Kurt Vonnegut

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Kurt Vonnegut
Vonnegut in 1965
Born	Kurt Vonnegut, Jr. November 11, 1922 Indianapolis, Indiana, U.S.
Died	April 11, 2007 (aged 84) New York City, U.S.
Occupation	Author
Education	Cornell University Carnegie Mellon University University of Tennessee University of Chicago (MA)
Genre	Satire gallows humor science fiction
Literary movement	Postmodernism
Years active	1951–2007
Notable works	Slaughterhouse-Five Cat's Cradle
Spouse	Jane Marie Cox ​ ​ (m. 1945; div. 1971)​ Jill Krementz ​ (m. 1979)​
Children	3 biological, including Mark and Edith 4 adopted, including Steve Adams
Signature

Kurt Vonnegut (/ˈvɒnəɡət/ VON-ə-gət; November 11, 1922 – April 11, 2007) was an American author known for his satirical and darkly humorous novels. His published work includes fourteen novels, three short-story collections, five plays, and five nonfiction works over fifty-plus years; further works have been published since his death.

Born and raised in Indianapolis, Vonnegut attended Cornell University, but withdrew in January 1943 and enlisted in the U.S. Army. As part of his training, he studied mechanical engineering at the Carnegie Institute of Technology and the University of Tennessee. He was then deployed to Europe to fight in World War II and was captured by the Germans during the Battle of the Bulge. He was interned in Dresden, where he survived the Allied bombing of the city in a meat locker of the slaughterhouse where he was imprisoned. After the war, he married Jane Marie Cox. He and his wife both attended the University of Chicago while he worked as a night reporter for the City News Bureau.

Vonnegut published his first novel, Player Piano, in 1952. It received positive reviews yet sold poorly. In the nearly 20 years that followed, several well regarded novels were published, including The Sirens of Titan (1959) and Cat's Cradle (1963), both of which were nominated for the Hugo Award for best science fiction novel of the year. His short-story collection, Welcome to the Monkey House, was published in 1968.

Vonnegut's breakthrough was his commercially and critically successful sixth novel, Slaughterhouse-Five (1969). Its anti-war sentiment resonated with its readers amid the Vietnam War, and its reviews were generally positive. It rose to the top of The New York Times Best Seller list and made Vonnegut famous. Later in his career, Vonnegut published autobiographical essays and short-story collections such as Fates Worse Than Death (1991) and A Man Without a Country (2005). He has been hailed for his darkly humorous commentary on American society. His son Mark published a compilation of his work, Armageddon in Retrospect, in 2008. In 2017, Seven Stories Press published Complete Stories, a collection of Vonnegut's short fiction.

Biography

Family and early life

Vonnegut was born in Indianapolis, on November 11, 1922, the youngest of three children of Kurt Vonnegut Sr. (1884–1957) and his wife Edith (1888–1944; née Lieber). His older siblings were Bernard (1914–1997) and Alice (1917–1958). He descended from a long line of German Americans whose immigrant ancestors settled in the United States in the mid-19th century; his paternal great-grandfather, Clemens Vonnegut, settled in Indianapolis and founded the Vonnegut Hardware Company. His father and grandfather Bernard were architects; the architecture firm under Kurt Sr. designed such buildings as Das Deutsche Haus (now called "The Athenæum"), the Indiana headquarters of the Bell Telephone Company, and the Fletcher Trust Building. Vonnegut's mother was born into Indianapolis's Gilded Age high society, as her family, the Liebers, were among the wealthiest in the city based on a fortune deriving from a successful brewery.

Both of Vonnegut's parents were fluent speakers of the German language, but pervasive anti-German sentiment during and after World War I caused them to abandon German culture; many German Americans were told at the time that this was a precondition for American patriotism. Thus, they did not teach Vonnegut to speak German or introduce him to German literature, cuisine, or traditions, leaving him feeling "ignorant and rootless". Vonnegut later credited Ida Young, his family's African-American cook and housekeeper during the first decade of his life, for raising him and giving him values; he said, "she gave me decent moral instruction and was exceedingly nice to me", and "was as great an influence on me as anybody". He described her as "humane and wise" and added that "the compassionate, forgiving aspects of [his] beliefs" came from her.

