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This relationship of artists with Achill was particularly intense in the early decades of the twentieth century when Eva O'Flaherty (1874–1963) became a focal point for artistic networking on the island. A network of over 200 artists linked to Achill is charted in "Achill Painters - An Island History" and includes painters such as the Belgian Marie Howet, the American Robert Henri, the modernist painter Mainie Jellett and contemporary artist Camille Souter. The 2018 "Coming Home Art & The Great Hunger" exhibition, in partnership with The Great Hunger Museum of Quinnipiac University, USA, featured Achill's Deserted Village and the island lazy beds prominently in works by Geraldine O'Reilly and Alanna O'Kelly; also included was an 1873 painting, 'Cottage, Achill Island' by Alexander Williams - one of the first artists to open up the island to a wider audience. Education. Hedge schools existed in most villages of Achill in various periods of history. A university was started by the missions to Achill in Mweelin.
At the turn of the 21st century there were two secondary schools in Achill: Mc Hale College and Scoil Damhnait. These two schools amalgamated, in 2011, to form Coláiste Pobail Acla. For primary education, there are eight national schools. These including Bullsmouth NS, Valley NS, Bunnacurry NS, Dookinella NS, Dooagh NS, Saula NS, Achill Sound NS and Tonragee NS. Transport. Rail. Achill railway station, still on the mainland and not on the island, was opened by the Midland Great Western Railway on 13 May 1895, the terminus of its line from Westport via Newport and Mulranny. The station, and the line, were closed by the Great Southern Railways on 1 October 1937. The Great Western Greenway, created during 2010 and 2011, follows the line's route and has proved to be very successful in attracting visitors to Achill and the surrounding areas. Road. The R319 road is the main road onto the island. Bus Éireann's route 450 operates several times daily to Westport and Louisburgh from the island. Bus Éireann also provides transport for the area's secondary school children.
Sport. Achill has a Gaelic football club which competes in the junior championship and division 1E of the Mayo League. There are also Achill Rovers which play in the Mayo Association Football League. There is a 9-hole links golf course on the island. Outdoor activities can be done through Achill Outdoor Education Centre. Achill Island's rugged landscape and the surrounding ocean offers multiple locations for outdoor adventure activities, like surfing, kite-surfing and sea kayaking. Fishing and watersports are also common. Sailing regattas featuring a local vessel type, the Achill Yawl, have been run since the 19th century. Demographics. In 2016, the population was 2,594, with 5.2% claiming they spoke Irish on a daily basis outside the education system. The island's population has declined from around 6,000 before the Great Famine of the mid-19th century. The table below reports data on Achill Island's population taken from "Discover the Islands of Ireland" (Alex Ritsema, Collins Press, 1999) and the census of Ireland. In popular culture. The island is featured throughout the film "The Banshees of Inisherin" in various locations on the island including Keem Bay, Cloughmore, and Purteen Pier. The island is also the primary setting of the visual novel "If Found...".
Allen Ginsberg Irwin Allen Ginsberg (; June 3, 1926 – April 5, 1997) was an American poet and writer. As a student at Columbia University in the 1940s, he began friendships with Lucien Carr, William S. Burroughs and Jack Kerouac, forming the core of the Beat Generation. He vigorously opposed militarism, economic materialism, and sexual repression, and he embodied various aspects of this counterculture with his views on drugs, sex, multiculturalism, hostility to bureaucracy, openness to Pederasty, and openness to Eastern religions. Best known for his poem "Howl", Ginsberg denounced what he saw as the destructive forces of capitalism and conformity in the United States. San Francisco police and US Customs seized copies of "Howl" in 1956, and a subsequent obscenity trial in 1957 attracted widespread publicity due to the poem's language and descriptions of heterosexual and homosexual sex at a time when sodomy laws made male homosexual acts a crime in every state. The poem reflected Ginsberg's own sexuality and his relationships with a number of men, including Peter Orlovsky, his lifelong partner. Judge Clayton W. Horn ruled that "Howl" was not obscene, asking: "Would there be any freedom of press or speech if one must reduce his vocabulary to vapid innocuous euphemisms?"
Ginsberg was a Buddhist who extensively studied Eastern religious disciplines. He lived modestly, buying his clothing in second-hand stores and residing in apartments in New York City's East Village. One of his most influential teachers was Tibetan Buddhist Chögyam Trungpa, the founder of the Naropa Institute in Boulder, Colorado. At Trungpa's urging, Ginsberg and poet Anne Waldman started The Jack Kerouac School of Disembodied Poetics there in 1974. For decades, Ginsberg was active in political protests across a range of issues from the Vietnam War to the war on drugs. His poem "September on Jessore Road" drew attention to refugees fleeing the 1971 Bangladeshi genocide, exemplifying what literary critic Helen Vendler described as Ginsberg's persistent opposition to "imperial politics" and the "persecution of the powerless". His collection "The Fall of America" shared the annual National Book Award for Poetry in 1974. In 1979, he received the National Arts Club gold medal and was inducted into the American Academy of Arts and Letters. He was a Pulitzer Prize finalist in 1995 for his book "Cosmopolitan Greetings: Poems 1986–1992".
Biography. Early life and family. Ginsberg was born into a Jewish family in Newark, New Jersey, and grew up in nearby Paterson. He was the second son of Louis Ginsberg, also born in Newark, a schoolteacher and published poet, and the former Naomi Levy, born in Nevel (Russia) and a fervent Marxist. As a teenager, Ginsberg began to write letters to "The New York Times" about political issues, such as World War II and workers' rights. He published his first poems in the "Paterson Morning Call". While in high school, Ginsberg became interested in the works of Walt Whitman, inspired by his teacher's passionate reading. In 1943, Ginsberg graduated from Eastside High School and briefly attended Montclair State College before entering Columbia University on a scholarship from the Young Men's Hebrew Association of Paterson. Ginsberg intended to study law at Columbia but later changed his major to literature. In 1945, he joined the Merchant Marine to earn money to continue his education at Columbia. While at Columbia, Ginsberg contributed to the "Columbia Review" literary journal, the "Jester" humor magazine, won the Woodberry Poetry Prize, served as president of the Philolexian Society (literary and debate group), and joined Boar's Head Society (poetry society).
He was a resident of Hartley Hall, where other Beat Generation poets such as Jack Kerouac and Herbert Gold also lived. Ginsberg has stated that he considered his required freshman seminar in Great Books, taught by Lionel Trilling, to be his favorite Columbia course. In 1948, he graduated from Columbia with a B.A in English and American Literature. According to The Poetry Foundation, Ginsberg spent several months in a mental institution after he pleaded insanity during a hearing. He was allegedly being prosecuted for harboring stolen goods in his dorm room. It was noted that the stolen property was not his, but belonged to an acquaintance. Ginsberg also took part in public readings at the Episcopal St. Mark's Church in-the-Bowery which would later hold a memorial service for him after his death. Relationship with his parents. Ginsberg referred to his parents in a 1985 interview as "old-fashioned delicatessen philosophers". His mother was also an active member of the Communist Party and took Ginsberg and his brother Eugene to party meetings. Ginsberg later said that his mother "made up bedtime stories that all went something like: 'The good king rode forth from his castle, saw the suffering workers and healed them.'" Of his father Ginsberg said: "My father would go around the house either reciting Emily Dickinson and Longfellow under his breath or attacking T. S. Eliot for ruining poetry with his 'obscurantism.' I grew suspicious of both sides."
Naomi Ginsberg had schizophrenia which often manifested as paranoid delusions, disordered thinking and multiple suicide attempts. She would claim, for example, that the president had implanted listening devices in their home and that her mother-in-law was trying to kill her. Her suspicion of those around her caused Naomi to draw closer to young Allen, "her little pet," as Bill Morgan says in his biography of Ginsberg, titled "I Celebrate Myself: The Somewhat Private Life of Allen Ginsberg". She also tried to kill herself by slitting her wrists and was soon taken to Greystone, a mental hospital; she would spend much of Ginsberg's youth in mental hospitals. His experiences with his mother and her mental illness were a major inspiration for his two major works, "Howl" and his long autobiographical poem "Kaddish for Naomi Ginsberg (1894–1956)". When he was in junior high school, he accompanied his mother by bus to her therapist. The trip deeply disturbed Ginsberg—he mentioned it and other moments from his childhood in "Kaddish". His experiences with his mother's mental illness and her institutionalization are also frequently referred to in "Howl." For example, "Pilgrim State, Rockland, and Grey Stone's foetid halls" is a reference to institutions frequented by his mother and Carl Solomon, ostensibly the subject of the poem: Pilgrim State Hospital and Rockland State Hospital in New York and Greystone Park Psychiatric Hospital in New Jersey. This is followed soon by the line "with mother finally ******." Ginsberg later admitted the deletion was the expletive "fucked." He also says of Solomon in section three, "I'm with you in Rockland where you imitate the shade of my mother," once again showing the association between Solomon and his mother.
Ginsberg received a letter from his mother after her death responding to a copy of "Howl" he had sent her. It admonished Ginsberg to be good and stay away from drugs; she says, "The key is in the window, the key is in the sunlight at the window—I have the key—Get married Allen don't take drugs—the key is in the bars, in the sunlight in the window." In a letter she wrote to Ginsberg's brother Eugene, she said, "God's informers come to my bed, and God himself I saw in the sky. The sunshine showed too, a key on the side of the window for me to get out. The yellow of the sunshine, also showed the key on the side of the window." These letters and the absence of a facility to recite kaddish inspired Ginsberg to write "Kaddish", which makes references to many details from Naomi's life, Ginsberg's experiences with her, and the letter, including the lines "the key is in the light" and "the key is in the window." New York Beats. In Ginsberg's first year at Columbia he met fellow undergraduate Lucien Carr, who introduced him to a number of future Beat writers, including Jack Kerouac, William S. Burroughs, and John Clellon Holmes. They bonded, because they saw in one another an excitement about the potential of American youth, a potential that existed outside the strict conformist confines of post–World War II, McCarthy-era America. Ginsberg and Carr talked excitedly about a "New Vision" (a phrase adapted from Yeats' "A Vision"), for literature and America. Carr also introduced Ginsberg to Neal Cassady, for whom Ginsberg had a long infatuation. In the first chapter of his 1957 novel "On the Road" Kerouac described the meeting between Ginsberg and Cassady. Kerouac saw them as the dark (Ginsberg) and light (Cassady) side of their "New Vision", a perception stemming partly from Ginsberg's association with communism, of which Kerouac had become increasingly distrustful. Though Ginsberg was never a member of the Communist Party, Kerouac named him "Carlo Marx" in "On the Road". This was a source of strain in their relationship.
Also, in New York, Ginsberg met Gregory Corso in the Pony Stable Bar. Corso, recently released from prison, was supported by the Pony Stable patrons and was writing poetry there the night of their meeting. Ginsberg claims he was immediately attracted to Corso, who was straight, but understood homosexuality after three years in prison. Ginsberg was even more struck by reading Corso's poems, realizing Corso was "spiritually gifted." Ginsberg introduced Corso to the rest of his inner circle. In their first meeting at the Pony Stable, Corso showed Ginsberg a poem about a woman who lived across the street from him and sunbathed naked in the window. Amazingly, the woman happened to be Ginsberg's girlfriend that he was living with during one of his forays into heterosexuality. Ginsberg took Corso over to their apartment. There the woman proposed sex with Corso, who was still very young and fled in fear. Ginsberg introduced Corso to Kerouac and Burroughs and they began to travel together. Ginsberg and Corso remained lifelong friends and collaborators.
Shortly after this period in Ginsberg's life, he became romantically involved with Elise Nada Cowen after meeting her through Alex Greer, a philosophy professor at Barnard College whom she had dated for a while during the burgeoning Beat generation's period of development. As a Barnard student, Elise Cowen extensively read the poetry of Ezra Pound and T. S. Eliot, when she met Joyce Johnson and Leo Skir, among other Beat players. As Cowen had felt a strong attraction to darker poetry most of the time, Beat poetry seemed to provide an allure to what suggests a shadowy side of her persona. While at Barnard, Cowen earned the nickname "Beat Alice" as she had joined a small group of anti-establishment artists and visionaries known to outsiders as beatniks, and one of her first acquaintances at the college was the beat poet Joyce Johnson who later portrayed Cowen in her books, including "Minor Characters" and "Come and Join the Dance", which expressed the two women's experiences in the Barnard and Columbia Beat community. Through his association with Elise Cowen, Ginsberg discovered that they shared a mutual friend, Carl Solomon, to whom he later dedicated his most famous poem "Howl." This poem is considered an autobiography of Ginsberg up to 1955, and a brief history of the Beat Generation through its references to his relationship to other Beat artists of that time.
The "Blake vision". In 1948, in an apartment in East Harlem, Ginsberg experienced an auditory hallucination while masturbating and reading the poetry of William Blake, which he later referred to as his "Blake vision". Ginsberg claimed to have heard the voice of God—also described as the "voice of the Ancient of Days"—or of Blake himself reading "Ah! Sun-flower", "The Sick Rose" and "The Little Girl Lost". The experience lasted several days, with him believing that he had witnessed the interconnectedness of the universe; Ginsberg recounted that after looking at latticework on the fire escape of the apartment and then at the sky, he intuited that one had been crafted by human beings, while the other had been crafted by itself. He explained that this hallucination was not inspired by drug use, but said he sought to recapture the feeling of interconnectedness later with various drugs. Later, in 1955, he referenced his "Blake vision" in his poem "Sunflower Sutra", saying "—I rushed up enchanted—it was my first sunflower, memories of Blake—my visions—".
