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Fernando Arrabal

Fernando Arrabal Terán (born August 11, 1932) is a Spanish playwright, screenwriter, film director, novelist, and poet. He was born in Melilla and settled in France in 1955. Regarding his nationality, Arrabal describes himself as "desterrado", or "half-expatriate, half-exiled".

Arrabal has directed seven full-length feature films and has published over 100 plays; 14 novels; 800 poetry collections, chapbooks, and artists' books; several essays; and his notorious "Letter to General Franco" during the dictator's lifetime. His complete plays have been published, in multiple languages, in a two-volume edition totaling over two thousand pages. The New York Times' theatre critic Mel Gussow has called Arrabal the last survivor among the "three avatars of modernism".

In 1962, Arrabal co-founded the Panic Movement with Alejandro Jodorowsky and Roland Topor, inspired by the god Pan. He was elected Transcendent Satrap of the Collège de Pataphysique in 1990. Forty other Transcendent Satraps have been elected over the past half-century, including Marcel Duchamp, Eugène Ionesco, Man Ray, Boris Vian, Dario Fo, Umberto Eco, and Jean Baudrillard. Arrabal spent three years as a member of André Breton's surrealist group and was a friend of Andy Warhol and Tristan Tzara.

Writer and critic Javier Villan wrote of Arrabal:"Arrabal's theatre is a wild, brutal, cacophonous, and joyously provocative world. It is a dramatic carnival in which the carcass of our 'advanced' civilizations is barbecued over the spits of a permanent revolution. He is the artistic heir of Kafka's lucidity and Jarry's humor; in his violence, Arrabal is related to Sade and Artaud. Yet he is doubtless the only writer to have pushed derision as far as he did. Deeply political and merrily playful, both revolutionary and bohemian, his work is the syndrome of our century of barbed wire and Gulags, a manner of finding a reprieve."

Childhood (1932–1946)
Arrabal (Terán is his second family name) was born to Carmen Terán González and painter Fernando Arrabal Ruiz.

On July 17, 1936, when insurrections within the military were staged against the constitutional government of the Second Spanish Republic, launching the Spanish Civil War, Arrabal's father remained faithful to the Republic and was sentenced to death for mutiny. His sentence was later commuted to 30 years' imprisonment. He was transferred between prisons, from Santi Espiritu in Melilla to Monte Hacho in Ceuta, where he attempted suicide, as well as Ciudad Rodrigo and Burgos. On December 4, 1941, he was sent to the Burgos Hospital due to apparent mental disorder. Later research has found that he likely feigned mental order in order to be transferred to a lower security prison. On December 29, 1941, he escaped from the hospital in his pajamas, despite three feet of snow covering the countryside. Despite extensive research, he was never seen again.

About his father, Arrabal has written: "Without trying to compare what is incomparable, when I confront these twilight episodes (and quite often without any logical connection), I often think of that scapegoat, my father. The day on which the Uncivil War began, he was locked up by his 'compassionate companions' in the flag room of the Melilla military barracks. He was meant to think carefully, since he risked a death sentence for mutiny if he did not join them in their insurrection (alzamiento). After an hour, Lieutenant Fernando Arrabal summoned his ex-comrades – already! – to inform them that he had pondered long enough. Today, because of this precedent, must I serve as witness, example, or symbol, as he did, of the most fundamental occurrences? I, who am a mere exile. If I am taken away from my beloved numerics, everything around me leads to over-the-counter confusion and disorder. I have no wish to be a scapegoat like my father, I only ask to die while still living, whenever Pan so wishes."

In 1936, Arrabal's mother returned to Ciudad Rodrigo with her young son, Fernando, and found a job at Burgos, then-capitol of the Nationalists and headquarters of General Franco's government. Fernando was enrolled in a local Catholic school from 1937 until 1940, when the Civil War ended and he moved with his mother to Madrid.

Arrabal was awarded the national prize for gifted children in 1941. He continued his studies at Las Escuelas Pías de San Antón, a church school whose alumni have also included Victor Hugo and Jacinto Benavente y Martínez. Arrabal later studied at another distinguished Madrid school, Colegio Padres Escolapios De Getafe. He was an avid reader and was eager to experience life.

Youth and young adulthood (1936–1946)
In 1947, when his mother ordered him to attend preparatory classes for entrance to the Academia General Militar, Arrabal protested by playing hooky. She subsequently sent him to Tolosa (Gipuzkoa), where he studied business at the Escuela Teórico-Práctica de la Industria y el Comercio del Paper, in 1949. By 1950, he had begun writing several plays, which remain unpublished.

In 1951, Arrabal began working in the paper industry at La Papelera Española. He moved to Valencia and passed his bachillerato, the first non-compulsory educational option in Spain for admission to university. He later moved to Madrid and began legal studies. During these years, he frequented the cultural institution Ateneo de Madrid and heard poets from the Postismo school. He was also finishing his early play Picnic, then titled The Soldiers, and writing El triciclo, at first titled Men with a Tricycle.

In 1954, Arrabal hitchhiked to Paris to attend a performance of Bertolt Brecht's Mother Courage and Her Children given by the touring Berliner Ensemble. Later that year, in Madrid, he met Luce Moreau, who became his wife. In 1955, he was awarded a three-month scholarship to study in Paris, during which time he lived at the Colegio de España at the Cité Universitaire. While in Paris he suffered a serious relapse of tuberculosis. He considered this disease to be a "lucky mishap" that allowed him to move permanently to his "veritable homeland, that of Kundera and Vives, Saint Ignatius of Loyola and Picasso: exile." In 1976 he appeared in Rosa von Praunheim's New York film Underground and Friends.

Politics
Arrabal had been known for being anti-Francoist and anti-monarchist and interested in anarchist trends in cultural production. Arrabal had a complicated relationship with Communism. He had ties with the Communist Party of Spain during his exile, but a rupture seems to have occurred in 1977 due to a conflict with his play The Architect and the Emperor of Assyria being performed in Barcelona with artists reputed to have Communist Party ties.

Awards and recognition
Arrabal was among the more controversial writers of his time, and his work has been recognized internationally. Awards include the Grand Prize for Theatre of the Académie Française, the Premio Mariano de Cavia for journalism, the Nabokov Prize for novels, the Espasa Prize for essays, and the World Theater Prize.

In 2001, he was nominated for the Premio Cervantes by Nobel Prize in Literature winner Camilo José Cela and José Hierro. He was reportedly a finalist for the Nobel Prize in 2005 due to the solicitation of several institutions and individuals. On July 14, 2005, he was named to France's Légion d'honneur. In 2007, he was awarded a doctorate of letters Honoris Causa by the Aristotle University of Thessaloniki in Greece.

His other awards and recognition include:

 * 2019: Grand Cross of the Civil Order of Alfonso X, the Wise, March 1, 2019
 * 2010: Premier Prix International Théâtre du Millénaire
 * 2008:
 * Hijo adoptivo de Ciudad Rodrigo (Spain)
 * Ciudadano de honor, Erlanger (Germany)
 * Fronteira do Pensamento with Bob Wilson, Wim Wenders, Philip Glass, and Bernard Henri Levy (Porto Alegre, Brazil)
 * 2007:
 * Prix Spinoza (Festival Teranova)
 * Doctorate of letters Honoris Causa (Thessaloniki, Greece)
 * Max de Honor, Teatro (Spain)
 * Prix Pasolini, cinéma (París)
 * 2006:
 * Gran Prix d'Interprétation (Festival de Quend, film: Avida)
 * Citoyen d'honneur de Spa (Belgium)
 * Clés de la ville de Fontenay (France)
 * 2005:
 * French Legion of Honor, July 14, 2005
 * Checa Association of Film Directors Prize, René Char Gold Medal, Avignon Festival
 * 2004
 * First Panic Award, International Book Fair (Brussels)
 * Francisco de Vitoria Prize (Puerto Rico)
 * Wittgenstein Prize (University of Murcia, Spain)
 * 2003
 * National Dramatic Literature Award (Spain)
 * Gold Medal of San Fando (Buenos Aires)
 * 2002: Gold Medal of the City of Avignon
 * 2001: Premio Nacional de Teatro (Spain)
 * 2000: National Prize for Literature (Spain)
 * 1999: Alessandro Manzoni Poetry Prize (Italy)
 * 1998: Prize of the Society of Authors (France)
 * 1995: Officer of Arts and Letters (France)
 * 1993: Theatre Prize of the Académie française
 * 1990: elected to honorary title of Transcendent Satrape of the Collège de 'Pataphysique; group founded in 1948 in homage to French author Alfred Jarry, has named previous Transcendent Satrapes including: Camilo José Cela, René Clair, Jean Dubuffet, Marcel Duchamp, Max Ernst, M. C. Escher, Eugène Ionesco, Michel Leiris, Man Ray, The Marx Brothers, Joan Miró, Jacques Prévert, Raymond Queneau, and Boris Vian; after Arrabal received this title, other Transcendent Satrapes have been named, including: Roland Topor, Umberto Eco, and Dario Fo
 * 1986: Fine Arts Gold Medal of the Ministry of Culture (Spain)
 * 1983: Chevalier of Arts and Letters (France)
 * 1982: Nadal Prize for La torre herida por el rayo
 * 1976: Obie Award for Theater (New York)
 * 1965 Lugné-Poë Theatre Prize (France)
 * 1959: Ford Foundation Award with Italo Calvino, Hugo Claus, Charles Tomlinson, Günter Grass, and Robert Pinget (New York)

Feature-length films
Arrabal has written and directed seven feature-length films, and has been awarded the Premio Pier Paolo Pasolini for his contributions to cinema.