The financial security and social prosperity that the Vonneguts had once enjoyed were destroyed in a matter of years. The Liebers' brewery closed down in 1921 after the advent of prohibition. When the Great Depression hit, few people could afford to build, causing clients at Kurt Sr.'s architectural firm to become scarce. Vonnegut's brother and sister had finished their primary and secondary educations in private schools, but Vonnegut was placed in a public school called Public School No. 43 (now the James Whitcomb Riley School). He was bothered by the Great Depression, and both his parents were affected deeply by their economic misfortune. His father withdrew from normal life and became what Vonnegut called a "dreamy artist". His mother became depressed, withdrawn, bitter, and abusive. She labored to regain the family's wealth and status, and Vonnegut said that she expressed hatred for her husband that was "as corrosive as hydrochloric acid". She often tried in vain to sell short stories she had written to Collier's, The Saturday Evening Post, and other magazines.

High school and Cornell University

Vonnegut as a teenager, from the Shortridge High School 1940 yearbook

Vonnegut enrolled at Shortridge High School in Indianapolis in 1936. While there, he played clarinet in the school band and became a co-editor (along with Madelyn Pugh) of the Tuesday edition of the school newspaper, The Shortridge Echo. Vonnegut said that his tenure with the Echo allowed him to write for a large audience—his fellow students—rather than for a teacher, an experience, he said, which was "fun and easy". "It just turned out that I could write better than a lot of other people", Vonnegut observed. "Each person has something he can do easily and can't imagine why everybody else has so much trouble doing it."

After graduating from Shortridge in 1940, Vonnegut enrolled at Cornell University in Ithaca, New York. He wanted to study the humanities and had aspirations of becoming an architect like his father, but his father and brother Bernard, an atmospheric scientist, urged him to study a "useful" discipline. As a result, Vonnegut majored in biochemistry, but he had little proficiency in the area and was indifferent towards his studies. As his father had been a member of the Delta Upsilon fraternity at MIT, Vonnegut was entitled to join and did so. He overcame stiff competition for a place at the university's independent newspaper, The Cornell Daily Sun, first serving as a staff writer, then as an editor. By the end of his first year, he was writing a column titled "Innocents Abroad", which reused jokes from other publications. He later penned a piece titled "Well All Right" focusing on pacifism, a cause he strongly supported, arguing against US intervention in World War II.

World War II

Vonnegut in army uniform during World War II

The attack on Pearl Harbor brought the United States into WWII. Vonnegut was a member of Cornell's Reserve Officers' Training Corps unit, but poor grades and a satirical article in Cornell's newspaper cost him his place there. He was placed on academic probation in May 1942 and dropped out the following January. No longer eligible for a deferment as a member of ROTC, he faced likely conscription into the U.S. Army. Instead of waiting to be drafted, he enlisted in the Army and in March 1943 reported to Fort Bragg, North Carolina, for basic training. Vonnegut was trained to fire and maintain howitzers and later received instruction in mechanical engineering at the Carnegie Institute of Technology and the University of Tennessee as part of the Army Specialized Training Program (ASTP).

In early 1944, the ASTP was canceled due to the Army's need for soldiers to support the D-Day invasion, and Vonnegut was ordered to an infantry battalion at Camp Atterbury, south of Indianapolis in Edinburgh, Indiana, where he trained as a scout. He lived so close to his home that he was "able to sleep in [his] own bedroom and use the family car on weekends".

On May 14, 1944, Vonnegut returned home on leave for Mother's Day weekend to discover that his mother had committed suicide the previous night by overdosing on sleeping pills. Possible factors that contributed to Edith Vonnegut's suicide include the family's loss of wealth and status, Vonnegut's forthcoming deployment overseas, and her own lack of success as a writer. She was inebriated at the time and under the influence of prescription drugs.

