Duality may refer to:

Mathematics

Duality (mathematics) In mathematics, a duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of is , then the ...

, a mathematical concept **

Dual (category theory) In category theory, a branch of mathematics, duality is a correspondence between the properties of a category ''C'' and the dual properties of the opposite category ''C''op. Given a statement regarding the category ''C'', by interchanging the sou ...

, a formalization of mathematical duality **

Duality (optimization) In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem. If the primal is a minimization problem then th ...

Duality (order theory) In the mathematical area of order theory, every partially ordered set ''P'' gives rise to a dual (or opposite) partially ordered set which is often denoted by ''P''op or ''P'd''. This dual order ''P''op is defined to be the same set, but with th ...

, a concept regarding binary relations **

Duality (projective geometry) In geometry, a striking feature of projective planes is the symmetry of the roles played by points and lines in the definitions and theorems, and (plane) duality is the formalization of this concept. There are two approaches to the subject of dua ...

, general principle of projective geometry **

Duality principle (Boolean algebra) In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas in ...

, the extension of order-theoretic duality to Boolean algebras **

S-duality (homotopy theory) In theoretical physics, S-duality (short for strong–weak duality, or Sen duality) is an equivalence of two physical theories, which may be either quantum field theories or string theories. S-duality is useful for doing calculations in theoret ...

Philosophy, logic, and psychology

Dualistic cosmology Dualism in cosmology or dualistic cosmology is the moral or spiritual belief that two fundamental concepts exist, which often oppose each other. It is an umbrella term that covers a diversity of views from various religions, including both traditi ...

, a twofold division in several spiritual and religious worldviews *

Dualism (philosophy of mind) Dualism most commonly refers to: * Mind–body dualism, a philosophical view which holds that mental phenomena are, at least in certain respects, not physical phenomena, or that the mind and the body are distinct and separable from one another ** ...

, where the body and mind are considered to be irreducibly distinct *

De Morgan's laws In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British mathem ...

, specifically the ability to generate the dual of any logical expression * Complementary duality of Carl Jung's functions and types in

Socionics Socionics, in psychology and sociology, is a pseudoscientific theory of information processing and personality types. It incorporates Carl Jung's work on '' Psychological Types'' with Antoni Kępiński's theory of information metabolism. Socioni ...

Duality (CoPs) In the theory of community of practice, an interdisciplinary field between sociology of education and educational psychology, the notion of a duality is used to capture the idea of the tension between two opposing forces which become a driving f ...

, refers to the notion of a duality in a Community of Practice

Science

Electrical and mechanical

Duality (electrical circuits) In electrical engineering, electrical terms are associated into pairs called duals. A dual of a relationship is formed by interchanging voltage and current in an expression. The dual expression thus produced is of the same form, and the reason t ...

, regarding isomorphism of electrical circuits *

Duality (mechanical engineering) In mechanical engineering, many terms are associated into pairs called duals. A dual of a relationship is formed by interchanging force (stress) and deformation (strain) in an expression. Here is a partial list of mechanical dualities: * force & ...

, regarding isomorphism of some mechanical laws

Physics

AdS/CFT correspondence In theoretical physics, the anti-de Sitter/conformal field theory correspondence, sometimes called Maldacena duality or gauge/gravity duality, is a conjectured relationship between two kinds of physical theories. On one side are anti-de Sitter s ...

(anti de Sitter/conformal field theory correspondence), sometimes called the Maldacena duality *

Dual resonance model In theoretical physics, a dual resonance model arose during the early investigation (1968–1973) of string theory as an S-matrix theory of the strong interaction. Overview The dual resonance model was based upon the observation that the amplitud ...

Duality (electricity and magnetism) In physics, the electromagnetic dual concept is based on the idea that, in the static case, electromagnetism has two separate facets: electric fields and magnetic fields. Expressions in one of these will have a directly analogous, or dual, ex ...

* Englert–Greenberger duality relation *

Holographic duality The holographic principle is an axiom in string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region — such as a l ...

