Some remarks on organization and structure

Abstract

Self-organizing systems are defined as able to change their structure, according to need, within specific equivalence classes. Once hierarchical levels and their value functions are assigned, requirements of invariance under transformations within an equivalence class can be used as a principle to determine the population of each level. This program is carried out in complete detail, as an example, for a particular class of systems (called “modular”), for which it is shown that a full Thermodynamics can be constructed. Modular systems are compared with linguistic, monetary, and military organizations; they are found to describe exactly the empirical data available on monetary circulation over the world, and to offer other perhaps suggestive indications. The emerging picture is that of a development, for any such system, which alternates phases of evolution (changes of level occupation numbers) with phases of revolution (changes of level structure within the given equivalence class).