Orienting numbers in mental space: Horizontal organization trumps vertical

Abstract

While research on the spatial representation of number has provided substantial evidence for a horizontally oriented mental number line, recent studies suggest vertical organization as well. Directly comparing the relative strength of horizontal and vertical organization, however, we found no evidence of spontaneous vertical orientation (upward or downward), and horizontal trumped vertical when pitted against each other (Experiment 1). Only when numbers were conceptualized as magnitudes (as opposed to nonmagnitude ordinal sequences) did reliable vertical organization emerge, with upward orientation preferred (Experiment 2). Altogether, these findings suggest that horizontal representations predominate, and that vertical representations, when elicited, may be relatively inflexible. Implications for spatial organization beyond number, and its ontogenetic basis, are discussed.

Keywords:

• Number
• Spatial organization
• Mental number line
• Spatial–numerical association of response codes (SNARC)

Acknowledgments

We thank Dede Addy, Edmund Fernandez, and Paul Pfeilschiefter for assistance with data collection. This research was supported by a Scholars Award from the John Merck Fund to Stella F. Lourenco.

Notes

¹ No explicit instructions were given concerning hand placement, but the vast majority of participants (polled immediately after the experiment) reported using two hands in both conditions.

² We do not consider leftward orientation in this description because there is no reason to expect that the participants in our experiments would represent number in this direction, given the wealth of prior research showing rightward orientation in Westerners (see Hubbard et al., 2005). Indeed, there was clear evidence of rightward orientation in all of the experiments reported here.

³ When completed second, the incongruent condition yielded a marginally positive slope (M = 5.60 ms/digit), t(15) = 2.03, p = .06, unlike when completed first. This difference is difficult to interpret, perhaps reflecting a combination of carryover from the congruent condition and strategic switching of orientations in the incongruent condition following the change in response locations. Future research might consider how the underlying representation of number interacts with such task-related factors.

⁴ When the vertical condition was completed second, the slope did not differ significantly from zero. It is possible that by the second half of the experiment, participants had disregarded the priming instructions (since they were irrelevant to judging parity). The attenuation of vertical orientation in this context is consistent with relatively weak vertical organization of number.