Mental Number Representations in 2D Space

Abstract

There is evidence both for mental number representations along a horizontal mental number line with larger numbers to the right of smaller numbers (for Western cultures) and a physically grounded, vertical representation where "more is up." Few studies have compared effects in the horizontal and vertical dimension and none so far have combined both dimensions within a single paradigm where numerical magnitude was task-irrelevant and none of the dimensions was primed by a response dimension. We now investigated number representations over both dimensions, building on findings that mental representations of numbers and space co-activate each other. In a Go/No-go experiment, participants were auditorily primed with a relatively small or large number and then visually presented with quasi-randomly distributed distractor symbols and one Arabic target number (in Go trials only). Participants pressed a central button whenever they detected the target number and elsewise refrained from responding. Responses were not more efficient when small numbers were presented to the left and large numbers to the right. However, results indicated that large numbers were associated with upper space more strongly than small numbers. This suggests that in two-dimensional space when no response dimension is given, numbers are conceptually associated with vertical, but not horizontal space.

Keywords: Go/No-go task; SNARC; horizontal space; spatial-numerical associations; vertical space.

FIGURE 1

Illustration of trial sequence (stimuli not to scale).

FIGURE 2

Mean IES (in ms) per target number (see headings) and spatial position within the 7 × 7 grid. Lower values/yellow color represent better performance and higher values/blue color represent worse performance (see color scale).

FIGURE 3

Differences between IES (dIES) when target numbers were presented at different locations on the screen. Left: left vs. right presentation, positive values indicate more efficient responses for left presentation; right: lower vs. upper presentation, negative values indicate more efficient responses for upper presentation. The spatial positions within the 7 × 7 grid that were compared against each other in the respective analysis are illustrated as dark areas in the depicted miniature 7 × 7 grids.

FIGURE 4

Differences between IES (dIES) when target numbers were presented at different locations on the screen. Left: left down vs. right up presentation, negative values indicate more efficient responses for right upper presentation; right: left up vs. right down presentation, positive values indicate more efficient responses for left upper presentation. The spatial positions within the 7 × 7 grid that were compared against each other in the respective analysis are illustrated as dark areas in the depicted miniature 7 × 7 grids.

FIGURE 5

Individual slopes resulting from the horizontal and vertical analyses (see axis labels). Each data point represents one participant. Circles: consistent finger counters (from thumb to pinkie with both hands); cross: inconsistent finger counter (from index finger to pinkie with the starting hand). Red: left-starters; blue: right-starters; gray triangles: missing counting data.