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.) 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 , philosophy , design , mathematics , computer science , organizational theory , systems theory , systematic biology , and the social sciences (especially political science ).
123-415: 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
246-505: A 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 modeling and animation for almost everything built as a 3D digital model. Many grammatical theories, such as phrase-structure grammar , involve hierarchy. Direct–inverse languages such as Cree and Mapudungun distinguish subject and object on verbs not by different subject and object markers, but via
369-505: A 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 modeling and animation for almost everything built as a 3D digital model. Many grammatical theories, such as phrase-structure grammar , involve hierarchy. Direct–inverse languages such as Cree and Mapudungun distinguish subject and object on verbs not by different subject and object markers, but via
492-514: A family tree ) and inheritance ( succession 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 equations 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 ,
615-514: A family tree ) and inheritance ( succession 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 equations 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 ,
738-475: 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. 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
861-474: 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. 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
984-468: A communicator of a tradition. Others scholars such as Bart D. Ehrman disagree, see for example Forged . While pseudo-Dionysius can be seen as a communicator of tradition, he can also be seen as a polemicist, who tried to alter Neo-Platonic tradition in a novel way for the Christian world that would make notions of complicated Divine Hierarchies more of an emphasis than notions of direct relationship with
1107-446: 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 . A subsumptive containment hierarchy
1230-444: 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. A subsumptive containment hierarchy
1353-460: 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. This
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#17330922450501476-459: 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. This
1599-461: A euphemism ("flowers and supersubstantial lights") when the said verbiage is found explicitly in the Corpus Dionysiacum. Dionysius attributed his inspiration to pseudo-Hierotheus, professing that he was writing to popularize the teachings of his master. Pseudo-Hierotheus was the author of "The book of Hierotheus on the hidden mysteries of the house of God." Pseudo-Hierotheus is believed to be
1722-402: 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
1845-402: 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
1968-428: 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: 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
2091-428: 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: 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
2214-511: A hierarchy of persons. In this system, the three (or four with Algonquian languages ) 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. The structure of
2337-511: A hierarchy of persons. In this system, the three (or four with Algonquian languages ) 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. The structure of
2460-444: A high priest', from hierarkhes , '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 , philosophy , design , mathematics , computer science , organizational theory , systems theory , systematic biology , and
2583-406: A higher-level entity can have on x' s properties and interactions. Furthermore, the entities found at each level are autonomous . 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 has a government and that every government
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#17330922450502706-400: A higher-level entity can have on x' s properties and interactions. Furthermore, the entities found at each level are autonomous . 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 has a government and that every government
2829-524: 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
2952-473: 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
3075-410: 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
3198-410: 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
3321-478: A pupil of Proclus, perhaps of Syrian origin, who knew enough of Platonism and the Christian tradition to transform them both. Since Proclus died in 485, and since the first clear citation of Dionysius' works is by Severus of Antioch between 518 and 528, then we can place Dionysius' authorship between 485 and 518-28. Ronald Hathaway provides a table listing most of the major identifications of Dionysius: e.g., Ammonius Saccas , Pope Dionysius of Alexandria , Peter
3444-439: 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 ), a human can be formulated as: Taxonomies may change frequently (as seen in biological taxonomy ), but the underlying concept of nested hierarchies
3567-438: 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 ), a human can be formulated as: Taxonomies may change frequently (as seen in biological taxonomy ), but the underlying concept of nested hierarchies