 * 1971: Viva la muerte; co-produced by Isabel-Films (Paris) and S.A.T.P.E.C. (Tunis); starring Nuria Espert, Ivan Henriques, and Anouk Ferjac
 * 1973: J'irai comme un cheval fou; produced by Société Générale de Production – Babylone Films; starring Emmanuelle Riva, Hachemi Marzouk, and George Shannon
 * 1975: L'arbre de Guernica; produced by C.V.C. Communication, Federico Mueller, and Harry N. Blum; starring Mariangela Melato and Ron Faber
 * 1982: The Emperor of Peru (also released as Odyssey of the Pacific and Treasure Train); produced by Babylone Films; starring Mickey Rooney and Monique Leclerc
 * 1983: Le cimetière des voitures; television film; co-produced by Antenne 2 and Babylone Films; starring Alain Bashung and Juliette Berto
 * 1992: Adieu, Babylone!; produced by Antenne 2 – Cinecim; starring Lélia Fischer and Spike Lee
 * 1998: Jorge Luis Borges: Una vida de poesía; produced by Alphaville – Spirali (Italy); starring Lélia Fischer and Alessandro Atti

In 2005, a 3-disc box set of Arrabal's films was released by Cult Epics with Viva la muerte, I Will Walk Like a Crazy Horse, and The Tree of Guernica.

Several of Arrabal's plays have been adapted for film, including Le grand cérémonial, directed by Pierre-Alain Jolivet; El triciclo, directed by Luis Argueta; El ladrón de sueños, directed by Arroyo; Pique-nique, directed by Louis Sénéchal; Guernica, directed by Peter Lilienthal; and Fando y Lis, directed by Alejandro Jodorowsky.

One critic wrote, "Viva la muerte is an absolute masterpiece, one of the most astonishing I have seen in my lifetime" (André Pieyre de Mandiargues). Another, for Rolling Stone, wrote, "Arrabal is ferociously original" (John Parrack). Amos Vogel wrote, in the Village Voice, "An audacious, paroxistic, and artistically successful work". Raymond Léopold Bruckberger wrote, for Le Monde, "I prefer Arrabal to Fellini or Ingmar Bergman... he is to cinema what Rimbaud is to poetry."

Short films

 * 1978: Sang et or; produced by Antenne 2; starring Edgar Rock and Joshua Watsky
 * 1990: Échecs et Mythe; produced by Antenne 2; starring Joël Lautier, Roland Topor, Julie Delpy, and Gabriel Matzneff
 * 1991: New York City!; produced by Antenne 2; starring Tom O'Horgan, Melvin Van Peebles, and Tom Bishop

Operas
Arrabal's opera Faustbal with music by Leonardo Balada premiered at the Teatro Real de Madrid on February 13, 2009, staged by the Comediants of Barcelona. Arrabal wrote of the opera, "Faustbal is a woman who, in the third millennium, is the reincarnation of Alfred Jarry's Doctor Faustroll, a new doctor Faust who asks God and Lucifer for words and prayers so that love and charity might be unified. Nothing can satisfy the hurricane of her scientific curiosity, nor calm the storms of her desires. A genius, very beautiful, and enriched by her transports and transfigurations, she vows a torrid love for her Amazon. She leaps between galaxies while the war to end all civilization rages, and moves through space at supersonic speed. Confronting her, Margarito, supreme leader of the armed forces, dons the armor of brutal, electronic repression. He is madly in love with Faustbal under the sky's cupola. He tries to possess her through the torrent of his tower, employing the services of Mephistopheles himself. Jesús López Cobos, music director of the Teatro Real de Madrid, will conduct the world premiere, which will be sung by sopranos Ana Ibarra and María Rodríguez. The mezzo-soprano Cecilia Diaz will sing the role of the Amazon, while tenors Gerhard Siegel and Eduardo Santamaría will be the two Margaritos, bass Stefano Palatchi will perform the role of God, and baritones Tomas Tomasson and Lauri Vasar will be Mephistopheles."

Four other operas with Arrabal's librettos have been staged, and the author describes them as "always having been as complex, yet suffering from as few complexes, as did Faustbal." They are:

 * Apokaliptica, music by Milko Kelemen.
 * L'opéra de la Bastille, music by Marcel Landowski
 * Picknick im Felde, music by Constantinos Stylianou
 * Guernica, music by Ostfiend Busing

In October 1985, Arrabal made his debut as an opera stage director at the Opéra Royal de Belgique, where he directed Manuel de Falla's La vida breve and Enrique Granados' Goyescas. "Of course," Arrabal commented, "under my direction the onstage chorus was nude, or to be more precise, panically covered with clay."

In 1994, Chamber Made produced the opera of Arrabal'sThe Two Executioners, with libretto by Douglas Horton and music by David Chesworth. The opera ran for two seasons in Melbourne, 1994 and 1996 at the Malthouse Theatre. Australia's The Independent Monthly wrote, "Easily the most impressive and memorable piece of music theatre in 1994."

Novels

 * Baal Babylone, 1959 (New York: Grove Press, 1960; Berlin: Luchterhand Literaturverlag, 1960; Milan: Lerici, 1960; Amsterdam: De Bezige Bij, 1972)
 * L'enterrement de la sardine (Julliard, 1961; The Burial of the Sardine, London: Calder and Boyars, 1966; El entierro de la sardina, Barcelona: Destino, 1984)
 * Fêtes et rites de la confusion (Madrid, Barcelona: Alfaguara, 1966; Riten und Feste der Konfusion, Stuttgart: Joseph Melzer, 1969)
 * La Tour prends garde (Paris: Grasset, 1983; La torre herida por el rayo, Barcelona: Destino, 1983; Destino libro, 1984; Círculo de Lectores, 1984; A Torre ferida pelo Raio, Lisboa: Inquirito, 1982; Hohe Türme trifft der Blitz, Colonia: Kiepenheuer & Witsch, 1986; The Tower Struck by Lightning, New York: Viking, 1988)
 * La Reverdie (Paris: Christian Bourgois, 1985)
 * La piedra iluminada (Barcelona: Destino, 1985; The Compass Stone, tr. Andrew Hurley, New York: Grove Press, 1987)
 * La vierge rouge (Paris: Acropole, 1986; La virgen roja, Barcelona: Seix Barral, 1987; A Virgen Vermelha, Lisboa: Dom Quixote, 1987; A Virgen Vermelha, Botafogo: Nova Frontera, 1988; Die rote Jungfrau, Göttingen: Steidl, 1990; The Red Virgin, New York, London: Penguin Books, 1993)
 * La fille de King-Kong (Paris: Acropole, 1988; La hija de King Kong, Barcelona: Seix Barral, 1988)
 * L' extravagante croisade d'un castrat amoureux (Paris: Ramsay, 1989; La extravagante cruzada de un castrado enamorado, Barcelona: Seix Barral, 1990)
 * La tueuse du jardin d'hiver (Paris: Écriture, 1994)
 * Le funambule de Dieu (Paris: Écriture, 1998)
 * Porté disparu (Paris: Plon, 2000)
 * Champagne pour tous (Paris: Stock, 2002)
 * Como un paraíso de locos (2008)

Artists' books
Arrabal has made over 700 artists' books in collaboration with Salvador Dalí, René Magritte, Roland Topor, Julius Baltazar, Antonio Saura, Olivier O. Olivier, Maxime Godard, Jean Cortot, Jorge Camacho, Ralph Gibson, Enrico Baj, Gustavo Charif, Milan Kundera, Michel Houellebecq and others. They include:

 * L'odeur de Sainteté (Paris: Yves Rivière, 1975; with Antonio Saura; 2 copies)
 * Cinq sonnets, cincq eaux-fortes (Paris: André Biren, 1980; with Balthazar; 80 copies)
 * Sous le flux libertin (Paris: Robert et Lydie Dutrou, 1991; with Jean Cortot)
 * Triptyque (Cuenca: Menú, 2004; with Catherine Millet and Michel Houellebecq; 36 copies)
 * Clitoris (2008 poem with 56 translations, including Czech by Milan Kundera)

Poetry

 * La pierre de la folie (Paris: Julliard, 1963)
 * Cent sonnets (Saragossa: El Ultimo Parnaso, 1965)
 * Humbles paradis (Paris: Christian Bourgois, 1985)
 * Liberté couleur de femme ou Adieu Babylone, Poèmes cinématographiques (Mortemart: Rougerie, 1993)
 * Arrabalesques – Lettres à Julius Baltazar (Mortemart: Rougerie)
 * Diez poemas pánicos y un cuento (Córdoba: Caja Sur y Rute, 1997)

In 2015, some of Arrabal's poems were adapted with music by the band Seagoat Bones on their etude album Phonèmes.

Plays
Arrabal has published over 100 plays in 19 volumes. His plays include, with translations noted:

