Hierarchy

In general, a hierarchy is a tree- or pyramid-like organization of a group of entities. See the illustration for an example. Different fields use the word in slightly different ways, but a particular definition, which the article will attempt first, captures the core of almost all uses.

General considerations (informal)

A precise, mathematical definition of hierarchy will be given in the next section. This section will try to explore the ideas behind that more compact definition.

A hierarchy is based on an asymmetrical relationship, such as "is the boss of", "is part of", or "is better than". Such relationships are "asymmetrical" in the sense that if they "work one way", they don't "work the other". For example, if Sally is the boss of Jim, then Jim is not the boss of Sally. When two nodes are related, one is designated the "superior" (or sometimes the "parent") and the other the "subordinate" (or sometimes the "child"). In the intuitive case of the "is the boss of" relation, the boss is the superior and the employee is the subordinate.

A hierarchy's asymmetrical relationship can link entities in one of three ways: directly, indirectly, or not at all. The illustration shows a direct link between the craft and culture sections; the craft section is directly linked to the culture section by the "contains" relationship. This is akin to how your boss in directly in charge of you. In contrast, the illustration shows an indirect link between craft and encyclopedia; the craft section is only "contained" by the encyclopedia as a whole by virtue of being "contained" by the culture section. This is akin to how the CEO of a company is in charge of a factory worker only via middle management. Finally, there is effectively no link between the art and the craft sections; neither section contains the other. This is akin to two co-workers, neither of whom is the other's boss.

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Every member is reachable from any other by following the relationship in either direction, but there is no way of coming back to a particular member by always following the relationship in the same direction.

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General considerations (formal)

A hierarchy can thus be represented as a connected directed acyclic graph.

Examples of reasoning with hierarchies

Many aspects of the world are analyzed, arguably fruitfully, from a hierarchical perspective. Science provides the following examples:

• In biology, organisms are commonly described as an assembly of parts (organs) which are themselves assemblies of yet smaller parts, and so on.
• In physics, the standard model decomposes bodies down to their smallest particle components.
• In linguistics, words or sentences are often broken down into hierarchies of parts and wholes.

In all of these examples, the asymmetric relationship is "is composed of".

Many human organizations, such as businesses, churches, armies and political movements are structured hierarchically, at least officially; commonly superiors, called bosses, have more power than their subordinates. Thus the asymmetrical relationship might be "has power over". (Some analysists question whether power "really" works as the traditional organizational chart indicates, however.)

Feminists talk about a hierarchy of gender, in which a culture sees males or masculine traits as superior to females or feminine traits. In the terms above, these feminists present us a hierarchy of only two nodes, "masculine" and "feminine", connected by the asymmetrical relationship "is valued more highly by society". An example of this usage:

The hierarchical nature of the dualism - the systematic devaluation of females and whatever is metaphorically understood as "feminine" - is what I identify as sexism. (Nelson 1992, p. 106)

Note that when feminists and other social critics use the word hierarchy, they usually hope to evoke negative connotations; hierarchy, for them, is a bad thing. In these contexts, hierarchy and power structure are basically synonyms.

Hierarchy is often used to control complexity in engineering endeavors. In object-oriented programming, for example, classes are organized hierarchically; the relationship between two related classes is called inheritance.

Misc

The Wikipedia community is remarkable for being not overtly hierarchically structured, as no contributor possesses inherently higher standing than another. However, some would note that although there is no explicit hierarchy there are social norms which make contributions unequal. Some contributors have more influence because their edits command higher respect and administrative privileges.

Those who frequent Wikis might label Wikipedia's organization "wikiarchical".

The concept of hierarchy qualifies as interdisciplinary.

History of the word

Originally hierarchy means rule by priests. Other senses of the word ultimately evolved from that one. In "hierarchical" churches, such as the Catholic and Orthodox churches, there are priests and bishops of various ranks, and so the association with rankings came about.

External link

Principles and annotated bibliography of hierarchy theory (http://www.isss.org/hierarchy.htm)

Generalizations: Structure

Specializations:

• purpose: hierarchical organization
• structural properties: hierarchical tree structure, rooted hierarchy
• nature of the hierarchical relationship: part-whole hierarchy[?], containment hierarchy, inheritance hierarchy[?], responsibility hierarchy[?], control hierarchy[?]

Relevant examples:

• Biology: Linnaean taxonomy
• Genealogy: genealogy tree[?]
• Linguistics: Chomsky hierarchy
• Psychology: Maslow hierarchy of needs

References

• Julie Nelson (1992). "Gender, Metaphor and the Definition of Economics". Economics and Philosophy, 8:103-125.