3690-404: A recovery of the huge impact of Dionysian thought in later Christian thought, because of an increasing repudiation of older criticisms that Dionysius's thought represented a fundamentally Neoplatonic approach to theology, and finally because of interest in parallels between aspects of modern linguistic theory and Dionysius's reflections on language and negative theology . Andrew Louth offers
3813-404: 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 refers to the effect that the incorporation of entity x into
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3936-403: 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 refers to the effect that the incorporation of entity x into
4059-466: A world in which complexity had to evolve from simplicity. System 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 . When biological systems are modeled as physical systems , in the most general abstraction, they are thermodynamic open systems that exhibit self-organised behavior, and
4182-458: A world in which complexity had to evolve from simplicity. System 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 . When biological systems are modeled as physical systems , in the most general abstraction, they are thermodynamic open systems that exhibit self-organised behavior, and
4305-539: 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 hierarchy (i.e., they have the same position or tenure status). Possibly the first use of the English word hierarchy cited by the Oxford English Dictionary
4428-422: 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 hierarchy (i.e., they have the same position or tenure status). Possibly the first use of the English word hierarchy cited by the Oxford English Dictionary
4551-441: 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
4674-438: 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
4797-404: Is a direct extrapolation of the nested hierarchy concept. All of the ordered sets are still nested, but every set must be " strict "—no two sets can be identical. The shapes example above can be modified to demonstrate this: The notation x ⊊ y {\displaystyle x\subsetneq y\,} means x is a subset of y but is not equal to y . A general example of
4920-404: Is a direct extrapolation of the nested hierarchy concept. All of the ordered sets are still nested, but every set must be " strict "—no two sets can be identical. The shapes example above can be modified to demonstrate this: The notation x ⊊ y {\displaystyle x\subsetneq y\,} means x is a subset of y but is not equal to y . A general example of
5043-480: Is a hierarchical ordering of nested sets . 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;
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5166-429: Is a hierarchical ordering of nested sets . 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;
5289-503: Is a member 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 " concepts ". 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. A compositional containment hierarchy
5412-451: Is a member 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 " concepts ". 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. A compositional containment hierarchy
5535-739: Is almost unintelligible. About twenty years later, a subsequent Carolingian Emperor, Charles the Bald , requested the Irishman John Scotus Eriugena to make a fresh translation. He finished this in 862. This translation itself did not widely circulate in subsequent centuries. Moreover, although Eriugena's own works, such as the Homily on the Prologue of St John , show the influence of Dionysian ideas, these works were not widely copied or read in subsequent centuries. The Benedictine monasticism that formed
5658-405: Is always transitive . The second requirement asserts that a hierarchy must have a leader or root that is common to all of the objects. Mathematically, in its most general form, a hierarchy is a partially ordered set or poset . The system in this case is the entire poset, which is constituted of elements. Within this system, each element shares a particular unambiguous property. Objects with
5781-404: Is always transitive . The second requirement asserts that a hierarchy must have a leader or root that is common to all of the objects. Mathematically, in its most general form, a hierarchy is a partially ordered set or poset . The system in this case is the entire poset, which is constituted of elements. Within this system, each element shares a particular unambiguous property. Objects with
5904-420: 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 itself is included as a subset of hierarchical programming, and recursive thinking can be synonymous with a form of hierarchical thinking and logic. A containment hierarchy
6027-419: 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 itself is included as a subset of hierarchical programming, and recursive thinking can be synonymous with a form of hierarchical thinking and logic. A containment hierarchy
6150-507: 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 , which are composed of molecules , which are composed of atoms . In fact,
6273-506: 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 , which are composed of molecules , which are composed of atoms . In fact,
