Experiential Origins of the Mental Number Line

Experiential Origins of the Mental Number Line Benjamin Pitt (bpitt@uchicago.edu) Daniel Casasanto (casasanto@uchicago.edu) Department of Psychology, University of Chicago 5848 S. University Avenue, Chicago, IL 60637 USA Abstract People map numbers onto horizontal space, forming an implicit mental number line (MNL). The direction of the MNL, which varies across cultures, has often been attributed to the direction of reading and writing words. Yet, this proposal is neither clearly motivated nor well supported by experimental data. Here we tested the hypothesis that finger- counting habits can determine the direction of the MNL. Americans were trained to count on their fingers from left to right or from right to left. After rightward counting, participants showed implicit associations of small numbers with left space and large numbers with right space, typical for Americans. After leftward counting, this space-number association was extinguished, overall, and was qualitatively reversed in a significant proportion of the individual participants. A few minutes of finger counting experience can redirect the MNL, supporting a causal role for finger counting in the acquisition and maintenance of culture-specific mental number lines. Keywords: SNARC; finger counting; embodied cognition; numerical cognition; motor experience Introduction Across many cultures, people use space to think about number. In English speaking cultures, small numbers are associated with the left side of an implicit mental number line (MNL), and large numbers with the right side (Restle, 1970). The most abundant source of evidence for this MNL is the Spatial-Numerical Association of Response Codes, or SNARC effect: People tend to respond faster to small numbers with their left hand and to large numbers with their right hand, even when the magnitude of the number is irrelevant to their response (Dehaene, Bossini, & Giraux, 1993). Although the MNL has been the subject of more than 100 experiments (Wood, Willems, Nuerk, & Fischer, 2008), there is little consensus about its developmental origins (de Hevia & Spelke, 2009; 2010; cf., Gebuis & Gevers, 2011). Where does this spatial mapping of number come from? Cross-cultural variation in the MNL provides clues to the origin of its directionality. According to one account, still widely accepted, the direction of reading and writing in a culture determines the direction of the MNL. In general, people from left-to-right reading cultures show MNLs that increase from left to right (e.g. French; Dehaene et al., 1993; Scots: Fischer, 2008; Canadians; Shaki, Fischer, & Petrusic, 2009), whereas people from some Arabic cultures show MNLs in the opposite direction (i.e. small numbers on the right, large numbers on the left), consistent with the right- to-left direction of reading in their cultures (Palestinians: Shaki et al., 2009; Lebanese: Zebian, 2005). Yet, overall, the available evidence calls into question the role of reading experience in determining the direction of the MNL. In their seminal study, Dehaene and colleagues (1993) found “no evidence” of a reversed SNARC effect in Iranian immigrants living in France who had extensive exposure to a right-to-left orthography. Another study found a reversed SNARC effect among Arabic-speaking Palestinians but no SNARC effect among Hebrew-speaking Israelis, who also read text from right to left (Shaki et al., 2009). Across cultures, the direction of people’s MNL appears to be only loosely correlated with the direction in which they read and write text. Furthermore, evidence of a culture-specific MNL has been found in preliterate children as young as 3 years old (Hoffmann, Hornung, Martin, & Schiltz, 2013; Opfer, Thompson, & Furlong, 2010; Shaki, Fischer, & Gobel, 2012). Finally, the only direct experimental test of the effect of reading experience on the direction of the MNL produced a null result. French participants responded to number words in either standard or mirror-reversed orthography. Orthography had no effect on the strength or direction of the SNARC (Dehaene et al., 1993; Experiment 8). Although Dehaene and colleagues concluded that, “[t]he particular direction of the spatial- numerical association seems to be determined by the direction of writing,” (1993, pg. 394) there is little empirical support for this claim. Some cultural practices appear to determine the direction of the MNL, but which ones? Does Finger Counting Shape the MNL? The direction of the MNL has also been attributed to finger counting. People whose finger-counting routines start with the left hand (habitual left-starters) were found to be more likely to show a standard SNARC effect than those who started with their right hand (habitual right-starters; Fischer, 2008). Across cultures, finger-counting habits appear to covary with writing direction. Reportedly, Americans and western Europeans tend to be left-starters, whereas Persian- speaking Iranians tend to be right-starters (Lindemann, Alipour, & Fischer, 2011; but see Di Luca, Grana, Semenza, Seron, & Pesenti, 2006; Sato, Cattaneo, Rizzolatti, & Gallese, 2007; Sato & Lalain, 2008). Could differences in finger-counting habits contribute to the observed cross- cultural variation in the MNL? A variety of behavioral, neuropsychological, and brain- imaging studies reveal tight links between fingers and