Then there are dualities in math, which can sometimes be interpreted physically as consequences of dualities between two quantum field theories.
|
|
Each portrait in Obert's series, entitled "Dualities," has two sides.
|
|
It's open-ended because there are so many different kinds of dualities.
|
|
It is multilayered and riven by dualities, male or female no matter.
|
|
These five string theories connect to each other through "dualities," or mathematical equivalences.
|
|
Does this (2000,229) theory play an important role in the web of dualities?
|
|
The ensemble is an unresolved one, encapsulating the dualities present in any wearer.
|
|
Dualities are interesting because they frequently answer questions that are otherwise out of reach.
|
|
Those kind of dualities are a rich place to write from because there's raging conflict.
|
|
Those are modern-day dualities that both queers and Satanists are all too familiar with.
|
|
Physicists are talking more than ever lately about dualities, but you've been studying them for decades.
|
|
According to WWD, Franco's "harmonious dualities" are what make him just the right fit for the gig.
|
|
"I've always been obsessed with the dualities that exist in the idea of American style," Dolan says.
|
|
Good Morning America meterologist Ginger Zee enjoys the dualities of running: It's a simple act, but also tough.
|
|
We see these dualities within the city, the clash of cultures that come together in this perfect symbiosis.
|
|
Black Panther, mixed-in with a fantastical story and commentary on identity and racial dualities changed that completely.
|
|
And Mr. Lynch, who is directing the entire revival, still has his penchant for dualities and eerie beauty.
|
|
This novel tries to talk about faith and doubt in a completely different way to move beyond dualities.
|
|
It all feels like a song about dualities, the subtle and airy music crossing with his booming, deep voice.
|
|
I think these dualities such as shy boi and hard femme also reflect in your artwork and fashion design.
|
|
An awful lot of important dualities in four and fewer dimensions follow from this six-dimensional theory and its properties.
|
|
The songs themselves hold dualities; "Cadillac Ranch," the album's most irresistibly twangy stomp and holler, praises cars yet contemplates death.
|
|
"I had to see things from two very different perspectives, so I've always been very interested in dualities," he says.
|
|
The work is about building up these dualities to then break them down and find a better identity that's less compartmentalised.
|
|
These include feminism and dualities of gender (though not yet homosexual love, still a matter of fierce political debate in India).
|
|
The Japanese writer-director Makoto Shinkai has a thing for dualities and a penchant for imaginatively blurring the divide between them.
|
|
Speaking of dualities, we've reached the point in this story in which O.J. the person is being eclipsed by O.J. the celebrity.
|
|
Heems: I'm used to thinking in dualities, especially when it comes to the Indian part of my identity and my American one.
|
|
Potential horrors must be presented with a positive dualities—a pair of scissors, a black family in America, and a horror film.
|
|
His preoccupations therein are with dualities, dichotomies and doubles: philanderer-penitent, solitude-solipsism, prince-pauper, Clark Kent-Superman, to name just a few.
|
|
So you can ask why dualities exist, but you can also ask why is there a 6-D theory with such and such properties?
|
|
He made himself a unifier of dualities — racial, sexual, musical, cultural — teasing at them in songs like "Controversy" and transcending them in his career.
|
|
It could touch on these dualities which I think he feels a lot in his own struggles between a personal and a public life.
|
|
Enter: Tory Burch's Gemini Link, a new collection anchored by a symmetrical, double-link design motif inspired by the many dualities in the designer's life.
|
|
Liz Collins' new solo show at LMAK Gallery is full of dynamic dualities: works both hard and soft, chaotic and orderly, three-dimensional and flat.
|
|
The ability to reconcile these dualities—to sift through all the internet's shit and embrace it anyway – is why The 1975's latest album is so refreshing.
|
|
Where Talking Heads had dealt in tensions and dualities, Ms. Kidjo's element was joyful empowerment: the joy of an all-conquering voice and a righteous, uplifting spirit.
|
|
But one of the offshoots of the string dualities of the 210s was that it was discovered that quantum field theories actually exist in five and six dimensions.
|
|
Dualities sometimes make it hard to maintain a sense of what's real in the world, given that there are radically different ways you can describe a single system.
|
|
It is, however, an apt name for a particularly bloody episode, and one that operates within dualities: What's on the outside may not match what's on the inside.
|
|
David Lynch and Mark Frost are captivated by dualities, whether they're giving their characters literal doppelgängers or they're exploring the extremes of good and evil within humanity as a whole.
|
|
Called "Urban Dualities," the work is a series of fragments and details of life at street level, a collaging of peculiar objects and sights seen while commuting on the train.
|
|
Garner's representations of the vagina are often deconstructed or abstracted, but the sheer relentlessness of this imagery reveals her interest in engaging with its culturally encoded symbolism, politics, and dualities.
|
|
Well, one thing I'll tell you is that in general, when you have dualities, things that are easy to see in one description can be hard to see in the other description.
|
|
The latest offering from the Los Angeles-based furniture design studio Waka Waka, the aptly named Compartment Chair, may appear simple, with its clean rectilinear form, but it's a study in dualities.
|
|
The rising star Arushi Mudgal from New Delhi in a classical Odissi solo, the North Indian vocalist Rattan Mohan Sharma and a new program: "Dualities in Dance" featuring Mesma Belsare and Kiran Rajagopalan.
|
|
Her books are interested in power and dualities; in the impulses we repress until we have the power to explore them, and in the anxieties expressed by dystopias and the fantasies implicit to utopias.
|
|
The Meyers-Briggs test revolves around dualities that don't really exist (introversion and extroversion, for instance, are assessed on a sliding scale, and are not opposites) and is entirely based on outmoded Jungian theories.
|
|
Frank Ocean mines the myriad dualities of his life and stunts about owning bundles of thousand-dollar Delta Air Lines gift cards on "Chanel," one of the several dynamic singles that Ocean released this year.
|
|
This playlist consists of musicians born under the sign of the twins, and pairs two of their songs representing the dualities of a Gemini: egotistical and vulnerable; hard and soft; frantic and formulaic; light and dark.
|
|
That such simultaneity defines the vagaries of daily life is hardly new; nor is the idea that women might be particularly well schooled — via the open-admission reality of sexism — to navigate these dualities in creative ways.
|
|
And I have come to distrust unstable dualities like mind or brain, artificial divisions like nature or nurture, and seductive dichotomies that should not end but merely begin an inquiry — such as having one office for answers and another for questions.
|
|
When Witten arrived minutes later, we spoke for an hour and a half about the meaning of dualities in physics and math, the current prospects of M-theory, what he's reading, what he's looking for, and the nature of reality.
|
|
There are dualities between a gauge theory [a theory, such as a quantum field theory, that respects certain symmetries] and another gauge theory, or between a string theory for weak coupling [describing strings that move almost independently from one another] and a string theory for strong coupling.
|
|
Now, in the limelight of their success, and with the diaspora communities in France and worldwide openly celebrating the dualities of their peripheral identities, the French establishment is pushing back, insisting that the players are purely "French" and that to bring up their African heritage is a racist sentiment.
|
|
For a horror film fixated on dualities and killer doubles, the most consistent thing about Jordan Peele's Us is the ease with which it navigates between our own man-made horrors—the effects of classism and marginalization—and a fiction that can entertain without those issues in mind.
|
|
You want to bottle it just as you hope someone may find a way to harness the reverberant energy of labels like Official Rebrand, whose collection was so rife with wacko references — graffiti, sloganeering, kiddie sketches and femme-butch dualities — that if the designer, MI Leggett, omitted the kitchen sink it must have been an oversight.
|
|
If we split Valentine's Day apart into its core values, we end up with a celebration of love and food — a set of complimentary dualities that Le Creuset just happens to be honoring in the most compelling way today: The French cookware company is hosting a sale timed to the upcoming February 14 holiday with slashed prices on a love-worthy spread of kitchen essentials. A.k.a.
|
|
Niru's homosexuality is very much the book's subject, and the text is interested in dualities — Americans and Africans, white and black, gay and straight, devout and skeptic, the black immigrant and the black American (a role filled by Damien, a college student with whom our hero has a sweet, chaste fling) — while always returning to the question of what his gayness says about who Niru is.
|
|
The dualities on the debut album from Swet Shop Boys are best expressed in the song "Half Moghul Half Mowgli" where Riz MC raps about being, "Raised like a concrete jungli / And a junglist and a Londonist / But my DNA wonder where my home should be…" Therein lies the anxiety for so many people of colour born in the diaspora, reconciling where they're from with where they're at.
|
|
A diagram of string theory dualities. Yellow arrows indicate S-duality. Blue arrows indicate T-duality. These dualities may be combined to obtain equivalences of any of the five theories with M-theory.
|
|
In string theory the hyperdeterminant first surfaced in connection with string dualities and black hole entropy.
|
|
In mathematics, there is an ample supply of categorical dualities between certain categories of topological spaces and categories of partially ordered sets. Today, these dualities are usually collected under the label Stone duality, since they form a natural generalization of Stone's representation theorem for Boolean algebras. These concepts are named in honor of Marshall Stone. Stone-type dualities also provide the foundation for pointless topology and are exploited in theoretical computer science for the study of formal semantics.
|
|
Zimmer, Jenny. "Grahame King: Dualities". In The Art of Grahame King by Sasha Grishin, 77–85. Zimmer, Jenny.
|
|
118 (1988) 411–449. to the check of various dualities, and precision tests of the AdS/CFT correspondence.
|
|
Put differently, the two theories are mathematically different descriptions of the same phenomena. Like many of the dualities studied in theoretical physics, T-duality was discovered in the context of string theory.Sathiapalan 1987. Other dualities that arise in string theory are S-duality, U-duality, mirror symmetry, and the AdS/CFT correspondence.
|
|
Theorems showing that certain objects of interest are the dual spaces (in the sense of linear algebra) of other objects of interest are often called dualities. Many of these dualities are given by a bilinear pairing of two K-vector spaces :A ⊗ B → K. For perfect pairings, there is, therefore, an isomorphism of A to the dual of B.
|
|
The different theories allow different types of strings, and the particles that arise at low energies exhibit different symmetries. In the mid 1990s, physicists noticed that these five string theories are actually related by highly nontrivial dualities. One of these dualities is S-duality. The existence of S-duality in string theory was first proposed by Ashoke Sen in 1994.
|
|
2003, p. xvi Such dualities play an important role in modern physics, especially in string theory.Other dualities that arise in string theory are S-duality, T-duality, and the AdS/CFT correspondence. Regardless of whether Calabi–Yau compactifications of string theory provide a correct description of nature, the existence of the mirror duality between different string theories has significant mathematical consequences.Zaslow 2008, p.
