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A hierarchy (from Greek: , from , 'president of sacred rites') is an arrangement of items (objects, names, values, categories, etc.) that are represented as being "above", "below", or "at the same level as" one another. Hierarchy is an important concept in a wide variety of fields, such as
architecture Architecture is the art and technique of designing and building, as distinguished from the skills associated with construction. It is both the process and the product of sketching, conceiving, planning, designing, and constructing buildings ...
,
philosophy Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. ...
,
design A design is a plan or specification for the construction of an object or system or for the implementation of an activity or process or the result of that plan or specification in the form of a prototype, product, or process. The verb ''to design' ...
,
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
,
computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...
, organizational theory, systems theory, systematic biology, and the social sciences (especially
political philosophy Political philosophy or political theory is the philosophical study of government, addressing questions about the nature, scope, and legitimacy of public agents and institutions and the relationships between them. Its topics include politics, ...
). A hierarchy can link entities either directly or indirectly, and either vertically or diagonally. 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 alternative hierarchies. Hierarchical links can extend "vertically" upwards or downwards via multiple links in the same direction, following a path. All parts of the hierarchy that are not linked vertically to one another nevertheless can be "horizontally" linked through a path by traveling up the hierarchy to find a common direct or indirect superior, and then down again. This is akin to two
co-worker Employment is a relationship between two parties regulating the provision of paid labour services. Usually based on a contract, one party, the employer, which might be a corporation, a not-for-profit organization, a co-operative, or any o ...
s or
colleague Collegiality is the relationship between colleagues. A colleague is a fellow member of the same profession. Colleagues are those explicitly united in a common purpose and respect each other's abilities to work toward that purpose. A colleague is ...
s; each reports to a common superior, but they have the same relative amount of authority. Organizational forms exist that are both alternative and complementary to hierarchy. Heterarchy is one such form.


Nomenclature

Hierarchies have their own special vocabulary. These terms are easiest to understand when a hierarchy is diagrammed (see
below Below may refer to: *Earth * Ground (disambiguation) *Soil *Floor * Bottom (disambiguation) *Less than *Temperatures below freezing *Hell or underworld People with the surname *Ernst von Below (1863–1955), German World War I general *Fred Below ...
). In an organizational context, the following terms are often used related to hierarchies: *
Object Object may refer to: General meanings * Object (philosophy), a thing, being, or concept ** Object (abstract), an object which does not exist at any particular time or place ** Physical object, an identifiable collection of matter * Goal, an ...
: one entity (e.g., a person, department or
concept Concepts are defined as abstract ideas. They are understood to be the fundamental building blocks of the concept behind principles, thoughts and beliefs. They play an important role in all aspects of cognition. As such, concepts are studied by ...
or element of arrangement or member of a set) *
System A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and express ...
: the entire set of objects that are being arranged hierarchically (e.g., an administration) *
Dimension In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coord ...
: another word for "system" from on-line analytical processing (e.g. cubes) *
Member Member may refer to: * Military jury, referred to as "Members" in military jargon * Element (mathematics), an object that belongs to a mathematical set * In object-oriented programming, a member of a class ** Field (computer science), entries in ...
: an (element or object) at any (level or rank) in a (class-system, taxonomy or dimension) *Terms about Positioning ** Rank: the relative
value Value or values may refer to: Ethics and social * Value (ethics) wherein said concept may be construed as treating actions themselves as abstract objects, associating value to them ** Values (Western philosophy) expands the notion of value beyo ...
, worth, complexity, power, importance, authority, level etc. of an object ** Level or Tier: a set of objects with the same rank OR importance **
Ordering Order, ORDER or Orders may refer to: * Categorization, the process in which ideas and objects are recognized, differentiated, and understood * Heterarchy, a system of organization wherein the elements have the potential to be ranked a number of ...
: the arrangement of the (ranks or levels) **Hierarchy: the arrangement of a particular set of members into (ranks or levels). Multiple hierarchies are possible per (dimension taxonomy or Classification-system), in which selected levels of the dimension are omitted to flatten the structure *Terms about Placement ** Hierarch, the apex of the hierarchy, consisting of one single orphan (object or member) in the top level of a dimension. The root of an inverted-tree structure **
Member Member may refer to: * Military jury, referred to as "Members" in military jargon * Element (mathematics), an object that belongs to a mathematical set * In object-oriented programming, a member of a class ** Field (computer science), entries in ...
, a (member or node) in any level of a hierarchy in a dimension to which (superior and subordinate) members are attached ** Orphan, a member in any level of a dimension without a parent member. Often the apex of a disconnected branch. Orphans can be grafted back into the hierarchy by creating a relationship (interaction) with a parent in the immediately superior level **
Leaf A leaf ( : leaves) is any of the principal appendages of a vascular plant stem, usually borne laterally aboveground and specialized for photosynthesis. Leaves are collectively called foliage, as in "autumn foliage", while the leaves, ...
, a member in any level of a dimension without subordinates in the hierarchy **
Neighbour Neighbour, Neighbor, Neighbours or Neighbors may refer to: * Person who lives in one's neighbourhood * The subject of the Great Commandment Films * ''Neighbors'' (1920 film), a short film starring Buster Keaton * ''Neighbours'' (1952 film), a ...
: a member adjacent to another member in the same (level or rank). Always a peer. **
Superior Superior may refer to: *Superior (hierarchy), something which is higher in a hierarchical structure of any kind Places *Superior (proposed U.S. state), an unsuccessful proposal for the Upper Peninsula of Michigan to form a separate state *Lake ...
: a higher level or an object ranked at a higher level (A parent or an ancestor) ** Subordinate: a lower level or an object ranked at a lower level (A child or a descendant) ** Collection: all of the objects at one level (i.e. Peers) **
Peer Peer may refer to: Sociology * Peer, an equal in age, education or social class; see Peer group * Peer, a member of the peerage; related to the term "peer of the realm" Computing * Peer, one of several functional units in the same layer of a ne ...
: an object with the same rank (and therefore at the same level) **
Interaction Interaction is action that occurs between two or more objects, with broad use in philosophy and the sciences. It may refer to: Science * Interaction hypothesis, a theory of second language acquisition * Interaction (statistics) * Interaction ...
: the relationship between an object and its direct superior or subordinate (i.e. a superior/inferior pair) *** a direct interaction occurs when one object is on a level exactly one higher or one lower than the other (i.e., on a tree, the two objects have a line between them) ** Distance: the minimum number of connections between two objects, i.e., one less than the number of objects that need to be "crossed" to trace a path from one object to another ** Span: a qualitative description of the width of a level when diagrammed, i.e., the number of subordinates an object has *Terms about Nature ** Attribute: a heritable characteristic of (members and their subordinates) in a level (e.g. ''hair-colour'') ** Attribute-value: the specific value of a heritable characteristic (e.g. ''Auburn'') In a mathematical context (in
graph theory In mathematics, graph theory is the study of '' graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conn ...
), the general terminology used is different. Most hierarchies use a more specific vocabulary pertaining to their subject, but the idea behind them is the same. For example, with data structures, objects are known as nodes, superiors are called parents and subordinates are called children. In a business setting, a superior is a supervisor/boss and a peer is a
colleague Collegiality is the relationship between colleagues. A colleague is a fellow member of the same profession. Colleagues are those explicitly united in a common purpose and respect each other's abilities to work toward that purpose. A colleague is ...
.


