Why do syntactic links not cross?R. Ferrer i Cancho
Departament de Física Fonamental, Universitat de Barcelona Martí i Franquès 1, 08028 Barcelona, Spain
received 20 July 2006; accepted in final form 31 October 2006
published online 29 November 2006
Here we study the arrangement of vertices of trees in a 1-dimensional Euclidean space when the Euclidean distance between linked vertices is minimized. We conclude that links are unlikely to cross when drawn over the vertex sequence. This finding suggests that the uncommonness of crossings in the trees specifying the syntactic structure of sentences could be a side-effect of minimizing the Euclidean distance between syntactically related words. As far as we know, nobody has provided a successful explanation of such a surprisingly universal feature of languages that was discovered in the 60s of the past century by Hays and Lecerf. On the one hand, support for the role of distance minimization in avoiding edge crossings comes from statistical studies showing that the Euclidean distance between syntactically linked words of real sentences is minimized or constrained to a small value.
89.75.Hc - Networks and genealogical trees.
87.53.Wz - Monte Carlo applications.
89.90.+n - Other topics in areas of applied and interdisciplinary physics.
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