The SNARC effect: a preregistered study on the interaction of horizontal, vertical, and sagittal spatial-numerical associations.

Small numbers are processed faster through left-sided than right-sided responses, whereas large numbers are processed faster through right-sided than left-sided responses [i.e., the Spatial-Numerical Association of Response Codes (SNARC) effect]. This effect suggests that small numbers are mentally represented on the left side of space, whereas large numbers are mentally represented on the right side of space, along a mental number line. The SNARC effect has been widely investigated along the horizontal Cartesian axis (i.e., left-right). Aleotti et al. (Cognition 195:104111, 2020), however, have shown that the SNARC effect could also be observed along the vertical (i.e., small numbers-down side vs. large numbers-up side) and the sagittal axis (i.e., small numbers-near side vs. large numbers-far side). Here, we investigated whether the three Cartesian axes could interact to elicit the SNARC effect. Participants were asked to decide whether a centrally presented Arabic digit was odd or even. Responses were collected through an ad hoc-made response box on which the SNARC effect could be compatible for one, two, or three Cartesian axes. The results showed that the higher the number of SNARC-compatible Cartesian axes, the stronger the SNARC effect. We suggest that numbers are represented in a three-dimensional number space defined by interacting Cartesian axes.

Numbers around Descartes: A preregistered study on the three-dimensional SNARC effect.

The Spatial-Numerical Association of Response Codes (SNARC) effect suggests that numbers are represented along a horizontal left-to-right oriented, mental number line, with small numbers on the left and large numbers on the right. Much less evidence exists for vertical (down-to-up) and sagittal (near-to-far) SNARC effects. This might be due to the employment of different experimental paradigms among studies and to the, sometimes, inexact definition of the vertical and sagittal axes. We investigated for the first time the SNARC effect along the horizontal, vertical, and sagittal axes, by means of a classic SNARC task. Our results suggest the presence of three equally-strong SNARC effects. Our findings can be considered as evidence in favor of a three-dimensional, mental representation of numbers, in the form of a mental number space, defined by Cartesian coordinates.