San Francisco Renaissance. Ginsberg moved to San Francisco during the 1950s. Before "Howl and Other Poems" was published in 1956 by City Lights, he worked as a market researcher. In 1954, in San Francisco, Ginsberg met Peter Orlovsky (1933–2010), with whom he fell in love and who remained his lifelong partner. Selections from their correspondence have been published. Also in San Francisco, Ginsberg met members of the San Francisco Renaissance (James Broughton, Robert Duncan, Madeline Gleason and Kenneth Rexroth) and other poets who would later be associated with the Beat Generation in a broader sense. Ginsberg's mentor William Carlos Williams wrote an introductory letter to San Francisco Renaissance figurehead Kenneth Rexroth, who then introduced Ginsberg into the San Francisco poetry scene. There, Ginsberg also met three budding poets and Zen enthusiasts who had become friends at Reed College: Gary Snyder, Philip Whalen, and Lew Welch. In 1959, along with poets John Kelly, Bob Kaufman, A. D. Winans, and William Margolis, Ginsberg was one of the founders of the "Beatitude" poetry magazine.
Wally Hedrick—a painter and co-founder of the Six Gallery—approached Ginsberg in mid-1955 and asked him to organize a poetry reading at the Six Gallery. At first, Ginsberg refused, but once he had written a rough draft of "Howl," he changed his "fucking mind," as he put it. Ginsberg advertised the event as "Six Poets at the Six Gallery." One of the most important events in Beat mythos, known simply as "The Six Gallery reading" took place on October 7, 1955. The event, in essence, brought together the East and West Coast factions of the Beat Generation. Of more personal significance to Ginsberg, the reading that night included the first public presentation of "Howl," a poem that brought worldwide fame to Ginsberg and to many of the poets associated with him. An account of that night can be found in Kerouac's novel "The Dharma Bums", describing how change was collected from audience members to buy jugs of wine, and Ginsberg reading passionately, drunken, with arms outstretched. Ginsberg's principal work, "Howl," is well known for its opening line: "I saw the best minds of my generation destroyed by madness, starving hysterical naked [...]." "Howl" was considered scandalous at the time of its publication, because of the rawness of its language. Shortly after its 1956 publication by San Francisco's City Lights Bookstore, it was banned for obscenity. The ban became a cause célèbre among defenders of the First Amendment, and was later lifted, after Judge Clayton W. Horn declared the poem to possess redeeming artistic value. Ginsberg and Shig Murao, the City Lights manager who was jailed for selling "Howl," became lifelong friends.
Biographical references in "Howl". Ginsberg claimed at one point that all of his work was an extended biography (like Kerouac's "Duluoz Legend"). "Howl" is not only a biography of Ginsberg's experiences before 1955, but also a history of the Beat Generation. Ginsberg also later claimed that at the core of "Howl" were his unresolved emotions about his schizophrenic mother. Though "Kaddish" deals more explicitly with his mother, "Howl" in many ways is driven by the same emotions. "Howl" chronicles the development of many important friendships throughout Ginsberg's life. He begins the poem with "I saw the best minds of my generation destroyed by madness", which sets the stage for Ginsberg to describe Cassady and Solomon, immortalizing them into American literature. This madness was the "angry fix" that society needed to function—madness was its disease. In the poem, Ginsberg focused on "Carl Solomon! I'm with you in Rockland", and, thus, turned Solomon into an archetypal figure searching for freedom from his "straightjacket". Though references in most of his poetry reveal much about his biography, his relationship to other members of the Beat Generation, and his own political views, "Howl," his most famous poem, is still perhaps the best place to start.
To Paris and the "Beat Hotel", Tangier and India. In 1957, Ginsberg surprised the literary world by abandoning San Francisco. After a spell in Morocco, he and Peter Orlovsky joined Gregory Corso in Paris. Corso introduced them to a shabby lodging house above a bar at 9 rue Gît-le-Cœur that was to become known as the Beat Hotel. They were soon joined by Burroughs and others. It was a productive, creative time for all of them. There, Ginsberg began his epic poem "Kaddish", Corso composed "Bomb" and "Marriage", and Burroughs (with help from Ginsberg and Corso) put together "Naked Lunch" from previous writings. This period was documented by the photographer Harold Chapman, who moved in at about the same time, and took pictures constantly of the residents of the "hotel" until it closed in 1963. During 1962–1963, Ginsberg and Orlovsky travelled extensively across India, living half a year at a time in Calcutta (now Kolkata) and Benares (Varanasi). On his road to India he stayed two months in Athens ( August 29, 1961 – October 31, 1961) where he visited various sites such as Delphi, Mycines, Crete, and then continued his journey to Israel, Kenya and finally India. Also during this time, he formed friendships with some of the prominent young Bengali poets of the time including Shakti Chattopadhyay and Sunil Gangopadhyay. Ginsberg had several political connections in India; most notably Pupul Jayakar who helped him extend his stay in India when the authorities were eager to expel him.
England and the International Poetry Incarnation. In May 1965, Ginsberg arrived in London, and offered to read anywhere for free. Shortly after his arrival, he gave a reading at Better Books, which was described by Jeff Nuttall as "the first healing wind on a very parched collective mind." Tom McGrath wrote: "This could well turn out to have been a very significant moment in the history of England—or at least in the history of English Poetry." Soon after the bookshop reading, plans were hatched for the International Poetry Incarnation, which was held at the Royal Albert Hall in London on June 11, 1965. The event attracted an audience of 7,000, who heard readings and live and tape performances by a wide variety of figures, including Ginsberg, Adrian Mitchell, Alexander Trocchi, Harry Fainlight, Anselm Hollo, Christopher Logue, George MacBeth, Gregory Corso, Lawrence Ferlinghetti, Michael Horovitz, Simon Vinkenoog, Spike Hawkins and Tom McGrath. The event was organized by Ginsberg's friend, the filmmaker Barbara Rubin.
Peter Whitehead documented the event on film and released it as "Wholly Communion". A book featuring images from the film and some of the poems that were performed was also published under the same title by Lorrimer in the UK and Grove Press in US. Continuing literary activity. Though the term "Beat" is most accurately applied to Ginsberg and his closest friends (Corso, Orlovsky, Kerouac, Burroughs, etc.), the term "Beat Generation" has become associated with many of the other poets Ginsberg met and became friends with in the late 1950s and early 1960s. A key feature of this term seems to be a friendship with Ginsberg. Friendship with Kerouac or Burroughs might also apply, but both writers later strove to disassociate themselves from the name "Beat Generation." Part of their dissatisfaction with the term came from the mistaken identification of Ginsberg as the leader. Ginsberg never claimed to be the leader of a movement. He claimed that many of the writers with whom he had become friends in this period shared many of the same intentions and themes. Some of these friends include: David Amram, Bob Kaufman; Diane di Prima; Jim Cohn; poets associated with the Black Mountain College such as Charles Olson, Robert Creeley, and Denise Levertov; poets associated with the New York School such as Frank O'Hara and Kenneth Koch. LeRoi Jones before he became Amiri Baraka, who, after reading "Howl", wrote a letter to Ginsberg on a sheet of toilet paper. Baraka's independent publishing house Totem Press published Ginsberg's early work. Through a party organized by Baraka, Ginsberg was introduced to Langston Hughes while Ornette Coleman played saxophone.
Later in his life, Ginsberg formed a bridge between the beat movement of the 1950s and the hippies of the 1960s, befriending, among others, Timothy Leary, Ken Kesey, Hunter S. Thompson, and Bob Dylan. Ginsberg gave his last public reading at Booksmith, a bookstore in the Haight-Ashbury neighborhood of San Francisco, a few months before his death. In 1993, Ginsberg visited the University of Maine at Orono to pay homage to the 90-year-old great Carl Rakosi. Buddhism and Krishna. In 1950, Kerouac began studying Buddhism and shared what he learned from Dwight Goddard's "Buddhist Bible" with Ginsberg. Ginsberg first heard about the Four Noble Truths and such sutras as the Diamond Sutra at this time. Ginsberg's endorsement helped establish the Krishna movement within New York's bohemian culture. Ginsberg's spiritual journey began early on with his spontaneous visions, and continued with an early trip to India with Gary Snyder. Snyder had previously spent time in Kyoto to study at the First Zen Institute at Daitoku-ji Monastery. At one point, Snyder chanted the Prajnaparamita, which in Ginsberg's words "blew my mind." His interest piqued, Ginsberg traveled to meet the Dalai Lama as well as the Karmapa at Rumtek Monastery. Continuing on his journey, Ginsberg met Dudjom Rinpoche in Kalimpong, who taught him: "If you see something horrible, don't cling to it, and if you see something beautiful, don't cling to it."
After returning to the United States, a chance encounter on a New York City street with Chögyam Trungpa Rinpoche (they both tried to catch the same cab), a Kagyu and Nyingma Tibetan Buddhist master, led to Trungpa becoming his friend and lifelong teacher. Ginsberg helped Trungpa and New York poet Anne Waldman in founding the Jack Kerouac School of Disembodied Poetics at Naropa University in Boulder, Colorado. Ginsberg was also involved with Krishnaism. He had started incorporating chanting the Hare Krishna mantra into his religious practice in the mid-1960s. After learning that A. C. Bhaktivedanta Swami Prabhupada, the founder of the Hare Krishna movement in the Western world had rented a store front in New York, he befriended him, visiting him often and suggesting publishers for his books, and a fruitful relationship began. This relationship is documented by Satsvarupa dasa Goswami in his biographical account "Srila Prabhupada Lilamrta". Ginsberg donated money, materials, and his reputation to help the Swami establish the first temple, and toured with him to promote his cause.
Despite disagreeing with many of Bhaktivedanta Swami's required prohibitions, Ginsberg often sang the Hare Krishna mantra publicly as part of his philosophy and declared that it brought a state of ecstasy. He was glad that Bhaktivedanta Swami, an authentic swami from India, was now trying to spread the chanting in America. Along with other counterculture ideologists like Timothy Leary, Gary Snyder, and Alan Watts, Ginsberg hoped to incorporate Bhaktivedanta Swami and his chanting into the hippie movement, and agreed to take part in the Mantra-Rock Dance concert and to introduce the swami to the Haight-Ashbury hippie community. On January 17, 1967, Ginsberg helped plan and organize a reception for Bhaktivedanta Swami at San Francisco International Airport, where fifty to a hundred hippies greeted the Swami, chanting Hare Krishna in the airport lounge with flowers in hands. To further support and promote Bhaktivedanta Swami's message and chanting in San Francisco, Allen Ginsberg agreed to attend the Mantra-Rock Dance, a musical event 1967 held at the Avalon Ballroom by the San Francisco Hare Krishna temple. It featured some leading rock bands of the time: Big Brother and the Holding Company with Janis Joplin, the Grateful Dead, and Moby Grape, who performed there along with the Hare Krishna founder Bhaktivedanta Swami and donated proceeds to the Krishna temple. Ginsberg introduced Bhaktivedanta Swami to some three thousand hippies in the audience and led the chanting of the Hare Krishna mantra.
Music and chanting were both important parts of Ginsberg's live delivery during poetry readings. He often accompanied himself on a harmonium, and was often accompanied by a guitarist. It is believed that the Hindi and Buddhist poet Nagarjun had introduced Ginsberg to the harmonium in Banaras. According to Malay Roy Choudhury, Ginsberg refined his practice while learning from his relatives, including his cousin Savitri Banerjee. When Ginsberg asked if he could sing a song in praise of Lord Krishna on William F. Buckley, Jr.'s TV show "Firing Line" on September 3, 1968, Buckley acceded and the poet chanted slowly as he played dolefully on a harmonium. According to Richard Brookhiser, an associate of Buckley's, the host commented that it was "the most unharried Krishna I've ever heard." At the 1967 Human Be-In in San Francisco's Golden Gate Park, the 1968 Democratic National Convention in Chicago, and the 1970 Black Panther rally at Yale campus Allen chanted "Om" repeatedly over a sound system for hours on end.
Ginsberg further brought mantras into the world of rock and roll when he recited the Heart Sutra in the song "Ghetto Defendant". The song appears on the 1982 album "Combat Rock" by British first wave punk band The Clash. Ginsberg came in touch with the Hungryalist poets of Bengal, especially Malay Roy Choudhury, who introduced Ginsberg to the three fish with one head of Indian emperor Jalaluddin Mohammad Akbar. The three fish symbolised coexistence of all thought, philosophy, and religion. In spite of Ginsberg's attraction to Eastern religions, the journalist Jane Kramer argues that he, like Whitman, adhered to an "American brand of mysticism" that was "rooted in humanism and in a romantic and visionary ideal of harmony among men." The Allen Ginsberg Estate and Jewel Heart International partnered to present "Transforming Minds: Kyabje Gelek Rimpoche and Friends", a gallery and online exhibition of images of Gelek Rimpoche by Allen Ginsberg, a student with whom he had an "indissoluble bond," in 2021 at Tibet House US in New York City. Fifty negatives from Ginsberg's Stanford University photo archive celebrated "the unique relationship between Allen and Rimpoche." The selection of never-before presented images, featuring great Tibetan masters including the Dalai Lama, Tibetologists, and students were "guided by Allen's extensive notes on the contact sheets and images he'd circled with the intention to print."
