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Jacobi identity

In mathematics, the Jacobi identity is a property of a binary operation that describes how the order of evaluation, the placement of parentheses in a multiple product, affects the result of the operation. By contrast, for operations with the associative property, any order of evaluation gives the same result (parentheses in a multiple product are not needed). The identity is named after the German mathematician Carl Gustav Jacob Jacobi. He derived the Jacobi identity for Poisson brackets in his 1862 paper on differential equations.

The cross product $$a\times b$$ and the Lie bracket operation $$[a,b]$$ both satisfy the Jacobi identity. In analytical mechanics, the Jacobi identity is satisfied by the Poisson brackets. In quantum mechanics, it is satisfied by operator commutators on a Hilbert space and equivalently in the phase space formulation of quantum mechanics by the Moyal bracket.

Definition
Let $$+$$ and $$\times$$ be two binary operations, and let $$0$$ be the neutral element for $$+$$. The  is

 * $$x \times (y \times z) \ +\ y \times (z \times x) \ +\ z \times (x \times y)\ =\ 0.$$

Notice the pattern in the variables on the left side of this identity. In each subsequent expression of the form $$a \times (b \times c)$$, the variables $$x$$, $$y$$ and $$z$$ are permuted according to the cycle $$x \mapsto y \mapsto z \mapsto x$$. Alternatively, we may observe that the ordered triples $$(x,y,z)$$, $$(y,z,x)$$ and $$(z,x,y)$$, are the even permutations of the ordered triple $$(x,y,z)$$.

Commutator bracket form
The simplest informative example of a Lie algebra is constructed from the (associative) ring of $$n\times n$$ matrices, which may be thought of as infinitesimal motions of an n-dimensional vector space. The × operation is the commutator, which measures the failure of commutativity in matrix multiplication. Instead of $$X\times Y$$, the Lie bracket notation is used:
 * $$[X,Y]=XY-YX.$$

In that notation, the Jacobi identity is:
 * $$[X, [Y, Z] ] + [Y, [Z, X] ] + [Z, [X, Y] ] \ =\ 0$$

That is easily checked by computation.

More generally, if $A$ is an associative algebra and $V$ is a subspace of $A$ that is closed under the bracket operation: $$[X,Y]=XY-YX$$ belongs to $V$ for all $$X,Y\in V$$, the Jacobi identity continues to hold on $V$. Thus, if a binary operation $$[X,Y]$$ satisfies the Jacobi identity, it may be said that it behaves as if it were given by $$XY-YX$$ in some associative algebra even if it is not actually defined that way.

Using the antisymmetry property $$[X,Y]=-[Y,X]$$, the Jacobi identity may be rewritten as a modification of the associative property:

 * $$X, Y], Z] = [X, [Y, Z - [Y, [X, Z]]~.$$

If $$[X,Z]$$ is the action of the infinitesimal motion $X$ on $Z$, that can be stated as: "The action of Y followed by X (operator $[X,[Y,\cdot\ ] ]$), minus the action of X followed by Y (operator $([Y,[X,\cdot\ ] ]$), is equal to the action of $[X,Y]$, (operator $[ [X,Y],\cdot\ ]$)."

There is also a plethora of graded Jacobi identities involving anticommutators $$\{X,Y\}$$, such as:

[\{X,Y\},Z]+ [\{Y,Z\},X]+[\{Z,X\},Y] =0,\qquad [\{X,Y\},Z]+ \{[Z,Y],X\}+\{[Z, X],Y\} =0. $$

Adjoint form
Most common examples of the Jacobi identity come from the bracket multiplication $$[x,y]$$ on Lie algebras and Lie rings. The Jacobi identity is written as:

 * $$[x,[y,z]] + [z,[x,y]] + [y,[z,x]] = 0.$$

Because the bracket multiplication is antisymmetric, the Jacobi identity admits two equivalent reformulations. Defining the adjoint operator $$\operatorname{ad}_x: y \mapsto [x,y]$$, the identity becomes:
 * $$\operatorname{ad}_x[y,z]=[\operatorname{ad}_xy,z]+[y,\operatorname{ad}_xz].$$

Thus, the Jacobi identity for Lie algebras states that the action of any element on the algebra is a derivation. That form of the Jacobi identity is also used to define the notion of Leibniz algebra.

Another rearrangement shows that the Jacobi identity is equivalent to the following identity between the operators of the adjoint representation:
 * $$\operatorname{ad}_{[x,y]}=[\operatorname{ad}_x,\operatorname{ad}_y].$$

There, the bracket on the left side is the operation of the original algebra, the bracket on the right is the commutator of the composition of operators, and the identity states that the $$\mathrm{ad}$$ map sending each element to its adjoint action is a Lie algebra homomorphism.

Related identities

 * The Hall–Witt identity is the analogous identity for the commutator operation in a group.

 * The following identity follows from anticommutativity and Jacobi identity and holds in arbitrary Lie algebra:

 * $$[x,[y,[z,w]]] + [y,[x,[w,z]]] + [z,[w,[x,y]]] + [w,[z,[y,x]]] = 0.$$

 * The Jacobi identity is equivalent to the Product Rule, with the Lie bracket acting as both a product and a derivative: $$[X,[Y,Z]] = X,Y], Z] + [Y, [X,Z$$.   If $$X, Y$$ are vector fields, then $$[X,Y]$$ is literally a derivative operator acting on $$Y$$, namely the Lie derivative $$\mathcal{L}_X Y$$.

title: Jacobi identity


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Sigil

A sigil is a type of symbol used in magic. The term usually refers to a pictorial signature of a deity or spirit (such as an angel or demon). In modern usage, especially in the context of chaos magic, a sigil refers to a symbolic representation of the practitioner's desired outcome.

History

The use of symbols for magical or cultic purposes has been widespread since at least the Neolithic era. The term sigil derives from the Latin sigillum (pl. sigilla or sigils), meaning "seal."

In medieval magic, the term sigil was commonly used to refer to occult signs which represented various angels and demons which the practitioner might summon. The magical training books called grimoires often listed pages of such sigils. A particularly well-known list is in The Lesser Key of Solomon, in which the sigils of the 72 princes of the hierarchy of hell are given for the magician's use. Such sigils are considered by some to be the equivalent of the true name of the spirit and thus granted the magician a measure of control over the beings.

A common method of creating the sigils of certain spirits was to use kameas, a special use case of magic squares — the names of the spirits were converted to numbers, which were then located on the magic square. The locations were then connected by lines, forming an abstract figure.

"The word sigil [...] has a long history in Western magic. The members of the Golden Dawn were perfectly familiar with it ("combining the letters, the colours, the attributions and their Synthesis, thou mayest build up a telesmatic Image of a Force. The Sigil shall then serve thee for the tracing of a Current which shall call into action a certain Elemental Force") and it was used in the making of talismans. The sigil was like a signature or sign of an occult entity."

Austin Osman Spare
Artist and occultist Austin Osman Spare (1886–1956) developed his own unique method of creating and using sigils, which has had a huge effect on modern occultism. Spare did not agree with medieval practice of using these, arguing that such supernatural beings were simply complexes in the unconscious, and could be actively created through the process of sigilization.

Spare's technique became a cornerstone of chaos magic (see next section). It also influenced artist Brion Gysin, who experimented with combining Spare's sigil method with the traditional form of magic squares:

"Calligraphic magick squares were one of the techniques most commonly applied by Gysin. He would reduce a name or an idea to a "glyph" and then write across the paper from right to left, turn the paper and do the same again, and so on, turning the paper around and around to create a multidimensional grid... The same techniques and consciously driven functional intention also permeated his paintings. In a very real sense, everything he created was an act of sorcery."

Chaos magic

In chaos magic, following Spare, sigils are commonly created in a well ordered fashion by writing an intention, then condensing the letters of the statement down to form a sort of monogram. The chaos magician then uses the gnostic state to "launch" or "charge" the sigil – essentially bypassing the conscious mind to implant the desire in the unconscious. To quote Ray Sherwin:

"The magician acknowledges a desire, he lists the appropriate symbols and arranges them into an easily visualised glyph. Using any of the gnostic techniques he reifies the sigil and then, by force of will, hurls it into his subconscious from where the sigil can begin to work unencumbered by desire."

After charging the sigil, it is considered necessary to repress all memory of it. In the words of Spare, there should be "a deliberate striving to forget it".

In modern chaos magic, when a complex of thoughts, desires, and intentions gains such a level of sophistication that it appears to operate autonomously from the magician's consciousness, as if it were an independent being, then such a complex is referred to as a servitor. When such a being becomes large enough that it exists independently of any one individual, as a form of "group mind", then it is referred to as an egregore.

Later chaos magicians have expanded on the basic sigilization technique. Grant Morrison coined the term hypersigil to refer to an extended work of art with magical meaning and willpower, created using adapted processes of sigilization. Their comic book series The Invisibles was intended as such a hypersigil. Morrison has also argued that modern corporate logos like "the McDonald's Golden Arches, the Nike swoosh and the Virgin autograph" are a form of viral sigil:

"Corporate sigils are super-breeders. They attack unbranded imaginative space. They invade Red Square, they infest the cranky streets of Tibet, they etch themselves into hairstyles. They breed across clothing, turning people into advertising hoardings... The logo or brand, like any sigil, is a condensation, a compressed, symbolic summoning up of the world of desire which the corporation intends to represent... Walt Disney died long ago but his sigil, that familiar, cartoonish signature, persists, carrying its own vast weight of meanings, associations, nostalgia and significance."

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Sigil


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Genesis P-Orridge

Genesis Breyer P-Orridge (born Neil Andrew Megson; 22 February 1950 – 14 March 2020) was an English singer-songwriter, musician, poet, performance artist, visual artist, and occultist who rose to notoriety as the founder of the COUM Transmissions artistic collective and lead vocalist of seminal industrial band Throbbing Gristle. They were also a founding member of Thee Temple ov Psychick Youth occult group, and fronted the experimental pop rock band Psychic TV.

