Monad

Definition: Monad

Monad

Noun

1. An atom having a valence of one.

2. A singular metaphysical entity from which material properties are said to derive.

Date "monad" was first used: 1615. (references)

Etymology: Monad \Mon"ad\, noun. [Latin expression monas, -adis, unit, Greek expression from alone.]. (Websters 1913)

Domain	Definitions
Satire	MONAD, n. The ultimate, indivisible unit of matter. (See Molecule.) According to Leibnitz, as nearly as he seems willing to be understood, the monad has body without bulk, and mind without manifestation -- Leibnitz knows him by the innate power of considering. He has founded upon him a theory of the universe, which the creature bears without resentment, for the monad is a gentlmean. Small as he is, the monad contains all the powers and possibilities needful to his evolution into a German philosopher of the first class -- altogether a very capable little fellow. He is not to be confounded with the microbe, or bacillus; by its inability to discern him, a good microscope shows him to be of an entirely distinct species. Source: Devil's Dictionary.
Computing	Monad /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 notaion): 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). Source: The Free On-line Dictionary of Computing.
Mining	An axial rotation of 360 degrees , one-fold. See also:axis of symmetry. (references)
Source: compiled by the editor from various references; see credits.

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 elementss 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.
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, specifically category theory, a monad is a type of functor important in the theory of adjoint functors. It is this usage that has led to the one in functional programming explained below. See monad (category theory).
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).
Technocracy Incorporated describes its symbol as being a geometric representation of the monad.
Monad is a codename for a command line interface that is up to come with Windows Longhorn. It includes many features borrowed from Unix and AmigaOS.

Monad (category theory)
(From Wikipedia, the free Encyclopedia)
In category theory, a monad is a type of functor important in the theory of pairs of adjoint functors. If F and G are an adjoint pair of functors, with F left adjoint to G, then the composition FoG will be a monad. Note that therefore a monad is a functor from a category to itself; and that if F and G were actually inverses as functors the corresponding monad would be the identity functor. In general adjunctions are not equivalences - they relate categories of different natures. The monad theory matters as part of the effort to capture what it is that adjunctions 'preserve'. The other half of the theory, of what can be learned likewise from consideration of GoF, is discussed under comonad.
The monad axioms can be seen at work in a simple example: let G be the forgetful functor from the category Group of groups to the category Set of sets. Then as F we can take the free group functor. This means that the monad T = FoG takes a group X and returns the free group Free(X) on the set underlying X. What we are given here consists of two observations: X ->T(X) by including any group X in Free(X) in the natural way. Further, T(T(X)) -> T(X) can be made out of a natural concatenation of 'strings of strings'. This amounts to two natural transformations I -> T, and ToT -> T. They will satisfy some axioms about identity and associativity based on the monoid axioms.
Hence in fact the name monad. Those axioms are taken as the definition of a general monad (not assumed a prior to be connected to an adjunction) on a category. Two constructions, the Kleisli category and the category of Eilenberg-Mac Lane algebras, are extremal solutions of the problem of constructing an adjunction starting with a given monad.
While monads are quite common, making them explicit is less so (the language belongs to the school of Mac Lane, and has rarely been used in the school of Grothendieck, which prefers to write out monads and comonads longhand). In categorical logic, an analogy has been drawn between the monad-comonad theory, and modal logic.

Synonym: Monad

Synonym: monas (n). (additional references)

Context	Synonyms within Context (source: adapted from Roget's Thesaurus).
Littleness	Animalcule, monad, mite, insect, emmet, fly, midge, gnat, shrimp, minnow, worm, maggot, entozoon; bacteria; infusoria; microzoa; phytozoaria; microbe; grub; tit, tomtit, runt, mouse, small fry; millet seed, mustard seed; barleycorn; pebble, grain of sand; molehill, button, bubble.
Source: adapted from Roget's Thesaurus.

Crosswords: Monad

English words defined with "monad": Diacid ♦ Monad deme, Monadical, Monadiform ♦ Plastide ♦ Quadrivalent. (references)

Specialty definitions using "monad": monad. (references)

Etymologies containing "monad": Monadaria, monas. (references)

Non-English Usage: "Monad" is also a word in the following languages with English translations in parentheses.

Swedish (monad), Turkish (monad).

