Editing Hierarchy (section)

==Contexts and applications==
<!--if you change this section's title, please also change the wikilinks throughout the article that link to it! -->
Kulish (2002) suggests that almost every system of organization which humans apply to the world is arranged hierarchically.<ref name="electrodynamics">{{cite book|title= Hierarchical Methods: Hierarchy and hierarchical asymptotic methods in electrodynamics|last= Kulish|first= V. V.|isbn= 1-4020-0757-4|year= 2002 |volume= 1|publisher= [[Springer Science+Business Media|Springer]]|pages= xvii–xx; 49–71}}</ref>{{request quotation|date=November 2021}} Some conventional definitions of the terms "nation"<ref>{{Cite book|contribution=nation|title=Compact Oxford English Dictionary|contribution-url=http://www.askoxford.com/concise_oed/nation?view=uk|isbn=978-0-19-861022-9|year=1991|title-link=Oxford English Dictionary|last1=Soanes|first1=Catherine|last2=Hawker|first2=Sara|publisher=Oxford University Press |access-date=2009-10-08|archive-date=2007-09-29|archive-url=https://web.archive.org/web/20070929230000/http://www.askoxford.com/concise_oed/nation?view=uk|url-status=dead}}</ref>{{failed verification|date=November 2021}} and "government"<ref>{{Cite book|contribution= government|title= Compact Oxford English Dictionary|contribution-url= http://www.askoxford.com/concise_oed/government?view=uk|isbn= 978-0-19-861022-9|year= 1991|title-link= Oxford English Dictionary|last1= Soanes|first1= Catherine|last2= Hawker|first2= Sara|publisher= Oxford University Press|access-date= 2009-10-08|archive-date= 2007-09-29|archive-url= https://web.archive.org/web/20070929082941/http://www.askoxford.com/concise_oed/government?view=uk|url-status= dead}}</ref>{{failed verification|date=November 2021}} suggest that every [[nation]] 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 name|systematic classification schemes]] ([[Taxonomy (general)|taxonomies]]) are hierarchical.<ref>{{Cite web |url=https://study.com/academy/lesson/social-stratification-definition-theories-examples.html |access-date=2022-06-24 |website=study.com |title=Social Stratification &#124; Overview, Theories & Examples - Video & Lesson Transcript |archive-date=2022-06-24 |archive-url=https://web.archive.org/web/20220624105232/https://study.com/academy/lesson/social-stratification-definition-theories-examples.html |url-status=live }}</ref> Most [[organized religion]]s, regardless of their internal governance structures, operate as a hierarchy under [[deities]] and [[priesthood]]s. Many [[Christian denomination]]s have an [[autocephalous]] [[Ecclesiastical polity|ecclesiastical hierarchy]] of [[leadership]]. Families can be viewed as hierarchical structures in terms of [[cousinship]] (e.g., first cousin once removed, second cousin, etc.), [[ancestry]] (as depicted in a [[family tree]]) and [[inheritance]] ([[order of succession|succession]] and [[heir]]ship). All the requisites of a well-rounded life and [[lifestyle (sociology)|lifestyle]] can be organized using [[Maslow's hierarchy of needs|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]]s one must first learn [[calculus]]; to learn calculus one must first learn [[elementary algebra]]; and so on. [[Nature]] offers hierarchical structures, as numerous schemes such as [[Linnaean taxonomy]], the [[biological organisation|organization of life]], and [[biomass pyramid]]s attempt to document.<ref>
{{cite book
 |last1                = Dawkins
 |first1               = Richard
 |author-link1         = Richard Dawkins
 |editor-last1         = Bateson
 |editor-first1        = P. P. G.
 |editor-link1         = Patrick Bateson
 |editor-last2         = Hinde
 |editor-first2        = R. A.
 |editor-link2         = Robert Hinde
 |chapter              = Hierarchical organization: a candidate principle for ethology
 |title                = Growing Points in Ethology: based on a conference sponsored by St. John's College and King's College, Cambridge
 |date = 7 October 1976
 |url                  = https://books.google.com/books?id=xIg8AAAAIAAJ
 |location             = Cambridge
 |publisher            = Cambridge University Press
 |publication-date     = 1976
 |page                 = 
 |isbn                 = 9780521212878
 |access-date          = 26 November 2021
 |quote                = 
}} 
</ref>{{request quotation|date=November 2021}}<ref>
{{cite book
 |last1                = Kulish
 |first1               = Viktor Vasylevych
 |author-link1         = 
 |orig-date            = 2002
 |title                = Hierarchical Methods: Hierarchy and Hierarchical Asymptotic Methods in Electrodynamics
 |url                  = https://books.google.com/books?id=0RXnBwAAQBAJ
 |series               = Volume 123 of Fundamental Theories of Physics
 |date = 11 April 2006
 |volume               = 1
 |location             = New York
 |publisher            = Springer Science & Business Media
 |publication-date     = 2006
 |page                 = xviii
 |isbn                 = 9780306480614
 |access-date          = 26 November 2021
 |quote                = At the same time, it is a trivial phenomenon of everyday life, too. Indeed, one can be convinced that there is a hierarchy in everyday life everywhere. We can affirm once more that a person lives in a completely hierarchical world.
}} 
</ref>