Born in Manchester, P-Orridge developed an early interest in art, occultism, and the avant-garde while at Solihull School. After dropping out of studies at the University of Hull, they moved into a counter-cultural commune in London and adopted Genesis P-Orridge as their pseudonym. On returning to Hull, they founded COUM Transmissions with Cosey Fanni Tutti, and in 1973 they relocated to London. COUM's confrontational performance work, dealing with such subjects as sex work, pornography, serial killers, and occultism, represented a concerted attempt to challenge societal norms and attracted the attention of the national press. COUM's 1976 Prostitution show at London's Institute of Contemporary Arts was particularly vilified by tabloids, gaining them the moniker of the "wreckers of civilisation." P-Orridge's band, Throbbing Gristle, grew out of COUM, and were active from 1975 to 1981 as pioneers in the industrial music genre. In 1981, P-Orridge co-founded Psychic TV, an experimental band that from 1988 onward came under the increasing influence of acid house.

In 1981, P-Orridge co-founded Thee Temple ov Psychick Youth, an informal occult order influenced by chaos magic and experimental music. P-Orridge was seen as the group's leader, but rejected that position, and left the group in 1991. Amid the Satanic ritual abuse hysteria, a 1992 Channel 4 documentary accused P-Orridge of sexually abusing children, resulting in a police investigation. P-Orridge was subsequently cleared and Channel 4 retracted their allegation. As a result of the incident, P-Orridge left the United Kingdom for the United States and settled in New York City. There, they married Jacqueline Breyer, later known as Lady Jaye, in 1995, and together they embarked on the Pandrogeny Project, an attempt to unite as a "pandrogyne", or single entity, through the use of surgical body modification to physically resemble one another. P-Orridge continued with this project of body modification after Lady Jaye's 2007 death. Although involved in reunions of both Throbbing Gristle and Psychic TV in the 2000s, they retired from music to focus on other artistic media in 2009.

P-Orridge was credited on over 200 releases during their lifetime. They were cited as an icon within the avant-garde art scene, accrued a cult following, and had been given the moniker of the "Godparent of Industrial Music". P-Orridge considered themself third-gender and used various gender-neutral pronouns.

1950–1964: Childhood
Genesis P-Orridge was born on 22 February 1950 in Victoria Park, Manchester, to Ronald and Muriel Megson. Ronald was a travelling salesman who had worked in repertory theatre and who played the drums in local jazz and dance bands. Muriel was from Salford and had first met Ronald after he returned to England after being injured with the British Army at the Battle of Dunkirk in 1940. As a child, they had a good relationship with their parents, who did not interfere with their artistic interests.

Due to Ronald's job, the family moved to Essex, where they attended Staples Road Infant School in Loughton, and for a time lived in a caravan near to Epping Forest while the family house was being completed. The family then moved from Essex to Cheshire, where they attended Gatley Primary School. Passing the 11-plus exam, they won a scholarship to attend Stockport Grammar School, doing so between 1961 and 1964.

1964–1968: Solihull School and Worm
After their father became the Midlands area manager of a cleaning and maintenance business, they were sent to the privately run Solihull School in Warwickshire between 1964 and 1968; a period they would refer to as "basically four years of being mentally and physically tortured", but also a time when they developed an interest in art, occultism and the avant-garde. At age fifteen, they became a fan of "The Hundred Headless Woman," a book that contained surrealist collages by various artists, including Max Ernst. The book became an early source of inspiration, and it was at that time that they took on the name "P-Orridge."

Unpopular with other pupils, they were bullied at the school, finding comfort in the art department at lunch-time and in the evenings. They befriended Ian "Spydeee" Evetts, Barry "Little Baz" Hermon and Paul Wolfson, three fellow pupils who shared their interest in art, literature, and poetry. They regularly discussed books and music, developing an interest in the writings of Aleister Crowley, William S. Burroughs, Jack Kerouac and Allen Ginsberg and the music of Frank Zappa, the Fugs and the Velvet Underground. They became interested in occultism, and also asserted that their grandmother was a medium.

In 1967, P-Orridge founded their first collective, Worm, with school friends Pingle Wad (Peter Winstanley), Spydeee Gasmantell (Ian Evetts) and P-Orridge's girlfriend Jane Ray. Worm was influenced by AMM and John Cage's 1961 book Silence: Lectures and Writings. In 1966, P-Orridge, Evetts, Hermon, Wolfson, and Winstanley began production of an underground magazine, entitled Conscience. Forbidden from selling it on school grounds, they sold copies outside the school gates. Included in Conscience were various articles criticising the school's administration, leading to proposed changes regarding such issues as school uniforms and prefects (known as benchers) privileges. That same year, influenced by newspaper accounts of "Swinging London", they organised the first happening at the school, doing so under the auspices of organising a school dance.

Brought up in the Anglican denomination of Christianity, P-Orridge became secretary of the school sixth form's Christian Discussion Circle, in this position inviting members of other ideological positions – including a Marxist from the British Communist Party – to speak to the group. Aged 18, P-Orridge began helping to run the local Sunday school classes, but came to reject organised Christianity. Afflicted with asthma throughout childhood, P-Orridge had to take cortisone and prednisone steroids to control the attacks. The latter of these drugs caused their adrenal glands to atrophy as a side-effect, and so the doctor advised P-Orridge to stop taking them. As a result, aged 17, P-Orridge suffered from a serious blackout; while in hospital recovering they decided to devote their life to art and writing.

With Hermon and Wolfson, P-Orridge founded a group called the Knights of the Pentecostal Flame. The Knights undertook a happening on 1 June 1968 which they titled Beautiful Litter. Taking place in Mell Square, Solihull, it involved the three students handing out cards to passersby that had a series of words written onto them; "fleece", "rainbow", "silken", "white", "flower" and "dewdrops". Ensuring that the local Solihull News was informed of the event, P-Orridge told reporters that the Knights wanted to ignite "an artistic revolution in Solihull, by making people aware of the life around them, its essential beauty and tranquillity." In mid-1968, Worm recorded their first and only album, entitled Early Worm, in P-Orridge's parents' attic in Solihull. It was pressed onto vinyl in November at Deroy Sound Services in Manchester, but only one copy was ever produced. A second album, Catching the Bird, was recorded but never pressed.

1968–1969: Hull University and Transmedia Explorations
In September 1968, P-Orridge began studying for a degree in Social Administration and Philosophy at the University of Hull. Hull was chosen in an attempt to study at "the most ordinary non-elitist, working-class, red brick university", but P-Orridge disliked the course and unsuccessfully tried to transfer to study English. With a group of friends, P-Orridge founded a 'free-form' student magazine entitled Worm which waived all editorial control, publishing everything placed into the magazine's pigeonhole, including instructions on how to build a molotov cocktail. Three issues were published between 1968 and 1970 before the Hull Student's Union banned the publication, considering it legally obscene and fearing prosecution. Developing a keen interest in poetry, P-Orridge won the 1969 Hull University Needler Poetry Competition, judged by Compton lecturer Richard Murphy and the poet Philip Larkin, who was then librarian at the university. P-Orridge became involved in radical student politics through their friendship with Tom Fawthrop, a member of the Radical Student Alliance who had led a student occupation of the university's administrative buildings as a part of the worldwide student protests of 1968. In 1969, P-Orridge attempted to reconstruct the occupation for a film, in the hopes that it would itself become a genuine protest occupation, but this venture failed due to a lack of participants.

In 1969, P-Orridge dropped out of university and moved to London, and joined the Transmedia Explorations commune, who were then living in a large run-down house in Islington Park Street. The group, initiated by the artist David Medalla and initially named the Exploding Galaxy, had been at the forefront of the London hippy scene since 1967, but had partially disbanded after a series of police raids and a damaging court case. Moving into their commune, P-Orridge was particularly influenced by one of the founding members of the group, Gerald Fitzgerald, a kinetic artist, and would recognise Fitzgerald's formative influence in P-Orridge's later work. The commune members adhered to a strict regime with the intention of deconditioning its members out of their routines and conventional behaviour; they were forbidden from sleeping in the same place on consecutive nights, food was cooked at irregular times of the day and all clothing was kept in a communal chest, with its members wearing something different on each day. P-Orridge stayed there for three months, until late October 1969. They left after becoming angered that the commune's leaders were given more rights than the other members and believing that the group ignored the counter-cultural use of music, something they took a great interest in. Julie Wilson later stated that although P-Orridge's time at the Transmedia Explorations commune had been brief, "the experiences (they) had there proved to be seminal" to their artistic development.

1969–1970: Founding COUM Transmissions
Leaving London, P-Orridge hitch-hiked across Britain before settling down in a new home in Shrewsbury. Here, they volunteered as an office clerk in Ronald Megson's new business. On one family trip to Wales, P-Orridge was sitting in the back of the car, then "became disembodied and heard voices and saw the COUM symbol and heard the words 'COUM Transmissions. Returning home that evening, P-Orridge filled three notebooks with artistic thoughts and ideas, influenced by the time spent at Transmedia Explorations.

In November 1969, P-Orridge returned to Hull to meet up with friend John Shapeero, who partnered with P-Orridge to turn COUM Transmissions into an avant-garde artistic and musical troupe. They initially debated as to how to define "COUM", later deciding that like the name "dada" it should remain open to interpretation. P-Orridge designed a logo for the group, consisting of a semi-erect penis formed out of the word COUM with a drip of semen coming out of the end, while the motto "Your Local Dirty Banned" (a pun on "band") was emblazoned underneath. Another logo designed by P-Orridge consisted of a hand-drawn seal accompanied by the statement "COUM guarantee disappointment"; from their early foundation, the group made use of wordplay in their artworks and adverts.

COUM's earliest public events were impromptu musical gigs performed at various pubs around Hull; titles for these events included Thee Fabulous Mutations, Space Between the Violins, Dead Violins and Degradation, and Clockwork Hot Spoiled Acid Test. The latter combined the names of Anthony Burgess' dystopian science-fiction novel A Clockwork Orange (1962) with Tom Wolfe's The Electric Kool-Aid Acid Test (1968), a work of literary journalism devoted to the Merry Pranksters, a US communal counter-cultural group who advocated the use of psychedelic drugs. COUM's music was anarchic and improvised, making use of such instruments as broken violins, prepared pianos, guitars, bongos and talking drums. As time went on, they added further theatrics to their performances, in one instance making the audience crawl through a polythene tunnel to enter the venue.

