Implementing Permutations in the Brain and SVO Frequencies of Languages

The subject-verb-object (SVO) word order prevalent in English is shared by about $42\%$ of world languages. Another $45\%$ of all languages follow the SOV order, $9\%$ the VSO order, and fewer languages use the three remaining permutations. None of the many extant explanations of this phenomenon take into account the difficulty of implementing these permutations in the brain. We propose a plausible model of sentence generation inspired by the recently proposed Assembly Calculus framework of brain function. Our model results in a natural explanation of the uneven frequencies. Estimating the parameters of this model yields predictions of the relative difficulty of dis-inhibiting one brain area from another. Our model is based on the standard syntax tree, a simple binary tree with three leaves. Each leaf corresponds to one of the three parts of a basic sentence. The leaves can be activated through lock and unlock operations and the sequence of activation of the leaves implements a specific word order. More generally, we also formulate and algorithmically solve the problems of implementing a permutation of the leaves of any binary tree, and of selecting the permutation that is easiest to implement on a given binary tree.