  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.
