The Spatial Representation of Angles

Analogue magnitude representation of angles and its relation to geometric expertise

The distance effect (comparing objects becomes easier with increasing differences in their magnitude) is observed in tasks ranging across domains, and its existence has been interpreted as evidence for analogue magnitude representation. Similarly, associations between response side and magnitude (faster left/right-sided responses to small/large objects, respectively) are observed across domains. We investigated the analogue processing of angles and the association between angle magnitude and response side in relation to geometric expertise. We compared the behavioural pattern of two groups-architects and controls-in a direct angle magnitude classification task (i.e., judge whether a presented angle was greater or less than 90°) and in an indirect task (i.e., judge whether an angle was drawn with a dashed or continuous line). We found a robust distance effect for reaction times and accuracy at the whole sample level and in each group separately. Architects revealed a smaller distance effect for accuracy than controls. This could be interpreted as an argument for a more precise analogue representation of angles in experts compared to non-experts. However, we did not find evidence for an association between angle magnitude and response side in any group.

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

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.

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.

Contrasting symbolic and non-symbolic numerical representations in a joint classification task

Both symbolic (digits) and non-symbolic (dots) numerals are spatially coded, with relatively small numbers being responded faster with a left key and large numbers being responded faster with a right key (spatial-numerical association of response codes [SNARC]). The idea of format independent SNARC seems to support the existence of a common system for symbolic and non-symbolic numerical representations, although evidence in the field is still mixed. The aim of the present study is to investigate whether symbolic and non-symbolic numerals interact in the SNARC effect when both information is simultaneously displayed. To do so, participants were presented with dice-like patterns, with digits being used instead of dots. In two separate magnitude classification tasks, participants had to respond either to the number of digits presented on the screen or to their numerical size. In the non-symbolic task, they had to judge whether the digits on the screen were more or less than three, irrespective of the numerical value of the digits. In the symbolic task, participants had to judge whether the digits on the screen were numerically smaller or larger than three, irrespective of the number of digits being present. The results show a consistent SNARC effect in the symbolic task and no effect in the non-symbolic one. Furthermore, congruency between symbolic and non-symbolic numerals did not modulate the response patterns, thus supporting the idea of independent representations and questioning some propositions of current theoretical accounts.

A systematic investigation reveals that Ishihara et al.'s (2008) STEARC effect only emerges when time is directly assessed

The Spatial-TEmporal Association of Response Codes (STEARC) effect (Ishihara et al. in Cortex 44:454-461, 2008) is evidence that time is spatially coded along the horizontal axis. It consists in faster left-hand responses to early onset timing and faster right-hand responses to late onset timing. This effect has only been established using tasks that directly required to assess onset timing, while no studies investigated whether this association occurs automatically in the auditory modality. The current study investigated the occurrence of the STEARC effect by using a procedure similar to Ishihara and colleagues. Experiment 1 was a conceptual replication of the original study, in which participants directly discriminated the onset timing (early vs. late) of a target sound after listening to a sequence of auditory clicks. This experiment successfully replicated the STEARC effect and revealed that the onset timing is mapped categorically. In Experiments 2, 3a and 3b participants were asked to discriminate the timbre of the stimuli instead of directly assessing the onset timing. In these experiments, no STEARC effect was observed. This suggests that the auditory STEARC effect is only elicited when time is explicitly processed, thus questioning the automaticity of this phenomenon.

Encoding Numbers in the Context of Multiple Overlapping Cues: Evidence from a Chinese Finger Number Cognition Study

How people encode numbers in the context of multiple overlapping encoded cues remains unclear. In this study, we explored Chinese finger numbers, which contain both a numerical magnitude cue and a left-right hand cue offered by the expressing hand, to investigate the number encoding mechanism in the context of multiple overlapping cues. Chinese finger numbers expressed by the left or right hand were randomly and centrally presented on a computer screen to participants who were asked to perform a hand classification task (Experiment 1), a magnitude classification task (Experiment 2), a parity classification task (Experiment 3) and a magnitude classification or ring classification task (Experiment 4). We discovered (a) only an association effect between the pressed key and the expressing hand in hand classification and parity classification tasks, (b) the SNARC effect only on the magnitude classification task, (c) the association effect between the pressed key and the expressing hand on the larger, Chinese finger number, magnitude classification task in Experiment 2, and (d) the SNARC effect and the association between the pressed key and the expressing hand were reversed on the ring classification task. From these results, we concluded that people can flexibly choose appropriate number encoding cues and how numbers are encoded in the context of multiple overlapping cues depending on (a) which cognition task individuals perform and (b) the character of the numbers involved.

