The Placement of the Head that Minimizes Online Memory

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.

Crosslinguistic word order variation reflects evolutionary pressures of dependency and information locality

“…Among the previous efficiency-based proposals, the one most closely related to our study, ref. 14 , agrees with our proposal that SVO is favored by DL but proposes that SOV is favored by a pressure toward predictability of the final verb. Despite the seeming similarity to our theoretical proposal, there are several key differences.…”

Crosslinguistic word order variation reflects evolutionary pressures of dependency and information locality

“…Among the previous efficiency-based proposals, the one most closely related to our study, ref. 14 , agrees with our proposal that SVO is favored by DL but proposes that SOV is favored by a pressure toward predictability of the final verb. Despite the seeming similarity to our theoretical proposal, there are several key differences.…”

Word Order Variation is Partially Constrained by Syntactic Complexity

“…To some extent this finding might be driven by the overrepresentation of European languages in the sample although our models condition of areal and family relations. To the extent it holds, such a preference is consistent with DLM observations: when there are two simultaneous dependents (S and O) of the same head (V), the total DL is minimal when they occur on either side of the head (Ferrer‐i Cancho, 2008 , 2015 ). However, DLM observations elsewhere furthermore suggest that long dependents should be more constrained than short dependents.…”

Bounds of the sum of edge lengths in linear arrangements of trees

“…The previous lemma generalizes a previous result on D star max , that is achieved when the hub of the star is located at one of the ends of the linear arrangement [37] (figure 7 (a)). In a star tree t, D t is determined by the sum of edge lengths of the hub vertex.…”

Crosslinguistic word order variation reflects evolutionary pressures of dependency and information locality

“…Among the previous efficiency-based proposals, the one most closely related to our study, ref. 14 , agrees with our proposal that SVO is favored by DL but proposes that SOV is favored by a pressure toward predictability of the final verb. Despite the seeming similarity to our theoretical proposal, there are several key differences.…”

Word Order Variation is Partially Constrained by Syntactic Complexity

“…To some extent this finding might be driven by the overrepresentation of European languages in the sample although our models condition of areal and family relations. To the extent it holds, such a preference is consistent with DLM observations: when there are two simultaneous dependents (S and O) of the same head (V), the total DL is minimal when they occur on either side of the head (Ferrer‐i Cancho, 2008 , 2015 ). However, DLM observations elsewhere furthermore suggest that long dependents should be more constrained than short dependents.…”

Bounds of the sum of edge lengths in linear arrangements of trees

“…The previous lemma generalizes a previous result on D star max , that is achieved when the hub of the star is located at one of the ends of the linear arrangement [37] (figure 7 (a)). In a star tree t, D t is determined by the sum of edge lengths of the hub vertex.…”

Crosslinguistic word order variation reflects evolutionary pressures of dependency and information locality

“…Among the previous efficiency-based proposals, the one most closely related to our study, ref. 14 , agrees with our proposal that SVO is favored by DL but proposes that SOV is favored by a pressure toward predictability of the final verb. Despite the seeming similarity to our theoretical proposal, there are several key differences.…”

Word Order Variation is Partially Constrained by Syntactic Complexity

“…To some extent this finding might be driven by the overrepresentation of European languages in the sample although our models condition of areal and family relations. To the extent it holds, such a preference is consistent with DLM observations: when there are two simultaneous dependents (S and O) of the same head (V), the total DL is minimal when they occur on either side of the head (Ferrer‐i Cancho, 2008 , 2015 ). However, DLM observations elsewhere furthermore suggest that long dependents should be more constrained than short dependents.…”

Bounds of the sum of edge lengths in linear arrangements of trees

“…The previous lemma generalizes a previous result on D star max , that is achieved when the hub of the star is located at one of the ends of the linear arrangement [37] (figure 7 (a)). In a star tree t, D t is determined by the sum of edge lengths of the hub vertex.…”