Illness and death. In 1960, he was treated for a tropical disease, and it is speculated that he contracted hepatitis from an unsterilized needle administered by a doctor, which played a role in his death 37 years later. Ginsberg was a lifelong smoker, and though he tried to quit for health and religious reasons, his busy schedule in later life made it difficult, and he always returned to smoking. In the 1970s, Ginsberg had two minor strokes which were first diagnosed as Bell's palsy, which gave him significant paralysis and stroke-like drooping of the muscles in one side of his face. Later in life, he also had constant minor ailments such as high blood pressure. Many of these symptoms were related to stress, but he never slowed down his schedule. Ginsberg won a 1974 National Book Award for ' (split with Adrienne Rich, '). In 1986, Ginsberg was awarded the Golden Wreath by the Struga Poetry Evenings International Festival in Macedonia, the second American poet to be so awarded since W. H. Auden. At Struga, Ginsberg met with the other Golden Wreath winners, Bulat Okudzhava and Andrei Voznesensky.
In 1989, Ginsberg appeared in Rosa von Praunheim's award-winning film "Silence = Death" about the fight of gay artists in New York City for AIDS-education and the rights of HIV infected people. In 1993, the French Minister of Culture appointed Ginsberg a Chevalier des Arts et des Lettres. Ginsberg continued to help his friends as much as he could: he gave money to Herbert Huncke out of his own pocket, regularly supplied neighbor Arthur Russell with an extension cord to power his home recording setup, and housed a broke, drug-addicted Harry Smith. With the exception of a special guest appearance at the NYU Poetry Slam on February 20, 1997, Ginsberg gave what is thought to be his last reading at The Booksmith in San Francisco on December 16, 1996. After returning home from the hospital for the last time, where he had been unsuccessfully treated for congestive heart failure, Ginsberg continued making phone calls to say goodbye to nearly everyone in his address book. Some of the phone calls were sad and interrupted by crying, and others were joyous and optimistic. Ginsberg continued to write through his final illness, with his last poem, "Things I'll Not Do (Nostalgias)", written on March 30.
He died on April 5, 1997, surrounded by family and friends in his East Village loft in Manhattan, succumbing to liver cancer via complications of hepatitis at the age of 70. Gregory Corso, Roy Lichtenstein, Patti Smith and others came by to pay their respects. He was cremated, and his ashes were buried in his family plot in Gomel Chesed Cemetery in Newark. He was survived by Orlovsky. In 1998, various writers, including Catfish McDaris, read at a gathering at Ginsberg's farm to honor Allen and the Beats. "Good Will Hunting" (released in December 1997) was dedicated to Ginsberg, as well as Burroughs, who died four months later. Social and political activism. Free speech. Ginsberg's willingness to talk about taboo subjects made him a controversial figure during the conservative 1950s, and a significant figure in the 1960s. In the mid-1950s, no reputable publishing company would even consider publishing "Howl". At the time, such "sex talk" employed in "Howl" was considered by some to be vulgar or even a form of pornography, and could be prosecuted under law.
In the mid-1950s, no reputable publishing company would even consider publishing "Howl". At the time, such "sex talk" employed in "Howl" was considered by some to be vulgar or even a form of pornography, and could be prosecuted under law. Ginsberg used phrases such as "cocksucker", "fucked in the ass", and "cunt" as part of the poem's depiction of different aspects of American culture. Numerous books that discussed sex were banned at the time, including "Lady Chatterley's Lover". The sex that Ginsberg described did not portray the sex between heterosexual married couples, or even longtime lovers. Instead, Ginsberg portrayed casual sex. For example, in "Howl", Ginsberg praises the man "who sweetened the snatches of a million girls." Ginsberg used gritty descriptions and explicit sexual language, pointing out the man "who lounged hungry and lonesome through Houston seeking jazz or sex or soup." In his poetry, Ginsberg also discussed the then-taboo topic of homosexuality. The explicit sexual language that filled "Howl" eventually led to an important trial on First Amendment issues.
The explicit sexual language that filled "Howl" eventually led to an important trial on First Amendment issues. Ginsberg's publisher was brought up on charges for publishing pornography, and the outcome led to a judge going on record dismissing charges, because the poem carried "redeeming social importance," thus setting an important legal precedent. Ginsberg continued to broach controversial subjects throughout the 1970s, 1980s, and 1990s. From 1970 to 1996, Ginsberg had a long-term affiliation with PEN American Center with efforts to defend free expression. When explaining how he approached controversial topics, he often pointed to Herbert Huncke: he said that when he first got to know Huncke in the 1940s, Ginsberg saw that he was sick from his heroin addiction, but at the time heroin was a taboo subject and Huncke was left with nowhere to go for help.
Role in Vietnam War protests. Ginsberg was a signer of the anti-war manifesto "A Call to Resist Illegitimate Authority", circulated among draft resistors in 1967 by members of the radical intellectual collective RESIST. Other signers and RESIST members included Mitchell Goodman, Henry Braun, Denise Levertov, Noam Chomsky, William Sloane Coffin, Dwight Macdonald, Robert Lowell, and Norman Mailer. In 1968, Ginsberg signed the "Writers and Editors War Tax Protest" pledge, vowing to refuse tax payments in protest against the Vietnam War, and later became a sponsor of the War Tax Resistance project, which practiced and advocated tax resistance as a form of anti-war protest. He was present the night of the Tompkins Square Park riot (1988) and provided an eyewitness account to "The New York Times". Relationship to communism. Ginsberg talked openly about his connections with communism and his admiration for past communist heroes and the labor movement at a time when the Red Scare and McCarthyism were still raging. He admired Fidel Castro and many other Marxist figures from the 20th century. Ginsberg was a member of the Fair Play for Cuba Committee. In "America" (1956), Ginsberg writes: "America, I used to be a communist when I was a kid I'm not sorry". Biographer Jonah Raskin has claimed that, despite his often stark opposition to communist orthodoxy, Ginsberg held "his own idiosyncratic version of communism." On the other hand, when Donald Manes, a New York City politician, publicly accused Ginsberg of being a member of the Communist Party, Ginsberg objected: "I am not, as a matter of fact, a member of the Communist party, nor am I dedicated to the overthrow of the U.S. government or any government by violence ... I must say that I see little difference between the armed and violent governments both Communist and Capitalist that I have observed".
Ginsberg travelled to several communist countries to promote free speech. He claimed that communist countries, such as China, welcomed him because they thought he was an enemy of capitalism, but often turned against him when they saw him as a troublemaker. For example, in 1965 Ginsberg was deported from Cuba for publicly protesting the persecution of homosexuals. The Cubans sent him to Czechoslovakia, where one week after being named the "Král majálesu" ("King of May", a students' festivity, celebrating spring and student life), Ginsberg was arrested for alleged drug use and public drunkenness, and the security agency StB confiscated several of his writings, which they considered to be lewd and morally dangerous. Ginsberg was then deported from Czechoslovakia on May 7, 1965, by order of the StB. Václav Havel points to Ginsberg as an important inspiration. Gay rights. One contribution that is often considered his most significant and most controversial was his openness about homosexuality. Ginsberg was an early proponent of freedom for gay people. In 1943, he discovered within himself "mountains of homosexuality." He expressed this desire openly and graphically in his poetry. He also struck a note for gay marriage by listing Peter Orlovsky, his lifelong companion, as his spouse in his "Who's Who" entry. Subsequent gay writers saw his frank talk about homosexuality as an opening to speak more openly and honestly about something often before only hinted at or spoken of in metaphor.
In writing about sexuality in graphic detail and in his frequent use of language seen as indecent, he challenged—and ultimately changed—obscenity laws. He was a staunch supporter of others whose expression challenged obscenity laws (William S. Burroughs and Lenny Bruce, for example). NAMBLA membership. Ginsberg was a supporter and member of the North American Man/Boy Love Association (NAMBLA), a pedophilia and pederasty advocacy organization in the United States that works to abolish age of consent laws and legalize sexual relations between adults and children. Saying that he joined the organization "in defense of free speech", Ginsberg stated: "Attacks on NAMBLA stink of politics, witchhunting for profit, humorlessness, vanity, anger and ignorance ... I'm a member of NAMBLA because I love boys too—everybody does, who has a little humanity". In 1994, Ginsberg appeared in a documentary on NAMBLA called "" (playing on the gay male slang term 'chickenhawk'), in which he read a "graphic ode to youth". He read his poem "Sweet Boy, Gimme Yr Ass" from the book "Mind Breaths".
In her 2002 book "Heartbreak", Andrea Dworkin claimed Ginsberg had ulterior motives for allying with NAMBLA: In reference to his onetime friend Dworkin, Ginsberg stated: Recreational drugs. Ginsberg talked often about drug use. He organized the New York City chapter of LeMar (Legalize Marijuana). Throughout the 1960s he took an active role in the demystification of LSD, and, with Timothy Leary, worked to promote its common use. He remained for many decades an advocate of marijuana legalization, and, at the same time, warned his audiences against the hazards of tobacco in his "Put Down Your Cigarette Rag (Don't Smoke):" "Don't Smoke Don't Smoke Nicotine Nicotine No / No don't smoke the official Dope Smoke Dope Dope." CIA drug trafficking.
Work. Most of Ginsberg's very early poetry was written in formal rhyme and meter like that of his father, and of his idol William Blake. His admiration for the writing of Jack Kerouac inspired him to take poetry more seriously. In 1955, upon the advice of a psychiatrist, Ginsberg dropped out of the working world to devote his entire life to poetry. Soon after, he wrote "Howl", the poem that brought him and his Beat Generation contemporaries to national attention and allowed him to live as a professional poet for the rest of his life. Later in life, Ginsberg entered academia, teaching poetry as Distinguished Professor of English at Brooklyn College from 1986 until his death. Inspiration from friends. Ginsberg claimed throughout his life that his biggest inspiration was Kerouac's concept of "spontaneous prose." He believed literature should come from the soul without conscious restrictions. Ginsberg was much more prone to revise than Kerouac. For example, when Kerouac saw the first draft of "Howl", he disliked the fact that Ginsberg had made editorial changes in pencil (transposing "negro" and "angry" in the first line, for example). Kerouac only wrote out his concepts of spontaneous prose at Ginsberg's insistence because Ginsberg wanted to learn how to apply the technique to his poetry.
The inspiration for "Howl" was Ginsberg's friend, Carl Solomon, and "Howl" is dedicated to him. Solomon was a Dada and Surrealism enthusiast (he introduced Ginsberg to Artaud) who had bouts of clinical depression. Solomon wanted to commit suicide, but he thought a form of suicide appropriate to dadaism would be to go to a mental institution and demand a lobotomy. The institution refused, giving him many forms of therapy, including electroshock therapy. Much of the final section of the first part of "Howl" is a description of this. Ginsberg used Solomon as an example of all those ground down by the machine of "Moloch." Moloch, to whom the second section is addressed, is a Levantine god to whom children were sacrificed. Ginsberg may have gotten the name from the Kenneth Rexroth poem "Thou Shalt Not Kill," a poem about the death of one of Ginsberg's heroes, Dylan Thomas. Moloch is mentioned a few times in the Torah and references to Ginsberg's Jewish background are frequent in his work. Ginsberg said the image of Moloch was inspired by peyote visions he had of the Francis Drake Hotel in San Francisco which appeared to him as a skull; he took it as a symbol of the city (not specifically San Francisco, but all cities). Ginsberg later acknowledged in various publications and interviews that behind the visions of the Francis Drake Hotel were memories of the Moloch of Fritz Lang's film "Metropolis" (1927) and of the woodcut novels of Lynd Ward. Moloch has subsequently been interpreted as any system of control, including the conformist society of post-World War II America, focused on material gain, which Ginsberg frequently blamed for the destruction of all those outside of societal norms.
He also made sure to emphasize that Moloch is a part of humanity in multiple aspects, in that the decision to "defy" socially created systems of control—and therefore go against Moloch—is a form of self-destruction. Many of the characters Ginsberg references in "Howl", such as Neal Cassady and Herbert Huncke, destroyed themselves through excessive substance abuse or a generally wild lifestyle. The personal aspects of "Howl" are perhaps as important as the political aspects. Carl Solomon, the prime example of a "best mind" destroyed by defying society, is associated with Ginsberg's schizophrenic mother: the line "with mother finally fucked" comes after a long section about Carl Solomon, and in Part III, Ginsberg says: "I'm with you in Rockland where you imitate the shade of my mother." Ginsberg later admitted that the drive to write "Howl" was fueled by sympathy for his ailing mother, an issue which he was not yet ready to deal with directly. He dealt with it directly with 1959's "Kaddish", which had its first public reading at a Catholic Worker Friday Night meeting, possibly due to its associations with Thomas Merton.
