Elsevier

Cognition

Volume 113, Issue 2, November 2009, Pages 248-253
Cognition

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

https://doi.org/10.1016/j.cognition.2009.08.005Get rights and content

Abstract

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.

Introduction

It is generally accepted that the mental representation of numerical magnitude is tightly linked to the mental representation of space. Evidence for spatial coding of numbers comes from studies in healthy participants and in brain-lesioned patients.

In a seminal study, Dehaene, Bossini, and Giraux (1993) asked healthy participants to perform a parity judgment task and observed faster left-hand responses to small numbers and faster right-hand responses to large numbers. This spatial–numerical association of response codes, the SNARC-effect, indicates that small numbers are associated with left and large numbers with right. It is a robust phenomenon that is also observed in tasks other than parity judgment, for example, phoneme monitoring (Fias, Brysbaert, Geypens, & d’Ydewalle, 1996) or magnitude comparison (Brysbaert, 1995). Importantly, it has been shown that the relation between numbers and space is not absolute but context-dependent. For example, Dehaene and colleagues (1993) observed that the SNARC-effect is range-dependent. Numbers 4 and 5 elicited faster left than right responses when the numbers ranged from 4 to 8, but elicited faster right than left responses when numbers ranged from 1 to 5. Bachtold, Baumuller, and Brugger (1998) extended this idea of context-dependency to mental imagery. When asked to imagine numbers on a clock face, the SNARC-effect reversed. This flexible relation between numbers and space suggests that the spatial code is not inherently associated with number representations but that it is constructed during task execution, suggesting the involvement of a mental workspace that is constructed in working memory. The involvement of working memory was recently confirmed by Herrera, Macizo, and Semenza (2008). They measured the SNARC-effect in a magnitude comparison task during the retention interval of a verbal and a spatial working memory task. The SNARC-effect disappeared under spatial, but not under verbal load, indicating the contribution of visuospatial processes to the SNARC-effect.

The idea of a spatially organized number representation is further supported by studies in hemineglect patients suffering from impaired attentional processing of contralesional hemispace. Zorzi, Priftis, and Umilta (2002) demonstrated that these patients not only show a bias when bisecting physical lines (Marshall & Halligan, 1989), but also when bisecting numerical intervals. When patients neglecting the left side of perceptual space bisect physical lines, they typically shift the subjective midpoint towards the right. Similarly, when indicating the midpoint of a numerical interval (e.g. what is in the middle between 1 and 9?) they overestimate the midpoint (e.g. 7). The spatial nature of the number bisection bias was further illustrated by the remediating effect of prism adaptation. Spatial remapping of the environment evoked by prism goggles not only reduced the bias in perceptual line bisection (Farne, Rossetti, Toniolo, & Ladavas, 2002), but also in number interval bisection (Rossetti et al., 2004).

The most widely accepted and influential view is that the SNARC-effect and the number bisection bias in neglect both derive from a common numerical–spatial representational system, conceivable as a mental number line, of which the spatial coding overlaps with or at least is very similar to the way perceptual space is represented and processed (Hubbard et al., 2005, Zorzi et al., 2002). The close link with perceptual space representations is supported by a number of additional observations such as the demonstration that numbers can initiate shifts of spatial attention (Fischer, Castel, Dodd, & Pratt, 2003), and by the fact that numbers can influence the kinematics of grasping movements (Andres, Davare, Pesenti, Olivier, & Seron, 2004).

