A model of exact small-number representation |
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Authors: | Email author" target="_blank">Tom?VergutsEmail author Wim?Fias Micha?l?Stevens |
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Institution: | Department of Experimental Psychology, Ghent University, H. Dunantlaan 2, 9000 Ghent, Belgium. tom.verguts@ugent.be |
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Abstract: | To account for the size effect in numerical comparison, three assumptions about the internal structure of the mental number
line (e.g., Dehaene, 1992) have been proposed. These are magnitude coding (e.g., Zorzi & Butterworth, 1999), compressed scaling
(e.g., Dehaene, 1992), and increasing variability (e.g., Gallistel & Gelman, 1992). However, there are other tasks besides
numerical comparison for which there is clear evidence that the mental number line is accessed, and no size effect has been
observed in these tasks. This is contrary to the predictions of these three assumptions. Moreover, all three assumptions have
difficulties explaining certain symmetries in priming studies of number naming and parity judgment. We propose a neural network
model that avoids these three assumptions but, instead, uses place coding, linear scaling, and constant variability on the
mental number line. We train the model on naming, parity judgment, and comparison and show that the size effect appears in
comparison, but not in naming or parity judgment. Moreover, no asymmetries appear in primed naming or primed parity judgment
with this model, in line with empirical data. Implications of our findings are discussed. This work was supported by Grant
P5/04 from the Interuniversity Attraction Poles Program—Belgian Science Policy and by a GOA grant from the Ghent University
Research Council to W.F. |
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