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 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 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.
• 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.