In December 1969, P-Orridge and Shapiro moved out of their flat and into a former fruit warehouse in Hull's docking area, overlooking the Humber. Named the Ho-Ho Funhouse by P-Orridge, the warehouse became the communal home to an assortment of counter-cultural figures, including artists, musicians, fashion designers and underground magazine producers. At Christmas 1969, a woman named Christine Carol Newby moved into the Funhouse after being thrown out of her home by her father. Having earlier befriended them at an acid test party, Newby became P-Orridge's roommate at the Funhouse, first taking the name Cosmosis, but latterly adopting the stage name Cosey Fanni Tutti after the title of Amadeus Mozart's 1790 opera Così fan tutte. Joining COUM, Tutti initially helped in building props and designing costumes, and was there when the group began including performance art and more theatrical happenings in its music events; Evetts, aka Spydeee Gasmantell, after being expelled from Solihull School joined COUM. The three of them lived in a derelict Georgian warehouse in Prince Street, Hull. An example performance involved the group turning up to play a gig but intentionally not bringing any instruments, something P-Orridge considered "much more theatrical, farcical and light-hearted" than their earlier performances.

1971–1973: Activities in Hull
On 5 January 1971, P-Orridge underwent a legal name change to Genesis P-Orridge by deed poll, combining the adopted nickname Genesis with an altered spelling of porridge, the foodstuff which they had lived off as a student. The new name was intentionally un-glamorous, and they hoped that it would trigger a personal "genius factor". In February, COUM caught the attention of The Yorkshire Post, which featured an article on them that led to further media attention from national newspapers. They also featured in an article in Torch, the publication of the University of Hull's student union, entitled "God Sucks Mary's Hairy Nipple"; the article's author, Haydn Robb (nowadays known as Haydn Nobb), subsequently joined COUM, as did maths lecturer Tim Poston. In April 1971, COUM, consisting of P-Orridge and Gasmantell, broadcast their first live radio session, for the On Cue programme for Radio Humberside. Following up the press attention they received, they performed further happenings, including their first street action, Absolute Everywhere, which brought problems with the police.

After performing another set, Riot Control, at Hull's Gondola Club, the premises were raided by police and closed soon after; most local clubs blamed COUM and unofficially banned them. COUM drew up a petition to gain support for the group, attaining a booking at the local Brickhouse; their first performance in which the audience applauded and called for an encore. The petition had contained their phallic logo, and the police charged P-Orridge and Robb with publishing an obscene advert, although the charges were later dropped. As they gained coverage in the music press, interest in the band grew, and they supported Hawkwind at St. George's Hall in Bradford in October 1971, where they performed a piece called Edna and the Great Surfers, where they led the crowd in shouting "Off, Off, Off". The following month, the band attracted the interest of music journalist John Peel, who publicly remarked that "[s]ome might say that Coum were madmen but constant exposure to mankind forces me to believe that we need more madmen like them."

Gaining an Experimental Arts Grant from the publicly funded Yorkshire Arts Association, COUM described themselves as performance artists, being inspired by the Dadaists and emphasising the amateur quality of their work. They entered the National Rock/Folk Contest at Hull's New Grange Club with a set titled This Machine Kills Music, and organised events for Hull City Council's celebrations to mark the UK's entry into the European Economic Community in 1973. They had also worked on solo projects, generating controversy in the local press over a conceptual artwork the artist entered at a local exhibition. Taking an increasing interest in infantilism, P-Orridge founded the fictitious L'ecole de l'art infantile and co-organised the "Baby's Coumpetition" [sic] at Oxford University's 1973 May Festival, also producing material as the fictitious Ministry of Antisocial Insecurity, a parody of the Ministry of Social Security. Meanwhile, P-Orridge created the character of Alien Brain, and in July 1972, performed as the character at an event entitled the World Premiere of the Alien Brain, at Hull Arts Centre. COUM also began publishing books; in 1972, they brought out the first volume of The Million and One Names of COUM, part of a proposed project to release 1001 slogans (such as "A thousand and one ways to COUM" and "COUM are Fab and Kinky"), while in 1973 P-Orridge published Copyright Breeches, which explored an ongoing personal fascination with the copyright symbol and its implications for art and society.

1973–1975: London and growing fame
Following continual police harassment, P-Orridge and Tutti relocated to London, moving into a squat and obtaining a basement studio in Hackney which they named the "Death Factory". After a brief correspondence, P-Orridge met American novelist and poet William S. Burroughs. Brion Gysin would become a major influence upon P-Orridge's ideas and works and was the latter's primary tutor in spiritual magic. 1973 saw COUM take part in the Fluxshoe retrospective that toured Britain exhibiting the work of the Fluxus artists; it was organised by David Mayor, who befriended P-Orridge. At that year's Edinburgh Festival, P-Orridge undertook a Marcel Duchamp-inspired performance art piece, Art Vandals, at the Richard Demarco Gallery, engaging guests in unconventional conversation, and spilling their food and drink on the floor. Exhibiting alongside the Viennese Actionists, P-Orridge came under increasing influence from these Austrian performance artists, adopting their emphasis on using shock tactics to combat conventional morality. P-Orridge's first film, Wundatrek Tours, was released in September 1973, and documented a day out to Brighton. Throughout the year the artist sent personally designed postcards to mail-art shows across the world.

In January 1974, COUM returned their attention to music, collaborating with the Canadian artist Clive Robertson to produce Marcel Duchamp's Next Work, which they premiered at an arts festival in the Zwarte Zaal Royal Conservatory of Ghent in Ghent, Belgium. COUM's next major work was Couming of Age, performed in March 1974 at the Oval House in Kennington, South London. After the show, they were approached by an audience member, Peter Christopherson, who shared many of their interests; P-Orridge and Tutti nicknamed him "Sleazy" because of the former's particular interest in the sexual aspects of COUM's work. Christopherson began to aid them using their skills as a photographer and graphic designer, and would first perform with them in their March 1975 work Couming of Youth. In May 1974, COUM issued a manifesto published on an A3 double-sided sheet titled Decoumpositions and Events.

In April 1974, the Arts Council of Great Britain gave COUM the first half of a £1,500 grant. The money stabilised the group, which now included P-Orridge and Tutti as directors, John Gunni Busck as technical director, and Lelli Maull as musical director. During that year, they made use of various artist-run venues in London, most notably the Art Meeting Place (AMP) in Covent Garden, where they regularly performed during 1974. A number of these works entailed P-Orridge and Tutti exploring the gender balance, including concepts of gender confusion. In one performance at the AWB, which was titled Filth, P-Orridge and Tutti performed sexual acts using a double-ended dildo. COUM were frustrated with the restrictions imposed on them by the Arts Council as a prerequisite for receiving funding; rather than performing at Council-accredited venues, they wanted to perform more spontaneously. In August 1974 they carried out a spontaneous unauthorised piece of performance art in Brook Green, Hammersmith; during the performance, police arrived and put a stop to the event, deeming it obscene.

In September 1974, COUM were invited to attend the Stadfest in Rottweil, West Germany, and they proceeded with a travel grant from the British Council. There, they published two performance art actions in the street, earning them praise from Bridget Riley and Ernst Jandl, both of whom were present. The acclaim that COUM received at Rottweil established the group's reputation as "one of the most innovative performance art groups then on the London art scene", convincing the Arts Council and British Council to take them more seriously and offer them greater support.

In February 1975, P-Orridge gained their first full-time job, working as an assistant editor at St. James Press, in which they helped to compile the Contemporary Artists reference book. The work meant that they had less time to devote to COUM but gained a wide range of contacts in the art world. During that year, COUM embarked on a series of five performance pieces which it termed Omissions; these were performed across Europe. In March 1975, COUM performed Couming of Youth at the Melkweg in Amsterdam. Adopting a more violent stance than their previous work – in this reflecting an influence from the Viennese Actionists – the performance involved self-mutilation, Cosey inserting lighted candles into her vagina, P-Orridge being crucified and whipped, and P-Orridge and Cosey having sexual intercourse. At Southampton's Nuffield Festival in July 1975, COUM performed Studio of Lust, where P-Orridge publicly masturbated and all of the members undressed and adopted sexual poses.

1975–1976: Establishing Throbbing Gristle and the Prostitution show
COUM were introduced to Chris Carter in 1975 through their mutual friend John Lacey. Lacey believed that Carter would be interested in COUM as a result of his particular interest in the experimental use of light and sound. Together, Carter, Christopherson, Cosey and P-Orridge founded a musical band, Throbbing Gristle, on 3 September 1975; they had deliberately chosen that date for it was the 36th anniversary of the United Kingdom joining the Second World War. The term "throbbing gristle" was deliberately chosen for it was a Yorkshire slang term for an erect penis. Throbbing Gristle, or TG as it was widely known, was aimed at a wider audience than COUM, thereby aiming to work within popular culture rather than the elite realm of the art scene. COUM and TG were largely treated as distinct entities; the music press ignored COUM and saw TG as experimental art rock, while the arts press ignored TG, viewing COUM as performance artists. Despite their intention of operating within the realms of popular culture, TG never had chart success, and remained a cult band; their audience was far larger than COUM.

COUM continued to operate alongside TG, and in October 1975 they performed Jusquà la balle crystal at the Ninth Paris Biennale at the Musée d'art modern. The prestige of being invited to such an event led to the Arts Council awarding them a grant for £1,600, although only the first half of this was ever paid out. COUM's mail art had taken on an increasingly pornographic dimension, and in November 1975 the police charged P-Orridge with distributing obscene material via in the postal system under the 1953 Post Office Act; this trial was set for February 1976. They were prosecuted in 1975 for making collages combining postcards of Queen Elizabeth with soft-core porn, but the jail term and fines were suspended on condition they did not continue.