While the above examples are often{{quantify|date=November 2021}} 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|postal-code]] systems are hierarchical. Using the [[Postal codes in Canada|Canadian postal code system]] as an example, the top level's binding concept, the [[forward sortation area|"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 [[#Degree_of_branching|overlapping hierarchy]], 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 Classification|Dewey Decimal System]] is infinitely hierarchical because there is no finite bound on the number of digits can be used after the decimal point.<ref name="Dewey">{{cite web|title=Tracking Nuclear Sources|date=May–June 2009|last= Walker |first= Randy|publisher=wellservicingmagazine.com|pages=28–30|url= http://wellservicingmagazine.com/sites/default/files/pdfmag/WSM_MAYJUN09.PDF}}{{dead link|date= November 2017 |bot=InternetArchiveBot |fix-attempted=yes}}</ref>

[[File:Organizational chart.svg|thumb|200px|A simple military [[hierarchical organization|organizational hierarchy]] depicted in the form of a [[tree structure|tree]]. Diagrams like this exemplify [[organizational chart]]s.]]

===Organizations===
{{Main|Organizational structure| Hierarchical organization}}

[[Organization]]s can be structured as a [[dominance hierarchy]]. In an organizational hierarchy, there is a single person or group with the most [[power (philosophy)|power]] or [[authority]], and each subsequent level represents a lesser authority. Most organizations are structured in this manner,<ref>{{Cite web |url=https://study.com/academy/lesson/organizational-chart-and-hierarchy-definition-examples.html |access-date=2022-06-24 |website=study.com |title=Organizational Chart and Hierarchy: Definition & Examples - Video & Lesson Transcript |archive-date=2022-06-24 |archive-url=https://web.archive.org/web/20220624105529/https://study.com/academy/lesson/organizational-chart-and-hierarchy-definition-examples.html |url-status=live }}</ref> including [[Forms of government|governments]], [[Company|companies]], [[Military|armed forces]], [[militia]] and [[organized religion]]s. The units or persons within an organization may be depicted hierarchically in an [[organizational chart]].

In a [[reverse hierarchy]], the conceptual [[pyramid (geometry)|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 ===
{{Main|Biological organisation#Fundamentals}}

Empirically, when we observe in nature a large proportion of the (complex) biological systems, they exhibit hierarchic structure.<ref>{{Cite journal |last=Simon |first=Herbert A. |date=1962 |title=The Architecture of Complexity |url=https://www.jstor.org/stable/985254 |journal=Proceedings of the American Philosophical Society |volume=106 |issue=6 |pages=467–482 |jstor=985254 |issn=0003-049X |access-date=2022-06-24 |archive-date=2022-06-24 |archive-url=https://web.archive.org/web/20220624110921/https://www.jstor.org/stable/985254 |url-status=live }}</ref> On theoretical grounds we could expect complex systems to be hierarchies in a world in which complexity had to evolve from simplicity.<ref>{{Cite web |title=Artificial Intelligence - foundations of computational agents -- 2 Agent Architectures and Hierarchical Control |url=https://artint.info/html/ArtInt_33.html |access-date=2022-06-24 |website=artint.info |archive-date=2022-07-04 |archive-url=https://web.archive.org/web/20220704035951/http://artint.info/html/ArtInt_33.html |url-status=live }}</ref> [[Systems theory|System]] hierarchies analysis performed in the 1950s,<ref>{{harvnb|Evans|1951}}</ref><ref>{{harvnb|Evans|1956}}</ref> laid the empirical foundations for a [[Branches of science|field]] that would become, from the 1980s, '''hierarchical ecology'''.<ref>{{harvnb|Margalef|1975}}</ref><ref>{{harvnb|O'Neill|1986}}</ref><ref>{{harvnb|Wicken|Ulanowicz|1988}}</ref><ref>{{harvnb|Pumain|2006}}</ref><ref>{{harvnb|Jordan|Jørgensen|2012}}</ref>

