# Monad

The word**monad**comes from the Greek 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 begat the*dyad*, which begat the numbers, the numbers begat points, which begat lines, which begat two-dimensional entities, which begat three-dimensional entities, which begat bodies, which begat the four elementss 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 inspiered by Monoimus, the
**Monad**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**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, 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.

- in non-standard analysis, a
- Technocracy Incorporated describes its symbol as being a geometric representation of the
**monad**. - Monad 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 or pitch class. See also: Dyad, Trichord, Tetrachord, Hexachord.

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