Domain	Title
Books	Monad (reference) Monad and Thou: Phenomenological Ontology of Human Being (Series in Continental Thought, No 27) (reference) Monad to Man: The Concept of Progress in Evolutionary Biology (reference) The Monad and Other Essays upon the Higher Consciousness, 1920 (reference) (more book examples)
Source: compiled by the editor from various references; see credits.

"Monad" is generally used as a noun (singular) -- approximately 76.92% of the time. "Monad" is used about 13 times out of a sample of 100 million words spoken or written in English. Its rank is based on over 700,000 words used in the English language. Some parts-of-speech are not covered due to the samples used by the British National Corpus. (note: percents less than one-hundredth of one percent have been omitted)

Parts of Speech	Percent	Usage per 100 Million Words	Rank in English
Noun (singular)	76.92%	10	111,207
Noun (proper)	23.08%	3	202,518
Total	100.00%	13	N/A

Expression using "monad": monad deme. Additional references.
Source: compiled by the editor from various references; see credits.

The following statistics estimate the number of searches per day across the major English-language search engines as identified by various trade publications. Hyperlinks lead to commercial use of the expression at Amazon.com.

Language		Translations for "monad"; alternative meanings/domain in parentheses.
Albanian		monadë, radikal njëvalent, njëqelizor (unicellular), atom (atom, atomy). (various references)

Greek		μονάδα (denomination, unit). (various references)

Hungarian		monász. (various references)

Italian		monade. (various references)

Japanese Kanji		単細胞�"�物 (unicellular organism), 単子 . (various references)

Japanese Katakana		た�"さいぼうせいぶつ (unicellular organism), た�"し (short-term loan, terminal, verselet). (various references)

Pig Latin		onadmay

Portuguese		úbere (bag, dugout, handbag, mammal, teat, udder). (various references)

Romanian		monadã, element monovalent. (various references)

Russian		монада. (various references)

Serbo-Croatian		monada, jednoćelijski organizam (protista). (various references)

Spanish		mónada. (various references)

Swedish		monad. (various references)

Turkish		monad, zerre (atom, corpuscle, corpuscule, crumb, grain, granule, iota, jot, mite, molecule, mote, particle, rap, Ray, scintilla, shadow, sparklet, speck, tittle, touch, vestige, whit), tek hücreli canlı (protista), birim (unit), atom (atom, atomic, atomical, atomy, nuclear). (various references)

Ukrainian		одноклітинний організм, одновалентний елемент, монада. (various references)
Source: compiled by the editor from various translation references.

Language	Period	Translations
Greek	700 BCE-300 CE	monas. (various references)
Source: compiled by the editor from various references.

Derivations
	Words beginning with "monad": monadal, monadelphous, monades, monadic, monadism, monadisms, monadnock, monadnocks, monads. (additional references)
	Words ending with "monad": pseudomonad, trichomonad. (additional references)
	Words containing "monad": lemonade, lemonades, pseudomonades, pseudomonads, trichomonads. (additional references)
Misspellings
	"Monad" is suggested in spellcheckers for the following: Emona, Mbna, menad, menda, Mgonja, migawd, Mignard, minda, mnbdo, Mnda, Mnod, moad, mogad, mohand, Moja, Molndal, Monal, monam, Monarda, Monat, monaw, monax, mond, monda, Mondal, mondo, Moneda, monel, monen, moneo, Monga, moni, monid, monig, Monix, moniz, Monja, monka, monlam, monnot, monot, montade, Moondah, mopad, mosad, Mosnal, Mounan, Moynan, Muhadi, muna, murad, omad, Omand, Omyniad, onad, Vonadk. (additional references)
Source: compiled by the editor, based on several corpora (additional references).

Words rhyming with "monad" (pronounced 'Mon"ad'): Barad, gonad, hexad, Mesad, Messiad, Microfarad, salad, triad. (additional references)

Scrabble® Enable2K-Verified Anagrams
	Direct Anagrams: nomad.
	Words within the letters "a-d-m-n-o"
	-1 letter: damn, dona, mano, moan, noma.
	-2 letters: ado, and, dam, dom, don, mad, man, moa, mod, mon, nam, nod, nom.
	-3 letters: ad, am, an, do, ma, mo, na, no, od, om, on.
	Words containing the letters "a-d-m-n-o"
	+1 letter: almond, daemon, daimon, damson, dolman, domain, dynamo, fandom, moaned, monads, nomads, random, rodman.
	+2 letters: abdomen, adenoma, almonds, amidone, bondman, command, daemons, daimons, damsons, diamond, dolmans, domains, doorman, dormant, dynamos, fandoms, goddamn, goodman, gormand, madonna, madrona, madrone, madrono, madzoon, mandola, mangold, manhood, masoned, monacid, monadal, monades, monadic, monarda, mordant, nomadic, osmunda, quondam, randoms, rodsman, womaned, woodman.
Source: compiled by the editor from various references; see credits. SCRABBLE® is a registered trademark. All intellectual property rights in and to the game are owned in the U.S.A and Canada by Hasbro Inc., and throughout the rest of the world by J.W. Spear & Sons Limited of Maidenhead, Berkshire, England, a subsidiary of Mattel Inc. Mattel and Spear are not affiliated with Hasbro.

