Numerical Association Of Response Codes Research Articles

Verbal-spatial and visuospatial coding of number–space interactions.

A tight correspondence has been postulated between the representations of number and space. The spatial numerical association of response codes (SNARC) effect, which reflects the observation that people respond faster with the left-hand side to small numbers and with the right-hand side to large numbers, is regarded as strong evidence for this correspondence. The dominant explanation of the SNARC effect is that it results from visuospatial coding of magnitude (e.g., the mental number line hypothesis). In a series of experiments, we demonstrated that this is only part of the story and that verbal-spatial coding influences processes and representations that have been believed to be purely visuospatial. Additionally, when both accounts were directly contrasted, verbal-spatial coding was observed in absence of visuospatial coding. Relations to other number-space interactions and implications for other tasks are discussed.

Increasing the difficulty of response selection does not increase the switch cost.

Several theories of task switching assume that basic task processes such as stimulus identification and response selection do not contribute to task-switch costs. This conclusion is mainly based on the finding that stimulus-identification manipulations have no influence on the size of the switch cost. The present study tested the influence of response-selection manipulations on the size of the switch cost. The authors manipulated the difficulty of response selection by using a semantically based response-side effect that is associated with numerical-judgement tasks, namely the Spatial Numerical Association of Response Codes (SNARC) effect. The authors observed a SNARC effect and a switch cost, but no interaction between the two: the task-switch cost did not differ between SNARC-compatible and -incompatible responses. The authors conclude that response selection does not contribute to the switch cost on the current trial, which provides further support for the idea that basic task processes and task-switch processes are separate.

What information is critical to elicit interference in number-form synaesthesia?

Numerous behavioural paradigms have demonstrated a close connection between numbers and space, suggesting that numbers may be represented on an internal mental number line. For example, in the Spatial Numerical Association of Response Codes (SNARC) effect, reaction times are faster for left-sided responses to smaller numbers and for right-sided responses to larger numbers. One valuable tool for exploring such numerical–spatial interactions is the study of number-form synaesthesia, in which participants report vivid, automatic associations of numerical and other ordinal sequences with precise, idiosyncratic, spatial layouts. Recent studies have demonstrated the influence of synaesthetic spatial experiences on behavioural number tasks. The aim of the present study is to further explore these internal spatial representations by presenting a case-study of an unusual synaesthete, DG, who reports highly detailed representations not only of numerical sequences (including representations of negative and Roman numbers), but also different representations for other ordinal sequences, such as time sequences (months, days and hours), the alphabet, financial sequences and different units of measure (e.g., kilograms, kilometres and degrees). Here, we describe DG's synaesthetic experiences and a series of behavioural experiments on numerical tasks concerning the automaticity of this phenomenon. DG's performance on number comparison and cued-detection tasks was modulated by his synaesthetic mental representation for the numerical sequence, such that his reaction times were slower when the spatial layout was incompatible with the orientation of his mental number line. We found that the spatial presentation of stimuli, rather than the implicit or explicit access to numerosity required by tasks, was essential to eliciting DG's number-forms. These results are consistent with previous studies and suggest that numerical–spatial interactions may be most strongly present in synaesthetes when both numerical and spatial information are explicitly task-relevant, consistent with a growing body of literature regarding the SNARC and other related effects.

Spatial forms and mental imagery

Four studies investigated how general mental imagery might be involved in mediating the phenomenon of ‘synaesthetic’ spatial forms – i.e., the experience that sequences such as months or numbers have spatial locations. In Study 1, people with spatial forms scored higher than controls on visual imagery self-report scales. This is consistent with the suggestion that strong general imagery is at least a necessary condition to experience spatial forms. However self-reported spatial imagery did not differ between groups, suggesting either that the spatial nature of forms is mediated by special synaesthetic mechanisms, or that forms are depictive visual images rather than explicit spatial models. A methodological implication of Study 1 was that a general tendency for people with spatial forms to use imagery strategies might account for some of their previously-reported behavioural differences with control groups. This concern was supported by Studies 2–4. Normal participants were encouraged to visually image the months in various spatial layouts, and spatial associations for months were tested using left/right key presses to classify month names as belonging to the first or second half of the year (Studies 2–3) or as odd/even (Study 4). Reaction times showed month-SNARC (Spatial Numerical Association of Response Codes) effects of similar magnitude to previously-reported data from spatial form participants (Price and Mentzoni, 2008). Additionally, reversing the spatial associations within instructed images was sufficient to reverse the direction of observed month-SNARC effects (i.e., positive vs negative slope), just as different spatial forms were previously shown to modulate the direction of effects (ibid.). Results challenge whether previously observed behavioural differences between spatial form and control groups need to be explained in terms of special synaesthetic mechanisms rather than intentional imagery strategies. It is argued that usually strong general imagery processes should complement synaesthetic mechanisms as possible explanations of spatial forms.

