  The structure of a sentence can be represented as a network where vertices
are words and edges indicate syntactic dependencies. Interestingly, crossing
syntactic dependencies have been observed to be infrequent in human languages.
This leads to the question of whether the scarcity of crossings in languages
arises from an independent and specific constraint on crossings. We provide
statistical evidence suggesting that this is not the case, as the proportion of
dependency crossings of sentences from a wide range of languages can be
accurately estimated by a simple predictor based on a null hypothesis on the
local probability that two dependencies cross given their lengths. The relative
error of this predictor never exceeds 5% on average, whereas the error of a
baseline predictor assuming a random ordering of the words of a sentence is at
least 6 times greater. Our results suggest that the low frequency of crossings
in natural languages is neither originated by hidden knowledge of language nor
by the undesirability of crossings per se, but as a mere side effect of the
principle of dependency length minimization.