Inspiration from mentors and idols. Ginsberg's poetry was strongly influenced by Modernism (most importantly the American style of Modernism pioneered by William Carlos Williams), Romanticism (specifically William Blake and John Keats), the beat and cadence of jazz (specifically that of bop musicians such as Charlie Parker), and his Kagyu Buddhist practice and Jewish background. He considered himself to have inherited the visionary poetic mantle handed down from the English poet and artist William Blake, the American poet Walt Whitman and the Spanish poet Federico García Lorca. The power of Ginsberg's verse, its searching, probing focus, its long and lilting lines, as well as its New World exuberance, all echo the continuity of inspiration that he claimed. He corresponded with William Carlos Williams, who was then in the middle of writing his epic poem "Paterson" about the industrial city near his home. After attending a reading by Williams, Ginsberg sent the older poet several of his poems and wrote an introductory letter. Most of these early poems were rhymed and metered and included archaic pronouns like "thee." Williams disliked the poems and told Ginsberg, "In this mode perfection is basic, and these poems are not perfect."
Though he disliked these early poems, Williams loved the exuberance in Ginsberg's letter. He included the letter in a later part of "Paterson". He encouraged Ginsberg not to emulate the old masters, but to speak with his own voice and the voice of the common American. From Williams, Ginsberg learned to focus on strong visual images, in line with Williams' own motto "No ideas but in things." Studying Williams' style led to a tremendous shift from the early formalist work to a loose, colloquial free verse style. Early breakthrough poems include "Bricklayer's Lunch Hour" and "Dream Record". Carl Solomon introduced Ginsberg to the work of Antonin Artaud ("To Have Done with the Judgement of God" and "Van Gogh: The Man Suicided by Society"), and Jean Genet ("Our Lady of the Flowers"). Philip Lamantia introduced him to other Surrealists and Surrealism continued to be an influence (for example, sections of "Kaddish" were inspired by André Breton's "Free Union"). Ginsberg claimed that the anaphoric repetition of "Howl" and other poems was inspired by Christopher Smart in such poems as "Jubilate Agno". Ginsberg also claimed other more traditional influences, such as: Franz Kafka, Herman Melville, Fyodor Dostoevsky, Edgar Allan Poe, and Emily Dickinson.
Ginsberg also made an intense study of haiku and the paintings of Paul Cézanne, from which he adapted a concept important to his work, which he called the "Eyeball Kick". He noticed in viewing Cézanne's paintings that when the eye moved from one color to a contrasting color, the eye would spasm, or "kick." Likewise, he discovered that the contrast of two seeming opposites was a common feature in haiku. Ginsberg used this technique in his poetry, putting together two starkly dissimilar images: something weak with something strong, an artifact of high culture with an artifact of low culture, something holy with something unholy. The example Ginsberg most often used was "hydrogen jukebox" (which later became the title of a song cycle composed by Philip Glass with lyrics drawn from Ginsberg's poems). Another example is Ginsberg's observation on Bob Dylan during Dylan's hectic and intense 1966 electric-guitar tour, fueled by a cocktail of amphetamines, opiates, alcohol, and psychedelics, as a "Dexedrine Clown". The phrases "eyeball kick" and "hydrogen jukebox" both show up in "Howl", as well as a direct quote from Cézanne: "Pater Omnipotens Aeterna Deus".
Inspiration from music. Allen Ginsberg also found inspiration in music. He frequently included music in his poetry, invariably composing his tunes on an old Indian harmonium, which he often played during his readings. He wrote and recorded music to accompany William Blake's "Songs of Innocence" and "Songs of Experience". He also recorded a handful of other albums. To create music for "Howl" and "Wichita Vortex Sutra", he worked with the minimalist composer, Philip Glass. Ginsberg worked with, drew inspiration from, and inspired artists such as Bob Dylan, The Clash, Patti Smith, Phil Ochs, and The Fugs. He worked with Dylan on various projects and maintained a friendship with him over many years. In 1981, Ginsberg recorded a song called "Birdbrain." He was backed by the Gluons, and the track was released as a single. In 1996, he recorded a song co-written with Paul McCartney and Philip Glass, "The Ballad of the Skeletons", which reached number 8 on the Triple J Hottest 100 for that year. Style and technique. From the study of his idols and mentors and the inspiration of his friends—not to mention his own experiments—Ginsberg developed an individualistic style that's easily identified as Ginsbergian. Ginsberg stated that Whitman's long line was a dynamic technique few other poets had ventured to develop further, and Whitman is also often compared to Ginsberg because their poetry sexualized aspects of the male form.
Many of Ginsberg's early long line experiments contain some sort of anaphora, repetition of a "fixed base" (for example "who" in "Howl", "America" in "America") and this has become a recognizable feature of Ginsberg's style. He said later this was a crutch because he lacked confidence; he did not yet trust "free flight." In the 1960s, after employing it in some sections of "Kaddish" ("caw" for example) he, for the most part, abandoned the anaphoric form. 'Latter-Day Beat' Bob Dylan is known for using anaphora, as in 'Tangled Up in Blue' where the phrase, returned to at the end of every verse, takes the place of a chorus. Several of his earlier experiments with methods for formatting poems as a whole became regular aspects of his style in later poems. In the original draft of "Howl", each line is in a "stepped triadic" format reminiscent of William Carlos Williams. He abandoned the "stepped triadic" when he developed his long line although the stepped lines showed up later, most significantly in the travelogues of "The Fall of America". "Howl" and "Kaddish", arguably his two most important poems, are both organized as an inverted pyramid, with larger sections leading to smaller sections. In "America", he also experimented with a mix of longer and shorter lines.
Ginsberg's mature style made use of many specific, highly developed techniques, which he expressed in the "poetic slogans" he used in his Naropa teaching. Prominent among these was the inclusion of his unedited mental associations so as to reveal the mind at work ("First thought, best thought." "Mind is shapely, thought is shapely.") He preferred expression through carefully observed physical details rather than abstract statements ("Show, don't tell." "No ideas but in things.") In these he carried on and developed traditions of modernism in writing that are also found in Kerouac and Whitman. In "Howl" and in his other poetry, Ginsberg drew inspiration from the epic, free verse style of the 19th-century American poet Walt Whitman. Both wrote passionately about the promise (and betrayal) of American democracy, the central importance of erotic experience, and the spiritual quest for the truth of everyday existence. J. D.
Both wrote passionately about the promise (and betrayal) of American democracy, the central importance of erotic experience, and the spiritual quest for the truth of everyday existence. J. D. His work is finally a history of our era's psyche, with all its contradictory urges." McClatchy's barbed eulogies define the essential difference between Ginsberg ("a beat poet whose writing was [...] journalism raised by combining the recycling genius with a generous mimic-empathy, to strike audience-accessible chords; always lyrical and sometimes truly poetic") and Kerouac ("a poet of singular brilliance, the brightest luminary of a 'beat generation' he came to symbolise in popular culture [...] [though] in reality he far surpassed his contemporaries [...] Kerouac is an originating genius, exploring then answering—like Rimbaud a century earlier, by necessity more than by choice—the demands of authentic self-expression as applied to the evolving quicksilver mind of America's only literary virtuoso [...]").
Honors. His collection "The Fall of America" shared the annual U.S. National Book Award for Poetry in 1974. Ginsberg won a 1974 National Book Award for ' (split with Adrienne Rich, '). In 1979, he received the National Arts Club gold medal and was inducted into the American Academy and Institute of Arts and Letters. In 1986, Ginsberg was awarded the Golden Wreath by the Struga Poetry Evenings International Festival in Macedonia, the second American poet to be so awarded since W. H. Auden. At Struga, Ginsberg met with the other Golden Wreath winners, Bulat Okudzhava and Andrei Voznesensky. In 1989, Ginsberg appeared in Rosa von Praunheim's award-winning film "Silence = Death" about the fight of gay artists in New York City for AIDS-education and the rights of HIV infected people. In 1993, the French Minister of Culture appointed Ginsberg a Chevalier des Arts et des Lettres. Ginsberg was a Pulitzer Prize finalist in 1995 for his book "Cosmopolitan Greetings: Poems 1986–1992". In 1993, he received a John Jay Award posthumously from Columbia. In 2014, Ginsberg was one of the inaugural honorees in the Rainbow Honor Walk, a walk of fame in San Francisco's Castro neighborhood noting LGBTQ people who have "made significant contributions in their fields."
Algebraically closed field In mathematics, a field is algebraically closed if every non-constant polynomial in (the univariate polynomial ring with coefficients in ) has a root in . In other words, a field is algebraically closed if the fundamental theorem of algebra holds for it. Every field formula_1 is contained in an algebraically closed field formula_2 and the roots in formula_3 of the polynomials with coefficients in formula_1 form an algebraically closed field called an algebraic closure of formula_5 Given two algebraic closures of formula_1 there are isomorphisms between them that fix the elements of formula_5 Algebraically closed fields appear in the following chain of class inclusions: Examples. As an example, the field of real numbers is not algebraically closed, because the polynomial equation formula_8 has no solution in real numbers, even though all its coefficients (1 and 0) are real. The same argument proves that no subfield of the real field is algebraically closed; in particular, the field of rational numbers is not algebraically closed. By contrast, the fundamental theorem of algebra states that the field of complex numbers is algebraically closed. Another example of an algebraically closed field is the field of (complex) algebraic numbers.
No finite field "F" is algebraically closed, because if "a"1, "a"2, ..., "an" are the elements of "F", then the polynomial ("x" − "a"1)("x" − "a"2) ⋯ ("x" − "a""n") + 1 has no zero in "F". However, the union of all finite fields of a fixed characteristic "p" ("p" prime) is an algebraically closed field, which is, in fact, the algebraic closure of the field formula_9 with "p" elements. The field formula_10 of rational functions with complex coefficients is not closed; for example, the polynomial formula_11 has roots formula_12, which are not elements of formula_10. Equivalent properties. Given a field "F", the assertion ""F" is algebraically closed" is equivalent to other assertions: The only irreducible polynomials are those of degree one. The field "F" is algebraically closed if and only if the only irreducible polynomials in the polynomial ring "F"["x"] are those of degree one. The assertion "the polynomials of degree one are irreducible" is trivially true for any field. If "F" is algebraically closed and "p"("x") is an irreducible polynomial of "F"["x"], then it has some root "a" and therefore "p"("x") is a multiple of . Since "p"("x") is irreducible, this means that , for some . On the other hand, if "F" is not algebraically closed, then there is some non-constant polynomial "p"("x") in "F"["x"] without roots in "F". Let "q"("x") be some irreducible factor of "p"("x"). Since "p"("x") has no roots in "F", "q"("x") also has no roots in "F". Therefore, "q"("x") has degree greater than one, since every first degree polynomial has one root in "F".
Every polynomial is a product of first degree polynomials. The field "F" is algebraically closed if and only if every polynomial "p"("x") of degree "n" ≥ 1, with coefficients in "F", splits into linear factors. In other words, there are elements "k", "x"1, "x"2, ..., "xn" of the field "F" such that "p"("x") = "k"("x" − "x"1)("x" − "x"2) ⋯ ("x" − "xn"). If "F" has this property, then clearly every non-constant polynomial in "F"["x"] has some root in "F"; in other words, "F" is algebraically closed. On the other hand, that the property stated here holds for "F" if "F" is algebraically closed follows from the previous property together with the fact that, for any field "K", any polynomial in "K"["x"] can be written as a product of irreducible polynomials. Polynomials of prime degree have roots. If every polynomial over "F" of prime degree has a root in "F", then every non-constant polynomial has a root in "F". It follows that a field is algebraically closed if and only if every polynomial over "F" of prime degree has a root in "F".
The field has no proper algebraic extension. The field "F" is algebraically closed if and only if it has no proper algebraic extension. If "F" has no proper algebraic extension, let "p"("x") be some irreducible polynomial in "F"["x"]. Then the quotient of "F"["x"] modulo the ideal generated by "p"("x") is an algebraic extension of "F" whose degree is equal to the degree of "p"("x"). Since it is not a proper extension, its degree is 1 and therefore the degree of "p"("x") is 1. On the other hand, if "F" has some proper algebraic extension "K", then the minimal polynomial of an element in "K" \ "F" is irreducible and its degree is greater than 1. The field has no proper finite extension. The field "F" is algebraically closed if and only if it has no proper finite extension because if, within the previous proof, the term "algebraic extension" is replaced by the term "finite extension", then the proof is still valid. (Finite extensions are necessarily algebraic.) Every endomorphism of "Fn" has some eigenvector. The field "F" is algebraically closed if and only if, for each natural number "n", every linear map from "Fn" into itself has some eigenvector.
An endomorphism of "Fn" has an eigenvector if and only if its characteristic polynomial has some root. Therefore, when "F" is algebraically closed, every endomorphism of "Fn" has some eigenvector. On the other hand, if every endomorphism of "Fn" has an eigenvector, let "p"("x") be an element of "F"["x"]. Dividing by its leading coefficient, we get another polynomial "q"("x") which has roots if and only if "p"("x") has roots. But if , then "q"("x") is the characteristic polynomial of the "n×n" companion matrix Decomposition of rational expressions. The field "F" is algebraically closed if and only if every rational function in one variable "x", with coefficients in "F", can be written as the sum of a polynomial function with rational functions of the form "a"/("x" − "b")"n", where "n" is a natural number, and "a" and "b" are elements of "F". If "F" is algebraically closed then, since the irreducible polynomials in "F"["x"] are all of degree 1, the property stated above holds by the theorem on partial fraction decomposition.