|
|
South African feminism aligns with the agenda of global feminism as a continuous project designed to deconstruct and challenge the dualities and binaries between men and women in the eyes of society and the state. Feminism in South Africa is rooted in distinctly different epistemologies and beliefs of women and women's work than the beliefs that ground other modern inequitable social structures, such as worker's compensation. International feminist theory asserts that exclusive dualities between men and women serve as the groundings on which discriminatory laws and practices lie. Modern South African feminists aim to deconstruct these dualities by politicizing the lives of women and demanding gender equality laws.
|
|
Dintenfass' themes explore the dualities of everyday pleasures; depending on the focus of a series, her symbols might conjure characters, candies, car wheels, or paint itself.
|
|
Similar dualities establish relations between free energies of other statistical models. For instance, in 3 dimensions the Ising model is dual to an Ising gauge model.
|
|
University of Southern California, Los Angeles, Future Perspectives in String Theory, March 13-18, 1995, E. Witten: Some problems of strong and weak coupling Witten's proposal was based on the observation that the five string theories can be mapped to one another by certain rules called dualities and are identified by these dualities. Witten's announcement led to a flurry of work now known as the second superstring revolution.
|
|
The different theories allow different types of strings, and the particles that arise at low energies exhibit different symmetries. In the mid 1990s, physicists noticed that these five string theories are actually related by highly nontrivial dualities. One of these dualities is T-duality. For example, it was shown that type IIA string theory is equivalent to type IIB string theory via T-duality and also that the two versions of heterotic string theory are related by T-duality.
|
|
In the words of Michael Atiyah, The following list of examples shows the common features of many dualities, but also indicates that the precise meaning of duality may vary from case to case.
|
|
These ideas put forth a story of an evolving universe and potential human experience of wholeness in which dualities dissipate—dualities that have marked past eras and contributed to the destruction of the earth as "other" than spirit. A Catholic nun interviewed by Sarah MacFarland Taylor, author of the 2009 book, “Green Sisters: Spiritual Ecology” (Harvard University Press, 2009), articulates this perspective of unity: “There is no division between planting new fields and prayer.”See Harvard University Press, Interview with Sarah McFarland Taylor on the HUP Podcast.
|
|
533–4 By applying mirror symmetry, theorists can translate difficult calculations in the A-model into equivalent but technically easier calculations in the B-model. These calculations are then used to determine the probabilities of various physical processes in string theory. Mirror symmetry can be combined with other dualities to translate calculations in one theory into equivalent calculations in a different theory. By outsourcing calculations to different theories in this way, theorists can calculate quantities that are impossible to calculate without the use of dualities.
|
|
Retrieved January 9, 2020. Critics often note various, resulting dualities in her work: banality and profundity, humorous spectacle and near- apocalyptic concern, scientific empiricism and faith.Chattopadhyay, Collette. "Lynn Aldrich at Gallery LASCA," Artweek July 1997, p. 25.
|
|
In the spacial case where the dualities are the canonical dualities and , the transpose of a linear map is always well- defined. This transpose is called the algebraic adjoint of F and it will be denoted by ; that is, . In this case, for all , where the defining condition for is: : for all , or equivalently, for all . ;Examples If for some integer , is a basis for with dual basis , is a linear operator, and the matrix representation of with respect to is , then the transpose of is the matrix representation with respect to ℰ of .
|
|
With Iain Moffat, Ellis-Monaghan is the author of the book Graphs on Surfaces: Dualities, Polynomials, and Knots (Springer, 2013). With Matt Boelkins, she is co-editor-in-chief of PRIMUS, a journal on the teaching of undergraduate mathematics.
|
|
Laster is an avant-garde, atmospheric black metal band hailing from Utrecht, The Netherlands. However, the band describes their music as obscure dance music, expressing dualities and a rebellious affirmation of human existence in their musical and lyrical themes.
|
|
Marylyn Dintenfass (born 1943) is an American painter, printmaker, and sculptor. She is primarily known for her oil paintings, which use a dynamic color palette and lexicon of gestural imagery to explore dualities in the human experience and everyday sensual pleasures.
|
|
Higher Self, exhibiting the poet's struggle between his internal dualities. The first single "Magic Man" featured Kanye West, Common and John Legend. Another song called "By Your Side" which featured Destiny's Child member Michelle Williams and singer Brando, leaked on the internet.
|
|
The existence of these dualities showed that the five string theories were in fact not all distinct theories. In 1995, at the string theory conference at University of Southern California, Edward Witten made the surprising suggestion that all five of these theories were just different limits of a single theory now known as M-theory.Witten 1995 Witten's proposal was based on the observation that different superstring theories are linked by dualities and the fact that type IIA and E8×E8 heterotic string theories are closely related to a gravitational theory called eleven-dimensional supergravity. His announcement led to a flurry of work now known as the second superstring revolution.
|
|
Thus, Punjabi popular music eventually "evolved to neatly represent certain dualities that are considered to characterize Punjabi identity: East/West, guardians of tradition/embracers of new technology, local/diaspora."Schreffler, Gibb. 2012. "Migration Shaping Media: Punjabi Popular Music in a Global Historical Perspective." Popular Music and Society 35(3): 355.
|
|
His works explored the inner and the outer worlds with a strange narrative, which usually expressed dualities such as: female against male, good against evil, or nature against technology. Jon Serl was categorized as prolific. This might be due to the fact that he began painting at a late age.
|
|
According to Thomas Keith in Masculinities in Contemporary American Culture, the longstanding cultural assumption that male–female dualities are "natural and immutable" partly explains the persistence of systems of patriarchy and male privilege in modern society. Hyde and colleagues suggest that gender being visibly marked makes it become unnaturally psychologically salient.
|
|
With Anton Kapustin, he has made deep mathematical connections between S-duality of gauge theories and the geometric Langlands correspondence. Partly in collaboration with Seiberg, one of his recent interests include aspects of field theoretical description of topological phases in condensed matter and non-supersymmetric dualities in field theories that, among other things, are of high relevance in condensed matter theory. From a generalization of SYK models from condensed matter and quantum chaos, he has also recently brought tensor models of Gurau to the relevance of holographic and quantum gravity theories. In general, Witten has done influential and insightful works in many aspects of quantum field theories and mathematical physics, including the physics and mathematics of anomalies, integrability, dualities, localization, homologies and so on.
|
|
The utility of an object cannot be separated from its artistry and the form that it takes. The “Circle of Time”, shows that only through the mastery of these dualities they can surpass their wildest dreams, being more than equal to any challenge ahead of them. At HKUST their will is greater than their ambition.
|
|
A diagram of string theory dualities. Blue edges indicate S-duality. Red edges indicate T-duality. Up until the mid 1990s, physicists working on string theory believed there were five distinct versions of the theory: type I, type IIA, type IIB, and the two flavors of heterotic string theory (SO(32) and E8×E8).
|
|
A diagram of string theory dualities. Blue edges indicate S-duality. Red edges indicate T-duality. Up until the mid 1990s, physicists working on string theory believed there were five distinct versions of the theory: type I, type IIA, type IIB, and the two flavors of heterotic string theory (SO(32) and E8×E8).
|
|
The term "low energy limits" labels some 10-dimensional supergravity theories. These arise as the massless, tree-level approximation of string theories. True effective field theories of string theories, rather than truncations, are rarely available. Due to string dualities, the conjectured 11-dimensional M-theory is required to have 11-dimensional supergravity as a "low energy limit".
|
|
This notion has made it possible to use the methods of graph theory in universal algebra and several other directions of discrete mathematics and computer science. Graph algebras have been used, for example, in constructions concerning dualities , equational theories , flatness , groupoid rings , topologies , varieties , finite state automata , finite state machines , tree languages and tree automata etc.
|
|
Dievturība is primarily based on Latvian folklore, old folk songs (dainas) and Latvian mythology. The main god is Dievs, who unifies spirit and matter, as well as other dualities such as father and mother or good and bad. Other deities are either aspects of Dievs or other types of non-deified spirits. The goddess Māra represents Dievs' material aspect.
|
|
"My body is large, white and savage. But all fierceness has become transformed into laughter ... Everywhere where I would formerly fly at throats, I now howl with laughter.".Lewis, Wyndham, The Wild Body (London:Penguin Books, 2004) pp. 5-6 Lewis focuses on dualities: duality of nationality, French and American, English and French, English and American and French and Spanish.
|
|
Other themes include dissecting dualities (in particular, the duality between good and evil;) free will versus fate; going against social norms; power; and, most of all, the concept of choice. The three books in the trilogy span just one year, with A Great and Terrible Beauty beginning in June 1895 and The Sweet Far Thing ending in June 1896.
|
|
Julia also studied spontaneous symmetry breaking and the Higgs mechanism in supergravity Other work includes a study, with A. Zee, of particles called dyons that carry both electric and magnetic charges and many papers on string theory, M-theory, and dualities. In 1986, Julia was awarded the Prix Paul Langevin of the Société Française de Physique.
|
|
Sherman began exploring three-dimensional form in ceramic sculpture in the early 1980s. The contemplative work from this period presents serne animal and human forms to the viewers gaze. The organic sensual shapes evoke or are explicitly feminine in form. The tactile and often delicate porcelain work were metaphorical juxtapositions of fundamental dualities: peace and war, life and death.
|
|
In mathematics, Koszul duality, named after the French mathematician Jean- Louis Koszul, is any of various kinds of dualities found in representation theory of Lie algebras, abstract algebras (semisimple algebra)Ben Webster, Koszul algebras and Koszul duality. November 1, 2007 as well as topology (e.g., equivariant cohomologyMark Goresky, Robert Kottwitz, and Robert MacPherson. Equivariant cohomology, Koszul duality, and the localization theorem.
|
|
For example, the Galois group G of a field extension L / F acts on L×, the nonzero elements of L. This Galois module plays a significant role in many arithmetic dualities, such as Poitou-Tate duality. The Brauer group of F, originally conceived to classify division algebras over F, can be recast as a cohomology group, namely H2(Gal (F), ×).
|
|
This is the union of all the S-duality and T-duality available in that topology. The narrow meaning of the word "U-duality" is one of those dualities that can be classified neither as an S-duality, nor as a T-duality - a transformation that exchanges a large geometry of one theory with the strong coupling of another theory, for example.
|
|
Likewise, in this > tantric tradition, the unification of all the phenomenal and ultimate > aspects of the vajra-family, which abolishes all dualities, is nothing other > than the state of self-knowing: the state of knowing oneself as the cosmos, > society, individual, and enlightened awareness; and that self-knowledge is > what is meant by omniscience (sarva-jnana) in the tradition of the > Kālacakratantra.