The objectification of overlearned sequences: A new view of spatial sequence synesthesia

In the phenomenon of spatial sequence synesthesia (SSS), subjects can articulate explicit spatial locations for sequences such as numbers, letters, weekdays, months, years, and other overlearned series. Similarly, abstract sequences can take on implicit spatial representations in non-synesthetes, as evidenced by the spatial numerical association of response codes (SNARC) effect. An open question is whether the two findings represent different degrees of the same condition, or different conditions. To address this, we developed computer programs to quantify three-dimensional (3D) month-form coordinates in 571 self-reported spatial sequence synesthetes; this approach opens the door for the first time to quantified large-scale analysis. First, despite the common assumption that month-forms tend to be elliptical, we find this to be true in only a minority of cases. Second, we find that 27% of month forms are in the shape of lines, consistent with the assumed shape of implicit spatial forms in the SNARC effect. Next, we find that the majority of month forms are biased in a left-to-right direction, also consistent with the directional bias in the SNARC effect (in Western speakers). Collectively, these findings support the possibility that SSS is directly related to the sequence representations in non-synesthetes. While the search for neural correlates has concentrated on areas in the parietal lobe involved in numeric manipulation and coordinate systems, we propose that the basis of this synesthesia may be the close proximity of temporal lobe regions implicated in sequence coding and visual object representation.

Transfer of magnitude and spatial mappings to the SNARC effect for parity judgments.

Left-right keypresses to numerals are faster for pairings of small numbers to left response and large numbers to right response than for the opposite pairings. This spatial numerical association of response codes (SNARC) effect has been attributed to numbers being represented on a mental number line. We examined this issue in 3 experiments using a transfer paradigm. Participants practiced a number magnitude-judgment task or spatial stimulus-response compatibility task with parallel or orthogonal stimulus-response dimensions prior to performing a parity-judgment task. The SNARC effect was enhanced following a small-left/large-right magnitude mapping but reversed following a small-right/large-left mapping, indicating that associations between magnitude and response defined for the magnitude-judgment task were maintained for the parity-judgment task. The SNARC effect was unaffected by practice with compatible or incompatible spatial mapping for the parallel spatial task but was larger following up-right/down-left mapping than up-left/down-right mapping for the orthogonal spatial task. These results are inconsistent with the SNARC effect being due to a horizontal number line representation but consistent with a view that correspondence of stimulus and response code polarities contributes to the effect.

The spatial representation of numbers: evidence from neglect and pseudoneglect

The aim of the present paper is to provide an overview of the evidence that links spatial representation with representation of number magnitude. This aim is achieved by reviewing the literature concerning the number interval bisection task in patients with left hemispatial neglect and in healthy participants (pseudoneglect). Phenomena like the Spatial Numerical Association of Response Codes (SNARC) effect and the shifts of covert spatial attention caused by number processing are thought to support the notion that number magnitude is represented along a spatially organized mental number line. However, the evidence provided by chronometric studies is not univocal and is open to alternative, non-spatial interpretations. In contrast, neuropsychological studies have offered convincing evidence that humans indeed represent numbers on a mental number line oriented from left to right. Neglect patients systematically misplace the midpoint of a numerical interval they are asked to bisect (e.g., they say that [5] is halfway between [2] and [6]) and their mistakes closely resemble the typical pattern found in bisection of true visual lines. The presence of dissociations between impaired explicit knowledge and spared implicit knowledge supports the notion that neglect produces a deficit in accessing an intact mental number line, rather than a distortion in the representation of that line. Other results show that the existence of a strong spatial connotation constitutes a specific property of number representations rather than a general characteristic of all ordered sequences.

