Spatial-numerical Association Of Response Codes Research Articles

Beyond fixed sets: boundary conditions for obtaining SNARC-like effects with continuous semantic magnitudes.

Previous research has demonstrated the presence of an effect (i.e., the spatial-numerical association of response codes or SNARC) in both numerical parity and magnitude judgment tasks in which smaller numerical magnitudes are manually responded to faster on the left side and larger numerical magnitudes on the right side. Such a result has typically been attributed to a spatially based representation of numerical magnitude in long-term memory, the format of which has recently been postulated to be positional in line with learning of a canonically ordered number sequence. As a test of this view, in the current research, participants made classification judgments involving either the size (N = 88) or the living-nonliving status (N = 114) corresponding to the names of animals/objects etc. to which no learned canonical ordering of size exists. Names were taken from a very large set of 400 animals/objects etc. and each name was presented only once in an experimental session. Responses were made using left and right manual keypresses. In this work, the relation between response time and the relative sizes of the animals/objects did not differ across the left-right side of response indicating that SNARC-like effects did not occur. As such, the results suggest that space is not an inherent aspect of the long-term representation of magnitude in the brain and that some form of positional coding of magnitude is necessary for SNARC-like effects to occur.

Walking to a number: is there affective involvement in generating the SNARC effect in numerical cognition?

The effect known as the spatial-numerical association of response codes (SNARC) documents fast reaction to small numbers with a response at the left and to large numbers with a response at the right. The common explanation appeals to a hypothetical mental number line of a left-to-right orientation with the numerical magnitudes on the line activated in an automatic fashion. To explore the possibility of emotional involvement in processing, we employed prototypical affective behaviors for responses in lieu of the usual spatial-numerical ones (i.e., of pressing lateralized keys). In the present series of experiments, the participants walked toward a number or walked away from a number (in a physical approach-avoidance setup) or said "good" or "bad" in response to a number. We recorded strong SNARC effects with affective responding. For example, it took participants longer to say "good" than "bad" to small numbers, but it took them longer to say "bad" than "good" to larger numbers. Although each particular outcome can still be accounted for by a spatial interpretation, the cumulative results are suggestive of the possibly of affective involvement in generating the effect.

High-definition turns timing-dependent: Different behavioural consequences during and following cathodal high-definition transcranial direct current stimulation (HD tDCS) in a magnitude classification task.

Neuromodulation with transcranial direct current stimulation (tDCS) can transiently alter neural activity, but its spatial precision is low. High-definition (HD) tDCS was introduced to increase spatial precision by placing additional electrodes over the scalp. Initial evaluations of HD tDCS indicated polarity-specific neurophysiological effects-similar to conventional tDCS albeit with greater spatial precision. Here, we compared the effects of cathodal tDCS or HD tDCS in a 4 × 1 configuration over prefrontal cortex (PFC) regions on behavioural outcomes in a magnitude classification task. We report results on overall performance, on the numerical distance effect as a measure of numerical processing, and on the spatial-numerical associations of response codes (SNARC) effect, which was previously affected by prefrontal tDCS. Healthy volunteers (n = 68) received sham or cathodal HD tDCS at 1 mA over the left dorsolateral prefrontal cortex (DLPFC) or the left inferior frontal gyrus (IFG). Results were compared to an identical protocol with conventional cathodal tDCS to the left PFC versus sham (n = 64). Mixed effects models showed performance gains relative to sham tDCS in all conditions after tDCS (i.e. 'offline'), whereas montages over PFC and DLPFC already showed performance gains during tDCS (i.e. 'online'). In contrast to conventional tDCS, HD tDCS did not reduce the SNARC effect. Neither condition affected numerical processing, as expected. The results suggest that HD tDCS with cathodal polarity might require further adjustments (i.e. regarding tDCS intensity) for effective modulations of cognitive-behavioural performance, which could be achieved by individualised current density in electric field modelling.

Temporal speed prevails on interval duration in the SNARC-like effect for tempo.