Kramers–Wannier duality The Kramers–Wannier duality is a symmetry in statistical physics. It relates the free energy of a two-dimensional square-lattice Ising model at a low temperature to that of another Ising model at a high temperature. It was discovered by Hendri ...

* *

Mirror symmetry (string theory) In algebraic geometry and theoretical physics, mirror symmetry is a relationship between geometric objects called Calabi–Yau manifolds. The term refers to a situation where two Calabi–Yau manifolds look very different geometrically but are n ...

Montonen–Olive duality Montonen–Olive duality or electric–magnetic duality is the oldest known example of strong–weak duality or S-duality according to current terminology. It generalizes the electro-magnetic symmetry of Maxwell's equations by stating that magne ...

Mysterious duality M-theory is a theory in physics that unifies all consistent versions of superstring theory. Edward Witten first conjectured the existence of such a theory at a string theory conference at the University of Southern California in 1995. Witten' ...

String duality String or strings may refer to: *String (structure), a long flexible structure made from threads twisted together, which is used to tie, bind, or hang other objects Arts, entertainment, and media Films * ''Strings'' (1991 film), a Canadian anim ...

, a class of symmetries **

S-duality In theoretical physics, S-duality (short for strong–weak duality, or Sen duality) is an equivalence of two physical theories, which may be either quantum field theories or string theories. S-duality is useful for doing calculations in theoret ...

T-duality In theoretical physics, T-duality (short for target-space duality) is an equivalence of two physical theories, which may be either quantum field theories or string theories. In the simplest example of this relationship, one of the theories descr ...

U-duality In physics, U-duality (short for unified duality)S. Mizoguchi,On discrete U-duality in M-theory, 2000. is a symmetry of string theory or M-theory combining S-duality and T-duality transformations. The term is most often met in the context of the ...

Wave–particle duality Wave–particle duality is the concept in quantum mechanics that every particle or quantum entity may be described as either a particle or a wave. It expresses the inability of the classical concepts "particle" or "wave" to fully describe the ...

Music

Albums

* ''Duality'' (Peter Leitch and John Hicks album), 1994 * ''Duality'' (Lisa Gerrard and Pieter Bourke album), 1998 * ''Duality'' (Set It Off album), 2014 * ''Duality'' (Ra album), 2005 * ''Duality'' (mixtape), 2012 * ''Duality'' (Luna Li album), 2022 * ''Duality'', a 2009 album by

Darker Half Darker-half is a heavy metal band from Sydney, led by vocalist Vo Simpson and known for their energetic live performances, their style has been described as power/thrash. History Singer/guitarist Vo Simpson started Darker Half in 2003 whil ...

* ''Duality'', a 2020 album by

Duke Dumont Adam George Dyment (born August 1981), better known by his stage name Duke Dumont, is an English DJ and record producer. He is best known for his hit singles "Need U (100%)" "I Got U", " Ocean Drive" and " Won't Look Back" which both reached n ...

* ''Duality'', a 2018 album by

Big Scoob Stewart D. Ashby Jr. (born May 9, 1973) better known by his stage name Big Scoob is an American rapper from Kansas City, Missouri, who records for Strange Music. Early life Big Scoob spent his late adolescence and part of his early adulthood ...

Songs

* "Duality", a 2014 single from pop rock/punk rock band Set It Off * "Duality" (song), a 2004 single by metal band Slipknot * "Duality", a 2007 single from alternative rock/punk band Bayside

Other

* ''Duality'' (film), a 2001 Star Wars fan film by Dave Macomber and Mark Thomas * Duality, a large format audio mixing console by

Solid State Logic Solid State Logic (SSL) is a British company based in Begbroke, Oxfordshire, England that designs and markets audio mixing consoles, signal processors, and other audio technologies for the post-production, video production, broadcast, sound ...

Dual (grammatical number) Dual (abbreviated ) is a grammatical number that some languages use in addition to singular and plural. When a noun or pronoun appears in dual form, it is interpreted as referring to precisely two of the entities (objects or persons) identified ...

, grammatical number that some languages use in addition to singular and plural