Three months after his mother's suicide, Vonnegut was sent to Europe as an intelligence scout with the 106th Infantry Division. In December 1944, he fought in the Battle of the Bulge, one of the last German offensives of the war. On December 22, Vonnegut was captured with about 50 other American soldiers. Vonnegut was taken by boxcar to a prison camp south of Dresden, in the German province of Saxony. During the journey, the Royal Air Force mistakenly attacked the trains carrying Vonnegut and his fellow prisoners of war, killing about 150 of them. Vonnegut was sent to Dresden, the "first fancy city [he had] ever seen". He lived in a slaughterhouse when he got to the city, and worked in a factory that made malt syrup for pregnant women. Vonnegut recalled the sirens going off whenever another city was bombed. The Germans did not expect Dresden to be bombed, Vonnegut said. "There were very few air-raid shelters in town and no war industries, just cigarette factories, hospitals, clarinet factories."

Dresden in 1945. More than 90% of the city's center was destroyed.

On February 13, 1945, Dresden became the target of Allied forces. In the hours and days that followed, the Allies engaged in a firebombing of the city. The offensive subsided on February 15, with about 25,000 civilians killed in the bombing. Vonnegut marveled at the level of both the destruction in Dresden and the secrecy that attended it. He had survived by taking refuge in a meat locker three stories underground. "It was cool there, with cadavers hanging all around", Vonnegut said. "When we came up the city was gone ... They burnt the whole damn town down." Vonnegut and other American prisoners were put to work immediately after the bombing, excavating bodies from the rubble. He described the activity as a "terribly elaborate Easter-egg hunt".

The American POWs were evacuated on foot to the border of Saxony and Czechoslovakia after U.S. General George S. Patton's 3rd Army captured Leipzig. With the captives abandoned by their guards, Vonnegut reached a prisoner-of-war repatriation camp in Le Havre, France, in May 1945, with the aid of the Soviets. Sent back to the United States, he was stationed at Fort Riley, Kansas, typing discharge papers for other soldiers. Soon after, he was awarded a Purple Heart, about which he remarked: "I myself was awarded my country's second-lowest decoration, a Purple Heart for frost-bite." He was discharged from the U.S. Army and returned to Indianapolis.

Marriage, University of Chicago, and early employment

After he returned to the United States, 22-year-old Vonnegut married Jane Marie Cox, his high-school girlfriend and classmate since kindergarten, on September 1, 1945. The pair moved to Chicago; there, Vonnegut enrolled in the University of Chicago on the G.I. Bill, as an anthropology student in an unusual five-year joint undergraduate/graduate program that conferred a master's degree. He studied under anthropologist Robert Redfield, his "most famous professor". He also worked as a reporter for the City News Bureau of Chicago.

Jane, who had graduated Phi Beta Kappa from Swarthmore, accepted a scholarship from the university to study Russian literature as a graduate student. Jane dropped out of the program after becoming pregnant with the couple's first child, Mark (born May 1947), while Kurt also left the university without any degree (despite having completed his undergraduate education). Vonnegut failed to write a dissertation, as his ideas had all been rejected. One abandoned topic was about the Ghost Dance and Cubist movements. A later topic, rejected "unanimously", had to do with the shapes of stories. Vonnegut received his graduate degree in anthropology 25 years after he left, when the university accepted his novel Cat's Cradle in lieu of his master's thesis.

Shortly thereafter, General Electric (GE) hired Vonnegut as a technical writer, then publicist, for the company's Schenectady, New York, News Bureau, a publicity department that operated like a newsroom. His brother Bernard had worked at GE since 1945, focusing mainly on a silver-iodide-based cloud seeding project that quickly became a joint GE–U.S. Army Signal Corps program, Project Cirrus. In The Brothers Vonnegut, Ginger Strand draws connections between many real events at General Electric, including Bernard's work, and Vonnegut's early stories, which were regularly being rejected everywhere he sent them. Throughout this period, Jane Vonnegut encouraged him, editing his stories, strategizing about submissions and buoying his spirits.

