Several people have asked me about Alexander M. Petersen et al., "Languages cool as they expand: Allometric scaling and the decreasing need for new words", Nature Scientific Reports 12/10/2012. The abstract (emphasis added):
We analyze the occurrence frequencies of over 15 million words recorded in millions of books published during the past two centuries in seven different languages. For all languages and chronological subsets of the data we confirm that two scaling regimes characterize the word frequency distributions, with only the more common words obeying the classic Zipf law. Using corpora of unprecedented size, we test the allometric scaling relation between the corpus size and the vocabulary size of growing languages to demonstrate a decreasing marginal need for new words, a feature that is likely related to the underlying correlations between words. We calculate the annual growth fluctuations of word use which has a decreasing trend as the corpus size increases, indicating a slowdown in linguistic evolution following language expansion. This “cooling pattern” forms the basis of a third statistical regularity, which unlike the Zipf and the Heaps law, is dynamical in nature.
The paper is thought-provoking, and the conclusions definitely merit further exploration. But I feel that the paper as published is guilty of false advertising. As the emphasized material in the abstract indicates, the paper claims to be about the frequency distributions of words in the vocabulary of English and other natural languages. In fact, I'm afraid, it's actually about the frequency distributions of strings in Google's 2009 OCR of printed books — and this, alas, is not the same thing at all.
It's possible that the paper's conclusions also hold for the distributions of words in English and other languages, but it's far from clear that this is true. At a minimum, the paper's quantitative results clearly will not hold for anything that a linguist, lexicographer, or psychologist would want to call "words". Whether the qualitative results hold or not remains to be seen.
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