The placement of the head that minimizes online memory: a complex systems approach

Abstract

It is well known that the length of a syntactic dependency determines its online memory cost. Thus, the problem of the placement of a head and its dependents (complements or modifiers) that minimizes online memory is equivalent to the problem of the minimum linear arrangement of a star tree. However, how that length is translated into cognitive cost is not known. This study shows that the online memory cost is minimized when the head is placed at the center, regardless of the function that transforms length into cost, provided only that this function is strictly monotonically increasing. Online memory defines a quasi-convex adaptive landscape with a single central minimum if the number of elements is odd and two central minima if that number is even. We discuss various aspects of the dynamics of word order of subject (S), verb (V) and object (O) from a complex systems perspective and suggest that word orders tend to evolve by swapping adjacent constituents from an initial or early SOV configuration that is attracted towards a central word order by online memory minimization. We also suggest that the stability of SVO is due to at least two factors, the quasi-convex shape of the adaptive landscape in the online memory dimension and online memory adaptations that avoid regression to SOV. Although OVS is also optimal for placing the verb at the center, its low frequency is explained by its long distance to the seminal SOV in the permutation space.

Minor changes (language improved; typos in Eqs. 5, 6 and 13 corrected)

References in corpus (4)

• Networks in Cognitive Science
• The risks of mixing dependency lengths from sequences of different length
• The failure of the law of brevity in two New World primates. Statistical caveats
• Hubiness, length, crossings and their relationships in dependency trees

Cited by in corpus (11)

• Optimal coding and the origins of Zipfian laws
• The scarcity of crossing dependencies: a direct outcome of a specific constraint?
• Non-crossing dependencies: least effort, not grammar
• Crossings as a side effect of dependency lengths
• The scaling of the minimum sum of edge lengths in uniformly random trees
• The sum of edge lengths in random linear arrangements
• Towards a theory of word order. Comment on "Dependency distance: a new perspective on syntactic patterns in natural language" by Haitao Liu et al
• Bounds of the sum of edge lengths in linear arrangements of trees
• Swap distance minimization in SOV languages. Cognitive and mathematical foundations
• The optimal placement of the head in the noun phrase. The case of demonstrative, numeral, adjective and noun
• The Maximum Linear Arrangement Problem for trees under projectivity and planarity