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For the various types of hierarchy, see hierarchy (disambiguation).

A hierarchy is an arrangement of items (objects, names, values, categories, etc.), in which the items are represented as being "above," "below," or "at the same level as" one another.^[1][2] The word derives from the Greek ἱεραρχία (hierarchia), from ἱεράρχης (hierarches), "president of sacred rites, high-priest" and that from ἱερός (hieros), "sacred" + ἄρχω (arkho), "to lead, to rule"^[3][4]. The word can also refer to a series of such items so arranged. 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.^[5] 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. The concept of hierarchy, originally meaning rule by priests, has been used metaphorically to describe many different things. ... The Oxford English Dictionary print set The Oxford English Dictionary (OED) is a dictionary published by the Oxford University Press (OUP), and is the most successful dictionary of the English language, (not to be confused with the one-volume Oxford Dictionary of English, formerly New Oxford Dictionary of English, of... Pseudo-Dionysius the Areopagite, also known as pseudo-Denys, refers to the anonymous theologian and philosopher of the 5th century whose Corpus Areopagiticum was falsely ascribed to Dionysius the Areopagite of Acts 17:34. ... The Roman Catholic Church, most often spoken of simply as the Catholic Church, is the largest Christian church, with over one billion members. ... ... This article is about the term God in the context of monotheism and henotheism. ...

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). This article is in need of attention from an expert on the subject. ...

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. Surface mount electronic components Electronics is the study of the flow of charge through various materials and devices such as semiconductors, resistors, inductors, capacitors, nano-structures and vacuum tubes. ... This article is about the machine. ... Integrated circuit of Atmel Diopsis 740 System on Chip showing memory blocks, logic and input/output pads around the periphery Microchips (EPROM memory) with a transparent window, showing the integrated circuit inside. ... Flowcharts are often used to graphically represent algorithms. ... This article is about computer files and file systems in general terms. ... For library and office filing systems, see Library classification. ... In computing, a directory, catalog, or folder[1] is an entity in a file system which contains a group of files and/or other directories. ... An operating system (OS) is a software that manages computer resources and provides programmers with an interface used to access those resources. ... Object-oriented programming (OOP) is a computer programming paradigm in which a software system is modeled as a set of objects that interact with each other. ... In computer sciences object-oriented programming, the mapped relationships of sub- and superclasses is known as a hierarchy. ... This article or section does not cite any references or sources. ... An IP address (or Internet Protocol address) is a unique address that certain electronic devices use in order to identify and communicate with each other on a computer network utilizing the Internet Protocol standard (IP)—in simpler terms, a computer address. ... Warning! This Article contains disinformation. ... This article is about routing in computer networks. ... A typical vision of a computer architecture as a series of abstraction layers: hardware, firmware, assembler, kernel, operating system and applications (see also Tanenbaum 79). ... This article does not cite any references or sources. ... The hierarchical arrangement of storage in current computer architectures is called the memory hierarchy. ...

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. Computer-generated imagery[1] (also known as CGI) is the application of the field of computer graphics or, more specifically, 3D computer graphics to special effects in films, television programs, commercials, simulators and simulation generally, and printed media. ... See also: Computer-generated imagery Computer animation is the art of creating moving images via the use of computers. ... A computer program is a collection of instructions that describe a task, or set of tasks, to be carried out by a computer. ... This article is about process of creating 3D computer graphics. ... This article is about computer modeling within an artistic medium. ... This article is about modern humans. ... Male Chest The chest is a part of the anatomy of humans and various other animals. ... A parent is a father or mother; one who begets or one who gives birth to or nurtures and raises a child; a relative who plays the role of guardian // Mother This article or section does not cite its references or sources. ... For other uses, see Hand (disambiguation). ... Model may refer to more than one thing : For models in society, art, fashion, and cosmetics, see; role model model (person) supermodel figure drawing modeling section In science and technology, a model (abstract) is understood as an abstract or theoretical representation of a phenomenon,see; geologic modeling model (economics) model... The bouncing ball animation (below) consists of these 6 frames. ... For other uses, see Digital (disambiguation). ...

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.) For other uses, see Biology (disambiguation). ... For the science of classifying living things, see alpha taxonomy. ... Binomial name Rafinesque, 1820 Eastern newt range The eastern newt (Notophthalmus viridescens) is a common salamander of eastern North America. ... For other uses, see Genus (disambiguation). ...

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. Domains and Kingdoms Nanobes Acytota Cytota Bacteria Neomura Archaea Eukaryota Bikonta Apusozoa Rhizaria Excavata Archaeplastida Rhodophyta Glaucophyta Plantae Heterokontophyta Haptophyta Cryptophyta Alveolata Unikonta Amoebozoa Opisthokonta Choanozoa Fungi Animalia An ericoid mycorrhizal fungus Life on Earth redirects here. ... A coral reef near the Hawaiian islands is an example of a complex marine ecosystem. ... For the journal, see Ecology (journal). ...

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. A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... The Standard Model of Fundamental Particles and Interactions For the Standard Model in Cryptography, see Standard Model (cryptography). ... For the novel, see The Elementary Particles. ... Energetics is the scientific study of energy flows under transformation. ... Energy quality the contrast between different forms of energy, the different trophic levels in ecological systems and the propensity of energy to convert from one form to another. ...