Action co-representation: The joint SNARC effect

Traditionally, communication has been defined as the intentional exchange of symbolic information between individuals. In contrast, the mirror system provides a basis for nonsymbolic and nonintentional information exchange between individuals. We believe that understanding the role of the mirror system in joint action has the potential to serve as a bridge between these two domains. The present study investigates one crucial component of joint action: the ability to represent others’ potential actions in the same way as one's own in the absence of perceptual evidence. In two experiments a joint spatial numerical association of response codes (SNARC) effect is demonstrated, providing further evidence that individuals form functionally equivalent representations of their own and others’ potential actions. It is shown that numerical (symbolic) stimuli that are mapped onto a spatially arranged internal representation (a mental number line) can activate a co-represented action in the same way as spatial stimuli. This generalizes previous results on co-representation. We discuss the role of the mirror system in co-representation as a basis for shared intentionality and communication.

Spatial associations in relational reasoning: Evidence for a SNARC-like effect

Relational reasoning (A > B, B > C, therefore A > C) shares a number of similarities with numerical cognition, including a common behavioural signature, the symbolic distance effect. Just as reaction times for evaluating relational conclusions decrease as the distance between two ordered objects increases, people need less time to compare two numbers when they are distant (e.g., 2 and 8) than when they are close (e.g., 3 and 4). Given that some remain doubtful about such analogical representations in relational reasoning, we determine whether numerical cognition and relational reasoning have other overlapping behavioural effects. Here, using relational reasoning problems that require the alignment of six items, we provide evidence showing that the subjects' linear mental representation affects motor performance when evaluating conclusions. Items accessible from the left part of a linear representation are evaluated faster when the response is made by the left, rather than the right, hand and the reverse is observed for items accessible from the right part of the linear representation. This effect, observed with the prepositions to the left of and to the right of as well as with above and below, is analogous to the SNARC (Spatial Numerical Association of Response Codes) effect, which is characterized by an interaction between magnitude of numbers and side of response.

Attentional SNARC: There’s something special about numbers (let us count the ways)

We report a study that examines whether the presentation of irrelevant, ordinal information at central fixation interacts with the allocation of attention beyond fixation. Previous research has demonstrated that number perception influences the allocation of spatial attention, such that the presentation of a spatially nonpredictive number at fixation results in attention being allocated to the left when the central number is low (e.g., 1), and attention being allocated to the right when the central number is high (e.g., 9). Here, we examine whether this attentional SNARC effect (spatial numerical association of response codes) generalizes to other ordinal sequences: letters, days, and months. Though we replicate the attentional SNARC we find that this effect is number-specific, unless participants are required to process the cue in an order-relevant fashion. This discovery of number-specificity has important implications both for the functional separation between SNARC and attention-SNARC effects, as well as lending support to recent theories regarding the specificity of a shared neural architecture between numbers and visuospatial attention.

Short Article: Coding Strategies in Number Space: Memory Requirements Influence Spatial–Numerical Associations

The tendency to respond faster with the left hand to relatively small numbers and faster with the right hand to relatively large numbers ( spatial numerical association of response codes, SNARC effect) has been interpreted as an automatic association of spatial and numerical information. We investigated in two experiments the impact of task-irrelevant memory representations on this effect. Participants memorized three Arabic digits describing a left-to-right ascending number sequence (e.g., 3– 4– 5), a descending sequence (e.g., 5– 4– 3), or a disordered sequence (e.g., 5– 3– 4) and indicated afterwards the parity status of a centrally presented digit (i.e., 1, 2, 8, or 9) with a left/right keypress response. As indicated by the reaction times, the SNARC effect in the parity task was mediated by the coding requirements of the memory tasks. That is, a SNARC effect was only present after memorizing ascending or disordered number sequences but disappeared after processing descending sequences. Interestingly, the effects of the second task were only present if all sequences within one experimental block had the same type of order. Taken together, our findings are inconsistent with the idea that spatial–numerical associations are the result of an automatic and obligatory cognitive process but do suggest that coding strategies might be responsible for the cognitive link between numbers and space.

“1-2-3”: Is There a Temporal Number Line?