On the other hand, suppose that the property stated above holds for the field "F". Let "p"("x") be an irreducible element in "F"["x"]. Then the rational function 1/"p" can be written as the sum of a polynomial function "q" with rational functions of the form "a"/("x" – "b")"n". Therefore, the rational expression can be written as a quotient of two polynomials in which the denominator is a product of first degree polynomials. Since "p"("x") is irreducible, it must divide this product and, therefore, it must also be a first degree polynomial. Relatively prime polynomials and roots. For any field "F", if two polynomials are relatively prime then they do not have a common root, for if was a common root, then "p"("x") and "q"("x") would both be multiples of and therefore they would not be relatively prime. The fields for which the reverse implication holds (that is, the fields such that whenever two polynomials have no common root then they are relatively prime) are precisely the algebraically closed fields. If the field "F" is algebraically closed, let "p"("x") and "q"("x") be two polynomials which are not relatively prime and let "r"("x") be their greatest common divisor. Then, since "r"("x") is not constant, it will have some root "a", which will be then a common root of "p"("x") and "q"("x").
If "F" is not algebraically closed, let "p"("x") be a polynomial whose degree is at least 1 without roots. Then "p"("x") and "p"("x") are not relatively prime, but they have no common roots (since none of them has roots). Other properties. If "F" is an algebraically closed field and "n" is a natural number, then "F" contains all "n"th roots of unity, because these are (by definition) the "n" (not necessarily distinct) zeroes of the polynomial "xn" − 1. A field extension that is contained in an extension generated by the roots of unity is a "cyclotomic extension", and the extension of a field generated by all roots of unity is sometimes called its "cyclotomic closure". Thus algebraically closed fields are cyclotomically closed. The converse is not true. Even assuming that every polynomial of the form "xn" − "a" splits into linear factors is not enough to assure that the field is algebraically closed. If a proposition which can be expressed in the language of first-order logic is true for an algebraically closed field, then it is true for every algebraically closed field with the same characteristic. Furthermore, if such a proposition is valid for an algebraically closed field with characteristic 0, then not only is it valid for all other algebraically closed fields with characteristic 0, but there is some natural number "N" such that the proposition is valid for every algebraically closed field with characteristic "p" when "p" > "N". Every field "F" has some extension which is algebraically closed. Such an extension is called an algebraically closed extension. Among all such extensions there is one and only one (up to isomorphism, but not unique isomorphism) which is an algebraic extension of "F"; it is called the algebraic closure of "F". The theory of algebraically closed fields has quantifier elimination.
Anatoly Karpov Anatoly Yevgenyevich Karpov (, ; born May 23, 1951) is a Russian and former Soviet chess grandmaster, former World Chess Champion, ⁣and politician. He was the 12th World Chess Champion from 1975 to 1985, a three-time FIDE World Champion (1993, 1996, 1998), twice World Chess champion as a member of the USSR team (1985, 1989), and a six-time winner of Chess Olympiads as a member of the USSR team (1972, 1974, 1980, 1982, 1986, 1988). The International Association of Chess Press awarded him nine Chess Oscars (1973–77, 1979, 1980, 1981, 1984). Karpov's chess tournament successes include over 160 first-place finishes. He had a peak Elo rating of 2780, and his 102 total months world number one is the third-longest of all time, behind Magnus Carlsen and Garry Kasparov. Karpov is also an elected Member of the State Duma in Russia. Since 2006, he has chaired the Commission for Ecological Safety and Environmental Protection of the Civic Chamber of the Russian Federation, and since 2007 he has been a member of the Public Council under the Ministry of Defence.
Early life. Karpov was born into a Russian family on May 23, 1951, in Zlatoust, in the Urals region of the former Soviet Union, and learned to play chess at the age of four. His early rise in chess was swift, as he became a candidate master by age 11. At 12, he was accepted into Mikhail Botvinnik's prestigious chess school, though Botvinnik made the following remark about the young Karpov: "The boy does not have a clue about chess, and there's no future at all for him in this profession." Karpov acknowledged that his understanding of chess theory was very confused at that time, and later wrote that the homework Botvinnik assigned greatly helped him, since it required that he consult chess books and work diligently. Karpov improved so quickly under Botvinnik's tutelage that he became the youngest Soviet master in history at the age of fifteen in 1966; this tied the record established by Boris Spassky in 1952. Career. Young master. Karpov finished first in his first international tournament, in Třinec, several months later, ahead of Viktor Kupreichik. In 1967, he won the annual Niemeyer Tournament in Groningen. Karpov won a gold medal for academic excellence in high school, and entered Moscow State University in 1968 to study mathematics. He later transferred to Leningrad State University, eventually graduating from there in economics. One reason for the transfer was to be closer to his coach, grandmaster Semyon Furman, who lived in Leningrad. In his writings, Karpov credits Furman as a major influence on his development as a world-class player.
In 1969, Karpov became the first Soviet player since Spassky (1955) to win the World Junior Championship, scoring an undefeated 10/11 in the final A group at Stockholm. This victory earned him the International Master title. In 1970, Karpov tied for fourth and fifth places with Pal Benko at an international tournament in Caracas, Venezuela, and earned the international grandmaster title. FIDE awarded him the title during its 41st congress, held during the Chess Olympiad in Siegen, West Germany in September 1970. Grandmaster. Karpov won the 1971 Alekhine Memorial tournament in Moscow (jointly with Leonid Stein), ahead of a star-studded field, for his first significant adult victory. His Elo rating shot from 2540 in 1971 to 2660 in 1973, during which he shared second place in the 1973 Soviet championship, one point behind Spassky, and qualified for the Leningrad Interzonal. Candidate. Karpov's world junior championship qualified him for one of the two Interzonals, a stage in the 1975 World Championship cycle to choose the challenger to play world champion Bobby Fischer. He finished equal first in the Leningrad Interzonal, qualifying for the 1974 Candidates Matches.
Karpov defeated Lev Polugaevsky by the score of +3=5 in the first Candidates' match, earning the right to face former champion Boris Spassky in the semifinal round. Karpov was on record saying that he believed Spassky would easily beat him and win the Candidates' cycle to face Fischer, and that he (Karpov) would win the following Candidates' cycle in 1977. Spassky won the first game as Black in good style, but tenacious, aggressive play from Karpov secured him overall victory by +4−1=6. The Candidates' final was played in Moscow with Victor Korchnoi. Karpov took an early lead, winning the second game against the Sicilian Dragon, then scoring another victory in the sixth game. Following ten consecutive draws, Korchnoi threw away a winning position in the seventeenth game to give Karpov a 3–0 lead. In game 19, Korchnoi succeeded in winning a long endgame, then notched a speedy victory after a blunder by Karpov two games later. Three more draws, the last agreed by Karpov when he was in a clearly better position, closed the match, with Karpov prevailing +3−2=19, entitling him to move on to challenge Fischer for the world title.
Match with Fischer in 1975. Though a world championship match between Karpov and Fischer was highly anticipated, those hopes were never realised. Fischer not only insisted that the match be the first to ten wins (draws not counting), but also that the champion retain the crown if the score was tied 9–9. FIDE, the International Chess Federation, refused to allow this proviso, and gave both players a deadline of April 1, 1975, to agree to play the match under the FIDE-approved rules. When Fischer did not agree, FIDE President Max Euwe declared on April 3, 1975, that Fischer had forfeited his title and Karpov was the new World Champion. Karpov later attempted to set up another match with Fischer, but the negotiations fell through. This thrust the young Karpov into the role of World Champion without having faced the reigning champion. Garry Kasparov argued that Karpov would have had good chances because he had beaten Spassky convincingly and was a new breed of tough professional, and indeed had higher quality games, while Fischer had been inactive for three years. This view is echoed by Karpov himself. Spassky thought that Fischer would have won in 1975, but Karpov would have qualified again and beaten Fischer in 1978. Karpov has said that if he had had the opportunity to play Fischer for the championship in his twenties, he could have been a much better player as a result.
World champion. Determined to prove himself a legitimate champion, Karpov participated in nearly every major tournament for the next ten years. He convincingly won the Milan tournament in 1975, and captured his first of three Soviet titles in 1976. He created a phenomenal streak of tournament wins against the strongest players in the world. Karpov held the record for most consecutive tournament victories (9) until it was shattered by Garry Kasparov (15). As a result, most chess professionals soon agreed that Karpov was a legitimate world champion. In 1978, Karpov's first title defence was against Viktor Korchnoi, the opponent he had defeated in the 1973–75 Candidates' cycle; the match was played at Baguio, Philippines, with the winner needing six victories. As in 1974, Karpov took an early lead, winning the eighth game after seven draws to open the match. When the score was +5−2=20 in Karpov's favour, Korchnoi staged a comeback, and won three of the next four games to draw level with Karpov. Karpov then won the very next game to retain the title (+6−5=21). Three years later, Korchnoi reemerged as the Candidates' winner against German finalist Robert Hübner to challenge Karpov in Merano, Italy. Karpov handily won this match, 11–7 (+6−2=10), in what is remembered as the "Massacre in Merano".
Karpov's tournament career reached a peak at the Montreal "Tournament of Stars" tournament in 1979, where he finished joint first (+7−1=10) with Mikhail Tal ahead of a field of strong grandmasters completed by Jan Timman, Ljubomir Ljubojević, Boris Spassky, Vlastimil Hort, Lajos Portisch, Robert Hübner, Bent Larsen and Lubomir Kavalek. He dominated Las Palmas in 1977 with 13½/15. He also won the prestigious Bugojno tournament in 1978 (shared), 1980 and 1986, the Linares tournament in 1981 (shared with Larry Christiansen) and 1994, the Tilburg tournament in 1977, 1979, 1980, 1982, and 1983, and the Soviet Championship in 1976, 1983, and 1988. Karpov represented the Soviet Union at six Chess Olympiads, in all of which the USSR won the team gold medal. He played as the first reserve at Skopje 1972, winning the board prize with 13/15. At Nice 1974, he advanced to board one and again won the board prize with 12/14. At La Valletta 1980, he was again board one and scored 9/12. At Lucerne 1982, he scored 6½/8 on board one. At Dubai 1986, he scored 6/9 on board two. His last was Thessaloniki 1988, where on board two he scored 8/10. In Olympiad play, Karpov lost only two games out of 68 played. To illustrate Karpov's dominance over his peers as champion, his score was +13−1=22 versus Spassky, +8=19 versus Robert Hübner, +12−1=29 versus Ulf Andersson, +3−1=10 versus Vasily Smyslov, +1=19 versus Mikhail Tal, +19-7=23 versus Ljubomir Ljubojević.
FIDE champion again (1993–1999). In 1992, Karpov lost a Candidates Match against Nigel Short. But in the World Chess Championship 1993, Karpov reacquired the FIDE World Champion title when Kasparov and Short split from FIDE. Karpov defeated Timman – the loser of the Candidates' final against Short. The next major meeting of Kasparov and Karpov was the 1994 Linares chess tournament. The field, in eventual finishing order, was Karpov, Kasparov, Shirov, Bareev, Kramnik, Lautier, Anand, Kamsky, Topalov, Ivanchuk, Gelfand, Illescas, Judit Polgár, and Beliavsky; with an average Elo rating of 2685, the highest ever at that time. Impressed by the strength of the tournament, Kasparov had said several days before the tournament that the winner could rightly be called the world champion of tournaments. Perhaps spurred on by this comment, Karpov played the best tournament of his life. He was undefeated and earned 11 points out of 13 (the best world-class tournament winning percentage since Alekhine won San Remo in 1930), finishing 2½ points ahead of second-place Kasparov and Shirov. Many of his wins were spectacular (in particular, his win over Topalov is considered possibly the finest of his career). This performance against the best players in the world put his Elo rating tournament performance at 2985, the highest performance rating of any player in history up until 2009, when Magnus Carlsen won the category XXI Pearl Spring chess tournament with a performance of 3002. Chess statistician Jeff Sonas considers Karpov's Linares performance the best tournament result in history.
Karpov defended his FIDE title against the rising star Gata Kamsky (+6−3=9) in 1996. In 1998, FIDE largely scrapped the old system of Candidates' Matches, instead having a large knockout event in which a large number of players contested short matches against each other over just a few weeks. In the first of these events, the FIDE World Chess Championship 1998, champion Karpov was seeded straight into the final, defeating Viswanathan Anand (+2−2=2, rapid tiebreak 2–0). In the subsequent cycle, the format was changed, with the champion having to qualify. Karpov refused to defend his title, and ceased to be FIDE World Champion after the FIDE World Chess Championship 1999. Towards retirement. Karpov's classical tournament play has been seriously limited since 1997, since he prefers to be more involved in Russian politics. He had been a member of the Supreme Soviet Commission for Foreign Affairs and the president of the Soviet Peace Fund before the Soviet Union dissolved. In addition, he has been involved in several disputes with FIDE. In the September 2009 FIDE rating list, he dropped out of the world's Top 100 for the first time. Karpov usually limits his play to exhibition events, and has revamped his style to specialize in rapid chess. In 2002, he won a match against Kasparov, defeating him in a rapid time control match 2½–1½. In 2006, he tied for first with Kasparov in a blitz tournament, ahead of Korchnoi and Judit Polgár.