Degree of branching

Degree of branching refers to the number of direct subordinates or children an object has (in graph theory, equivalent to the number of other vertices connected to via outgoing arcs, in a directed graph) a node has. Hierarchies can be categorized based on the "maximum degree", the highest degree present in the system as a whole. Categorization in this way yields two broad classes: ''linear'' and ''branching''. In a linear hierarchy, the maximum degree is 1. In other words, all of the objects can be visualized in a line-up, and each object (excluding the top and bottom ones) has exactly one direct subordinate and one direct superior. Note that this is referring to the ''objects'' and not the ''levels''; every hierarchy has this property with respect to levels, but normally each level can have an infinite number of objects. An example of a linear hierarchy is the hierarchy of life. In a branching hierarchy, one or more objects has a degree of 2 or more (and therefore the minimum degree is 2 or higher). For many people, the word "hierarchy" automatically evokes an image of a branching hierarchy. Branching hierarchies are present within numerous systems, including
organization An organization or organisation (Commonwealth English; see spelling differences), is an entity—such as a company, an institution, or an association—comprising one or more people and having a particular purpose. The word is derived f ...
s and classification schemes. The broad category of branching hierarchies can be further subdivided based on the degree. A flat hierarchy (also known for companies as flat organization) is a branching hierarchy in which the maximum degree approaches infinity, i.e., that has a wide span. Most often, systems intuitively regarded as hierarchical have at most a moderate span. Therefore, a flat hierarchy is often not viewed as a hierarchy at all. For example,
diamond Diamond is a solid form of the element carbon with its atoms arranged in a crystal structure called diamond cubic. Another solid form of carbon known as graphite is the chemically stable form of carbon at room temperature and pressure, b ...
s and
graphite Graphite () is a crystalline form of the element carbon. It consists of stacked layers of graphene. Graphite occurs naturally and is the most stable form of carbon under standard conditions. Synthetic and natural graphite are consumed on la ...
are flat hierarchies of numerous
carbon Carbon () is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent—its atom making four electrons available to form covalent chemical bonds. It belongs to group 14 of the periodic table. Carbon ma ...
atoms that can be further decomposed into subatomic particles. An overlapping hierarchy is a branching hierarchy in which at least one object has two parent objects. For example, a graduate student can have two co-supervisors to whom the student reports directly and equally, and who have the same level of authority within the
university A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United Stat ...
hierarchy (i.e., they have the same position or tenure status).