Evidence suggests that numbers are intimately related to space (Dehaene, Bossini, & Giraux, 1993; Hubbard, Piazza, Pinel, & Dehaene, 2005). Recently, Walsh (2003) suggested that numbers might also be closely related to time. To investigate this hypothesis we asked participants to compare two digits that were presented in a serial manner, i.e., one after another. Temporally ascending digit pairs (such as 2-3) were responded to faster than temporally descending pairs (3-2). This effect was, in turn, qualified by a local SNARC (spatial numerical association of response codes) effect and a local semantic congruity effect (SCE). Moreover, we observed a global numerical SCE only for temporally descending digit pairs. However, we did not observe a global SNARC effect, i.e., an interaction of numerical magnitude and the right/left response hand. We discuss our results in terms of overlearned forward-associations ("1-2-3") as formed by our ubiquitous cognitive routines to count off objects or events.

Semantic numerical representation in blind subjects: The role of vision in the spatial format of the mental number line

Does vision play a role in the elaboration of the semantic representation of small and large numerosities, notably in its spatial format? To investigate this issue, we decided to compare in the auditory modality the performance of congenitally and early blind people with that of a sighted control group, in two number comparison tasks (to 5 and to 55) and in one parity judgement task. Blind and sighted participants presented exactly the same distance and SNARC (Spatial Numerical Association of Response Codes) effects, indicating that they share the same semantic numerical representation. In consequence, our results suggest that the spatial dimension of the numerical representation is not necessarily attributable to the visual modality and that the absence of vision does not preclude the elaboration of this representation for 1-digit (Experiment 1) and 2-digit numerosities (Experiment 2). Moreover, as classical semantic numerical effects were observed in the auditory modality, the postulate of the amodal nature of the mental number line for both small and large magnitudes was reinforced.

Spatial associations for musical stimuli: A piano in the head?

This study was aimed at examining whether pitch height and pitch change are mentally represented along spatial axes. A series of experiments explored, for isolated tones and 2-note intervals, the occurrence of effects analogous to the spatial numerical association of response codes (SNARC) effect. Response device orientation (horizontal vs. vertical), task, and musical expertise of the participants were manipulated. The pitch of isolated tones triggered the automatic activation of a vertical axis independently of musical expertise, but the contour of melodic intervals did not. By contrast, automatic associations with the horizontal axis seemed linked to music training for pitch and, to a lower extent, for intervals. These results, discussed in the light of studies on number representation, provide a new example of the effects of musical expertise on music cognition.

The mental representation of numerical fractions: Real or integer?

Numerical fractions are commonly used to express ratios and proportions (i.e., real numbers), but little is known about how they are mentally represented and processed by skilled adults. Four experiments employed comparison tasks to investigate the distance effect and the effect of the spatial numerical association of response codes (SNARC) for fractions. Results showed that fractions were processed componentially and that the real numerical value of the fraction was not accessed, indicating that processing the fraction's magnitude is not automatic. In contrast, responses were influenced by the numerical magnitude of the components and reflected the simple comparison between numerators, denominators, and reference, depending on the strategy adopted. Strategies were used even by highly skilled participants and were flexibly adapted to the specific experimental context. In line with results on the whole number bias in children, these findings suggest that the understanding of fractions is rooted in the ability to represent discrete numerosities (i.e., integers) rather than real numbers and that the well-known difficulties of children in mastering fractions are circumvented by skilled adults through a flexible use of strategies based on the integer components.

Digit ratio (2D:4D) and the spatial representation of magnitude

Digit ratio (as a putative indicator of prenatal androgen exposure) is related to a range of sexually dimorphic abilities, including spatial skills and mathematical ability. This study examined a phenomenon known as the SNARC effect (Spatial Numerical Association of Response Codes), which is taken as evidence of a mental representation of magnitude along a left–right-oriented number line, with low magnitudes associated with the left side of space, and high numbers with the right side of space. Participants made a parity judgement of numbers with responses made with a left key to odd numbers and a right key to even numbers. This was reversed for a second block of trials. Response times to numbers one to nine with both the right and left hand were calculated, and regression analyses conducted to analyse whether lower magnitudes were responded to faster with the left hand and higher magnitudes with the right hand. Participants with lower (more masculine) digit ratios on the right hand showed a stronger SNARC effect compared to participants with high digit ratios. This pattern of results was also found when the analyses were conducted separately for men and women. Results from left hand digit ratios indicated that only low digit ratio females showed a significant SNARC effect. These findings add to a growing literature on the relationship between digit ratio and cognitive abilities; in this case, simple cognitive representations that are accessed automatically rather than complex skills such as mental rotation or ‘mathematics’ where a variety of solution strategies may be utilised.