|
|
The operators are related to one another by similar dualities to quantifiers do (for example by the analogous correspondents of De Morgan's laws). I.e., Something is necessary iff its negation is not possible, i.e. inconsistent. Syntactically, the operators are not quantifiers, they do not bind variables, but govern whole sentences. This gives rise to the problem of Referential Opacity, i.e.
|
|
Transpartisan, or transpartisanship, represents an emerging paradigm of political thought which accepts the validity of truths across a range of political perspectives and seeks to synthesize them into an inclusive, pragmatic container beyond typical political dualities. It is distinct from bipartisanship, which aims to negotiate between "right" and "left", resulting in a dualistic perspective, and nonpartisanship, which tends to avoid political affiliation altogether.
|
|
The invented biology reflects and exemplifies, according to Parker, the opposing but united dualities of Taoism such as light and darkness, maleness and femaleness, yin and yang. So too do the opposed characters of Genly Ai with his carefully objective reports, and of Estraven with his or her highly personal diary, as the story unfolds, illuminating humanity through adventure and science fiction strangeness.
|
|
Some compare the concept of a duality to that of yin and yang, i.e. two mutually defining opposites. The opposing entities in a duality need to be viewed from a perspective of balance rather than opposition. The term implies a dynamism, continual change and mutual adjustment as the tensions that are inherent in dualities can be both creative and constraining.
|
|
They moved to > Amsterdam and started techno group, Sushumna. "Sushumna is a Sanskrit word > which means the merging of dualities," explains Chris. :The Deckkers soon > moved to London, drawn by its techno scene, and events quickened apace. A > friend of Chris and Antara's, Sara Sol, was languishing in jail in India, > and the couple wanted to hold a party to raise money for her.
|
|
Ishwar Chandra Sharma describes it as "Absolute Reality, beyond all dualities of existence and non-existence, light and darkness, and of time, space and cause".Ishwar Chandra Sharma, Ethical Philosophies of India, Harper & Row, 1970, p.75. Influential ancient and medieval Hindu philosophers, states philosophy professor Roy Perrett, teach their spiritual ideas with a world created ex nihilo and "effectively manage without God altogether".
|
|
He has made several important contributions to dualities and other aspects of quantum field theories, in particular topological field theories and supersymmetric gauge theories. With Edward Witten he discovered deep connections between the S-duality of supersymmetric gauge theories and the geometric Langlands correspondence. In recent years, he has focused on mathematical structures in and classification schemes of topological field theories and symmetry protected topological phases.
|
|
In addition to the De Morgan dualities described above, some important equivalences in linear logic include: ; Distributivity : A\otimes(B\oplus C)\equiv(A\otimes B)\oplus(A\otimes C) ; Exponential isomorphism : \,!(A \& B)\equiv \,!A \otimes \,!B (Here A\equiv B\quad=\quad(A\multimap B)\&(B\multimap A).) Assume that ⅋ is any of the binary operators times, plus, with or par (but not linear implication).
|
|
The underlying theme of the novel is identity. It explores many dualities such as male/female, black/white, and famous/non-famous. Joss's experienced are shaped by his hidden transgender identity, as well as his identity as a black English man. The story explores the importance of identity, and other themes include familial relations, specifically between father and son, secrecy, insecurity, respect, and fame.
|
|
He is also interested in understanding the underlying meaning of string dualities, as well as trying to apply superstring theory to some unsolved questions of elementary particle physics such as the hierarchy problem and the cosmological constant problem. He has made contributions to topological string theories and to the understanding of mirror symmetry. He is a trustee of Network of Iranians for Knowledge and Innovation (NIKI).
|
|
According to the Shih wu yüan hui, quoted in the 19th century compilation Chi shuo ch'üan chén, the Eight Immortals represent dualities of characteristics: old and young, male and female, rich and poor, honored and humble, warriors and scholars, noble and disabled. Of these, says the Shih wu yüan hui, Lan is supposed to represent the young.Yetts, W. Perceval. “More Notes on the Eight Immortals.” p. 399.
|
|
Together with Dennis Gaitsgory and Kari Vilonen, he has proved the geometric Langlands conjecture for GL(n). His joint work with Robert Langlands and Ngô Bảo Châu suggested a new approach to the functoriality of automorphic representations and trace formulas. He has also been investigating (in particular, in a joint work with Edward Witten) connections between the geometric Langlands correspondence and dualities in quantum field theory.
|
|
He often works in distinct but interrelated series that play off one another conceptually and formally to explore various dualities: photographic authenticity and digital manipulation, function and dysfunctionality, the real and imaginary, two-dimensional surface and three-dimensional form.Michno, Christopher. "Amir Zaki – ACME," Artillery Magazine, May/June 2017, p. 51. Reviewers frequently note that despite Zaki's conceptual focus, his work also conveys strong formalist and sensual concerns.
|
|
To every Boolean algebra B we can associate a Stone space S(B) as follows: the elements of S(B) are the ultrafilters on B, and the topology on S(B), called the Stone topology, is generated by the sets of the form {F∈S(B) : b∈F}, where b is an element of B. Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to the Boolean algebra of clopen sets of the Stone space S(B); and furthermore, every Stone space X is homeomorphic to the Stone space belonging to the Boolean algebra of clopen sets of X. These assignments are functorial, and we obtain a category-theoretic duality between the category of Boolean algebras (with homomorphisms as morphisms) and the category of Stone spaces (with continuous maps as morphisms). Stone's theorem gave rise to a number of similar dualities, now collectively known as Stone dualities.
|
|
Kapoor often relies on tenets of Hinduism in his art and says that "The experience of opposites allows for the expression of wholeness." Primal dualities that are one, such as the lingam and yoni, are important to Indian culture, and Cloud Gate represents both the male and female in one entity by symbolizing both the vagina and testicles. Thus, it represents the tension between the masculine and the feminine.
|
|
Yet in the Memphite Theology, Geb, as judge, first apportions the realm between the claimants and then reverses himself, awarding sole control to Horus. In this peaceable union, Horus and Set are reconciled, and the dualities that they represent have been resolved into a united whole. Through this resolution, order is restored after the tumultuous conflict. A different view of the myth's end focuses on Horus's sole triumph.
|
|
Beyond this vocally feminine sound, the way consumers heard Brit funk shifted as the role of live performance joined the popularity of the 1970s DJ in clubs. By the 1980s, it was common for clubs to bring in Brit funk performers alongside DJs incorporating both an open and intimate space on the dancefloor. Brit funk was marked by these dualities: feminine and masculine, pleasure and politics, exclusionary and accessible.Strachan, Robert.
|
|
In Buddhist thought, this must be overcome, states Martin Southwold, through "the realization of anatta, which is nirvana". Nirvana in some Buddhist traditions is described as the realization of sunyata (emptiness or nothingness).; ; Madhyamika Buddhist texts call this as the middle point of all dualities (Middle Way), where all subject-object discrimination and polarities disappear, there is no conventional reality, and the only ultimate reality of emptiness is all that remains.
|
|
On the north side of the building, blues dominate, with brighter colors on the south side. The sun is placed on the east side. The windows are the largest of their kind in the world. The theme depicted by the windows centers on universal dualities and antagonisms, the struggle between life and death, good and evil, day and night and creation and destruction, all shown in a cosmic continuum.
|
|
Paul Stephen Aspinwall (born 26.January 1964 in England) is a British theoretical physicist and mathematician, who works on string theory (including dualities, mirror symmetry, D-branes, and Calabi-Yau manifolds) and also algebraic geometry. Aspinwall received his early education at Bydales School, Marske-by-the-Sea and Prior Pursglove College, Guisborough. He then studied at the University of Oxford with a focus on theoretical elementary particle physics.
|
|
In 1977 while at CERN Montonen, together with Olive, made the remarkable conjecture that there should exist an electromagnetic dual theory in which the roles of magnetic monopoles and gauge bosons are interchanged. The Montonen-Olive duality was later found to emerge from a deeper web of dualities underlying M-theory, ushering in the second superstring revolution of the mid 1990s, through the work of Ed Witten and others.
|
|
He affirms that all philosophical concepts come in dualities, which can be classified in two categories: sympathetic (or parallel) and antipathetic. A sympathetic duality is formed by two "positive" terms, which indicate an existence: time / space; spirit / matter; right / duty etc. An antipathetic duality contains a positive and a negative term: life / death; movement / inertia; good / evil etc. Now, each sympathetic duality produces a third term, through which the dualism is overcome.
|
|
The relationship towards her mother was torn between hatred and love, the last overweighing. Vita was not to dwarf her own beauty or question her value system. Therefore Vita tended to suppress her feminine side and adopt traits of masculine courting behaviour. Lady Sackville-West was a major model for the aristocratic ladies in The Edwardians, where Vita also dealt with the mother-daughter relationship of the Edwardian age. Vita’s personality was embossed by dualities.
|
|
The protagonist finds himself battling opposing dualities such as freedom versus responsibility, the individual versus society, and love versus death. Ward simplified his approach after the more complex, novelistic story of his previous book, Madman's Drum (1930), returning to the simplicity of his first, Gods' Man (1929). Wild Pilgrimage achieves more fluid pacing and varied imagery than the first two books, incorporating the influence of art movements such as American Regionalism and Futurism.
|
|
The Yoga Sutras 2:46 state that asanas, here Natarajasana, should be "steady and comfortable". In the Yoga Sutras, the only rule Patanjali suggests for practicing asana is that it be "steady and comfortable". The body is held poised with the practitioner experiencing no discomfort. When control of the body is mastered, practitioners are believed to free themselves from dualities such as heat and cold, hunger and satiety, or joy and grief.
|
|
The Brief and Frightening Reign of Phil is a 130-page novella by the American writer George Saunders. It has been described as a parable, and has been likened to Animal Farm by George Orwell. Its author has said it is about "the human tendency to continuously divide the world into dualities". Saunders wrote the book over a number of years at Syracuse University, New York, where he is a creative-writing professor.
|
|
This gives rise to a number of useful categorical dualities between the categories of all complete semilattices with morphisms preserving all meets or joins, respectively. Another usage of "complete meet-semilattice" refers to a bounded complete cpo. A complete meet-semilattice in this sense is arguably the "most complete" meet-semilattice that is not necessarily a complete lattice. Indeed, a complete meet-semilattice has all non-empty meets (which is equivalent to being bounded complete) and all directed joins.
