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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:

  1. 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.)
  2. 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.
  3. In the writings of the philosopher Gottfried Leibniz, the monads appear as spiritual entities which make up the essence of our world. They do not interact with our world (are "windowless"), and do not have volume (do not take up space) and are thus impossible to detect by scientific methods. The arrangements of the monads make up the faith and structure of this world, which to Leibniz was "the best of all possible worlds".
  4. Within mathematics a monad is a set consisting of one single element (query non-standard usage - that's normally a singleton). In category theory a monad is a type of functor important in the theory of adjoint functors. It is that usage that has led to the below.
  5. In pure functional programming languages such as Haskell, monads are 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).
  6. Technocracy Incorporated[?] describes its symbol as being a geometric representation of the monad.



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