The model described above assumes that the acquisition of numerical symbols such as Arabic numerals is simply a matter of relating these arbitrary shapes to the log-Gaussian representation of the corresponding numerosity, so that decision-making involves quantities rather than the symbols themselves. However, converging evidence suggests that this view is a little too simple, and that the acquisition of symbols for numbers also profoundly changes the non-verbal representation of numerical quantities.
Verguts and Fias (2004) simulated unsupervised learning in a formal neural network that is exposed either to numbers alone, or to numbers paired with the corresponding symbol. In the first case, the network develops "numerosity detector" neurons very similar to those described by Nieder and Miller, with a log-Gaussian tuning curve. Symbol matching, however, profoundly alters this representation. Although neurons remain tuned to approximate numerosity, they respond very precisely to each numerical symbol. The neurons' tuning curve still shows a distance effect, but with a large all-or-nothing component coupled with a small linear effect. On the other hand, contrary to Weber's law, all neurons present the same tuning curve, with a fixed width for all numbers tested (1 to 5). In this way, the network exposed to the symbols develops a new type of representation that can be described as linear with fixed variability.