|
|
His work spans a range of different subjects, including string perturbation theory at higher orders, quantum field theories on Riemann surfaces, quantum groups, as well as dualities in string theory and black holes in string theory.Luis Álvarez-Gaumé, Cesar Gomez, Miguel Vázquez-Mozo: Scaling phenomena in Gravity from QCD, Phys. Lett. B649 (2007)478. , Luis Álvarez-Gaumé Scaling Phenomena in gravity and Yang-Mills theories, or black hole formation and its unitarization, Fortschritte der Physik 57 (2010) 327.
|
|
A bijection between the point set and the line set that preserves incidence is called a duality and a duality of order two is called a polarity. Dualities can be viewed in the context of the Heawood graph as color reversing automorphisms. An example of a polarity is given by reflection through a vertical line that bisects the Heawood graph representation given on the right. The existence of this polarity shows that the Fano plane is self-dual.
|
|
Yet in the Memphite Theology, Geb, as judge, first apportions the realm between the claimants and then reverses himself, awarding sole control to Horus. In this peaceable union, Horus and Set are reconciled, and the dualities that they represent have been resolved into a united whole. Through this resolution, order is restored after the tumultuous conflict. Egyptologists have often tried to connect the conflict between the two gods with political events early in Egypt's history or prehistory.
|
|
Advaita Vedantins assert that ātman is same as Brahman, and this Brahman is within each human being and all life, all living beings are spiritually interconnected, and there is oneness in all of existence.John Koller (2007), in Chad Meister and Paul Copan (Editors): The Routledge Companion to Philosophy of Religion, Routledge, , pages 98-106 They hold that dualities and misunderstanding of māyā as the spiritual reality that matters is caused by ignorance, and are the cause of sorrow, suffering.
|
|
PT Raju (2006), Idealistic Thought of India, Routledge, , page 426 and Conclusion chapter part XIIPaul Deussen, Sixty Upanishads of the Veda, Volume 1, Motilal Banarsidass, , page 91 Different schools of thought interpret Brahman as either personal, impersonal or transpersonal. Ishwar Chandra Sharma describes it as "Absolute Reality, beyond all dualities of existence and non-existence, light and darkness, and of time, space and cause."Ishwar Chandra Sharma, Ethical Philosophies of India, Harper & Row, 1970, p.75.
|
|
Rather than focusing on themes of political-social opposition between the two feuding clans, this Romeo and Juliet highlights the dualities and ambiguities of adolescence. In 2007, Peter Martins made Romeo + Juliet on New York City Ballet to the Prokofiev music. In 2008, Krzysztof Pastor presented his version by the Scottish Ballet at the Edinburgh Festival Theatre. The Polish premiere of this version was by the Polish National Ballet in Warsaw, and the United States premiere was by the Joffrey Ballet in 2014.
|
|
Cosmogony is a centrepiece in the Pech belief system as it presents the way they believe the universe is structured and created. Much of Pech cosmogony is based on dualities. For instance, the father God, named Patako-ko, is divided into two separate parts, one celestial and the other terrestrial and is in a constant struggle to vanish the celestial part. For the Pech people, the universe takes on the form of a sphere and has four beams supporting its structure.
|
|
She was a columnist with Asian Age for two years and has a sex and relationship column in the Maxim magazine. She has also won a National Award for her documentary on women’s issues called Between Dualities. She has been the face of Revlon as their Relationship Expert for their campaign Choices. She has been called by Cosmo magazine as the Carrie Bradshaw of India and been featured in the India Today Woman magazine twice in her six years as an author.
|
|
There is no longer a clear line between the old dualities of human/machine, human/environment, and technology/environment. Brenda Brasher thinks that this revelation of the hybridity of human nature present insurmountable problems for scriptural based theological metaphors bound in "pastoral and agrarian imagery." Garner, however sees a multitude of metaphors within Christian tradition and scripture that already speak to this reality. He says, that in the three major areas of hybridity in Christianity are eschatology, Christology, and theological anthropology.
|
|
The artist often questions and plays with such dualities as solidity-emptiness or reality-reflection, which in turn allude to such paired opposites as flesh-spirit, the here-the beyond, east-west, sky-earth, etc. that create the conflict between internal and external, superficial and subterranean, and conscious and unconscious. Kapoor also creates a tension between masculine and feminine within his art by having concave points of focus that invite the entry of visitors and multiplies their images when they are positioned correctly.Gilfoyle, pp. 271–2.
|
|
Barclay creates large-scale installations, often made in situ and in response to the spaces in which they are shown. Her practice is also deeply rooted in process and craftsmanship; accordingly, her installations include an array of materials that oscillate between those associated with mechanization and those associated with the domestic: steel, cast-concrete, machined aluminium, rubber, brass mesh, ceramic, leather, canvas and printed fabric. These dualities further position her artistic process between the handcrafted and industrially produced, as well as the natural and man-made.
|
|
These two trials, separated by most of the book, may also be part of a deeper exploration by Blixen into one of her pet notions: the “Unity” of contrasts. Perhaps her greatest elucidation of this idea comes in Shadows on the Grass, which she wrote thirty years after leaving Kenya: Her life in Africa offered her no shortage of such contrasting dualities: town and country, dry season and rainy season, Muslim and Christian. Her most constant theme is the contrast of African and European.
|
|
Filmed just before passage of the Production Code of 1933, Vidor's Billy the Kid is free of the fixed moral dualities that came to typify subsequent Good Guy vs. Bad Guy Westerns in Hollywood. Starring former football champion Johnny Mack Brown as Billy and Wallace Beery as his nemesis Sheriff Pat Garrett, the protagonists display a gratuitous violence that anticipates Vidor's 1946 masterpiece Duel in the Sun (1946). Homicidal behavior resonates with the brutal and deadly desert landscape, Hemingwayesque in its brevity and realism.
|
|
In prajñāpāramitā sutras Śāriputra is often depicted as the counterpoint to the true meaning of prajñāpāramitā. In the Astasahasrika Prajñāpāramitā Sutra, Śāriputra is portrayed as being unable to understand the ultimate meaning of prajñāpāramitā and instead must be instructed by the disciple Subhūti. According to Buddhist scholar Edward Conze, the sutra depicts Śāriputra as being preoccupied with dualities, making him unable to grasp the true meaning of prajnaparamita. In the Mahaprajnaparamita Sutra, Śāriputra is one of the principal interlocutors, asking questions and being instructed.
|
|
Illmatic has also received notable attention from scholars and authors outside the music industry. Since its release, the album has become the subject of scholarship within academic and literary circles. In 2009, as part of the 33⅓ book series, author Matthew Gasteier published a deconstruction of Illmatic, that focuses on the dualities that inform its narratives. In 2012, playwright Shaun Neblett created a tribute play titled Homage 3: Illmatic, which tells the story of an aspiring artist and explores the themes found in Nas' debut.
|
|
Some of the verses of Devi Gita are almost identical to the Devi Upanishad. The Devi Gita frequently explains Shakta ideas by quoting from the Bhagavad Gita. The Devi is described by the text as "universal, cosmic energy" resident within each individual, weaving in the terminology of Samkhya school of Hindu philosophy. It is suffused with Advaita Vedanta ideas, wherein nonduality is emphasized, all dualities are declared as incorrect, and interconnected oneness of all living being's soul with Brahman is held as the liberating knowledge.
|
|
Via a series of T-dualities one obtains the result that in any type II superstring theory, when an NS5-brane and a Dp-brane cross one necessarily creates or destroys a D(p-2)-brane. Lifting this statement to M-theory one finds that when two M5-branes cross, one creates or destroys an M2-brane. Using S-duality one may obtain transitions without NS5-brane. For example, when a D5-brane and a D3-cross one creates or destroys a fundamental string.
|
|
Imagine that this torus represents the "spacetime" for a physical theory. The fundamental objects of this theory will be strings propagating through the spacetime according to the rules of quantum mechanics. One of the basic dualities of string theory is T-duality, which states that a string propagating around a circle of radius R is equivalent to a string propagating around a circle of radius 1/R in the sense that all observable quantities in one description are identified with quantities in the dual description.Zaslow 2008, p.
|
|
On the other hand, men are associated with the exterior and with external relation among clans as well as communication with the spiritual being. Similarly, the door on the right front is reserved for male access, while the one on the left rear is reserved for female access; each leading to a slightly lower verandah and to the exterior. The right-left and front-back dualities are further reflected onto the four main posts of the roof. These four posts supported the peak of the roof.
|
|
In the real world, spacetime is four-dimensional, at least macroscopically, so this version of the correspondence does not provide a realistic model of gravity. Likewise, the dual theory is not a viable model of any real-world system since it describes a world with six spacetime dimensions. Nevertheless, the (2,0)-theory has proven to be important for studying the general properties of quantum field theories. Indeed, this theory subsumes many mathematically interesting effective quantum field theories and points to new dualities relating these theories.
|
|
Han Ren is developing a drawing praxis. He works almost solely with lead pencil-a technique whose visual properties he is methodically exploring. So his wall drawings involve huge panoramas wavering between abstract landscape and cartography.Elfi Turpin, Supplément Semaine Volume VI - Demain c'est loin, Analogues, 2011 His drawings and installations, borrow the labyrinth, the mirror, the virtual landscape to evoke dualities ambivalence or opposition of opposites which are the key fundamental of his artistic research, and we reposition the face of the paradoxes of our conflicting instincts.
|
|
Hegel rendered these dualities intelligible by (ultimately) his argument in the "Quality" chapter of the "Science of Logic". The finite has to become infinite in order to achieve reality. The idea of the absolute excludes multiplicity so the subjective and objective must achieve synthesis to become whole. This is because, as Hegel suggeste by his introduction of the concept of "reality", what determines itself—rather than depending on its relations to other things for its essential character—is more fully "real" (following the Latin etymology of "real", more "thing-like") than what does not.
|
|
This is an exposition of the Kālakārāma Sutta (AN 4.24), a canonical discourse of hallowed tradition that had subsequently fallen into neglect. Ven. Ñāṇananda gives an annotated translation of the sutta prologued by a humorously conceived parable of a magic show. The main theme of the work is the illusory nature of Viññaṇa. The book attempts to draw out the psychological and philosophical implications of the text, centered on a discussion of Paticcasamuppada as a golden mean which freely transcends the dualities of existence and non-existence and mind-and-matter.