Karpov and Kasparov played a mixed 12-game match from September 21–24, 2009, in Valencia, Spain. It consisted of four rapid (or semi-rapid) and eight blitz games and took place exactly 25 years after the two players' legendary encounter at the World Chess Championship 1984. Kasparov won the match 9–3. Karpov played a match against Yasser Seirawan in 2012 in St. Louis, Missouri, an important center of the North American chess scene, winning 8–6 (+5−3=6). In November 2012, he won the Cap d'Agde rapid tournament that bears his name (Anatoly Karpov Trophy), beating Vasyl Ivanchuk (ranked 9th in the October 2012 FIDE world rankings) in the final. Professional and political career after retirement from chess. In 2003, Karpov opened his first American chess school in Lindsborg, Kansas. On March 2, 2022, the school announced a name change to International Chess Institute of the Midwest due to the Russian invasion of Ukraine. Karpov has been a member of the sixth, seventh and eighth Russian State Dumas. Since 2005, he has been a member of the Public Chamber of Russia. He has involved himself in several humanitarian causes, such as advocating the use of iodised salt. On December 17, 2012, Karpov supported the Dima Yakovlev Law banning adoption of Russian orphans by U.S. citizens.
Karpov expressed support of the unilateral annexation of Crimea by the Russian Federation, and accused Europe of trying to demonize Putin. In August 2019, Maxim Dlugy said that Karpov had been waiting since March for the approval of a non-immigrant visa to the United States, despite frequently visiting the country since 1972. Karpov had been scheduled to teach a summer camp at the Chess Max Academy. Dlugy said that Karpov had been questioned at the US embassy in Moscow about whether he planned to communicate with American politicians. Karpov was among the Russian State Duma members placed under sanctions by the EU and UK during the Russo-Ukrainian War. In March 2022, after the start of the Russian invasion of Ukraine, the FIDE Council suspended Karpov's title of FIDE Ambassador for Life. In November 2022, Karpov was placed in an induced coma after receiving a head injury. Karpov's daughter Sofia and the Russian Chess Federation said that he had accidentally fallen. Karpov made a full recovery from the injury.
Candidate for FIDE presidency. In March 2010, Karpov announced that he would be a candidate for the presidency of FIDE. The election took place in September 2010 at the 39th Chess Olympiad. In May, a fundraising event took place in New York with the participation of Kasparov and Magnus Carlsen, who both supported his bid and campaigned for him. Nigel Short also supported Karpov's candidacy. On September 29, 2010, Kirsan Ilyumzhinov was reelected as president of FIDE, 95 votes to 55. Style. Karpov's playing style, described as a "boa constrictor", is solidly positional, taking minimal risks but reacting mercilessly to the slightest error by his opponent. As a result, he is often compared to José Raúl Capablanca, the third world champion. Karpov himself describes his style as follows:Let us say the game may be continued in two ways: one of them is a beautiful tactical blow that gives rise to variations that don't yield to precise calculations; the other is clear positional pressure that leads to an endgame with microscopic chances of victory... I would choose [the latter] without thinking twice. If the opponent offers keen play I don't object; but in such cases I get less satisfaction, even if I win, than from a game conducted according to all the rules of strategy with its ruthless logic.
Hobbies. Karpov's extensive stamp collection of Belgian philately and Belgian Congo stamps and postal history covering mail from 1742 through 1980 was sold by David Feldman's auction company between December 2011 and 2012. He is also known to have large chess stamp and chess book collections. His private chess library consists of 9,000 books. Karpov is also an enthusiastic Backgammon player. Books. Karpov has authored or co-authored several books, most of which have been translated into English. External links.
Aspect ratio The aspect ratio of a geometric shape is the ratio of its sizes in different dimensions. For example, the aspect ratio of a rectangle is the ratio of its longer side to its shorter side—the ratio of width to height, when the rectangle is oriented as a "landscape". The aspect ratio is most often expressed as two integer numbers separated by a colon (x:y), less commonly as a simple or decimal fraction. The values x and y do not represent actual widths and heights but, rather, the proportion between width and height. As an example, 8:5, 16:10, 1.6:1, and 1.6 are all ways of representing the same aspect ratio. In objects of more than two dimensions, such as hyperrectangles, the aspect ratio can still be defined as the ratio of the longest side to the shortest side. Applications and uses. The term is most commonly used with reference to: Aspect ratios of simple shapes. Rectangles. For a rectangle, the aspect ratio denotes the ratio of the width to the height of the rectangle. A square has the smallest possible aspect ratio of 1:1.
Examples: Ellipses. For an ellipse, the aspect ratio denotes the ratio of the major axis to the minor axis. An ellipse with an aspect ratio of 1:1 is a circle. Aspect ratios of general shapes. In geometry, there are several alternative definitions to aspect ratios of general compact sets in a d-dimensional space: If the dimension "d" is fixed, then all reasonable definitions of aspect ratio are equivalent to within constant factors. Notations. Aspect ratios are mathematically expressed as "x":"y" (pronounced "x-to-y"). Cinematographic aspect ratios are usually denoted as a (rounded) decimal multiple of width vs unit height, while photographic and videographic aspect ratios are usually defined and denoted by whole number ratios of width to height. In digital images there is a subtle distinction between the "display" aspect ratio (the image as displayed) and the "storage" aspect ratio (the ratio of pixel dimensions); see Distinctions.
Auto racing Auto racing (also known as car racing, motor racing, or automobile racing) is a motorsport involving the racing of automobiles for competition. In North America, the term is commonly used to describe all forms of automobile sport including non-racing disciplines. Auto racing has existed since the invention of the automobile. Races of various types were organized, with the first recorded as early as 1867. Many of the earliest events were effectively reliability trials, aimed at proving these new machines were a practical mode of transport, but soon became an important way for automobile makers to demonstrate their machines. By the 1930s, specialist racing cars had developed. There are now numerous different categories, each with different rules and regulations. History. The first prearranged match race of two self-powered road vehicles over a prescribed route occurred at 4:30 A.M. on August 30, 1867, between Ashton-under-Lyne and Old Trafford, England, a distance of . It was won by the carriage of Isaac Watt Boulton.
Internal combustion auto racing events began soon after the construction of the first successful gasoline-fueled automobiles. The first organized contest was on April 28, 1887, by the chief editor of Paris publication "", Monsieur Fossier. It ran from Neuilly Bridge to the Bois de Boulogne. On July 22, 1894, the Parisian magazine "" organized what is considered to be the world's first motoring competition, from Paris to Rouen. One hundred and two competitors paid a 10-franc entrance fee. The first American automobile race is generally considered to be the Thanksgiving Day "Chicago Times-Herald" race of November 28, 1895. Press coverage of the event first aroused significant American interest in the automobile. The Targa Florio was an open road endurance automobile race held in the mountains of Sicily, Italy near the island's capital of Palermo. Founded in 1906, it was the oldest sports car racing event, part of the World Sportscar Championship between 1955 and 1973, and it was discontinued in 1977. The oldest surviving sports car racing event is the 24 Hours of Le Mans, begun in 1923. It is run by the Automobile Club of the West (ACO). Team Ferrari won the race in 2023.
With auto construction and racing dominated by France, the French automobile club ACF staged a number of major international races, usually from or to Paris, connecting with another major city, in France or elsewhere in Europe. Aspendale Racecourse, in Australia, was the world's first purpose-built motor racing circuit, opening in January 1906. The pear-shaped track was close to a mile in length, with slightly banked curves and a gravel surface of crushed cement. Brooklands, in Surrey, England, was the first purpose-built 'banked' motor racing venue, opening in June 1907. It featured a concrete track with high-speed banked corners. One of the oldest existing purpose-built and still in use automobile race course in the United States is the Indianapolis Motor Speedway in Speedway, Indiana. It is the largest capacity sports venue of any variety worldwide, with a top capacity of some 257,000+ seated spectators. NASCAR was founded by Bill France Sr. on February 21, 1948, with the help of several other drivers. The first NASCAR "Strictly Stock" race ever was held on June 19, 1949, at Daytona Beach, Florida, U.S..
From 1962, sports cars temporarily took a back seat to GT cars, with the (FIA) replacing the World Championship for Sports Cars with the International Championship for GT Manufacturers. From 1962 through 2003, NASCAR's premier series was called the Winston Cup Series, sponsored by R. J. Reynolds Tobacco Company cigarette brand Winston. The changes that resulted from RJR's involvement, as well as the reduction of the schedule from 56 to 34 races a year, established 1972 as the beginning of NASCAR's "modern era". The IMSA GT Series evolved into the American Le Mans Series, which ran its first season in 1998. The European races eventually became the closely related European Le Mans Series, both of which mix prototypes and GTs. (TC) is a popular touring car racing series in Argentina, and one of the oldest car racing series still active in the world. The first TC competition took place in 1931 with 12 races, each in a different province. Future Formula One star Juan Manuel Fangio (Chevrolet) won the 1940 and 1941 editions of the TC. It was during this time that the series' Chevrolet-Ford rivalry began, with Ford acquiring most of its historical victories.
Over the last few years, auto racing has seen a transformative shift, echoing past pivots. The industry, much like the cars it champions, has had to navigate through a global pandemic and a persistent chip shortage, each threatening to derail production schedules. At the same time, a new course is being charted towards an electric future, a dramatic change in direction that is challenging the old guard of gasoline engines. There is also a growing number of events for electric racing cars, such as the Formula E, the Eco Grand Prix or the Electric GT Championship. Categories. Open-wheel racing. In single-seater (open-wheel) racing, the wheels are not covered, and the cars often have aerofoil wings front and rear to produce downforce and enhance adhesion to the track. The most popular varieties of open-wheel road racing are Formula One, IndyCar Series and Super Formula. In Europe and Asia, open-wheeled racing is commonly referred to as 'Formula', with appropriate hierarchical suffixes. In North America, the 'Formula' terminology is not followed (with the exception of Formula One). The sport is usually arranged to follow an international format (such as Formula One), a regional format (such as the Formula 3 Euro Series), and/or a domestic, or country-specific, format (such as the German Formula 3 championship, or the British Formula Ford).
Formula One is a worldwide series that runs only street circuit and race tracks. These cars are heavily based on technology and their aerodynamics. The speed record was set in 2005 by Juan Pablo Montoya hitting 373 km/h (232 mph). Some of the most prominent races are the Monaco Grand Prix, the Italian Grand Prix, and the British Grand Prix. The season ends with the crowning of the World Championship for drivers and constructors. In the United States, the most popular series is the IndyCar Series. The cars have traditionally been similar to, though less technologically sophisticated than, F1 cars, with more restrictions on technology aimed at controlling costs. While these cars are not as technologically advanced, they are faster, in part due to their lower downforce compared to Formula One cars, and also because they compete on oval race tracks, being able to average a lap at 388 km/h (241 mph). The series' biggest race is the Indianapolis 500, which is commonly referred to as "The Greatest Spectacle in Racing" due to being the longest continuously run race in the series and having the largest crowd for a single-day sporting event (350,000+).
The other major international single-seater racing series is Formula 2 (formerly known as Formula 3000 and GP2 Series). Regional series include Super Formula and Formula V6 Asia (specifically in Asia), Formula Renault 3.5 (also known as the World Series by Renault, succession series of World Series by Nissan), Formula Three, Formula Palmer Audi and Formula Atlantic. In 2009, the FIA Formula Two Championship brought about the revival of the F2 series. Domestic, or country-specific, series include Formula Three and Formula Renault, with the leading introductory series being Formula Ford. Single-seater racing is not limited merely to professional teams and drivers. There exist many amateur racing clubs. In the UK, the major club series are the Monoposto Racing Club, BRSCC F3 (formerly ClubF3, formerly ARP F3), Formula Vee and Club Formula Ford. Each series caters to a section of the market, with some primarily providing low-cost racing, while others aim for an authentic experience using the same regulations as the professional series (BRSCC F3). The SCCA is also responsible for sanctioning single-seater racing in much of North America.
There are other categories of single-seater racing, including kart racing, which employs a small, low-cost machine on small tracks. Many of the current top drivers began their careers in karts. Formula Ford represents the most popular first open-wheel category for up-and-coming drivers stepping up from karts. The series is still the preferred option, as it has introduced an aero package and slicks, allowing the junior drivers to gain experience in a race car with dynamics closer to Formula One. The Star Mazda Series is another entry-level series. Indy Lights represent the last step on the Road to Indy, being less powerful and lighter than an IndyCar racer. Students at colleges and universities can also take part in single-seater racing through the Formula SAE competition, which involves designing and building a single-seater car in a multidisciplinary team and racing it at the competition. This also develops other soft skills, such as teamwork, while promoting motorsport and engineering. The world's first all-female Formula racing team was created in 2006. The group was an assemblage of drivers from different racing disciplines and formed for an MTV reality pilot, which was shot at Mazda Raceway Laguna Seca.
