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• W2577753386 abstract "Horizontal Trumps Vertical in the Spatial Organization of Numerical Magnitude Kevin J. Holmes (kevin.holmes@emory.edu) Stella F. Lourenco (stella.lourenco@emory.edu) Department of Psychology, Emory University 36 Eagle Row, Atlanta, GA 30322 Abstract The vast majority of research on the spatial nature of numerical representation has focused on the horizontal axis, highlighting the left-to-right orientation of increasing values (i.e., the mental number line). Recent evidence points to spatial organization along the vertical (bottom-to-top) axis as well. We argue, however, that these findings are better characterized as generalized magnitude mappings between number and other magnitude dimensions (e.g., near-far spatial extent), rather than genuine vertical orientation. Here we replicate generalized magnitude mappings for number (Exp. 1A) and show that they take precedence over left-to-right orientation (Exp. 1B), likely because of the direct mapping between dimensions. In contrast, we find no evidence of spontaneous organization along the true vertical axis (Exp. 2A), and left-to-right orientation trumped bottom-to-top orientation when the two were inconsistent with each other (Exp. 2B). Reliable bottom-to-top orientation was evident only after priming of magnitude relations among numbers (Exp. 3). Together, these findings demonstrate that number is more strongly represented horizontally than vertically. We suggest that experience with cultural tools may drive this asymmetry, and we highlight other cognitive and environmental factors that may influence the mental organization of magnitude dimensions beyond number. Keywords: number; spatial organization; SNARC effect; mental magnitude line. Introduction Across a wide range of common cultural tools and artifacts, numbers are spatially organized. Many of these external symbolic representations depict numbers horizontally (e.g., rulers, measuring tapes), but some do so vertically (e.g., mercury thermometers, measuring cups). Despite this variation in spatial forms, the vast majority of research on the mental association between number and space has focused almost exclusively on the horizontal axis. Many such studies have suggested that numerical representations take the form of a mental number line, running from left to right in representational space (at least in Western cultures; for reviews, see Fias & Fischer, 2005; Hubbard et al., 2005), without examining other spatial axes on which number might also be mentally organized. Recent findings suggest, however, that the vertical axis (specifically, bottom-to-top orientation) may also be recruited in the mental organization of number. In a parity judgment task, with response buttons arranged vertically on a tabletop, Ito and Hatta (2004) found that as numerical magnitude increased, “top” responses became faster relative to “bottom” responses (see also Gevers et al., 2006; Muller & Schwarz, 2007). Using saccadic latency as a dependent measure, Schwarz and Keus (2004) found that larger numbers elicited faster upward (relative to downward) saccades, and Loetscher et al. (2010) showed that vertical (not just horizontal) changes in participants’ eye position were predictive of the magnitude of numbers they subsequently generated. While such findings have been regarded as evidence for vertical orientation of number, they are also compatible with the notion that number is but one component of a more general system of magnitude representation (Walsh, 2003). On this account, different dimensions of magnitude are spontaneously aligned, producing generalized mappings of more/less relations across dimensions (e.g., number, duration, size). As such mappings have been observed even in preverbal infants (Lourenco & Longo, 2010), they do not appear to require the same degree of cultural support as organization of number along spatial axes (e.g., left-to-right orientation), and hence may be especially robust. In the case of previous findings for vertical orientation, generalized magnitude mappings can fully account for the observed effects without invoking spatial axes, or a specific orientation, at all. That is, numerical magnitude may have been mapped to another magnitude dimension rather than to the vertical axis per se. In studies using tabletop responses, number may have been mapped to distance, given that response buttons were not arranged along the true vertical bottom-top axis (i.e., sagittal plane). Instead, they differed in relative spatial extent from the body (i.e., transverse plane; see Fig. 1); the “top” and “bottom” responses in these studies may be better characterized as “far” and “near” responses, respectively. Thus, larger numerical values may have been associated with greater distance, rather than upward locations in space. Generalized magnitude mappings may also underlie the effects observed with saccadic measures. In these studies, number may be associated with effort, since upward and downward saccades may be considered more and less effortful, respectively. Vision research has shown that upward saccades are slower than downward saccades, and the resting position of the eyes is slightly lower than the actual vertical midpoint (Collewijn, Erkelens, & Steinman, 1988). Overall downward shifts in eye position have also been observed during number bisection tasks (Loetscher, Bockisch, & Brugger, 2008), suggesting that upward saccades may require greater effort, particularly during number processing. Thus, in studies using saccadic measures to examine vertical orientation, larger numerical values may have been associated with more effortful bodily actions (as has been shown for grasping; e.g., Lindemann et al., 2007). Given that the vertical axis has been confounded with other magnitude dimensions in previous studies, whether number is" @default.
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• W2577753386 title "Horizontal Trumps Vertical in the Spatial Organization of Numerical Magnitude" @default.
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