The theoretical foundations are summarized by [[thermodynamics]].
When [[biological systems]] are modeled as [[physical system]]s, in the most general abstraction, they are [[Thermodynamic system#Open system|thermodynamic open systems]] that exhibit [[self-organisation|self-organised]] behavior, and the [[Set theory|set/subset]] relations between [[dissipative structures]] can be characterized{{by whom|date=November 2021}} in a hierarchy.

Other hierarchical representations related to biology include [[ecological pyramids]] which illustrate energy flow or [[trophic levels]] in [[ecosystems]], and [[Taxonomy (general)|taxonomic]] hierarchies, including the [[Linnean classification]] scheme and [[phylogenetic trees]] that reflect inferred patterns of evolutionary relationship among living and extinct species.

===Computer-graphic imaging===
{{Main|3D modeling}}
[[Computer-generated imagery|CGI]] and [[computer animation|computer-animation]] [[computer program|programs]] mostly use hierarchies for models. On a [[3D computer graphics|3D]] model of a [[human]] 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 [[3D modeling|modeling]] and [[animation]] for almost everything built as a 3D [[Digital data|digital]] model.

===Linguistics===
Many grammatical theories, such as [[phrase-structure grammar]], involve hierarchy.

[[Direct–inverse language]]s such as [[Cree language|Cree]] and [[Mapudungun language|Mapudungun]] distinguish subject and object on [[verb]]s not by different subject and object markers, but via a hierarchy of persons.

In this system, the three (or four with [[Algonquian languages]]) persons occur in a hierarchy of [[salience (language)|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|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)|pitches]] and [[Musical form|form]] of [[Tonality|tonal]] music are organized hierarchically, all pitches deriving their importance from their relationship to a [[Tonic (music)|tonic]] key, and secondary themes in other  [[Key signature|keys]] are brought back to the tonic in a recapitulation of the primary theme.

=== Examples of other applications ===
<!-- This section is for direct examples of a hierarchical system ONLY, and only ones that have not been summarized above. Methodologies belong in the appropriate section below. Related concepts are listed under the "See also" section. If you are uncertain where a link belongs, place it in the "See also" section. HINT: If you can't easily say what it's a hierarchy OF, it doesn't belong here (but that doesn't imply that if you can say what its a hierarchy of, it belongs here). -->

{{col-begin}}
{{col-3}}
==== Information-based ====
<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "information-based hierarchies"-->
* [[Library classification]]
** [[Dewey Decimal Classification]]
{{col-3}}
==== City planning-based ====
<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "city planning-based hierarchies"-->
* [[Green transport hierarchy]]
* [[Hierarchy of roads|Roads]]
** [[Street hierarchy|Streets]]
* [[Settlement hierarchy]]
** [[Settlement hierarchy#Example of a settlement hierarchy|As of 2010]]
** [[Ekistic units|As of 2100 (estimate according to Doxiadis, 1968)]]
{{col-3}}

==== Linguistics-oriented ====
<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "linguistics-oriented hierarchies"-->
* [[Tree model|Language family tree]]
* [[Levels of adequacy|Levels of adequacy for evaluating grammars]]
* [[Direct–inverse language]]s
* [[Structural linguistics]]
** [[Parse tree]]
** [[Formal grammar]]s
** [[Abstract syntax tree]]
* [[Color terms#Basic color terms|Evolution of basic color terminology in languages]]
{{col-end}}