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. For the journal, see Linguistics (journal). ... Avram Noam Chomsky (born December 7, 1928) is an American linguist, philosopher, political activist, author and lecturer. ... Generative linguistics is a school of thought within linguistics that makes use of the concept of a generative grammar. ... Ray Jackendoff (born 1945) is an influential contemporary linguist who has always straddled the boundary between generative linguistics and cognitive linguistics, committed as he is both to the existence of an innate Universal Grammar (an all-important thesis of generative linguistics) and to giving an account of language that meshes... Universal grammar is a theory of linguistics postulating principles of grammar shared by all languages, thought to be innate to humans. ...

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. A direct-inverse language is a language where clauses with transitive verbs can be expressed either using a direct or an inverse construction. ... Cree (also known as Cree-Montagnais, Cree-Montagnais-Naskapi) is the name for a group of closely-related Algonquian languages spoken by approximately 117,000 people across Canada, from the Northwest Territories to Labrador, making it by far the most spoken aboriginal language in Canada. ... Mapudungun is an Araucanian language spoken in Chile and Argentina by the Mapuche people. ... It has been suggested that Verbal agreement be merged into this article or section. ...

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. The Algonquian (also Algonkian) languages are a subfamily of Native American languages that includes most of the languages in the Algic language family (the two Algic languages that are not Algonquian are Wiyot and Yurok of northwestern California). ... Because too much data can cause “cognitive clutter”, individuals need a system to enable them to rank available data in terms of its immediate importance. ...

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. For other uses, see Music (disambiguation). ... Schenkerian analysis is a method of musical analysis based on the theories of Heinrich Schenker. ... Fred Lerdahl, Fritz Reiner Professor of Musical Composition at Columbia University, is a composer and music theorist, best known for his work on pitch space and cognitive constraints on compositional systems or musical grammars. ... Ray Jackendoff is a Professor of Linguistics and Chair of the Linguistics Program at Brandeis University. ... Schenkerian analysis is an approach to musical analysis devised by Heinrich Schenker. ...

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." Pitch is the perceived fundamental frequency of a sound. ... The term musical form refers to two related concepts: the type of composition (for example, a musical work can have the form of a symphony, a concerto, or other generic type -- see Multi-movement forms below) the structure of a particular piece (for example, a piece can be written in... Tonality is a system of writing music according to certain hierarchical pitch relationships around a key center or tonic. ... The tonic is the first note of a musical scale, and in the tonal method of music composition it is extremely important. ... This key signature – A major or F# minor – consists of three sharps placed after the clef In musical notation, a key signature is a series of sharp symbols or flat symbols placed on the staff, designating notes that are to be consistently played one semitone higher or lower than the... Susan McClary (born 2 October 1946) is a musicologist considered to be a significant figure in the New Musicology. She is noted for her work combining musicology and feminism. ... Sonata form refers to both the standard layout of an entire work and more specifically to the standardized form of the first movement. ...

Ethics, behavioral psychology, philosophies of identity

In ethics, various virtues are enumerated and sometimes organized hierarchically according to certain brands of virtue theory. For other uses, see Ethics (disambiguation). ... Virtue (Greek αρετη; Latin virtus) is the habitual, well-established, readiness or diposition of mans powers directing them to some goodness of act. ... Virtue (Greek αρετη; Latin virtus) is the habitual, well-established, readiness or disposition of mans powers directing them to some goodness of act. ...

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. This article needs additional references or sources for verification. ... Michel Foucault (pronounced ) (15 October 1926–25 June 1984) was a French philosopher, historian, critic and sociologist. ... Theory of knowledge redirects here: for other uses, see theory of knowledge (disambiguation) Epistemology (from Greek επιστήμη - episteme, knowledge + λόγος, logos) or theory of knowledge is a branch of philosophy concerned with the nature and scope of knowledge. ...

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. Feminism is a social theory and political movement primarily informed and motivated by the experience of women. ... Marxism is the political practice and social theory based on the works of Karl Marx, a 19th century philosopher, economist, journalist, and revolutionary, along with Friedrich Engels. ... Anarchists can refer to several things, among which: The movie Anarchists Supporters of the principles of anarchism The Anarchists (Les Anarchistes), a famous song from Léo Ferré A List of anarchists Category: ... This article is about communism as a form of society, as an ideology advocating that form of society, and as a popular movement. ... In the humanities and social sciences, critical theory has two quite different meanings with different origins and histories. ...

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. A hierarchy (in Greek hieros = sacred, arkho = rule) is a system of ranking and organizing things. ... For the science of classifying living things, see alpha taxonomy. ...

• In geometry: {shape {polygon {quadrilateral {rectangle {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]]]

For other uses, see Square. ... For other uses, see Golden Eagle (disambiguation). ... The Chomsky hierarchy is a containment hierarchy of classes of formal grammars that generate formal languages. ... For other uses, see Electron (disambiguation). ...

References

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.
• Exploration, Exploitation, and Knowledge Management Strategies in Multi-Tier Hierarchical Organizations on SSRN

External links

• Principles and annotated bibliography of hierarchy theory
• Summary of the Principles of Hierarchy Theory — S.N. Salthe