Issue
Europhys. Lett.
Volume 76, Number 6, December 2006
Page(s) 1228 - 1234
Section Interdisciplinary physics and related areas of science and technology
DOI http://dx.doi.org/10.1209/epl/i2006-10406-0
Published online 29 November 2006
Europhys. Lett., 76 (6), pp. 1228-1234 (2006)
DOI: 10.1209/epl/i2006-10406-0

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

Abstract
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.

On the other hand, that distance is considered a measure of the cost of syntactic relationships in various frameworks. By cost, we mean the amount of computational resources needed by the brain. The absence of crossings in syntactic trees may be universal just because all human brains have limited resources.

PACS
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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