In 1949, Kurt and Jane had a daughter named Edith. Still working for GE, Vonnegut had his first piece, titled "Report on the Barnhouse Effect", published in the February 11, 1950, issue of Collier's, for which he received $750. The story concerned a scientist who fears that his invention will be used as a weapon, much as Bernard was fearing at the time about his cloudseeding work. Vonnegut wrote another story, after being coached by the fiction editor at Collier's, Knox Burger, and again sold it to the magazine, this time for $950. While Burger supported Vonnegut's writing, he was shocked when Vonnegut quit GE as of January 1, 1951, later stating: "I never said he should give up his job and devote himself to fiction. I don't trust the freelancer's life, it's tough." Nevertheless, in early 1951 Vonnegut moved with his family to Cape Cod, Massachusetts, to write full time, leaving GE behind. He initially moved to Osterville, but he ended up purchasing a home in Barnstable.

First novel

In 1952, Vonnegut's first novel, Player Piano, was published by Scribner's. The novel has a post-World War III setting, in which factory workers have been replaced by machines. Player Piano draws upon Vonnegut's experience as an employee at GE. The novel is set at a General Electric-like company and includes many scenes based on things Vonnegut saw there. He satirizes the drive to climb the corporate ladder, one that in Player Piano is rapidly disappearing as automation increases, putting even executives out of work. His central character, Paul Proteus, has an ambitious wife, a backstabbing assistant, and a feeling of empathy for the poor. Sent by his boss, Kroner, as a double agent among the poor (who have all the material goods they want, but little sense of purpose), he leads them in a machine-smashing, museum-burning revolution. Player Piano expresses Vonnegut's opposition to McCarthyism, something made clear when the Ghost Shirts, the revolutionary organization Paul penetrates and eventually leads, is referred to by one character as "fellow travelers".

In Player Piano, Vonnegut originates many of the techniques he would use in his later works. The comic, heavy-drinking Shah of Bratpuhr, an outsider to this dystopian corporate United States, is able to ask many questions that an insider would not think to ask, or would cause offense by doing so. For example, when taken to see the artificially intelligent supercomputer EPICAC, the Shah asks it "what are people for?" and receives no answer. Speaking for Vonnegut, he dismisses it as a "false god". This type of alien visitor would recur throughout Vonnegut's later novels.

The New York Times writer and critic Granville Hicks gave Player Piano a positive review, favorably comparing it to Aldous Huxley's Brave New World. Hicks called Vonnegut a "sharp-eyed satirist". None of the reviewers considered the novel particularly important. Several editions were printed—one by Bantam with the title Utopia 14, and another by the Doubleday Science Fiction Book Club—whereby Vonnegut gained the reputation as a writer of science fiction, a genre held in disdain by writers at that time. He defended the genre and deplored a perceived sentiment that "no one can simultaneously be a respectable writer and understand how a refrigerator works".

Struggling writer

Vonnegut with his wife Jane and children (from left to right): Mark, Edith and Nanette, in 1955

After Player Piano, Vonnegut continued to sell short stories to various magazines. Contracted to produce a second novel (which eventually became Cat's Cradle), he struggled to complete it, and the work languished for years. In 1954, the couple had a third child, Nanette. With a growing family and no financially successful novels yet, Vonnegut's short stories helped to sustain the family, though he frequently needed to find additional sources of income. In 1957, he and a partner opened a Saab automobile dealership on Cape Cod, but it went bankrupt by the end of the year. He designed a World War II–themed board game called "GHQ" (General Headquarters), but publishers did not buy it.

In 1958, his sister, Alice, died of cancer two days after her husband, James Carmalt Adams, was killed in a train accident. The Vonneguts took in three of the Adamses' young sons—James, Steven, and Kurt, aged 14, 11, and 9, respectively. A fourth Adams son, Peter, age 2, also stayed with the Vonneguts for about a year before being given to the care of a paternal relative in Georgia.

Grappling with family challenges, Vonnegut continued to write, publishing novels vastly dissimilar in terms of plot.

The Sirens of Titan (1959) features a Martian invasion of Earth as experienced by a bored billionaire, Malachi Constant. He meets Winston Niles Rumfoord, an aristocratic space traveler, who is virtually omniscient but stuck in a time warp that causes him to appear on Earth only every 59 days. The billionaire learns that his actions and the events of all of history are determined by a race of robotic aliens from the planet Tralfamadore, who need a replacement part that can only be produced by an advanced civilization in order to repair their spaceship and return home. Human history has been manipulated to produce it. Some human structures, such as the Kremlin, are coded signals from the aliens to their ship as to how long it may expect to wait for the repair to take place. Reviewers were uncertain what to think of the book, with one comparing it to Offenbach's opera The Tales of Hoffmann.