The Spatial-Numerical Association of Response Codes (SNARC) effect is evidence of an association between number magnitude and response position, with faster left-key responses to small numbers and faster right-key responses to large numbers. Similarly, recent studies revealed a SNARC-like effect for tempo, defined as the speed of an auditory sequence, with faster left-key responses to slow tempo and faster right-key responses to fast tempo. In order to address some methodological issues of previous studies, in the present study we designed an experiment to investigate the occurrence of a SNARC-like effect for tempo, employing a novel procedure in which only two auditory beats in sequence with a very short interstimulus interval were used. In the "temporal speed" condition, participants were required to judge the temporal speed (slow or fast) of the sequence. In the "interval duration" condition, participants were required to judge the duration of the interval between the two beats (short or long). The results revealed a consistent SNARC-like effect in both conditions, with faster left-hand responses to slow tempo and faster right-hand responses to fast tempo. Interestingly, the consistency of the results across the two conditions indicates that the direction of the SNARC-like effect was influenced by temporal speed even when participants were explicitly required to focus on interval duration. Overall, the current study extends previous findings by employing a new paradigm that addresses potential confounding factors and strengthens evidence for the SNARC-like effect for tempo.

The spatial representation of loudness in a timbre discrimination task.

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.

Collective nouns are conceptually plural: Evidence from the grammatical SNARC effect.

To develop theories of how comprehenders extract the message from a linguistic stream, it is critical to understand how they conceptually represent referents. The experiments reported here focus on singular collective nouns (e.g., committee, team), which introduce a single group into the discourse and test whether they nonetheless are conceptually plural (i.e., construed as consisting of multiple entities) by using the spatial-numerical association of response codes (SNARC) paradigm (Dehaene & Changeux, 1993). In this paradigm, participants are typically faster to respond to smaller numbers or numerical stimuli when making a response on their left and faster to respond to larger numbers or numerical stimuli when making a response on their right. In three experiments, participants saw German words on a computer screen and decided whether each one described a single entity or something that could be subdivided into multiple entities (Experiment 1) or whether they would use "ist" or "sind" ("is" or "are") in combination with the word if it were the subject of a sentence (Experiments 2 and 3). The mapping of responses to participants' left and right hands was counterbalanced. Experiment 1 failed to show a grammatical SNARC effect. Experiments 2 and 3 showed a grammatical SNARC effect that extended to collective noun phrases. The results of these experiments suggest that collective noun phrases are instantiated as conceptually plural in comprehenders' minds. We discuss the differential task effects and the implications of these data on theories of language comprehension. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

It's SNARC o' clock: manipulating the salience of the context in a conceptual replication of Bächtold et al.'s (1998) clockfacestudy.

The Spatial-Numerical Association of Response Codes (SNARC) effect consists in faster left-/right-key responses to small/large numbers. (Bächtold et al., Neuropsychologia 36:731-735, 1998) reported the reversal of this effect after eliciting the context of a clockface-where small numbers are represented on the right and large numbers on the left. The present study investigates how the salience of a particular spatial-numerical context, which reflects the level of activation of the context in working memory, can alter Spatial Numerical Associations (SNAs). Four experiments presented the clockface as context and gradually increased its salience using different tasks. In the first two experiments (low salience), the context was presented at the beginning of the experiment and its retrieval was not required to perform the tasks (i.e., random number generation in Experiment 1, magnitude classification and parity judgement in Experiment 2). Results revealed regular left-to-right SNAs, unaffected by the context. In Experiment 3 (medium salience), participants performed magnitude classification and parity judgement (primary task), and a Go/No-go (secondary task) which required the retrieval of the context. Neither the SNARC effect nor a reversed-SNARC emerged, suggesting that performance was affected by the context. Finally, in Experiment 4 (high salience), the primary task required participants to classify numbers based on their position on the clockface. Results revealed a reversed SNARC, as in (Bächtold et al., Neuropsychologia 36:731-735, 1998). In conclusion, SNARC is disrupted when the context is retrieved in a secondary task, but its reversal is observed only when the context is relevant for the primary task.

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.

Spatial-numerical associations of manual response codes are strongly asymmetrical

The spatial-numerical association of response codes (SNARC) effect denotes the observation that humans respond faster and more accurately with a left-side response to smaller numbers and a right-side response to larger numbers, as compared to the opposite mapping. Existing accounts, such as the mental number line hypothesis or the polarity correspondence principle, differ in whether they assume symmetrical associations between numerical and spatial stimulus and response codes or not. In two experiments, we investigated the reciprocity of the SNARC effect in manual choice-response tasks with two conditions. In the number-location task, participants pressed a left or right key to a number stimulus (dots in Experiment 1, digits in Experiment 2). In the location-number task, participants made one or two consecutive keypresses with one hand to a left- or right-side stimulus. Both tasks were performed with a compatible (one-left, two-right; left-one, right-two) and an incompatible (one-right, two-left; left-two, right-one) mapping. In both experiments, results showed a strong compatibility effect in the number-location task, reflecting the typical SNARC effect. In contrast, in both experiments, there was no mapping effect in the location-number task when outliers were excluded. However, when outliers were not excluded, small reciprocal SNARC effects occurred in Experiment 2. Together, the findings suggest that priming of spatial responses by numerical stimuli is much stronger than priming of numerical responses by spatial stimuli. The results are consistent with some accounts of the SNARC effect (e.g., the mental number line hypothesis), but not with others (e.g., the polarity correspondence principle).

