Stimulus conflict predicts conflict adaptation in a numerical flanker task

Conflict monitoring theory states that response conflict triggers conflict adaptation, resulting in reduced congruency effects after response-incongruent trials (Botvinick, Braver, Barch, Carter, & Cohen, 2001). Verbruggen, Notebaert, Liefooghe, and Vandierendonck (2006) observed conflict adaptation after stimulus-incongruent trials without any response conflict. In this study, we further explore the hypothesis that stimulus conflict is an important trigger for conflict adaptation. We propose a measure for stimulus conflict that adequately explains the data of Verbruggen et al. and new data from a numerical flanker task. We conclude that stimulus conflict and response conflict have dissociable effects on behavior Whereas response conflict is a good predictor of response times, stimulus conflict is a better predictor of the adaptation effect.     

Differences between digit naming and number word reading in a flanker task

Numbers can be represented as number words or as digits, but are the two notations processed differently? Two experiments in which a flanker paradigm with a naming task was used were conducted, with digits and number words as targets and flankers. Reaction times were shortest when the flanker denoted the same numerical value as the target. The numerical distance between the target and a numerically different flanker modulated reaction times in all conditions, except for number word targets with digit flankers. The direction of this effect—targets were named faster when the flanker was numerically close than when it was far—indicates that the numerical magnitude representations of numbers are associatively connected. When the target and the flanker were presented in the same format, no difference was observed in the distance effects for the two formats. This indicates that number words activate the abstract representation of their numerical value in a way that is very similar to that for digits.     

The role of numerical and non-numerical cues in nonsymbolic number processing: Evidence from the line bisection task

In line bisection tasks, adults and children bisect towards the numerically larger of two nonsymbolic numerosities [de Hevia, M. D., & Spelke, E. S. (2009 de Hevia, M. D., & Spelke, E. S. (2009). Spontaneous mapping of number and space in adults and young children. Cognition, 110, 198–207. doi:10.1016/j.cognition.2008.11.003[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Spontaneous mapping of number and space in adults and young children. Cognition, 110, 198–207. doi:10.1016/j.cognition.2008.11.003]. However, it is not clear whether this effect is driven by number itself or rather by visual cues such as subtended area [Gebuis, T., & Gevers, W. (2011 Gebuis, T., & Gevers, W. (2011). Numerosities and space: Indeed a cognitive illusion! A reply to de Hevia and Spelke (2009). Cognition, 121, 248–252. doi:10.1016/j.cognition.2010.09.008[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Numbers and space: Indeed a cognitive illusion! A reply to de Hevia and Spelke (2009 de Hevia, M. D., & Spelke, E. S. (2009). Spontaneous mapping of number and space in adults and young children. Cognition, 110, 198–207. doi:10.1016/j.cognition.2008.11.003[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Cognition, 121, 248–252. doi:10.1016/j.cognition.2010.09.008]. Furthermore, this effect has only been demonstrated with flanking displays of two and nine items. Here, we report three studies that examined whether this “spatial bias” effect occurs across a range of absolute and ratio numerosity differences; in particular, we examined whether the bias would occur when both flankers were outside the subitizing range. Additionally, we manipulated the subtended area of the stimulus and the aggregate surface area to assess the influence of visual cues. We found that the spatial bias effect occurred for a range of flanking numerosities and for ratios of 3:5 and 5:6 when subtended area was not controlled (Experiment 1). However, when subtended area and aggregate surface area were held constant, the biasing effect was reversed such that participants bisected towards the flanker with fewer items (Experiment 2). Moreover, when flankers were identical, participants bisected towards the flanker with larger subtended area or larger aggregate surface area (Experiments 2 and 3). On the basis of these studies, we conclude that the spatial bias effect for nonsymbolic numerosities is primarily driven by visual cues.     

Orientation asymmetry in the flanker task

Experiments 1 and 2 of this study show that when the target is either a vertical or a horizontal line, diagonal-line flankers tilted 45° either to the right or to the left have the same effect as do incongruent flankers. When the target is a diagonal line tilted either to the right or to the left, vertical- or horizontal-line flankers do not have the same effect as do incongruent flankers. Experiment 3 demonstrates that this asymmetry is not caused by the temporal-dynamic aspects of the processing. Together, these experiments suggest that there is an asymmetrical relation between diagonal lines and either vertical or horizontal lines otttside of the central focus of attention. Experiment 4 shows that despite this asymmetry in the flanker task, visual search for a vertical- or a horizontal-line target among diagonal-line distractors is not affected by the number of distractors. Possible explanations of this phenomenon are discussed.     