In December 2005, the FIA gave approval to Superleague Formula racing, which debuted in 2008, whereby the racing teams are owned and run by prominent sports clubs such as A.C. Milan and Liverpool F.C. After 25 years away from the sport, former Formula 2 champion Jonathan Palmer reopened the F2 category again; most drivers have graduated from the Formula Palmer Audi series. The category is officially registered as the FIA Formula Two championship. Most rounds have two races and are support races to the FIA World Touring Car Championship. Touring car racing. Touring car racing is a style of road racing that is run with production-derived four-seat race cars. The lesser use of aerodynamics means following cars have a much easier time following and passing than in open-wheel racing. It often features full-contact racing with subtle bumping and nudging due to the small speed differentials and large grids. The major touring car championships conducted worldwide are the Supercars Championship (Australia), British Touring Car Championship, Deutsche Tourenwagen Masters (DTM), World Touring Car Championship and the World Touring Car Cup. The European Touring Car Cup is a one-day event open to Super 2000 specification touring cars from Europe's many national championships. While Super GT traces its lineage to the now-defunct JGTC, the cars are much more similar to GT3 race cars than proper touring cars, and also have much more aggressive aerodynamics.
The Sports Car Club of America's SPEED World Challenge Touring Car and GT championships are dominant in North America. America's historic Trans-Am Series is undergoing a period of transition, but is still the longest-running road racing series in the U.S. The National Auto Sport Association also provides a venue for amateurs to compete in home-built factory-derived vehicles on various local circuits. Sports car racing. In sports car racing, production-derived versions of two-seat sports cars, also known as grand tourers (GTs), and purpose-built sports prototype cars compete within their respective classes on closed circuits. The premier championship series of sports car racing is the FIA World Endurance Championship. The main series for GT car racing is the GT World Challenge Europe, divided into two separate championships: the GT World Challenge Europe Sprint Cup and the GT World Challenge Europe Endurance Cup. This series has formed after the folding of the various FIA GT championships. The prevailing classes of GT cars are GT3, GT4 and GT2 class cars. GT2 cars have powerful engines, often exceeding 600 horsepower. However, they have less downforce than GT3 cars and also have less driver aids. GT3 cars are far and away the most popular class of GT cars, with premier racing series such as the FIA World Endurance Championship and IMSA both using GT3 as their top class of GT car. GT3 cars have more significant aero than a GT2 car, but also have less horsepower, typically falling in between 500 and 550 horsepower. GT4 class cars have very little aerodynamics and less horsepower than GT3 machinery, typically around 450 horsepower. GT4 typically serves as the last step up to premier GT-class racing.
Other major GT championships include the GT World Challenge America, GT World Challenge Asia, Super GT, and the International GT Open. There are minor regional and national GT series using mainly GT4 and GT3 cars featuring both amateur and professional drivers. Sports prototypes, unlike GT cars, do not rely on road-legal cars as a base. They are closed-wheel and often closed-cockpit purpose-built race cars intended mainly for endurance racing. They have much lower weight, more horsepower and more downforce compared to GT cars, making them much faster. They are raced in the 24 hours of Le Mans (held annually since 1923) and in the (European) Le Mans series, Asian Le Mans Series and the WeatherTech SportsCar Championship. These cars are referred to as LMP (Le Mans prototype) cars with LMH and LMDh cars being run mainly by manufacturers and the slightly less powerful LMP2 cars run by privateer teams. All three Le Mans Series run GT cars in addition to Le Mans Prototypes; these cars have different restrictions than the FIA GT cars.
Another prototype and GT racing championship exists in the United States; the Grand-Am, which began in 2000, sanctions its own endurance series, the Rolex Sports Car Series, which consists of slower and lower-cost Daytona Prototype race cars compared to LMP and FIA GT cars. The Rolex Sports Car Series and American Le Mans Series announced a merger between the two series forming the WeatherTech SportsCar Championship starting in 2014. These races are often conducted over long distances, at least , and cars are driven by teams of two or more drivers, switching every few hours. Due to the performance difference between production-based sports cars and purpose-built sports prototypes, one race usually involves several racing classes, each fighting for its own championship. Famous sports car races include the 24 Hours of Le Mans, the Rolex 24 at Daytona, 24 Hours of Spa-Franchorchamps, the 12 Hours of Sebring, the 6 Hours of Watkins Glen, and the Petit Le Mans at Road Atlanta. There is also the 24 Hours of the Nürburgring on the famed Nordschleife track and the Dubai 24 Hour, which is aimed at GT3 and below cars with a mixture of professional and pro-am drivers.
Production-car racing. Production-car racing, otherwise known as "showroom stock" in the US, is an economical and rules-restricted version of touring-car racing, mainly used to restrict costs. Numerous production racing categories are based on particular makes of cars. Most series, with a few exceptions, follow the Group N regulation. There are several different series that are run all over the world, most notably, Japan's Super Taikyu and IMSA's Firehawk Series, which ran in the 1980s and 1990s all over the United States. Stock car racing. In North America, stock car racing is the most popular form of auto racing. Primarily raced on oval tracks, stock cars vaguely resemble production cars, but are in fact purpose-built racing machines that are built to tight specifications and, together with touring cars, also called Silhouette racing cars. The largest stock car racing governing body is NASCAR (National Association for Stock Car Auto Racing). NASCAR's premier series is the NASCAR Cup Series, its most famous races being the Daytona 500, the Southern 500, the Coca-Cola 600, and the Brickyard 400. NASCAR also runs several feeder series, including the Xfinity Series and Craftsman Truck Series (a pickup truck racing series). The series conduct races across the entire continental United States. NASCAR also sanctions series outside of the United States, including the NASCAR Canada Series, NASCAR Mexico Series, NASCAR Whelen Euro Series, and NASCAR Brasil Sprint Race.
NASCAR also governs several smaller regional series, such as the Whelen Modified Tour. Modified cars are best described as open-wheel cars. Modified cars have no parts related to the stock vehicle for which they are named after. A number of modified cars display a "manufacturer's" logo and "vehicle name", yet use components produced by another automobile manufacturer. There are also other stock car governing bodies, most notably the Automobile Racing Club of America (ARCA). In the UK, British Stock car racing is also referred to as "Short Circuit Racing". UK Stock car racing started in the 1950s and grew rapidly through the 1960s and 1970s. Events take place on shale or tarmac tracks – usually around 1/4 mile long. There are around 35 tracks in the UK and upwards of 7000 active drivers. The sport is split into three basic divisions – distinguished by the rules regarding car contact during racing. The most famous championship are the BriSCA F1 Stock Cars. Full-contact formulas include Bangers, Bombers, and Rookie Bangers – and racing features Demolition Derbies, Figure of Eight, and Oval Racing.
Semi Contact Formulas include BriSCA F1, F2, and Superstox – where bumpers are used tactically. Non-contact formulas include National Hot Rods, Stock Rods, and Lightning Rods. One-make racing. One-make, or single marque, championships often employ production-based cars from a single manufacturer or even a single model from a manufacturer's range. There are numerous notable one-make formulae from various countries and regions, some of which – such as the Porsche Supercup and, previously, IROC – have fostered many distinct national championships. Single marque series are often found at the club level, to which the production-based cars, limited modifications, and close parity in performance are very well suited. Some of the better-known single-make series are the Mini 7 Championship (Europe's longest-running one-make championship), the Radical European Masters, John Cooper Mini Challenge, Clio Cup, Ginettas, Caterhams, BMWs, and MX5s. There are also single-chassis single seater formulae, such as Formula Renault and Formula BMW, usually as "feeder" series for "senior" race formula (in the fashion of farm teams).
Drag racing. In drag racing, the objective is to complete a given straight-line distance, from a standing start, ahead of a vehicle in a parallel lane. This distance is traditionally , though and are also common. The vehicles may or may not be given the signal to start at the same time, depending on the class of racing. Vehicles range from the everyday car to the purpose-built dragster. Speeds and elapsed time differ from class to class. Average street cars cover the mile in 12 to 16 seconds, whereas a top fuel dragster takes 4.5 seconds or less, reaching speeds of up to . Drag racing was organized as a sport by Wally Parks in the early 1950s through the National Hot Rod Association (NHRA). The NHRA was formed to discourage street racing. When launching, a top fuel dragster will accelerate at 3.4 g (33 m/s2), and when braking parachutes are deployed the deceleration is 4 g (39 m/s2), more than the Space Shuttle experiences. A top fuel car can be heard over away and can generate a reading from 1.5 to 3.9 on the Richter scale.
Drag racing is two cars head-to-head, the winner proceeding to the next round. Professional classes are all first to the finish line wins. Sportsman racing is handicapped (slower car getting a head start) using an index (a lowest e.t. allowed), and cars running under (quicker than) their index "break out" and lose. The slowest cars, bracket racers, are also handicapped, but rather than an index, they use a dial-in. Off-road racing. In off-road racing, various classes of specially modified vehicles, including cars, compete in races through off-road environments. In North America these races often take place in the desert, such as the famous Baja 1000. Another format for off-road racing happens on closed-course short course tracks such as Crandon International Off-Road Raceway. In the 1980s and 1990s, the short course was extended to racing inside stadiums in the Mickey Thompson Entertainment Group; this format was revived by Robby Gordon in 2013 with his Stadium Super Trucks series. In Europe, "offroad" refers to events such as autocross or rallycross, while desert races and rally-raids such as the Paris-Dakar, Master Rallye or European "bajas" are called "cross-country rallies".
Kart racing. The modern kart was invented by Art Ingels, a fabricator at the Indianapolis-car manufacturer Kurtis-Kraft, in Southern California in 1956. Ingels took a small chainsaw engine and mounted it to a simple tube-frame chassis weighing less than 100 lb. Ingels, and everyone else who drove the kart, were startled at its performance capabilities. The sport soon blossomed in Southern California, and quickly spread around the world. Although often seen as the entry point for serious racers into the sport, kart racing, or karting, can be an economical way for amateurs to try racing and is also a fully-fledged international sport in its own right. A large proportion of professional racing drivers began in karts, often from a very young age, such as Michael Schumacher and Fernando Alonso. Several former motorcycle champions have also taken up the sport, notably Wayne Rainey, who was paralysed in a racing accident and now races a hand-controlled kart. As one of the cheapest ways to race, karting is seeing its popularity grow worldwide.
Despite their diminutive size, karts of the most powerful class, superkart (assuming a weight of 205 kg (452 lb), and a power output of 100 hp (75 kW)), can have a power-to-weight ratio (including the driver) of 490 hp/tonne (0.22 hp/lb). Without the driver, this figure doubles, to almost 980 hp/tonne (0.44 hp/lb). Historical racing. Historic motorsport or vintage motorsport uses vehicles limited to a particular era. Only safety precautions are modernized in these hobbyist races. A historical event can be of various types of motorsport disciplines, from road racing to rallying. Because it is based on a particular era it is more hobbyist-oriented, reducing corporate sponsorship. The only modern equipment used is related to safety and timing. A historical event can be of a number of different motorsport disciplines. Some of the most famous events include the Goodwood Festival of Speed and Goodwood Revival in Britain and Monterey Historic in the United States. Championships range from "grass root" Austin Seven racing to the FIA Thoroughbred Grand Prix Championship for classic Formula One chassis. While there are several professional teams and drivers in historical racing, this branch of auto sport tends to be contested by wealthy car owners and is thus more amateur and less competitive in its approach.
Scoring. Each motor racing series has a points system, and a set of rules and regulations that define how points are accrued. Nearly all series award points according to the finishing position of the competitors in each race. Some series only award points for a certain number of finishing positions. In Formula One, for example, only the top ten finishers get points. Drivers may be forced to finish the race or complete a certain number of the laps in order to score points. In some series, points are also awarded based on lap leading, lap times, overtaking and qualifying positions (in particular by achieving pole positions and fastest laps). In NASCAR, for example, besides receiving points depending on the final standings, one point is awarded for leading a lap and one point for leading the most laps in the race. In other series, such as for the National Hot Rod Association, points are awarded for attempting the race along with a podium finish in any of the four qualifying rounds, as an incentive to have drivers participate week after week to compete.
Use of flags. In many types of auto races, particularly those held on closed courses, flags are displayed to indicate the general status of the track and to communicate instructions to competitors. While individual series have different rules, and the flags have changed from the first years (e.g., red used to start a race), these are generally accepted. Accidents. The worst accident in racing history is the 1955 Le Mans disaster, where more than 80 people died, including the French driver Pierre Levegh. Racing-car setup. In auto racing, the racing setup or car setup is the set of adjustments made to the vehicle to optimize its behaviour (performance, handling, reliability, etc.). Adjustments can occur in suspensions, brakes, transmissions, engines, tires, and many others. Aerodynamics. Aerodynamics and airflow play big roles in the setup of a race car. Aerodynamic downforce improves the race car's handling by lowering the center of gravity and distributing the weight of the car equally on each tire. Once this is achieved, fuel consumption decreases and the forces against the car are significantly lowered. Many aerodynamic experiments are conducted in wind tunnels, to simulate real-life situations while measuring the various drag forces on the car. These "Rolling roads" produce many wind situations and direct air flow at certain speeds and angles. When a diffuser is installed under the car, the amount of drag force is significantly lowered, and the overall aerodynamics of the vehicle is positively adjusted. Wings and canards channel the airflow in the most efficient way to get the least amount of drag from the car. It is experimentally proven that downforce is gained and the vehicle's handling is considerably changed when aerodynamic wings on the front and rear of the vehicle are installed.