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#17330922450506396-425: Is better characterized and approached by negations than by affirmations . All names and theological representations must be negated. According to pseudo-Dionysius, when all names are negated, "divine silence, darkness, and unknowing" will follow. His thought was initially used by Miaphysites to back up parts of their arguments but his writings were eventually adopted by other church theologians, primarily due to
6519-483: Is credited with first use of it as an abstract noun. Since hierarchical churches, such as the Roman Catholic (see Catholic Church hierarchy ) 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. A hierarchy
6642-427: Is credited with first use of it as an abstract noun. Since hierarchical churches, such as the Roman Catholic (see Catholic Church hierarchy ) 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. A hierarchy
6765-670: Is criticized later in the century, and defended by Theodore of Raithu ; and by the 7th century, it is taken as demonstrated, affirmed by both Maximus the Confessor and the Lateran Council of 649 . From that point until the Renaissance, the authorship was less questioned, though Thomas Aquinas , Peter Abelard and Nicholas of Cusa expressed suspicions about its authenticity; their concerns were generally ignored. The Florentine humanist Lorenzo Valla (d. 1457), in his 1457 commentaries on
6888-631: 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 denominations have an autocephalous 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
7011-630: 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 denominations have an autocephalous 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
7134-598: Is infinitely hierarchical because there is no finite bound on the number of digits can be used after the decimal point. Organizations 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
7257-596: Is infinitely hierarchical because there is no finite bound on the number of digits can be used after the decimal point. Organizations 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
7380-420: Is one such form. Hierarchies have their own special vocabulary. These terms are easiest to understand when a hierarchy is diagrammed (see below ). In an organizational context, the following terms are often used related to hierarchies: In a mathematical context (in graph theory ), the general terminology used is different. Most hierarchies use a more specific vocabulary pertaining to their subject, but
7503-418: Is one such form. Hierarchies have their own special vocabulary. These terms are easiest to understand when a hierarchy is diagrammed (see below ). In an organizational context, the following terms are often used related to hierarchies: In a mathematical context (in graph theory ), the general terminology used is different. Most hierarchies use a more specific vocabulary pertaining to their subject, but
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#17330922450507626-563: Is possible that pseudo-Dionysius was himself a member of this group, though debate continues over whether his writings do in fact reveal a miaphysite understanding of Christ. It seems likely that the writer was located in Syria, as revealed, for example, by the accounts of the sacramental rites he gives in The Ecclesiastical Hierarchy , which seem only to bear resemblance to Syriac rites. The author pseudonymously identifies himself in
7749-590: 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. 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 organizations and classification schemes . The broad category of branching hierarchies can be further subdivided based on
7872-588: 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. 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 organizations and classification schemes . The broad category of branching hierarchies can be further subdivided based on
7995-420: 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
8118-419: 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
8241-559: Is undertaken by John of Scythopolis , whose commentary, the Scholia ( c. 540 ), on the Dionysian Corpus constitutes the first defense of its apostolic dating, wherein he specifically argues that the work is neither Apollinarian nor a forgery, probably in response both to monophysites and Hypatius—although even he, given his unattributed citations of Plotinus in interpreting Dionysius, might have known better. Dionysius' authenticity
8364-537: Is with Damascius , the last scholarch of the Neoplatonic Academy of Athens . There is therefore no current scholarly consensus on the question of pseudo-Dionysius' identification. The Stanford Encyclopedia of Philosophy claims: It must also be recognized that "forgery" is a modern notion. Like Plotinus and the Cappadocian Fathers before him, Dionysius does not claim to be an innovator, but rather
8487-484: 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 , 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
8610-484: 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 , 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
8733-525: The New Testament , did much to establish that the author of the Corpus Areopagiticum could not have been St. Paul's convert, though he was unable to identify the actual historical author. William Grocyn pursued Valla's lines of textual criticism, and Valla's critical viewpoint of the authorship of the highly influential Corpus was accepted and publicized by Erasmus from 1504 onward, for which he