|
|
Wonder Woman, 2014 Siri Kaur (b. Boston, MA,1976) is an artist and photographer who examines identities that occupy dualities, diversity, and contradiction, with a rigorous eye for the photographic quality of magic. She received her MFA from The California Institute of the Arts, and an MA and a BA from Smith College. Kaur’s work has been the subject of solo exhibitions at Blythe Projects, Cohen Gallery, and Kopeikin Gallery, Los Angeles; at 99¢ Plus, New York; at the Vermont Center for Photography, and at the Los Angeles County Museum of Art.
|
|
There was a comparatively quiet period at the beginning of the 1990s; however, several important tools were developed. For example, it became apparent that the various superstring theories were related by "string dualities", some of which relate weak string-coupling - perturbative - physics in one model with strong string-coupling - non-perturbative - in another. Then the second superstring revolution occurred. Joseph Polchinski realized that obscure string theory objects, called D-branes, which he discovered six years earlier, equate to stringy versions of the p-branes known in supergravity theories.
|
|
For example, momentum in one description takes discrete values and is equal to the number of times the string winds around the circle in the dual description. The idea of T-duality can be extended to more complicated theories, including superstring theories. The existence of these dualities implies that seemingly different superstring theories are actually physically equivalent. This led to the realization, in the mid-1990s, that all of the five consistent superstring theories are just different limiting cases of a single eleven-dimensional theory called M-theory.
|
|
The kampong served as the main subject of interest in the documentary Selak Kain The Last Kampong. The film received national air-time on free-to-air television channel Arts Central. The documentary focused on the residents' struggles to maintain their way of life in the kampong in the 21st century. The documentary juxtaposes modernities and nostalgic kampong life to bring out the dualities of living in a kampong in a cosmopolitan city like Singapore and how both young and old residents adapt to the changes both within, and without.
|
|
During her Concrete Art phase, when the Grupo Frente was operative, Lygia Clark made paintings that were very geometric in nature, but had a strong sense of dynamism due to her use of diagonal lines. Unlike others in the group, her works created the illusion of three-dimensionality. When she broke off to found the Neo-Concrete Movement, she moved onto working with metals and making pieces out of them that involved the spectator. After that, Clark focused more on sensory art and the mind body dualities, which means the spectator interacts with the art.
|
|
This duality means that in addition to the correspondence between Boolean algebras and their Stone spaces, each homomorphism from a Boolean algebra A to a Boolean algebra B corresponds in a natural way to a continuous function from S(B) to S(A). In other words, there is a contravariant functor that gives an equivalence between the categories. This was an early example of a nontrivial duality of categories. The theorem is a special case of Stone duality, a more general framework for dualities between topological spaces and partially ordered sets.
|
|
' It set out to critique and comment on a world it felt outside of."Jaime Rojo and Steven Harrington, "The Generational Shift in Street Art Culture," The Huffington Post, 30 June 2010. Such a critique is sometimes ambivalent, as FAILE’s work is marked by the consistent juxtaposition of dualities. Other times, it is more direct, as in the seemingly explicit pictures in the Lost in Glimmering Shadows exhibition, or in the public wheatpasting in 2010 of images of kissing women amid the text "No Change Will My Heart Fear.
|
|
More detailed studies have shown that different string theories in different background spacetimes can be related by dualities. There is also good evidence that string theory supports changes in topology of spacetime. Relativists have therefore criticised string theory for not being formulated in a background independent way, so that changes of spacetime geometry and topology can be more directly expressed in terms of the fundamental degrees of freedom of the strings. The difficulty in achieving a truly background independent formulation for string theory is demonstrated by a problem known as Witten's Puzzle.
|
|
In the song, Madonna enhanced the rhythmic sounds more and compressed the bass sounds, in order to cater to the then musical trend. Containing multiple hooks, "Survival"'s lyrics are about dualities like heaven/hell, up/down, angels/saints. "Secret", the second song, begins with just the sound of Madonna's voice singing over a rhythmic, folksy guitar in descending chord sequence, before opening up to a sparse, retro rhythm section. A deep percussion starts around the one minute mark, accompanied by wah-wah ascending string line, supporting the descending guitar.
|
|
After earning a bachelor's degree in mathematics in 1980 from the University of North Carolina, with highest honors and Phi Beta Kappa, Dietrich went to Cornell University intending to get a graduate degree in mathematics. However, after working as an intern at the United States Department of Energy, she switched to operations research. She completed her Ph.D. in 1986; her dissertation, A Unifying Interpretation of Several Combinatorial Dualities, was supervised by Robert G. Bland. Dietrich began working at IBM's Thomas J. Watson Research Center while still a graduate student.
|
|
String duality is a class of symmetries in physics that link different string theories. In the 1990s, it was realized that the strong coupling limit of the HO theory is type I string theory -- a theory that also contains open strings; this relation is called S-duality. The HO and HE theories are also related by T-duality. Because the various superstring theories were shown to be related by dualities, it was proposed that each type of string was a different limit of a single underlying theory called M-theory.
|
|
Polchinski's contributions to D-brane physics were a primary trigger of the 2nd superstring revolution and the physics of holographic gauge-gravity dualities. After co-discovering D-branes in 1989, his 1995 work conjectured and partially demonstrated the equivalence between D-branes and black p-branes. The duality between these objects was soon understood to be a demonstration of holography, in which a theory of quantum gravity (the black p-branes) is equivalent to a lower-dimensional theory without gravity (the D-branes), as later demonstrated in Maldacena's AdS-CFT duality.
|
|
Nathan Hylden (born 1978 in Fergus Falls, Minnesota) is a contemporary American abstract painter based in Los Angeles, California. He is known for creating abstract paintings exploring philosophical relationships between cause and effect, absence and presence, and emptiness and meaning; as well as for process-oriented artworks that investigate dualities of existence. Hylden earned his Bachelor of Fine Arts from Minnesota State University in 2001 and Master of Fine Arts from Art Center College of Design in Los Angeles in 2006. He later studied with abstract painter Michael Krebber in Frankfurt, photographer Christopher Williams, and multimedia artist Richard Hawkins in Los Angeles.
|
|
Chicago (Rand McNally) 1966, p.92. - See also Ramesh Kumar Arora who notes that “Weber was not unmindful of the limitations of bureaucratic rationality in practice. This became evident in his analysis of the dysfunctions of Prussian bureaucracy under Bismarck (…)”Ramesh Kumar Arora, Administrative Theory. (Indian Institute of Public Administration) 1984, p.XVIII. What mattered, according to Diamant, was to ‘modify,’ adapt, or surpass Weber's constructs. It is well known that in the 20th century, several sociologists and political scientists “have sought to construct typologies that are closer approximations of the mixes or dualities existing in the real world.
|
|
The worldview that results from the practice of yujism is symbolised by Ynglists as an image of a "flat earth sustained by three elephants sustained by a turtle which swims in an unlimited ocean": the flat earth represents the twofold structure of perception (articulating in all dualities, from "yes–no" to "up–down"); the three elephants are symbols of the three dimensions of reality—Yav, Nav and Prav—material, ideal (which realises in word) and mystical, which are also three forms of life; the turtle is yuj itself, awakened consciousness, which draws information from the ocean, which represents infinite energy.
|
|
This series of sculptures continues Gupta's inspections of dualities in his artwork, including themes of war and peace, public and private, global and local. The phrase "See no evil, Hear no evil, Speak no evil" first emerged in Japan in the 17th century and was later adopted worldwide as a message of peace and tolerance due to Mahatma Gandhi's visual metaphor of the three monkeys, with one of them covering his eyes, the second his mouth, and the third his ears. Gupta's sculptures recall Gandhi's vision of these three monkeys as a way to peacefully fight against contemporary colonialism, oppression and injustice.
|
|
In his work the exploration of various phenomena related to dualisms and interaction provide the primary point of departure. In his photographic works Thull generates dualisms by removing everyday objects and situations from their original framework and placing them in a different context using means that range from unconventional cropping and camera techniques to shaking or moving the camera while shooting. These interactions lead to a break with traditional visual habits, provide motifs with a new identity and reveal dualities. Thus they "contain propositions and possibilities for viewers to stir their imagination and to activate creative impulses through their own contemplation and activity".
|
|
British anthropologist, Gregory Bateson, is the most influential and one of the earliest founders of System Theory in anthropology. He developed an interdisciplinary approach that included communication theory, cybernetics, and mathematical logic. In his collection of essays, The Sacred Unity, Bateson argues that there are "ecological systems, social systems, and the individual organism plus the environment with which it interacts is itself a system in this technical sense."Gregory Bateson, A Sacred Unity: Further Steps to an Ecology of Mind, 260 By adding environment with systems, Bateson closes the gap between the dualities such as subject and object.
|
|
The third title is the Horus of Gold, with the Horus falcon above the hieroglyphic sign for gold. The fourth title is often translated as “He of the Sedge and Bee,” with the sedge plant symbolic of Upper Egypt and the bee symbolic of Lower Egypt. This is also known as nswt-bìty, a title which expressed the many dualities over which the king exercised rule: Upper and Lower Egypt, the Black Land of cultivation and the Red Land of desert, the realms of day and night, and the natural and the supernatural.Wilkinson (2000), p. 200.
|
|
Howard has stated: "In my painting (as in all my work) I am deeply involved with light as the movement and inter- action of colours; the integrity of colour and form, hence with the integrity of the total work which has to do with spirit and abstract essence, not representation. I am preoccupied with life's ambiguities and dualities and in my later work I am reaching more and more from the dark toward light, freedom, and a transcending exuberance." Howard's paintings, drawings, wood engravings and book designs can be viewed on the website Barbara Howard's Unfolding Visual World.
|
|
For want of any other term, we are > obliged to designate all that is thus outside and beyond Being as "Non- > Being", but for us this negative term is in no way synonym for > 'nothingness'.The Multiple states of the Being, chapter: "Being and Non- > Being". Hermes' caduceus: example of a symbol associated to the possession of lesser mysteries, and showing an example of horizontal duality (the two snakes' heads are placed in the horizontal dual position, hence referring to apparent dualities such as life and death). In Studies in Hinduism, Guénon mentions a relation between the symbol and the Kundalini shakti.
|
|
The song was written by Max, Madison Love, Tix, Cook Classics, and Cirkut, with the latter of the five solely handling production. When Max was a child, her parents said that "you're sweet, but you're a little psycho"; this inspired the song's title. In an interview with Idolator, Max discussed the message of the song, stating it is "about a girl who's not afraid to show all of her sides and her dualities, and about a guy loving all those sides". Max continued, saying she was misunderstood as a "psycho" but was "an outspoken girl ... speaking her mind".