The SNARC effect does not imply a mental number line

In this study, we directly contrast two approaches that have been proposed to explain the SNARC effect. The traditional direct mapping account suggests that a direct association exists between the position of a number on the mental number line and the location of the response. On the other hand, accounts are considered that propose an intermediate step in which numbers are categorized as either small or large between the number magnitude and the response representations. In a magnitude comparison task, we departed from the usual bimanual left/right response dimension and instead introduced the unimanual close/far dimension. A spatial-numerical association was observed: small numbers were associated with a close response, while large numbers were associated with a far response, regardless of the movement direction (left/right). We discuss why these results cannot be explained by assuming a direct mapping from the representation of numbers on a mental number line to response locations and discuss how the results can be explained by the alternative accounts.     

The mental time line: An analogue of the mental number line in the mapping of life events

A crucial aspect of the human mind is the ability to project the self along the time line to past and future. It has been argued that such self-projection is essential to re-experience past experiences and predict future events. In-depth analysis of a novel paradigm investigating mental time shows that the speed of this “self-projection” in time depends logarithmically on the temporal-distance between an imagined “location” on the time line that participants were asked to imagine and the location of another imagined event from the time line. This logarithmic pattern suggests that events in human cognition are spatially mapped along an imagery mental time line. We argue that the present time-line data are comparable to the spatial mapping of numbers along the mental number line and that such spatial maps are a fundamental basis for cognition.     

The neural basis of the Weber-Fechner law: a logarithmic mental number line

The recent discovery of number neurons allows for a dissection of the neuronal implementation of number representation. In a recent article, Nieder and Miller demonstrate a neural correlate of Weber's law, and thus resolve a classical debate in psychophysics: the mental number line seems to be logarithmic rather than linear.     

The mental number line in depth revealed by vection

To explore how numbers are represented in depth in our mental space, we asked participants to sequentially speak random numbers while they observed forward/backward vection. We found that participants tended to generate larger numbers when they perceived backward self-motion. The results suggest that numerical magnitudes were topographically mapped onto our mental space from front to rear in an ascending order.     

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.     

Calibrating the mental number line

Human adults are thought to possess two dissociable systems to represent numbers: an approximate quantity system akin to a mental number line, and a verbal system capable of representing numbers exactly. Here, we study the interface between these two systems using an estimation task. Observers were asked to estimate the approximate numerosity of dot arrays. We show that, in the absence of calibration, estimates are largely inaccurate: responses increase monotonically with numerosity, but underestimate the actual numerosity. However, insertion of a few inducer trials, in which participants are explicitly (and sometimes misleadingly) told that a given display contains 30 dots, is sufficient to calibrate their estimates on the whole range of stimuli. Based on these empirical results, we develop a model of the mapping between the numerical symbols and the representations of numerosity on the number line.     

Event-related brain potentials and subjective probability in a learning task

In a paired associate learning task, subjects responded to each presentation of a nonsense syllable by typing both a three-letter associate and a rating of their confidence that this response was correct or incorrect. Average event-related potentials (ERPs) elicited by the subsequent presentation of the actual paired syllable varied with the interaction of confidence and trial outcome. A larger amplitude P300 was elicited by syllables that informed subjects that they were correct when they thought they were incorrect or that they were incorrect when they thought they were correct than by syllables that confirmed subjects expectations. That this average ERP result was indeed an effect on P300 amplitude, and not an artifact of single-trial variability in P30O latency, was confirmed with a trial-by-trial latency adjustment procedure. Consistent with findings from other tasks, P300 amplitude varied inversely with the subj ective probability of the ERP-eliciting events.     