Their Prostitution show, in 1976 at the Institute of Contemporary Arts (ICA) in London, included displays of Tutti's pornographic images from magazines as well as erotic nude photographs; the show featured a stripper, used tampons in glass, and transvestite guards. Prostitutes, punks, and people in costumes were among those hired to mingle with the gallery audience. The show caused debate in Parliament about the public funding of such events. In the House of Commons, Scottish Conservative MP Sir Nicholas Fairbairn demanded an explanation from Arts Minister Harold Lever and proclaimed P-Orridge and Tutti as "wreckers of civilisation". Fleet Street was not slow to pick up the story. The reviews were cut up, framed, and put on display for the remainder of the exhibition. This was also reported in newspapers, so cut-ups about the cut-ups were also put on display. COUM was found so offensive that it lost its government grant, and went on to become the private company Industrial Records. Toward the end of COUM, performances would often consist of only P-Orridge, Cosey and Sleazy, the core group who went on to form Throbbing Gristle.

Throbbing Gristle
Throbbing Gristle was formed in late 1975 as a four-piece band, consisting of P-Orridge, Cosey Fanni Tutti, Peter "Sleazy" Christopherson and Chris Carter. The name "Throbbing Gristle" was adopted after a Northern English slang term for an erect penis. P-Orridge's involvement in Throbbing Gristle led to the artist being regularly cited as the "Godfather of Industrial Music", or in some later sources, "godparent".

The first Throbbing Gristle performance was held at the Air Gallery in London in July 1976. At that point, Throbbing Gristle's headquarters was located at 10 Martello Street, Hackney, East London, the address of an artist collective. P-Orridge and Tutti's living and work space was the postal address of Industrial Records (IR). Throbbing Gristle released "Discipline" in 1980. TG came to be identified as the founders of industrial music, although at the same time the academic Drew Daniel asserted that as a result of its eclecticism, their music resists clear analysis.

Throbbing Gristle's best-selling single was "Zyklon B Zombie" (1978), the title being a reference to the Zyklon B poison gas used at Auschwitz extermination camp. With their album 20 Jazz Funk Greats they attempted to move away from their industrial sound, and produced songs in a variety of different musical genres. P-Orridge received a number of threatening phone calls, proceeding to record them and use them as a backing track for the TG song "Death Threats".

The final IR release was called Nothing Here Now But the Recordings, a best-of album taken from the archives of William S. Burroughs, who provided P-Orridge and Christopherson with access to his reel-to-reel tape archive.

The final Throbbing Gristle live event, Mission of Dead Souls, occurred in May 1981 at the Kezar Pavilion in San Francisco. Shortly after the San Francisco event, P-Orridge and Paula Brooking were married.

During this period, P-Orridge befriended an English musician named David Bunting; P-Orridge already knew another man named David, so coined the moniker David Tibet, which Bunting adopted as a stage name. Through an introduction provided by Burroughs, P-Orridge met Brion Gysin in Paris, probably in 1980, coming to be deeply influenced by Gysin's cut-up method; P-Orridge understood this to be a revolutionary method of escaping current patterns of thought and developing something new.

Psychic TV and Thee Temple Ov Psychic Youth

Following the break-up of Throbbing Gristle, in 1981 P-Orridge founded a band with Peter Christopherson and Alex Fergusson that they named Psychic TV. Involved in video art, they also performed psychedelic, punk, electronic and experimental music. The decision to name the band "Psychic TV" stemmed from P-Orridge's belief that while mainstream television was a form of mass indoctrination and mind control, it could be used as an "esoterrorist" form of magick to combat the establishment's control. Historian Dave Evans described Psychic TV as "a band dedicated to musical eclecticism and magical experiment, their performances being in part ritual (ab)use of sound samples, the creation of 'auditory magical sigils' and the destruction of consensus language in order to find meaning".

The band's first song, "Just Drifting", was based on a poem by P-Orridge. For their first album, Force the Hand of Chance (1982), P-Orridge used a kangling, or Tibetan trumpet made out of a human thigh-bone; the instrument had been introduced to P-Orridge by David Tibet, and attracted attention to their music. P-Orridge had become acquainted with Anton LaVey, founder of the Church of Satan and ideologue of LaVeyan Satanism, with LaVey making an appearance on the Psychic TV song "Joy", in which he recites the Lord's Prayer backwards. From 1988, the band came under the increasing influence of the acid house genre of dance music, and were responsible for helping the popularisation of acid house music in Europe.

Psychic TV made its debut in 1982 at an event organised by P-Orridge, David Dawson, and Roger Ely, called The Final Academy. It was a 4-day multimedia celebratory rally held in Manchester and at the Ritzy Cinema in Brixton, South London. It brought performers and audience together with literature, performance, film and music. PTV, Cabaret Voltaire, 23 Skidoo, Z'EV, John Giorno, William S. Burroughs, Brion Gysin, Terry Wilson, Jeff Nuttall, and the Last Few Days participated to honour the cut-up techniques and theories of William S. Burroughs, Ian Sommerville, Antony Balch and Gysin. Video projection and early sampling were used here, as well as whispered utterances by P-Orridge reprocessed as a soundtrack to Gysin's Dreammachine by the Hafler Trio. In the mid-1980s, Psychic TV aimed to release a live album on the 23rd of each month for 23 months in recognition of the 23 enigma. The group did not reach its goal but still managed fourteen albums in eighteen months, thus earning them an entry in the Guinness Book of World Records. Following the culmination of Psychic TV but before embarking on Thee Majesty, P-Orridge and several Psychic TV musicians formed Splinter Test, a name adopted from one of P-Orridge's essays on sampling.

In 1981, P-Orridge also founded a loosely organised network of occultists named Thee Temple ov Psychick Youth (TOPY), with the aid of John Balance, Tibet, and a number of members of the Process Church of the Final Judgement, a group which had exerted an influence on P-Orridge's occult thought. TOPY was conceived not as an occult order of teaching, but a forum to facilitate discussions on occult ideas by like-minded people, and from its beginnings was understood by its founders to be a successor to the late 19th and early 20th century Ordo Templi Orientis (OTO), especially as the latter had been run under Crowley's leadership. Evans described TOPY as "a 'fusion' organisation, creating a crossover of punk/experimental music with chaos magical thinking and practice", making particular use of the sigilisation practices of occult artist Austin Osman Spare. Journalist Gavin Baddeley described TOPY as "perhaps the most influential new occult order of the 1980s". P-Orridge had never wanted to be seen as the leader of an occult order, although many of those involved in TOPY were frustrated that outsiders regularly described P-Orridge as the group's leader. Accordingly, P-Orridge separated from TOPY in 1991, although it continued as a fan community after the departure.

Having been encouraged by groups involved in propagating the moral panic about alleged Satanic ritual abuse, the Channel 4 1992 documentary show Dispatches claimed to have discovered videotapes depicting P-Orridge sexually abusing children in a ritual setting. Police from the Obscene Publications Squad subsequently raided P-Orridge's home, and confiscated several tonnes of art work. At the time, P-Orridge was in Thailand undertaking famine relief work; fearing arrest and loss of child custody upon return to the UK, P-Orridge stayed out of the country for several years, settling in the United States. P-Orridge believed that the negative press and police attention were the result of a campaign organised by a Christian group. It was subsequently revealed that the footage obtained did not depict child abuse. Instead, it was a video artwork titled First Transmissions that had been made in the early 1980s, partially funded by Channel 4 itself; the footage depicted sex-magic rites between adults, bloodletting performances, and scenes of the filmmaker Derek Jarman reading passages from the work of Geoffrey Chaucer. Embarrassed by these revelations, Channel 4 retracted its initial accusations.

In 2016, the film director Jacqueline Castel began work on the feature-length documentary titled A Message from the Temple, about Thee Temple Ov Psychick Youth and P-Orridge.

1993–2009: The Pandrogeny Project
At 45 years of age P-Orridge met Lady Jaye (née Jacqueline Breyer) in a BDSM dungeon in New York City and would eventually marry for a second time. Jaye worked as a nurse during the daytime, providing care for children with terminal illnesses and disabilities. In the evenings, Lady Jaye worked as a dominatrix at the dungeon, and Genesis was a visiting customer. The night they met, the two visited Paddles, an underground BDSM club in Manhattan. The two became a couple from that point forward.

In January 1993, P-Orridge and Jaye moved to Ridgewood, Queens, in New York City. Here, they embarked on the "Pandrogeny Project"; influenced by the cut-up technique, the duo underwent body modification to resemble one another, thus coming to identify themselves as a single pandrogynous being named "Breyer P-Orridge". In doing so, the pair spent $200,000 on surgical alteration, receiving breast implants, cheek and chin implants, lip plumping, eye and nose jobs, tattooing, and hormone therapy, while also adopting gender neutral and alternating pronouns. With this project, P-Orridge's intent was to express a belief that the self is pure consciousness trapped within the DNA-governed body. The couple adopted the term "pandrogyne" because – in their words – "we wanted a word without any history or any connections with things – a word with its own story and its own information". They also stated that:

"We started out, because we were so crazy in love, just wanting to eat each other up, to become each other and become one. And as we did that, we started to see that it was affecting us in ways that we didn't expect. Really, we were just two parts of one whole; the pandrogyne was the whole and we were each other's other half."

During this era, a book was published of P-Orridge's writings, poems, and observations, called Ooh, You Are Awful ... But I Like You!. In the mid-1990s, P-Orridge collaborated with different people in music, including Pigface, Skinny Puppy, and Download. P-Orridge also performed with Nik Turner and other former members of Hawkwind.

In June 1998, P-Orridge won a $1.5 million lawsuit against producer Rick Rubin and his American Recordings label for injuries sustained while trying to escape a fire at Rubin's home in April 1995. According to P-Orridge's attorney, David D. Stein, P-Orridge was staying at Rubin's home, as a guest of Love and Rockets, when the fire broke out. P-Orridge tried to escape the house by crawling through a second-storey window and fell onto concrete stairs. P-Orridge suffered a broken wrist, broken ribs, and a pulmonary embolism, as well as a shattered left elbow that, according to Stein, prevented P-Orridge from playing bass or keyboards. They remained in hospital for a total of ten days. The jury found that the liability for the fire rested with Rubin and American Recordings, and awarded P-Orridge US$1,572,000 in compensation.