|
|
In theoretical physics the Hanany–Witten transition, also called the Hanany–Witten effect, refers to any process in a superstring theory in which two p-branes cross resulting in the creation or destruction of a third p-brane. A special case of this process was first discovered by Amihay Hanany and Edward Witten in 1996. All other known cases of Hanany–Witten transitions are related to the original case via combinations of S-dualities and T-dualities.This effect can be expanded to string theory, 2 strings cross together resulting in the creation or destruction of a third string.
|
|
Quite apart from their diagrammatic purpose the paintings have a freshness and a modern aesthetic of tentative line and hastily captured image: a segmented circle, a helix bisected and divided into a spectrum of lightly painted colours. The artistic world of Hilma af Klint is impregnated with symbols, letters, and words. The paintings often depict symmetrical dualities, or reciprocities: up and down, in and out, earthly and esoteric, male and female, good and evil. The colour choice throughout is metaphorical: blue stands for the female spirit, yellow for the male one, and pink / red for physical / spiritual love.
|
|
Although Imsai Arasan 23rd Pulikesi is a historical film set in the late 18th century AD, most of the issues it raises are contemporary. Topics discussed include child labour, globalisation, the bureaucratic inefficiency of government, pesticide usage in soft drinks, and divisions in the caste system. In their 2010 book, Cinemas of South India: Culture, Resistance, Ideology under the section Dualities and Negotiation 23rd Imsai Arasan Pulikesi, Sowmya Dechamma C. C., Elavarthi Sathya Prakash and Jananie Kalyanaraman mention the soft drinks that are satirized include Coca-Cola and Pepsi. The two are called Akka Mala and Gup-C respectively.
|
|
The paintings offer tactile, often aerial, views through what Suzanne Muchnic calls "a veil of mysticism," composed of hazy curtains of color, shafts of light, louvered blinds and ornate grillwork.Andreoli-Woods, Lynn. "And Now, Substance," The Reader (Los Angeles), March 9, 1990. They maintain Simonian's mixed-media approach, often using mosaic tiles to further dualities between interior and exterior (e.g., El Capitan), decorative and pictorial, and abstract and illusionistic; critics compare the effect to Mondrian’s transformation of natural imagery into patterns of squares and Bonnard's collapse of indoor and outdoor. Judith Simonian, Red Coliseum, watercolor, acrylic, collage on canvas, 42" x 60", 2005.
|
|
In 2007, Sneha starred in Naan Avanillai a hit, while her Telugu films Madhumasam, which run over 100 days and Maharadhi and Tamil film Pallikoodam turned out to be above-average grosser at the box office. Pirivom Santhippom, which saw her collaborating with Karu Pazhaniappan again, was her first film in 2008. Co-starring Cheran, the film opened to critical acclaim and emerged a sleeper hit, while fetching Sneha plaudits and several accolades. A review from Sify noted that she was "superb as Sala, a woman torn by the dualities of her existence", labelling it as her "career best performance".
|
|
The buildings on the west, on the other hand, are open earth mounds lined in stone for public displays. This visual structure defines the eastern side as lending toward the Puebloan peoples of North America and the west as referencing the cultures to the south in Mesoamerica. This visual motif is prevalent throughout the other sites sharing the same longitudinal line, indicating that they were built by a common group."Complementary Dualities: The Significance of East/West Architectural Difference in Paquimé", Hughes, Delain, 2005 The homes at Paquimé were circular and semi-circular pit houses and coursed-adobe room blocks built around plazas.
|
|
Sage Narada offering respect to Vishnu on Garuda. Firstly bhakti itself is defined as being "the most elevated, pure love for God" which is eternal by nature and through following which one obtains perfect peace and immortality (release from samsara). The symptoms of such devotion are that one no longer has any selfish desires, nor is affected by the dualities of loss or gain for himself being fully content with (and experiencing ecstasy through) the process of bhakti itself. Narada describes that lust is absent in those who execute bhakti purely because they naturally have no personal desires to fulfill.
|
|
The Devi Gita describes the Devi (or Goddess) as "universal, cosmic energy" resident within each individual. It thus weaves in the terminology of Samkhya school of Hindu philosophy. The text is suffused with Advaita Vedanta ideas, wherein nonduality is emphasized, all dualities are declared as incorrect, and interconnected oneness of all living being's soul with Brahman is held as the liberating knowledge. However, adds Tracy Pintchman – a professor of Religious Studies and Hinduism, Devi Gita incorporates Tantric ideas giving the Devi a form and motherly character rather than the gender-neutral concept of Adi Shankara's Advaita Vedanta.
|
|
Adaptation of the taichi symbol for Yin and yang by . 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 force for change and creativity. Wenger uses the concept of dualities to examine the forces that create and sustain a community of practice. He describes a duality as "a single conceptual unit that is formed by two inseparable and mutually constitutive elements whose inherent tensions and complementarity give the concept richness and dynamism" .
|
|
Thomas has two lives, two families, and is a part of two cultures; many things in the novel are also viewed from two perspectives. For example, Thomas's last name, Just, was given as a way of demeaning him, yet Lin looks at it as a name representing justice and balance, and Thomas's massacre of his troop is described as dishonorable, yet “the only, the most honorable thing he’d done the whole time.” These dualities are symbolic of the conflict within Thomas – he struggles to resolve his two lives and find peace. By the end of the story, Thomas has corrected the imbalance in himself to become a whole individual again.
|
|
Sen 1994 It was shown that type IIB string theory with the coupling constant g is equivalent via S-duality to the same string theory with the coupling constant 1/g. Similarly, type I string theory with the coupling g is equivalent to the SO(32) heterotic string theory with the coupling constant 1/g. The existence of these dualities showed that the five string theories were in fact not all distinct theories. In 1995, at the string theory conference at University of Southern California, Edward Witten made the surprising suggestion that all five of these theories were just different limits of a single theory now known as M-theory.
|
|
Homogeneous coordinates may be used to give an algebraic description of dualities. To simplify this discussion we shall assume that is a field, but everything can be done in the same way when is a skewfield as long as attention is paid to the fact that multiplication need not be a commutative operation. The points of can be taken to be the nonzero vectors in the ()-dimensional vector space over , where we identify two vectors which differ by a scalar factor. Another way to put it is that the points of -dimensional projective space are the 1-dimensional vector subspaces, which may be visualized as the lines through the origin in .
|
|
Mark Williams is one of the first academics to focus his publications predominantly on contemporary New Zealand writing. His work is also informed by a strong international context which has enabled him to argue in Leaving the Highway: Six Contemporary New Zealand Novelists (1990) against the "violent dualities" of New Zealand culture and the "binary habits of New Zealand criticism" and advocate instead independence, difference, continuities, and "complex wholeness". In November 2012, with his wife and fellow Victoria academic, Jane Stafford, Williams published a major anthology of New Zealand literature.Jane Stafford and Mark Williams (eds), Anthology of New Zealand Literature, Auckland University Press, Auckland, 2012.
|
|
Jamgon Kongtrul, The Treasury of Knowledge: Book Five: Buddhist Ethics, Shambhala Publications, 5 June 2003, p. 345. Buddhist Tantras also promote certain practices which are antinomian, such as sexual rites or the consumption of disgusting or repulsive substances (the "five ambrosias", feces, urine, blood, semen, and marrow.). These are said to allow one to cultivate nondual perception of the pure and impure (and similar conceptual dualities) and thus it allows one to prove one's attainment of nondual gnosis (advaya jñana).Wedemeyer, Christian K. Making Sense of Tantric Buddhism: History, Semiology, and Transgression in the Indian Traditions, Columbia University Press, 6 May 2014, p. 145.
|
|
For Harrison, the concept of duality also appealed on a philosophical level, consistent with his interest in Eastern religion. Neil Aspinall, the Beatles' assistant, later recalled Harrison employing the metaphysical theme of opposites to disperse some Hells Angels who had taken up residence in the Beatles' Apple headquarters over Christmas 1968 and refused to leave. According to theologian Dale Allison, "Old Brown Shoe" is a further reflection of Harrison's interest in "dualities and contradictions", but stated in terms that avoid the religiosity evident in much of his songwriting. Before returning to England for Christmas, Harrison spent time with Bob Dylan and the Band in upstate New York.
|
|
Each theory of quantum gravity uses the term "quantum geometry" in a slightly different fashion. String theory, a leading candidate for a quantum theory of gravity, uses the term quantum geometry to describe exotic phenomena such as T-duality and other geometric dualities, mirror symmetry, topology-changing transitions, minimal possible distance scale, and other effects that challenge intuition. More technically, quantum geometry refers to the shape of a spacetime manifold as experienced by D-branes which includes quantum corrections to the metric tensor, such as the worldsheet instantons. For example, the quantum volume of a cycle is computed from the mass of a brane wrapped on this cycle.
|
|
Vafa's research in string theory is focused on the nature of quantum gravity and the relation between geometry and quantum field theories. He is known in the string theory community for his co-discovery with Strominger that the Bekenstein-Hawking entropy of a black hole can be accounted for by solitonic states of superstring theory, and for expounding the relation between geometry and field theories that arise through string dualities (culminating in the Gopakumar–Vafa conjecture). This topic has been known as "geometric engineering of quantum field theories". In 1997, he developed F-theory, a 12-dimensional theory that compactifies to 10-D Type IIB superstring theory.
|
|
Although these theories appeared, at first, to be very different, work by several physicists showed that the theories were related in intricate and nontrivial ways. Physicists found that apparently distinct theories could be unified by mathematical transformations called S-duality and T-duality. Witten's conjecture was based in part on the existence of these dualities and in part on the relationship of the string theories to a field theory called eleven-dimensional supergravity. Although a complete formulation of M-theory is not known, such a formulation should describe two- and five-dimensional objects called branes and should be approximated by eleven-dimensional supergravity at low energies.
|
|
He has also done important works in the area of quantum spin liquids, often using the aforementioned dualities to provide theoretical descriptions of various spin liquid phenomena (with Leon Balents, Michael Hermele, Jason Alicea, Shinsei Ryu and others). He has also made important contributions to the physics of carbon nanotubes (with Leon Balents and Charles Kane) and emergent Majorana fermions and related phenomena in quasi- one-dimensional problems (with Jason Alicea and others). In recent years, Fisher has developed new interests in neuroscience, where in particular he has proposed the possibility (and mechanisms) of quantum information processing (specifically, quantum mind) in the human brain.
|
|
Note that an MNC can be of two-digit form and three-digit form with leading zeros, so that 01 and 001 are actually two distinct MNCs. Hence the PLMNs 001-02 and 001-002 would be in the same country, but belong to two completely distinct operators (02 and 002). From PLMN assignments, it is apparent that such dualities of two-digit and three-digit MNCs with the same number value are avoided (see the List of Mobile Country Codes and Mobile Network Codes). An example for an actual three-digit MNC with leading zeros is 750–001, of the operator Cable and Wireless South Atlantic Ltd (Falkland Islands).
