Liu, Yu; Di, Zengru; Gerlee, Philip
The notion of information and complexity are important concepts in many scientific fields such as molecular biology, evolutionary theory, and exobiology. Most measures of these quantities, such as Shannon entropy and related complexity measures, are only defined for objects drawn from a statistical ensemble and cannot be computed for single objects. Based on assembly theory, we attempt to fill this gap by introducing the notion of a ladderpath which describes how an object can be decomposed into a hierarchical structure using repetitive elements. From the ladderpath two measures naturally emerge: the ladderpath-index and the order-index, which represent two axes of complexity. We show how the ladderpath approach can be applied to both strings and spatial patterns and argue that all systems that undergo evolution can be described as ladderpaths. Further, we discuss possible applications to human language and the origins of life. The ladderpath approach provides a novel characterization of the information that is contained in a single object (or a system) and could aid in our understanding of evolving systems and the origin of life in particular.