Elsevier

Cognition

Volume 106, Issue 2, February 2008, Pages 770-779
Cognition

Visuospatial priming of the mental number line

https://doi.org/10.1016/j.cognition.2007.04.013Get rights and content

Abstract

It has been argued that numbers are spatially organized along a “mental number line” that facilitates left-hand responses to small numbers, and right-hand responses to large numbers. We hypothesized that whenever the representations of visual and numerical space are concurrently activated, interactions can occur between them, before response selection. A spatial prime is processed faster than a numerical target, and consistent with our hypothesis, we found that such a spatial prime affects non-spatial, verbal responses more when the prime follows a numerical target (backward priming) then when it precedes it (forward priming). This finding emerged both in a number-comparison and a parity judgment task, and cannot be ascribed to a “Spatial–Numerical Association of Response Codes” (SNARC). Contrary to some earlier claims, we therefore conclude that visuospatial–numerical interactions do occur, even before response selection.

Introduction

A few decades ago, it was suggested that the representation of numbers could be spatially organized along a mental number line (Restle, 1970). That this mental number line is more than a metaphor has been shown by Zorzi, Priftis, and Umiltà (2002), who found that the pattern of errors of neglect patients in a mental-number-line-bisection task are remarkably similar to those in a physical-line bisection task (see also Priftis et al., 2006, Zorzi et al., 2006).

Since Dehaene, Bossini, and Giraux (1993), it has often been assumed that the mental number line affects spatial aspects of response selection. Dehaene et al. presented single digits at fixation, asked subjects to indicate their parity (odd or even), and found that small numbers lead to faster left-hand responses than right-hand responses, and that large numbers lead to faster right-hand responses than left-hand responses. Dehaene et al. interpreted the effect as due to a Spatial–Numerical Association of Response Codes (SNARC), an association between the spatially organized “mental number line” and a response preparation that is also spatial in nature and could, for example, involve left and right hands (Fias, 2001), saccades (Schwarz & Keus, 2004), or the left and right fingers of one single hand (Priftis et al., 2006).

However, Caessens et al., 2004, Fischer et al., 2003, provided some evidence suggesting that the mental number line could affect processing before response selection. They presented subjects with a dot, either to the right or left of fixation, and asked them to detect it as quickly as possible, but always with the same hand. The dot was preceded by one of four digits (1, 2, 8, or 9) and, although the digit was uninformative about the location of the dot (and subjects knew this), it nevertheless led to faster target detection on the left when it represented a number that was small, and to faster detection on the right when it represented a number that was large. Response selection was irrelevant, and the authors attributed their result to a lateral shift of attention, induced upon number perception by the activation of the mental number line.

Ristic, Wright, and Kingstone (2006) and Galfano, Rusconi, and Umilta (2006) replicated the result, but also found that the attentional shift is not obligatory, and reflects top–down rather than bottom–up processes. Nevertheless, using temporal order judgments rather than detection, Casarotti, Michielin, Zorzi, and Umiltà (2007) corroborated Fischer et al.’s conjecture that attention might play a mediating role. Casarotti et al. found that when two dots, that are presented at the same time, are preceded by a small number, the left dot is judged to appear sooner, and when they are preceded by a large number, the right dot is judged to appear sooner. The effects did require active processing of the cue as a number, and only appeared when it had to be reported, but with that condition fulfilled, the attentional temporal order effect could offset an opposite physical temporal order difference of about 5–6 ms.

In the current article, as in the studies we just mentioned, we investigate visuospatial–numerical interactions that precede response selection. However, whereas Fischer, Castel, Dodd, and Pratt (2003) investigated whether a number can affect the processing of a non-number, we do the opposite, and explore whether a non-number can affect the processing of a number. Given that the representations of visual and numerical space are homeomorphic (Zorzi et al., 2002; but cf. Doricchi, Guariglia, Gasparini, & Tomaiuolo, 2005), we hypothesize that the two representations interact when they are concurrently activated and that, in particular, a concurrently processed visuospatial cue and a numerical target can affect each other in this way.

Keus and Schwarz (2005) also investigated whether non-numerical information can affect numerical processing. Their subjects had to indicate the parity of a number that could appear either to the right or left of fixation. The task ensured the numbers were processed – shown to be important by Casarotti et al. (2007) – but nevertheless they only obtained an effect of the position of the numbers on lateralized manual responses, and not on (non-lateralized) voice key responses. Keus and Schwarz concluded that visuospatial–numerical effects can only occur at, and not before, response selection.

However, spatial information is coded fast and automatically (e.g., Lu & Proctor, 1995) and could decay or be inhibited (e.g., Zorzi & Umiltà, 1995) before concurrently presented numerical information is processed, especially when this spatial information is task-irrelevant. Consequently, it is possible that the concurrently presented visuospatial and numerical information in the stimuli of Keus and Schwarz (2005) did not activate their respective representations at the same time, and that this is why they did not find an interaction in their verbal task. In Fischer et al. (2003), in contrast, a numerical prime was presented well in advance of a spatial target, and with the processing of the numerical prime being slower than of the spatial target, it is consistent with our conjecture that Fischer et al. did, and Keus and Schwarz did not, find visuospatial–numerical interactions before response selection.

In two experiments, we test our conjecture that there are visuospatial effects on numerical processing, even before response selection, provided the representations of visual space and numerical space are activated concurrently. More specifically, we predict that a spatial prime does affect the processing of a numerical target, but that this effect emerges when the prime follows rather than precedes the target. That is, we predict that backward priming is more effective than forward priming. By employing a verbal task, we avoid the use of lateralized effectors, and control a SNARC effect that could otherwise confound our results. Moreover, in order to collect converging evidence for our claim, we use two different tasks: a number comparison task (Experiment 1), and a parity judgment task (Experiment 2).

Section snippets

Participants

Twenty naïve undergraduates of the Università di Padova participated in Experiment 1 (for course credit) and twenty different ones in Experiment 2 (for a small fee).

Apparatus

We used an IBM-compatible computer with a 17 in. flat-screen monitor (85 Hz refresh rate), and recorded responses with the help of a voice key, with a Sigma Tel soundcard, that had a sensitivity of −59 dBm, and 80–12,000 Hz. With the help of a custom made MATLAB program, the onset of the voice key responses was detected with millisecond

Results

We averaged across the counterbalanced voice key responses of “Ti” and “To”, and submitted the reaction time (RT) data to an ANOVA. Only correct trials were considered with RTs no smaller than 200 ms, no larger than 1000 ms, and no larger than two standard deviations above the mean of the condition in which the trial occurred (Miller, 1988, Ratcliff, 1993), leading to the exclusion of 4.0% and 3.9% of the data as outliers in, respectively, Experiments 1 and 2. Results were similar when outliers

Discussion

Based on neuropsychological evidence that the representations of visual and numerical space are homeomorphic (Zorzi et al., 2002), we hypothesized that interactions between a spatial prime and a numerical target should be possible. However, semantic processing of a target digit must be preceded by its perceptual processing, whereas a non-numerical visuospatial prime does not require any more than just perceptual processing. For this reason, the spatial coding of a number (activation of the

Acknowledgements

This research was supported by grants from the Università di Padova (research Grant 238-2005 to I.S.) and the European Commission (Marie Curie Research Training Network “Numeracy and Brain Development” to M.Z. and P.K.).

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