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Closure, open systems, and the modeling imperative

Alvarez De Lorenzana JM1

  • 1Institute of International Relations, University of British Columbia, Canada. alvarez@interchange.ubc.ca

Annals of the New York Academy of Sciences
|May 20, 2000
PubMed
Summary

Natural systems grow through cycles of openness and closure. This fundamental tension drives development, creating hierarchies via transitive and algebraic closure mechanisms for spatial and temporal organization.

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Area of Science:

  • Systems theory
  • Theoretical biology
  • Cybernetics

Background:

  • Natural systems are inherently open to their environment.
  • System development necessitates a degree of closure for structural integrity.
  • The interplay between openness and closure is a primary driver of system evolution.

Purpose of the Study:

  • To elucidate the fundamental tension between openness and closure in natural systems.
  • To identify the mechanisms by which systems maintain closure during expansion.
  • To provide a formal representation of system development driven by cycles of openness and closure.

Main Methods:

  • Conceptual analysis of system dynamics.
  • Formalization of closure principles in system expansion.
  • Distinction between intra-level (transitive) and inter-level (algebraic) closure.

Main Results:

  • System organization emerges from cyclical processes of openness and closure.
  • Transitive closure facilitates additive space closure within a system level.
  • Algebraic closure enables multiplicative topological or time closure between system levels.

Conclusions:

  • The conjunction of transitive and algebraic closure generates hierarchical system structures.
  • Semantic closure exists prior to and external to the system itself.
  • Understanding these closure dynamics is key to comprehending natural system organization and development.

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