8856-472: The organization of life , and biomass pyramids attempt to document. 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,
8979-418: The organization of life , and biomass pyramids attempt to document. 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,
9102-574: 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 scheme and phylogenetic trees that reflect inferred patterns of evolutionary relationship among living and extinct species. CGI and computer-animation programs mostly use hierarchies for models. On
9225-524: 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 scheme and phylogenetic trees that reflect inferred patterns of evolutionary relationship among living and extinct species. CGI and computer-animation programs mostly use hierarchies for models. On
9348-473: The social sciences (especially political science ). 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
9471-528: The "prince of mystics". It was subsequently in the area of mysticism that Dionysius, especially his portrayal of the via negativa , was particularly influential. In the fourteenth and fifteenth centuries his fundamental themes were hugely influential on thinkers such as Marguerite Porete , Meister Eckhart , Johannes Tauler , John of Ruusbroec , the author of The Cloud of Unknowing (who made an expanded Middle English translation of Dionysius' Mystical Theology ), Jean Gerson , Nicholas of Cusa , Denis
9594-706: The Apostle mentioned in Acts 17:34 . In the early sixth century, a series of writings of a mystical nature , employing Neoplatonic language to elucidate Christian theological and mystical ideas, was ascribed to the Areopagite. They have long been recognized as pseudepigrapha , and their author is now called "Pseudo-Dionysius the Areopagite". The surviving corpus comprises: Seven other works are mentioned repeatedly by pseudo-Dionysius in his surviving works, and are presumed either to be lost or to be fictional works mentioned by
9717-531: 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 or Corpus Dionysiacum . The author pseudepigraphically identifies himself in the corpus as "Dionysios", portraying himself as Dionysius the Areopagite , the Athenian convert of Paul
9840-483: The Areopagite as a literary device to give the impression to his sixth-century readers of engaging with the surviving fragments of a much larger first-century corpus of writings. These seven other works are: In terms of the latest date for the composition of the Corpus , the earliest datable reference to Dionysius' writing comes in 528, the year in which the treatise of Severus of Antioch entitled Adversus apologiam Juliani
9963-546: The Areopagite' only after the philological work of J. Stiglmayr and H. Koch, whose papers, published independently in 1895, demonstrated the thoroughgoing dependence of the Corpus upon Proclus. Both showed that Dionysius had used, in his treatise on evil in Chapter 4 of The Divine Names , the De malorum subsistentia of Proclus. Dionysius' identity is still disputed. Corrigan and Harrington find pseudo-Dionysius to be most probably... ...
10086-652: The Carthusian , Julian of Norwich , Hendrik Herp and Catherine of Genoa ["The Mystical Element of Religion as Studied in Saint Catherine of Genoa and Her Friends (1908)]. His influence can also be traced in the Spanish Carmelite thought of the sixteenth century among Teresa of Ávila and John of the Cross . In recent decades, interest has increased again in the Corpus Areopagiticum , for three main reasons: because of
10209-818: The Dionysian corpus. Soon after, the Dominican Albertus Magnus did likewise. The thirteenth-century Parisian corpus provided an important reference point by combining the "Old Translation" of John Scotus Eriugena with the "New Translation" of John Sarrazin , along with glosses and scholia by Maximus the Confessor , John of Scythopolis and others, as well as the "Extracts" by Thomas Gallus , and several commentaries such as John Scotus Eriugena, John Sarrazin and Hugh of Saint Victor on The Celestial Hierarchy . It quickly became common to make reference to Dionysius. Thomas Aquinas wrote an explanation for several works, and cites him over 1700 times. Bonaventure called him
10332-520: The East, amongst both Chalcedonians and non-Chalcedonians. Gregory Palamas , for example, in referring to these writings, calls the author, "an unerring beholder of divine things". The Corpus is also present in Syriac and Armenian versions, the former of which, by Sergius of Reshaina in the early sixth century, serves as a terminus ante quem for the dating of the original Greek. The first notice of Dionysius in
10455-534: The Epistle to the Hebrews; according to Eusebius, he was also said to be the first bishop of Athens. It is therefore not surprising that that author of these works would have chosen to adopt the name of this otherwise briefly mentioned figure. The authorship of the Dionysian Corpus was initially disputed; Severus and his party affirmed its apostolic dating, largely because it seemed to agree with their Christology. This dating
10578-589: The Fuller , Dionysius the Scholastic, Severus of Antioch , Sergius of Reshaina , unnamed Christian followers of everyone from Origen to Basil of Caesarea , Eutyches to Proclus . In the past half-century, Alexander Golitzin, Georgian academician Shalva Nutsubidze and Belgian professor Ernest Honigmann have all proposed identifying pseudo-Dionysius the Areopagite with Peter the Iberian . A more recent identification
