Abstract
The previous chapters in Part IV mainly considered the relation between the statistical universals and elements of language. This chapter instead considers the relation between long memory and the structure of sentences. Part III explained the long memory underlying language, which is characterized by clustering phenomena among linguistic events, such that words occur in a clustered manner. Such clustering phenomena have been reported in many complex systems, and their appearance in language is intuitively comprehensible as being caused by shifts in context.
The original version of this chapter was revised. The correction to this chapter is available at https://doi.org/10.1007/978-3-030-59377-3_23
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Change history
29 November 2022
The original version of the chapter “Language as a Complex System” was previously published without updating missing reference in footnote 4, page 22. This change has now been included and the chapter and the book have been updated with the change.
Notes
- 1.
Symbols such as S and VP appearing in the typewriter font indicate the inner nodes of the tree and represent grammatical elements such as a sentence (S) and verb phrase (VP). The linguistic meanings of each symbol are not necessary to explain the main point of this chapter.
- 2.
The “S” of basic word order and “S” of CFG use the same symbol (with different fonts), but they are different. The former signifies the subject, whereas the latter signifies a sentence.
- 3.
There is a fundamental relation between a context-free grammar and a dependency grammar, via the notion of head explained in the main text. A sentence structure description by the former framework, however, has more information than that by the latter. A context-free grammar can almost be transformed into a dependency grammar (Buchholz, 2002), but the reverse is difficult (Kong et al., 2015; Fernández-González and Martins, 2015) because of the lack of grammatical information for the inner nodes of the tree. The latter grammar has the advantage of simplicity, and numerous treebanks have been constructed accordingly; the CoNLL database is a representative example.
- 4.
Note that ∗ at the beginning of a linguistic example indicates that it is grammatically incorrect.
- 5.
The field of linguistics thoroughly studies such regularities and irregularities of word order, as in the database presented in Haspelmath et al. (2005), called the World Atlas of Language Structures (WALS).
- 6.
The original article (Lin and Tegmark, 2017) showed that \(k \propto \log \phi \), where ϕ is the second largest eigenvalue of a probabilistic transition matrix M that generates the sequence, as such a matrix’s largest eigenvalue is 1.
- 7.
ε = 0.00565, with a few negative values at large s > 500.
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Tanaka-Ishii, K. (2021). Grammatical Structure and Long Memory. In: Statistical Universals of Language. Mathematics in Mind. Springer, Cham. https://doi.org/10.1007/978-3-030-59377-3_14
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