The word monad comes from the Greek language word μονάς (from the word μόνος, which means "one", "single", "unique") and has had many meanings in different contexts: *Among the Pythagoreans (followers of Pythagoras) the monad was the first thing that came into existence. The monad begot the ''dyad'', which begot the numbers, the numbers begat points, which begot lines, which begot two-dimensional entities, which begat three-dimensional entities, which begot bodies, which begot the four classical elements earth, water, fire and air, from which the rest of our world is built up. The monad was thus a central concept in the cosmology of the Pythagoreans, who held the belief that the world was - ''literally'' - built up by numbers. (The source of this claim is Diogenes Laertius' book ''Lives of Eminent Philosophers''.) *Within certain variations of Gnosticism, especially those inspired by Monoimus, the Monad (Gnosticism) was the higher being which created lesser gods, or elements (similar to aeons). This view was according to Hippolytus inspired by the Pythagoreans. *The Monad appears in the Alchemy texts of the Hermetica, part four of the corpus is called ''The Cup or Monad''. *The Monad (Chinese symbol) is the Chinese symbol of duality in nature. *In the writings of the philosopher Gottfried Leibniz, monads are atomistic mental objects which experience the world from a particular point of view. Leibniz's theory does not posit physical space; rather, physical objects are constructs of the collective experiences of monads. This way of putting it is misleading, however; monads do not interact with each other (are "windowless"), but rather are imbued at creation with all their future experiences in a system of pre-established harmony. The arrangements of the monads make up the faith and structure of this world, which to Leibniz was "the best of all possible worlds". *Within mathematics: ** in non-standard analysis, a monad consists of all those numbers infinitesimally close to a given number; ** in category theory, a monad, also known as triple, is a type of functor important in the theory of adjoint functors. This term has a different root than the ones described above; it was formed by combining "monoid" and "triad". See monad (category theory). **In pure functional programming languages such as Haskell programming language, monads are used as data types that encapsulate the functional I/O-activity, in such a manner that the side-effects of IO are not allowed to spread out of the part of the program that is not functional (imperative). See monads in functional programming. *Technocracy Incorporated describes its symbol as being a geometric representation of the monad. *MSH (shell) is the codename for a command line interface in development as part of Microsoft's Windows Longhorn project. It includes many features from traditional Unix shells, as well as object-oriented concepts. *In music a monad is a single pitch (music) or pitch class. See also: Dyad (music), Trichord, Tetrachord, Hexachord. *Monas, an acronym for ''Monumen Nasional'', is the landmark monument of Jakarta, Indonesia. ==See also== *Monism
Has anyone some more information about monads in category theory? --User:JensMueller Isn't the term monad also used for the Asian yin-yang symbol, which was also used as a corporate logo by the Northern Pacific Railroad? --User:Chris Rodgers There is also a monad associated with Haskell (a programming language). http://www.nomaware.com/monads/html/ Dictionaries such as 1913 Webster tell that a monad can be "4. (Biol.) A simple, minute organism; a primary cell, germ, or plastid." and even "5. (Chem.) An atom or radical whose valence is one, or which can combine with, be replaced by, or exchanged for, one atom of hydrogen." Monad is also a name for Microsoft new project for new CLI tools, which intend to be better than CLI tools in UNIX (and Linux).
