  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. Through empirical measurements across
grammatically annotated data, the Strahler number of natural language sentences
is shown to be almost 3 or 4, similarly to the case of river bifurcation as
reported by Strahler (1957). From the theory behind the number, we show that it
is one kind of lower limit on the amount of memory required to process
sentences. We consider the Strahler number to provide reasoning that explains
reports showing that the number of required memory areas to process sentences
is 3 to 4 for parsing (Schuler et al., 2010), and reports indicating a
psychological "magical number" of 3 to 5 (Cowan, 2001). An analytical and
empirical analysis shows that the Strahler number is not constant but grows
logarithmically; therefore, the Strahler number of sentences derives from the
range of sentence lengths. Furthermore, the Strahler number is not different
for random trees, which could suggest that its origin is not specific to
natural language.
