant asymmetry in Reaction Times (RTs), with slower RTs to number "4", that was immediately precedent to the numerical reference "5", with respect to the number "6", that immediately followed the same reference. This RTs asymmetry was correlated with lesion of white matter tracts, i.e. Fronto-Occipital-Fasciculus, that allows prefrontal Ba 8 and 46 to regulate the distribution of attention on sensory and memory traces in posterior occipital, temporal and parietal areas. In contrast, no similar RTs asymmetry was found in the Go/No-Go task. These findings suggest that while in the SNARC task numbers get mentally organised from left-to-right as a function of their increasing magnitude, so that N+ patients display a delay in the processing of number-magnitudes that are immediately smaller than a given numerical reference, in the Go/No-Go task no left-to-right organization is activated. These results support the idea that it is the use of contrasting left/right spatial codes, whether motor or conceptual, that triggers the generation of a spatially left-to-right organised MNL and that the representation of number magnitude is not endowed with an inherent spatial component.

The Force of Numbers: Investigating Manual Signatures of Embodied Number Processing

The study has two objectives: (1) to introduce grip force recording as a new technique for studying embodied numerical processing; and (2) to demonstrate how three competing accounts of numerical magnitude representation can be tested by using this new technique: the Mental Number Line (MNL), A Theory of Magnitude (ATOM) and Embodied Cognition (finger counting-based) account. While 26 healthy adults processed visually presented single digits in a go/no-go n-back paradigm, their passive holding forces for two small sensors were recorded in both hands. Spontaneous and unconscious grip force changes related to number magnitude occurred in the left hand already 100–140 ms after stimulus presentation and continued systematically. Our results support a two-step model of number processing where an initial stage is related to the automatic activation of all stimulus properties whereas a later stage consists of deeper conscious processing of the stimulus. This interpretation generalizes previous work with linguistic stimuli and elaborates the timeline of embodied cognition. We hope that the use of grip force recording will advance the field of numerical cognition research.

How to trigger and keep stable directional Space-Number Associations (SNAs)

Humans are prone to mentally organise the ascending series of integers according to reading habits so that in western cultures small numbers are positioned to the left of larger ones on a mental number line. Despite 140 years since seminal observations by Sir Francis Galton (Galton, 1880a, b), the functional mechanisms that give rise to directional Space-Number Associations (SNAs) remain elusive. Here, we contrasted three different experimental conditions, each including a different version of a Go/No-Go task with intermixed numerical and arrow-targets (Shaki and Fischer, 2018; Pinto et al., 2019a). We show that directional SNAs are not "all or none" phenomena. We demonstrate that SNAs get progressively less noisy and more stable the more contrasting small/large magnitude-codes and contrasting left/right spatial-codes are explicitly and fully combined in the task set. The analyses of the time-course of space-number congruency effects showed that both the absence and presence of the SNA were independent of the speed of reaction times. In agreement with our original proposal (Aiello et al., 2012), these findings show that conceptualising the ascending series of integers in spatial terms depends on the use of spatial codes in the numerical task at hand rather than on the presence of an inherent spatial dimension in the semantic representation of numbers. This evidence suggests that directional SNAs, like the SNARC effect, are secondary to the primary transfer of spatial response codes to number stimuli, rather than deriving from a primary congruency or incongruence between independent spatial-response and spatial-number codes.

A purely power-space association without spatial and strategic biases

Previous studies have shown that powerful and powerless concepts are metaphorically associated with top and bottom spaces respectively. However, this association might be contaminated by spatial and strategic biases due to the involvement of spatialized stimuli or responses. It is unknown whether power by itself can automatically activate spatial representations. To eliminate spatial and strategic biases, Experiment 1 separately presented power and spatial stimuli at the center of the screen, and participants had to classify power words and HIGH/LOW labels (Experiment 1a) or indicate up/down arrows (Experiment 1b) using a single key and follow different response rules that were combined with a Go/no-go task. Experiment 2 replicated the non-spatialized design but used an implicit power judgment task. Based upon the non-spatialized method, the results provide the first evidence that a power-space association effect still exists when eliminating spatial and strategic biases, revealing the nonconscious spatial nature of power.

Is 'heavy' up or down? Testing the vertical spatial representation of weight

Smaller numbers are typically responded to faster with a bottom than a top key, whereas the opposite occurs for larger numbers (a vertical spatial-numerical association of response codes: i.e. the vertical SNARC effect). Here, in four experiments, we explored whether a vertical spatial-magnitude association can emerge for lighter vs. heavier items. Participants were presented with a central target stimulus that could be a word describing a material (e.g. 'paper', 'iron': Experiment 1), a numerical quantity of weight (e.g. '1 g', '1 kg': Experiment 2) or a picture associated with a real object that participants weighed before the experiment (Experiments 3a/3b). Participants were asked to respond either to the weight (Experiments 1-3a) or to the size (i.e. weight was task-irrelevant; Experiment 3b) of the stimuli by pressing vertically placed keys. In Experiments 1 and 2, faster responses emerged for the lighter-bottom/heavier-top mapping-in line with a standard SNARC-like effect-whereas in Experiment 3a the opposite mapping emerged (lighter-top/heavier-bottom). No evidence of an implicit weight-space association emerged in Experiment 3b. Overall, these results provide evidence indicating a possible context-dependent vertical spatial representation of weight.

