NoteNumber magnitude determines gaze direction: Spatial–numerical association in a free-choice task
Introduction
Previous studies have reported an association between numbers and space (e.g., Moyer and Landauer, 1967; for reviews see Dehaene, 1997; Fias and Fischer, 2005). Specifically, the results of these studies suggest that numbers are cognitively placed along a horizontal “mental number line” with small numbers (e.g., 1 or 2) represented on the left and large numbers (e.g., 8 or 9) represented on the right. Evidence for this spatial representation of numbers provides, for example, the SNARC effect (Spatial–Numerical Association of Response Codes effect), which was first reported by Dehaene et al. (1993). In their study, a number was presented in the middle of the screen and participants were asked to decide whether the presented number was odd or even by pressing a left or a right response key. Results showed that left hand responses were faster for small numbers whereas right hand responses were faster for large numbers.
Such number–space interactions have been demonstrated in various tasks (e.g., Ben Nathan et al., 2009, Dehaene and Akhavein, 1995, Fias et al., 1996, Fischer, 2001, Fischer, 2003), with different response modalities, such as manual (e.g., Fias, 2001, Fischer and Rottmann, 2005), verbal (Brysbaert, 1995, Stoianov et al., 2008, Zorzi et al., 2002), foot responses (e.g., Schwarz and Müller, 2006), and eye movement responses (e.g., Fischer et al., 2004, Schwarz and Keus, 2004).
Consistent with the notion of a mental number line, there is also evidence that thinking about numbers affects the free choice of a response (Daar and Pratt, 2008, Loetscher et al., 2010). Participants in the study of Daar and Pratt had to choose between making either a left or a right manual response when a number or a neutral character appeared in the middle of the screen. Participants produced more left (right) hand responses when small (large) numbers were presented, supporting the notion that number magnitude influences the selection of manual responses. Participants in the study of Loetscher et al. acted as a “random number generator” by naming subsequently 40 numbers between 1 and 30 in a random sequence. Verbal responses of participants were recorded and synchronized with their eye movements. The results of this study showed that leftward eye movements were associated with smaller numbers, whereas rightward eye movements were associated with larger numbers. Because the methodological approach taken by Loetscher et al. (2010) was correlational, it is possible that gaze direction influenced the mental selection of numbers, that thinking about numbers influenced gaze direction, or both. Therefore, the direction of the causal link between gaze direction and the reported number is unclear. It is thus premature to conclude that number magnitude influences gaze direction in free-choice response situations.
Nevertheless, it is possible that thinking about numbers may influence the direction of gaze. For example, it has been documented that number magnitude affects the direction of spatial attention (e.g., Fischer et al., 2003, Knops et al., 2009, Ristic et al., 2006, Stoianov et al., 2008) that is, participants tend to shift their spatial attention to the left (right) after the presentation of small (large) numbers. This shift of attention has been also attested by the results of event-related potentials (e.g., Priftis et al., 2008, Ranzini et al., 2009, Salillas et al., 2008, Salillas et al., 2009). In addition, it is known that there is a strong link between eye movements and spatial attention (e.g., Hoffman, 1998). Specifically, the pre-motor theory of attention (Rizzolatti et al., 1987) holds that spatial attention involves the pre-programming of eye movements towards the spatial region that is covertly attended. Therefore, according to this theory and the established effect of number magnitude on spatial attention, one should expect that number magnitude significantly influences gaze direction in a free-choice situation.
Hence, the purpose of the present study was to examine whether an influence of number magnitude on eye movements can be observed in a free-choice task. We expected that the mere presence of a number would be sufficient to activate its spatial number representation and thus would influence gaze direction. A small or a large number was presented in the middle of the screen followed by two faces displayed simultaneously on its left and right side. Participants were asked to explore the screen after the presentation of the number. According to the spatial association of numbers, we expected that participants tend to look to the left after presentation of a small number and to the right after presentation of a large number.
Section snippets
Participants
One hundred and fifty participants (M = 22.3 years, SD = 2.9) took part in this 20-min experiment. They reported normal or corrected-to-normal vision. All participants received course credits for their participation.
Apparatus
Participants were tested individually in a sound-attenuated room. They sat in a chair at a distance of approximately 40 cm from an overhead projector (50 Hz) upon which the visual stimuli were presented. Head movements were constrained by a head restraint and a chin rest. Eye movements
Results
Participants with more than 30% of not registered eye movements were excluded from further analysis (11 participants). As the number 5 was the middle number of the number range, trials including this number were also excluded. The first eye fixation after the presentation of the number was collected. Three areas of interest were defined: the center of the screen and the left and right positions where the faces appeared. In order to exclude saccades or false apparatus feedback, an eye fixation
Discussion
The purpose of the present experiment was to examine whether number magnitude influences the choice of gaze direction. Participants were asked to explore visually the screen after the presentation of a number. Gaze direction was not constrained by the experimenter. The results of this study show that the direction of the first gaze (i.e., left or right eye movement) was clearly affected by the magnitude of the preceding number (i.e., small or large respectively). This means that thinking about
Acknowledgments
We thank Álvaro Sánchez, Daniel Bratzke, Michael Steinborn, Bettina Rolke, Florian Wickelmaier, Marc Brysbaert and an anonymous reviewer for their helpful comments. This research was supported by Programa Nacional de I+D (Subprograma de Acciones Integradas DE2009-0040, PSI2008-02889-E, SEJ-PSI2009-13922), Programme des Projektbezogenen Personenaustauschs des DAAD (Z-50282682), and the Deutsche Forschungsgemeinschaft (SFB 833).
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