To introduce the hierarchical approach, one could try to formulate its basic principles. Of course, this list can hardly be exhaustive; other enumerations would emphasize some other aspects of the same. The very thought of a complete inventory of relevant categories and principles is incompatible with the hierarchical approach. However, any practical application requires some mental framework, and this summary could be as useful as any other to grasp the general idea of hierarchy as an intrinsic mechanism of any development.
The category "a hierarchy" conveys the idea of a self-contained thing that remains the same in all the possible contexts. Though it may differently exhibit itself in different respects, all such special manifestations are intrinsically interconnected, being determined by the same organizational center, the whole of the thing. While interaction with the environment is necessary to define to form of the thing and its motion, the thing's development is initiated by its inner dynamics, albeit externally regulated and shaped.
Each hierarchy manifests a number of distinct levels, with the higher levels dominating over the lower levels in certain sense; this distinction depends on the aspect of hierarchy under consideration. The elements of an upper level may, for instance, represent classes of lower level elements, or some integral characteristics of lower level motion. In any case, the higher levels are "built" on the basis of lower levels, and they cannot exist without them, despite the apparent higher level control over lower level behaviors.
At any instance, each hierarchy interacts with its environment as a hierarchical system, transforming some hierarchically structured input into hierarchically structured output. This assumes some inner hierarchy of the system, which can be formally represented by the hierarchy of the system's states. Hierarchical systems are impossible without a hierarchy of feedback channels, and systemic motion is hierarchically structured by feedback cycles. The distinction between "inner" and "outer" structures hence becomes relative, typically determined by the characteristic times of the cyclic processes.
The relations between any two levels of a hierarchy constitute a specific entity which may be considered as a level of the same hierarchy lying between the two original levels. Therefore, there is no "final" structure in any hierarchy, since one can always find a new level between any two previously discovered. This procedure will be referred to as unfolding the hierarchy.
The collection of intermediate levels between any two levels of hierarchy can be treated as mere mediation of their connection. All the intermediate levels are thus considered as the inner organization of the connection, which does not determine the interrelations of the two selected levels. Folding that mediation, we observe the two levels as adjacent. In this way, the total number of levels in a hierarchical structure or system can decrease, and we arrive to grosser view, which presents a logical inverse of hierarchical unfolding.
Any hierarchy can be folded, and then unfolded in a different way, hence manifesting a hierarchical structure or system quite unlike the original (another position of the hierarchy). Therefore, no hierarchical structure or system should be considered as absolute and rigid; the hierarchy is thus comprehended as the unity of all its possible positions. This multi-faceted nature of any hierarchy is referred to as its convertibility, and the transition from one hierarchical position to another is called conversion of hierarchy (or rotation).
Relativity of subordination
Because of convertibility, there is no absolute "topmost level" in a hierarchy, though any hierarchical structure or system will certainly have one. Any element of hierarchy can become its topmost element in some hierarchical structure, thus representing the hierarchy as a whole.
Within hierarchy, the distinction between the elements and their relations can only refer to a particular position of hierarchy, and therefore this distinction is relative. In the same way, any functional distinctions (like input and output, inner and outer) are related to a particular hierarchical system, a specific position of hierarchy.
Any component of hierarchy is a hierarchy too, and it may be unfolded in the same way as the whole hierarchy. The very distinction between the part and the whole therefore becomes relative, and any part of hierarchy may be said to contain the whole of it, the part being virtually equivalent to the whole. To put it differently, a hierarchy is reflected in any one of its elements.
Hierarchy does not imply any strict ordering of levels; it rather is a multidimensional formation. The number of its dimensions is "infinite", in the same sense as the number of levels. However, every position of hierarchy implies a one-dimensional ordering of levels, and any level of hierarchical structure or system has a definite dimensionality.