| This text is submitted as a thesis by publications. It consists of four articles already published in the Journal of Applied Statistics, making up sequences of an argument, preceded by an Over-arching statement. The thesis applies mathematical concepts and reasoning to aspects of Aboriginal languages and in this way throws new light on some problems that have hitherto proved intractable for Aboriginal linguists. Mathematical forms of analysis have not previously been much used in mainstream linguistics in general, or applied to Aboriginal languages, with the major exception of the work of George Zipf (1949), whose application of Power Laws to language phenomena has influenced researchers in many other fields while being ignored in Zipf's own home discipline of Linguistics. The thesis uses Power Laws allied to other mathematical ideas and operations, including Lagrange forms, van der Waals effects, Huygens principle and Snell's law, to illuminate basic aspects of Aboriginal languages. Mathematical methods can provide new ways of treating data and drawing conclusions, and produce a revolutionary new picture of the original forms of the early language. They can be used to trace major processes of change over the 60,000-70,000 years currently estimated as the time Australian Aboriginal people have lived in Australia. This thesis shows how mathematical analysis can be a powerful tool and resource for linguistics. It is able to reconstruct a proto-form of Aboriginal language from a much greater time-depth than linguists have believed is possible for any language. This takes the scientific study of language closer to the probable time when human language itself first emerged. |
