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.

Gamble on gaze: Eye movements reflect the numerical value of blackjack hands

“…The latter effect contrasts with those observed in previous studies, in which values were generally found to increase from bottom to top rather than the reverse (e.g., Holmes & Lourenco, 2012;Loetscher et al, 2010; but see Hung et al, Together with the lack of overt spatial cues, this suggests the activation of an MNL stored in long-term memory, as opposed to an ad-hoc spatial representation driven by task demands (cf. Fias, 2015). 2008).…”

“…Thus, after eliminating procedural confounds that may have primed vertical eye movements, horizontal gaze patterns continued to reflect the total hand value and were not driven merely by the last card's value, whereas vertical gaze patterns were weaker and driven solely by the last card's value. Moreover, the observed top-to-bottom orientation is surprising, given the opposite orientation (bottom-to-top) found in previous studies (e.g., Holmes & Lourenco, 2012;Loetscher et al, 2010). Hung et al (2008) found top-to-bottom orientation in Chinese speakers when processing Chinese number words, but our English-speaking participants had no particular experience, linguistic or otherwise, that might be expected to yield such an orientation.…”

“…We expected that vertical eye movements would now reflect hand value only weakly, if at all (cf. Gevers, Lammertyn, Notebaert, Verguts, & Fias, 2006;Holmes & Lourenco, 2012).…”

“…On the basis of evidence for left-to-right orientation of number in Westerners, and that gaze patterns reflect this orientation (Hartmann et al, 2015;Loetscher, Bockisch, & Brugger, 2008;Loetscher, Bockisch, Nicholls, & Brugger, 2010), we expected that smaller-value and larger-value hands would elicit more leftward and rightward eye movements, respectively. Because vertical orientation of number has also been observed (e.g., Hartmann, Gashaj, Stahnke, & Mast, 2014;Loetscher et al, 2010;Winter & Matlock, 2013; for discussion of mixed findings, see Hartmann et al, 2014;Holmes & Lourenco, 2012), we assessed whether upward and downward eye movements also reflected the value of participants' hands.…”

Dividing attention increases operational momentum

“…Many researchers have studied the vertically oriented mental number line in which smaller quantities are on the bottom and larger quantities are on the top (e.g., Holmes & Lourenco, 2012;Ito & Hatta, 2004;Shaki & Fischer, 2012;Wiemers, Bekkering, & Lindemann, 2014). Many claims regarding a horizontal mental number line are applicable to a vertical mental number line if "bottom" is substituted for "left" and "top" is substituted for "right".…”