The Trade-Off Between Mean Dependency Distance and Mean Hierarchical Distance in Contemporary Written Japanese: An Analysis Based on Dependency Structure Matrix

To explore, mathematically, how mean dependency distance (MDD) and mean hierarchical distance (MHD) interact to create a trade-off relationship based on the inherent two-dimensional structure of language, this study introduces ‘Dependency Structure Matrix’ into quantitative syntax analysis, proposes ‘Minimal Change Matrix Pair’, and determines the theoretical and empirical method of adding a node that maximizes the growth rate (GR) of MDD and MHD in contemporary written Japanese, respectively. We found that the direct cause of the discrepancies between the theoretical and empirical maximum of MDD GR and MHD GR lies in the interaction between DD and HD of turning-point nodes that should lie on the diagonal of the smaller matrix and nodes that exceed the threshold of predicate valency and move to deeper layers, through which the trade-off between MDD and MHD is maintained. This interaction is numerically reflected in the fact that increases in HD tend to slow down MDD’s growth, and vice versa. The underlying cause of such discrepancies is assumed to be that Japanese native speakers cannot tolerate increased cognitive load in either the linear or hierarchical dimension alone, and therefore tend to alleviate the cognitive burden in one dimension by increasing syntactic complexity in the other.