The SNARC effect in two dimensions: Evidence for a frontoparallel mental number plane

The existence of an association between numbers and space is known for a long time. The most prominent demonstration of this relationship is the spatial numerical association of response codes (SNARC) effect, describing the fact that participants' reaction times are shorter with the left hand for small numbers and with the right hand for large numbers, when being asked to judge the parity of a number (Dehaene et al., J. Exp. Psychol., 122, 371-396, 1993). The SNARC effect is commonly seen as support for the concept of a mental number line, i.e. a mentally conceived line where small numbers are represented more on the left and large numbers are represented more on the right. The SNARC effect has been demonstrated for all three cardinal axes and recently a transverse SNARC plane has been reported (Chen et al., Exp. Brain Res., 233(5), 1519-1528, 2015). Here, by employing saccadic responses induced by auditory or visual stimuli, we measured the SNARC effect within the same subjects along the horizontal (HM) and vertical meridian (VM) and along the two interspersed diagonals. We found a SNARC effect along HM and VM, which allowed predicting the occurrence of a SNARC effect along the two diagonals by means of linear regression. Importantly, significant differences in SNARC strength were found between modalities. Our results suggest the existence of a frontoparallel mental number plane, where small numbers are represented left and down, while large numbers are represented right and up. Together with the recently described transverse mental number plane our findings provide further evidence for the existence of a three-dimensional mental number space.