Abstract
We investigated, in a university student population, spontaneous (non-speeded) fast and slow number-to-line mapping responses using non-symbolic (dots) and symbolic (words) stimuli. Seeking for less conventionalized responses, we used anchors 0–130, rather than the standard 0–100. Slow responses to both types of stimuli only produced linear mappings with no evidence of non-linear compression. In contrast, fast responses revealed distinct patterns of non-linear compression for dots and words. A predicted logarithmic compression was observed in fast responses to dots in the 0–130 range, but not in the reduced 0–100 range, indicating compression in proximity of the upper anchor 130, not the standard 100. Moreover, fast responses to words revealed an unexpected significant negative compression in the reduced 0–100 range, but not in the 0–130 range, indicating compression in proximity to the lower anchor 0. Results show that fast responses help revealing the fundamentally distinct nature of symbolic and non-symbolic quantity representation. Whole number words, being intrinsically mediated by cultural phenomena such as language and education, emphasize the invariance of magnitude between them—essential for linear mappings, and therefore, unlike non-symbolic (psychophysical) stimuli, yield spatial mappings that don’t seem to be influenced by the Weber-Fechner law of psychophysics. However, high levels of education (when combined with an absence of standard upper anchors) may lead fast responses to overestimate magnitude invariance on the lower end of word numerals.
Highlights
Numerical estimation research has shown that, among people in the industrialized world, number-to-space mappings are highly intuitive
The difference in nonlinear compression between responses to non-symbolic and symbolic stimuli was further corroborated with ordinary least squares (OLS) multiple regressions containing linear and logarithmic regressors and an added “dummy variable” (D)—a technique widely used in other domains [21]—aimed at evaluating the discriminability between responses to non-symbolic and symbolic stimuli with respect to logarithmic compression
When adding the dummy variable the weight of the dummy x logarithmic interaction was highly significant (BD x log = 0.029, st. error = 0.006, t ratio = 4.727, df = 22, p < 0.001), confirming that significant differences in logarithmic compression do exist between fast responses to nonsymbolic and symbolic stimuli
Summary
Numerical estimation research has shown that, among people in the industrialized world, number-to-space mappings are highly intuitive. Studies analyzing data with educated western participants have shown that when reporting on a line, participants exhibit a linear pattern in two main situations: [1] when the stimuli are symbolic (e.g., words)—which are intrinsically cultural, and [2] when they are non-symbolic (primarily psychophysical) as long as they are presented visually, and are easy to evaluate (e.g., small numerosity of dots in the 1–10 range) As it is argued elsewhere [9], the latter case, reproduces the conditions in which the learning of the number line occurs, that is, via the support of visible, discrete entities (e.g., dots or jumps performed by a bunny), presented in small quantities [9]
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