 * 1952
 * Le toit (unpublished)
 * Le char de foin (unpublished)
 * La blessure incurable (unpublished)
 * 1958
 * Oraison (Paris: Julliard) (Plays, Vol. 1: Orison, etc. translated by Barbara Wright, London: Calder and Boyars, 1962; Orazione, etc., Milan: Lerici, 1962)
 * Les deux bourreaux (Paris: Julliard) (The two executioners translated by Richard Howard, New York: Grove Press, 1960; Plays, Vol. 1: The Two Executioners, etc., translated by Barbara Wright, London: Calder and Boyars, 1962; I due Carnefici, etc., Milan: Lerici, 1962)
 * Fando et Lis (Paris: Julliard) (Plays, Vol. 1: Fando and Lis, etc. translated by Barbara Wright, London: Calder and Boyars, 1962)
 * Le cimetière des voitures (Paris: Julliard) (The Automobile Graveyard translated by Richard Howard, New York: Grove Press, 1960; Plays, Vol. 1: The Car Cemetery, etc. translated by Barbara Wright, London: Calder and Boyars, 1962; Automobil Kirkegaarden, Copenhagen: Arena, 1964)
 * 1961
 * Guernica (Paris: Julliard) (Plays, Vol. 2: Guernica, etc. translated by Barbara Wright, London, Calder and Boyars: 1967)
 * Le labyrinthe (Paris: Julliard) (Plays, Vol. 2: The Labyrinth, etc. translated by Barbara Wright, London, Calder and Boyars: 1967)
 * Le tricycle (Paris: Julliard) (Plays, Vol. 2: The Tricycle, etc. translated by Barbara Wright, London: Calder and Boyars, 1967; The Tricycle translated by David Herzberger, Modern International Drama 9.2, 1976, p. 65-91)
 * Pique-nique en campagne (Paris: Julliard). (Picnic on the Battlefield translated by James Hewitt, Evergreen Review 4.15, 1960, p. 76-90; Pic-nic, etc., Milan: Lerici, 1962; Plays, Vol. 2: Picnic on the Battlefield, etc., translated by Barbara Wright, London: Calder and Boyars, 1967)
 * La bicyclette du condamné (Paris: Julliard) (Plays, Vol. 2: The Condemned Man's Bicycle, etc. translated by Barbara Wright, London: Calder and Boyars, 1967)
 * 1965
 * Le grand cérémonial (Paris: Christian Bourgois) (Plays, Vol. 3: The Grand Ceremonial, etc. translated by Jean Benedetti; London: Calder and Boyars, 1970)
 * Cérémonie pour un noir assassiné (Paris: Christian Bourgois)
 * Cérémonie pour une chèvre et un nuage (Daily Bul)
 * 1966
 * Le couronnement (Paris: Christian Bourgois)
 * Concert dans un oeuf (Paris: Christian Bourgois)
 * 1967
 * L'architecte et l'empereur d'Assyrie (Paris: Christian Bourgois) (De Architekt en de Keiser van Assyrië, Amsterdam: Uitgeverij de Bezige Bij, 1969; Plays, Vol. 3: The Architect and the Emperor of Assyria translated by Jean Benedetti, London: Calder and Boyars, 1970; The Architect and the Emperor of Assyria translated by Everard d'Harnoncourt and Adele Shank, New York: Grove Press, 1969; Der Architekt und der Kaiser von Assyrien, Berlin: Kiepenheuer & Witsch, 1971; O Arquitecto e o Imperador da Assiria, São Paulo: Desta, 1976)
 * Les amours impossibles (Paris: Christian Bourgois) (Impossible Lovers, etc. translated by Bettina Knapp, The Drama Review 13, 1968, p. 71-86)
 * Les quatre cubes (Paris: Christian Bourgois)
 * La communion solennelle (Paris: Christian Bourgois) (First Communion translated by Michel Benedikt in Modern Spanish Theatre, New York: E. P. Dutton, 1968, p. 309–317; Solemn Communion, etc. translated by Bettina Knapp, The Drama Review 13, 1968, p. 71-86; Plays, Vol. 3: The Solemn Communion, etc. translated by John Calder, London: Calder and Boyars, 1970)
 * Streap-tease de la jalousie (Paris: Christian Bourgois) (Striptease of Jealousy, etc. translated by Bettina Knapp, The Drama Review 13, 1968, p. 71-86)
 * La jeunesse illustrée (Paris: Christian Bourgois)
 * Dieu est-il devenu fou? (Paris: Christian Bourgois)
 * 1968
 * Le jardin des délices (Paris: Christian Bourgois) (Garden of Delights translated by Helen Gary Bishop and Tom Bishop, New York: Grove Press, 1974)
 * Bestialité érotique (Paris: Christian Bourgois)
 * Une tortue nommée Dostoïevski (Paris: Christian Bourgois)
 * Théâtre choisi (4 volumes en japonais) (Tokyo: Shichosha)
 * 1969
 * ...Et ils passèrent des menottes aux fleurs (Paris: Christian Bourgois) (And They Put Handcuffs on the Flowers translated by Charles Marowitz, New York: Grove Press, 1973)
 * L'aurore rouge et noire (Groupuscule de mon coeur; Tous les parfums d'Arabie; Sous les pavés la plage; Les fillettes) (Paris: Christian Bourgois)
 * Le lai de Barrabas (Le couronnement) (Paris: Christian Bourgois)
 * 1970
 * Happening at the Théâtre Plaisance in Paris in February (Grand-Guignol)
 * 1972
 * Ars Amandi (opéra "Panique") (Paris: Christian Bourgois)
 * Dieu tenté par les mathématiques (opéra "Panique") (Paris: Christian Bourgois)
 * Le ciel et la merde (Paris: Christian Bourgois)
 * La grande revue du XXe siècle (Paris: Christian Bourgois)
 * 1975
 * Jeunes barbares d'aujourd'hui (Paris: Christian Bourgois)
 * 1976
 * La guerre de mille ans (Bella Ciao) (Paris: Christian Bourgois)
 * Sur le fil ou la ballade du train fantôme (Paris: Christian Bourgois)
 * 1978
 * La tour de Babel (Oyez Patria mi affliccion) (Paris: Christian Bourgois)
 * La marche royale (Paris: Christian Bourgois)
 * Une orange sur le mont de Vénus (Paris: Christian Bourgois)
 * La gloire en images (Paris: Christian Bourgois)
 * Vole-moi un petit milliard (Théâtre Bouffe) (Paris: Christian Bourgois)
 * Le pastaga des loufs ou Ouverture Orang-outan (Théâtre Bouffe) (Paris: Christian Bourgois)
 * Punk et punk et colégram (Théâtre Bouffe) (Paris: Christian Bourgois)
 * 1979
 * Inquisición (Granada: Don Quijote)
 * 1980
 * Mon doux royaume saccagé (Paris: Christian Bourgois)
 * Le roi de Sodome (Paris: Christian Bourgois)
 * Le ciel et la merde II (Paris: Christian Bourgois)
 * 1982
 * L'extravagante réussite de Jésus-Christ, Karl Marx et William Shakespeare (Paris: Christian Bourgois)
 * Lève-toi et rêve (Paris: Christian Bourgois)
 * 1983
 * Le cheval-jument ou hommage à John Kennedy T.
 * 1984
 * Les délices de la chair (Paris: Christian Bourgois)
 * La ville dont le prince était une princesse (Paris: Christian Bourgois)
 * 1985
 * Bréviaire d'amour d'un haltérophile (Paris: Christian Bourgois)
 * Apokalyptica (Paris: Christian Bourgois)
 * La charge des centaures (Paris: Christian Bourgois)
 * 1988
 * Les "cucarachas" de Yale (Paris: Christian Bourgois)
 * Une pucelle pour un gorille (Paris: Christian Bourgois)
 * La madonne rouge (Paris: Christian Bourgois)
 * La traversée de l'Empire (Paris: Christian Bourgois)
 * 1989
 * L'extravagante croisade d'un révolutionnaire obese (Luxembourg: Phi)
 * 1990
 * La nuit est aussi un soleil (Actes Sud)
 * Roues d'infortune (Actes Sud)
 * L'opéra de la Bastille (opéra écrit pour le bicentenaire de la Révolution française)
 * 1992
 * Oeuvres Tome I (théâtre, poésie, roman) (Milan: Spirali – Vel)
 * 1994
 * Lully (Actes Sud)
 * Entends la nuit douce qui marche (Actes Sud)
 * Le fou rire des liliputiens (Actes Sud)
 * 1996
 * Comme un lis entre les épines (Actes Sud)
 * 1997
 * Théâtre complet (7 volumes en langue coréenne) (Séoul: Coréenne)
 * 1999
 * Lettre d'amour (Actes Sud)
 * Comme un supplice chinois (Actes Sud)
 * Théâtre complet (2 volumes en langue espagnole) (Madrid: Espasa)

Arrabal's plays were frequently produced at La MaMa Experimental Theatre Club in the East Village of Manhattan, New York City throughout the 1970s. Productions at La MaMa included:

 * The Two Executioners (1962) directed by Andy Milligan; Arrabal performed alongside Martine Barrat
 * Fando and Lis (1971) directed by Franz Marijnen
 * Dos Obras de Arrabal (1972) directed by Delfor Peralta
 * The Architect and the Emperor of Assyria (1976) directed by Tom O'Horgan
 * The Architect and the Emperor of Assyria (1977) directed by Tom O'Horgan
 * Dance/Theater of Richard S. Bach (1984) choreographed by Richard S. Bach

A traveling company from La MaMa also took The Architect and the Emperor of Assyria on tour to Philadelphia, Amsterdam, Venezuela, and Taormina in 1977–1979.

For a more extensive list of productions of Arrabal's plays, see his official website.

Paintings

 * Arrabal has described himself as a "frustrated painter". He has produced approximately 50 canvases and 100 drawings and collages, which have been exhibited in museums such as the Paris Art Center, Musée de Bayeux, and the Villa San Carlo Borromeo Art Museum in Milan.
 * His approach to painting involves close collaboration with artists who produce large-format oil paintings based on the detailed sketches he provides.
 * In 1962, his first painting was chosen for reproduction in the art publication La Brèche: Action Surréaliste Revue by its founding editor, André Breton.
 * Arrabal has collaborated with sculptor and video artist Christèle Jacob, with whom he has created a dozen videos and photomontage series, including Les artilleurs des échecs et de la littérature (The artillery corps of chess and literature), inspired by a 1909 artwork by Henri Rousseau.

Essays and non-fiction

 * Carta al General Franco (bilingual Spanish-French edition, Paris: Bourgois, 1972, col. 10–18; Paris: Anonyme Anarchiste Pop, 1971; Buenos Aires: Granica, 1973; Noce: Babilonia, 1976; Barcelona: Actuales, 1978).
 * Le Panique (Paris: Union Générale d'Edition, 1973).
 * Sur Fischer: Initiation aux échecs (Monaco: du Rocher, 1974; Fischer, le roi maudit [revised edition], Luxembourg: Phi, 1988).
 * Carta a los militantes comunistas españoles (Sueño y mentira del eurocomunismo) (bilingual Spanish-French edition, Paris: Bourgois, 1978; Barcelona: Actuales, 1978; Acción directa, 1980).
 * Les échecs féeriques et libertaires (articles from L'Express) (Monaco: du Rocher, 1980).
 * Carta a los comunistas españoles y otras cartas (Letters to Franco, to the King, etc.) (Murcia: Godoy, 1981).
 * Carta a Fidel Castro (Madrid: Playor, 1983; Mexico: Diana, 1984; Europa, América, Portugal, 1984).
 * Echecs et mythe (Paris: Payot, 1984; Mitos em Xeque, Río de Janeiro: Globo, 1988).
 * Introducción a Feliciano de Silva (Cátedra, col. Letras Hispánicas, 1986).
 * El Greco (Steidl, Kiepenheuer & Witsch, 1991; El Greco, Barcelona: Destino, 1991; El Greco, London: Calder and Boyars; New York: Grove Press – Viking, 1991; El Greco, Milan: Spirali, 1991; El Greco: Le frénétique du spasme, Paris: Flohic, 1991).
 * Goya / Dalí (Milan: Spirali – Vel; Rome: Studio di Val Cervo, 1992).
 * Fêtes et défaites sur l'échiquier (Paris: L'Archipel, 1992).
 * Cartas a Baltazar (versión de F. Torres Monreal, 1993).
 * Genios y figuras (preface by A. Berenguer, Espasa Calpe, 1993).
 * Las manazas del Samaritano. Conversaciones con Ionesco (La Vuelta, nº 210, mayo, 1994).
 * La dudosa luz del día (translated into Spanish from the original French with notes by F. Torres Monreal, Espasa Calpe, 1994).
 * Carta al Rey de España (Madrid: Espasa Calpe, 1995).
 * Un esclave nommé Cervantès (Paris: Plon, 1996; Un esclavo llamado Cervantes, Madrid Espasa Calpe, 1996).
 * Diccionario pánico (Bruxelles: Escritos, 1998).
 * Lettre à Staline (Paris: Flammarion, 2004).
 * Houellebecq! (Paris: Le cherche midi, 2005).
 * El Pánico, Manifiesto para el tercer milenio, 2007.
 * Diccionario pánico, 2008.
 * Universos arrabalescos, 2009.
 * Defensa de Kundera, 2009.