Sex differences in number line estimation: The role of numerical estimation

Sex differences in mathematical performance have frequently been examined over the last decades indicating an advantage for males especially when numerical problems cannot be solved by (classroom‐)learnt strategies and/or estimation. Even in basic numerical tasks such as number line estimation, males were found to outperform females – with sex differences argued to emerge from different solution strategies applied by males and females. We evaluated the latter using two versions of the number line estimation task: a bounded and an unbounded task version. Assuming that women tend more strongly to apply known procedures, we expected them to be at a particular disadvantage in the unbounded number line estimation task, which is less prone to be solved by specific strategies such as proportion judgement but requires numerical estimation. Results confirmed more pronounced sex differences for unbounded number line estimation with males performing significantly more accurately in this task version. This further adds to recent evidence suggesting that estimation performance in the bounded task version may reflect solution strategies rather than numerical estimation. Additionally, it indicates that sex differences regarding the spatial representation of number magnitude may not be universal, but associated with spatial–numerical estimations in particular.     

The importance of irrelevant-dimension variability in the stroop flanker task

Two experiments in which the Stroop flanker task was used were conducted in order to examine the influence of irrelevant dimension invariance on congruency effects. Participants responded manually to a central color patch flanked by a Stroop stimulus. In Experiment 1, invariance in flanker location was found to have no influence on word and color congruency effects. In contrast, invariance of flanker identity led to the disappearance of congruency effects. Experiment 2 indicated that the elimination of a congruency effect was restricted to the dimension that remained constant and did not influence the congruency effect of the other dimension that was presented at the same location. Results suggest that variance is a prerequisite to congruity effects, determining the activation of irrelevant dimensions.     

Exploring the mental number line: evidence from a dual-task paradigm

In a parity-judgment task smaller numbers are responded to faster with the left-hand key and vice versa for larger numbers (SNARC effect; Dehaene et al., in Journal of Experimental Psychology: General, 122, 371-396, 1993). We used the psychological refractory period paradigm involving a parity-judgment task and tone-discrimination task to address the question at which stage this effect arises. When the parity-judgment task is performed second, then we found equal SNARC effects for the short and the long SOA. According to the central bottleneck model, this indicates that the effect arises during the response-selection or execution stage. In Experiment 2 the parity-judgment task was performed first. The pattern of results indicates that the SNARC effect originates during the perceptual encoding or response-selection. Together, our results suggest that the SNARC effect originates while the response is selected.     

Interactions between color and word processing in a flanker task

To examine interactions between color and word attributes, participants responded, either manually or vocally, to a central target (color patch or word) flanked by a Stroop stimulus. Color and word attributes of the flanker affected both vocal and manual responding to color patches. Color and word flankers also affected manual responding to word targets, but only word flanker affected vocal responding to word targets. These results are not consistent with models (e.g., translational models) of Stroop tasks, which posit that interactions between colors and words occur only when vocal responding is required.     

On-the-fly adaptation of selectivity in the flanker task

The processing selectivity in the flanker task has been shown to depend on the ratio of congruent trials to incongruent trials in a task (Gratton, Coles, & Donchin, 1992). If congruent trials are more frequent than incongruent ones, the flankers are more attended and, consequently, the flanker congruency effect is increased. Recent results suggest that participants can even allocate attention on the fly to the flankers-that is, in a highly flexible way after stimulus onset-depending on the frequency of incongruent trials on a certain stimulus location. Because location plays a unique role in stimulus selection, we investigated in two experiments whether selectivity can also be adjusted on the fly depending on stimulus color. The results demonstrate that color can be used for such an adjustment, but only if the association between color and frequency has be enpreviously learned under blocked conditions.     

A mental number line in human newborns

Humans represent numbers on a mental number line with smaller numbers on the left and larger numbers on the right side. A left‐to‐right oriented spatial–numerical association, (SNA), has been demonstrated in animals and infants. However, the possibility that SNA is learnt by early exposure to caregivers’ directional biases is still open. We conducted two experiments: in Experiment 1, we tested whether SNA is present at birth and in Experiment 2, we studied whether it depends on the relative rather than the absolute magnitude of numerousness. Fifty‐five‐hour‐old newborns, once habituated to a number (12), spontaneously associated a smaller number (4) with the left and a larger number (36) with the right side (Experiment 1). SNA in neonates is not absolute but relative. The same number (12) was associated with the left side rather than the right side whenever the previously experienced number was larger (36) rather than smaller (4) (Experiment 2). Control on continuous physical variables showed that the effect is specific of discrete magnitudes. These results constitute strong evidence that in our species SNA originates from pre‐linguistic and biological precursors in the brain.