Synchronic and diachronic hierarchies of living systems

Abstract

Living systems (entities) possess the property of maintaining their organization by continual renewal or production of components by themselves. Based on this self-maintenance ability, they reproduce systems of similar organization. This two-fold property forms unique hierarchical organizations, foreign to physical systems. This paper explores how the living world is organized by the two-fold property, where two types of hierarchical organizations, or part-whole relationships, are distinguished: one is synchronic participation in organizing an entity; the other is diachronic. The former implies that the composition of an entity is fixed through time, regardless of organizational patterns, while the latter involves changes in composition to maintain a pattern. Both types of organization are mathematically formalized, and organizational hierarchies of the living world are analyzed in biological space-time. This analysis reveals that biological systems are arrayed in a complex two-dimensional hierarchical matrix of synchronic and diachronic organization.