Interaction mechanism between location and sequence in letter cognition

A previous study used days as a sequence symbol to investigate the interaction mechanism between location and sequence in sequence symbol cognition; the study findings suggested that the spatial stimulus-response compatibility effect and the Simon effect could not co-exist with the SNARC-like effect when processing sequence symbols. The previous study did not include the influence of the difficulty of identifying sequence symbols on the Simon effect in the investigation, so it is unclear whether the conclusion about processing sequence symbols with considerable identification difficulty can be extended to the processing of sequence symbols with less identification difficulty. Therefore, the present study explored letters that have a low level of identification difficulty to investigate the interaction mechanism between location and sequence in sequence symbol cognition. Participants were asked to classify a probe letter, which was randomly displayed on the left or right side of the screen, according to its location (Experiment 1), its sequence (Experiment 2) or its colour (Experiment 3). The results indicated that (1) only the spatial stimulus-response compatibility effect and Simon effect were present in the letter location classification task and letter colour classification task, respectively. (2) The Simon effect co-existed with the SNARC-like effect, and these two effects interacted with each other in the letter sequence classification task. From these results, it can be concluded that the task determines whether the Simon effect and the SNARC-like effect can co-exist, with differences presented across sequence symbols.

A SNARC-like effect for music notation: The role of expertise and musical instrument

The Spatial-Numerical Association of Response Codes (SNARC) suggests the existence of an association between number magnitude and response location, with faster left key-press responses to small numbers and faster right key-press responses to large numbers. We investigated whether a similar association exists between musical notes on the stave and the space of response execution, involving amateur and expert musicians (Experiment 1). Moreover, in Experiment 2 we further investigated such association in two groups of expert musicians (piano and transverse flute players) who differ in the note mapping on their instruments. Results indicate a clear association between musical notes and the space of response execution only for musicians with formal education. Furthermore, this association seems not to be influenced by the specific instrument played, as both piano and transverse flute players showed the same effect direction (left key-press advantage for low notes, and vice versa).

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.

The influence of the location of ordered symbols on the ordinal position effect: The involvement of the task performed

Since the ordinal position effect was identified, several studies have investigated its mechanism in various contexts; however, how the space location of ordinal symbols influences this effect remains unclear. Thus, the present study explored Chinese words representing the day before yesterday, yesterday, tomorrow, and the day after tomorrow as ordinal symbols to investigate how the stimulus space location influences the ordinal position effect across different task contexts. We randomly and equally presented days on the left or right location of a display and asked participants to perform a stimulus space location, a stimulus colour and a stimulus order classification task in three consecutive experiments, respectively. The results revealed that the spatial stimulus-response compatibility effect and Simon effect prevailed in the stimulus space location and colour classification task. Conversely, the ordinal position effect prevailed in the stimulus order classification task. These results suggested that (1) the spatial stimulus-response compatibility effect (or Simon effect) and the ordinal position effect cannot appear simultaneously in some experimental contexts and that (2) the task context predicted which of these effects prevailed. From these results, we conclude that the ordinal symbols could be coded depending on multiple reference frames, including spatial and non-spatial reference frame, and the use of the reference frame was mediated by the task context.

Factoring in the spatial effects of symbolic number representation

Spatial constituents of adult symbolic number representation produce effects of size-value congruity, Spatial Numerical Association of Response Codes (SNARC), and numerical distance. According to behavioral experiments, these effects belong to distinct processing stages. Yet, these effects evoke overlapping responses in both early and late Event Related Potentials (ERPs). To probe whether these overlaps indicate sharing of resources, all relevant stimulus and response conditions were factorially combined in a numerical value comparison task. To secure ERP validity, same numbers were compared against variable reference values. This design resulted in previously unobserved interactions in behavior but inhibited late ERP effects. All effects arose early in the P1 component (around 100 ms) and most showed hemispheric specificity. Independency of congruity and SNARC effects was observed, whereas SNARC and numerical distance were closely intertwined. Differences in hemispheric specificity, rather than stage-wise separation, were key to independence.

