Spatial frequency equalization does not prevent spatial-numerical associations

Abstract

There is an intense debate surrounding the origin of spatial-numerical associations (SNAs), according to which small numbers are mapped onto the left side of the space and large numbers onto the right. Despite evidence suggesting that SNAs would emerge as an innate predisposition to map numerical information onto a left-to-right spatially oriented mental representation, alternative accounts have challenged these proposals, maintaining that such a mapping would be the result of a mere spatial frequency (SF) coding of any visual image. That is, any smaller or larger array of objects would naturally contain more low or high SF information and, accordingly, each hemisphere would be preferentially tuned only for one SF range (e.g., right hemisphere tuned for low SF and left hemisphere tuned for high SF). This would determine the typical SNA (e.g., faster RTs for small numerical arrays with the left hand and for large numerical arrays with the right hand). To directly probe the role of SF coding in SNAs, we tested participants in a typical dot-arrays comparison task with two numerical sets: one in which SFs were confounded with numerosity (Experiment 1) and one in which the full SF power spectrum was equalized across all stimuli, keeping this cue uninformative about numerosity (Experiment 2). We found that SNAs emerged in both experiments, independently of whether SF was confounded or not with numerosity. Taken together, these findings suggest that SNAs cannot simply originate from SF power spectrum alone, and, thus, they rule out the brain's asymmetric SF tuning as a primary cause of such an effect.

Keywords: Hemispheric asymmetries; Numerical processing; Spatial frequency; Spatial–numerical association.

Fig. 1

Example of original stimuli used in Experiment 1 as generated with the method of Gebuis and Reynvoet (2011)

Fig. 2

The number comparison task. The participant had to decide whether the test stimulus was numerically larger or smaller than reference stimulus. A total of 192 trials (96 trials × 2 blocks) were displayed.

Fig. 3

a Percentage of correct responses as a function of the absolute ratio and the mapping condition. b Reaction times as a function the absolute ratio and the mapping condition. c RT difference between responses with the right and left hands as a function of the numerosity in test stimuli. Shaded regions represent the 95% CI of the regression line. d Coefficient of variation for each mapping condition. Bars represent ±1 SEM

Fig. 4

Example of SF equalized stimuli used in Experiment 2 as generated with the method of Willenbockel et al. (2010)

Fig. 5

Rotational average of the Fourier energy spectrum (a and b) and luminance histogram profile (c and d) for two stimuli comparisons with different ratios (0.66 and 0.8), as presented in Experiment 2. Panels a and c show the low-level feature statistics for the test stimuli with eight items compared with the Reference (ratio 0.66), whereas Panels b and d show the low-level feature statistics for the test stimuli with 10 items compared with the Reference (ratio 0.8). Note that in all figures the curve profiles almost fully overlap, thus indicating an extremely high equalization of the low-level statistical properties of the stimuli. Stimuli images were coded in linear RGB 8-bit grayscale values

Fig. 6

a Percentage of correct responses as a function of the absolute ratio and the mapping condition. b Reaction times as a function the absolute ratio and the mapping condition. c RT difference between right-hand and left-hand responses as a function of the numerosity in test stimuli. Shaded regions represent the 95% CI of the regression line. d Coefficient of Variation for each mapping condition. Bars represent ±1 SEM