Panini’s 5th century BC generative Sanskrit grammar is shown to be sufficient to describe any formal or computational system in oral form, using a new observation regarding Panini’s “auxilary markers” and the methods of Post production systems. Modern universal computation is described using rules modeled on Sanskrit positional number words representing large numbers in versified sutras. Two versions of “Panini arithmetic” are defined to contrast the computational strength of non-positional and positional numeration. The computational increase between additive and multiplicative arithmetic is attributed to the cognitive skills required for the grammaticalization of positional number words. Positional notations are formally described using Presburger arithmetic and results of Fischer-Rabin on bounded multiplication. As a whole the construction shows how mathematical computation is constructed from natural language structure and the cognitive skills needed for language use. The modern origins of generative linguistics and Turing’s universal computation are described in a new historical light, with Indian positional notation providing computational expertise needed for modern logic. The paper will interest Sanskritists, computer scientists and logicians, and cognitive linguists. No knowledge of Panini grammar, Sanskrit or linguistic grammaticalization is assumed. |
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