﻿ Hierarchies: Structures and Systems
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## Structures, Systems, Hierarchies

 The reason has always been seeking for integrity. For a primitive mind, there are only infinitely diverse situations requiring some adaptive reaction. A wiser person will also distinguish the classes of similar situations, as determined by the similarity of reactive activities. Thus the world's diversity is comprehended as a manifestation of its integrity. Here, I am not going to consider the hierarchy of integrity in general. It is enough to say that, on a certain level of integrity, we consider the possible ways of joining isolated entities (elements) into a whole, and there are three complementary and mutually opposite possibilities, which we denote as structure, system and hierarchy. Of course, real things can never present a pure case of a particular type of organization; rather, one will speak about the structural, systemic and hierarchical aspects of the same thing. 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, we could say that there this element is linked to that. When an element is related to two other elements, these latter become related via their common relation; 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. Since the inner distinctions are determined by the quality of the object, structural description is essentially static. System is the way to describe the outer (apparent) complexity of an object; we often speak about the object's "behavior", or, rather, "functioning". In general, a system would input something from its environment, and produce some output, depending on the system's state, which comprises both internal and external factors that do not belong to the 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 determined by the structure of the system (comprising both inner structure and the structure of the system's environment). The systemic description of an object is dynamic, since the sequences of its reactions to various external influences are of interest. Different systems can be "wired" to each other, becoming the components of a wider system. Hierarchy assumes the transformation of the external aspects of the object into its inner complexity, and conversely, the inner organization becoming an explicit distinction. Reflexivity (or self-reflection) is the key to comprehending such transformations. For instance, a system can change its environment so that its input gets affected, as in the common feed-back schemes. However, the portions of the environment that provide such a feed-back can be included in the original system, which thus becomes hierarchical, with one level corresponding to the original "pure" functionality and a higher level introducing a kind of "self-regulation". Similarly, rearranging reflexive links will make a structure hierarchical. Considered as an objective phenomenon, such reorganization of structures and systems is commonly known as development. Though these three levels of organization are qualitatively different, describing the complementary aspects of the whole, they are mutually reflected as well. The structural traits can be reinterpreted in the functional terms, and a system's functioning can, in some respects, be described in the structural terms. For example, in physics, structures are often considered as invariants of the dynamic groups, while time coordinate is treated along with the spatial coordinates, so that dynamics is represented by the geometry of space-time. Similarly, hierarchical order can be modeled in physics introducing various effective quantities (average potentials, self-consistent fields, asymptotic conditions etc.). However, all such models cannot entirely reduce structures to system, or systems to structures, and, of course, hierarchies can only be structurally or systemically represented in a very limited way. In particular, the time coordinate does not represent time in all its respects; one needs the hierarchical approach to comprehend historical time as different from mere systemic dynamics. Developmental study synthesizes both static and dynamic descriptions, considering the same thing as a sequence of its developmental phases reflected in the levels of its hierarchy. From philosophy, we know that any definite thing has three complementary aspects. Primarily, it consists of something, which we call its material. There is nothing in the world that can exist without some material, though, sometimes, it may be quite a nontrivial task to tell what its material exactly is. Still, the material does not yet completely characterize the thing; many different things can be made of the same material, and the way they differ from each other is their form. In particular, the visible shape of the thing is a characteristic of its form. However, the separate consideration of the thing's material and form does not tell us why this particular material has to take this particular form to produce this particular thing. Neither the material, nor the form implies its necessity, its unique place in the world. There is something in the thing that has to do with its being itself, the history of its birth, development and annihilation. A philosopher would call it content, the unity of the material and the form. Structure, system and hierarchy as the levels of organization all pertain to the form of a thing. However, one could observe that the stability of structure is related to the material composition of the thing, while the content of the thing has to do with its development, and hence hierarchy. The important difference of the hierarchical approach from considering mere hierarchical structures and hierarchical systems is that the existence of multiple levels is explained by objective development, while within the structural or systemic approach it can only be postulated, imposed from the outside. As soon as we accept hierarchy to be different from system, or structure, hierarchical structures are readily understood as the imprint of the object's development on its internal organization, while hierarchical systems manifest the dependence of an object's functionality on its natural history.