Numbers and space: Associations and dissociations

Abstract

578Is 7 odd or even? The time it takes people to answer this simple question depends on the side of the response key used to indicate parity. People respond faster to 7 and to other large (single) numbers with a right-hand key but they respond faster to 3 and to other small numbers with a lefthand key. The presence of this spatial-numerical association of response codes (SNARC) has given currency to the idea that numerical magnitude is activated in an automatic manner whenever a numeral is presented for any purpose (note that retrieval of numerical magnitude is not strictly required for parity decision). In this study, we challenge the idea of a unique, automatic link between numbers and space and argue instead that an automatically activated link exists between relative (numerical) magnitude and spatial location. We first show that the widely accepted idea of an association between a particular number and a specific spatial location is based on a common confound between absolute and relative magnitude in existing SNARC studies. We then show that removing the confound results in the collapse of the traditional number-based SNARC effect but not of a relative-magnitude-based SNARC effect.The canonical experimental setup for assaying the SNARC effect entails manual performance of a task with numerals under alternative regimes of left-right key assignment. Under such conditions, the SNARC effect has been reported in a gamut of tasks-from parity decision (Dehaene, Bossini, & Giraux, 1993) to samedifferent judgments (Dehaene & Akhavein, 1995; but see Wood, Nuerk, & Willmes, 2006) to detecting the presence of a phoneme in the name of the digit (Fias, Brysbaert, Geypens, & d'Ydewalle, 1996) to bisection of lines composed of digits (Fischer, 2001) to finger-pointing the digit's location (Fischer, 2003) to judgments of numerical magnitude themselves (Gevers, Verguts, Reynvoet, Caessens, & Fias, 2006). Apart from the last measure, what is remarkable about these tasks is that none strictly requires retrieval of numerical magnitude for successful performance. However, in virtually all SNARC studies, the two properties of number, absolute and relative magnitude, were inextricably yoked. Is it absolute magnitude or relative magnitude that is associated with location in space?The difference between magnitude and relative magnitude (of, say, natural numbers) is subtle yet crucial for an understanding of the SNARC effect. The former notion is closely related to cardinal numbers, whereas the latter is closely related to ordinal numbers. The number 8 denotes a certain magnitude or numerosity (the first sense), but it also conveys the idea that 8 is larger than 5 or that it is smaller than 9 (the second sense). These two senses of number are confounded in existing research. Consider testing the SNARC effect with judgments of magnitude themselves (e.g., Gevers et al., 2006). In one block, the observer responds with the left-hand key when the presented number is smaller than 5 (the typical standard) and with the right-hand key when ...

Beyond left and right: Automaticity and flexibility of number-space associations

“…2). Similar to studies on the SNARC effect (e.g., Ben Nathan et al, 2009;Fias et al, 1996), our experiments demonstrate that the association between magnitude information and close/far response locations is activated in an automatic and flexible manner.…”

“…A marker of this flexibility is range dependency: in a parity judgment task, the digits 4 and 5 are associated with a right-sided response when the tested range is 0−5, but with a leftsided response if the tested range goes from 4 to 9 (Dehaene et al, 1993;Fias et al, 1996). More recently, Ben Nathan, Shaki, Salti, and Algom (2009) observed in a magnitude comparison task, in which the referent varied on a trial-by-trial basis, that the SNARC effect is driven by the relative magnitude of a number rather than by the absolute (range-based) magnitude. The same number of the tested range was associated with a left (right)-sided response if it was smaller (larger) than the referent, regardless of its absolute magnitude.…”

SNARC for numerosities is modulated by comparative instruction (and resembles some non-numerical effects)

“…In such a context, both aspects of numerical information-relative and absolute-could potentially be mapped to space (cf. Nathan et al 2009 for evidence on relative magnitude mapping in a comparison task with a varying standard). When adult subjects compare Arabic numbers, only absolute magnitudes are mapped onto space.…”

Spatial representations of numbers and letters in children

“…The present study, however, revealed a similar effect for letters with bias toward the letter succeeding in the alphabet, indicating that a spontaneous spatial coding of information is not specific for the numerical domain. Instead of assuming domain-specific forms of spatial representations like a mental number line or an “alphabet line” for letters (Berteletti et al, 2012), the spatial bias for digits and letters might be explained by the notion that spatial coding comes into play whenever relations are established (Nathan et al, 2009). Indeed, each line in the bisection task was flanked by two different digits/letters, thereby building up a relation.…”

“…In light of this finding, the authors questioned the adequacy of an interpretation in terms of a mental number line involving cardinal representations of numbers. Instead, they assumed that spatial bias arises from a spatial organization of categorical or relative magnitude information (see Nathan et al, 2009 for a similar view). Within this perspective, any kind of ordered information may be spatially organized.…”