Beyond the SNARC effect: distance–number mapping occurs in the peripersonal space

Abstract

Estimating distance of objects relative to one's body is important for interaction with the environment. Given that distance is an interval of magnitude describing space, distance and the commonly used estimations of magnitude, i.e., numbers, may share a common representation system (the ATOM theory, Walsh in Trends Cogn Sci 7(11):483-488, 2003). The current study systematically examined the association between distance and number representations on both the sagittal and transverse axes on the transverse plane in the peripersonal space. Participants in Experiment 1 judged the parity of digits by pressing one of two buttons (both were in front of participants): One was near the body and the other away from it. We found that near responses were faster when paired with smaller numbers and far responses with larger numbers. When one button was set in front and the other in back in Experiment 2, no mapping was found. In Experiment 3, when both buttons were on the right side aligned with the transverse axis, small-near and large-far mapping were found. However, no such effect was found on the left side. These results suggest that numbers are mapped onto the whole transverse plane of the peripersonal space, not only a left-right oriented number line.

Distance in depth: A comparison of explicit and implicit numerical distances in the horizontal and radial dimensions.

“…As in Experiment 1, the correlation between implicit-DE and explicit-DE was not significant. As hypothesized, the SNARC effect driven by the numerical magnitude was modulated by the diagonal response mappings: Only the diagonal congruent with the MNL (i.e., from leftclose to right-far) led to negative and significant regression slopes, indicating an association of small/large numbers with left-close and right-far space (Aleotti et al, 2022;Chen et al, 2015;Gevers, Lammertyn et al, 2006; confirmed by the Bayesian analyses, see Appendix B). Conversely, the diagonal incongruent with the MNL (i.e., from left-far to right-close) led to positive and significant regression slopes (the Bayesian analyses reported inconclusive evidence, see Appendix B).…”

Spatio–Numerical Mapping in 3D

“…The vertical SNA could be based on gravity and more broadly on the natural laws according to which "More is Up -Less is down" (Lakoff & Johnson, 2008). While experimental studies regarding the sagittal axis are scarce, SNAs related to depth (near vs. far) could emerge in the peripersonal space (Chen et al, 2015). We posit that processing the spatial distance between an object/stimulus and usmore space, larger magnitude, and vice-versacould be a reliable hypothesis for accounting for the SNAs observed across vertical and sagittal axes.…”

“…Investigating SNAs along this axis is of critical interest given the scarcely available literature about it. For instance, Chen et al (2015) conducted a SNARC-like experiment to understand SNAs in a peripersonal space in which the response buttons were organized as near and far, and they found a reliable effect in performance favoring responses of the sort small/near versus large/far. Nevertheless, this axis is thought to share many mechanisms with the vertical axis, and in fact, the vertical and midsagittal axes are often interchanged with one another in the literature (Ito & Hatta, 2004).…”

Early is left and up: Saccadic responses reveal horizontal and vertical spatial associations of serial order in working memory

“…We used saccadic responses because they allow to separate the responses along the true horizontal and vertical spatial axes by placing gaze trigger keys to the left and right, and also below and above the centre of the screen. Moreover, saccadic responses do not induce a near-far dimension (as it is the case for manual responses along the sagittal axis, or for up/down keys located below the screen), and they do not induce a left/right hand confound for the up/down responses, all of which can bias spatial associations (Chen et al, 2015;Hartmann, Gashaj, et al, 2014;Santens & Gevers, 2008;Wiemers et al, 2017;Zhou et al, 2019Zhou et al, , 2020. Thus, saccadic responses overcome critical issues that were observed in previous studies that used manual responses.…”

“…This study further established that the oculomotor system is a valid alternative to manual responses when exploring the link between space and serial order (Rinaldi et al, 2015). In this study, we used saccadic responses in order to avoid problems that are typically induced by manual responses along the vertical axis, such as the closefar dimension or the left-right hand association (e.g., Chen et al, 2015;Hartmann, Gashaj, et al, 2014;Wiemers et al, 2017;Zhou et al, 2020). Besides these rather technical aspects, eye movements might generally play a special role in exploring the spatial nature of thoughts (e.g., Hartmann, 2015;Loetscher et al, 2010;Mast & Kosslyn, 2002;Rinaldi et al, 2015).…”