Interest in chess
Arrabal has a strong interest in chess and has attended many chess tournaments. He is close to American chess Grandmaster Gata Kamsky and advocated for Kamsky on his chess blog during Kamsky's negotiations with FIDE over a World Chess Championship match.

For over thirty years, Arrabal has written a column on chess for the French weekly news magazine L'Express. His columns have included, among many others:

 * Echecs et mythes
 * Fêtes et défaites sur l'échiquier
 * Les échecs féériques et libertaires
 * Bobby Fischer: el rey maldito

title: Fernando Arrabal


text:
Talk:Bockscar

Comments
If the actual name is "Bockscar", shouldn't that be the name of the article? - Molinari 19:05, 11 Aug 2003 (UTC)

Google thinks so: That, combined with the fact that the US Air Force Museum Archives calls it "Bockscar" is good enough for me: http://www.wpafb.af.mil/museum/research/bombers/b3-35.htm -- Bill 19:12, 11 Aug 2003 (UTC)
 * Bock's Car (795)
 * Bocks Car (259)
 * Bockscar (819)
 * New link: http://www.nationalmuseum.af.mil/factsheets/factsheet.asp?id=2546 USAF Museum - BOCKSCAR Story. LanceBarber 18:52, 2 August 2007 (UTC)

"BOCK'S CAR"?
As painted on the plane, the name is "BOCKS CAR"; there's a small but clear space between the S and C. In my opinion, since "Bockscar" and "Bocks Car" don't parse, and "[Frederick] Bock's Car" does--and probably was a pun on Boxcar--we should call it that. My guess is that the apostrophe went the way of Neil Armstrong's "a" in "That's one small step for [a] man,..." —wwoods 03:02, 12 Dec 2004 (UTC)

In his book Mission : Hiroshima (originally published as The Tibbets Story) (Stein & Day, 1979, ISBN 0-8128-8169-9) Colonel Paul W. Tibbets refers to the aircraft as "Bock's Car" throughout. Is this not definitive? Dawkeye 23:27, 29 May 2006 (UTC)

 * I would say that the spelling used by the National Museum of the United States Air Force, where they have professional curators and try to be as accurate as possible, would be the best source. They use "Bockscar" .  --rogerd 17:54, 24 June 2006 (UTC)

 * That it was a pun on "boxcar" (one word) is indisputable--the painted cartoon is of a boxcar. The "perceived" gap between the S and the C is in the eye of the beholder and therefore, in the absence of any documentation showing that the namer or the artist intended it to be such is ORIGINAL RESEARCH and therefore forbidden. The point about Tibbets is irrelevant--he wasn't the namer nor the artist, nor do we know under what circumstances the ghost writer/editor of his book chose that spelling ("Bockscar" looks odd--very possibly an editor chose the spelling). The point about the NMUSAF exhibit is well-taken. An impeccably-credible source has defined the name: Bockscar. We don't, in the words of the first editor above, need to "guess".--Buckboard 05:25, 9 May 2007 (UTC)

 * It is completely silly and foolish to say that Col/Gen. Tibbets's opinion is "irrelevant". (Are you in the business of handing out insults?) Col. Tibbets was the commanding officer of the USAAF 509th Composite Group, and as such, he was responsible for everything in that B-29 Group, including the names of all the airplanes and all the nose art. It is insulting to say that he did not KNOW the name of such an important airplane as "Bock's Car".

 * To say so is like saying that a commanding Admiral did not know the names of every ship in his Task Force, or in his squadron of ships (in the example of the commander of a destroyer or submarine squadron, or a cruiser division). It is just completely unbelievable.

Bocks Car
Well, I'll give a reason for the third possible choice: I think the spelling on the aircraft should be definitive, grammatical or not, most commonly used or not. So I think the article should be titled Bocks Car, although the space between S and C is pretty thin, more the absence of an overlap than an actual space.

In any case, I've put a link to the above image on the article page and edited it to leave it to the reader to decide whether there's a space in there. 207.176.159.90 00:03, 26 Feb 2005 (UTC)

 * I agree, Bocks Car makes most sense. The Enola Gay was also all caps, but it is written in this format. —Preceding unsigned comment added by Ragesoss (talk • contribs)
 * Wow, look at the change from the older photo to the newer. Clearly, someone has done a poor job restoring here. There is a clear absence of an overlap in the older photo, and not in the newer one. Still, even the oldest version must have been made after the mission. Does anyone know who the artist was? Greswik 13:29, 25 July 2007 (UTC)

The Great Artiste
According to The Bomb: A Life, Bocks Car (or whatever the format) was the original name, after it's normal pilot, and it was renamed The Great Artiste by Sweeney but the name didn't stick. The line about manning the Great Artiste is confusing and seems to suggest that the plane flown by Bock on the Nagasaki mission was the The Great Artiste.--ragesoss 00:14, 22 January 2006 (UTC)
 * I can't see any confusion. The intro quite clearly says "On the day of the attack Bockscar was manned by the crew of The Great Artiste and was commanded by Major Charles W. Sweeney of Massachusetts." Also, it is probably more accurate to say Sweeney attempted to rename the aircraft, not that he actually did so. Does the book say exactly when the BOCKSCAR name was painted on the aircraft? Moriori 02:00, 22 January 2006 (UTC)

 * The plane that flew the instrumentation missions for both Hiroshima and Nagasaki was already named the Great Artiste. The Great Artiste was originally scheduled to drop the second bomb, but when it was realised that there was not enough time to move the instrumentation from the Great Artiste to Bocks Car, the crews were swapped. The document at, which is an External link from the article, explains most of this. The initial press releases said that the second bomb had been dropped from the Great Artiste because that had been the plan. Note that the press release states the mission was flown in no. 77, which was the BocksCar. As for when the nose art was painted on Bocks Car, a photo taken right after the mission shows a clean nose; the nose art was added later. Unfortunately, I can't find the photo right now. --  Dalbury ( Talk )  05:09, 22 January 2006 (UTC)

 * None of the aircraft except Enola Gay were "named" (i.e. painted on the nose) before the missions. One (Luke the Spook) was not named until the next year, and one (Jabit III) very possibly never carried a name. All nose art was unofficial and there are no documents showing when any were applied, except that Tibbets has confirmed that the plane was lettered the day before the mission. The reason the Nagasaki press release gives a victor number is that it was the only ID painted on the a/c at the time. The debate over "all caps" etc is a little overblown--nose art lettering came out in the style of the artist, without regard to caps etc. Enola Gay was lettered in BLOCK lettering. Many nicknames were painted by their artists using quotation marks, so some here would have them shown in an article as ""Name"". Also, the reason victor 77 was chosen to drop the Kokura-Nagasaki bomb was that it had been used by Sweeney and Albury's crew to conduct all three Fat Man test drops on August 1, 5, and 8. It was ready to go and they were comfortable flying it. The switchover of instrumentation could have been done, but why bother? Of the 393rd B-29s, only one (Some Punkins) was flown exclusively by its assigned crew, and one (Big Stink) was flown on missions by nine of the fifteen 393rd crews.--Buckboard 05:14, 9 May 2007 (UTC)

 * The main article may engender some confusion regarding when the "Bocks Car" nose art was restored and contains a reference to the nose art having been "restored" AFTER the aircraft arrived at the Air Force Museum. While that is no doubt literally true, one may infer from the article that the "Great Artiste" art may have lasted until after the plane had been flown to the Museum. At least as early as Spring 1960 the "Bocks Car" nose art was back on the plane. It was photographed in April or May of that year on display at Davis-Monthan AFB bearing the "Bocks Car" nose art. It is evident from the photograph that sometime during the plane's "stay" at DMAFB the "Bocks Car" nose art was restored or reapplied. That photograph is available for downloading, if appropriate. Herandher (talk) 05:54, 2 July 2011 (UTC)

Restoration
Should it be mentioned that that there are plans to bring the box car to flight status? The idea came about when inspection of the Enola Gay reviled her to be in remarkable shape, except for severed wire bundles dooming a restoration project. These wires where cut when the Enola Gay was disassembled for storage purposes. Bockscar never underwent such disassembly, and was store better than any other of the B-29's on display (almost all survivors but Bockscar and the Enola Gay sat at China Lake missile range as unused missile targets for years, Including FiFi). Inspection of Bockscar relieved a little more damage than was hoped but is still hands down the best candidate for a second flying Super-fortress. —Preceding unsigned comment added by 69.155.113.22 (talk) 06:18, 10 August 2010 (UTC)

Requested move

 * The following discussion is an archived 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. No further edits should be made to this section.