Suspension. Suspension plays a huge part in giving the race car the ability to be driven optimally. Shocks are mounted vertically or horizontally to prevent the body from rolling in the corners. The suspension is important because it makes the car stable and easier to control and keeps the tires on the road when driving on uneven terrain. It works in three different ways including vertically, longitudinally, and laterally to control movement when racing on various tracks. Tyres. Tyres called R-Compounds are commonly used in motorsports for high amounts of traction. The soft rubber allows them to expand when they are heated up, making more surface area on the pavement, therefore producing the most traction. These types of tyres do not have grooves on them. Tyre pressure is dependent on the temperature of the tyre and track when racing. Each time a driver pulls into the pits, the tyre pressure and temperature should be tested for optimal performance. When the tyres get too hot they will swell or inflate and need to be deflated to the correct pressure. When the tyres are not warmed up they will not perform as well.
Brakes. Brakes on a race car are imperative in slowing and stopping the car at precise times and wear quickly depending on the road or track on which the car is being raced, how many laps are being run, track conditions due to weather, and how many caution runs require more braking. There are three variables to consider in racing: brake pedal displacement, brake pedal force, and vehicle deceleration. Various combinations of these variables work together to determine the stiffness, sensitivity, and pedal force of the brakes. When using the brakes effectively, the driver must go through a buildup phase and end with a modulating phase. These phases include attaining maximum deceleration and modulating the brake pressure. Brake performance is measured in bite and consistency. Bite happens when the driver first applies the brakes and they have not warmed up to the correct temperature to operate efficiently. Consistency is measured in how consistent the friction is during the entire time of braking. These two measurements determine the wear of the brakes.
Engine. The race car's engine needs a considerable amount of air to produce maximum power. The air intake manifold sucks the air from scoops on the hood and front bumper and feeds it into the engine. Many engine modifications to increase horsepower and efficiency are commonly used in many racing-sanctioning bodies. Engines are tuned on a machine called a dynamometer, which is commonly known in the racing world as a DYNO. The car is driven onto the DYNO and many gauges and sensors are hooked up to the car that are controlled by an online program to test force, torque, or power. Through the testing, the car's engine maps can be changed to get the most horsepower and ultimately speed out of the vehicle. Racing drivers. Racing drivers, at the highest levels, can be paid by the team, or by sponsors, and can command substantial salaries. Drivers who pay for their positions, or "seats", within racing teams are typically known as pay drivers, or "gentleman drivers". Drivers may also enter events as privateers. Contrary to popular assumption, racing drivers as a group do not have unusually strong reflexes or peripheral response time. During repeated physiological and psychological evaluations of professional racing drivers, the two characteristics that stand out are racers' near-obsessive need to control their surroundings—psychological—and an unusual ability to process fast-moving information —physiological. Researchers have noted a strong correlation between racing driver psychological profiles and those of fighter pilots. In tests comparing racing drivers to the general public, the greater the complexity of the information processing matrix, the greater the speed gap between the two groups.
Due partly to the performance capabilities of modern racing cars, racing drivers require a high level of fitness, focus, and the ability to concentrate at high levels for long periods in an inherently difficult environment. They often complain about injuries in the lumbar, shoulder, and neck regions. Racing drivers experience large g-forces due to formula cars and sports prototypes generating high levels of downforce, and being able to corner at high speeds. Formula One drivers routinely experience lateral loads in excess of , requiring drivers to commit to frequent neck training regimens.
Anarcho-capitalism Anarcho-capitalism (colloquially: ancap or an-cap) is a political philosophy and economic theory that advocates for the abolition of centralized states in favor of stateless societies, where systems of private property are enforced by private agencies. Anarcho-capitalists argue that society can self-regulate and civilize through the voluntary exchange of goods and services. This would ideally result in a voluntary society based on concepts such as the non-aggression principle, free markets and self-ownership. In the absence of statute private defence agencies and/or insurance companies would operate competitively in a market and fulfill the roles of courts and the police, similar to a state apparatus. Some anarcho-capitalist philosophies understand control of private property as part of the self, and some permit slavery if agreed to by the person to become a slave. The vast majority of anarcho-capitalists deny this, and critics of capitalism argue that this minority opinion is not unique to anarcho-capitalists, but is an essential consequence of the capitalist contract theory (wage slavery).
According to its proponents, various historical theorists have espoused philosophies similar to anarcho-capitalism. While the earliest extant attestation of "anarchocapitalism" is in Karl Hess's essay "The Death of Politics" published by "Playboy" in March 1969, American economist Murray Rothbard was credited with coining the terms "anarcho-capitalist" and "anarcho-capitalism" in 1971. A leading figure in the 20th-century American libertarian movement, Rothbard synthesized elements from the Austrian School, classical liberalism and 19th-century American individualist anarchists and mutualists Lysander Spooner and Benjamin Tucker, while rejecting the labor theory of value. Rothbard's anarcho-capitalist society would operate under a mutually agreed-upon "legal code which would be generally accepted, and which the courts would pledge themselves to follow". This legal code would recognize contracts between individuals, private property, self-ownership and tort law in keeping with the non-aggression principle. Unlike a state, enforcement measures would only apply to those who initiated force or fraud. Rothbard views the power of the state as unjustified, arguing that it violates individual rights and reduces prosperity, and creates social and economic problems.
Anarcho-capitalists and right-libertarians cite several historical precedents of what they believe to be examples of quasi-anarcho-capitalism, including the Republic of Cospaia, Acadia, Anglo-Saxon England, Medieval Iceland, the American Old West, Gaelic Ireland, and merchant law, admiralty law, and early common law. Anarcho-capitalism is distinguished from minarchism, which advocates a minimal governing body (typically a night-watchman state limited to protecting individuals from aggression and enforcing private property) and from objectivism (which is a broader philosophy advocating a limited role, yet unlimited size, of said government). Anarcho-capitalists consider themselves to be anarchists despite supporting private property and private institutions. Classification. Anarcho-capitalism developed from Austrian School-neoliberalism and individualist anarchism. Almost all anarchist movements do not consider anarcho-capitalism to be anarchist because it lacks the historically central anti-capitalist emphasis of anarchism. They also argue that anarchism is incompatible with capitalist structures. According to several scholars, Anarcho-capitalism lies outside the tradition of the vast majority of anarchist schools of thought and is more closely affiliated with capitalism, right-libertarianism and neoliberalism. Traditionally, anarchists oppose and reject capitalism, and consider "anarcho-capitalism" to be a contradiction in terms, although anarcho-capitalists and some right-libertarians consider anarcho-capitalism to be a form of anarchism.
According to the "Encyclopædia Britannica":Anarcho-capitalism is occasionally seen as part of the New Right. Philosophy. Author J Michael Oliver says that during the 1960s, a philosophical movement arose in the US that championed "reason, ethical egoism, and free-market capitalism". According to Oliver, anarcho-capitalism is a political theory which logically follows the philosophical conclusions of Objectivism, a philosophical system developed by Ayn Rand, but he acknowledges that his advocacy of anarcho-capitalism is "quite at odds with Rand's ardent defense of 'limited government. Professor Lisa Duggan also says that Rand's anti-statist, pro–"free market" stances went on to shape the politics of anarcho-capitalism. According to Patrik Schumacher, the political ideology and programme of anarcho-capitalism envisages the radicalization of the neoliberal "rollback of the state", and calls for the extension of "entrepreneurial freedom" and "competitive market rationality" to the point where the scope for private enterprise is all-encompassing and "leaves no space for state action whatsoever".
On the state. Anarcho-capitalists oppose the state and seek to privatize any useful service the government presently provides, such as education, infrastructure, or the enforcement of law. They see capitalism and the "free market" as the basis for a free and prosperous society. Murray Rothbard stated that the difference between free-market capitalism and state capitalism is the difference between "peaceful, voluntary exchange" and a "collusive partnership" between business and government that "uses coercion to subvert the free market". Rothbard argued that all government services, including defense, are inefficient because they lack a market-based pricing mechanism regulated by "the voluntary decisions of consumers purchasing services that fulfill their highest-priority needs" and by investors seeking the most profitable enterprises to invest in. Maverick Edwards of the Liberty University describes anarcho-capitalism as a political, social, and economic theory that places markets as the central "governing body" and where government no longer "grants" rights to its citizenry.
Non-aggression principle. Writer Stanisław Wójtowicz says that although anarcho-capitalists are against centralized states, they believe that all people would naturally share and agree to a specific moral theory based on the non-aggression principle. While the Friedmanian formulation of anarcho-capitalism is robust to the presence of violence and in fact, assumes some degree of violence will occur, anarcho-capitalism as formulated by Rothbard and others holds strongly to the central libertarian nonaggression axiom, sometimes non-aggression principle. Rothbard wrote: Rothbard's defense of the self-ownership principle stems from what he believed to be his falsification of all other alternatives, namely that either a group of people can own another group of people, or that no single person has full ownership over one's self. Rothbard dismisses these two cases on the basis that they cannot result in a universal ethic, i.e. a just natural law that can govern all people, independent of place and time. The only alternative that remains to Rothbard is self-ownership which he believes is both axiomatic and universal.
In general, the non-aggression axiom is described by Rothbard as a prohibition against the initiation of force, or the threat of force, against persons (in which he includes direct violence, assault and murder) or property (in which he includes fraud, burglary, theft and taxation). The initiation of force is usually referred to as aggression or coercion. The difference between anarcho-capitalists and other libertarians is largely one of the degree to which they take this axiom. Minarchist libertarians such as libertarian political parties would retain the state in some smaller and less invasive form, retaining at the very least public police, courts, and military. However, others might give further allowance for other government programs. In contrast, Rothbard rejects any level of "state intervention", defining the state as a coercive monopoly and as the only entity in human society, excluding acknowledged criminals, that derives its income entirely from coercion, in the form of taxation, which Rothbard describes as "compulsory seizure of the property of the State's inhabitants, or subjects."
Some anarcho-capitalists such as Rothbard accept the non-aggression axiom on an intrinsic moral or natural law basis. It is in terms of the non-aggression principle that Rothbard defined his interpretation of anarchism, "a system which provides no legal sanction for such aggression ['against person and property']"; and wrote that "what anarchism proposes to do, then, is to abolish the State, i.e. to abolish the regularized institution of aggressive coercion". In an interview published in the American libertarian journal "The New Banner", Rothbard stated that "capitalism is the fullest expression of anarchism, and anarchism is the fullest expression of capitalism". Property. Private property. Anarcho-capitalists postulate the privatization of everything, including cities with all their infrastructures, public spaces, streets and urban management systems. Central to Rothbardian anarcho-capitalism are the concepts of self-ownership and original appropriation that combines personal and private property. Hans-Hermann Hoppe wrote:
Rothbard however rejected the Lockean proviso, and followed the rule of "first come, first served", without any consideration of how much resources are left for other individuals. Anarcho-capitalists advocate private ownership of the means of production and the allocation of the product of labor created by workers within the context of wage labour and the free market – that is through decisions made by property and capital owners, regardless of what an individual needs or does not need. Original appropriation allows an individual to claim any never-before-used resources, including land and by improving or otherwise using it, own it with the same "absolute right" as their own body, and retaining those rights forever, regardless of whether the resource is still being used by them. According to Rothbard, property can only come about through labor, therefore original appropriation of land is not legitimate by merely claiming it or building a fence around itit is only by using land and by mixing one's labor with it that original appropriation is legitimized: "Any attempt to claim a new resource that someone does not use would have to be considered invasive of the property right of whoever the first user will turn out to be". Rothbard argued that the resource need not continue to be used in order for it to be the person's property as "for once his labor is mixed with the natural resource, it remains his owned land. His labor has been irretrievably mixed with the land, and the land is therefore his or his assigns' in perpetuity".
Rothbard also spoke about a theory of justice in property rights: In "Justice and Property Rights", Rothbard wrote that "any identifiable owner (the original victim of theft or his heir) must be accorded his property". In the case of slavery, Rothbard claimed that in many cases "the old plantations and the heirs and descendants of the former slaves can be identified, and the reparations can become highly specific indeed". Rothbard believed slaves rightfully own any land they were forced to work on under the homestead principle. If property is held by the state, Rothbard advocated its confiscation and "return to the private sector", writing that "any property in the hands of the State is in the hands of thieves, and should be liberated as quickly as possible". Rothbard proposed that state universities be seized by the students and faculty under the homestead principle. Rothbard also supported the expropriation of nominally "private property" if it is the result of state-initiated force such as businesses that receive grants and subsidies. Rothbard further proposed that businesses who receive at least 50% of their funding from the state be confiscated by the workers, writing: "What we libertarians object to, then, is not government "per se" but crime, what we object to is unjust or criminal property titles; what we are for is not 'private' property "per se" but just, innocent, non-criminal private property".

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