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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 in philosophy, mathematics, computing and music:

• 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 begat two-dimensional entities, which begat three-dimensional entities, which begat bodies, which begot 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 inspired 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 appears in the alchemical texts of the Hermetica, part four of the corpus is called The Cup or Monad.
• 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". The British author Stephen Baxter uses the term monad to describe mental objects at the beginning of the universe in his novel Exultant.
• 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 functional programming languages such as Haskell, monads are type constructors that are used to capture various notions of sequential computation, such as I/O and state-activity or operations which may fail, as well as nondeterministic computation. The definition is the same as the category theoretic one. See monads in functional programming.
• In music a monad is a single pitch or pitch class. See also: Dyad, Trichord, Tetrachord, Hexachord.
• Technocracy Incorporated describes its symbol as being a geometric representation of the Monad.
• Northern Pacific Railway used a red and black monad symbol in its trademark.
• Microsoft uses the codename Monad about a command line interface and scripting language product that it has under development. See MSH (shell).
• The Hieroglyphic Monad was a glyph developed by John Dee.

See also

• Monadology
• Monism