The mental representation of ordinal sequences is spatially organized

Abstract

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.

Introduction

Although considerable advances have been made in the understanding of the internal representation and processing of ordinal information (see Leth-Steensen & Marley, 2000, for a recent review), one aspect of it, the association between order and space, has barely been investigated. This is surprising because numbers, which convey ordinal meaning (hierarchically implied by their real and integer meaning; Gallistel & Gelman, 2000), are generally accepted to be spatially coded.

An explicit indication of an association between numbers and space was first demonstrated by a response-side effect in number comparison (Dehaene et al., 1990, Hinrichs et al., 1981). When participants had to indicate whether a number was smaller or larger than a predetermined reference number by pressing one of two response buttons, it was found that ‘large’ responses were faster with the right hand than with the left hand. The reverse was true for small numbers.

In a study investigating the mental processing of parity judgement, Dehaene, Bossini, and Giraux (1993) provided further evidence concerning the response-side effect (and called it SNARC effect for Spatial Numerical Association of Response Codes). In evaluating a number's parity status, shorter latencies were obtained for small numbers responded to with the left hand than with the right hand. Conversely, large numbers were responded to preferentially with the right hand. Because parity is a numerical property which alternates between consecutive numbers, this study extends the response-side effect by showing that the effect is not specific to the stimulus-response mapping of the comparison task. It also follows that the effect is not related to the use of a reference number for comparison.

Importantly, the results also show that the numerical value is automatically activated, because in principle the parity judgement task needs no access to numerical magnitude information for correct task performance. Further support for the possibility of automatic activation of spatially coded numerical magnitudes comes from a series of experiments which showed that the SNARC effect was elicited, even when digits served merely as a background distracter with a non-numerical target superimposed in an orientation discrimination task (Fias, Lauwereyns, & Lammertyn, 2001).

In the present paper we investigate whether a similar association exists between non-numerical ordered sequences and spatial properties of the response. Dehaene et al. (1993; Experiment 4) already used letters in situations that were structurally analogous to the parity judgement task. In a first condition subjects had to classify the letters A–F into the categories ACE or BDF. No SNARC effect was obtained. One could argue, however, that the categories along which the letters had to be classified were arbitrary. This may have induced an atypical way of performing the task. This assumption is supported by the fact that the pattern of response times (RTs) was compatible with a serial search strategy. In a second condition, letters were used in a consonant–vowel classification task spanning almost the entire alphabet, but a significant SNARC effect was not obtained. However, there was a tendency toward a SNARC effect. Given the small number of subjects (n=10), one could argue that the experiment did not have enough statistical power. Most importantly, in both conditions the ordering of the stimuli was irrelevant to the task. One could imagine that the mental representation of order is spatially organized, but that, unlike numbers, this spatially organized representation is not accessed automatically. Taken together, there are a number of reasons why the conditions to test a possible spatial association of order and space were suboptimal.

In the following experiments we investigate the possible spatial organization of two ordered sequences, namely months of the year (Experiment 1) and letters (Experiment 2). For each stimulus type, subjects performed both an order-relevant task (comparison with a fixed standard) and an order-irrelevant task (letter detection in Experiment 1 and consonant–vowel classification in Experiment 2).

The order-relevant task allows judging of the spatial coding of internally ordered information, and with the order-irrelevant task the automaticity of activation of the spatial codes can be evaluated.