Lexigenesis in ancestral south-east Australian Aboriginal language

The 1/x frequency distribution is known to researchers ranging from economists and biologists to electronic engineers. It is known to linguists as Zipf's Law (Zipf, 1949) and has recently been shown not to be a consequence of the Central Limit Theorem (Troll & Graben, 1998)--leaving an "unsolved problem' in information theory (Jones, 1999). This 1/x distribution, associated with scale-invariant physical systems (Machlup & Hoshiko, 1980), is a special case of the general power law x^λ arising from the Lagrangian L(x,Fdot](x)) = ½x^1-λFdot]² and, as λ need not be an integer, some related research understandably involves fractals (Allison et al. , 2001). The present paper generalizes this Lagrangian to include a van der Waals effect. It is argued that ancestral Aboriginal language consisted of root-morphemes that were built up into, and often condensed within, subsequent words or lexemes. Using discrete-optimization techniques pioneered elsewhere (Illert, 1987; Reverberi, 1985), and the new morpho-statistics, this paper models lexeme-condensation in ancestral south-east Australian Aboriginal language.