Hexadecimal (or equivalents, 770AD-1900s) (references)

4D 6F 6E 61 64

Leonardo da Vinci (1452-1519; backwards) (references)

American Sign Language (origins from 1620-1817 in Italy and, especially, France) (references)

⁼

Semaphore (1791, in France) (references)

Braille (1829, in France) (references)

Morse Code (1836) (references)

-- --- -. .- -..

Dancing Men (Sir Arthur Conan Doyle, 1903) (references)

Binary Code (1918-1938, probably earlier) (references)

01001101 01101111 01101110 01100001 01100100

HTML Code (1990) (references)

&#77 &#111 &#110 &#97 &#100

ISO 10646 (1991-1993) (references)

004D 006F 006E 0061 0064

British Sign Language (Fingerspelling, BSL; 1992, British Deaf Association Dictionary of British Sign Language) (references)

Encryption (beginner's substitution cypher): (references)

4781806770

Non-English Dictionaries with "Monad"

Language	Coverage	Language Translations
Albanian	fjalor, qartësi, përcaktim, saktësi, transmetim, transferim	shqip, αλβανικόσ, Αλβανός, αλβανόσ, albán, albanese, albanês, arnãut, albanez, arnãuţesc, албанский, albanski, albanac, albanés, alban, Arnavut, албанський, албанка, албанець
Greek	λεξικό, ορισμός, μετάφραση	ελληνικόσ, 'Ελληνας, görög, greco, ギリシア語 , ギリシア�", grego, greacã, греческий, грек, grčki, grk, grčki jezik, griego, grek, yunanistan'a ait, yunanca, yunan, Yunanli, yunanlı, Rumca, rum, грецький, гречанка, грецька мова
Hungarian	szótár, meghatározás, definíció, fordítás	Ούγγρος, magyar, ungherese, unguresc, limba ungarã, limba maghiarã, ungureşte, ungur, maghiar, венгр, венгерский, mađarski jezik, mađarski, mađar, húngaro, ungrare, macarca, macar, угорська мова, угорський, угорка, угорець
Italian	dizionario, definizione, traduzione	Ιταλός, olasz, italiano, italienesc, italieneşte, italian, italianã, итальянский язык, итальянец, итальянский, italijan, italijanski jezik, italijanski, italiensk, italienska, italienare, italyanca, italyan, італі�"ць, італійська мова, італійський, італійка
Japanese Kanji	辭典 , 辞典 , 字引 , 辞林 , 字書 , ディーゼル電気車 , 言海 , 辞彙 , 辞書 , 確定 , ディーゼル電気車 , デ�'ドロ酢酸 , 翻訳	japonez, ιαπωνικόσ, Ιάπωνας· �"ιαπωνέζος, ιάπωνεσ, ιάπων, ιαπωνικά, japán, giapponese, 邦語 , 邦人 , ジャスミン茶 , ほう�", ジャパニーズ , ほうじ�", japonês, japonezã, японский, японец, japanski, japanski jezik, japanac, japonés, japansk, Japonca, японська мова, японський, японка, японець
Japanese Katakana	じい, じびき, じて�", ディクショナリー , じり�", じしょ, �'�"かい, ディクショナリ , デフィニション , ディフィニション , ていぎ, かくてい, へい�"ういどう, やくじゅつ, トランスレーション , やくしょ, やくしゅつ, �"うどく, ほ�"やく, ほ�"やくしょ	japonez, ιαπωνικόσ, Ιάπωνας· �"ιαπωνέζος, ιάπωνεσ, ιάπων, ιαπωνικά, japán, giapponese, 邦語 , 邦人 , ジャスミン茶 , ほう�", ジャパニーズ , ほうじ�", japonês, japonezã, японский, японец, japanski, japanski jezik, japanac, japonés, japansk, Japonca, японська мова, японський, японка, японець
Portuguese	dicionário, definição, tradução	portugez, portugalisht, πορτογάλοσ, � ορτογάλος, portugál, portoghese, ポルトガル語 , ポルトガル�", português, portughez, португальский, portugalski jezik, portugalac, portugalski, portugués, portugis, portekizce, portekiz, Portekízlí, portekizli, португальський, португальська мова, португалець
