Jean-Philippe van Dijck

A Working Memory Account for Spatial-Numerical Associations.

Several psychophysical and neuropsychological investigations have suggested that the mental representation of numbers takes the form of a number line along which magnitude is positioned in ascending order according to our reading habits. A longstanding debate is whether this spatial frame is triggered automatically as intrinsic part of the number semantics or whether it constitutes a short-term representation constructed during task execution. Although several observations clearly favor the working memory account, its causal involvement has not yet been demonstrated. In two experiments we show that information stored in working memory get spatially coded in function of its ordinal position in the sequence and that the spatial-numerical associations typically observed in number categorization tasks draw upon this mechanism.

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.

Spatial Attention Interacts With Serial-Order Retrieval From Verbal Working Memory

The ability to maintain the serial order of events is recognized as a major function of working memory. Although general models of working memory postulate a close link between working memory and attention, such a link has so far not been proposed specifically for serial-order working memory. The present study provided the first empirical demonstration of a direct link between serial order in verbal working memory and spatial selective attention. We show that the retrieval of later items of a sequence stored in working memory—compared with that of earlier items—produces covert attentional shifts toward the right. This observation suggests the conceptually surprising notion that serial-order working memory, even for nonspatially defined verbal items, draws on spatial attention.

How number is associated with space?: the role of working memory

Publisher Summary This chapter reviews recent evidence on number bisection bias in neglect and on the Spatial Numerical Association of Response Codes (SNARC) effect challenging the homeomorphic relationship between numerical and spatial processing. The parallelism between number interval bisection and physical line bisection in neglect offers a high degree of face validity to the mental number line hypothesis. Just like patients ignore the left side of physical space and, therefore, produce a rightward bias in line bisection, the patients are assumed to ignore the left side of the number line which then leads to a bisection towards the right side of the number line where the large numbers are located. First, the spatial response code that is associated to numbers does not seem to be of a visuospatial nature but is rather situated at the level of conceptual categories. Second, serial position in working memory is the primary determinant of associations with response codes, not numerical magnitude.

A working memory account of the interaction between numbers and spatial attention

Rather than reflecting the long-term memory construct of a mental number line, it has been proposed that the relation between numbers and space is of a more temporary nature and constructed in working memory during task execution. In three experiments we further explored the viability of this working memory account. Participants performed a speeded dot detection task with dots appearing left or right, while maintaining digits or letters in working memory. Just before presentation of the dot, these digits or letters were used as central cues. These experiments show that the “attentional SNARC-effect” (where SNARC is the spatial–numerical association of response codes) is not observed when only the lastly perceived number cue—and no serially ordered sequence of cues—is maintained in working memory (Experiment 1). It is only when multiple items (numbers in Experiment 2; letters in Experiment 3) are stored in working memory in a serially organized way that the attentional cueing effect is observed as a function of serial working memory position. These observations suggest that the “attentional SNARC-effect” is strongly working memory based. Implications for theories on the mental representation of numbers are discussed.

The heterogeneous nature of number-space interactions

It is generally accepted that the mental representation of numerical magnitude consists of a spatial “mental number line” (MNL) with smaller quantities on the left and larger quantities on the right. However, the amount of dissociations between tasks that were believed to tap onto this representational medium is accumulating, questioning the universality of this model. The aim of the present study was to unravel the functional relationship between the different tasks and effects that are typically used as evidence for the MNL. For this purpose, a group of right brain damaged patients (with and without neglect) and healthy controls were subjected to physical line bisection, number interval bisection, parity judgment, and magnitude comparison. Using principal component analysis, different orthogonal components were extracted. We discuss how this component structure captures the dissociations reported in the literature and how it can be considered as a first step toward a new unitary framework for understanding the relation between numbers and space.

