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M. Ramscar et al. / Topics in Cognitive Science 6 (2014)




Fig. 2. The non-linear dynamics of vocabulary growth. A: Upper left: the relative frequencies of the Lemhoefer and Broersma (2012) vocabulary test items. Each vertical gray line represents an individual item, and
the black curve plots the empirical lemma rank-frequency distribution of English. B: Upper right: the black
circles plot an individual vocabulary growth curve, while the gray circles plot the vocabulary that this simulated speaker has in common with the 19 other speakers in the simulation. C: Lower left: the same simulated
learner’s score on the vocabulary measure over time (because language exposure rates vary dramatically
across individuals [Hart & Risley, 1995], age is expressed in these plots as a function of the size of the sample an individual has experienced, rather than time). D: Lower right: error (actual vocabulary – predicted
vocabulary) as a function of age.

with age, such that the heterogeneity of the vocabularies in the simulation increased over
Consistent with this observation, one of the highly educated reviewers of this article
noted that he had never encountered the word lemmata prior to reading it here. Given that
we can safely assume that the reviewer knows many technical terms that we have not
encountered, this may help illustrate why knowing that someone has one very low-frequency word—such as lemmata—in his or her vocabulary is of little to no benefit when
it comes to predicting whether the person knows another very low-frequency word. It
might also, in turn, help illustrate why it is inevitable that any word anyone might reasonably consider including in a “general” vocabulary test will tend to have a fairly high frequency relative to the overall vocabulary of the language, namely because the whole