EXPRESS: Influence of Different Spatial Representations on the SNARC Effect for Letters: Electrophysiological Evidence.

Studies have previously demonstrated that different spatial representations may affect the spatial-numerical association of response codes (SNARC) effect for numbers; however, limited studies have assessed the SNARC effect for letters. In this study, event-related potentials (ERPs) were used to measure the influence of two spatial representation modes (ruler and clock) on the SNARC effect. The ruler produced a SNARC-like effect; i.e., the left hand reacted faster than the right to the letters that appear before N in the alphabet; the right hand reacted faster than the left to the letters after N, whereas the clock produced a reverse SNARC effect. In addition, the ERP data showed that the SNARC-like effect for letters in both representations induced significant activation in the frontal and parietal regions, indicating that the same brain areas are involved in processing letters and numbers in terms of spatial dimensions. This study further identified the conditions for the SNARC effect and proved that the SNARC effect is attributed to the simultaneous participation of brain regions for sequence and spatial information processing.

Stronger spatial bias induced more by numbers in mind than numbers in eye: Evidence from event-related potentials

The relationship between number and space is an important issue in numerical cognition. The spatial-numerical association of response codes (SNARC) effect is a classic example of the association between numbers and spaces. It refers to the phenomenon whereby left-handed responses occur faster to small number and right-handed responses occur faster to large number. The current study explored the shared and distinct neural correlates of the SNARC effect considering numbers in eye and numbers in mind, by using event-related potentials (ERPs) technology. In each trial of the task, participants were asked to press freely one of two keys as a response to a number presented visually (numbers in eye) or via imagination (numbers in mind). The behavioral results indicated that the free-choice key presses were affected by the magnitudes of the numbers either in eye or in mind. Electrophysiological results observed that the SNARC effect appeared only in the 110–140 ms time window for numbers in eye. In contrast, for numbers in mind, the SNARC effect appeared during a longer time window (110–330 ms). These results suggest that both, numbers in eye and numbers in mind, can induce spatial bias at the early stimulus-representation stage, but the time duration of the spatial bias is longer for numbers in mind than numbers in eye. This may reflect a closer connection between numbers in mind and mental number line.

Influences of cognitive control on number processing: New evidence from switching between two numerical tasks.

A growing body of research suggests that basic numerical abilities such as number magnitude and number parity processing are influenced by cognitive control. So far, however, evidence for number processing being influenced by cognitive control came primarily from observed adaptations to stimulus set characteristics (e.g., ratio or order of specific stimulus types) and switches between a numerical and non-numerical task. Complementing this previous research, the present study employed a task switching paradigm exclusively involving numerical tasks (i.e., magnitude comparisons and parity judgements) to examine how cognitive control processes influence number processing. Participants were presented with a single-digit number and had to either judge its parity or compare its magnitude with a standard of 5, depending on a preceding cue. Based on previous results, we expected the numerical distance effect and the spatial-numerical association of response codes (SNARC) effect to be modulated in switch trials requiring the exertion of cognitive control. Partly in line with our expectations, the numerical distance effect was reduced in switch trials. However, no modulation of the SNARC effect was observed. The results pattern suggests that number processing is influenced by cognitive control, depending on task requirements and the type of numerical information (i.e., numerical magnitude vs spatial association of numbers) that is processed. To reconcile the present and previous results, we propose an information prioritisation account, suggesting that cognitive control primarily influences the processing of the information type that requires the most explicit processing.

No conclusive evidence for number-induced attentional shifts in a temporal order judgement task.

