Languages cool as they expand: Allometric scaling and the decreasing need for new words

Alexander M. Petersen, Joel N. Tenenbaum, Shlomo Havlin, H. Eugene Stanley, Matjaž Perc

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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.

Original languageEnglish
Article number943
Pages (from-to)943
JournalScientific Reports
StatePublished - 2012

Bibliographical note

Funding Information:
AMP acknowledges support from the IMT Lucca Foundation. JT, SH and HES acknowledge support from the DTRA, ONR, the European EPIWORK and LINC projects, and the Israel Science Foundation. MP acknowledges support from the Slovenian Research Agency.


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