Different Types of Complexity

McShea identifies a number of methodological problems with many previous studies of complexity increase, and remarks that ``specifying an operational metric remains a difficult problem'' [McShea 91] (p.318). In a later paper, he provides a useful analysis of the concept of complexity, and suggests that it can be broken down into a number of independent measures [McShea 96]. McShea's hope is that these measures are both operational (they can unambiguously be measured in real systems) and universal (they can be applied to all systems).

The definitions that McShea proposes are based upon two dichotomies: object versus process, and hierarchical versus nonhierarchical structure. These dichotomies yield four different types of complexity: (1) Nonhierarchical object complexity; (2) nonhierarchical process complexity; (3) hierarchical object complexity; and (4) hierarchical process complexity.^2.22 These different types are illustrated in Figure 2.1. In the context of his work on metazoan complexity, object complexity refers to morphological complexity, and process complexity to developmental complexity. McShea discusses various measures and proxies for obtaining these data from fossils. By taking this narrower, more specific view of complexity, a much needed degree of objectivity can be introduced. As a final remark on the notion of overall complexity, McShea says ``Is a human more complex than a trilobite overall? The question seems unanswerable in principle because the types of complexity are conceptually independent ... Thus, it is hard to imagine how a useful notion of overall complexity could be devised'' [McShea 96] (p.480).

   

Figure 2.1: Different Types of Complexity. (A, B) Nonhierarchical complexity: A has greater nonhierarchical object complexity than B (it has more different parts); B has greater nonhierarchical process complexity than A. (C, D) Hierarchical complexity: C has a degree of hierarchical object complexity, D has a degree of hierarchical process complexity. Adapted from [McShea 96].