I've seen Paul Bloom's book, as well as a number of book chapters containing similar arguments. I don't disagree with him at all. I think his points are two-fold. First, there's nothing sudden or stage-like about the vocabulary explosion--rather, it represents smooth, continuous acceleration. This was elegantly demonstrated empirically by Ganger & Brent (2004, Developmental Psychology). Second, the major acceleration may be occurring late. But the [smaller] gains made by children in their second year are particularly noticeable given that they are starting from nothing.
That said, he doesn't offer an explanation for why we see acceleration at all. Moreover, these two points are all perfectly consistent with my model. The model doesn't make strong predictions about when the acceleration occurs. In fact, if you examine its rate of acquisition after the first 50 words (analogous to an 18 m.o.) it's a lot lower than it is after 2000 words (maybe a 3 year old? I'm not sure). What it does show is that acceleration is a guaranteed result in any parallel-learning situation. I think any system in which growth is the integral of a Gaussian distribution of difficulty will actually show faster learning much later than late infancy. I'm certainly not arguing that the acceleration we see at 18 m.o. (and that is apparent in your own numbers) is the top speed of the learning-system.
I think what's important here is that the model offers an explanation for acceleration at all. It simply shows that two commonly held assumptions (parallelism and variation in difficulty), when implemented, can have surprising results. They may be all you need to account for acceleration.
Actually, Bloom does suggest a variety of possible explanations including neurological changes, accumulation of adequate phonological knowledge, increases in memory, increased understanding of kinds and individuals, emergence of theory of mind, increased use of syntax, and exposure to an increasing number of words as children begin to read. Perhaps I'll ask him for his thoughts on McMurray's paper.
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