Romanian	dicţionar, definiţie, determinare, definire, translaţie, traducere, tãlmãcire	rumun, ρουμανόσ, Ρουμάνος, román, rumeno, romeno, român, румынский, румын, rumunski jezik, rumunski, rumano, rumänsk, румунський, румунка, румунська мова, румун
Russian	словарь, определение, трансляция, сдвиг, перевод, перемещение	Ρώσος, orosz, russo, ロシア語 , ロシア�", русский, ruski jezik, ruski, ruso, ryss, Rusça, росіянка, росіянин, російська мова, російський
Serbo-Croatian	leksikon, rečnik, definicija, tumačenje	servo-croata, sârbo-croat, srpsko-hrvatski jezik, srpsko-hrvatski, serbokroatiska, serbokroatisk
Spanish	diccionario, definición, traducción	spanjoll, ισπανικά, ισπανικόσ, ισπανοί, spanyol, spagnolo, スペイン語 , スパイ罪 , スペイン�", スパニッシュ , espanhol, spaniol, spaniolesc, spanioleşte, испанский, španski, španski jezik, español, spanska språk, spansk, ispanyollar, ispanyol, ispanyolca, іспанський, іспанська мова
Swedish	ordbok, lexikon, översättning	suedez, σουηδικόσ, σουηδικά, svéd, svedese, スウェーデン語 , スウェーデン�", шведский, švedski jezik, švedski, sueco, svensk, isveççe, isveç dili, isveç, Ísveçlí, шведська мова, шведський
Turkish	sözlük, ansiklopedik sözlük, açıklama, belirleme, belirtme, kesinleştirme, tanım, tarif, seçiklik, tanımlama, tercüme	turk, τούρκικοσ, török, turcesc, turc, турецкий, turski jezik, turski, turco, turkisk, türkçe, türk, турецький, турецька мова
Ukrainian	словник, довідник, чіткість, тлумачення, виразність, визначення, дефініція, ясність, чітка чутність, процес перекладу, переклад, пояснення, переміщення	ukrainisht, ukrainas, ουκρανικόσ, Ουκρανός, ουκρανόσ, ukrán, ucraino, ucraniano, ucrainean, украинский язык, украинский, украинец украинский, ukrajinski, ukrajina, ucranio, ukrainare, ukraynalı, ukrayna, ukraynaca, український, українець
English	Dictionary, Definition, Translation	anglezët, anglez, gjuhë zngleze, anglishte, anglisht, εγγλέζοσ, αγγλικόσ, angol, inglese, inglês, englezesc, английский, engleski, englez, engleski jezik, inglés, engelsk, ingiltere, ingiliz, Íngílízce, ingilizce, Íngílíz, ýngilizce, англійський, англійці, англійська мова

Expression	Frequency per Day
monad	53
leibniz monad	3
Source: compiled by the editor from various references; see credits.

Monad

Definition: Monad

Monad

Noun

Specialty Definitions: Monad

Specialty Definition: Monad

Monad (category theory)

Synonym: Monad

Synonyms within Context: Monad

Littleness

Crosswords: Monad

Commercial Usage: Monad

Books

Usage Frequency: Monad

Expression: Monad

Frequency of Internet Keywords: Monad

Modern Translation: Monad

Albanian

Greek

Hungarian

Italian

Japanese Kanji

Japanese Katakana

Pig Latin

Portuguese

Romanian

Russian

Serbo-Croatian

Spanish

Swedish

Turkish

Ukrainian

Ancestral Language Translations: Monad

Derivations & Misspellings: Monad

Derivations

Misspellings

Rhyming with "Monad"

Anagrams: Monad

Scrabble® Enable2K-Verified Anagrams

Alternative Orthography: Monad

4D 6F 6E 61 64

-- --- -. .- -..

01001101 01101111 01101110 01100001 01100100

&#77 &#111 &#110 &#97 &#100

004D 006F 006E 0061 0064

4781806770

Non-English Dictionaries with "Monad"

INDEX