Demiarcs, creaons and genons

Abstract

Useful insights into the representation of natural systems can be gained by decomposing directed graphs (digraphs) into elementary components. Arcs of digraphs can be split into male demiarcs (outarcs) which leave vertices and female demiarcs (inarcs) which enter demiarcs. Likewise, a vertex can be split into an input perceiving side called the creaon and an output generating side called the genon. Digraphs can be regarded as being hierarchically organized because each vertex in a level-l digraph can be expanded into a level-2 digraph. In general, each vertex of a level-i digraph can be expanded into a level-(i+l) digraph. Arcs of a level-i digraph can be regarded as bundles of level-(i + 1) arcs which are split at the vertex boundary. These elementary graphical components are shown to be useful for depicting input-output systems such as organisms, ecosystems and societies.

Holons, creaons, genons, environs, in hierarchy theory: Where we have gone

“…Rosen was explicit as to putting organisms into physics as analogies, and that is what Patten and Auble suggest. So too are Bosserman and Harary (1981) when, in our Fig. 2 below, they move up to put the organism in its context.…”

“…They have stepped their way through the mine-field of the change in level. In Bosserman and Harary (1981) we see a touch of mystery in their use Patten and Auble's scheme. They use the Taoist symbol for ying and yang, indicating male and female duality for input versus output (Fig.2).…”

“…While there are applications of both to physical systems, the most important applications of network and hierarchy theory are in biological schema. Patten and Auble (1980) and Bosserman and Harary (1981) both investigate how biology is different from physics. When we look at Patten and Auble (1980) developing a network for the California Thrasher in its ecosystem, they were anticipating Rosen (2000).…”