Etymology

Possibly the first use of the English word ''hierarchy'' cited by the ''
Oxford English Dictionary The ''Oxford English Dictionary'' (''OED'') is the first and foundational historical dictionary of the English language, published by Oxford University Press (OUP). It traces the historical development of the English language, providing a c ...
'' was in 1881, when it was used in reference to the three orders of three angels as depicted by
Pseudo-Dionysius the Areopagite Pseudo-Dionysius the Areopagite (or Dionysius the Pseudo-Areopagite) was a Greek author, Christian theologian and Neoplatonic philosopher of the late 5th to early 6th century, who wrote a set of works known as the ''Corpus Areopagiticum'' ...
(5th–6th centuries). Pseudo-Dionysius used the related Greek word (ἱεραρχία, ) both in reference to the celestial hierarchy and the
ecclesiastical hierarchy The hierarchy of the Catholic Church consists of its bishops, priests, and deacons. In the ecclesiological sense of the term, "hierarchy" strictly means the "holy ordering" of the Church, the Body of Christ, so to respect the diversity of gif ...
. The Greek term ''hierarchia'' means 'rule of a high priest', from (ἱεράρχης, 'president of sacred rites, high-priest') and that from ''hiereus'' (ἱερεύς, 'priest') and ''arche'' (ἀρχή, 'first place or power, rule'). Dionysius is credited with first use of it as an abstract noun. Since hierarchical churches, such as the
Roman Catholic Roman or Romans most often refers to: * Rome, the capital city of Italy *Ancient Rome, Roman civilization from 8th century BC to 5th century AD * Roman people, the people of ancient Rome *'' Epistle to the Romans'', shortened to ''Romans'', a let ...
(see
Catholic Church hierarchy The hierarchy of the Catholic Church consists of its bishops, priests, and deacons. In the ecclesiological sense of the term, "hierarchy" strictly means the "holy ordering" of the Church, the Body of Christ, so to respect the diversity of gifts ...
) and Eastern Orthodox churches, had tables of organization that were "hierarchical" in the modern sense of the word (traditionally with God as the pinnacle or head of the hierarchy), the term came to refer to similar organizational methods in secular settings.


Representing hierarchies

A hierarchy is typically depicted as a pyramid, where the height of a level represents that level's status and width of a level represents the quantity of items at that level relative to the whole. For example, the few Directors of a company could be at the apex, and the base could be thousands of people who have no subordinates. These pyramids are often diagrammed with a triangle diagram which serves to emphasize the size differences between the levels (but note that not all triangle/pyramid diagrams are hierarchical; for example, the 1992 USDA food guide pyramid). An example of a triangle diagram appears to the right. Another common representation of a hierarchical scheme is as a tree diagram. Phylogenetic trees,
charts A chart (sometimes known as a graph) is a graphical representation for data visualization, in which "the data is represented by symbols, such as bars in a bar chart, lines in a line chart, or slices in a pie chart". A chart can represent tabu ...
showing the structure of , and playoff brackets in sports are often illustrated this way. More recently, as computers have allowed the storage and navigation of ever larger data sets, various methods have been developed to represent hierarchies in a manner that makes more efficient use of the available space on a computer's screen. Examples include fractal maps, TreeMaps and Radial Trees.


Visual hierarchy

In the design field, mainly graphic design, successful layouts and formatting of the content on documents are heavily dependent on the rules of visual hierarchy. Visual hierarchy is also important for proper organization of files on computers. An example of visually representing hierarchy is through nested clusters. Nested clusters represent hierarchical relationships using layers of information. The child element is within the parent element, such as in a Venn diagram. This structure is most effective in representing simple hierarchical relationships. For example, when directing someone to open a file on a computer desktop, one may first direct them towards the main folder, then the subfolders within the main folder. They will keep opening files within the folders until the designated file is located. For more complicated hierarchies, the stair structure represents hierarchical relationships through the use of visual stacking. Visually imagine the top of a downward staircase beginning at the left and descending on the right. Child elements are towards the bottom of the stairs and parent elements are at the top. This structure represents hierarchical relationships through the use of visual stacking.


Informal representation

In plain English, a hierarchy can be thought of as a
set Set, The Set, SET or SETS may refer to: Science, technology, and mathematics Mathematics *Set (mathematics), a collection of elements *Category of sets, the category whose objects and morphisms are sets and total functions, respectively Electro ...
in which: # No element is superior to itself, and # One element, the (''apex'' or ''hierarch''), is superior to all of the other elements in the set. The first requirement is also interpreted to mean that a hierarchy can have no circular relationships; the association between two objects is always transitive. The second requirement asserts that a hierarchy must have a leader or root that is common to all of the objects.


Mathematical representation

Mathematically, in its most general form, a hierarchy is a
partially ordered set In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a binary ...
or ''poset''. The
system A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and express ...
in this case is the entire poset, which is constituted of elements. Within this system, each element shares a particular unambiguous property. Objects with the same property value are grouped together, and each of those resulting levels is referred to as a
class Class or The Class may refer to: Common uses not otherwise categorized * Class (biology), a taxonomic rank * Class (knowledge representation), a collection of individuals or objects * Class (philosophy), an analytical concept used differently ...
. "Hierarchy" is particularly used to refer to a poset in which the classes are organized in terms of increasing complexity. Operations such as addition, subtraction, multiplication and division are often performed in a certain sequence or order. Usually, addition and subtraction are performed after multiplication and division has already been applied to a problem. The use of parentheses is also a representation of hierarchy, for they show which operation is to be done prior to the following ones. For example: (2 + 5) × (7 - 4). In this problem, typically one would multiply 5 by 7 first, based on the rules of mathematical hierarchy. But when the parentheses are placed, one will know to do the operations within the parentheses first before continuing on with the problem. These rules are largely dominant in algebraic problems, ones that include several steps to solve. The use of hierarchy in mathematics is beneficial to quickly and efficiently solve a problem without having to go through the process of slowly dissecting the problem. Most of these rules are now known as the proper way into solving certain equations.


