The compositional nature of number concepts: Insights from number frequencies

The frequency with which humans use words provides a window into the psychological representation of the corresponding concepts. Capitalizing on the availability of massive lexical databases, we evaluate the frequency with which specific number words and their combinations (e.g. "twenty-four", "quatre-vingt-douze") are used in six different languages. We use these data to probe the hypothesis that complex concepts arise as syntactic combinations of simpler ones in a language of thought. First, we confirm our previous report of a regular and reproducible profile of decrease in frequency with number size, with local peaks for round numbers. Second, we show that frequency varies with the simplicity of the decomposition of a number into small prime factors. Third, we demonstrate that the entire frequency profile, including its overall decrease and local peaks, can be modeled by a grammar of algebraic combinations, whereby each number arises from addition and multiplication operations on smaller numbers. Those findings strengthen the hypothesis that compositionality in a language of thought underlies the emergence of exact number concepts.