In 1999, P-Orridge performed with the briefly reunited late-1980s version of Psychic TV for an event at London's Royal Festival Hall, called Time's Up. The MC for the event, via pre-recorded video, was Quentin Crisp, it was recorded and released as a DVD. Time's Up is also the title of the first CD by Thee Majesty, P-Orridge's spoken-word project with "noise" guitarist, Bryin Dall.

In December 2003, P-Orridge, using the alias Djinn, unveiled PTV3, a new act drawing upon the early "Hyperdelic" work of Psychic TV with media theorist Douglas Rushkoff among its members. On 16 May 2004, all four former members of Throbbing Gristle performed at the London Astoria for the first time in 23 years.

P-Orridge appeared in the 1998 film and 2000 book versions of Modulations, as well as appearing in the 1999 film Better Living Through Circuitry, the 2004 film DiG!, Bruce LaBruce's 2004 film The Raspberry Reich, the 2006 documentary Monks: The Transatlantic Feedback, in Nik Sheehan's 2007 feature documentary on the Dreamachine entitled FLicKeR, the 2010 documentary William S. Burroughs: A Man Within, and the 2011 film The Ballad of Genesis and Lady Jaye.

In January 2006, the new PTV album was announced on P-Orridge's website. Hell Is Invisible... Heaven Is Her/e was recorded in NYC and features Nick Zinner (Yeah Yeah Yeahs) and Gibby Haynes (Butthole Surfers) guesting on some tracks. To inaugurate the release of Hell Is Invisible ... Heaven Is Her/e, PTV3 hosted a five night residency in September 2006 at Galapagos Art Space in Williamsburg, Brooklyn, New York. Mr. Alien Brain Vs. the Skinwalkers was released on Sweet Nothing Records on 8 December 2008.

On 9 October 2007, Lady Jaye Breyer P-Orridge died. The cause of death was heart arrhythmia, a heart condition that was possibly related to stomach cancer. Psychic TV cancelled its North American tour dates in the aftermath of Lady Jaye's death. A memorial was held at the Participant Inc. Gallery in New York City on 8 March 2008. As of January 2013, P-Orridge's official website said:

"Since that time Genesis continues to represent the amalgam Breyer P-Orridge in the material 'world' and Lady Jaye represents the amalgam Breyer P-Orridge in the immaterial 'world' creating an ongoing interdimensional collaboration."

Thus, P-Orridge continued the Pandrogyne Project, having further surgical operations to alter their body and using "we" when in reference to themselves; to a reporter P-Orridge admitted that without Lady Jaye:

"It's very hard. The bottom line is that we know she [sic] would continue. She wouldn't stop because it was complicated."

From this point, P-Orridge began referring to themselves in the plural in order to keep Breyer's memory alive.

In 2013, Dale Eisinger of Complex ranked the Pandrogeny project the greatest work of performance art ever.

2009–2020: Semi-retirement, illness and death
In September 2009, a retrospective of P-Orridge's collages, entitled "30 Years of Being Cut Up", opened at Invisible-Exports. On 4 November 2009 it was announced that P-Orridge would retire from touring in any and all bands (including Throbbing Gristle and Psychic TV) to concentrate on art, writing and music. In June 2010, P-Orridge sold the Ridgewood property, holding a garage sale in the basement of a local art gallery to sell off a range of personal items, in addition to an array of dildos. This accomplished, P-Orridge moved to a one-bedroom apartment in New York's Lower East Side, and continued producing art in this home.

P-Orridge visited Australia for the first (and only) time in 2012, performing two live shows with Psychic TV; one as part of the Adelaide Festival, and another secret show in Melbourne following a screening of the documentary film The Ballad of Genesis and Lady Jaye. P-Orridge returned to regular touring with Psychic TV in 2016, in support of the release of their album Alienist. The tour lasted from mid-September to early December, with concerts in Greece, Israel, Poland, Russia, Ukraine, the United Kingdom and the United States.

In August 2015, P-Orridge gained publicity for an interview critical of Caitlyn Jenner's self-description as a "spokesperson" for the transgender community, stating that Jenner was "clueless" and did not know what life was like for the majority of transgender people around the world. In mid-2016, P-Orridge's artwork was the subject of an exhibition, "Try to Altar Everything", at the Rubin Museum of Art in New York City. The exhibition contained paintings, sculptures, and installations inspired by the Hindu mythology that P-Orridge had encountered in Kathmandu. In June 2016, P-Orridge was featured as a model in a campaign by the designer Marc Jacobs, who described P-Orridge as "a sort of come-to-life definition of realness and authenticity".

P-Orridge was diagnosed with chronic myelomonocytic leukaemia in October 2017, and died in New York City on 14 March 2020, aged 70. P-Orridge's memoir, Nonbinary, was published a year later, in June 2021,  a project P-Orridge had been working on in collaboration with writer Tim Mohr for several years, according to the New York Times.

Work
Influenced by concepts from both Western esotericism and contemporary Paganism, P-Orridge's work is designed to confront the audience with ways of thinking alien to the mainstream values of Western society. The religious studies scholar Christopher Partridge characterised P-Orridge's work as being a "confluence of pornography, violence, death, degradation, the confrontation of taboo subjects, noise and Paganism", deliberately courting controversy and expressing an anti-establishment stance. Partridge suggested that this intent to shock emerged both out of a serious attempt to highlight the mechanisms of social control in Western society and also out of "a juvenile delight gained from extreme behaviour and the offence caused".

P-Orridge's work was particularly influenced by the early 20th-century English artist and occultist Austin Osman Spare, who shared their disdain for mainstream morality and fascination with sexuality and the human body. P-Orridge adopted Spare's views on sigils, coming to see their own work as a form of sigil magic. Spare's sigilisation process entailed writing down one's desires, before crossing out any letters that are repeated and then combining the remaining letters into an abstract design, or sigil; the magician must then focus on that sigil and mentally absorb it, and – according to Spare's claims – psychic energies operating on the subconscious ensure that the original desire is manifested in reality. P-Orridge adopted this theory, believing that their work operates according to its principles.

A further element of P-Orridge's work is their common use of idiosyncratic grammar and spelling, such as "Thee" in place of "the", "ov" in place of "of" and (especially in early writings) "butter" in place of "but". The purpose of this is to challenge thought and established ways of reading.

Personal life
P-Orridge had two daughters with former wife Paula P-Orridge (born Paula Brooking). An interview with Genesis and Paula P-Orridge appeared in the book RE/Search: Modern Primitives in 1989, and the Icelandic publication Eintak in 1994.

On a religious or spiritual level, Christopher Partridge described P-Orridge as representing "a particularly interesting, influential and subversive example of contemporary paganism". Asserting that their "industrial paganism" was different from most forms of contemporary paganism, Partridge described it as "confrontational, subversive, experimental and, to a large extent, dystopian", with it serving as "an ideological tool" with which to analyse society "from its underbelly; an immersion in the dark side; the subversion of Christian hegemony, conservative politics and what nowadays might be described as neoliberalism". P-Orridge was devoted to the deity Eshu Elegguá, an entity from the Afro-Caribbean syncretic religion of Santería. P-Orridge also stated disbelief in the literal existence of gods, deeming such entities to instead be "early attempts at psychology, trying to understand the light and dark side of human nature".

P-Orridge vociferously criticised contemporary Christianity, describing it as "an incredibly sick social pseudo-religion", and arguing that it was based upon the tenet of "Be good now, agree, or else we will punish you forever and ever when you're dead. And we may punish you while you're alive ..." P-Orridge maintained that such an attitude was established in Christianity by St. Paul and the early Roman Catholic Church, and that it differed from the "ecstatic mysticism of the original Christianity, the Gnostic Christianity".

In her memoir, Art Sex Music, former bandmate Cosey Fanni Tutti claimed P-Orridge had been abusive during their relationship. P-Orridge denied the allegations.

Reception and legacy
According to New York magazine, P-Orridge became "an icon of the London avant-garde" in 1976. Writing for The New Yorker in 2016, the reporter Hermione Hoby described P-Orridge as a "cult figure" considered to be "a treasure of the avant-garde by global art institutions".

The quote that P-Orridge attributed to their mentor, "I feel your pain, I feel your shame, but you're not to blame", was used as the catchphrase for the Shirley Ghostman psychic clairvoyant character by comedian Marc Wootton.

P-Orridge's mock-cult of TOPY has been criticized as being a front for abuses of power and developing a cult of personality.

Musician Electrosexual and Syrian German industrial/techno artist Hanin Elias, founding member of Atari Teenage Riot, recorded a cover version of Hot on the Heels of Love with all proceeds from the sales of both the CD and digital versions going to aid Genesis P-Orridge and their battle against leukemia.

Musician Trent Reznor cites P-Orridge as a major inspiration behind his work.

In 2022, writer Christophe Becker published an essay discussing P-Orridge's relationship with American writer William S. Burroughs and their influence on his work, Géométrie de la Souffrance, Genesis P-Orridge + William S. Burroughs.

title: Genesis P-Orridge


text:
Great Smog of London

The Great Smog of London, or Great Smog of 1952, was a severe air pollution event that affected London, England, in December 1952. A period of unusually cold weather, combined with an anticyclone and windless conditions, collected airborne pollutants—mostly arising from the use of coal—to form a thick layer of smog over the city. It lasted from Friday 5 December to Tuesday 9 December 1952, then dispersed quickly when the weather changed.

The smog caused major disruption by reducing visibility and even penetrating indoor areas, far more severely than previous smog events, called "pea-soupers". Government medical reports in the weeks following the event estimated that up to 4,000 people had died as a direct result of the smog and 100,000 more were made ill by the smog's effects on the human respiratory tract. More recent research suggests that the total number of fatalities was considerably greater, with estimates of between 10,000 and 12,000 deaths.

London's poor air quality had been a problem since at least the 13th century. The diarist John Evelyn had written about "the inconveniencie of the aer and smoak of London [sic]" in Fumifugium, the first book written about air pollution, in 1661. However, the Great Smog was many times worse than anything the city had ever experienced before: it is thought to be the worst air pollution event in the history of the United Kingdom, and the most significant for its effects on environmental research, government regulation, and public awareness of the relationship between air quality and health. It led to several changes in practices and regulations, including the Clean Air Act 1956.