Subtypes


Nested hierarchy

A nested hierarchy or ''inclusion hierarchy'' is a hierarchical ordering of
nested set In a naive set theory, a nested set is a set containing a chain of subsets, forming a hierarchical structure, like Russian dolls. It is used as reference-concept in all scientific hierarchy definitions, and many technical approaches, like the ...
s. The concept of nesting is exemplified in Russian matryoshka dolls. Each doll is encompassed by another doll, all the way to the outer doll. The outer doll holds all of the inner dolls, the next outer doll holds all the remaining inner dolls, and so on. Matryoshkas represent a nested hierarchy where each level contains only one object, i.e., there is only one of each size of doll; a generalized nested hierarchy allows for multiple objects within levels but with each object having only one parent at each level. The general concept is both demonstrated and mathematically formulated in the following example: : \text \subset \text \subset \text \subset \text \, A square can always also be referred to as a quadrilateral, polygon or shape. In this way, it is a hierarchy. However, consider the set of polygons using this classification. A square can ''only'' be a quadrilateral; it can never be a triangle, hexagon, etc. Nested hierarchies are the organizational schemes behind taxonomies and systematic classifications. For example, using the original Linnaean taxonomy (the version he laid out in the 10th edition of ''
Systema Naturae ' (originally in Latin written ' with the ligature æ) is one of the major works of the Swedish botanist, zoologist and physician Carl Linnaeus (1707–1778) and introduced the Linnaean taxonomy. Although the system, now known as binomial ...
''), a human can be formulated as: : \text \subset \text \subset \text \subset \text \subset \text Taxonomies may change frequently (as seen in
biological taxonomy In biology, taxonomy () is the scientific study of naming, defining ( circumscribing) and classifying groups of biological organisms based on shared characteristics. Organisms are grouped into taxa (singular: taxon) and these groups are given ...
), but the underlying concept of nested hierarchies is always the same. In many programming taxonomies and syntax models (as well as fractals in mathematics), nested hierarchies, including Russian dolls, are also used to illustrate the properties of self-similarity and
recursion Recursion (adjective: ''recursive'') occurs when a thing is defined in terms of itself or of its type. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematic ...
. Recursion itself is included as a subset of hierarchical programming, and recursive thinking can be synonymous with a form of hierarchical thinking and logic.


Containment hierarchy

A containment hierarchy is a direct extrapolation of the nested hierarchy concept. All of the ordered sets are still nested, but every set must be "
strict In mathematical writing, the term strict refers to the property of excluding equality and equivalence and often occurs in the context of inequality and monotonic functions. It is often attached to a technical term to indicate that the exclusive ...
"—no two sets can be identical. The shapes example above can be modified to demonstrate this: : \text \subsetneq \text \subsetneq \text \subsetneq \text \, The notation x \subsetneq y \, means ''x'' is a subset of ''y'' but is not equal to ''y''. A general example of a containment hierarchy is demonstrated in class inheritance in object-oriented programming. Two types of containment hierarchies are the ''subsumptive'' containment hierarchy and the ''compositional'' containment hierarchy. A subsumptive hierarchy " subsumes" its children, and a compositional hierarchy is " composed" of its children. A hierarchy can also be both subsumptive ''and'' compositional.


Subsumptive containment hierarchy

A '' subsumptive'' containment hierarchy is a classification of object classes from the general to the specific. Other names for this type of hierarchy are "taxonomic hierarchy" and " IS-A hierarchy". The last term describes the relationship between each level—a lower-level object "is a" member of the higher class. The taxonomical structure outlined above is a subsumptive containment hierarchy. Using again the example of Linnaean taxonomy, it can be seen that an object that is part of the level ''Mammalia'' "is a" member of the level ''Animalia''; more specifically, a human "is a" primate, a primate "is a" mammal, and so on. A subsumptive hierarchy can also be defined abstractly as a hierarchy of "
concept Concepts are defined as abstract ideas. They are understood to be the fundamental building blocks of the concept behind principles, thoughts and beliefs. They play an important role in all aspects of cognition. As such, concepts are studied by ...
s". For example, with the Linnaean hierarchy outlined above, an entity name like ''Animalia'' is a way to group all the species that fit the
conceptualization In information science a conceptualization is an abstract simplified view of some selected part of the world, containing the objects, concepts, and other entities that are presumed of interest for some particular purpose and the relationships betw ...
of an animal.