The result of the move request was: not moved. With three editors each supporting a different version, this defaults to no move without consensus. Of the arguments put forward, the most convincing is In ictu oculi's: gbooks does have far more "Bock's car" (with apostrophe) than "Bockscar", which might indicate that as the common form, but both forms are found. DrKiernan (talk) 11:05, 23 October 2012 (UTC)

Bockscar → Bocks Car – The name of the aircraft is clearly shown in the photo of the nose-art as being written in two words, so I feel that the ghost should be laid to rest, particularly as the evidence is already published in Wikipedia. Relisted. Jenks24 (talk) 09:22, 7 October 2012 (UTC) Petebutt (talk) 02:32, 11 September 2012 (UTC)
 * A more proper Alternative would be all caps as BOCKS CAR, the same goes for ENOLA GAYPetebutt (talk) 02:34, 11 September 2012 (UTC)
 * Arguments that museum spellings are paramount are obviously bogus due to the evidence availablePetebutt (talk) 02:37, 11 September 2012 (UTC)

 * Support Bock's Car gets twice the hits, 2,800, in GB of Bockscar - in addition to the likelihood of someoneone misreading "Bock Scar"., plus the nose art photo which shows S not overlapping with C like the other letters. In ictu oculi (talk) 12:52, 13 September 2012 (UTC)
 * Is Bock's a typo since the request you are supporting was for Bocks Car not Bock's Car?--174.93.171.108 (talk) 00:12, 16 September 2012 (UTC)

 * Oppose "Bockscar" is correct. It's supported by the nose art, the museum, and the pun on "Boxcar".  "Bocks Car" is against both WP capitalisation conventions and grammar. "Bock's Car" would at least have grammar in its favour, but it's very clear that no halfway decent sources claim there's an apostrophe in there. Andy Dingley (talk) 01:22, 12 October 2012 (UTC)
 * The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.

Contradiction - How much damage to Nagasaki?
This article (Bockscar) indicates that 44% of Nagasaki was destroyed. But, the Wikipedia article on Charles Sweeney states that 60% of Nagasaki was destroyed. https://en.wikipedia.org/wiki/Charles_Sweeney

Which is correct? — Preceding unsigned comment added by 70.73.52.186 (talk) 17:30, 18 May 2013 (UTC)
 * Richard Rhodes, in The Making of the Atomic Bomb (New York, Simon & Schuster, 1986, ISBN 0-684-81378-5), pp.740-742, 'The steep hills confined the larger explosion; it caused less damage and less loss of life than Little Boy. But 70,000 died in Nagasaki by the end of 1945, and 140,000 altogether across the next five years, a death rate like Hiroshima's of 54 percent.' The Wiki article on Nagasaki claims a population of 263,000 the day of the strike. The purpose of the atomic attacks was to kill people, for shock effect to force surrender, not so much to destroy property or war production. Khamba Tendal (talk) 18:48, 7 October 2023 (UTC)
 * The atomic attacks were deliberately targeted at military installations and war production industries. While a shock effect was hoped for, there was no certainty about it, much less about it forcing surrender, whereas the destruction of installations and property was far more likely. Hawkeye7   (discuss)  20:56, 7 October 2023 (UTC)

Which Type of Boeing ?
In the right upper square, we read : "Type 	Boeing B-29A-40BN Superfortress". But the Airplane History section starts by : "Bockscar, B-29-36-MO 44-27297, (...)". — Preceding unsigned comment added by 195.6.224.137 (talk) 10:47, 1 December 2013 (UTC)
 * Well spotted. The latter is correct. I have corrected the article accordingly. Hawkeye7 (talk) 11:41, 1 December 2013 (UTC)

Salt Lake
The drawing on the fuselage depicts a route from "Salt Lake" to "Nagasaki". What is the relevance of Salt Lake [City?] to the Bockscar? —jameslucas (" " / +) 20:43, 17 August 2015 (UTC)
 * Wendover Field Andy Dingley (talk) 21:34, 17 August 2015 (UTC)
 * I was thinking that too. Hawkeye7 (talk) 23:09, 17 August 2015 (UTC)
 * I guess it's more romantic than the hexagonal outline of Utah, even if the the base is not exactly near the lake. I wonder if it should be more explicit in the article. —jameslucas (" " / +) 17:07, 19 August 2015 (UTC)
 * Only if you can find a reliable source. Hawkeye7 (talk) 20:58, 19 August 2015 (UTC)

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Casualties
This article cites three sources with wildly inaccurate casualty figures. According to the tabulation given most of the dead were munition workers, Korean laborers or Japanese soldiers. In reality, most of the casualties were civilians. The Urakami Valley was predominantly residential. Incidentally, the bomb exploded above and destroyed the largest Roman Catholic cathedral in Asia. This area had the highest concentration of Catholics in Japan and it is estimated that at least 10,000 died there as a result of the bombing. Of coirse, many other non-Catholic Japanese also died in the bombing as well as American POWs. Polambda (talk) 03:08, 1 April 2024 (UTC)

 * You have a better source breaking down the casualties? Hawkeye7   (discuss)  05:02, 1 April 2024 (UTC)
 * The two best sources on casualties are Richard B. Frank's Downfall and Paul Ham's Hiroshima Nagasaki. These are fairly reasonable sources but still come to the question from different angles. There are a lot of secondary sources that grossly distort what little is known to prove a point. The sources cited in this Wikipedia article are among those. Honestly, even broad-brush casualty estimates are speculative. I think it is futile to try and break down the death total at too granular a level. Polambda (talk) 19:33, 1 April 2024 (UTC)

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

title: Talk:Bockscar


text:
Athol

Athol may refer to:

Scotland

 * Atholl, Scotland, a district in central Scotland

Canada

 * Athol, Nova Scotia, a small community
 * Athol, Prince Edward County, Ontario, a municipality and census division
 * Athol, a rural community in North Glengarry, Ontario

United States

 * Athol, Idaho, a city
 * Athol, Kansas, a city
 * Athol, Kentucky, an unincorporated community
 * Athol, Massachusetts, a town
 * Athol (CDP), Massachusetts, a census-designated place within the town
 * Athol, original name of Thurman, New York, a town
 * Athol, South Dakota, an unincorporated community

Elsewhere

 * Athol, Queensland, Australia, a rural locality
 * Athol, New Zealand, a town
 * Athol Island, Bahamas

Buildings

 * Athol (Henderson, Maryland), a home on the National Register of Historic Places (NRHP)
 * Athol (Simpsonville, Maryland), a historic plantation house
 * Athol (Edenton, North Carolina), a plantation house on the NRHP
 * Athol Manor, Columbia, Maryland

People

 * Athol (given name)

title: Athol


text:
Talk:Artificial consciousness

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Wiki Education Foundation-supported course assignment
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"Self-simulation"
Hi, "self-simulation" is a concept and methode advocated by Hod Lipson as pre-stage to self-awareness of robots.

Now I do not know where that could fit, if it is even this article or worth an own article? Nsae Comp (talk) 16:37, 21 October 2019 (UTC)
 * I started writing a description of this "self-modeling" concept, but it's far from complete. Jarble (talk) 04:09, 17 December 2020 (UTC)

Intriguing work re. MC
Hi, if anyone hasn't seen this it appears that Orch-OR may indeed be correct and verifiable. Its actually a very accurate model from certain points of view, such as the action of xenon and other anaesthetics on consciousness. Its entirely possible that the technology to make a conscious machine already exists but what is lacking is the specific program and model to run in limited hardware. — Preceding unsigned comment added by 88.81.156.140 (talk) 08:15, 9 April 2021 (UTC)

Difficult to understand for a non-technical audience
This article feels like it is written for a technical audience, it's really hard to understand for newcomers. I understand the endeavor to be technically accurate, and maybe it's also a complicated subject in itself. For example, the definition "Define that which would have to be synthesized were consciousness to be found in an engineered artifact" feels very convoluted to me, and I didn't understand the paragraph on the Computational Foundation argument. Alenoach (talk) 22:56, 22 June 2023 (UTC)

Integrated information theory
I think the integrated information theory is a major aspect of the topic, and should be discussed in the article. Alenoach (talk) 07:00, 16 August 2023 (UTC)

 * Perhaps also Attention schema theory and Global workspace theory. Alenoach (talk) 10:12, 16 August 2023 (UTC)

title: Talk:Artificial consciousness


text:
Von Neumann algebra

In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. It is a special type of C*-algebra.

Von Neumann algebras were originally introduced by John von Neumann, motivated by his study of single operators, group representations, ergodic theory and quantum mechanics. His double commutant theorem shows that the analytic definition is equivalent to a purely algebraic definition as an algebra of symmetries.

Two basic examples of von Neumann algebras are as follows:
 * The ring $$L^\infty(\mathbb R)$$ of essentially bounded measurable functions on the real line is a commutative von Neumann algebra, whose elements act as multiplication operators by pointwise multiplication on the Hilbert space $$L^2(\mathbb R)$$ of square-integrable functions.
 * The algebra $$\mathcal B(\mathcal H)$$ of all bounded operators on a Hilbert space $$\mathcal H$$ is a von Neumann algebra, non-commutative if the Hilbert space has dimension at least $$2$$.

Von Neumann algebras were first studied by in 1929; he and Francis Murray developed the basic theory, under the original name of rings of operators, in a series of papers written in the 1930s and 1940s, reprinted in the collected works of.

Introductory accounts of von Neumann algebras are given in the online notes of and  and the books by, ,  and. The three volume work by gives an encyclopedic account of the theory. The book by discusses more advanced topics.

Definitions
There are three common ways to define von Neumann algebras.

The first and most common way is to define them as weakly closed *-algebras of bounded operators (on a Hilbert space) containing the identity. In this definition the weak (operator) topology can be replaced by many other common topologies including the strong, ultrastrong or ultraweak operator topologies. The *-algebras of bounded operators that are closed in the norm topology are C*-algebras, so in particular any von Neumann algebra is a C*-algebra.

The second definition is that a von Neumann algebra is a subalgebra of the bounded operators closed under involution (the *-operation) and equal to its double commutant, or equivalently the commutant of some subalgebra closed under *. The von Neumann double commutant theorem says that the first two definitions are equivalent.

The first two definitions describe a von Neumann algebra concretely as a set of operators acting on some given Hilbert space. showed that von Neumann algebras can also be defined abstractly as C*-algebras that have a predual; in other words the von Neumann algebra, considered as a Banach space, is the dual of some other Banach space called the predual. The predual of a von Neumann algebra is in fact unique up to isomorphism. Some authors use "von Neumann algebra" for the algebras together with a Hilbert space action, and "W*-algebra" for the abstract concept, so a von Neumann algebra is a W*-algebra together with a Hilbert space and a suitable faithful unital action on the Hilbert space. The concrete and abstract definitions of a von Neumann algebra are similar to the concrete and abstract definitions of a C*-algebra, which can be defined either as norm-closed *-algebras of operators on a Hilbert space, or as Banach *-algebras such that ||aa*||=||a|| ||a*||.