Finding the answer in space: the mental whiteboard hypothesis on serial order in working memory

Various prominent models on serial order coding in working memory (WM) build on the notion that serial order is achieved by binding the various items to-be-maintained to fixed position markers. Despite being relatively successful in accounting for empirical observations and some recent neuro-imaging support, these models were largely formulated on theoretical grounds and few specifications have been provided with respect to the cognitive and/or neural nature of these position markers. Here we outline a hypothesis on a novel candidate mechanism to substantiate the notion of serial position markers. Specifically, we propose that serial order WM is grounded in the spatial attention system: (I) The position markers that provide multi-item WM with a serial context should be understood as coordinates within an internal, spatially defined system; (II) internal spatial attention is involved in searching through the resulting serial order representation; and (III) retrieval corresponds to selection by spatial attention. We sketch the available empirical support and discuss how the hypothesis may provide a parsimonious framework from which to understand a broad range of observations across behavioral, neural and neuropsychological domains. Finally, we pinpoint what we believe are major questions for future research inspired by the hypothesis.

Non-spatial neglect for the mental number line

Several psychophysical investigations, expanding the classical introspective observations by Galton, have suggested that the mental representation of numbers takes the form of a number line along which magnitude is positioned in ascending order according to reading habits, i.e. from left to right in Western cultures. In keeping with the evidence, pathological rightward deviations in the bisection of number intervals due to right brain damage are generally interpreted as originating from a purely spatial-attentional deficit in the processing of the left side of number intervals. However, consistent double dissociations between defective processing of the left side of physical and mental number space have called into question the universality of this interpretation. Recent evidence suggests a link between rightward deviations in number space and defective memory for both spatial and non-spatial sequences of items. Here we describe the case of a left brain-damaged patient exhibiting right-sided neglect for extrapersonal and representational space, and left-sided neglect on the mental number line. Accurate neuropsychological examination revealed that the apparent left-sided neglect in the bisection of number intervals had a purely non-spatial origin and was based on mnemonic difficulties for the initial items of verbal sequences presented visually at an identical spatial position. These findings show that effective position-based verbal working memory might be crucial for numerical tasks that are usually considered to involve purely spatial representation of numerical magnitudes.

The impact of verbal working memory on number–space associations

Spatial-numerical associations are observed when participants perform number categorization tasks. One such observation is the spatial numerical associations of response codes (SNARC) effect, showing an association between small numbers and the left-hand side and between large numbers and the right-hand side. It has long been argued that this spatial association is automatically activated by the long-term representation underlying numbers processing. Instead, van Dijck and Fias (2011) argued that this association is a short-term representation that is constructed during task execution. This argument was based on the observation of an association between the ordinal position of an item in working memory and response side (e.g., the ordinal position effect). Four different experiments were set up to systematically investigate this assumption. Our results indicate that the activation of the canonical order of numbers in working memory (e.g., 1, 2, 3, etc.) is indeed necessary to observe the SNARC effect. The activation of the standard sequence of numbers (e.g., from 1 to 9) can be overruled when a new random sequence is memorized. However, this is only observed when retrieval of the memorized sequence is required during the numbers classification task.

Effects of Interhemispheric Communication on Two-Digit Arabic Number Processing

We investigated interhemispheric communication and hemispheric style differences (analytic vs. holistic) in two-digit Arabic number comparison by employing the divided visual field paradigm. Interhemispheric communication modulated two-digit number comparison in a very specific way. While no advantage of interhemispheric communication was found with unit-decade compatible trials (e.g., 52 and 67, the decade comparison and unit comparison of the two numbers lead to the same response; see Nuerk et al., 2001), a significant advantage of interhemispheric interactions emerged in the attentionally more demanding incompatible trials (e.g., 47 and 62, decade and unit comparisons do not lead to the same response, because 4 < 6 but 7 > 2), thereby enhancing the efficiency of selective attention (c.f., Banich, 1998). Additionally, some results indicated a more analytical processing style in the left hemisphere and a relatively more holistic processing style in the right hemisphere.