Compositional containment hierarchy

A ''compositional'' containment hierarchy is an ordering of the parts that make up a system—the system is "composed" of these parts. Most engineered structures, whether natural or artificial, can be broken down in this manner. The compositional hierarchy that every person encounters at every moment is the hierarchy of life. Every person can be reduced to organ systems, which are composed of organs, which are composed of tissues, which are composed of
cells Cell most often refers to: * Cell (biology), the functional basic unit of life Cell may also refer to: Locations * Monastic cell, a small room, hut, or cave in which a religious recluse lives, alternatively the small precursor of a monastery w ...
, which are composed of
molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and b ...
s, which are composed of
atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, a ...
s. In fact, the last two levels apply to all matter, at least at the macroscopic scale. Moreover, each of these levels inherit all the properties of their children. In this particular example, there are also '' emergent properties''—functions that are not seen at the lower level (e.g., cognition is not a property of
neuron A neuron, neurone, or nerve cell is an electrically excitable cell that communicates with other cells via specialized connections called synapses. The neuron is the main component of nervous tissue in all animals except sponges and placozoa ...
s but is of the
brain A brain is an organ (biology), organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. It is located in the head, usually close to the sensory organs for senses such as Visual perception, vision. I ...
)—and a scalar quality (molecules are bigger than atoms, cells are bigger than molecules, etc.). Both of these concepts commonly exist in compositional hierarchies, but they are not a required general property. These ''level hierarchies'' are characterized by bi-directional causation. ''Upward causation'' involves lower-level entities causing some property of a higher level entity; children entities may interact to yield parent entities, and parents are composed at least partly by their children. ''
Downward causation In philosophy, downward causation is a causal relationship from higher levels of a system to lower-level parts of that system: for example, mental events acting to cause physical events. The term was originally coined in 1974 by the philosopher and ...
'' refers to the effect that the incorporation of entity ''x'' into a higher-level entity can have on ''xs properties and interactions. Furthermore, the entities found at each level are '' autonomous''.


Contexts and applications

Kulish (2002) suggests that almost every system of organization which humans apply to the world is arranged hierarchically. Some conventional definitions of the terms "nation" and "government" suggest that every
nation A nation is a community of people formed on the basis of a combination of shared features such as language, history, ethnicity, culture and/or society. A nation is thus the collective identity of a group of people understood as defined by th ...
has a government and that every government is hierarchical. Sociologists can analyse socioeconomic systems in terms of stratification into a social hierarchy (the social stratification of societies), and all systematic classification schemes ( taxonomies) are hierarchical. Most organized religions, regardless of their internal governance structures, operate as a hierarchy under deities and priesthoods. Many
Christian denomination A Christian denomination is a distinct Religion, religious body within Christianity that comprises all Church (congregation), church congregations of the same kind, identifiable by traits such as a name, particular history, organization, leadersh ...
s have an
autocephalous Autocephaly (; from el, αὐτοκεφαλία, meaning "property of being self-headed") is the status of a hierarchical Christian church whose head bishop does not report to any higher-ranking bishop. The term is primarily used in Eastern O ...
ecclesiastical hierarchy The hierarchy of the Catholic Church consists of its bishops, priests, and deacons. In the ecclesiological sense of the term, "hierarchy" strictly means the "holy ordering" of the Church, the Body of Christ, so to respect the diversity of gif ...
of
leadership Leadership, both as a research area and as a practical skill, encompasses the ability of an individual, group or organization to "lead", influence or guide other individuals, teams, or entire organizations. The word "leadership" often gets v ...
. Families can be viewed as hierarchical structures in terms of
cousinship Most generally, in the lineal kinship system used in the English-speaking world, a cousin is a type of familial relationship in which two relatives are two or more familial generations away from their most recent common ancestor. Commonly, ...
(e.g., first cousin once removed, second cousin, etc.), ancestry (as depicted in a
family tree A family tree, also called a genealogy or a pedigree chart, is a chart representing family relationships in a conventional tree structure. More detailed family trees, used in medicine and social work, are known as genograms. Representations ...
) and
inheritance Inheritance is the practice of receiving private property, titles, debts, entitlements, privileges, rights, and obligations upon the death of an individual. The rules of inheritance differ among societies and have changed over time. Of ...
(
succession Succession is the act or process of following in order or sequence. Governance and politics *Order of succession, in politics, the ascension to power by one ruler, official, or monarch after the death, resignation, or removal from office of ...
and heirship). All the requisites of a well-rounded life and lifestyle can be organized using Maslow's hierarchy of human needs - according to Maslow's hierarchy of human needs. Learning steps often follow a hierarchical scheme—to master
differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, ...
s one must first learn
calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizati ...
; to learn calculus one must first learn elementary algebra; and so on.
Nature Nature, in the broadest sense, is the physical world or universe. "Nature" can refer to the phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. Although humans are ...
offers hierarchical structures, as numerous schemes such as Linnaean taxonomy, the organization of life, and biomass pyramids attempt to document. Hierarchies are so infused into daily life that they are viewed as trivial. While the above examples are often clearly depicted in a hierarchical form and are classic examples, hierarchies exist in numerous systems where this branching structure is not immediately apparent. For example, most postal-code systems are hierarchical. Using the Canadian postal code system as an example, the top level's binding concept, the "postal district", consists of 18 objects (letters). The next level down is the "zone", where the objects are the digits 0–9. This is an example of an
overlapping hierarchy A hierarchy (from Greek: , from , 'president of sacred rites') is an arrangement of items (objects, names, values, categories, etc.) that are represented as being "above", "below", or "at the same level as" one another. Hierarchy is an important ...
, because each of these 10 objects has 18 parents. The hierarchy continues downward to generate, in theory, 7,200,000 unique codes of the format ''A0A 0A0'' (the second and third letter positions allow 20 objects each). Most library classification systems are also hierarchical. The Dewey Decimal System is infinitely hierarchical because there is no finite bound on the number of digits can be used after the decimal point. See also Wikipedia article.


