Statics and dynamics of hierarchy

The purpose of this paper is to describe how ordered pairs representing related objects in static state are used to create hierarchical structures yielding rapidly increasing choices of complex objects to be selected by objects in their environment and how “purposive systems” evolve for the production of such structures.

Basic notions transcending discipline boundaries and natural language formalised into one‐ and two‐place sentences are suggested as related constituents of complexity and hierarchy, the “systemic view”. This leads into sets of ordered pairs and sequences of qualified predicate logic statements forming dynamics of systems.

Hierarchies in general can be expressed as ordered pairs. An analytical method for showing how ordered pairs are organised into progressively more complex structures of objects and “products” with increased chances of being selected by environmental objects in evolution or design. Correspondingly, groups of purposive systems operating according to algorithms are needed for the production of products or their evolution is left to chance.

The approach uses natural language as the primary model transformed into a formal language for reasoning about outcomes of scenarios with inanimate and animate components with predominantly qualitative properties, emotions and will. The desirability of such an approach, although it matches the generality of the systemic view, needs to be debated.

Once past the test of acceptability and software development, the approach can be used as part of “design methodology” for the design of “systems and products” in the context of human activity and technical scenarios.

The formal language exhibits properties, relations and interactions or impressions of objects of great diversity and variety. It exhibits the effects of these constituents on the production of outcomes based on semantic and mathematical relationships; it is widely applicable and may facilitate the appreciation of how “related objects evolve”.