- For the various types of hierarchy, see hierarchy
(disambiguation)
A hierarchy (in Greek: Ἱεραρχία, derived from
ἱερός — hieros, 'sacred', and ἄρχω — arkho, 'rule')
is a system of ranking and organizing things or people, where each element of the system (except
for the top element) is a subordinate to a single other element.
The first use of the word "hierarchy" cited by the Oxford English
Dictionary was in 1880, when it was used in reference to the three orders of three angels as
depicted by Pseudo-Dionysius the Areopagite. Pseudo-Dionysius used the
word both in reference to the celestial hierarchy and the ecclesiastical hierarchy [1]. His term is derived from the
Greek for 'Bishop' (hierarch), and Dionysius is credited with first use of it as an abstract noun. Since hierarchical
churches, such as the Roman Catholic and
Eastern Orthodox churches, had tables of organization that were "hierarchical"
in the modern sense of the word (traditionally with God as the pinnacle of the
hierarchy), the term came to refer to similar organizational methods in more general settings.
A hierarchy can link entities either directly or indirectly, and either vertically or horizontally. The only direct links in a
hierarchy, insofar as they are hierarchical, are to one's immediate superior or to one of one's subordinates, although a system
that is largely hierarchical can also incorporate other organizational patterns. Indirect hierarchical links can extend
"vertically" upwards or downwards via multiple links in the same direction. All parts of the hierarchy which are not vertically
linked to one another can nevertheless be "horizontally" linked by traveling up the hierarchy to find a common direct or indirect
superior, and then down again. This is akin to two co-workers, neither of whom is the other's boss, but both of whose chains of
command will eventually meet.
These relationships can be formalized mathematically; see hierarchy
(mathematics).
Computation and electronics
Large electronic devices such as computers are usually
composed of modules, which are themselves created out of smaller components (integrated
circuits), which in turn are internally organized using hierarchical methods (e.g. using standard cells). The order of
tasks in a computational algorithm is often managed hierarchically, with repeated loops nested
within one another. Computer files in a file system
are stored in a hierarchy of directories in most operating systems. In object-oriented programming,
classes are organized hierarchically; the relationship between two related classes is called inheritance. In the Internet, IP addresses are increasingly organized in a hierarchy (so that the routing will continue to function
as the Internet grows).
Computer graphic imaging (CGI)
Within most CGI and computer
animation programs is the use of hierarchies. On a 3D model of a human, the
chest is a parent of the upper left arm, which is a
parent of the lower left arm, which is a parent of the
hand. This is used in modeling and animation of almost everything built as a 3D digital model.
Biological taxonomy
In biology, the study of taxonomy is one of the most
conventionally hierarchical kinds of knowledge, placing all living beings in a nested structure of divisions related to their
probable evolutionary descent. Most evolutionary biologists assert a hierarchy extending from the level of the specimen (an
individual living organism — say, a single newt), to the species of which it is a member (perhaps the Eastern Newt), outward to further successive levels of genus, family, order,
class, phylum, and kingdom. (A newt is a kind of salamander (family), and all salamanders are types of amphibians (class), which
are all types of vertebrates (phylum).) Essential to this kind of reasoning is the proof that members of a division on one level
are more closely related to one another than to members of a different division on the same level; they must also share ancestry
in the level above. Thus, the system is hierarchical because it forbids the possibility of overlapping categories. For example,
it will not permit a 'family' of beings containing some examples that are amphibians and others that are reptiles — divisions on
any level do not straddle the categories of structure that are hierarchically above it. (Such straddling would be an example of
heterarchy.)
Organisms are also commonly described as assemblies of parts (organs) which are themselves
assemblies of yet smaller parts. When we observe that the relationship of cell to organ is like that of the relationship of organ
to body, we are invoking the hierarchical aspects of physiology. (The term "organic" is often used to describe a sense of the
small imitating the large, which suggests hierarchy, but isn't necessarily hierarchical.) The analogy of organ to body also
extends to the relationship of a living being as a system that might resemble an ecosystem
consisting of several living beings; physiology is thus hierarchically nested in ecology.
Physics
In physics, the standard model of reasoning on the
nature of the physical world decomposes large bodies down to their smallest particle
components. Observations on the subatomic (particle) level are often seen as fundamental constituent axioms, on which conclusions
about the atomic and molecular levels depend. The relationships of energy and gravity between celestial bodies are, in turn,
dependent upon the atomic and molecular properties of smaller bodies. In energetics,
energy quality is sometimes used to quantify energy hierarchy.
Language and semiotics
In linguistics, especially in the work of Noam Chomsky, and of later generative linguistics theories, such
as Ray Jackendoff's, words or sentences are often broken down into hierarchies of parts
and wholes. Hierarchical reasoning about the underlying structure of language expressions leads some linguists to the hypothesis
that the world's languages are bound together in a broad array of variants subordinate to a single Universal Grammar.