Sources of pollution
A period of unusually cold weather preceding and during the Great Smog led Londoners to burn much more coal than usual to keep themselves warm. While better-quality "hard" coals (such as anthracite) tended to be exported to pay off World War II debts, post-war domestic coal tended to be of a relatively low-grade, sulphurous variety called "nutty slack" (similar to lignite) which increased the amount of sulphur dioxide in the smoke. There were also numerous coal-fired electric power stations in the Greater London area, including Fulham, Battersea, Bankside, Greenwich, West Ham and Kingston upon Thames, all of which added to the pollution. According to the UK's Met Office, the following pollutants were emitted each day during the smoggy period: 1,000 tonnes of smoke particles, 140 tonnes of hydrochloric acid, 14 tonnes of fluorine compounds and 370 tonnes of sulphur dioxide which may have been converted to 800 tonnes of sulphuric acid. The relatively large size of the water droplets in the London fog allowed for the production of sulphates without the acidity of the liquid rising high enough to stop the reaction, and for the resultant dilute acid to become concentrated when the fog was burned away by the sun.

Research suggests that additional pollution-prevention systems fitted at Battersea worsened the air quality. Flue gas washing reduced the temperature of the flue gases so they did not rise, but instead slumped to ground level, causing a local nuisance.

Additionally, there was pollution and smoke from vehicle exhaust, particularly from steam locomotives and diesel-fuelled buses which had replaced the recently abandoned electric tram system. Other industrial and commercial sources also contributed to the air pollution.

Weather
On 4 December 1952, an anticyclone settled over a windless London, causing a temperature inversion with relatively cool, stagnant air trapped under a layer of warmer air. The resultant fog, mixed with smoke from home and industrial chimneys, particulates such as those from motor vehicle exhausts, and other pollutants such as sulphur dioxide, formed a persistent smog, which blanketed the capital the following day. The presence of tarry particles of soot gave the smog its greenish-yellow colour, hence the nickname "pea-souper". The absence of significant wind prevented its dispersal and allowed an unprecedented accumulation of pollutants.

Although the event is now widely described as the "London" smog, air pollution, in fact, extended far beyond the capital. According to E.T. Wilkins (of the Department of Scientific and Industrial Research, whose measurements would make clear the connection between smoke, sulphur dioxide, and rising deaths), fog, white mist, or grimy smog covered "many parts of the British Isles", while "In London and the Thames Valley, fog or smog covered upwards of 1000 square miles". However, it was in London that the smog's effects were the greatest.

Effect on London
There was no panic, as London was infamous for its fog. However, this one was denser and longer-lasting than any previous "pea-souper". Visibility was reduced to a few metres, with one visitor stating that it was "like you were blind", rendering driving difficult or at times impossible.

Public transport ceased, apart from the London Underground, and the ambulance service stopped, forcing individuals to transport themselves to hospitals. The smog was so dense that it even seeped indoors, resulting in the cancellation or abandonment of concerts and film screenings, as visibility decreased in large enclosed spaces, and stages and screens became harder to see from the seats. Outdoor sports events were also cancelled.

In the inner London suburbs and away from town centres, there was no disturbance by moving traffic to thin out dense fog in the back streets. As a result, visibility could be down to a metre or so in the daytime. Walking out of doors became a matter of shuffling to feel for potential obstacles such as kerbs. This was made even worse at night since each back street lamp was fitted with an incandescent light bulb, which gave no penetrating light onto the pavement for pedestrians to see their feet or even a lamp post. Fog-penetrating fluorescent lamps did not become widely available until later in the 1950s. "Smog masks" were worn by those who were able to purchase them from chemists.

Health effects

In the weeks that ensued, statistics compiled by medical services found that the fog had killed 4,000 people. Many of the victims were very young or elderly, or had pre-existing respiratory or cardiovascular problems. In February 1953, Marcus Lipton suggested in the House of Commons that the fog had caused 6,000 deaths and that 25,000 more people had claimed sickness benefits in London during that period.

Mortality remained elevated for months after the fog. A preliminary report, never finalised, blamed those deaths on an influenza epidemic. Emerging evidence revealed that only a fraction of the deaths could be from influenza. E. T. Wilkins, who, as Officer in Charge of Atmospheric Pollution at the government's Department of Scientific and Industrial Research was effectively the UK's top pollution expert at the time, plotted a chart of elevated death rates for the period from December 1952 to March 1953 and found that there had been an additional 8,000 deaths beyond those initially counted, making 12,000 in total. Most of the deaths were caused by respiratory tract infections, from hypoxia and as a result of mechanical obstruction of the air passages by pus arising from lung infections caused by the smog. The lung infections were mainly bronchopneumonia or acute purulent bronchitis superimposed upon chronic bronchitis.

Research published in 2004 suggests that the number of fatalities was about 12,000, around three to four times greater than the official government total at the time, but very close to the figure Wilkins had originally estimated. In the long term, individuals who were foetuses or infants at the time of the smog ended up having lower intelligence and worse respiratory health than their peers.

Environmental impact
Environmental legislation since 1952, such as the City of London (Various Powers) Act 1954 and the Clean Air Acts of 1956 and 1968, led to a reduction in air pollution. Financial incentives were offered to householders to replace open coal fires with alternatives (such as gas fires), or to burn coke instead, which produces minimal smoke. Central heating (using gas, electricity, oil, or permitted solid fuel) was rare in most dwellings at that time, not finding favour until the late 1960s onwards. Despite improvements, insufficient progress had been made to prevent one further smog event approximately ten years later, in early December 1962.

In media
The Great Smog is the central focus of season 1, episode 4 of Netflix's The Crown. The portrayal of the event was regarded as reasonably accurate by critics, although the political importance and the chaos in the hospitals were thought to have been greatly exaggerated.

An episode of The Goon Show entitled 'Forog', broadcast on the BBC Home Service 21 December 1954 was a thinly veiled satire on the killer fog crisis. The script by Eric Sykes and Spike Milligan concerned the statues of London's monuments, who could get up and move about the city undisturbed only at times when it was enveloped in a characteristic smog. Government-sponsored scientific research sought to dispense with the choking fog, to the annoyance of the statues.

The Great Smog is the setting of the Doctor Who audio play The Creeping Death and the novel Amorality Tale.

The Boris Starling novel Visibility is set in the 1952 smog event.

The D. E. Stevenson novel The Tall Stranger (1957) opens with a dense "fog" that penetrates indoors and endangers hospital patients, in an apparent reference to the 1952 smog event.

Kate Winkler Dawson's book Death in the Air (2017) interweaves the story of the Great Smog of London with that of serial killer John Christie.

title: Great Smog of London


text:
Talk:English phrasal verbs

Phrasal verbs in other languages
There's a number of verbs that are originally made of a verb and a particle joined together, such as understand, undertake, forgive and so on. Supposedly, in English they were predecessors of phrasal verbs - there still are separable verbs in German, which work like something in between ('aufstehen' becomes 'stehen *** auf'). And the fact is, verbs made of a prefix particle and a verb are really often in Indo-European languages - I personally also know they are in Ancient Greek, Latin (and, consequently, French / Spanish / Italian / etc) and Russian.

I'm not a linguist, so it's just a piece of idea for someone who actually knows if that's a piece of information that worths adding to the article. — Preceding unsigned comment added by 14.200.83.169 (talk) 15:16, 4 March 2022 (UTC)

 * Your description of word compounding differs from the phrasing comprehended by phrasal verbs as construed in English. Kent Dominic·(talk) 13:12, 6 May 2022 (UTC)
 * As the article already says, English particle verbs and German separable verbs are independent but parallel developments of old verb prefixes. That much is true. However, the point of talking about "phrasal verbs" is to explain to language students why there are verb phrases containing extra words. There is really no merit in including verbs where the prefix is still a prefix. The use of prefixes is a basic element of all Indo-European languages, and in all the languages you mention, elements like "under" can be prefixes, prepositions, adverbs or particles, since they migrate easily from one part of speech to another in the course of a language's history. --Doric Loon (talk) 14:06, 6 May 2022 (UTC)
 * Particle verbs do exist in every Germanic language and the so-called separable verbs of the Continental West Germanic languages (primarily known by the major written languages (High) German and Dutch) are just a form of them and a result of the (underlying) verb-object word order of these languages. 2A0A:A541:10F4:0:2942:173E:5F5B:CC8B (talk) 21:51, 5 October 2023 (UTC)

Apology re recent change to lede definition
My edit from moments ago represents a lede that is hugely at odds with the definition in my own lexicon, which limits the concept of a phrasal verb to collocations excluding the following In short, I consider phrasal verbs as limited solely to verb + particle as collocated without an intervening noun/pronoun. In my book, the four items ID'd above are verb phrases although #3 from above is a verb phrase that entails the put up phrasal verb followed by with (someone or something) as a predicative object. My apology: My edit to the lede leaves intact the adverb and preposition elements traditionally associated with phrasal verbs and as had been presented in the article. Please don't shoot the messenger for emending the lede's semantics without emending its substance. I'm just abiding by the WP:OR guidelines. Cheers. --Kent Dominic·(talk) 14:02, 6 May 2022 (UTC)
 * 1) verb + adverb e.g., talk fast
 * 2) verb + preposition e.g., it comes in three colors
 * 3) verb + particle + preposition e.g., put up with
 * 4) verb + noun/pronoun + particle e.g., piss them off; took the signs down

 * I agree that it is far better to restrict the term "phrasal verb" to the particle construction. As a teacher, that's what I do too. Unfortunately, the grammar books are inconsistent, so we have to do justice to a complicated situation. But I think we are at least beginning to become more precise about what types are meant. --Doric Loon (talk) 14:27, 6 May 2022 (UTC)
 * It boils down to swimming against a tide of traditional grammars that mix up terminology in naive ways. My challenge both here and in my own work: how to simply and effectively describe stuff without sacrificing precision. Soldier on! Kent Dominic·(talk) 15:45, 6 May 2022 (UTC)

