提出量化语言与手势顺序优化程度的新方法，揭示跨语言手势高效排序的数学原理。
How to measure the optimality of word or gesture order with respect to the principle of swap distance minimization
- 基于排列多面体和相邻交换距离构建评估框架
- 发现跨语言手势排序至少77%符合最优交换距离原则
- 将二次分配问题引入语言研究，统一多种语言优化机制
所有序列排列的结构可表示为排列多面体，其顶点为排列，两点相连当且仅当其中一个排列通过相邻元素交换得到另一个。已有假说认为语言中的词序倾向于最小化排列多面体中的交换距离：给定源顺序，交换距离越近的词序越省力且更可能被使用。本文阐明如何衡量词序或手势顺序相对于交换距离最小化的优化程度。通过新提出的数学框架，我们证明跨语言手势至少有77%的优化率，这一结果极不可能由随机偶然造成。本研究建立语言与手势顺序优化的理论基础，并首次将二次分配问题（QAP）引入语言学，作为多种优化问题的统一体，进而提出一个普遍的最优分配原则，涵盖交换距离最小化等各类语言学优化机制。
原文摘要 · Abstract (English)
The structure of all the permutations of a sequence can be represented as a permutohedron, a graph where vertices are permutations and two vertices are linked if a swap of adjacent elements in the permutation of one of the vertices produces the permutation of the other vertex. It has been hypothesized that word orders in languages minimize the swap distance in the permutohedron: given a source order, word orders that are closer in the permutohedron should be less costly and thus more likely. Here we explain how to measure the degree of optimality of word order variation with respect to swap distance minimization. We illustrate the power of our novel mathematical framework by showing that crosslinguistic gestures are at least $77\%$ optimal. It is unlikely that the multiple times where crosslinguistic gestures hit optimality are due to chance. We establish the theoretical foundations for research on the optimality of word or gesture order with respect to swap distance minimization in communication systems. Finally, we introduce the quadratic assignment problem (QAP) into language research as an umbrella for multiple optimization problems and, accordingly, postulate a general principle of optimal assignment that unifies various linguistic principles including swap distance minimization.
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