Emotional Semantic Congruency based on stimulus driven comparative judgements

A common cognitive process in everyday life consists in the comparative judgements of emotions given a pair of facial expressions and the choice of the most positive/negative among them. Results from three experiments on complete-facial expressions (happy/angry) and mixed-facial expressions (neutral/happy-or-angry) pairs viewed with (Experiment 1 and 3) or without (Experiment 2) foveation and performed in conditions in which valence was either task relevant (Experiment 1 and 2) or task irrelevant (Experiment 3), show that comparative judgements of emotions are stimulus driven. Judgements' speed increased as the target absolute emotion intensity grew larger together with the average emotion of the pair, irrespective of the compatibility between the valence and the side of motor response: a semantic congruency effect in the domain of emotion. This result undermines previous interpretation of results in the context of comparative judgements based on the lateralization of emotions (e.g., SNARC-like instructional flexibility), and is fully consistent with our formalization of emotional semantic congruency: the direct Speed-Intensity Association model.

Individual Differences in Implicit and Explicit Spatial Processing of Fractions

Recent studies have explored the foundations of mathematical skills by linking basic numerical processes to formal tests of mathematics achievement. Of particular interest is the relationship between spatial-numerical associations-specifically, the Spatial Numerical Association of Response Codes (SNARC) effect-and various measures of math ability. Thus far, studies investigating this relationship have yielded inconsistent results. Here, we investigate how individual implicit and explicit spatial representations of fractions relate to fraction knowledge and other formal measures of math achievement. Adult participants (n = 105) compared the magnitude of single digit, irreducible fractions to ½, a task that has previously produced a reliable SNARC effect. We observed a significant group-level SNARC effect based on overall fraction magnitude, with notable individual variability. While individual SNARC effects were correlated with performance on a fraction number-line estimation (NLE) task, only NLE significantly predicted scores on a fractions test and basic standardized math test, even after controlling for IQ, mean accuracy, and mean reaction time. This suggests that-for fractions-working with an explicit number line is a stronger predictor of math ability than implicit number line processing. Neither individual SNARC effects nor NLE performance were significant predictors of algebra scores; thus, the mental number line may not be as readily recruited during higher-order mathematical concepts, but rather may be a foundation for thinking about simpler problems involving rational magnitudes. These results not only characterize the variability in adults' mental representations of fractions, but also detail the relative contributions of implicit (SNARC) and explicit (NLE) spatial representations of fractions to formal math skills.

SNARC-like compatibility effects for physical and phenomenal magnitudes: a study on visual illusions

Both numerical and non-numerical magnitudes elicit similar Spatial-Numerical Association of Response Codes (SNARC) effects, with small magnitudes associated with left hand responses and large magnitudes associated with right hand responses (Dehaene et al., J Exp Psychol Gen 122(3), 371, 1993). In the present study, we investigated whether the phenomenal size of visual illusions elicits the same SNARC-like effect revealed for the physical size of pictorial surfaces. Four experiments were conducted by using the Delboeuf illusion (Experiment 1) and the Kanizsa triangle illusion (Experiments 2, 3 and 4). Experiment 1 suggests the presence of a SNARC-like compatibility effect for the physical size of the inducers, while this effect was not revealed for the phenomenal size of the induced elements, possibly masked by a stronger effect of the inducers. A SNARC-like effect for the phenomenal size of the Kanizsa triangle was revealed when participants directly compared the size of the triangles (Experiment 4). Conversely, when participants performed an indirect task (orientation judgment), the SNARC-like effect was present neither for the illusory nor for the physical displays (Experiments 2 and 3). The effect revealed for the size of illusory triangles was comparable to that of real triangles with physical contours, suggesting that both phenomenal and physical magnitudes similarly elicit SNARC-like effects.