10701-621: The West comes from Pope Gregory I , who probably brought a codex of the Corpus Areopagitum back with him on his return from his mission as papal legate to the Emperor in Constantinople in c. 585 . Gregory refers occasionally in his writings to Dionysius, although Gregory's Greek was probably not adequate to fully engage with Dionysius's work. In the seventh and eighth centuries, Dionysius
10824-498: The corpus as "Dionysios", portraying himself as the figure of Dionysius the Areopagite , the Athenian convert of Paul the Apostle mentioned in Acts 17:34. Various legends existed surrounding the figure of Dionysius, who became emblematic of the spread of the gospel to the Greek world. A tradition quickly arose that he became the first bishop of Cyprus or of Milan, or that he was the author of
10947-539: The corpus. All Greek manuscripts of the Corpus Areopagiticum surviving today stem from an early sixth-century manuscript containing John's Scholia and Prologue — so John of Scythopolis had an enormous influence on how Dionysius was read in the Greek-speaking world. Theologians such as John of Damascus and Germanus I of Constantinople also made ample use of Dionysius' writing. The Dionysian writings and their mystical teaching were universally accepted throughout
11070-515: 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, diamonds and graphite are flat hierarchies of numerous carbon atoms that can be further decomposed into subatomic particles. An overlapping hierarchy
11193-514: 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, diamonds and graphite are flat hierarchies of numerous carbon atoms that can be further decomposed into subatomic particles. An overlapping hierarchy
11316-465: The fifth century Syrian monk Stephen Bar Sudhaile , a pantheistic writer. The works of Dionysius are mystical , and show strong Neoplatonic influence . For example, he uses Plotinus ' well-known analogy of a sculptor cutting away that which does not enhance the desired image, and shows familiarity with Proclus . He also shows influence from Clement of Alexandria , the Cappadocian Fathers , Origen , and others. According to pseudo-Dionysius, God
11439-410: The figure of Christ as Mediator. A minority of scholars, including Romanian theologian Dumitru Staniloae , argue in favor of the Dionysian corpus being authentic, citing internal historical details and the existence of explicit citations of Dionysius predating Proclus by writers such as Dionysius of Alexandria and Gregory Nazianzus . Even Proclus himself appears to cite an external authority for
11562-524: The first time by Hilduin , abbot of the monastery. It may well have been Hilduin himself who promoted his work (and his abbey) by developing the legend (which would be widely accepted during subsequent centuries), that Denis was the same person as Dionysius the Areopagite of Acts 17.34, and that he had traveled to Rome and then was commissioned by the Pope to preach in Gaul , where he was martyred. Hilduin's translation
11685-465: The following modern appraisal of the Areopagite; Dionysius/Denys' vision is remarkable because, on the one hand, his understanding of hierarchy makes possible a rich symbolic system in terms of which we can understand God and the cosmos and our place within it, and, on the other, he finds room within this strictly hierarchical society for an escape from it, beyond it, by transcending symbols and realizing directly one's relationship with God as his creature,
11808-430: 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. Subordinate A hierarchy (from Greek : ἱεραρχία , hierarkhia , 'rule of
11931-713: 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. Pseudo-Dionysius the Areopagite Autocephaly recognized by some autocephalous Churches de jure : Autocephaly and canonicity recognized by Constantinople and 3 other autocephalous Churches: Spiritual independence recognized by Georgian Orthodox Church: Semi-Autonomous: Pseudo-Dionysius
12054-453: 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 . 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
12177-453: 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 . 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
12300-527: 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 neurons but is of the brain )—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
12423-527: 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 neurons but is of the brain )—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
12546-429: 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. In plain English, a hierarchy can be thought of as a set in which: The first requirement is also interpreted to mean that a hierarchy can have no circular relationships ; the association between two objects
12669-428: 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. In plain English, a hierarchy can be thought of as a set in which: The first requirement is also interpreted to mean that a hierarchy can have no circular relationships ; the association between two objects
12792-407: 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. A nested hierarchy or inclusion hierarchy
12915-407: 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. A nested hierarchy or inclusion hierarchy