Apology re lede, Part II
The current lede continues to be at odds with how I'd characterize phrasal verbs if left to my druthers, but it now more closely reflects current theory and practice. Feel free to add cites and/or editing tweaks, as needed. --Kent Dominic·(talk) 21:58, 7 May 2022 (UTC)

Shifting
The section on Shifting characterizes its occurrence when objects "are very light." I know of no source for light objects. Indeed, the whole section describes tmesis rather than shifting since there's nothing "noncanonical" about a transitive object that immediately follows a transitive verb. Fair notice: I'm eventually gonna take a scalpel to the section unless someone beats me to it. --Kent Dominic·(talk) 17:57, 26 May 2022 (UTC)

 * what prasal verb mean 152.36.220.115 (talk) 01:42, 17 April 2023 (UTC)

Requested move 4 December 2023

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: Not moved. There isn't consensus to move to the singular "English phrasal verb" either, at least in this discussion. (non-admin closure) BegbertBiggs (talk) 22:57, 13 December 2023 (UTC)

English phrasal verbs → Phrasal verb – WP:SINGULAR and WP:OVERPRECISION. The article was boldly moved in 2021 for disambiguation, but disambiguation from what? There is no hatnote indicating other Wikipedia articles that discuss phrasal verbs in non-English languages. It also does not seem clear why the topic was made plural in that move. — BarrelProof (talk) 21:34, 4 December 2023 (UTC)

 * Oppose at an article titled "phrasal verb(s)", I'm expecting a linguistic overview of the general concept as it exists in multiple languages. Given that phrasal verbs occur in other languages the title should clarify that the scope is restricted to English. (t · c)  buidhe  23:06, 4 December 2023 (UTC)

 * Oppose per buidhe ; WP:PRECISE the proposed title lacks precision, as it is not a general article on the concept of phrasal verbs -- 65.92.247.90 (talk) 07:51, 6 December 2023 (UTC)
 * Oppose; the proposed title would be the right place for a new article on the broader topic if you want to write one. This article would not benefit from being broadened to include full details of world languages. Sometimes we need articles that aim for depth rather than breadth, and that is what this one should do. Doric Loon (talk) 08:05, 6 December 2023 (UTC)
 * Actually, when I think about it, I'm not sure there is a broader topic. Although this article talks about similar constructions in other languages, I am not aware that the term "phrasal verb" is actually used in the grammar of those languages. Analyzed in this particular way, I suspect that this is a purely English phenomenon. Doric Loon (talk) 17:21, 7 December 2023 (UTC)
 * Any opinions on the WP:SINGULAR aspect? — BarrelProof (talk) 15:55, 6 December 2023 (UTC)
 * If you were to propose a move to English phrasal verb I could go along with it on analogy to Germanic strong verb etc. But keep "English" in the title please. Doric Loon (talk) 17:18, 7 December 2023 (UTC)
 * It is not unusual for the outcome of an RM to be a renaming that is different from what was proposed. Removing "English" doesn't seem popular in this conversation so far, but I don't notice an objection to making the title singular. — BarrelProof (talk) 18:11, 7 December 2023 (UTC)
 * Oppose I think the title is perfect. Denisarona (talk) 16:21, 6 December 2023 (UTC)

 * Support: As it now stands, the article itself suggests that 'The category "phrasal verb" is mainly used in English as a second language teaching.' (Italics added for emphasis.) Which raises the question, for me anyway, how is the phrasal verb concept applied in other languages? Any such evidence argues in favor of the article's title change. Kent Dominic·(talk) 15:37, 10 December 2023 (UTC)
 * Well, surely the point is, we have no evidence of the category being used in any other languages. We have evidence of parallel phenomena in other languages being made points of comparison in order to understand the English concept better, but not of those languages using this category themselves. Doric Loon (talk) 16:31, 10 December 2023 (UTC)
 * Then, remedies in the alternative: (A) Support the move/renaming, or (B) remove "mainly" from the sentence quoted above from the article's Types section. Kent Dominic·(talk) 18:17, 10 December 2023 (UTC)
 * Ah, I see. "Mainly" was meant to mean that the term is sometimes also used in other areas of English studies besides language teaching. I think I wrote that sentence, so apologies if it was not clear, but I don't think it ever intended to say "mainly English but also other languages." Feel free to reword. Doric Loon (talk) 10:19, 11 December 2023 (UTC)
 * Doric, I reworded it accordingly. In so doing, I deep-sixed the reference to "prepositional verb", which (I know, I know) is part of the ESL erudition but not, IMHO, a cromulent description re the pertinent syntax. I hope the rewording looks pretty, but the editor who's part of the "comprised of" police is likely to have something to say about that. Cheers. Kent Dominic·(talk) 14:32, 11 December 2023 (UTC)
 * Not clear if it's mainly used in ESL. Book search overwhelmingly gives that impression, but academic search does not. What is clear, is that the market for ESL books has increased twentyfold since 1960, probably a result of commercial interest in serving the vast and growing number of ESL students reflecting the hegemony of English as the de facto global language established over this period. Mathglot (talk) 21:48, 12 December 2023 (UTC)

Perhaps a bad idea for good intentions
Is there anything someone can cite for the proposition that the so-called full infinitive (aka a to-infinitive) constitutes a phrasal verb as an infinitive verb collocated with "to" as a prepositive adverbial particle? Any editor who's hell-bent on finding such a cite and accordingly adding a pertinent section to this article would be my hero. Here's to a discussion of how a full infinitive may be deemed a phrasal verb nominalized as a subject (e.g. "To be a medical doctor requires a proper license") or as part of a predicate object (e.g. "I want to be free"). Kent Dominic·(talk) 15:01, 11 December 2023 (UTC)

 * That would be a new one on me, and I don't really buy it. You're right that the full infinitive can be a subject in the example sentence you give, but so can the gerund: "Being a medical doctor requires a proper licence." There are bound to be a range of theories about what is going on there. But I can't see how any of them could involve this being a phrasal verb.
 * If I understand correctly, you are saying that "I want to go" is a (phrasal?) verb "want" followed by a preposition "to" and a noun "go". That indeed is how it would have been understood in Old English (complete with dative noun inflections on the infinitive), but I don't know of any analysis that sees the infinitive marker "to" as still being a preposition today. And I don't see how it is going to help anyone to say that "go" is a noun.
 * Besides, we say in the article that a phrasal verb in the strict sense is a particle verb (type 1), and that verbs with prepositions (type 2) are only phrasal verbs (if at all) when the collocation is semantically unintuitive. But what you are suggesting would be type 2 with no semantic difficulty. Doric Loon (talk) 21:27, 11 December 2023 (UTC)
 * I totally empathize with all of that except to quibble how "I want to go" includes to as a particle, not a preposition. The "to go" full infinitive item thus is a particle + verb rather than the verb + particle construct primarily addressed in the article. I don't include a to-infinitive under the rubric of a phrasal verb in my own work, but I often get the nagging feeling that someone in a far corner of the linguistic world is going to criticize me for not doing so. I do think such a person would have a valid analysis that "I want to go" comprises want as a transitive verb and to go as a predicate object in the form of a nominalized verb phrase (according to you, thankfully, and everyone else, I hope) but NOT a phrasal verb and NOT a noun. Cheers for the input. Kent Dominic·(talk) 13:47, 13 December 2023 (UTC)

F. Schmidt
@Mathglot, in your recent edit summary you mentioned that before the term was used in its modern sense, it was used by F. Schmidt (1900) in a different sense. Since I don't have that book here, could you possibly tell us what Schmidt meant by it? I don't know if that belongs in the article, but at least here on talk it would be good to air it to give us more context. Thanks. Doric Loon (talk) 10:27, 13 December 2023 (UTC)
 * I may have been too conservative in my edit summary; upon second glance, it's not entirely clear to me that it is being used in a different sense. It may, in fact, be the modern sense, or a precursor or more likely subset of the modern sense. It's a bit difficult to determine from context, and it's hapax, which makes it even harder.
 * "Note. The phrasal verb speke of often occurs in the passive voice without the preposition, e.g., 'these (sc. textis) whiche schulen be spoken' 477; 'the now spoken bokis' 47; 'in the manner of leefulnes spoken before' 161."

- Frederik Schmidt

 * (This is page 48, but when I found it before, I distinctly recall it was p. 51, and I can't account for the difference. Perhaps a different edition or reprint?) Upon further examination, this does appear to be the modern sense, at least in the sense of a non-idiomatic use of verb + particle (prep.) where the meaning is easily determinable from the phrase. This isn't obvious from the limited context of the quotation on p. 48 and the somewhat opaque wording, but if you go back to p. 47, it becomes clearer what Schmidt is talking about in context, in his § 61. where he gives examples including spoken of, and attended to, as in, "the feith in oon God is so weel attended to". Schmidt discusses the separation of the preposition from the noun ("substantive") and some of the examples in Pecock's Middle English are hard to understand, but the examples of "brougte in and offrid up" seem clear. Schmidt may be attempting a description, if not quite a definition of 'phrasal verb' on the cusp of pp. 47–48:
 * "In the former group of verbs, what was originally a preposition is turned into an adverb and forms with the preceding verb a species of compound; in the latter, the combination of verb + adverb (or separable particle) is earlier, a fact, which may have contributed in measure to the formation given in the other group. This kind of assimilation is especially illustrated by examples where verbs of both groups are coordinated with each other, e.g., 'the freelnes of the persoon ougte bi rigt be fougt agens and be leid away 514, or where the same verb is combined twice with a particle, which sometimes has the function of a preposition, sometimes that of an adverb.""

 * This sure sounds like he's describing (some subset of) phrasal verbs to me, and then two sentences later, he uses the term phrasal verb on the same page, referring to one example of what he was just talking about.
 * If this stands up to scrutiny, we may have back-dated first use of the term a quarter century, which would be exciting. Obviously, we can't use any of this analysis in the article, as it would be WP:OR, so I'd look for confirmation, first. If it doesn't hold up, then that's that; but I think it would be worth a query to Linguist List, and if that leads to a response online, we could use that as the citation. Even more exciting (at least to me) than possibly backdating first use of the term, is that we may have found some of the first usages of phrasal verbs in English, in the writings of Pecock, or perhaps Wycliffe, at least according to Schmidt, who says:
 * "This separation of the substantive from its governing preposition (see Paul, Prinzipien, § 204) would seem to be an original characteristic of Pecock's style, since Mätzner (II, 67) and Kellner (Eng. Stud. XXII, 81) give but few instances before his time, mostly from Wycliffe."