{{col-begin}}
{{col-3}}

==== Power- or authority-based ====
<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "power- or authority-based hierarchies"-->
* [[Noble ranks|Aristocratic hierarchies]]
** In [[Royal and noble ranks#General chart of "translations" between languages|Europe]]
** In [[Chinese nobility#Sovereign and ruling family ranks|China]]
* [[Ecclesiastical polity|Ecclesiastical hierarchies]]
** [[Catholic Church hierarchy]]
** [[Priesthood (LDS Church)|LDS Church hierarchy]]
** [[Kimbanguism#Hierarchy|Kimbanguist Church hierarchy]]
** [[Raëlism#Member hierarchy|Raëlism Church hierarchy]]
** see also [[autocephaly]]
* [[Prussian three-class franchise]]<ref>
{{cite book
 |last1                = Tipton
 |first1               = Frank
 |author-link1         = Frank Tipton
 |chapter              = Politics, Governance, and Diplomacy between Neoclassicism and Modernism
 |title                = A History of Modern Germany Since 1815
 |date = January 2003
 |url                  = https://books.google.com/books?id=SQGMYLJRdXoC
 |location             = London
 |publisher            = A&C Black
 |publication-date     = 2003
 |page                 = 239
 |isbn                 = 9780826449108
 |access-date          = 26 November 2021
 |quote                = Kühne believes the Prussian franchise lasted for over sixty years because it accurately reflected the social realities of the relatively closed, hierarchical, and conformist communities of rural Prussia.
}} 
</ref>
* Political party hierarchies
** [[Ranks and insignia of the Nazi Party|Nazi Party]] (''pace'' overlapping fields<ref>
Compare:
{{cite book
 |last1                = Lee
 |first1               = Stephen J.
 |orig-date            = 1987
 |chapter              = Dictatorship in Germany
 |title                = European Dictatorships 1918-1945
 |date = 12 February 2016
 |url                  = https://books.google.com/books?id=D32PCwAAQBAJ
 |edition              = 4, revised
 |location             = London
 |publisher            = Routledge
 |publication-date     = 2016
 |page                 = 217
 |isbn                 = 9781317294221
 |access-date          = 26 November 2021
 |quote                = [...] Nazi administration is now regarded as an overlapping and confusing 'polycracy'. The basis of the criticism is that the multi-layering of agencies and the lack of proper delineation between them generated conflict and hampered efficiency. There was, for example, extensive rivalry between the Four-Year plan Office, the Ministry of Economics, the War ministry and the Plenipotentiary for Economics.
}} 
</ref>)
*** [[SS Ranks#Final SS ranks 1934–1945|SS]]
*** [[Glossary of Nazi Germany#G|Hierarchy of subdivisions within the Gau]]
** [[Communist Party of the Soviet Union#Structure|Communist Party of the Soviet Union]]
** [[Chinese Communist Party]]
* [[Command hierarchy|Chain of command]]
** [[List of comparative military ranks|Military ranks]]
** [[Military organization#Hierarchy of modern armies|Military units]]
** [[Unified Combatant Command|U.S. Military Combatant Commands]]
* [[Dominance hierarchy|Intraspecial dominance]]
** [[Pecking order]]
* [[Social stratification|Social classes]]
** [[Caste system in India]]
** [[Hierarchical structure of Feudal Japan]]
** [[Master race#Hierarchy|White racist hierarchy]]
** [[Hierarchy of Exclusion]] (Ender's Game)

{{col-3}}

==== Value-related ====
<!--value meaning both money and relative importance--> <!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "value-related hierarchies"-->
* [[Hierarchy of genres|Hierarchy of genres in art]]
* [[Hierarchy of evidence|Evidence]]
* [[Maslow's hierarchy of needs|Human needs]]
* [[Hierarchy of precious substances|Precious substances]]
* [[Hierarchy of values|Judicial hierarchy of social values]]

{{col-3}}

==== Perception-based ====
<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "perception-based hierarchies"-->
* [[Color wheel]]
** [[Primary colors]]
*** [[Secondary colors]]
**** [[Tertiary colors]]
{{col-end}}

{{col-begin}}
{{col-3}}

==== History-oriented ====
<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "history-oriented hierarchies"-->
* [[Three-age system]]
* [[Comparative history|Cyclic theory of civilization]]
** [[Spengler's civilization model|Oswald Spengler]]
** [[A Study of History#List of civilizations|Arnold J. Toynbee]]
* [[Spiral dynamics]]

{{col-3}}

==== Science-focussed ====
 <!--[[WP:HYPHEN]]—this category's logical title is "science-focussed hierarchies"-->
* [[Earth's location in the universe#Earth in the universe|Hierarchy of organization within the Universe]]
* [[Hierarchical ternary star system|Star systems]]
* [[Biological classification]]
* [[Biological organization]]
* [[Phylogenetic tree]]
* [[Timeline of evolution|Evolutionary development]]
* [[Ecological land classification#Hierarchy of classification levels in ecology compared to other fields|Hierarchy of ecological georegions]]

