title: Closure, open systems, and the modeling imperative
abstract: Natural systems cannot be closed to the environment. At the same time there is a necessity for closure in order to build the system. It is this quint-essential tension between openness and closure that drives systems to unfold into further stages or levels of growth and development. In other words, the emergence of organization in natural systems is a result of cycles of openness and closure. There are two distinct and complementary ways by which a system will carry over closure while involved in a process of expansion across the environment. These two ways need to be expressed in any formal representation: (1) within a level this will be by means of transitive closure, which is additive; and (2) between levels (i.e., from one level to the next higher level) this requires algebraic closure, which is multiplicative. The former expresses space closure, whereas the latter expresses topological or time closure. The conjunction of these two closures generates a hierarchy of levels. Prior to, and outside of, the system lies semantic closure.
authors.affiliation: Institute of International Relations, University of British Columbia, Canada. alvarez@interchange.ubc.ca
authors.lastname: Alvarez De Lorenzana JM