 * Note that there is an earlier reference to phrasal insertion from Am J Philology (1881) "On the Position of 'Rhematic To", p. 458, again about Pecock, and again mentioning 'Wickliffe'. However, this use seems to be more about what I'd call a split infinitive. I hope this provides the additional context you requested, and is helpful.
 * If I had more time, I'd write to Linguist List and follow up all those citations from Schmidt, to see what more could be learned, and hopefully use the result as a kernel of a history section, which the article currently lacks. If you have the time and the inclination, I'd love to see what you find out. Cheers, Mathglot (talk) 20:10, 14 December 2023 (UTC)
 * @Mathglot Thank you so much for taking the time to write such a full response. I am certain you are right: Schmidt's is an earlier use of the term, though the way he writes it, it sounds like he is not really aware of it as "a term", so much as as a brief description. And yes, the Middle English examples he is citing are undoubtedly phrasal verbs in the modern sense.
 * It would certainly be possible to add Pecock examples to the article, citing Schmidt as a source - that is not OR as Schmidt is a respectable RS for that. And it would might even possible to list Schmidt as one who used the term, at least in a footnote, though for that we would be citing him himself as a primary source, and wouldn't have a secondary source, which means we couldn't put great weight on it. What we can't do without a secondary source is to say he was the first to use the term. Doric Loon (talk) 07:49, 15 December 2023 (UTC)
 * I agree, I thought it was descriptive use as well, not yet gelled as a term. Had it been a new term, he might have put it in double quotes, or said something about where he heard it (or not; don't know the fella!) Anyway, if you think it's ready for the article (not as coiner, I agree with you on that we still need a 2ary source) please go ahead and do so. Would still love to get further input from the Linguist List angle; have you ever contacted them? I did, and got an online response (but that was years ago) which is perfect, because then you can cite it; responders are usually working linguists at universities. Mathglot (talk) 08:27, 15 December 2023 (UTC)
 * I think it probably can be added, but I'd like to mull it over a little longer. I am not on Linguist List, but I agree I'd be very interested in what they have to say, if you do find time to mail them. Doric Loon (talk) 10:06, 15 December 2023 (UTC)

title: Talk:English phrasal verbs


text:
2001 in art

The year 2001 in art involves various significant events.

Events

 * 1 January – A black monolith measuring approximately 9 feet tall appears in Seattle, Washington's Magnuson Park, placed by an anonymous artist in reference to the movie 2001: A Space Odyssey.
 * 4 June – Unveiling of Rachel Whiteread's Untitled Monument on the Fourth plinth, Trafalgar Square, London.
 * 17 July – Inauguration of the Altamira cave replica created by Manuel Franquelo and Sven Nebel.
 * 11 September
 * An estimated $100 million worth of art is destroyed in the 11 September attacks on New York City. Public artwork accounts for around $10 million of this figure, which includes works by Alexander Calder, Joan Miró and Roy Lichtenstein.
 * Fritz Koenig's Great Spherical Caryatid ("The Sphere") is the only surviving artwork following the September 11 attacks. It is repurposed as a memorial.
 * Several works of photojournalism become iconic for their portrayal of the events surrounding the September 11 attacks, including The Falling Man and Raising the Flag at Ground Zero.
 * 27 September – Resale Rights Directive in the European Union provides a Droit de suite for artists.
 * 1 October – The Ghibli Museum opens in Mitaka, Tokyo.
 * 16 November – The Neue Galerie New York opens in Manhattan.

Undated

 * A new wing in the Genia Schreiber University Art Gallery of the University of Tel Aviv, Israel, is dedicated to the memory of Michel Kikoine.
 * The Leopold Museum opens in Vienna.
 * The Pupils is created by Michaël Borremans in Belgium.
 * They Could Still Serve is created by Ellen Gallagher in the United States.
 * Traditional Chinese Studies Institute is created by Chen Danqing in China.

Exhibitions

 * September 11 until November 11 - Caspar David Freidrich: Moonwatchers at the Metropolitan Museum of Art in New York City.
 * Max Beckmann retrospective at the Pompidou Centre, Paris

Awards

 * Archibald Prize – Nicholas Harding for John Bell as King Lear
 * Beck's Futures – Tim Stoner
 * Schock Prize in Visual Arts – Giuseppe Penone
 * Turner Prize – Martin Creed for Work No. 227: The lights going on and off (Tate)
 * Venice Biennial
 * Lion d'Or Golden Lion for Lifetime Achievement: Richard Serra (USA), Cy Twombly (USA)
 * Lion d'Or for Best Pavilion: Gregor Schneider (Germany)

Works

 * Michaël Borremans – The Pupils
 * Ingvar Cronhammar - Elia in Herning, Denmark
 * Jeremy Deller – Battle of Orgreave
 * Lucian Freud – Portrait of Queen Elizabeth II
 * Tracy Harris – Funnel
 * Michael Landy - Breakdown
 * Daniel Richter – Tarifa
 * Rigga - sculptures in Portland, Oregon jointly with artists
 * Ean Eldred - Echo Gate
 * James Harrison - Ghost Ship
 * Peter Nylen - Alluvial Wall
 * Tamsie Ringler - Living Room (sculpture, Gresham, Oregon)
 * Michael Stutz - Facing the Crowd
 * Zeng Fanzhi – The Last Supper

January to June

 * 14 January - Fred Hughes, American art executive (Founder of the Warhol Foundation) (b. 1943)
 * 30 January – O. Winston Link, American photographer. (b. 1914)
 * 12 February – Kristina Söderbaum, Swedish-German film actress, producer and photographer (b. 1912)
 * 17 February – Barry Burman, English painter and educator (b. 1943)
 * 18 February – Balthus, French modern artist (b. 1908)
 * 4 March
 * Jean René Bazaine, French painter, stained glass window designer and writer (b. 1904)
 * Fred Lasswell, American cartoonist (b. 1916)
 * 1 June – Hank Ketcham, American cartoonist (b. 1920)
 * 19 June – David Sylvester, English art critic and curator (b. 1924)
 * 27 June – Tove Jansson, Swedish-Finnish novelist, painter, illustrator and comic strip author (b. 1914)

July to December

 * 1 July – Hélène de Beauvoir, French painter (b. 1910)
 * 4 July – Anne Yeats, Irish painter and stage designer (b. 1919)
 * 11 July – Herman Brood, Dutch musician, painter and media personality (b. 1946)
 * 28 August – Juan Muñoz, Spanish sculptor (b. 1953)
 * 23 October
 * Josh Kirby, English commercial artist (b. 1928)
 * Daniel Wildenstein, French international art dealer and scholar (b. 1917)
 * 3 November – Sir Ernst Gombrich, Austrian-born art historian (b. 1909)
 * 19 November – Marcelle Ferron, Canadian painter and stained glass artist (b. 1924)
 * 25 November – Harry Devlin, American painter and illustrator (b. 1918)
 * December – Mercedes Matter, American painter (b. 1913)
 * 29 December – György Kepes, Hungarian-born painter, designer, educator and art theorist (b. 1906)

title: 2001 in art


text:
Chern–Simons form

In mathematics, the Chern–Simons forms are certain secondary characteristic classes. The theory is named for Shiing-Shen Chern and James Harris Simons, co-authors of a 1974 paper entitled "Characteristic Forms and Geometric Invariants," from which the theory arose.

Definition
Given a manifold and a Lie algebra valued 1-form $$\mathbf{A}$$ over it, we can define a family of p-forms:

In one dimension, the Chern–Simons 1-form is given by
 * $$\operatorname{Tr} [ \mathbf{A} ].$$

In three dimensions, the Chern–Simons 3-form is given by
 * $$\operatorname{Tr} \left[ \mathbf{F} \wedge \mathbf{A}-\frac{1}{3} \mathbf{A} \wedge \mathbf{A} \wedge \mathbf{A} \right] = \operatorname{Tr} \left[ d\mathbf{A} \wedge \mathbf{A} + \frac{2}{3} \mathbf{A} \wedge \mathbf{A} \wedge \mathbf{A}\right].$$

In five dimensions, the Chern–Simons 5-form is given by

\begin{align} & \operatorname{Tr} \left[ \mathbf{F}\wedge\mathbf{F} \wedge \mathbf{A}-\frac{1}{2} \mathbf{F} \wedge\mathbf{A}\wedge\mathbf{A}\wedge\mathbf{A} +\frac{1}{10} \mathbf{A} \wedge \mathbf{A} \wedge \mathbf{A} \wedge \mathbf{A} \wedge\mathbf{A} \right] \\[6pt] = {} & \operatorname{Tr} \left[ d\mathbf{A}\wedge d\mathbf{A} \wedge \mathbf{A} + \frac{3}{2} d\mathbf{A} \wedge \mathbf{A} \wedge \mathbf{A} \wedge \mathbf{A} +\frac{3}{5} \mathbf{A} \wedge \mathbf{A} \wedge \mathbf{A}\wedge\mathbf{A}\wedge\mathbf{A} \right] \end{align} $$

where the curvature F is defined as
 * $$\mathbf{F} = d\mathbf{A}+\mathbf{A}\wedge\mathbf{A}.$$

The general Chern–Simons form $$\omega_{2k-1}$$ is defined in such a way that
 * $$d\omega_{2k-1}= \operatorname{Tr}(F^k),$$

where the wedge product is used to define Fk. The right-hand side of this equation is proportional to the k-th Chern character of the connection $$\mathbf{A}$$.

In general, the Chern–Simons p-form is defined for any odd p.

Application to physics
In 1978, Albert Schwarz formulated Chern–Simons theory, early topological quantum field theory, using Chern-Simons forms.

In the gauge theory, the integral of Chern-Simons form is a global geometric invariant, and is typically gauge invariant modulo addition of an integer.

title: Chern–Simons form