The Strahler number was originally proposed to characterize the complexity of river bifurcation and has found various applications. This article proposes computation of the Strahler number's upper and lower limits for natural language sentence tree structures, which are available in a large dataset allowing for statistical mechanics analysis. Through empirical measurements across grammatically annotated data, the Strahler number of natural language sentences is shown to be almost always 3 or 4, similar to the case of river bifurcation as reported by Strahler (1957) and Horton (1945). From the theory behind the number, we show that it is the lower limit of the amount of memory required to process sentences under a particular model. A mathematical analysis of random trees provides a further conjecture on the nature of the Strahler number, revealing that it is not a constant but grows logarithmically. This finding uncovers the statistical basics behind the Strahler number as a characteristic of a general tree structure target.

翻译：Strahler数最初提出用于刻画河流分叉的复杂度，并已得到多种应用。本文提出利用大规模数据集中可用的自然语言句子树结构，计算Strahler数的上下限，从而进行统计力学分析。通过对语法标注数据的实证测量，自然语言句子的Strahler数几乎总是3或4，这与Strahler（1957）和Horton（1945）报告的河流分叉情况相似。从该数的理论出发，我们证明其在特定模型下是处理句子所需内存量的下限。对随机树的数学分析进一步提出了关于Strahler数性质的猜想，揭示其并非恒定常数，而是呈对数增长。这一发现揭示了Strahler数作为一般树结构目标特征的统计基础。