Structures, Systems, Hierarchies

Hierarchical approach naturally continues the historical line of understanding complexity. The end of the XIX century has put forward structuralism, the second half of the XX century has been dominated by systemic research - now I am trying to preview the synthesis of structurology and systemology, the hierarchical approach.

The idea of hierarchical approach is conveyed by its very name. Any object (and anything at all) is treated as at different levels, and the relations between these levels are of a kind other than the relations inside a level.

Of course, multilevel consideration has long since penetrated both structural and systemic studies. Still, the focus has always been elsewhere, so that it was hierarchical structures and hierarchical systems that were considered, rather than hierarchies themselves. The typical problem with such an attitude was that nobody could say where the multiple levels came from, and therefore hierarchies had to be postulated, thus becoming rigid abstractions never subject to development.

Things become much more logical if one suggests that a hierarchy is something different from a system or a structure, and that its levels represent the history of development. In this sense, one can speak of hierarchical structures as imprints of the object's development on its internal organization, while hierarachical systems reflect the dependence of an object's functionality on its natural history.

Thus one obtains a clear criterion for distinguishing structures, systems and hierarchies, or rather structural, systemic and hierarchical aspects in the same thing.

1. Structure refers to the inner complexity of an object. The object consists of a number of elements, with some relations between them; when one element of the structure is immediately related to another, it is said that there is a link between them. If an element has relations with two other elements, these latter become related via this common element; thus an element of the structure may mediate the links between other elements. Such mediated (or indirect) links can be rather complex, with numerous intermediate elements and multiple alternative mediations. The collection of all direct and indirect relations between any two elements in the structure is called their connection in that structure.

2. System describes the external (apparent) complexity of an object, that is, the complexity of its "behaviour". In general, a system would input some information about its environment, and produce some output, depending on the system's state, which comprises both internal and external factors that do not belong to either input or output channels. In other words, system is the way of transforming one structure (input) into another (output), the mechanism of this transformation being defined by the structure of the system.

3. Hierarchy shows how the external of an object transforms into its internal, and vice versa; therefore, hierarchy concerns the object's integrity. The key to such transformations lies in reflexivity, that is, the interaction of the object with itself via its environment. Thus, the output of a system may change its environment, which may affect the input, and so on; this is the common feed-back scheme. However, the parts of the environment that provide such feed-back can become a part of the original system - then it will have at least two levels, one of which will correspond to the "pure" functioning, while the other will include "self-regulation". One obtains a hierarchical system. Similarly, reflexive links make a structure hierarchical.

The structural aspects of a thing provide its "static" picture, while its systemic aspects bring in the idea of "dynamics". Systemic dynamics is an inverse of the system's structure, and systemic description is complementary to structural description. This leads to the relativity of the distinction, so that structural aspects may become functional in a different context, and inversely, systemic features can be treated structurally. Such transformations are well known in physics, where time coordinate is like spatial coordinates in any respect.

However, time coordinate does not fully represent time, and it is only in the hierarchical approach that historical time can be understood as different from mere systemic dynamics. Developmental study synthesizes both static and dynamic views, regarding a thing that changes, while being the very same thing.