Terminology
Some of the terminology in von Neumann algebra theory can be confusing, and the terms often have different meanings outside the subject.

 * A factor is a von Neumann algebra with trivial center, i.e. a center consisting only of scalar operators.
 * A finite von Neumann algebra is one which is the direct integral of finite factors (meaning the von Neumann algebra has a faithful normal tracial state $$\tau: M \rarr \mathbb{C}$$ ). Similarly, properly infinite von Neumann algebras are the direct integral of properly infinite factors.
 * A von Neumann algebra that acts on a separable Hilbert space is called separable. Note that such algebras are rarely separable in the norm topology.
 * The von Neumann algebra generated by a set of bounded operators on a Hilbert space is the smallest von Neumann algebra containing all those operators.
 * The tensor product of two von Neumann algebras acting on two Hilbert spaces is defined to be the von Neumann algebra generated by their algebraic tensor product, considered as operators on the Hilbert space tensor product of the Hilbert spaces.

By forgetting about the topology on a von Neumann algebra, we can consider it a (unital) *-algebra, or just a ring. Von Neumann algebras are semihereditary: every finitely generated submodule of a projective module is itself projective. There have been several attempts to axiomatize the underlying rings of von Neumann algebras, including Baer *-rings and AW*-algebras. The *-algebra of affiliated operators of a finite von Neumann algebra is a von Neumann regular ring. (The von Neumann algebra itself is in general not von Neumann regular.)

Commutative von Neumann algebras
The relationship between commutative von Neumann algebras and measure spaces is analogous to that between commutative C*-algebras and locally compact Hausdorff spaces. Every commutative von Neumann algebra is isomorphic to L∞(X) for some measure space (X, μ) and conversely, for every σ-finite measure space X, the *-algebra L∞(X) is a von Neumann algebra.

Due to this analogy, the theory of von Neumann algebras has been called noncommutative measure theory, while the theory of C*-algebras is sometimes called noncommutative topology.

Projections
Operators E in a von Neumann algebra for which E = EE = E* are called projections; they are exactly the operators which give an orthogonal projection of H onto some closed subspace. A subspace of the Hilbert space H is said to belong to the von Neumann algebra M if it is the image of some projection in M. This establishes a 1:1 correspondence between projections of M and subspaces that belong to M. Informally these are the closed subspaces that can be described using elements of M, or that M "knows" about.

It can be shown that the closure of the image of any operator in M and the kernel of any operator in M belongs to M. Also, the closure of the image under an operator of M of any subspace belonging to M also belongs to M. (These results are a consequence of the polar decomposition).

Comparison theory of projections
The basic theory of projections was worked out by. Two subspaces belonging to M are called (Murray–von Neumann) equivalent if there is a partial isometry mapping the first isomorphically onto the other that is an element of the von Neumann algebra (informally, if M "knows" that the subspaces are isomorphic). This induces a natural equivalence relation on projections by defining E to be equivalent to F if the corresponding subspaces are equivalent, or in other words if there is a partial isometry of H that maps the image of E isometrically to the image of F and is an element of the von Neumann algebra. Another way of stating this is that E is equivalent to F if E=uu* and F=u*u for some partial isometry u in M.

The equivalence relation ~ thus defined is additive in the following sense: Suppose E1 ~ F1 and E2 ~ F2. If E1 ⊥ E2 and F1 ⊥ F2, then E1 + E2 ~ F1 + F2. Additivity would not generally hold if one were to require unitary equivalence in the definition of ~, i.e. if we say E is equivalent to F if u*Eu = F for some unitary u. The Schröder–Bernstein theorems for operator algebras gives a sufficient condition for Murray-von Neumann equivalence.

The subspaces belonging to M are partially ordered by inclusion, and this induces a partial order ≤ of projections. There is also a natural partial order on the set of equivalence classes of projections, induced by the partial order ≤ of projections. If M is a factor, ≤ is a total order on equivalence classes of projections, described in the section on traces below.

A projection (or subspace belonging to M) E is said to be a finite projection if there is no projection F < E (meaning F ≤ E and F ≠ E) that is equivalent to E. For example, all finite-dimensional projections (or subspaces) are finite (since isometries between Hilbert spaces leave the dimension fixed), but the identity operator on an infinite-dimensional Hilbert space is not finite in the von Neumann algebra of all bounded operators on it, since it is isometrically isomorphic to a proper subset of itself. However it is possible for infinite dimensional subspaces to be finite.

Orthogonal projections are noncommutative analogues of indicator functions in L∞(R). L∞(R) is the ||·||∞-closure of the subspace generated by the indicator functions. Similarly, a von Neumann algebra is generated by its projections; this is a consequence of the spectral theorem for self-adjoint operators.

The projections of a finite factor form a continuous geometry.

Factors
A von Neumann algebra N whose center consists only of multiples of the identity operator is called a factor. As showed, every von Neumann algebra on a separable Hilbert space is isomorphic to a direct integral of factors. This decomposition is essentially unique. Thus, the problem of classifying isomorphism classes of von Neumann algebras on separable Hilbert spaces can be reduced to that of classifying isomorphism classes of factors.

showed that every factor has one of 3 types as described below. The type classification can be extended to von Neumann algebras that are not factors, and a von Neumann algebra is of type X if it can be decomposed as a direct integral of type X factors; for example, every commutative von Neumann algebra has type I1. Every von Neumann algebra can be written uniquely as a sum of von Neumann algebras of types I, II, and III.

There are several other ways to divide factors into classes that are sometimes used:

 * A factor is called discrete (or occasionally tame) if it has type I, and continuous (or occasionally wild) if it has type II or III.
 * A factor is called semifinite if it has type I or II, and purely infinite if it has type III.
 * A factor is called finite if the projection 1 is finite and properly infinite otherwise. Factors of types I and II may be either finite or properly infinite, but factors of type III are always properly infinite.

Type I factors
A factor is said to be of type I if there is a minimal projection E ≠ 0, i.e. a projection E such that there is no other projection F with 0 < F < E. Any factor of type I is isomorphic to the von Neumann algebra of all bounded operators on some Hilbert space; since there is one Hilbert space for every cardinal number, isomorphism classes of factors of type I correspond exactly to the cardinal numbers. Since many authors consider von Neumann algebras only on separable Hilbert spaces, it is customary to call the bounded operators on a Hilbert space of finite dimension n a factor of type In, and the bounded operators on a separable infinite-dimensional Hilbert space, a factor of type I∞.

Type II factors
A factor is said to be of type II if there are no minimal projections but there are non-zero finite projections. This implies that every projection E can be "halved" in the sense that there are two projections F and G that are Murray–von Neumann equivalent and satisfy E = F + G. If the identity operator in a type II factor is finite, the factor is said to be of type II1; otherwise, it is said to be of type II∞. The best understood factors of type II are the hyperfinite type II1 factor and the hyperfinite type II∞ factor, found by. These are the unique hyperfinite factors of types II1 and II∞; there are an uncountable number of other  factors of these types that are the subject of intensive study. proved the fundamental result that a factor of type II1 has a unique finite tracial state, and the set of traces of projections is [0,1].

A factor of type II∞ has a semifinite trace, unique up to rescaling, and the set of traces of projections is [0,∞]. The set of real numbers λ such that there is an automorphism rescaling the trace by a factor of λ is called the fundamental group of the type II∞ factor.

The tensor product of a factor of type II1 and an infinite type I factor has type II∞, and conversely any factor of type II∞ can be constructed like this. The fundamental group of a type II1 factor is defined to be the fundamental group of its tensor product with the infinite (separable) factor of type I. For many years it was an open problem to find a type II factor whose fundamental group was not the group of positive reals, but Connes then showed that the von Neumann group algebra of a countable discrete group with Kazhdan's property (T) (the trivial representation is isolated in the dual space), such as SL(3,Z),  has a countable fundamental group. Subsequently, Sorin Popa showed that the fundamental group can be trivial for certain groups, including the semidirect product of Z2 by SL(2,Z).

An example of a type II1 factor is the von Neumann group algebra of a countable infinite discrete group such that every non-trivial conjugacy class is infinite. found an uncountable family of such groups with non-isomorphic von Neumann group algebras, thus showing the existence of uncountably many different separable type II1 factors.

Type III factors
Lastly, type III factors are factors that do not contain any nonzero finite projections at all. In their first paper were unable to decide whether or not they existed; the first examples were later found by. Since the identity operator is always infinite in those factors, they were sometimes called type III∞ in the past, but recently that notation has been superseded by the notation IIIλ, where λ is a real number in the interval [0,1]. More precisely, if the Connes spectrum (of its modular group) is 1 then the factor is of type III0, if the Connes spectrum is all integral powers of λ for 0 < λ < 1, then the type is IIIλ, and if the Connes spectrum is all positive reals then the type is III1. (The Connes spectrum is a closed subgroup of the positive reals, so these are the only possibilities.) The only trace on type III factors takes value ∞ on all non-zero positive elements, and any two non-zero projections are equivalent. At one time type III factors were considered to be intractable objects, but Tomita–Takesaki theory has led to a good structure theory. In particular, any type III factor can be written in a canonical way as the crossed product of a type II∞ factor and the real numbers.

The predual
Any von Neumann algebra M has a predual M∗, which is the Banach space of all ultraweakly continuous linear functionals on M. As the name suggests, M is (as a Banach space) the dual of its predual. The predual is unique in the sense that any other Banach space whose dual is M is canonically isomorphic to M∗. showed that the existence of a predual characterizes von Neumann algebras among C* algebras.

The definition of the predual given above seems to depend on the choice of Hilbert space that M acts on, as this determines the ultraweak topology. However the predual can also be defined without using the Hilbert space that M acts on, by defining it to be the space generated by all positive normal linear functionals on M. (Here "normal" means that it preserves suprema when applied to increasing nets of self adjoint operators; or equivalently to increasing sequences of projections.)

