Wim Gevers

The mental representation of ordinal sequences is spatially organized

In the domain of numbers the existence of spatial components in the representation of numerical magnitude has been convincingly demonstrated by an association between number magnitude and response preference with faster left- than right-hand responses for small numbers and faster right- than left-hand responses for large numbers (Dehaene, S., Bossini, S., & Giraux, P. (1993) The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122, 371-396). Because numbers convey not only real or integer meaning but also ordinal meaning, the question of whether non-numerical ordinal information is spatially coded naturally follows. While previous research failed to show an association between ordinal position and spatial response preference, we present two experiments involving months (Experiment 1) and letters (Experiment 2) in which spatial coding is demonstrated. Furthermore, the response-side effect was obtained with two different stimulus-response mappings. The association occurred both when ordinal information was relevant and when it was irrelevant to the task, showing that the spatial component of the ordinal representation can be automatically activated.

Post-error slowing: An orienting account

It is generally assumed that slowing after errors is a cognitive control effect reflecting more careful response strategies after errors. However, clinical data are not compatible with this explanation. We therefore consider two alternative explanations, one referring to the possibility of a persisting underlying problem and one on the basis of the low frequency of errors (orienting account). This latter hypothesis argues that infrequent events orient attention away from the task. Support for the orienting account was obtained in two experiments. Using a new experimental procedure, Experiment 1 demonstrated post-error slowing after infrequent errors and post-correct slowing after infrequent correct trials. In Experiment 2, slowing was observed following infrequent irrelevant tones replacing the feedback signals.

Numbers and space: A computational model of the SNARC effect

The SNARC (spatial numerical associations of response codes) effect reflects the tendency to respond faster with the left hand to relatively small numbers and with the right hand to relatively large numbers (S. Dehaene, S. Bossini, & P. Giraux, 1993). Using computational modeling, the present article aims to provide a framework for conceptualizing the SNARC effect. In line with models of spatial stimulus-response congruency, the authors modeled the SNARC effect as the result of parallel activation of preexisting links between magnitude and spatial representation and short-term links created on the basis of task instructions. This basic dual-route model simulated all characteristics associated with the SNARC effect. In addition, 2 experiments tested and confirmed new predictions derived from the model.

The mental representation of ordinal sequences is spatially organised: evidence from days of the week

In the domain of numbers the existence of spatial components in the representation of numerical magnitude has been convincingly demonstrated by an association between number magnitude and response preference with faster leftthan right-hand responses for small numbers and faster rightthan left-hand responses for large numbers (Dehaene, S., Bossini, S., & Giraux, P. (1993) The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122, 371–396). Because numbers convey not only real or integer meaning but also ordinal meaning, the question of whether non-numerical ordinal information is spatially coded naturally follows. While previous research failed to show an association between ordinal position and spatial response preference, we present two experiments involving months (Experiment 1) and letters (Experiment 2) in which spatial coding is demonstrated. Furthermore, the response-side effect was obtained with two different stimulus-response mappings. The association occurred both when ordinal information was relevant and when it was irrelevant to the task, showing that the spatial component of the ordinal representation can be automatically activated. q 2003 Elsevier Science B.V. All rights reserved.

Dissecting the symbolic distance effect: Comparison and priming effects in numerical and nonnumerical orders

When participants are asked to compare two stimuli, responses are slower for stimuli close to each other on the relevant dimension than for stimuli further apart. Previously, it has been proposed that this comparison distance effect originates from overlap in the representation of the stimuli. This idea is generally accepted in numerical cognition, where it is assumed that representational overlap of numbers on a mental number line accounts for the effect (e.g., Cohen Kadosh et al., 2005). In contrast, others have emphasized the role of response-related processes to explain the comparison distance effect (e.g., Banks, 1977). In the present study, numbers and letters are used to show that the comparison distance effect can be dissociated from a more direct behavioral signature of representational overlap, the priming distance effect. The implication is that a comparison distance effect does not imply representational overlap. An interpretation is given in terms of a recently proposed model of quantity comparison (Verguts, Fias, & Stevens, 2005).

Top-down and bottom-up sequential modulations of congruency effects.

Several studies have demonstrated reduced congruency effects after incongruent trials. The conflict monitoring hypothesis (Botvinick, Braver, Barch, Carter, & Cohen, 2001) assumes that this sequential modulation is based on top-down cognitive control and suggests that more control is engaged after the detection of conflict. An alternative account is based on repetition effects of stimulus and response features and can be considered bottom up. This study investigates both modulatory sources. In a Stroop task with two response-stimulus intervals (RSIs), we demonstrate that top-down modulation does not occur with a very short RSI, suggesting that it takes some time before the system can be reconfigured. Bottom-up modulation is observed for both RSIs. This finding demonstrates that two different sources simultaneously reduce congruency effects after incongruent trials.

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 Brain Locus of Interaction between Number and Size: A Combined Functional Magnetic Resonance Imaging and Event-related Potential Study

Whether the human brain is equipped with a special neural substrate for numbers, or rather with a common neural substrate for processing of several types of magnitudes, has been the topic of a long-standing debate. The present study addressed this question by using functional magnetic resonance imaging (fMRI) and event-related potentials (ERPs) together with the size-congruity paradigm, a Stroop-like task in which numerical values and physical sizes were varied independently. In the fMRI experiment, a region-of-interest analysis of the primary motor cortex revealed interference effects in the hemisphere ipsilateral to the response hand, indicating that the stimulus-stimulus conflict between numerical and physical magnitude is not completely resolved until response initiation. This result supports the assumption of distinct comparison mechanisms for physical size and numerical value. In the ERP experiment, the cognitive load was manipulated in order to probe the degree to which information processing is shared across cognitive systems. As in the fMRI experiment, we found that the stimulus-stimulus conflict between numerical and physical magnitude is not completely resolved until response initiation. However, such late interaction was found only in the low cognitive load condition. In contrast, in the high load condition, physical and numerical dimensions interacted only at the comparison stage. We concluded that the processing of magnitude can be subserved by shared or distinct neural substrates, depending on task requirements.

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.

Numbers are associated with different types of spatial information depending on the task

In this study, we examined the nature of the spatial-numerical associations underlying the SNARC-effect by imposing a verbal or spatial working memory load during a parity judgment and a magnitude comparison task. The results showed a double dissociation between the type of working memory load and type of task. The SNARC-effect disappeared under verbal load in parity judgment and under spatial load in magnitude comparison. These findings provide the first direct empirical evidence against the view that all behavioral signatures of spatial-numerical associations have their origin in a common spatial code. Instead they show that numbers are associated with different spatial codes which, depending on the task, have a visuospatial or verbally mediated nature.