See other meanings of words starting from letter:
Words begining with Monad:
Monad
Monad
Monadic
Monadic_Boolean_algebra
Monadic_logic
Monadman
Monadnock
Monadnock
Monadnock_Region
Monado
Monado
Monadologie
Monadology
Monads_in_functional_programming
Monads_in_functional_programming
Monad_(category_theory)
Monad_(category_theory)
Monad_(functional_programming)
Monad_(functional_programming)
Monad_(Gnosticism)
Monad_(Gnosticism)
Monad
The word monad comes from the Greek language word μονάς (from the word μόνος, which means "one", "single", "unique") and has had many meanings in different contexts: *Among the Pythagoreans (followers of Pythagoras) the monad was the first thing that came into existence. The monad begot the ''dyad'', which begot the numbers, the numbers begat points, which begot lines, which begot two-dimensional entities, which begat three-dimensional entities, which begot bodies, which begot the four classical elements earth, water, fire and air, from which the rest of our world is built up. The monad was thus a central concept in the cosmology of the Pythagoreans, who held the belief that the world was - ''literally'' - built up by numbers. (The source of this claim is Diogenes Laertius' book ''Lives of Eminent Philosophers''.) *Within certain variations of Gnosticism, especially those inspired by Monoimus, the Monad (Gnosticism) was the higher being which created lesser gods, or elements (similar to aeons). This view was according to Hippolytus inspired by the Pythagoreans. *The Monad appears in the Alchemy texts of the Hermetica, part four of the corpus is called ''The Cup or Monad''. *The Monad (Chinese symbol) is the Chinese symbol of duality in nature. *In the writings of the philosopher Gottfried Leibniz, monads are atomistic mental objects which experience the world from a particular point of view. Leibniz's theory does not posit physical space; rather, physical objects are constructs of the collective experiences of monads. This way of putting it is misleading, however; monads do not interact with each other (are "windowless"), but rather are imbued at creation with all their future experiences in a system of pre-established harmony. The arrangements of the monads make up the faith and structure of this world, which to Leibniz was "the best of all possible worlds". *Within mathematics: ** in non-standard analysis, a monad consists of all those numbers infinitesimally close to a given number; ** in category theory, a monad, also known as triple, is a type of functor important in the theory of adjoint functors. This term has a different root than the ones described above; it was formed by combining "monoid" and "triad". See monad (category theory). **In pure functional programming languages such as Haskell programming language, monads are used as data types that encapsulate the functional I/O-activity, in such a manner that the side-effects of IO are not allowed to spread out of the part of the program that is not functional (imperative). See monads in functional programming. *Technocracy Incorporated describes its symbol as being a geometric representation of the monad. *MSH (shell) is the codename for a command line interface in development as part of Microsoft's Windows Longhorn project. It includes many features from traditional Unix shells, as well as object-oriented concepts. *In music a monad is a single pitch (music) or pitch class. See also: Dyad (music), Trichord, Tetrachord, Hexachord. *Monas, an acronym for ''Monumen Nasional'', is the landmark monument of Jakarta, Indonesia. ==See also== *Monism
Monad
Has anyone some more information about monads in category theory? --User:JensMueller Isn't the term monad also used for the Asian yin-yang symbol, which was also used as a corporate logo by the Northern Pacific Railroad? --User:Chris Rodgers There is also a monad associated with Haskell (a programming language). http://www.nomaware.com/monads/html/ Dictionaries such as 1913 Webster tell that a monad can be "4. (Biol.) A simple, minute organism; a primary cell, germ, or plastid." and even "5. (Chem.) An atom or radical whose valence is one, or which can combine with, be replaced by, or exchanged for, one atom of hydrogen." Monad is also a name for Microsoft new project for new CLI tools, which intend to be better than CLI tools in UNIX (and Linux).
See other meanings of words starting from letter:
M
MA | MB | MC | MD | ME | MF | MG | MH | MI | MJ | MK | ML | MN | MO | MP | MR | MS | MT | MU | MW | MX | MY | MZ |Words begining with Monad:
Monad
Monad
Monadic
Monadic_Boolean_algebra
Monadic_logic
Monadman
Monadnock
Monadnock
Monadnock_Region
Monado
Monado
Monadologie
Monadology
Monads_in_functional_programming
Monads_in_functional_programming
Monad_(category_theory)
Monad_(category_theory)
Monad_(functional_programming)
Monad_(functional_programming)
Monad_(Gnosticism)
Monad_(Gnosticism)
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