monad

From Latin monas (“unit”) (from Ancient Greek μονάς (monás), from μόνος (mónos), from Proto-Indo-European *men-) +‎ -ad.

• (Received Pronunciation) IPA^(key): /ˈmɒnæd/

• Audio (Southern England):

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• (General American) IPA^(key): /ˈmoʊnæd/
• Rhymes: (US) -oʊnæd
• Hyphenation: mon‧ad

monad (plural monads)

1. One thing, one being, one item.
2. A group of entites or items treated as one entity.
3. (philosophy) An ultimate atom, or simple, unextended point; something ultimate and indivisible.
   • 1787, Immanuel Kant, translated by John Meiklejohn, The Critique of Pure Reason‎, published 1855:

     Hence Leibnitz, who looked upon things as noumena, after denying them everything like external relation, and therefore also composition or combination, declared that all substances, even the component parts of matter, were simple substances with powers of representation, in one word, monads.

   • 1813, J. D. Falk, quoting Johann Wolfgang von Goethe, translated by David Luke and Robert Pick, Goethe: Conversations and Encounters, London: O. Wolff, published 1966, page 88:

     “If we are to embark upon speculation”, said Goethe, continuing his discourse, “then I really do not see why the monad to which we owe Wieland's appearance on our planet should be unable in its new condition to enter into the highest combinations that are possible in this universe.

   • 1855, Thomas Bulfinch, chapter XXXIV, in The Age of Fable:

     Pythagoras considered numbers as the essence and principle of all things, and attributed to them a real and distinct existence; so that, in his view, they were the elements out of which the universe was constructed. […] The "Monad" or unit he regarded as the source of all numbers.

   • 1918, H[enry] Rider Haggard, chapter I, in Love Eternal‎:

     More than thirty years ago two atoms of the eternal Energy sped forth from the heart of it which we call God […]. Perhaps these two atoms, or essences, or monads indestructible, did but repeat an adventure, or many, many adventures.

4. (botany) A single individual (such as a pollen grain) that is free from others, not united in a group.
5. (biology, dated) A single-celled organism.
6. (category theory) A monoid object in the category of endofunctors of a fixed category.

   Coordinate term: comonad

7. (functional programming) A data type which represents a specific form of computation, along with the operations "return" and "bind".
   • 2008, Bryan O'Sullivan, John Goerzen, Donald Bruce Stewart, chapter 14, in Real World Haskell, O'Reilly Media, →ISBN, page 328:

     The properties that make the Maybe type a monad are its type constructor Maybe a, our chaining function (>>?), and the injector function Just.

• (group) monad, duad/dyad, triad, tetrad, pentad, hexad, hebdomad/heptad, ogdoad/octad, ennead/nonad, decad/decade, hendecad, dodecad/duodecade, chiliad

• monad on Wikipedia.Wikipedia

• Damon, Doman, Domna, Mando, Monda, NoMad, mad on, mad-on, mando, nomad