Large as being on top of the world and small as hitting the roof: a common magnitude representation for the comparison of emotions and numbers

Previous work on the direct speed-intensity association (SIA) on comparative judgement tasks involved spatially distributed responses over spatially distributed stimuli with high motivational significance like facial expressions of emotions. This raises the possibility that the inferred stimulus-driven regulation of lateralized motor reactivity described by SIA, which was against the one expected on the basis of a valence-specific lateral bias, was entirely due to attentional capture from motivational significance (beyond numerical cognition). In order to establish the relevance of numerical cognition on the regulation of attentional capture we ran two complementary experiments. These involved the same direct comparison task on stimulus pairs that were fully comparable in terms of their analog representation of intensity but with different representational domain and motivational significance: symbolic magnitudes with low motivational significance in experiment 1 vs. emotions with rather high motivational significance in experiment 2. The results reveal a general SIA and point to a general mechanism regulating comparative judgements. This is based on the way spatial attention is captured toward locations that contain the stimulus which is closest in term of relative intensity to the extremal values of the series, regardless from its representational domain being it symbolic or emotional.

Symbol grounding of number words in the subitization range

In three experiments, we explored whether number words are grounded in a nonsymbolic representation of numerosity. We used a sentence-picture verification task, where participants are required to check whether the concept given in a sentence corresponds to the subsequently presented object. We concurrently manipulated numerical congruency by orthogonally varying the number word attached to the concept and the quantity of objects. The number words and numerosities varied from one to four in Experiment 1 and from six to nine in Experiment 2. In Experiment 3, we employed number words six and eight with the constraint that, in the incongruent condition, a constant number-to-numerosity ratio of 2:1 was used. In Experiment 1, we found that participants were faster and more efficient when concept-object matches were accompanied by numerical congruency relative to incongruency. On the other hand, no such difference was observed in Experiments 2 and 3 for numbers falling outside of the subitization range. The results are consistent with the hypothesis that number words from one to four are grounded in a nonsymbolic representation of the size of small sets.

Implicit and explicit spatial-numerical representations diverge in number-form synesthetes

In number-form (NF) synesthesia-a condition in which people report vivid, automatic and consistent mental layouts for numerical sequences-numbers and space are closely linked. These explicit associations are similar to the implicit associations demonstrated by the Spatial-Numerical Association of Response Codes (SNARC) effect. Thus, NF synesthesia offers a unique opportunity to investigate spatial-numerical associations. We tested implicit and explicit representations in NF synesthetes using a multiple case-study design. Over two sessions, synesthetes participated in a semi-structured interview focusing on the nature of their associations, as well as SNARC and number line estimation tasks. Contrary to our hypotheses, only one synesthete demonstrated SNARC effects congruent with her reported form, whereas two others exhibited SNARC effects that were the opposite of their explicit NFs. While this inconsistency between implicit and explicit representations may indicate separate underlying cognitive mechanisms, factors such as task-specific constraints and strategic variability must also be considered.

Non-symbolic numerosities do not automatically activate spatial-numerical associations: Evidence from the SNARC effect

The SNARC (spatial-numerical association of response codes) effect is the finding that people are generally faster to respond to smaller numbers with left-sided responses and larger numbers with right-sided responses. The SNARC effect has been widely reported for responses to symbolic representations of number such as digits. However, there is mixed evidence as to whether it occurs for non-symbolic representations of number, particularly when magnitude is irrelevant to the task. Mitchell et al. reported a SNARC effect when participants were asked to make orientation decisions to arrays of one-to-nine triangles (pointing upwards vs. pointing downwards) and concluded that SNARC effects occur for non-symbolic, non-canonical representations of number. They additionally reported that this effect was stronger in the subitising range. However, here we report four experiments that do not replicate either of these findings. Participants made upwards/inverted decisions to one-to-nine triangles where total surface area was either controlled across numerosities (Experiments 1, 2, and 4) or increased congruently with numerosity (Experiment 3). There was no evidence of a SNARC effect either across the full range or within the subset of the subitising range. The results of Experiment 4 (in which we presented the original stimuli of Mitchell et al.) suggested that visual properties of non-symbolic displays can prompt SNARC-like effects driven by visual cues rather than numerosity. Taken in the context of other recent findings, we argue that non-symbolic representations of number do not offer a direct and automatic route to numerical-spatial associations.

Low numbers from a low head? Effects of observed head orientation on numerical cognition

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.