Rumfoord, who is based on Franklin D. Roosevelt, physically resembles the former president. Rumfoord is described this way: he "put a cigarette in a long, bone cigarette holder, lighted it. He thrust out his jaw. The cigarette holder pointed straight up." William Rodney Allen, in his guide to Vonnegut's works, stated that Rumfoord foreshadowed the fictional political figures who would play major roles in God Bless You, Mr. Rosewater and Jailbird.

Mother Night, published in 1961, received little attention at the time of its publication. Howard W. Campbell Jr., Vonnegut's protagonist, is an American who is raised in Germany from age 11 and joins the Nazi Party during the war as a double agent for the US Office of Strategic Services, rising to the regime's highest ranks as a radio propagandist. After the war, the spy agency refuses to clear his name, and he is eventually imprisoned by the Israelis in the same cell block as Adolf Eichmann. Vonnegut wrote in a foreword to a later edition, "We are what we pretend to be, so we must be careful about what we pretend to be". Literary critic Lawrence Berkove considered the novel, like Mark Twain's Adventures of Huckleberry Finn, to illustrate the tendency for "impersonators to get carried away by their impersonations, to become what they impersonate and therefore to live in a world of illusion".

Also published in 1961 was Vonnegut's short story "Harrison Bergeron", set in a dystopic future where all are equal, even if that means disfiguring beautiful people and forcing the strong or intelligent to wear devices that negate their advantages. Fourteen-year-old Harrison is a genius and athlete forced to wear record-level "handicaps" and imprisoned for attempting to overthrow the government. He escapes to a television studio, tears away his handicaps, and frees a ballerina from her lead weights. As they dance, they are killed by the Handicapper General, Diana Moon Glampers. Vonnegut, in a later letter, suggested that "Harrison Bergeron" might have sprung from his envy and self-pity as a high-school misfit. In his 1976 biography of Vonnegut, Stanley Schatt suggested that the short story shows that "in any leveling process, what really is lost, according to Vonnegut, is beauty, grace, and wisdom". Darryl Hattenhauer, in his 1998 journal article on "Harrison Bergeron", theorized that the story was a satire on American Cold War understandings of communism and socialism.

With Cat's Cradle (1963), Allen wrote, "Vonnegut hit full stride for the first time". The narrator, John, intends to write of Dr. Felix Hoenikker, one of the fictional fathers of the atomic bomb, seeking to cover the scientist's human side. Hoenikker, in addition to the bomb, has developed another threat to mankind, "ice-nine", which is solid water stable at room temperature but more dense than liquid water. If a particle of ice-nine is dropped in water, all of the surrounding water becomes ice-nine. Felix Hoenikker is based on Bernard Vonnegut's boss at the GE Research Lab, Irving Langmuir, and the way ice-nine is described in the novel is reminiscent of how Bernard Vonnegut explained his own invention, silver-iodide cloudseeding, to Kurt. Much of the second half of the book is spent on the fictional Caribbean island of San Lorenzo, where John explores a religion called Bokononism, whose holy books (excerpts from which are quoted) give the novel the moral core science does not supply. After the oceans are converted to ice-nine, wiping out most of humankind, John wanders the frozen surface, seeking to save himself and to make sure that his story survives.

Vonnegut based the title character of God Bless You, Mr. Rosewater (1964) on an accountant he knew in Cape Cod who specialized in clients in trouble and often had to comfort them. Eliot Rosewater, the wealthy son of a Republican senator, seeks to atone for his wartime killing of noncombatant firefighters by serving in a volunteer fire department and giving away money to those in trouble or need. Stress from a battle for control of his charitable foundation pushes him over the edge, and he is placed in a mental hospital. He recovers and ends the financial battle by declaring the children of his county to be his heirs. Allen deemed God Bless You, Mr. Rosewater more "a cry from the heart than a novel under its author's full intellectual control", that reflected family and emotional stresses Vonnegut was going through at the time.

