Hierarchy
A hierarchy (from Greek: ἱεραρχία, hierarkhia, 'rule of a high priest', from hierarkhes, 'president of sacred rites') is an arrangement of items (objects, names, values, categories, etc.)
This is akin to two co-workers or colleagues; each reports to a common superior, but they have the same relative amount of authority.
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.
[2] Branching hierarchies are present within numerous systems, including organizations and classification schemes.
For example, diamonds and graphite are flat hierarchies of numerous carbon atoms that can be further decomposed into subatomic particles.
[4] The Greek term hierarchia means 'rule of a high priest',[5] from hierarches (ἱεράρχης, 'president of sacred rites, high-priest')[6] and that from hiereus (ἱερεύς, 'priest')[7] and arche (ἀρχή, 'first place or power, rule').
Phylogenetic trees, charts showing the structure of § Organizations, and playoff brackets in sports are often illustrated this way.
For more complicated hierarchies, the stair structure represents hierarchical relationships through the use of visual stacking.
Mathematically, in its most general form, a hierarchy is a partially ordered set or poset.
The general concept is both demonstrated and mathematically formulated in the following example: A square can always also be referred to as a quadrilateral, polygon or shape.
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.
A general example of a containment hierarchy is demonstrated in class inheritance in object-oriented programming.
[14] A subsumptive containment hierarchy is a classification of object classes from the general to the specific.
[16] 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 of an animal.
Kulish (2002) suggests that almost every system of organization which humans apply to the world is arranged hierarchically.
[21] Most organized religions, regardless of their internal governance structures, operate as a hierarchy under deities and priesthoods.
Nature offers hierarchical structures, as numerous schemes such as Linnaean taxonomy, the organization of life, and biomass pyramids attempt to document.
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).
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.
Empirically, when we observe in nature a large proportion of the (complex) biological systems, they exhibit hierarchic structure.
[27] System hierarchies analysis performed in the 1950s,[28][29] laid the empirical foundations for a field that would become, from the 1980s, hierarchical ecology.
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 scheme and phylogenetic trees that reflect inferred patterns of evolutionary relationship among living and extinct species.
For example, the relationship between a pronoun and a prior noun-phrase to which it refers commonly crosses grammatical boundaries in non-hierarchical ways.
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 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 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.
In the work of diverse theorists such as William James (1842 to 1910), Michel Foucault (1926 to 1984) and Hayden White (1928 to 2018), 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.