13038-477: 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
13161-477: 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
13284-501: 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-workers or colleagues ; 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
13407-501: 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-workers or colleagues ; 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
13530-469: The same property value are grouped together, and each of those resulting levels is referred to as a class . "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
13653-469: The same property value are grouped together, and each of those resulting levels is referred to as a class . "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
13776-470: The size differences between the levels (but 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 showing the structure of § Organizations , and playoff brackets in sports are often illustrated this way. More recently, as computers have allowed
13899-470: The size differences between the levels (but 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 showing the structure of § Organizations , and playoff brackets in sports are often illustrated this way. More recently, as computers have allowed
14022-479: The standard monasticism of the eighth to eleventh centuries, therefore, in general paid little attention to Dionysius. In the twelfth century, greater use gradually began to be made of Dionysius among various traditions of thought: During the thirteenth century, the Franciscan Robert Grosseteste made an important contribution by bringing out between 1240 and 1243 a translation, with commentary, of
14145-399: 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 . In the design field, mainly graphic design, successful layouts and formatting of the content on documents are heavily dependent on
14268-399: 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 . In the design field, mainly graphic design, successful layouts and formatting of the content on documents are heavily dependent on
14391-427: The work of John of Scythopolis and Maximus the Confessor in producing an orthodox interpretation. Writing a single generation at most after Dionysius, perhaps between 537 and 543, John of Scythopolis composed an extensive set ( c. 600 ) of scholia (that is, marginal annotations) to the works of Dionysius. These were in turn prefaced by a long prologue in which John set out his reasons for commenting on
14514-674: Was criticized by Catholic theologians. In the Leipzig disputation with Martin Luther , in 1519, Johann Eck used the Corpus , specifically the Angelic Hierarchy , as argument for the apostolic origin of papal supremacy, pressing the Platonist analogy, "as above, so below". During the 19th century modernist Catholics too came generally to accept that the author must have lived after the time of Proclus . The author became known as 'Pseudo-Dionysius
14637-650: Was disputed by Hypatius of Ephesus , who met the monophysite party during the 532 meeting with Emperor Justinian I ; Hypatius denied its authenticity on the ground that none of the Fathers or Councils ever cited or referred to it. Hypatius condemned it along with the Apollinarian texts, distributed during the Nestorian controversy under the names of Pope Julius and Athanasius, which the monophysites entered as evidence supporting their position. The first defense of its authenticity
14760-547: Was in 1881, when it was used in reference to the three orders of three angels as depicted by Pseudo-Dionysius the Areopagite (5th–6th centuries). Pseudo-Dionysius used the related Greek word (ἱεραρχία, hierarchia ) both in reference to the celestial hierarchy and the ecclesiastical hierarchy . The Greek term hierarchia means 'rule of a high priest', from hierarches (ἱεράρχης, 'president of sacred rites, high-priest') and that from hiereus (ἱερεύς, 'priest') and arche (ἀρχή, 'first place or power, rule'). Dionysius
14883-542: Was in 1881, when it was used in reference to the three orders of three angels as depicted by Pseudo-Dionysius the Areopagite (5th–6th centuries). Pseudo-Dionysius used the related Greek word (ἱεραρχία, hierarchia ) both in reference to the celestial hierarchy and the ecclesiastical hierarchy . The Greek term hierarchia means 'rule of a high priest', from hierarches (ἱεράρχης, 'president of sacred rites, high-priest') and that from hiereus (ἱερεύς, 'priest') and arche (ἀρχή, 'first place or power, rule'). Dionysius
15006-609: Was not widely known in the West, aside from a few scattered references. The real influence of Dionysius in the West began with the gift in 827 of a Greek copy of his works by the Byzantine emperor Michael II to the Carolingian emperor Louis the Pious . King Louis in turn gave the manuscript to the Abbey of St. Denis near Paris where, in about 838, Dionysius' works were translated into Latin for
15129-497: Was translated into Syriac —though it is possible the treatise may originally have been composed up to nine years earlier. Another widely cited latest date for Dionysius' writing comes in 532, when, in a report on a colloquy held between two groups ( dyophysite and miaphysite ) debating the decrees of the Council of Chalcedon , Severus of Antioch and his miaphysite supporters cited Dionysius' Fourth Letter in defence of their view. It
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