{{col-3}}

==== Technology-based ====
* [[Memory hierarchy]]
** [[Cache hierarchy]]
* [[Hierarchical clustering|Clusters]]
* [[Hierarchy (object-oriented programming)|Class constructs]]
* [[Hierarchical database model|Data organization]]
** [[Hierarchical query]]
* [[Hierarchical Data Format|Data storage]]
** [[Hierarchical file system|Computer files]]
* [[Hierarchical control system|Devices]]
* [[Classless Inter-Domain Routing|IP addresses]]
* [[Memory hierarchy|Memory]]
** [[Hierarchical page tables|Virtual memory allocation]]
* [[Hierarchical internetworking model|Networks]]
* [[Hierarchical cell structure|Radio cells]]
* [[Hierarchical state machine|States (configurations)]]
* [[Hierarchical name space|Web addresses]]
* [[Structure]]
** [[Data Structure]]
* [[Inheritance (object-oriented programming)]]
{{col-end}}

==== Religion-related ====
<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "religion- and mythology-related hierarchies"-->
* Levels of consciousness
**[[Chakra#The seven major chakras|Chakras]]
**[[Great chain of being]]
**[[Ray of Creation|G.I. Gurdjieff]]
**[[Eight Circuit Model of Consciousness#The eight circuits|Timothy Leary]]
* Levels of spiritual development
** In [[Four stages of enlightenment|Theravada Buddhism]]
** In [[Bhumi (Buddhism)|Mahayana Buddhism]]
* Ages in the evolution of society
** In [[Astrological age#Past ages|Astrology]]
** In [[Ages of Man|Hellenism (the Ancient Greek Religion)]]
**[[Dispensation (period)#Protestant dispensations|Dispensations in Protestantism]]
**[[Dispensation (period)#Latter Day Saint dispensations|Dispensations in Mormonism]]
*[[Hierarchical communion|Degrees of communion between various Christian churches]]
*[[UFO religion]]s
**[[Master Jesus#Airborne Division of the Brotherhood of Light|Command hierarchy of the ''Ashtar Galactic Command'' flying saucer fleet]]
* Deities
** In [[Japanese Buddhist pantheon#Hierarchical structure of the Buddhist pantheon|Japanese Buddhism]]
** In [[Spiritual Hierarchy#Levels of the spiritual hierarchy|Theosophy]]
* Angels
** In [[Christian angelic hierarchy|Christianity]]
** In [[Islamic view of angels#Angel hierarchy|Islam]]
** In [[Jewish angelic hierarchy|Judaism]]
***[[Kabbalistic angelic hierarchy|Kabbalistic]]
** In [[Yazata|Zoroastrianism]]
* Devils and Demons
**[[Hierarchy of devils|Devils]]
**[[Hierarchy of demons|Demons]]
*[[Hell]]s
** In [[Inferno (Dante)|Catholicism (Nine Levels of Hell)]]
** In [[Naraka (Buddhism)|Buddhism (Sixteen Levels of Hell)]]
*[[Religious stratification|Religions in society]]
* (organizational&nbsp;hierarchies are listed under {{nowrap|"[[#Power- or authority-based|Power- or authority-based]]"}})<!--non-breaking spaces used for neatness at all resolutions-->

===Methods using hierarchy===
<!-- See note at "Examples of other applications"-->
{{columns-list|colwidth=22em|
* [[Analytic Hierarchy Process]]
** [[Hierarchical Decision Process]]
* [[HOOD method|Hierarchic Object-Oriented Design]]
* [[Hierarchical Bayes model]]
* [[Hierarchical clustering]]
** [[Hierarchical clustering of networks]]
* [[Hierarchical constraint satisfaction]]
* [[Hierarchical linear modeling]]
* [[Hierarchical modulation]]
* [[Hierarchical proportion]]
* [[Hierarchical RBF|Hierarchical radial basis function]]
* [[Hierarchical storage management]]
* [[Hierarchical task network]]
* [[Hierarchical temporal memory]]
* [[Hierarchical Token Bucket|Hierarchical token bucket]]
* [[Hierarchical visitor pattern]]
* [[Presentation-abstraction-control]]
** [[Hierarchical-Model-View-Controller]]
}}