Music
In music, the structure of a composition is often understood hierarchically (for example by
Heinrich Schenker (1868–1935, see Schenkerian
analysis), and in the (1985) Generative Theory of Tonal Music, by composer Fred
Lerdahl and linguist Ray Jackendoff). The sum of all notes in a piece is
understood to be an all-inclusive surface, which can be reduced to successively more sparse and more fundamental types of motion.
The levels of structure that operate in Schenker's theory are the foreground, which is seen in all the details of the musical
score; the middle ground, which is roughly a summary of an essential contrapuntal progression and voice-leading; and the
background or Ursatz, which is one of only a few basic "long-range counterpoint"
structures that are shared in the gamut of tonal music literature.
The pitches and form of tonal music are organized hierarchically, all pitches deriving their importance
from their relationship to a tonic key, and
secondary themes in other keys are brought back to the tonic in a recapitulation of the primary theme. Susan McClary connects this specifically in the sonata-allegro form
to the feminist hierarchy of gender (see above) in her book Feminine Endings, even pointing out that primary themes were
often previously called "masculine" and secondary themes "feminine."
Ethics, behavioral psychology, philosophies of identity
In ethics, various virtues are enumerated and sometimes
organized hierarchically according to certain brands of virtue theory.
In all of these examples, there is an asymmetry of 'compositional' significance between levels of structure, so that small
parts of the whole hierarchical array depend, for their meaning, on their membership in larger parts.
In the work of diverse theorists such as William James (1842–1910), Michel Foucault (1926–1984) and Hayden White, important critiques
of hierarchical epistemology are advanced. James famously asserts in his work "Radical
Empiricism" that clear distinctions of type and category are a constant but unwritten goal of scientific reasoning, so that when
they are discovered, success is declared. But if aspects of the world are organized differently, involving inherent and
intractable ambiguities, then scientific questions are often considered unresolved. A hesitation to declare success upon the
discovery of ambiguities leaves heterarchy at an artificial and subjective disadvantage in
the scope of human knowledge. This bias is an artifact of an aesthetic or pedagogical preference for hierarchy, and not
necessarily an expression of objective observation.
Feminists, marxists, critical theorists and others have criticized the hierarchies commonly found within human society,
especially in social relationships. Hierarchies are present in all parts of society: in businesses, schools, families, etc. These
relationships are often viewed as necessary; in many instances, they probably are. However, feminists, marxists, critical
theorists and others analyze hierarchy in terms of the values and power that it arbitrarily assigns to one group over another.
These scholars look at hierarchy in terms of how it promotes and stabilizes the oppression of women, racial and ethnic
minorities, the poor and working classes, gays, lesbians and other sexual minorities, children, the elderly, etc.
Hierarchies in programming
The concept of hierarchies plays a large part in object oriented
programming. For more information see Hierarchy (object-oriented
programming) and memory hierarchy.
Containment hierarchy
-
A containment hierarchy of the subsumption kind is a collection of strictly nested sets. Each entry in the hierarchy
designates a set such that the previous entry is a strict superset, and the next entry is a strict subset. For example, all
rectangles are quadrilaterals, but not all quadrilaterals are rectangles, and all squares are rectangles, but not all rectangles
are squares. (See also: Taxonomy.) A containment hierarchy of the compositional kind refers to
parts and wholes, as well as to rates of change. Generally the bigger changes more slowly. Parts are contained in wholes and
change more rapidly than do wholes.
- In geometry: {shape {polygon {quadrilateral {rectangle {Square (geometry)|square }}}}}
- In biology:subsumption hierarchy {animal {bird {bird of prey|raptor {eagle {golden eagle}}}}}
- compositional hierarchy: [population [organism [biological cell [macromolecule]]]]
- The Chomsky hierarchy in formal languages: recursively enumerable,
context-sensitive, context-free, and regular
- In physics: subsumption hierarchy {elementary particle {fermion {lepton {electron }}}}
- compositional hierarchy: [galaxy [star system [star]]]
Social hierarchies
-
Many human organizations, such as businesses,
churches, armies and political movements are hierarchical organizations, at
least officially; commonly seniors, called "bosses", have more power than their
subordinates. Thus the relationship defining this hierarchy is "commands" or "has power over". (Some analysts question whether
power "really" works as the traditional organizational chart indicates, however.) See also chain of command.
Alternatives
Hierarchies and hierarchical thinking and modelling has been criticized by some[citation needed], as shown above in Social hierarchies
and Hierarchical nomenclatures in the arts and sciences.
Possible hierarchy alternatives include:
Applied
Theoretic
Footnotes
References
See also
External links
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