Organizations

Organization An organization or organisation (Commonwealth English; see spelling differences), is an entity—such as a company, an institution, or an association—comprising one or more people and having a particular purpose. The word is derived f ...
s can be structured as a dominance hierarchy. In an organizational hierarchy, there is a single person or group with the most power or authority, and each subsequent level represents a lesser authority. Most organizations are structured in this manner, including governments, companies, armed forces, militia and organized religions. The units or persons within an organization may be depicted hierarchically in an organizational chart. In a reverse hierarchy, the conceptual pyramid of authority is turned upside-down, so that the apex is at the bottom and the base is at the top. This mode represents the idea that members of the higher rankings are responsible for the members of the lower rankings.


Biology

Empirically, when we observe in nature a large proportion of the (complex) biological systems, they exhibit hierarchic structure. On theoretical grounds we could expect complex systems to be hierarchies in a world in which complexity had to evolve from simplicity.
System A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and express ...
hierarchies analysis performed in the 1950s, laid the empirical foundations for a field that would become, from the 1980s, hierarchical ecology. The theoretical foundations are summarized by
thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws ...
. When
biological systems A biological system is a complex network which connects several biologically relevant entities. Biological organization spans several scales and are determined based different structures depending on what the system is. Examples of biological syst ...
are modeled as physical systems, in the most general abstraction, they are thermodynamic open systems that exhibit self-organised behavior, and the set/subset relations between dissipative structures can be characterized in a hierarchy. Other hierarchical representations related to biology include ecological pyramids which illustrate energy flow or trophic levels in ecosystems, and taxonomic hierarchies, including the
Linnean classification Linnaean taxonomy can mean either of two related concepts: # The particular form of biological classification (taxonomy) set up by Carl Linnaeus, as set forth in his '' Systema Naturae'' (1735) and subsequent works. In the taxonomy of Linnaeus ...
scheme and phylogenetic trees that reflect inferred patterns of evolutionary relationship among living and extinct species.


Computer-graphic imaging

CGI and computer-animation
programs Program, programme, programmer, or programming may refer to: Business and management * Program management, the process of managing several related projects * Time management * Program, a part of planning Arts and entertainment Audio * Progra ...
mostly use hierarchies for models. On a 3D model of a
human Humans (''Homo sapiens'') are the most abundant and widespread species of primate, characterized by bipedalism and exceptional cognitive skills due to a large and complex brain. This has enabled the development of advanced tools, cultu ...
for example, 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 pattern is used in modeling and animation for almost everything built as a 3D digital model.


Linguistics

Many grammatical theories, such as phrase-structure grammar, involve hierarchy. Direct–inverse languages such as Cree and Mapudungun distinguish subject and object on
verb A verb () is a word ( part of speech) that in syntax generally conveys an action (''bring'', ''read'', ''walk'', ''run'', ''learn''), an occurrence (''happen'', ''become''), or a state of being (''be'', ''exist'', ''stand''). In the usual descr ...
s not by different subject and object markers, but via a hierarchy of persons. In this system, the three (or four with
Algonquian languages The Algonquian languages ( or ; also Algonkian) are a subfamily of indigenous American languages that include most languages in the Algic language family. The name of the Algonquian language family is distinguished from the orthographically simi ...
) persons occur in a hierarchy of salience. To distinguish which is subject and which object, ''inverse markers'' are used if the object outranks the subject. On the other hand, languages include a variety of phenomena that are not hierarchical. For example, the relationship between a pronoun and a prior noun-phrase to which it refers commonly crosses grammatical boundaries in non-hierarchical ways.


Music

The structure of a musical 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 Alfred Whitford (Fred) Lerdahl (born March 10, 1943, in Madison, Wisconsin) is the Fritz Reiner Professor Emeritus of Musical Composition at Columbia University, and a composer and music theorist best known for his work on musical grammar an ...
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 In Schenkerian analysis, the fundamental structure (german: Ursatz) describes the structure of a tonal work as it occurs at the most remote (or " background") level and in the most abstract form. A basic elaboration of the tonic triad, it consi ...
, 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 Form is the shape, visual appearance, or configuration of an object. In a wider sense, the form is the way something happens. Form also refers to: *Form (document), a document (printed or electronic) with spaces in which to write or enter data * ...
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.