The Spatial Numerical Association of Response Codes (SNARC) effect refers to the observation that relatively small (e.g., 1) and large numbers (e.g., 9) elicit faster left- and right-sided manual responses, respectively. In a variation known as the attentional SNARC effect, merely looking at numbers caused a left- or right-ward shift in covert spatial attention, depending on the number's magnitude. In our study, we probed the notion that numbers induce shifts of spatial attention in accordance with their position on a mental number line (MNL). Critically, we removed any putative spatial response code that may contaminate the responses. We used a square and a tilted square as targets, thereby situating the decisive response dimension in the ventral, non-spatial processing stream. In two experiments where numbers were used as non-informative cues preceding a temporal order judgement (TOJ) task, we did not observe a deflection of the locus of spatial attention as a function of the numerical magnitude of the cue. In a third experiment, finding a significant modulation of TOJ performance as a function of the pointing direction of arrow cues allowed us to rule out the possibility that the absence of any significant modulation in Experiments 1 and 2 was due to a lack of sensitivity of our task set-up. We conclude from the current findings that the spatial codes that the perception and naming of numbers potentially elicit are not in and by themselves sufficient to elicit deflections of spatial attention.

Mental Number Representations Are Spatially Mapped Both by Their Magnitudes and Ordinal Positions

The Spatial-Numerical Association of Response Codes (SNARC) effect – i.e., faster responses to small numbers with the left compared to the right side and to large numbers with the right compared to the left side – suggests that numbers are associated with space. However, it remains unclear whether the SNARC effect evolves from a number’s magnitude or the ordinal position of a number in working memory. One problem is that, in different paradigms, the task demands influence the role of ordinality and magnitude. While single-task setups in which participants judge the parity of a displayed number indicate the importance of magnitude for the SNARC effect, evidence for ordinal influences usually comes from experiments where ordinal sequences have to be memorized or setups in which participants possess pre-existing knowledge of the ordinality of stimuli. Therefore, in this preregistered study, we employed a SNARC task without secondary ordinal sequence memorization. We dissociate ordinal and magnitude accounts by carefully manipulating experimental stimulus sets. The results indicate that even though the magnitude model better accounts for the observed data, the ordinal position seems to matter as well. Hence, numbers are associated with space in both a magnitude- and an order-respective manner, yielding a mixture of both compatibility effects. Moreover, a multiple coding framework may most accurately explain the roots of the SNARC effect.

Probing the Dual-Route Model of the SNARC Effect by Orthogonalizing Processing Speed and Depth.

The dual-route model explains the SNARC (Spatial-Numerical Association of Response Codes) effect assuming two routes of parallel information processing: the unconditional route (automatic activation of pre-existing links) and the conditional route (activation of task-specific links). To test predictions derived from this model, we evaluated whether response latency in superficial number processing modulates the SNARC effect in a color task (participants judged the color of a number). In Experiment 1, participants performed a parity task, an easy color task (short RTs), and a difficult color task (RTs similar to those of the parity task). A SNARC effect emerged only in the parity task. In Experiment 2, participants performed a color task and a secondary task under four conditions chosen to orthogonally manipulate response latency (short vs. long) and processing depth (semantic vs. perceptual). Only the long-latency perceptual-processing condition elicited a SNARC effect. To explain these results, we suggest that the cognitive resources required by a secondary task might dilute the SNARC effect. Our results indicate that the dual-route model should be modified to take into account additional factors (e.g., working memory load) that influence the level of activation of the unconditional route.

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.

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.

No fingers, no SNARC? Neither the finger counting starting hand, nor its stability robustly affect the SNARC effect

The Spatial-Numerical Association of Response Codes (SNARC) effect (i.e., faster left/right sided responses to small/large magnitude numbers, respectively) is considered to be strong evidence for the link between numbers and space. Studies have shown considerable variation in this effect. Among the factors determining individual differences in the SNARC effect is the hand an individual uses to start the finger counting sequence. Left-starters show a stronger and less variable SNARC effect than right-starters. This observation has been used as an argument for the embodied nature of the SNARC effect. For this to be the case, one must assume that the finger counting sequence (especially the starting hand) is stable over time. Subsequent studies challenged the view that the SNARC differs depending on the finger counting starting hand. At the same time, it has been pointed out that the temporal stability of the finger counting starting hand should not be taken for granted. Thus, in this preregistered study, we aimed to replicate the difference in the SNARC between left- and right-starters and explore the relationship between the self-reported temporal stability of the finger counting starting hand and the SNARC effect. In line with the embodied cognition account, left-starters who declare more temporarily stable finger counting habits should reveal a stronger SNARC effect. Results of the preregistered analysis did not show the difference between left- and right-starters. However, further exploratory analysis provided weak evidence that this might be the case. Lastly, we found no evidence for the relationship between finger counting starting hand stability and the SNARC effect. Overall, these results challenge the view on the embodied nature of the SNARC effect.

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.