The predual M∗ is a closed subspace of the dual M* (which consists of all norm-continuous linear functionals on M) but is generally smaller. The proof that M∗ is (usually) not the same as M* is nonconstructive and uses the axiom of choice in an essential way; it is very hard to exhibit explicit elements of M* that are not in M∗. For example, exotic positive linear forms on the von Neumann algebra l∞(Z) are given by free ultrafilters; they correspond to exotic *-homomorphisms into C and describe the Stone–Čech compactification of Z.

Examples:
 * 1) The predual of the von Neumann algebra L∞(R) of essentially bounded functions on R is the Banach space L1(R) of integrable functions. The dual of L∞(R) is strictly larger than L1(R) For example, a functional on L∞(R) that extends the Dirac measure δ0 on the closed subspace of bounded continuous functions C0b(R) cannot be represented as a function in L1(R).
 * 2) The predual of the von Neumann algebra B(H) of bounded operators on a Hilbert space H is the Banach space of all trace class operators with the trace norm ||A||= Tr(|A|). The Banach space of trace class operators is itself the dual of the C*-algebra of compact operators (which is not a von Neumann algebra).

Weights, states, and traces
Weights and their special cases states and traces are discussed in detail in.

 * A weight ω on a von Neumann algebra is a linear map from the set of positive elements (those of the form a*a) to [0,∞].
 * A positive linear functional is a weight with ω(1) finite (or rather the extension of ω to the whole algebra by linearity).
 * A state is a weight with ω(1) = 1.
 * A trace is a weight with ω(aa*) = ω(a*a) for all a.
 * A tracial state is a trace with ω(1) = 1.

Any factor has a trace such that the trace of a non-zero projection is non-zero and the trace of a projection is infinite if and only if the projection is infinite. Such a trace is unique up to rescaling. For factors that are separable or finite, two projections are equivalent if and only if they have the same trace. The type of a factor can be read off from the possible values of this trace over the projections of the factor, as follows:
 * Type In: 0, x, 2x, ....,nx for some positive x (usually normalized to be 1/n or 1).
 * Type I∞: 0, x, 2x, ....,∞ for some positive x (usually normalized to be 1).
 * Type II1: [0,x] for some positive x (usually normalized to be 1).
 * Type II∞: [0,∞].
 * Type III: {0,∞}.

If a von Neumann algebra acts on a Hilbert space containing a norm 1 vector v, then the functional a → (av,v) is a normal state. This construction can be reversed to give an action on a Hilbert space from a normal state: this is the GNS construction for normal states.

Modules over a factor
Given an abstract separable factor, one can ask for a classification of its modules, meaning the separable Hilbert spaces that it acts on. The answer is given as follows: every such module H can be given an M-dimension dimM(H) (not its dimension as a complex vector space) such that modules are isomorphic if and only if they have the same M-dimension. The M-dimension is additive, and a module is isomorphic to a subspace of another module if and only if it has smaller or equal M-dimension.

A module is called standard if it has a cyclic separating vector. Each factor has a standard representation, which is unique up to isomorphism. The standard representation has an antilinear involution J such that JMJ = . For finite factors the standard module is given by the GNS construction applied to the unique normal tracial state and the M-dimension is normalized so that the standard module has M-dimension 1, while for infinite factors the standard module is the module with M-dimension equal to ∞.

The possible M-dimensions of modules are given as follows:
 * Type In (n finite): The M-dimension can be any of 0/n, 1/n, 2/n, 3/n, ..., ∞. The standard module has M-dimension 1 (and complex dimension n2.)
 * Type I∞ The M-dimension can be any of 0, 1, 2, 3, ..., ∞. The standard representation of B(H) is H⊗H; its M-dimension is ∞.
 * Type II1: The M-dimension can be anything in [0, ∞]. It is normalized so that the standard module has M-dimension 1. The M-dimension is also called the coupling constant of the module H.
 * Type II∞: The M-dimension can be anything in [0, ∞]. There is in general no canonical way to normalize it; the factor may have outer automorphisms multiplying the M-dimension by constants. The standard representation is the one with M-dimension ∞.
 * Type III: The M-dimension can be 0 or ∞. Any two non-zero modules are isomorphic, and all non-zero modules are standard.

Amenable von Neumann algebras
and others proved that the following conditions on a von Neumann algebra M on a separable Hilbert space H are all equivalent:

 * M is hyperfinite or AFD or approximately finite dimensional or approximately finite: this means the algebra contains an ascending sequence of finite dimensional subalgebras with dense union. (Warning: some authors use "hyperfinite" to mean "AFD and finite".)
 * M is amenable: this means that the derivations of M with values in a normal dual Banach bimodule are all inner.
 * M has Schwartz's property P: for any bounded operator T on H the weak operator closed convex hull of the elements uTu* contains an element commuting with M.
 * M is semidiscrete: this means the identity map from M to M is a weak pointwise limit of completely positive maps of finite rank.
 * M has property E or the Hakeda–Tomiyama extension property: this means that there is a projection of norm 1 from bounded operators on H to M '.
 * M is injective: any completely positive linear map from any self adjoint closed subspace containing 1 of any unital C*-algebra A to M can be extended to a completely positive map from A to M.

There is no generally accepted term for the class of algebras above; Connes has suggested that amenable should be the standard term.

The amenable factors have been classified: there is a unique one of each of the types In, I∞, II1, II∞, IIIλ, for 0 < λ ≤ 1, and the ones of type III0 correspond to certain ergodic flows. (For type III0 calling this a classification is a little misleading, as it is known that there is no easy way to classify the corresponding ergodic flows.) The ones of type I and II1 were classified by, and the remaining ones were classified by , except for the type III1 case which was completed by Haagerup.

All amenable factors can be constructed using the group-measure space construction of Murray and von Neumann for a single ergodic transformation. In fact they are precisely the factors arising as crossed products by free ergodic actions of Z or Z/nZ on abelian von Neumann algebras L∞(X). Type I factors occur when the measure space X is atomic and the action transitive. When X is diffuse or non-atomic, it is equivalent to [0,1] as a measure space. Type II factors occur when X admits an equivalent finite (II1) or infinite (II∞) measure, invariant under an action of Z. Type III factors occur in the remaining cases where there is no invariant measure, but only an invariant measure class: these factors are called Krieger factors.

Tensor products of von Neumann algebras
The Hilbert space tensor product of two Hilbert spaces is the completion of their algebraic tensor product. One can define a tensor product of von Neumann algebras (a completion of the algebraic tensor product of the algebras considered as rings), which is again a von Neumann algebra, and act on the tensor product of the corresponding Hilbert spaces. The tensor product of two finite algebras is finite, and the tensor product of an infinite algebra and a non-zero algebra is infinite. The type of the tensor product of two von Neumann algebras (I, II, or III) is the maximum of their types. The commutation theorem for tensor products states that

 * $$(M\otimes N)^\prime = M^\prime\otimes N^\prime,$$

where  denotes the commutant of M.

The tensor product of an infinite number of von Neumann algebras, if done naively, is usually a ridiculously large non-separable algebra. Instead showed that  one should choose a state on each of the von Neumann algebras, use this to define a state on the algebraic tensor product, which can be used to produce a Hilbert space and a (reasonably small) von Neumann algebra. studied the case where all the factors are finite matrix algebras; these factors are called Araki–Woods factors or ITPFI factors (ITPFI stands for "infinite tensor product of finite type I factors"). The type of the infinite tensor product can vary dramatically as the states are changed; for example, the infinite tensor product of an infinite number of type I2 factors can have any type depending on the choice of states. In particular found an uncountable family of non-isomorphic hyperfinite type IIIλ factors for 0 < λ < 1, called Powers factors, by taking an infinite tensor product of type I2 factors, each with the state given by:

 * $$x\mapsto {\rm Tr}\begin{pmatrix}{1\over \lambda+1}&0\\ 0&{\lambda\over \lambda+1}\\ \end{pmatrix} x.$$

All hyperfinite von Neumann algebras not of type III0 are isomorphic to Araki–Woods factors, but there are uncountably many of type III0 that are not.

Bimodules and subfactors
A bimodule (or correspondence) is a Hilbert space H with module actions of two commuting von Neumann algebras. Bimodules have a much richer structure than that of modules. Any bimodule over two factors always gives a subfactor since one of the factors is always contained in the commutant of the other. There is also a subtle relative tensor product operation due to Connes on bimodules. The theory of subfactors, initiated by Vaughan Jones, reconciles these two seemingly different points of view.

Bimodules are also important for the von Neumann group algebra M of a discrete group Γ. Indeed, if V is any unitary representation of Γ, then, regarding Γ as the diagonal subgroup of Γ × Γ, the corresponding induced representation on l2(Γ, V) is naturally a bimodule for two commuting copies of M. Important representation theoretic properties of Γ can be formulated entirely in terms of bimodules and therefore make sense for the von Neumann algebra itself. For example, Connes and Jones gave a definition of an analogue of Kazhdan's property (T) for von Neumann algebras in this way.

Non-amenable factors
Von Neumann algebras of type I are always amenable, but for the other types there are an uncountable number of different non-amenable factors, which seem very hard to classify, or even distinguish from each other. Nevertheless, Voiculescu has shown that the class of non-amenable factors coming from the group-measure space construction is disjoint from the class coming from group von Neumann algebras of free groups. Later Narutaka Ozawa proved that group von Neumann algebras of hyperbolic groups yield prime type II1 factors, i.e. ones that cannot be factored as tensor products of type II1 factors, a result first proved by Leeming Ge for free group factors using Voiculescu's free entropy. Popa's work on fundamental groups of non-amenable factors represents another significant advance. The theory of factors "beyond the hyperfinite" is rapidly expanding at present, with many new and surprising results; it has close links with rigidity phenomena in geometric group theory and ergodic theory.