In the mid-1960s, Vonnegut contemplated abandoning his writing career. In 1999, he wrote in The New York Times, "I had gone broke, was out of print and had a lot of kids..." But then, on the recommendation of an admirer, he received a surprise offer of a teaching job at the Iowa Writers' Workshop, employment that he likened to the rescue of a drowning man.

Slaughterhouse-Five

Main article: Slaughterhouse-Five

Vonnegut in 1972

After spending almost two years at the writer's workshop at the University of Iowa, teaching one course each term, Vonnegut was awarded a Guggenheim Fellowship for research in Germany. By the time he won it, in March 1967, he was becoming a well-known writer. He used the funds to travel in Eastern Europe, including to Dresden, where he found many prominent buildings still in ruins.

Vonnegut had been writing about his war experiences at Dresden ever since he returned from the war, but unable to write anything that was acceptable to himself or his publishers; chapter one of Slaughterhouse-Five tells of his difficulties. Released in 1969, the novel rocketed Vonnegut to fame. It tells of the life of Billy Pilgrim, who like Vonnegut was born in 1922 and survives the bombing of Dresden. The story is told in a non-linear fashion, with many of the story's climaxes—Billy's death in 1976, his kidnapping by aliens from the planet Tralfamadore nine years earlier, and the execution of Billy's friend Edgar Derby in the ashes of Dresden for stealing a teapot—disclosed in the story's first pages.

Slaughterhouse-Five received generally positive reviews, with Michael Crichton writing in The New Republic:

he writes about the most excruciatingly painful things. His novels have attacked our deepest fears of automation and the bomb, our deepest political guilts, our fiercest hatreds and loves. No one else writes books on these subjects; they are inaccessible to normal novelists.

The book went immediately to the top of The New York Times Best Seller list. Vonnegut's earlier works had appealed strongly to many college students, and the antiwar message of Slaughterhouse-Five resonated with a generation marked by the Vietnam War. He later stated that the loss of confidence in government that Vietnam caused finally allowed an honest conversation regarding events like Dresden.

In 1970, Vonnegut was also a correspondent in Biafra during the Nigerian Civil War.

Later life

New York, 228 East 48th Street (center), Kurt Vonnegut's house from 1973 to 2007

After Slaughterhouse-Five was published, Vonnegut embraced the fame and financial security that attended its release. He was hailed as a hero of the burgeoning anti-war movement in the United States, was invited to speak at numerous rallies, and gave college commencement addresses around the country. In addition to briefly teaching at Harvard University as a lecturer in creative writing in 1970, Vonnegut taught at the City College of New York as a distinguished professor during the 1973–1974 academic year. He was later elected vice president of the National Institute of Arts and Letters and given honorary degrees by, among others, Indiana University and Bennington College. Vonnegut also wrote a play called Happy Birthday, Wanda June, which opened on October 7, 1970, at New York's Theatre de Lys. Receiving mixed reviews, it closed on March 14, 1971. In 1972, Universal Pictures adapted Slaughterhouse-Five into a film, which the author said was "flawless".

Requiem (ending)

When the last living thing
has died on account of us,
how poetical it would be
if Earth could say,
in a voice floating up
perhaps
from the floor
of the Grand Canyon,
"It is done."
People did not like it here.

Kurt Vonnegut,
A Man Without a Country, 2005

Vonnegut's difficulties in his personal life thereafter materialized in numerous ways, including the painfully slow progress made on his next novel, the darkly comical Breakfast of Champions. In 1971, he stopped writing the novel altogether. When it was finally released in 1973, it was panned critically. In Thomas S. Hischak's book American Literature on Stage and Screen, Breakfast of Champions was called "funny and outlandish", but reviewers noted that it "lacks substance and seems to be an exercise in literary playfulness". Vonnegut's 1976 novel Slapstick, which meditates on the relationship between him and his sister (Alice), met a similar fate. In The New York Times's review of Slapstick, Christopher Lehmann-Haupt said that Vonnegut "seems to be putting less effort into [storytelling] than ever before" and that "it still seems as if he has given up storytelling after all". At times, Vonnegut was disgruntled by the personal nature of his detractors' complaints.