Recent evidence, however, may contradict the hypothesis of a common spatial–number representation underlying both the SNARC-effect and the bisection bias in neglect. Priftis and colleagues (2006) described neglect patients showing a number interval bisection bias with the SNARC-effect in a parity judgment task being unaffected. They suggested that the explicit use of number magnitude information in interval bisection versus its implicit involvement in parity judgment explains the dissociation, but an alternative explanation is equally meaningful and needs to be considered. Even though the bisection bias in neglect, and especially its modulation by prism adaptation, suggests that the type of spatial representation involved in number bisection is analogous to the representations of physical space, such a perceptual representation is not the only way to cognitively represent spatial knowledge. There is substantial evidence that spatial information can also be represented in conceptual form expressing spatial relations using linguistic elements like above, below, left and right (Logan, 1994). Conceptual and perceptual spatial representations have been shown not to correspond (Crawford, Regier, & Huttenlocher, 2000) and to rely on dissociable neural systems (Jager & Postma, 2003).

Proctor and Cho (2006) recently proposed that not perceptual but conceptual spatial representations are the determining factor of the SNARC-effect. They assume that space, like many other cognitive representations, is organized in binary categories (e.g. left/right; small/large; hot/cold). Moreover, such conceptual categories have a polarity (e.g. left is negative and right is positive; small is negative and large is positive, …) and it is the correspondence between the polarity of the stimulus (viz. the number magnitude) and the response (viz. position of the response) that induces the SNARC-effect. Gevers and colleagues (2006) proposed a computational model that incorporates this idea and show that it captures the behavioral details of the SNARC-effect. Noteworthy, this model shows that the linear relationship between number magnitude and RT difference between right and left hand is consistent with the binary classification that is inherent to the conceptual explanation of the SNARC-effect. This is because in the model, numbers are categorized as small or large in a graded fashion and it is this gradedness that generates the linearity of the SNARC-effect.

In sum, there is currently no agreement on the nature of the spatial codes from which the SNARC-effect originates. While a visuospatial mental number line representation is most commonly seen as the determinant of the SNARC-effect, recently a conceptual spatial representation has been proposed as an alternative. However, this proposal remained exclusively based on theoretical (Proctor & Cho, 2006) and computational (Gevers et al., 2006) arguments that merely illustrate that a conceptual basis of the SNARC-effect is logically possible. So far, however, this idea has not received direct empirical support.

The present study aimed to investigate the idea that multiple types of spatial information are associated with numbers and that they might be engaged differently in different tasks. From the study of Herrera et al. (2008), showing that a visuospatial but not a verbal load eliminates the SNARC-effect in a magnitude comparison task, it can be concluded that magnitude comparison primarily depends on perceptual spatial associations. However, from the patient study of Priftis and colleagues (2006), showing a normal SNARC-effect in parity judgment in the presence of biased number bisection performance, we predict that the SNARC-effect in parity judgment originates from a spatial code that differs from the perceptual spatial representations. Based on Proctor and Cho (2006) we hypothesize this spatial code is of a conceptual nature. Although concepts are not necessarily represented linguistically (see e.g. Quinn (2004) showing that preverbal infants can make left/right distinctions), we assume that the spatial concepts related to numbers are verbally mediated. Given the importance of language and education for the development of numerical cognition in general (Dehaene & Cohen, 1995) and for some specific aspects of numerical knowledge, like parity, in particular (Nuerk, Iversen, & Willmes, 2004), we predict that a verbal but not a visuospatial load will abolish the SNARC-effect in a parity judgment task.

Section snippets

Experiment 1

To evaluate the involvement of verbally mediated and visuospatial representations in parity judgment, we asked participants to perform a parity judgment task while keeping verbal or spatial information in working memory.

Experiment 2

Our findings combined with the finding of Herrera et al. (2008) (showing that a spatial but not a verbal load abolishes the SNARC-effect in a magnitude comparison task) establish a double dissociation between memory load (verbal or spatial) and task (parity judgment or magnitude comparison). To ensure that the double dissociation is not due to differences in the experimental procedures, we tried to replicate the findings of Herrera et al. (2008) by applying the same procedural details of

General discussion

We investigated 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. In Experiment 1 it was shown that during parity judgment, the SNARC-effect was abolished under verbal load but not under spatial load. This result provides the necessary empirical argument to substantiate the claim that verbally mediated spatial representations can be the critical determinants

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