Crossword clues for monad
monad
The Collaborative International Dictionary
Monad \Mon"ad\, n. [L. monas, -adis, a unit, Gr. ?, ?, fr. mo`nos alone.]
An ultimate atom, or simple, unextended point; something ultimate and indivisible.
(Philos. of Leibnitz) The elementary and indestructible units which were conceived of as endowed with the power to produce all the changes they undergo, and thus determine all physical and spiritual phenomena.
(Zo["o]l.) One of the smallest flagellate Infusoria; esp., the species of the genus Monas, and allied genera.
(Biol.) A simple, minute organism; a primary cell, germ, or plastid.
-
(Chem.) An atom or radical whose valence is one, or which can combine with, be replaced by, or exchanged for, one atom of hydrogen.
Monad deme (Biol.), in tectology, a unit of the first order of individuality.
Douglas Harper's Etymology Dictionary
"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.
Wiktionary
n. 1 An ultimate atom, or simple, unextended point; something ultimate and indivisible. 2 (context mathematics computing English) A monoid in the category of endofunctors. 3 (cx botany English) A single individual (such as a pollen grain) that is free from others, not united in a group.
WordNet
Wikipedia
Monad may refer to:
In category theory, a branch of mathematics, a monad (also triple, triad, standard construction and fundamental construction) is an endofunctor (a functor mapping a category to itself), together with two natural transformations. Monads are used in the theory of pairs of adjoint functors, and they generalize closure operators on partially ordered sets to arbitrary categories.
The Monad in early Christian gnostic writings is an adaptation of concepts of the Monad in Greek philosophy to Christian gnostic belief systems.
Monad (from Greek μονάς monas, "unit" in turn from μόνος monos, "alone"), refers in cosmogony (creation theories) to the first being, divinity, or the totality of all beings. The concept was reportedly conceived by the Pythagoreans and may refer variously to a single source acting alone and/or an indivisible origin. The concept was later adopted by other philosophers, such as Leibniz, who referred to the monad as an elementary particle. It had a geometric counterpart, which was debated and discussed contemporaneously by the same groups of people.
In music, a monad is a single note or pitch. The Western chromatic scale, for example, is composed of twelve monads. Monads are contrasted to dyads, groups of two notes, triads, groups of three, and so on.
In non-standard analysis, a monad (also called halo) is the set of points infinitesimally close to a given point.
Given a hyperreal number x in R, the monad of x is the set
monad(x) = {y ∈ R ∣ x − yis infinitesimal}.
If x is finite (limited), the unique real number in the monad of x is called the standard part of x.
In linear and homological algebra, a monad is a 3-term complex
A → B → Cof objects in some abelian category whose middle term B is projective and whose first map A → B is injective and whose second map B → C is surjective. Equivalently a monad is a projective object together with a 3-step filtration (B ⊃ ker(B → C) ⊃ im(A → B)). In practice A, B, and C are often vector bundles over some space, and there are several minor extra conditions that some authors add to the definition. Monads were introduced by .
In functional programming, monads are a way to build computer programs by joining simple components in predictable and robust ways. A monad is a structure that represents computations defined as sequences of steps: a type with a monad structure defines what it means to chain operations together, or nest functions of that type. This allows the programmer to build pipelines that process data in a series of steps (i.e. a series of actions applied to the data), in which each action is decorated with additional processing rules provided by the monad.
Monads allow a programming style where programs are written by putting together highly composable parts, combining in flexible ways the possible actions that can work on a particular type of data. As such, monads have been described as "programmable semicolons"; a semicolon is the operator used to chain together individual statements in many imperative programming languages, thus the expression implies that extra code will be executed between the actions in the pipeline. Monads have also been explained with a physical metaphor as assembly lines, where a conveyor belt transports data between functional units that transform it one step at a time. They can also be seen as a functional design pattern to build generic types.
Purely functional programs can use monads to structure procedures that include sequenced operations like those found in structured programming. Many common programming concepts can be described in terms of a monad structure without losing the beneficial property of referential transparency, including side effects such as input/output, variable assignment, exception handling, parsing, nondeterminism, concurrency, continuations, or domain-specific languages. This allows these concepts to be defined in a purely functional manner, without major extensions to the language's semantics. Languages like Haskell provide monads in the standard core, allowing programmers to reuse large parts of their formal definition and apply in many different libraries the same interfaces for combining functions.
The name and concept comes from category theory, where monads are one particular kind of functor, a mapping between categories; although the term monad in functional programming contexts is usually used with a meaning corresponding to that of the term strong monad in category theory.
Usage examples of "monad".
But, leaving aside all such incidental speculations, the chief interest of the dynamic atomistic or monad theory, as affording a solid basis for immortality, is in relation to the arrogance of a shallow and conceited materialism.
The union of the Monad and Duad produces the Triad, signifying the world formed by the creative principle out of matter.
Or perhaps there is one monad for each member, or a monad for the first, with a dyad for its next, since there exists a series, and a corresponding number for every successive total, decad for ten, and so on.
The final particles or monads of air or granite are not dissolvingly blended into continuity of unindividualized atmosphere or rock when united with their elemental masses, but are thrust unapproachably apart by molecular repulsion.
This monad was once supposed to be a single animal, but the microscope shows it to be a group of animals connected by means of six processes, and each little growing volvox exhibits his red-eye speck and two long spines, or horns.
Its oneness must not be entitled to that of monad and point: for these the mind abstracts extension and numerical quantity and rests upon the very minutest possible, ending no doubt in the partless but still in something that began as a partible and is always lodged in something other than itself.
Hume must have admitted, and in fact does admit, the possibility that the mind is a Leibnitzian monad, or a Fichtean world-generating Ego, the universe of things being merely the picture produced by the evolution of the phenomena of consciousness.
The interpretation of the Hermetic fables shows, among every ancient people, in their principal gods, first, 1, the Creating Monad, then 3, then 3 times 3, 3 times 9, and 3 times 27.
Nuit, Hehu and Hehit, Kaku and Kakit, Ninu and Ninit, the god One and the god Eight, the Monad and the Ogdoad.
And just as there is, primarily or secondarily, some form or idea from the monad in each of the successive numbers--the later still participating, though unequally, in the unit--so the series of Beings following upon The First bear, each, some form or idea derived from that source.
Each particular, considered in itself, would be a manifold of monads, totalling to a collective unity.
I have ignored the fact that humans are not isolated monads, existing trapped inside their own heads, but are profoundly social beings, continually interact-with the outside worlds of things and people.
Tiny particles, or life monads, assemble and reassemble, in this form and that form.
Some monads intermingle and ascend the life cycle from sand and water through the vegetable and animal realms to those higher creatures who possess five senses, a category that includes not only human beings but the gods themselves.
Father Caspar describes it as a “Sphynx Mystagoga, an Oedipus Aegyp-tiacus, a Monad leroglyphica, a Clavis Convenientia Lin-guarum, a Theatrum Cosmographicum Historicum, a Sylva Sylvarum of every alphabet natural and artificial, an Archi-tectura Curiosa Nova, a Combinatory Lamp, Mensa Isiaca, Metametricon, Synopsis Anthropoglottogonica, Basilica Cryp-tographica, an Amphitheatrum Sapientiae, Cryptomenesis Patefacta, Catoptron Polygraphicum, a Gazophylacium Ver-borum, a Mysterium Artis Steganographicae, Area Arithmo-logica, Archetypon Polyglotta, an Eisagoge Horapollinea, Congestorium Artificiosae Memoriae, Pantometron de Furtivis Literarum Notis, Mercurius Redivivus, and an Etymologicon Lustgartlein!