Examples of other applications


Information-based

* Library classification ** Dewey Decimal Classification


City planning-based

* Green transport hierarchy * Roads ** Streets * Settlement hierarchy ** As of 2010 ** As of 2100 (estimate according to Doxiadis, 1968)


Linguistics-oriented

* Language family tree * Levels of adequacy for evaluating grammars * Direct–inverse languages *
Structural linguistics Structural linguistics, or structuralism, in linguistics, denotes schools or theories in which language is conceived as a self-contained, self-regulating semiotic system whose elements are defined by their relationship to other elements within t ...
** Parse tree ** Formal grammars ** Abstract syntax tree * Evolution of basic color terminology in languages


Power- or authority-based

* Aristocratic hierarchies ** In
Europe Europe is a large peninsula conventionally considered a continent in its own right because of its great physical size and the weight of its history and traditions. Europe is also considered a Continent#Subcontinents, subcontinent of Eurasia ...
** In
China China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's List of countries and dependencies by population, most populous country, with a Population of China, population exceeding 1.4 billion, slig ...
* Ecclesiastical hierarchies **
Catholic Church hierarchy The hierarchy of the Catholic Church consists of its bishops, priests, and deacons. In the ecclesiological sense of the term, "hierarchy" strictly means the "holy ordering" of the Church, the Body of Christ, so to respect the diversity of gifts ...
** LDS Church hierarchy ** Kimbanguist Church hierarchy ** Raëlism Church hierarchy ** see also autocephaly * Prussian three-class franchise * Political party hierarchies **
Nazi Party The Nazi Party, officially the National Socialist German Workers' Party (german: Nationalsozialistische Deutsche Arbeiterpartei or NSDAP), was a far-right political party in Germany active between 1920 and 1945 that created and supported t ...
(''pace'' overlapping fields Compare: ) *** SS *** Hierarchy of subdivisions within the Gau ** Communist Party of the Soviet Union **
Chinese Communist Party The Chinese Communist Party (CCP), officially the Communist Party of China (CPC), is the founding and sole ruling party of the People's Republic of China (PRC). Under the leadership of Mao Zedong, the CCP emerged victorious in the Chinese Ci ...
* Chain of command ** Military ranks ** Military units **
U.S. Military Combatant Commands A unified combatant command (CCMD), also referred to as a combatant command, is a joint military command of the United States Department of Defense that is composed of units from two or more service branches of the United States Armed Forces, ...
* Intraspecial dominance ** Pecking order * Social classes ** Caste system in India ** Hierarchical structure of Feudal Japan ** White racist hierarchy ** Hierarchy of Exclusion (Ender's Game)


Value-related

* Hierarchy of genres in art * Evidence * Human needs * Precious substances * Judicial hierarchy of social values


Perception-based

* Color wheel **
Primary colors A set of primary colors or primary colours (see spelling differences) consists of colorants or colored lights that can be mixed in varying amounts to produce a gamut of colors. This is the essential method used to create the perception of a b ...
***
Secondary colors A secondary color is a color made by mixing of two primary colors in a given color space. Additive secondaries Light (RGB) For the human eye, good primary colors of light are red, green, and blue. Combining lights of these colors produces ...
**** Tertiary colors


History-oriented

* Three-age system * Cyclic theory of civilization **
Oswald Spengler Oswald Arnold Gottfried Spengler (; 29 May 1880 – 8 May 1936) was a German historian and philosopher of history whose interests included mathematics, science, and art, as well as their relation to his organic theory of history. He is best k ...
**
Arnold J. Toynbee Arnold Joseph Toynbee (; 14 April 1889 – 22 October 1975) was an English historian, a philosopher of history, an author of numerous books and a research professor of international history at the London School of Economics and King's Colleg ...
* Spiral dynamics


Science-focussed

* Hierarchy of organization within the Universe *
Star systems A star system or stellar system is a small number of stars that orbit each other, bound by gravitational attraction. A large group of stars bound by gravitation is generally called a ''star cluster'' or ''galaxy'', although, broadly speaking ...
* Biological classification * Biological organization * Phylogenetic tree * Evolutionary development * Hierarchy of ecological georegions


Technology-based

* Memory hierarchy ** Cache hierarchy * Clusters * Class constructs * Data organization **
Hierarchical query A hierarchical query is a type of SQL query that handles hierarchical model data. They are special cases of more general recursive fixpoint queries, which compute transitive closures. In standard SQL:1999 hierarchical queries are implemented ...
* Data storage ** Computer files (Macintosh) * Devices * IP addresses *
Memory Memory is the faculty of the mind by which data or information is encoded, stored, and retrieved when needed. It is the retention of information over time for the purpose of influencing future action. If past events could not be remember ...
** Virtual memory allocation * Networks * Radio cells * States (configurations) * Web addresses *
Structure A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such a ...
** Data Structure *
Inheritance (object-oriented programming) In object-oriented programming, inheritance is the mechanism of basing an object or class upon another object ( prototype-based inheritance) or class ( class-based inheritance), retaining similar implementation. Also defined as deriving new clas ...


