The Fundamental Principles of the Hierarchical Approach

These are not the only principles that can be formulated, but they help to grasp the general idea of hierarchy as an intrinsic mechanism of any development.

• Hierarchical structure.
  Each hierarchy manifests a number of distinct levels, with the higher levels dominating over the lower levels in certain sense depending 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 control over lower level behaviors.

• Infinite divisibility.
  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 is known as unfolding of hierarchy.

• Foldability.
  The collection of intermediate levels between any two levels of hierarchy effectuating their connection can be treated as their immediate connection, with the two levels thus becoming near neighbours. The total number of levels in the hierarchical structure is decreased due to such folding, which is the inverse of hierarchical unfolding described above.

• Refoldability.
  Any hierarchy may be folded, and then unfolded in a different way, manifesting a hierarchical structure quite unlike the original. Therefore, no hierarchical structure can be absolute and rigid, and the hierarchy as a whole should be comprehended as the unity of all its unfoldings. This multi-faceted nature of hierarchy is also called rotabilty, and the process of replacing one hierarchical structure with another is called refolding, or rotation.

• Relativity of domination.
  Because of refoldability, there is no absolute "topmost level", though any hierarchical structure will have one. Any element of a hierarchy may become a topmost element of some hierarchical structure, thus representing the hierarchy as a whole.

• Strong integrity.
  Within hierarchy, the distinction between the elements and their relations can only refer to a particular unfolding, thus being relative. In the same way, any functional distinctions (like input, output, or internal state) are related to a definite hierarchical system, based on a specific undolding of the hierarchy.

• Self-conformity.
  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 it all, thus being equivalent to it. In other words, hierarchy is reflected in every one of its elements.

• Qualitative infinity.
  Hierarchy is not a simple ordering of levels, but rather a multidimensional formation. The number of its dimensions is "infinite", in the same sense as the number of levels. However, every specific unfolding of the hierarchy implies one-dimensional ordering of its levels, any one of which being characterized with a definite dimensionality.