Elsevier

Cognition

Volume 102, Issue 1, January 2007, Pages 101-117
Cognition

Temporal order judgment reveals how number magnitude affects visuospatial attention

https://doi.org/10.1016/j.cognition.2006.09.001Get rights and content

Abstract

The existence of spatial components in the mental representation of number magnitude has raised the question regarding the relation between numbers and spatial attention. We present six experiments in which this relation was examined using a temporal order judgment task to index attentional allocation. Results demonstrate that one important consequence of numerical processing is the automatic allocation of spatial attention, which in turn affects the perception of the temporal order of visual events. Given equal onset time, left-side stimuli are perceived to occur before right-side stimuli when a small number (1, 2) is processed, whereas right-side stimuli are perceived to occur before left-side stimuli when a larger number (8, 9) is processed. In addition, we show that this attentional effect is specific to quantity processing and does not generalize to non-numerical ordinal sequences.

Introduction

Several studies investigating the mental representation of numbers demonstrated a tight coupling between numbers processing and spatial cognition. Dehaene and collaborators (Dehaene et al., 1993, Dehaene et al., 1990) first demonstrated an association between number magnitude and response side: small numbers are associated with left-side responses and large numbers with right-side responses. This effect is known as the Spatial-Numerical Association of Response Codes (SNARC) effect and suggests that number magnitude is represented along a mental ‘number line’ that has a spatial orientation. Importantly, the spatial processing of numbers seems to be fast and automatic (Dehaene et al., 1993, Mapelli et al., 2003).

More direct evidence for the spatial nature of number representations comes from the study of Zorzi, Priftis, and Umiltà (2002), in which patients with left hemispatial neglect showed a systematic bias in a number bisection task as if they were neglecting the left part (smaller numbers) of the mental number line. Neglect patients in the Zorzi et al. (2002) study systematically misplaced the midpoint of the numerical interval (e.g., responding that 5 is halfway between 2 and 6) and their errors closely resembled the typical pattern found in bisection of true visual lines, including the modulating effect of line length (also see Priftis et al., 2006, Zorzi et al., 2006).

The automatic spatial coding of numbers has raised the question regarding the relation between numbers and spatial attention (Fischer, Castel, Dodd, & Pratt, 2003). Fischer and collaborators have shown that number perception causes a shift in covert attention to one side of visual space depending on number magnitude. Participants were required to detect as fast as possible a peripheral target that was preceded by an irrelevant digit cue. Results indicated that right targets were detected faster when preceded by a large digit (8 or 9), whereas left targets were detected faster when preceded by a small digit (1 or 2).

The orienting of attention in space allows the human visual system to sample sensory information to increase processing efficiency. Spotlight (Posner, Snyder, & Davidson, 1980), zoom lens (Eriksen & St. James, 1986) and gradient (LaBerge & Brown, 1989) models of spatial attention share the assumption that attention influences the speed of processing in the visual system. Stelmach and Herdman (1991) have provided evidence in favor of this assumption showing that the perception of temporal order is influenced by attentional allocation. Attentional effects were measured using a temporal order judgment (TOJ) task in which participants were required to report which of two visual stimuli occurred first. When the stimuli were presented at the same time, attended stimuli were perceived to occur before unattended stimuli (also see Shore, Spence, & Klein, 2001). Thus, the TOJ technique is a sensitive index of attentional allocation allowing one to assess attentional effects without requiring speeded manual responses.

We report a series of six experiments in which we investigated the relation between number processing and spatial attention using the TOJ technique to index attention orienting. Experiment 1 addressed the question of whether presentation of irrelevant numbers affects the perceived temporal order of two visual stimuli. In Experiments 2, 3A and 3B, number processing was engaged by requiring participants to report the identity of the digit after performing the TOJ task. That is, numbers were task-relevant, but unrelated to the temporal order of the visual stimuli. Experiments 4A and 4B examined whether modulation of temporal order depended on number magnitude or on ordinal information. Experiments 5 and 6 were designed to rule out the possibility that the results of the previous experiments depended on a response bias rather than on attention orienting. Moreover, Experiment 6 allowed us to measure the amount of temporal bias induced by the digit cues.

Section snippets

Experiment 1

In Experiment 1, we examined whether the simple perception of irrelevant digits may determine an automatic allocation of spatial attention depending on number magnitude. Our aim was to replicate the results of Fischer et al. (2003) using the TOJ technique to index the allocation of attention in space. Participants were required to report which of two brief flashes of light (TOJ stimuli), presented on either side of fixation, occurred first. TOJ stimuli were presented simultaneously or separated

Experiment 2

In Experiment 1, the presence of the irrelevant number at fixation did not produce attentional effects, contrary to the findings of Fischer et al. (2003) with a cueing paradigm. One possible explanation of the null result is that irrelevant numbers constitute a weak cue for the automatic triggering of attention shifts, as shown by a recent study that compared different types of irrelevant cues, including numerals (Bonato, Priftis, Marenzi, & Zorzi, 2005). Moreover, Galfano, Rusconi, and Umiltà

Experiments 3A and B

In Experiment 2 we demonstrated that number processing affects perception of temporal order. The purpose of Experiment 3 was to replicate this finding using a simplified experimental design. Therefore, only two numbers were used (digits 1 and 9 in Experiment 3A; digits 2 and 8 in Experiment 3B), whereas the delay between the digit and the TOJ stimuli was of about 250 ms (note that this delay was most effective in Experiment 2).

Experiments 4A and B

The results of Experiments 2 and 3 demonstrate that number processing affects the perceived temporal order of simultaneous events by causing an automatic shift of attention in space. However, attentional allocation might be linked to the ordinal character of numbers rather than to quantity information. Gevers, Reynvoet, and Fias (2003) have investigated the mental representation of non-numerical ordinal sequences such as letters and months, which share ordinality with numbers but not quantity.

Experiment 5

Our previous experiments indicate an automatic orienting of attention during number processing, the direction of which depends on number magnitude. However, one might argue that these results did not arise from attention orienting, but from the association between number processing and response side – that is, a SNARC effect (Dehaene et al., 1993). Specifically, it is possible that when TOJ stimuli were perceived simultaneously, participants were biased to respond with the left hand in the

Experiment 6

In Experiment 5, we showed that temporal order judgments are affected by number magnitude even when participants are required to indicate vocally which stimulus appeared first, using the Italian words corresponding to ”left” and ”right”. Even thought these results indicate that the observed effects did not depend on a bias of manual responses, they may be attributed to a response bias depending on an association between number and space at a conceptual level. In order to rule out this

General discussion

The relation between number processing and orienting of visuospatial attention was examined in six experiments using the TOJ technique to index attentional allocation. Our results clearly demonstrate that number processing determines an automatic shift of visuospatial attention, which in turn modulates the speed with which information is processed in the visual system and affects the perceived temporal order of visual events (e.g., Shore et al., 2001, Stelmach and Herdman, 1991). We also

Acknowledgments

This research was supported by grants from the Italian Ministry of Education, University and Research (PRIN 2003 to C.U., PRIN 2004 to M.Z.) and from the European Commission (Marie Curie Research Training Network “Numeracy and Brain Development” to M.Z.). We thank Giulio Vidotto and three anonymous reviewers for their helpful comments.

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    This manuscript was accepted under the editorship of Jacques Mehler.

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