Religion-related

* Levels of consciousness **
Chakras Chakras (, ; sa , text=चक्र , translit=cakra , translit-std=IAST , lit=wheel, circle; pi, cakka) are various focal points used in a variety of ancient meditation practices, collectively denominated as Tantra, or the esoteric or ...
** Great chain of being ** G.I. Gurdjieff ** Timothy Leary * Levels of spiritual development ** In Theravada Buddhism ** In Mahayana Buddhism ** In
Theosophy Theosophy is a religion established in the United States during the late 19th century. It was founded primarily by the Russian Helena Blavatsky and draws its teachings predominantly from Blavatsky's writings. Categorized by scholars of religion a ...
* Ages in the evolution of society ** In
Astrology Astrology is a range of divinatory practices, recognized as pseudoscientific since the 18th century, that claim to discern information about human affairs and terrestrial events by studying the apparent positions of celestial objects. Di ...
** In Hellenism (the Ancient Greek Religion) ** Dispensations in Protestantism ** Dispensations in Mormonism * Degrees of communion between various Christian churches * UFO religions ** Command hierarchy of the ''Ashtar Galactic Command'' flying saucer fleet * Deities ** In Japanese Buddhism ** In
Theosophy Theosophy is a religion established in the United States during the late 19th century. It was founded primarily by the Russian Helena Blavatsky and draws its teachings predominantly from Blavatsky's writings. Categorized by scholars of religion a ...
* Angels ** In
Christianity Christianity is an Abrahamic monotheistic religion based on the life and teachings of Jesus of Nazareth. It is the world's largest and most widespread religion with roughly 2.38 billion followers representing one-third of the global popula ...
** In
Islam Islam (; ar, ۘالِإسلَام, , ) is an Abrahamic monotheistic religion centred primarily around the Quran, a religious text considered by Muslims to be the direct word of God (or '' Allah'') as it was revealed to Muhammad, the ...
** In
Judaism Judaism ( he, ''Yahăḏūṯ'') is an Abrahamic, monotheistic, and ethnic religion comprising the collective religious, cultural, and legal tradition and civilization of the Jewish people. It has its roots as an organized religion in th ...
*** Kabbalistic ** In Zoroastrianism * Devils and Demons **
Devils A devil is the personification of evil as it is conceived in many and various cultures and religious traditions. Devil or Devils may also refer to: * Satan * Devil in Christianity * Demon * Folk devil Art, entertainment, and media Film and ...
** Demons * Hells ** In Catholicism (Nine Levels of Hell) ** In Buddhism (Sixteen Levels of Hell) * Religions in society * (organizational hierarchies are listed under )


Methods using hierarchy


Criticisms

In the work of diverse theorists such as William James (1842 to 1910), Michel Foucault (1926 to 1984) and
Hayden White Hayden V. White (July 12, 1928 – March 5, 2018) was an American historian in the tradition of literary criticism, perhaps most famous for his work '' Metahistory: The Historical Imagination in Nineteenth-Century Europe'' (1973/2014). Career ...
(1928 to 2018), important critiques of hierarchical
epistemology Epistemology (; ), or the theory of knowledge, is the branch of philosophy concerned with knowledge. Epistemology is considered a major subfield of philosophy, along with other major subfields such as ethics, logic, and metaphysics. Epi ...
are advanced. James famously asserts in his work
Radical Empiricism Radical empiricism is a philosophical doctrine put forth by William James. It asserts that experience includes both particulars and relations between those particulars, and that therefore both deserve a place in our explanations. In concrete terms: ...
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. Entities that stand in hierarchical arrangements are animals, humans, plants, etc.


Ethics, behavioral psychology, philosophies of identity

In
ethics Ethics or moral philosophy is a branch of philosophy that "involves systematizing, defending, and recommending concepts of right and wrong behavior".''Internet Encyclopedia of Philosophy'' The field of ethics, along with aesthetics, concer ...
, various virtues are enumerated and sometimes organized hierarchically according to certain brands of
virtue theory Virtue ethics (also aretaic ethics, from Greek ἀρετή arete_(moral_virtue).html"_;"title="'arete_(moral_virtue)">aretḗ''_is_an_approach_to_ethics_that_treats_the_concept_of_virtue.html" ;"title="arete_(moral_virtue)">aretḗ''.html" ;" ...
. In some 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. There is a hierarchy of activities in human life: productive activity serves or is guided by the moral life; the moral life is guided by practical reason; practical reason (used in moral and political life) serves contemplative reason (whereby we contemplate God). Practical reason sets aside time and resources for contemplative reason.


See also


Structure-related concepts

''(For example, in )'' * Is-a **
Hypernymy In linguistics, semantics, general semantics, and ontologies, hyponymy () is a semantic relation between a hyponym denoting a subtype and a hypernym or hyperonym (sometimes called umbrella term or blanket term) denoting a supertype. In other wo ...
(and
supertype In programming language theory, subtyping (also subtype polymorphism or inclusion polymorphism) is a form of type polymorphism in which a subtype is a datatype that is related to another datatype (the supertype) by some notion of substitutability ...
) ** Hyponymy (and subtype) * Has-a ** Holonymy ** Meronymy


Footnotes


Further reading

* * * * * * * * * ** Also includes full copies of: ** **


External links

*
Principles and annotated bibliography of hierarchy theory

Summary of the Principles of Hierarchy Theory
— S.N. Salthe {{Authority control Patterns Structure Political culture