Explicit versus Implicit Processing of Representational Space in Neglect: Dissociations in Accessing the Mental Number Line

The present study investigated the effects of left hemispatial neglect on two tasks activating the mental number line (MNL). Six patients with left neglect performed a mental number bisection task and a modified version of the Spatial Numerical Association of Response Codes (SNARC) task. Effects of left neglect were observed in the number bisection task, but not in the SNARC task. We argue that the dissociation between number bisection and SNARC resembles, in the representational space of the MNL, previously reported dissociations on neglect between explicit knowledge (assessed by direct tasks) and implicit knowledge (assessed by indirect tasks).

Crossed Hands and the Snarc Effect: Afailure to Replicate Dehaene, Bossini and Giraux (1993)

Dehaene et al. (1993, Experiment 6) presented evidence that the mental number line is left-to-right oriented with respect to representational associations and not with respect to left and right hands. Here we tried to replicate the study of Dehaene et al. (1993) in a larger sample (n = 32) using four different stimulus notations (Arabic numbers, number words, auditory number words, and dice patterns). As in the study by Dehaene et al. (1993), the spatial numerical association of response codes (SNARC) effect was examined with an incongruent hand assignment to left/right response keys (crossed hands). In contrast to Dehaene et al. (1993), we did not observe a SNARC effect in any condition. Power analyses revealed that n = 32 should have been large enough to detect SNARC effects of usual size. Furthermore, time-course analyses revealed no SNARC slope in faster and slower responses, so that the null effect could not be due to relatively slow responses with crossed hands. Joint analyses with previous data (Nuerk et al., 2005b) revealed significantly steeper SNARC slopes with congruent hand assignment, and no interaction between hand assignment and notation. Altogether, these findings suggest that the results of Dehaene et al. (1993) only hold under specific conditions. Differences between studies are discussed. We suggest that spatial context has an influence on the SNARC effect and that hand-based associations (and not only representational associations) are relevant for the SNARC effect.

On the mental representation of negative numbers: Context-dependent SNARC effects with comparative judgments

In one condition, positive and negative number pairs were compared in separate blocks of trials. In another condition, the positive and the negative number pairs were intermixed. In the intermixed condition, comparisons involving negative numbers were faster with the left hand than with the right, and comparisons were faster with the right hand than with the left hand with the positive numbers; that is, a spatial numerical association of response codes (SNARC) effect was obtained, in which the mental number line was extended leftward with the negative numbers. On the other hand, in the blocked condition, a reverse SNARC effect was obtained with the negative numbers; that is, negative number pairs have the same underlying spatial representation as the positive numbers in this context. Nongraded semantic congruity effects, obtained in both the blocked and the intermixed conditions, are consistent with the idea that magnitude information is extracted prior to the generation of discrete semantic codes.

Notational Modulation of the SNARC and the MARC (Linguistic Markedness of Response Codes) Effect

Number magnitude and number parity representation are fundamental number representations. However, the representation of parity is much less understood than that of magnitude: Therefore, we investigated it by examining the (new) Linguistic Markedness of Response Codes (MARC) effect: Responses are facilitated if stimuli and response codes both have the same (congruent) linguistic markedness (even-right, odd-left) while incongruent conditions (even-left, odd-right) lead to interference. We examined systematically the MARC (for parity) and the Spatial Numerical Association of Response Codes (SNARC; for magnitude) effect for different number notations (positive Arabic, negative Arabic, number words) and with different methods of data analysis. In a parity judgement task, the SNARCeffect indicating a magnitude representation was replicated for all notations except for negative numerals. The MARCeffect was found for number words in all analyses, but less consistently for the other notations. In contrast, a correlational analysis of the reaction time (RT) data, as suggested by Sternberg (1969) using a nonmetric multi-dimensional scaling (MDS) procedure, produced a clear association of parity and response code for all notations (MARCeffect), but little evidence of the SNARCeffect. We discuss the extent to which these notation-specific MARC and SNARC effects constrain current models of number processing and elaborate on the possible functional locus of the MARC effect.