Hierarchy

Hierarchy - Wikipedia, the free encyclopedia
A hierarchy is an arrangement of objects, people, elements, values, grades, ... Items in a hierarchy are typically thought of as being "above," "below," or "at ...
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Hierarchy of the Catholic Church
Current and historical information about its bishops and dioceses.
www.catholic-hierarchy.org

hierarchy: Definition from Answers.com
hierarchy n. , pl. -chies . A body of persons having authority. Categorization of a group of people according to ability or status
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Hierarchy - Catholic Encyclopedia
Provides the history of the Catholic Church's hierarchy of order and jurisdiction.
www.newadvent.org

Hierarchy - P2P Foundation
2.1 How Hierarchy hinders Complexity. 2.2 The historical development of complexity ... Hierarchy here is the creative leadership which seeks to promote the values of ...
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Extension:Hierarchy - MediaWiki
Each page can only belong to a single hierarchy, though. The hierarchy definition is centralized in an index page, not on the individual pages. ...
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hierarchy definition | Dictionary.com
Definition of hierarchy at Dictionary.com with free audio pronunciation. ... hierarchy - 6 dictionary results. hierarchy ... hierarchy. c.1343, from O.Fr. ...
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Hierarchical organization - Wikipedia, the free encyclopedia
Hierarchy originally meant "rule by priests", and it is from the organization of ... As a result, superiors in a hierarchy generally have higher status and command ...
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hierarchy - Definition from the Merriam-Webster Online Dictionary
Definition of hierarchy from the Merriam-Webster Online Dictionary with audio pronunciations, thesaurus, Word of the Day, and word games.
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hierarchy - Definition of hierarchy at Your Dictionary
Definition of hierarchy from Webster's New World Dictionary. Meaning of hierarchy. ... imply: There is no hierarchy implied by the title, the President's distinctive ...
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For the various types of hierarchy, see hierarchy (disambiguation) A hierarchy (in Greek language: , derived from — hieros, 'sacred', and — 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 . 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 Catholicism and Eastern Orthodoxy 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 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 directory (file systems) in most operating systems. In object-oriented programming, classes are organized hierarchically; the relationship between two related classes is called inheritance-oop. In the Internet, IP addresses are increasingly organized in a Classless inter-domain routing (so that the routing will continue to function as the Internet grows).

Computer graphic imaging (CGI) Within most Computer-generated imagery and computer animation programs is the use of hierarchies. On a 3D computer graphics 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 Elementary 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 pitch (music) and Musical form of Tonality music are organized hierarchically, all pitches deriving their importance from their relationship to a Tonic (music) Key signature, 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: 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: [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 (sociology) 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, as shown above in #Social hierarchies and #Hierarchical nomenclatures in the arts and sciences. Possible hierarchy alternatives include:

Applied

Democracy — Command hierarchy and Workplace democracy
Anarchism as a social/political theory and practice
Markets and associated tools such as contracts and property
Peer-to-peer networks

Theoretic

Directed graph
Triarchy Theory, which proposes also Heterarchy and Responsible autonomy. See The Three Ways of Getting Things Done.
Set theory

Footnotes

References

Julie Nelson (1992). "Gender, Metaphor and the Definition of Economics". Economics and Philosophy, 8:103–125.
Exploration, Exploitation, and Knowledge Management Strategies in Multi-Tier Hierarchical Organizations on SSRN