Complexity and universality in the long-range order of words

Abstract: As is the case of many signals produced by complex systems, language presents a statistical structure that is balanced between order and disorder. Here we review and extend recent results from quantitative characterisations of the degree of order in linguistic sequences that give insights into two relevant aspects of language: the presence of statistical universals in word ordering, and the link between semantic information and the statistical linguistic structure. We first analyse a measure of relative entropy that assesses how much the ordering of words contributes to the overall statistical structure of language. This measure presents an almost constant value close to 3.5 bits/word across several linguistic families. Then, we show that a direct application of information theory leads to an entropy measure that can quantify and extract semantic structures from linguistic samples, even without prior knowledge of the underlying language.