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Hierarchy
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A hierarchy is an arrangement of items (objects, names, values, categories, etc.) The word derives from the Greek (hierarchia), from ?e?????? (hierarches), "president of sacred rites, high-priest" and that from (hieros), "sacred" + (arkho), "to lead, to rule". The word can also refer to a series of such items so arranged. Items in a hierarchy are thought of typically as including or being "above," included by or being "below," or independent of (being "at the same level as") one another.
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.
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A hierarchy is an arrangement of items (objects, names, values, categories, etc.) The word derives from the Greek (hierarchia), from ?e?????? (hierarches), "president of sacred rites, high-priest" and that from (hieros), "sacred" + (arkho), "to lead, to rule". The word can also refer to a series of such items so arranged. Items in a hierarchy are thought of typically as including or being "above," included by or being "below," or independent of (being "at the same level as") one another.
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. 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 linked vertically to one another nevertheless can 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 an 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 an hierarchy (so that the routing will continue to function as the Internet grows). Modern computer architectures also organize memory in a hierarchical arrangement.
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.
Hierarchical verbal alignment
In some languages, such as Cree and Mapudungun, subject and object on verbs are distinguished not by different subject and object markers, but via a hierarchy of persons.
In this system, the three (or four with Algonquian languages) persons are placed in a hierarchy of salience. To distinguish which is subject and which object, inverse markers are used if the object outranks the subject.
In music, the structure of a composition is often understood hierarchically (for example by Heinrich Schenker (1768–1835, 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 random 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.
Feminists, Marxists, anarchists, communists, critical theorists and others, all of whom have multiple interpretations, criticize 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. 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.
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:
- In biology:subsumption hierarchy
- 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
- compositional hierarchy: [galaxy [star system [star]]]
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Further reading
- Valerie Ahl & Timothy F. H. Allen (1996). Hierarchy Theory. New York: Columbia University Press.
- Julie Nelson (1992). "Gender, Metaphor and the Definition of Economics". Economics and Philosophy, 8:103–125.
- A. Rosenbaum (1999). Les représentations hiérarchiques en philosophie. Paris: Desclee de Brouwer.
- on SSRN
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