Hierarchy
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:''For the various types of hierarchy, see [[hierarchy (disambiguation)]]''
A '''hierarchy''' is an arrangement of objects, people, elements, values, grades, orders, classes, etc., in a [[ranking|ranked]] or [[graduated]] series. The word derives from the [[Greek language|Greek]] <!-- OOP! - often used in Geographic studies -->'''{{Polytonic|ἱεραρχία}}''' (''hierarchia''), from ''ἱεράρχης'' (''hierarches''), "president of sacred rites, high-priest" and that from ''{{Polytonic|ἱερός}}'' (''hieros''), "sacred" + ''{{Polytonic|ἄρχω}}'' (''arkho''), "to lead, to rule"<ref>[http://www.perseus.tufts.edu/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3D%2349989 Hierarches, Henry George Liddell, Robert Scott, ''A Greek-English Lexicon'', at Perseus]</ref><ref>[http://www.etymonline.com/index.php?search=Hierarchy&searchmode=none Online Etymology Dictionary]</ref>. The word can also refer to a series of such items so arranged. Items in a hierarchy are typically thought of as being "above," "below," or "at the same level as" one another.<ref>{{cite book | last = Simpson | first = John, ed. | authorlink = | coauthors = Edmund Weiner, ed. | title = Oxford English Dictionary | publisher = Clarendon Press | date = 1989 | location = | pages = | url = | doi = | id = | isbn = 0-19-861186-2 }}</ref><ref>{{cite book | last = Gove | first = Philip Babcock, ed. | authorlink = | coauthors = | title = Webster's Third New International Dictionary, Unabridged | publisher = Merriam-Webster, Inc. | date = 2002 | location = Springfield, Massachusetts | pages = | url = | doi = | id = | isbn = 0-87779-201-1 }}</ref>
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. <ref>[http://www.newadvent.org/cathen/07322c.htm CATHOLIC ENCYCLOPEDIA: Hierarchy<!-- Bot generated title -->]</ref> 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 [[church]]es, such as the [[Roman Catholicism|Roman Catholic]] and [[Eastern Orthodoxy|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 [[electronics|electronic]] devices such as [[computer]]s are usually composed of modules, which are themselves created out of smaller components ([[integrated circuit]]s), 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 file]]s in a [[file system]] are stored in an hierarchy of [[directory (file systems)|directories]] in most [[operating system]]s. In [[object-oriented]] programming, classes are organized hierarchically; the relationship between two related classes is called [[inheritance-oop|inheritance]]. In the [[Internet]], [[IP address]]es are increasingly organized in an [[Classless inter-domain routing|hierarchy]] (so that the [[routing]] will continue to function as the Internet grows).
=== Computer graphic imaging (CGI) ===
Within most [[Computer-generated imagery|CGI]] and [[computer animation]] [[computer program|programs]] is the use of hierarchies. On a [[3D computer graphics|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]].)
[[Organism]]s 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 [[Elementary particle|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====
:''Main article: [[Direct-inverse language]]''
In some languages, such as [[Cree language|Cree]] and [[Mapudungun language|Mapudungun]], suject and object on [[verb]]s 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 [[pitch (music)|pitches]] and [[Musical form|form]] of [[Tonality|tonal]] [[music]] are organized hierarchically, all pitches deriving their importance from their relationship to a [[Tonic (music)|tonic]] [[Key signature|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]], [[anarchists]], [[communists]], [[critical theorists]] and others 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. 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. However, they often neglect to explain how society will function withouth hierarchical relationships, or to admit that they really just press for the adoption of a new hierarchy with their own particular group (i.e., women, gays, etc.) in a position of dominance within that hierarchy.
== 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 ==
{{main|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 ==
{{main|Social hierarchy}}
Many human [[organization]]s, such as governments, educational institutions, [[business]]es, churches, armies and political movements are [[hierarchical organization]]s, at least officially; commonly seniors, called "bosses", have more [[power (sociology)|power]] than their subordinates. Thus the relationship defining this hierarchy is "commands" or "has power over". Some analysts question whether power "actually" works in the way the traditional organizational chart indicates, however. This view tends to emphasize the significance of the [[informal organization]]. See also [[chain of command]].
==See also==
* [[Heterarchy]]
* [[Homoarchy]]
* [[Holoarchy]]
==References==
{{reflist}}
== 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.
* [http://papers.ssrn.com/sol3/papers.cfm?abstract_id=961043 Exploration, Exploitation, and Knowledge Management Strategies in Multi-Tier Hierarchical Organizations] on SSRN
== External links ==
* [http://www.isss.org/hierarchy.htm Principles and annotated bibliography of hierarchy theory]
* [http://www.nbi.dk/~natphil/salthe/Summary_of_the_Principles_o.pdf Summary of the Principles of Hierarchy Theory] — S.N. Salthe
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