Abstract
Human number understanding is thought to rely on the analog number system (ANS), working according to Weber’s law. We propose an alternative account, suggesting that symbolic mathematical knowledge is based on a discrete semantic system (DSS), a representation that stores values in a semantic network, similar to the mental lexicon or to a conceptual network. Here, focusing on the phenomena of numerical distance and size effects in comparison tasks, first we discuss how a DSS model could explain these numerical effects. Second, we demonstrate that the DSS model can give quantitatively as appropriate a description of the effects as the ANS model. Finally, we show that symbolic numerical size effect is mainly influenced by the frequency of the symbols, and not by the ratios of their values. This last result suggests that numerical distance and size effects cannot be caused by the ANS, while the DSS model might be the alternative approach that can explain the frequency-based size effect.
Highlights
Whereas in the present work we focus on the DSS explanation of the distance and size effects, the DSS explanation can be readily extended to other effects, too, and it can be a comprehensive model of symbolic number processing
With the present models and/or signal-to-noise ratio, the test was not decisive. This means that the DSS model is a viable alternative to the ANS model, because the goodness of fit of the DSS model is in the same range as the goodness of fit of the ANS model
We found that in a diffusion model analysis the drift rate pattern is more in line with the DSS model than with the ANS model, the uncertainties about the method may question the reliability of these results
Summary
Whereas in the present work we focus on the DSS explanation of the distance and size effects, the DSS explanation can be readily extended to other effects, too, and it can be a comprehensive model of symbolic number processing. While mostly it would not be too difficult to find DSS explanations for different phenomena, in the present work we only focus on the numerical distance and size effects in comparison tasks As it was mentioned above, the DSS model can only account for symbolic number processing. It has been shown that performance of the symbolic and non-symbolic number comparison tasks do not correlate in children (Holloway and Ansari, 2009; Sasanguie et al, 2014), and in an fMRI study the size of the symbolic and non-symbolic number activations did not correlate (Lyons et al, 2015) As another example, whereas former studies found common brain areas activated by both symbolic and non-symbolic stimuli (Eger et al, 2003; Piazza et al, 2004), later works with more sensitive methods found only notation-dependent activations (Damarla and Just, 2013; Bulthé et al, 2014, 2015). All of these findings are in line with the present proposal, suggesting that symbolic and non-symbolic numbers are processed by different systems
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