A Stochastic Model for the Vocabulary Explosion

During the second year of life, the rate at which most children learn words accelerates dramatically, the so–called “vocabulary explosion”. Most accounts posit changes in the child or specialized learning mechanisms to account for this sudden change. However, recently McMurray (2007) demonstrated that acceleration is a mathematical consequence of parallel learning and the statistical distribution of word difficulty across the language. We generalize this model by developing a stochastic version. It demonstrates that the gradual nature of learning is critical for producing acceleration, and given sufficient gradualness, virtually any distribution of word difficulty can yield acceleration. Thus, the vocabulary explosion may be even more mathematically robust than previously thought.