There's a SNARC in the Size Congruity Task

The size congruity effect involves interference between numerical magnitude and physical size of visually presented numbers: congruent numbers (either both small or both large in numerical magnitude and physical size) are responded to faster than incongruent ones (small numerical magnitude/large physical size or vice versa). Besides, numerical magnitude is associated with lateralized response codes, leading to the Spatial Numerical Association of Response Codes (SNARC) effect: small numerical magnitudes are preferably responded to on the left side and large ones on the right side. Whereas size congruity effects are ascribed to interference between stimulus dimensions in the decision stage, SNARC effects are understood as (in)compatibilities in stimulus-response combinations. Accordingly, size congruity and SNARC effects were previously found to be independent in parity and in physical size judgment tasks. We investigated their dependency in numerical magnitude judgment tasks. We obtained independent size congruity and SNARC effects in these tasks and replicated this observation for the parity judgment task. The results confirm and extend the notion that size congruity and SNARC effects operate in different representational spaces. We discuss possible implications for number representation.

Profiles of Motor Laterality in Young Athletes' Performance of Complex Movements: Merging the MOTORLAT and PATHoops Tools

Laterality is a key aspect of the analysis of basic and specific motor skills. It is relevant to sports because it involves motor laterality profiles beyond left-right preference and spatial orientation of the body. The aim of this study was to obtain the laterality profiles of young athletes, taking into account the synergies between the support and precision functions of limbs and body parts in the performance of complex motor skills. We applied two instruments: (a) MOTORLAT, a motor laterality inventory comprising 30 items of basic, specific, and combined motor skills, and (b) the Precision and Agility Tapping over Hoops (PATHoops) task, in which participants had to perform a path by stepping in each of 14 hoops arranged on the floor, allowing the observation of their feet, left-right preference and spatial orientation. A total of 96 young athletes performed the PATHoops task and the 30 MOTORLAT items, allowing us to obtain data about limb dominance and spatial orientation of the body in the performance of complex motor skills. Laterality profiles were obtained by means of a cluster analysis and a correlational analysis and a contingency analysis were applied between the motor skills and spatial orientation actions performed. The results obtained using MOTORLAT show that the combined motor skills criterion (for example, turning while jumping) differentiates athletes' uses of laterality, showing a clear tendency toward mixed laterality profiles in the performance of complex movements. In the PATHoops task, the best spatial orientation strategy was “same way” (same foot and spatial wing) followed by “opposite way” (opposite foot and spatial wing), in keeping with the research assumption that actions unfolding in a horizontal direction in front of an observer's eyes are common in a variety of sports.

The influence of time units on the flexibility of the spatial numerical association of response codes effect

The Spatial Numerical/Temporal Association of Response Codes (SNARC/STEARC) effects are considered evidence of the association between number or time and space, respectively. As the SNARC effect was proposed by Dehaene, Bossini, and Giraux in 1993, several studies have suggested that different tasks and cultural factors can affect the flexibility of the SNARC effect. This study explored the influence of time units on the flexibility of the SNARC effect via materials with Arabic numbers, which were suffixed with time units and subjected to magnitude comparison tasks. Experiment 1 replicated the SNARC effect for numbers and the STEARC effect for time units. Experiment 2 explored the flexibility of the SNARC effect when numbers were attached to time units, which either conflicted with the numerical magnitude or in which the time units were the same or different. Experiment 3 explored whether the SNARC effect of numbers was stable when numbers were near the transition of two adjacent time units. The results indicate that the SNARC effect was flexible when the numbers were suffixed with time units: Time units influenced the direction of the SNARC effect in a way which could not be accounted for by the mathematical differences between the time units and numbers. This suggests that the SNARC effect is not obligatory and can be easily adapted or inhibited based on the current context.

Perceiving Musical Note Values Causes Spatial Shift of Attention in Musicians

The Spatial-Numerical Association of Response Codes (SNARC) suggests the existence 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. The attentional SNARC effect (Att-SNARC) suggests that perceiving numbers can also affect the allocation of spatial attention, causing a leftward (vs. rightward) target detection advantage after perceiving small (vs. large) numbers. Considering previous findings that revealed similar spatial association effects for both numbers and musical note values (i.e., the relative duration of notes), the aim of this study is to investigate whether presenting note values instead of numbers causes a spatial shift of attention in musicians. The results show an advantage in detecting a leftward (vs. rightward) target after perceiving small (vs. large) musical note values. The fact that musical note values cause a spatial shift of attention strongly suggests that musicians process numbers and note values in a similar manner.