monad

[mon-ad, moh-nad] /ˈmɒn æd, ˈmoʊ næd/
noun
1.
Biology.
  1. any simple, single-celled organism.
  2. any of various small, flagellate, colorless ameboids with one to three flagella, especially of the genus Monas.
2.
Chemistry. an element, atom, or group having a valence of one.
Compare dyad (def 3), triad (def 2a).
3.
Philosophy.
  1. (in the metaphysics of Leibniz) an unextended, indivisible, and indestructible entity that is the basic or ultimate constituent of the universe and a microcosm of it.
  2. (in the philosophy of Giordano Bruno) a basic and irreducible metaphysical unit that is spatially and psychically individuated.
  3. any basic metaphysical entity, especially having an autonomous life.
4.
a single unit or entity.
Origin
1605-15; < Late Latin monad- (stem of monas) < Greek (stem of monás): unity. See mon-, -ad1
Related forms
monadic
[muh-nad-ik] /məˈnæd ɪk/ (Show IPA), monadical, monadal, adjective
monadically, adverb
British Dictionary definitions for monad

monad

/ˈmɒnæd; ˈməʊ-/
noun
1.
(philosophy) (pl) -ads, -ades (-əˌdiːz)
  1. any fundamental singular metaphysical entity, esp if autonomous
  2. (in the metaphysics of Leibnitz) a simple indestructible nonspatial element regarded as the unit of which reality consists
  3. (in the pantheistic philosophy of Giordano Bruno) a fundamental metaphysical unit that is spatially extended and psychically aware
2.
a single-celled organism, esp a flagellate protozoan
3.
an atom, ion, or radical with a valency of one
Also called (for senses 1, 2) monas
Derived Forms
monadical, adjective
monadically, adverb
Word Origin
C17: from Late Latin monas, from Greek: unit, from monos alone
Word Origin and History for monad
n.

"unity, arithmetical unit," 1610s, from Late Latin monas (genitive monadis), from Greek monas "unit," from monos "alone" (see mono-). In Leibnitz's philosophy, "an ultimate unit of being" (1748). Related: Monadic.

monad in Medicine

monad mo·nad (mō'nād')
n.

  1. An atom or a radical with a valence of 1.

  2. A single-celled microorganism, especially a protozoan of the genus Monas.

  3. Any of the four chromatids of a tetrad that, after the first and second meiotic divisions, separate to become the chromosomal material in each of the four daughter cells.

mo·nad'ic (mə-nād'ik) or mo·nad'i·cal adj.
monad in Technology
theory, functional programming
/mo'nad/ A technique from category theory which has been adopted as a way of dealing with state in functional programming languages in such a way that the details of the state are hidden or abstracted out of code that merely passes it on unchanged.
A monad has three components: a means of augmenting an existing type, a means of creating a default value of this new type from a value of the original type, and a replacement for the basic application operator for the old type that works with the new type.
The alternative to passing state via a monad is to add an extra argument and return value to many functions which have no interest in that state. Monads can encapsulate state, side effects, exception handling, global data, etc. in a purely lazily functional way.
A monad can be expressed as the triple, (M, unitM, bindM) where M is a function on types and (using Haskell notation):
unitM :: a -> M a bindM :: M a -> (a -> M b) -> M b
I.e. unitM converts an ordinary value of type a in to monadic form and bindM applies a function to a monadic value after de-monadising it. E.g. a state transformer monad:
type S a = State -> (a, State) unitS a = \ s0 -> (a, s0) m `bindS` k = \ s0 -> let (a,s1) = m s0 in k a s1
Here unitS adds some initial state to an ordinary value and bindS applies function k to a value m. (`fun` is Haskell notation for using a function as an infix operator). Both m and k take a state as input and return a new state as part of their output. The construction
m `bindS` k
composes these two state transformers into one while also passing the value of m to k.
Monads are a powerful tool in functional programming. If a program is written using a monad to pass around a variable (like the state in the example above) then it is easy to change what is passed around simply by changing the monad. Only the parts of the program which deal directly with the quantity concerned need be altered, parts which merely pass it on unchanged will stay the same.
In functional programming, unitM is often called initM or returnM and bindM is called thenM. A third function, mapM is frequently defined in terms of then and return. This applies a given function to a list of monadic values, threading some variable (e.g. state) through the applications:
mapM :: (a -> M b) -> [a] -> M [b] mapM f [] = returnM [] mapM f (x:xs) = f x `thenM` ( \ x2 -> mapM f xs `thenM` ( \ xs2 -> returnM (x2 : xs2) ))
(2000-03-09)
Encyclopedia Article for monad

(from Greek monas "unit"), an elementary individual substance that reflects the order of the world and from which material properties are derived. The term was first used by the Pythagoreans as the name of the beginning number of a series, from which all following numbers derived. Giordano Bruno in De monade, numero et figura liber (1591; "On the Monad, Number, and Figure") described three fundamental types: God, souls, and atoms. The idea of monads was popularized by Gottfried Wilhelm Leibniz in Monadologia (1714). In Leibniz's system of metaphysics, monads are basic substances that make up the universe but lack spatial extension and hence are immaterial. Each monad is a unique, indestructible, dynamic, soullike entity whose properties are a function of its perceptions and appetites. Monads have no true causal relation with other monads, but all are perfectly synchronized with each other by God in a preestablished harmony. The objects of the material world are simply appearances of collections of monads.

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