Language and Mathematics: An evolutionary model of grammatical communication

Author: Komarova, Natalia
Almanac: History & Mathematics: Analyzing and Modeling Global Development

History and mathematics are often thought to belong to different realms. His-tory is not easily expressed in equations. There are no proofs there, and when it comes to interactions among thinking individuals, things are less than straight-forward. There are however ways in which history can be quantified, and also ways in which mathematical methodology can be applied to describe these quantities. The subject of this article is the natural history of human language, the main mode of communication among thinking individuals, which is proba-bly responsible for much of the rest of the history of humans.

The study of language and grammar dates back to classical India and Greece. In the 18th century, the "discovery'' of Indo-European led to the sur-prising realization that very different languages can be related to each other, which initiated the field of historical linguistics. Formal language theory emerged only in the 20th century (Chomsky 1956, 1957, Harrison 1978): the main goals are to describe the rules that a speaker uses to generate linguistic forms (descriptive adequacy) and to explain how language competence emerges in the human brain (explanatory adequacy). These efforts were supported by advances in the mathematical and computational analysis of the process of lan-guage acquisition, a field that became known as learning theory. Currently there are increasing attempts to bring linguistic inquiry in contact with various disciplines of biology, including neurobiology (Deacon 1996, Vargha-Khadem et al. 1998), animal behavior (Dunbar 1996, Hauser 1996, Fitch 2000), evolu-tion (Lieberman 1984, 1991, Pinker and Bloom 1990, Bickerton 1990, Hawkins and Gell-Mann 1992, Batali 1994, Maynard Smith and Szathmary 1995, Aitchinson 1996, Hurford at al. 1998, Jackendoff 1999, Knight et al 2000) and genetics (Gopnik and Crago 1991, Lai et al. 2001). The new aim is to study language as a product of evolution and as the extended phenotype of a species of primates.