|
|
While still at CERN, Olive had begun to study the magnetic monopoles which 't Hooft and Polyakov had shown existed in non-abelian gauge theories, publishing a paper with Peter Goddard and Jean Nuyts. In 1977, together with Claus Montonen, he made the remarkable conjecture that there should exist an electromagnetic dual theory in which the roles of monopoles and gauge bosons are interchanged. In subsequent work with Ed Witten, Olive showed that this duality is realised in a certain class of supersymmetric theories. This Montonen-Olive duality was later found to emerge from a deeper web of dualities underlying M-theory, ushering in the second superstring revolution of the mid 1990s.
|
|
Katleman's work addresses dualities between nature and culture; order and chaos; kitsch and fine art; dark humor and optimism; consumption and desire. Her sculpture is informed by parallels and differences between classic European decorative arts and American pop culture. The objects that she casts into sculpture are sourced from dime store trinkets, gadgets, dolls and toys. Katleman is influenced by porcelain rooms, such as The Royal Palace of Aranjuez in Spain; Toile de Jouy wallpaper found in Versailles and the Victoria and Albert Museum; and time studying Italian porcelain reliefs in the Salottino di Porcellana room at the Royal Palace of Capodimonte, Naples, which she visited during an artist residency at the American Academy in Rome.
|
|
The sublime state of self-consciousness is reached after the Seeker after Truth devoid of egoism and delusion, overcoming the flaws of attachment, firm in spirituality, free from lusts, released from dualities called pleasures and pains, the un-deluded repairs to the imperishable status, because for a knower of Brahman who has realised the Ultimate Truth, there is much profit from reservoirs when all around there is an inundation. Through Self-consciousness one gains the knowledge of Existence which is the knowledge of Sole Reality. It is not mere intellectual apprehension of Truth, it is the apprehension of the Oneness which has to be realised here in this very life. In the Bhagavad Gita XIV.
|
|
As with so many other parts of the myth, the resolution is complex and varied. Often, Horus and Set divide the realm between them. This division can be equated with any of several fundamental dualities that the Egyptians saw in their world. Horus may receive the fertile lands around the Nile, the core of Egyptian civilization, in which case Set takes the barren desert or the foreign lands that are associated with it; Horus may rule the earth while Set dwells in the sky; and each god may take one of the two traditional halves of the country, Upper and Lower Egypt, in which case either god may be connected with either region.
|
|
A number of dualities relate the above theories. The A-model and B-model on two mirror manifolds are related by mirror symmetry, which has been described as a T-duality on a three-torus. The A-model and B-model on the same manifold are conjectured to be related by S-duality, which implies the existence of several new branes, called NS branes by analogy with the NS5-brane, which wrap the same cycles as the original branes but in the opposite theory. Also a combination of the A-model and a sum of the B-model and its conjugate are related to topological M-theory by a kind of dimensional reduction.
|
|
Fox argued that bioethicists should be trained in the social sciences before being trained in bioethics. In an abstract of a collection of her essays, the author writes that “Dr. Fox has explored basic cultural phenomena and questions associated with health, illness, and medicine: values, beliefs, symbols, rites, and the nuances of language: ethical and existential dilemmas and dualities; and the complex interrelationships between medicine, science, religion, and magic. She draws systematically and imaginatively upon anthropological, psychological, historical, and biological insights and integrates observations and analyses from her own studies in American, Western European, and Central African societies.” Fox went on to combine ethnography with history in her study of the development of the Congolese medical profession (1968).
|
|
Other researchers studied her language such as Mahmoud Haider in his book The contiguity of language, Fadel Alameen who studied the "Intimate affiliation in Suad Al- Sabah, the poet of the intimate affiliation" and Samir Staityeah in his research "The linguistic function and texts analysis in the poetry of Suad Al- Sabah". This research is an attempt to take another path in critical study, and it embodies the duality of the subject and the object, and their dialectical relationship that appears with other dualities. These contrasts such as life and death, man and women, treachery and loyalty, abstract and concrete, subject and object are reflected in her poetry. She is a director of the Kuwait Stock Exchange.
|
|
Mainetti’s personal work outside the development world continues in the expression of the dualities of nature & humanity, drawing heavily from her commitment to improving the way we live through environmental awareness, activism and sustainable practice. Her on- going conceptual photography series often explore common themes of rebirth in the human condition, likening the human body to Mother Earth and vice versa. In Spring 2017, an interactive photo/video exhibit titled The Rebirth showed at the Flatiron Building, in the exclusive Prow Art Space. On display 24 hours a day through the front windows of the building, The Rebirth looped continuously for the duration of the exhibit, witnessed by hundreds of thousands of people on a weekly basis.
|
|
Many natural dualities (such as light and dark, fire and water, expanding and contracting) are thought of as physical manifestations of the duality symbolized by yin and yang. This duality lies at the origins of many branches of classical Chinese science and philosophy, as well as being a primary guideline of traditional Chinese medicine, and a central principle of different forms of Chinese martial arts and exercise, such as baguazhang, taijiquan (t'ai chi), and qigong (Chi Kung), as well as appearing in the pages of the I Ching. The notion of duality can be found in many areas, such as Communities of Practice. The term "dualistic-monism" or dialectical monism has been coined in an attempt to express this fruitful paradox of simultaneous unity and duality.
|
|
Additionally, within the tradition itself resides a deep, developing spiritual vision of a collective human/earth/divine evolution that is expanding consciousness beyond the dualities of human/earth, heaven/earth, mind/body. This belongs to the contemporary movement that recognizes the unity and interrelationship, or "interbeing," the interconnectedness of all of creation. Visionaries carrying this thread include Rudolf Steiner (1861-1925) who founded the spiritual movement of anthroposophy, and described a "co- evolution of spirituality and nature"Leslie E. Sponsel, Spiritual Ecology: A Quiet Revolution, p. 66. and Pierre Teilhard de Chardin, a French Jesuit and paleontologist (1881-1955) who spoke of a transition in collective awareness toward a consciousness of the divinity within every particle of life, even the most dense mineral.
|
|
Chac Chel is a powerful and ancient Mayan goddess of creation, destruction, childbirth, water, weaving and spinning, healing, and divining. She is half of the original Creator Couple, seen most often as the wife of Chaac, who is the pre-eminent god of lightning and rain, although she is occasionally paired with the Creator God Itzamna in the Popol Vuh, the highland Maya bible. This highlights her importance, as dualities such as male/female and husband/wife were extremely important to the Maya, and one cannot function without the other. Chac Chel is also called Goddess O by many Mayanists and she is the aged, grandmotherly counterpart to the young goddess of childbirth and weaving, Ix Chel (also known as Goddess I and Ixik Kab).
|
|
These address the role of topos theory in understanding quantum theory (in particular the Kochen–Specker theorem), and the status of time in the various quantum gravity research programmes. In recent years, Butterfield has argued for a reconciliation of the idea of emergence – the idea that novel structures, not described by "fundamental" theories, appear at a certain level of complexity – with the possibility of inter-theoretic reduction. He has illustrated the reconciliation in various areas such as phase transitions, renormalization, and gauge theories. He has also worked, often in collaboration with research students, on other topics, including: (i) identity and individuation of systems in quantum physics; (ii) dualities especially gauge/gravity duality; (iii) under-determination, and scientific realism, in modern cosmology.
|
|
Mythology, published by DBP, Chapter: Egypt's divine kingship After the New Kingdom, Set was still considered lord of the desert and its oases. In many versions of the story, Horus and Set divide the realm between them. This division can be equated with any of several fundamental dualities that the Egyptians saw in their world. Horus may receive the fertile lands around the Nile, the core of Egyptian civilization, in which case Set takes the barren desert or the foreign lands that are associated with it; Horus may rule the earth while Set dwells in the sky; and each god may take one of the two traditional halves of the country, Upper and Lower Egypt, in which case either god may be connected with either region.
|
|
There are also a number of dualities that relate configurations with D-branes, which are described by open strings, to those with branes the branes replaced by flux and with the geometry described by the near-horizon geometry of the lost branes. The latter are described by closed strings. Perhaps the first such duality is the Gopakumar-Vafa duality, which was introduced by Rajesh Gopakumar and Cumrun Vafa in On the Gauge Theory/Geometry Correspondence. This relates a stack of N D6-branes on a 3-sphere in the A-model on the deformed conifold to the closed string theory of the A-model on a resolved conifold with a B field equal to N times the string coupling constant.
|
|
Kachru's research has explored a broad range of topics in string theory and quantum field theory,World Science Festival and their applications in cosmology, condensed matter physics, and elementary particle theory. He has made central contributions to the study of compactifications of string theory from ten to four dimensions, especially in the investigation of mechanisms which could yield string models of dark energy or cosmic inflation. He has also made notable contributions to the discovery and exploration of string dualities, to the study of models of supersymmetry breaking in string theory, and to the construction of calculable dual descriptions of strongly coupled particle physics and condensed matter systems. More recently, his work has focused on connections between geometry, number theory, and string theory.
|
|
Joan Miró – GuggenheimCahiers d'art: bulletin mensuel d'actualité artistique / director Christian Zervos, Galerie la Licorne, catalogue, 1934, pp. 21–36, Gallica, Bibliothèque nationale de France In 1924, Miró joined the Surrealist group. The already symbolic and poetic nature of Miró's work, as well as the dualities and contradictions inherent to it, fit well within the context of dream-like automatism espoused by the group. Much of Miró's work lost the cluttered chaotic lack of focus that had defined his work thus far, and he experimented with collage and the process of painting within his work so as to reject the framing that traditional painting provided. This antagonistic attitude towards painting manifested itself when Miró referred to his work in 1924 ambiguously as "x" in a letter to poet friend Michel Leiris.
|
|
Subsequently Kabbalistic doctrine reached its fullest classic expression among Castilian Kabbalists from the latter 1200s, with the Zohar (Book of "Splendor") literature, concerned with cosmic healing of gnostic dualities between the lower, revealed male and female attributes of God. Rishonim ("Elder Sages") of exoteric Judaism who were deeply involved in Kabbalistic activity, gave the Kabbalah wide scholarly acceptance, including Nahmanides and Bahya ben Asher (Rabbeinu Behaye) (died 1340), whose classic commentaries on the Torah reference Kabbalistic esotericism. Many Orthodox Jews reject the idea that Kabbalah underwent significant historical development or change such as has been proposed above. After the composition known as the Zohar was presented to the public in the 13th century, the term "Kabbalah" began to refer more specifically to teachings derived from, or related to, the Zohar.
