Numbers and Space: Associations and Dissociations

Article excerpt

A cornerstone of contemporary research in numerical cognition is the surprising link found between numbers and space. In particular, people react faster and more accurately to small numbers with a left-hand key and to large numbers with a right-hand key. Because this contingency is found in a variety of tasks, it has been taken to support the automatic activation of magnitude as well as the notion of a mental number line arranged from left to right. The present study challenges the presence of a link between left-right location, on the one hand, and small-large number, on the other hand. We show that a link exists between space and relative magnitude, a relationship that might or might not be unique to numbers.

Is 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 same- different 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 the number is larger than 5; in a second block, key assignment reverses. Note that within a block, the number 8 is always large and always maps onto the same fixed response key. …