Complexity and Its Relation to Variation

Abstract

This paper is concerned with the relationship between complexity and variation. The main goal is to lay out the conceptual foundations and to develop and systematize reasonable hypotheses such as to set out concrete research questions for future investigations. I first compare how complexity and variation have synchronically been studied and what kinds of questions have been asked in those studies. Departing from earlier surveys of different definitions of complexity, here I classify the majority of complexity studies into two broad types based on two ways of defining this concept. The first type determines and measures linguistic complexity by counting numbers of items (e.g., linguistic forms or rules and interactions between forms). The second type makes use of transparency and the principle of One-Meaning–One-Form. In addition, linguistic complexity has been defined by means of concepts from information theory, namely in terms of description length or information content, but those studies are in the minority. Then I define linguistic variation as a situation when two or more linguistic forms have identical or largely identical meaning and it is possible to use either the one or the other variant. Variation can be free or linguistically or socially conditioned. I argue that there is an implicational relationship between complexity of the first type that is defined in terms of numbers of items and variation. Variation is a type of complexity because it implies the existence of more than one linguistic form per meaning. But not every type of complexity involves variation because complexity defined on the basis of transparency does not necessarily imply the existence of more than one form. In the following I discuss extralinguistic factors that (possibly) have an impact on socially conditioned variation and/or complexity and can lead to an increase or decrease of complexity and/or variation. I conclude with suggestions of how to further examine the relationship between complexity and variation.

Utility of Kolmogorov complexity measures: Analysis of L2 groups and L1 backgrounds

“…In contrast to typical complexity metrics, information-theoretic-based complexity metrics are non-language-specific and relatively less subjective. In the information theory literature, complexity is typically quantified and measured in terms of description length and/or predictability using two measurements: Shannon entropy and Kolmogorov complexity [38,50,61,62]. Relevant to this study is Kolmogorov complexity, which approximates how much information a specific text holds by measuring the length of the shortest possible description of this text [40].…”