Examples

 * The essentially bounded functions on a σ-finite measure space form a commutative (type I1) von Neumann algebra acting on the L2 functions. For certain non-σ-finite measure spaces, usually considered pathological, L∞(X) is not a von Neumann algebra; for example, the σ-algebra of measurable sets might be the countable-cocountable algebra on an uncountable set. A fundamental approximation theorem can be represented by the Kaplansky density theorem.
 * The bounded operators on any Hilbert space form a von Neumann algebra, indeed a factor, of type I.
 * If we have any unitary representation of a group G on a Hilbert space H then the bounded operators commuting with G form a von Neumann algebra ', whose projections correspond exactly to the closed subspaces of H invariant under G. Equivalent subrepresentations correspond to equivalent projections in '. The double commutant  of G is also a von Neumann algebra.
 * The von Neumann group algebra of a discrete group G is the algebra of all bounded operators on H = l2(G) commuting with the action of G on H through right multiplication. One can show that this is the von Neumann algebra generated by the operators corresponding to multiplication from the left with an element g ∈ G. It is a factor (of type II1) if every non-trivial conjugacy class of G is infinite (for example, a non-abelian free group), and is the hyperfinite factor of type II1 if in addition G is a union of finite subgroups (for example, the group of all permutations of the integers fixing all but a finite number of elements).
 * The tensor product of two von Neumann algebras, or of a countable number with states, is a von Neumann algebra as described in the section above.
 * The crossed product of a von Neumann algebra by a discrete (or more generally locally compact) group can be defined, and is a von Neumann algebra. Special cases are the group-measure space construction of Murray and von Neumann and Krieger factors.
 * The von Neumann algebras of a measurable equivalence relation and a measurable groupoid can be defined. These examples generalise von Neumann group algebras and the group-measure space construction.

Applications
Von Neumann algebras have found applications in diverse areas of mathematics like knot theory, statistical mechanics, quantum field theory, local quantum physics, free probability, noncommutative geometry, representation theory, differential geometry, and dynamical systems.

For instance, C*-algebra provides an alternative axiomatization to probability theory. In this case the method goes by the name of Gelfand–Naimark–Segal construction. This is analogous to the two approaches to measure and integration, where one has the choice to construct measures of sets first and define integrals later, or construct integrals first and define set measures as integrals of characteristic functions.

title: Von Neumann algebra


text:
Ashton

Ashton may refer to:

Names

 * Ashton (given name)
 * Ashton (surname)

Australia

 * Ashton, Elizabeth Bay, a heritage-listed house in Sydney, New South Wales
 * Ashton, South Australia

Canada

 * Ashton, Ontario

New Zealand

 * Ashton, New Zealand

South Africa

 * Ashton, Western Cape

England

 * Ashton, Cambridgeshire
 * Ashton, Cornwall
 * Ashton, Devon
 * Ashton, Hampshire
 * Ashton, Herefordshire
 * Ashton, North Northamptonshire, near Oundle
 * Ashton, West Northamptonshire, near Northampton
 * Ashton, Somerset, a hamlet in the parish of Chapel Allerton, Sedgemoor district
 * Long Ashton or Ashton, North Somerset
 * Ashton Court
 * Ashton Gate, Bristol
 * Ashton Vale, now in Bristol
 * Bower Ashton, now in Bristol
 * Ashton Common, Wiltshire
 * Ashton Green, East Sussex
 * Ashton Hayes, Cheshire
 * Ashton Keynes, Wiltshire
 * Ashton under Hill, Worcestershire
 * Ashton upon Mersey, Greater Manchester
 * Ashton-in-Makerfield, Greater Manchester in the Metropolitan Borough of Wigan
 * Ashton (ward), an electoral ward in Wigan
 * Ashton-on-Ribble, Lancashire
 * Ashton-under-Lyne, Greater Manchester
 * Ashton Canal

Scotland

 * Ashton, Inverclyde
 * Ashton Lane, Glasgow

United States

 * Ashton, Georgia
 * Ashton, Idaho
 * Ashton, Illinois
 * Ashton, Iowa
 * Ashton, Kansas
 * Ashton, Maryland
 * Ashton, Michigan
 * Ashton, Minnesota
 * Ashton, Missouri
 * Ashton, Nebraska
 * Ashton, South Dakota
 * Ashton, West Virginia
 * Ashton, Wisconsin
 * Ashton Corners, Wisconsin

Other uses

 * Ashton Middle School, formerly Dunstable Grammar School, Dunstable
 * Avro Ashton, a 1950s British experimental jet airliner
 * Ashton Builders, a former UK home builder
 * Ashton Music, a brand of mainly entry-level musical instruments and related equipment
 * Ashton Cricket Club, Ashton-under-Lyne
 * Ashton Sixth Form College, Ashton-under-Lyne
 * Ashton United F.C., Ashton-under-Lyne
 * Ashton Observatory, an observatory within Ashton-Wildwood Park in Jasper County, Iowa
 * Ashton (cigar), a brand of cigar established in 1985, manufactured by Arturo Fuente
 * Ashton (horse)
 * The Ashton, a residential skyscraper in Austin, Texas, U.S.

title: Ashton


text:
Tâmega (river)

The Tâmega (Tamaca) or Támega is a river in Galicia, Spain and Portugal. It begins its course near Verín, Galicia, Spain, and flows to Portugal in the provinces of Trás-os-Montes and Douro Litoral.

The Tâmega River is a tributary of the Douro River. From Verín, it flows south to Portuguese city of Chaves; then it flows through a fertile valley called the Veiga. Below Chaves the river narrows to pass through mountains and valleys. Owing to low water level and frequent small dams it is not navigable, passing through the cities of Amarante and Marco de Canaveses, flowing in the Douro River, near Entre-os-Rios: in fact Entre-os-Rios means between the rivers.

The Tâmega is more important historically than economically. It has always served as an invasion route for foreign armies intent on reaching the richer southern lands of Portugal. The valley around Chaves has especially seen its share of battles and invading armies.

Like many rivers, the Tâmega suffers from pollution and the ravages of sand and gravel extraction companies. The quality of the water has deteriorated greatly. Another problem is the periodic occurrence of flooding.

Since the completion of the Torrão dam in 1988 less than 1 kilometre above the Douro river and the town of Entre-os-Rios in the municipality of Marco de Canaveses, the Tâmega has been recovering slowly from the effects of pollution. Sand extraction activities have been prohibited and many upstream cities installed modern sewage treatment plants.

A new dam is planned between the city of Amarante and the town of Mondim de Basto. Besides producing electricity, the project will feature a flood control system that will divert the waterflow towards the smaller Olo River. A 220 MW pumped-storage hydroelectricity facility started operating in 2022, storing 40 GWh of electricity. It cost €1.5 billion. Three more turbines are scheduled for the site, bringing the storage power to 880 MW. The project also includes two run-of-the-river hydroelectricity facilities.

Transport
The Tâmega line, which closed in 2009, was a narrow gauge railway line which closely followed the river.

title: Tâmega (river)


text:
Williston

Williston may refer to:

People

 * Williston (surname)

Places

 * United States
 * Williston, Florida, a city in Levy County
 * Williston, Kentucky, former name of Murray, Kentucky
 * Williston, Maryland, a town in Caroline County
 * Williston, North Dakota, a city in Williams County
 * Williston, Ohio, a town in Ottawa County
 * Williston, South Carolina, a town in Barnwell County
 * Williston, Tennessee, a city in Fayette County
 * Williston, Vermont, a town in Chittenden County
 * Williston (Orange, Virginia), a historic home and farm complex in Orange County, Virginia
 * Williston Highlands, Florida, a census-designated place in Levy County
 * Williston Park, New York, a village in Nassau County
 * South Africa
 * Williston, Northern Cape, a town in the Northern Cape Province
 * Canada
 * Williston Lake, the largest man-made lake in North America, located in the Peace River Country of northern British Columbia

Schools

 * Williston Northampton School, a prep school in Easthampton, Massachusetts

title: Williston


text:
Harold Bennett

Harold Frank Bennett (17 November 1898 – 11 September 1981) was an English actor, active in stage, television and film best remembered for being in sitcoms written and produced by David Croft, having played 'Young Mr. Grace' in the 1970s British sitcom Are You Being Served?, as well as minor character Sidney Bluett in Dad's Army.

Biography
Bennett was born in Hastings, Sussex. After leaving school at the age of twelve, in his early life he toured America as a clown with a circus, and later taught English at the Working Men's College in London. During World War I he served as a courier, initially on horseback, then on motorcycle. After the war he took up acting and eventually worked as stage producer in the Tower Theatre, London. He subsequently pursued a career as a draughtsman for an electric company, only taking up his acting career again following retirement.

Harold Bennett died of a heart attack on 11 September 1981, aged 82. His wife predeceased him in the 1930s; he was survived by their three children. One of his children, John, was also an actor.

Acting career
He played the recurring character Mr (Sidney) Bluett in Dad's Army from 1969 to 1977, but it was as Young Mr Grace, the ancient, amiably callous owner of Grace Brothers department store in British sitcom Are You Being Served? that he achieved his greatest fame. His last appearance in Are You Being Served? aired some three months after his death, having been recorded earlier in the year.

Bennett also played the role of the aged Archdeacon Pulteney in The Stalls of Barchester, the BBC A Ghost Story for Christmas broadcast 24 December 1971 and adapted from the M.R. James story of the same name. Bennett also appeared in Vote, Vote, Vote for Nigel Barton (1965), and in several films, including as a photographer in Games That Lovers Play (1971) and as the aged odd-job man Gasper in The Ups and Downs of a Handyman (1975).

On the stage, he appeared in a Royal Shakespeare Company production of London Assurance, and in an Open University production of Chekhov's The Three Sisters.

Film

 * The Sky Bike (1967) – Old Man
 * Games That Lovers Play (1971) – Old photographer
 * Au Pair Girls (1972) – Lord Tryke
 * The Ups and Downs of a Handyman (1976) – Gasper
 * Are You Being Served? (1977) – Young Mr. Grace

title: Harold Bennett


text:
East Williston

East Williston is the name of several places in the United States of America:

 * East Williston, Florida
 * East Williston, New York

title: East Williston


text:
Hamiltonian

Hamiltonian may refer to:
 * Hamiltonian mechanics, a function that represents the total energy of a system
 * Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system
 * Dyall Hamiltonian, a modified Hamiltonian with two-electron nature
 * Molecular Hamiltonian, the Hamiltonian operator representing the energy of the electrons and nuclei in a molecule
 * Hamiltonian (control theory), a function used to solve a problem of optimal control for a dynamical system
 * Hamiltonian path, a path in a graph that visits each vertex exactly once
 * Hamiltonian group, a non-abelian group the subgroups of which are all normal
 * Hamiltonian economic program, the economic policies advocated by Alexander Hamilton, the first United States Secretary of the Treasury

title: Hamiltonian