|
|
The New York Times Book Review praised the novel for its place in the broader Vietnam War literature, and for its treatment of dualities in a way that "compares favorably with masters like Conrad, Greene and le Carré". Writing for The Washington Post, Ron Charles called the novel "surely a new classic of war fiction" which is "startlingly insightful and perilously candid". For Charles, it is less the particulars of the thematic explosion of the response to the Vietnam war that makes the novel relevant, but rather how "Nguyen plumbs the loneliness of human life, the costs of fraternity and the tragic limits of our sympathy". Randy Boyagoda, writing for The Guardian, describes it as a "bold, artful and globally minded reimagining of the Vietnam war and its interwoven private and public legacies".
|
|
In string theory, D-branes, short for Dirichlet membrane, are a class of extended objects upon which open strings can end with Dirichlet boundary conditions, after which they are named. D-branes were discovered by Dai, Leigh and Polchinski, and independently by Hořava, in 1989. In 1995, Polchinski identified D-branes with black p-brane solutions of supergravity, a discovery that triggered the Second Superstring Revolution and led to both holographic and M-theory dualities. D-branes are typically classified by their spatial dimension, which is indicated by a number written after the D. A D0-brane is a single point, a D1-brane is a line (sometimes called a "D-string"), a D2-brane is a plane, and a D25-brane fills the highest-dimensional space considered in bosonic string theory.
|
|
Many mathematical dualities between objects of two types correspond to pairings, bilinear functions from an object of one type and another object of the second type to some family of scalars. For instance, linear algebra duality corresponds in this way to bilinear maps from pairs of vector spaces to scalars, the duality between distributions and the associated test functions corresponds to the pairing in which one integrates a distribution against a test function, and Poincaré duality corresponds similarly to intersection number, viewed as a pairing between submanifolds of a given manifold. From a category theory viewpoint, duality can also be seen as a functor, at least in the realm of vector spaces. This functor assigns to each space its dual space, and the pullback construction assigns to each arrow its dual .
|
|
The features of the cube and its dual octahedron correspond one-for-one with dimensions reversed. There are many distinct but interrelated dualities in which geometric or topological objects correspond to other objects of the same type, but with a reversal of the dimensions of the features of the objects. A classical example of this is the duality of the platonic solids, in which the cube and the octahedron form a dual pair, the dodecahedron and the icosahedron form a dual pair, and the tetrahedron is self-dual. The dual polyhedron of any of these polyhedra may be formed as the convex hull of the center points of each face of the primal polyhedron, so the vertices of the dual correspond one-for-one with the faces of the primal.
|
|
The story grew out of a challenge from the illustrator Lane Smith, who suggested Saunders "write a story in which all the characters were abstract shapes". Saunders wrote "Once there was a country that was too small for all its inhabitants to fit inside at once" and the story developed from that point. The abstract shapes became what Saunders regarded as "Conglomerates, composed of flesh and machine parts and vegetative portions" divided into two groups, one of which, led by Phil, trying to eradicate the other. In his essay "Why I wrote Phil", Saunders said the story became about "the human tendency to continuously divide the world into dualities, and, soon after, cast one's lot in with one side of the duality and begin energetically trying to eliminate the other".
|
|
For example, the dualistic devotional traditions such as Madhvacharya's Dvaita Vedanta tradition of Hinduism champion a theistic premise, assert that human soul and Brahman are different, loving devotion to Brahman (god Vishnu in Madhvacharya's theology) is the means to release from Samsara, it is the grace of God which leads to moksha, and spiritual liberation is achievable only in after-life (videhamukti). The nondualistic traditions such as Adi Shankara's Advaita Vedanta tradition of Hinduism champion a monistic premise, asserting that the individual human soul and Brahman are identical, only ignorance, impulsiveness and inertia leads to suffering through Saṃsāra, in reality there are no dualities, meditation and self-knowledge is the path to liberation, the realization that one's soul is identical to Brahman is moksha, and spiritual liberation is achievable in this life (jivanmukti).
|
|
Twins Seven Seven's work is influenced by traditional Yoruba mythology and culture, and creates a fantastic universe of humans, animals, plants and Yoruba gods. Visually, his work resembles Yoruba carvings in the segmentation, division and repetition of his compositions; conceptually, it reflects this influence in the emphasis on transformation and balance, as well as its embodiment of dualities such as the earthly and the spiritual, past and present, industry and agriculture. Early works such as Dreams of the Abiku Child (1967) make allusion to concepts or figures in Yoruba cosmology and mythology, such as the abiku (devil child), and the orisha Osun. However, Twins Seven Seven also described his work as "contemporary Yoruba traditional art", not only paying homage to the influence of his cultural background but also to noting his responsiveness to current events and the postcolonial experience.
|
|
The (2,0)-theory has proven to be important for studying the general properties of quantum field theories. Indeed, this theory subsumes a large number of mathematically interesting effective quantum field theories and points to new dualities relating these theories. For example, Luis Alday, Davide Gaiotto, and Yuji Tachikawa showed that by compactifying this theory on a surface, one obtains a four-dimensional quantum field theory, and there is a duality known as the AGT correspondence which relates the physics of this theory to certain physical concepts associated with the surface itself.Alday, Gaiotto, and Tachikawa 2010 More recently, theorists have extended these ideas to study the theories obtained by compactifying down to three dimensions.Dimofte, Gaiotto, Gukov 2010 In addition to its applications in quantum field theory, the (2,0)-theory has spawned a number of important results in pure mathematics.
|
|
Fisher is one of the leading figures in condensed matter physics, and has made important contributions to many areas in condensed matter physics. Some of his most important works have been in the theories of quantum phase transitions, in particular superconductor-insulator transitions (with Daniel Fisher, Steven Girvin and others) and deconfined quantum criticality (with Subir Sachdev, T. Senthil, Ashvin Vishwanath and Leon Balents). He has also made important contributions to superconductivity, in particular, introducing vortex-glass superconductivity as a possible new phase of matter and using bosonic particle-vortex dualities to describe the properties of superconductors (with Dung-Hai Lee). He has also made significant advances in the transport and other aspects of the physics of Luttinger liquids (with Charles Kane) and other one-dimensional problems in condensed matter such as the edges of quantum Hall states.
|
|
In another group of dualities, the objects of one theory are translated into objects of another theory and the maps between objects in the first theory are translated into morphisms in the second theory, but with direction reversed. Using the parlance of category theory, this amounts to a contravariant functor between two categories and : which for any two objects X and Y of C gives a map That functor may or may not be an equivalence of categories. There are various situations, where such a functor is an equivalence between the opposite category of , and . Using a duality of this type, every statement in the first theory can be translated into a "dual" statement in the second theory, where the direction of all arrows has to be reversed.. Therefore, any duality between categories and is formally the same as an equivalence between and ( and ).
|
|
Classics scholar Kyle Harper says Both the ancient Greeks and the Romans cared and wrote about sexual morality within categories of good and bad, pure and defiled, and ideal and transgression. But the sexual ethical structures of Roman society were built on status, and sexual modesty meant something different for men than it did for women, and for the well-born, than it did for the poor, and for the free citizen, than it did for the slave—for whom the concepts of honor, shame and sexual modesty could be said to have no meaning at all. Slaves were not thought to have an interior ethical life because they could go no lower socially and were commonly used sexually; the free and well born were thought to embody social honor and were therefore able to exhibit the fine sense of shame suited to their station. Roman literature indicates the Romans were aware of these dualities.
|
|
Set as the flashback in a coerced confession of a political prisoner, the book tells the story of the South Vietnamese Government in 1975 and subsequent events in American exile in Los Angeles, through the eyes of a half-Vietnamese, half-French undercover communist agent. The spy remains unnamed throughout the novel from the fall of Saigon, to refugee camps and relocation in Los Angeles, to his time as a film consultant in the Philippines, and finally to his return and subsequent imprisonment in Vietnam. The narrator lives in a series of dualities, at times contradictions: he is of mixed blood descent (Vietnamese mother, and French Catholic priest father), raised in Vietnam but attended college in the U.S., and a North Vietnamese mole yet a friend to South Vietnamese military officials and soldiers and a United States CIA agent. During the imminent fall of Saigon, he, as an aide-de-camp, arranges for a last minute flight as part of Operation Frequent Wind, to secure the safety of himself, his best friend Bon, and the General he advises.
|
|
The "Meeting" series featured large-scale brush drawings, prints and paintings (up to seven-and-a-half by thirty-two feet) that intensified Himmelfarb's use of overall patterning, but developed a more dramatic narrative focus sometimes suggesting enlarged, elaborated details from the earlier drawings. Most often these works, such as Lava Flow (Meeting) Red (1986) or Lumber Street Meeting (1988), depicted a pair or trio of grotesque, totemic heads (usually a man in frontal and profile views and a snarling dog), rendered in choppy interlaced brushstrokes and searing colors against black, that emerged and disappeared out of writhing vegetation. While some critics detected the strain of "divided alter-egos" in the new work, others like Art in America’s Frederick Ted Castle saw "baroque brashness," engaging "human messiness" and a rich play of dualities: representation versus non-representation, confrontation versus resolution, man versus nature/beast, the integrated personality versus its parts. Andy Argy noted an intriguing play between form and image "suggesting a calligraphic version of an Abstract Expressionist gone haywire" that enabled the work to seem both serenely decorative and intensely expressionistic, and like Grimm or Andersen fairy tales, both humorous and scary.
|
|
Anciently, the wild goose was one of the 9 Chinese gù (雇), or migratory types of birds employed (the modern meaning of the word) as seasonal indicators for initiating appropriate agricultural practices: the annual autumnal appearance of wild geese indicated the time to begin the harvest gathering (Wilder & Ingram, sub #361, 僱). The annual migratory pattern of geese makes their bi-annual appearances in spring and autumn symbolically useful, as poetic short-hand for the changing seasons. The place of geese in the cosmological order was indicated by the conceptualization that the geese fly south to avoid the effects of the rise of the cold and dark associated with the rise of the yin forces of winter, in the balance of yin-yang; and when, in the balance, the yang forces begin to predominate, the geese fly up north to avoid the accompanying excess heat of summer (Murck, 75). Yin-yang is a religico-philosophical concept of how opposite and contrary forces are operated in the process of the natural world: how they give rise to each other through natural dualities, such as light and dark, high and low, hot and cold, fire and water, male and female, and life and death.
|
|