In subsequent years, his popularity resurged as he published several satirical books, including Jailbird (1979), Deadeye Dick (1982), Galápagos (1985), Bluebeard (1987), and Hocus Pocus (1990). Although he remained a prolific writer in the 1980s, Vonnegut struggled with depression and attempted suicide in 1984. Two years later, Vonnegut was seen by a younger generation when he played himself in Rodney Dangerfield's film Back to School. The last of Vonnegut's fourteen novels, Timequake (1997), was, as University of Detroit history professor and Vonnegut biographer Gregory Sumner said, "a reflection of an aging man facing mortality and testimony to an embattled faith in the resilience of human awareness and agency". Vonnegut's final book, a collection of essays entitled A Man Without a Country (2005), became a bestseller.

Personal life

Vonnegut married his first wife, Jane Marie Cox, in 1945. She later embraced Christianity, which was contrary to Vonnegut's atheistic beliefs; further, after five of their six children had left home, Vonnegut said that the two were forced to find "other sorts of seemingly important work to do". The couple battled over their differing beliefs until Vonnegut moved from their Cape Cod home to New York in 1971. Vonnegut called the disagreements "painful" and said that the resulting split was a "terrible, unavoidable accident that we were ill-equipped to understand". The couple divorced but remained friends until Jane's death in late 1986.

Beyond his failed marriage, Vonnegut was deeply affected when his son Mark suffered a mental breakdown in 1972, which exacerbated Vonnegut's chronic depression and led him to take Ritalin. When he stopped taking the drug in the mid-1970s, he began to see a psychologist weekly.

In 1979, Vonnegut married Jill Krementz, a photographer whom he met while she was working on a series about writers in the early 1970s. With Jill, he adopted a daughter, Lily, when the baby was three days old. They remained married until his death.

Death and legacy

Vonnegut's sincerity, his willingness to scoff at received wisdom, is such that reading his work for the first time gives one the sense that everything else is rank hypocrisy. His opinion of human nature was low, and that low opinion applied to his heroes and his villains alike—he was endlessly disappointed in humanity and in himself, and he expressed that disappointment in a mixture of tar-black humor and deep despair. He could easily have become a crank, but he was too smart; he could have become a cynic, but there was something tender in his nature that he could never quite suppress; he could have become a bore, but even at his most despairing he had an endless willingness to entertain his readers: with drawings, jokes, sex, bizarre plot twists, science fiction, whatever it took.

Lev Grossman, Time, 2007

In a 2006 Rolling Stone interview, Vonnegut sardonically stated that he would sue the Brown & Williamson tobacco company, the maker of the Pall Mall-branded cigarettes he had been smoking since he was around 12 or 14 years old, for false advertising: "And do you know why? Because I'm 83 years old. The lying bastards! On the package Brown & Williamson promised to kill me."

Vonnegut died in Manhattan on the night of April 11, 2007, as a result of brain injuries incurred several weeks prior in a fall at his brownstone home. His death was reported by his wife, Jill. He was 84 years old. At the time of his death he had written fourteen novels, three short-story collections, five plays, and five nonfiction books. A book composed of his unpublished pieces, Armageddon in Retrospect, was compiled and posthumously published by his son Mark in 2008.

When asked about the impact Vonnegut had on his work, author Josip Novakovich stated that he has "much to learn from Vonnegut—how to compress things and yet not compromise them, how to digress into history, quote from various historical accounts, and not stifle the narrative. The ease with which he writes is sheerly masterly, Mozartian." Los Angeles Times columnist Gregory Rodriguez said that the author will "rightly be remembered as a darkly humorous social critic and the premier novelist of the counterculture", and Dinitia Smith of The New York Times dubbed Vonnegut the "counterculture's novelist".

Vonnegut has inspired numerous posthumous tributes and works. In 2008, the Kurt Vonnegut Society was established, and in November 2010, the Kurt Vonnegut Museum and Library was opened in Vonnegut's hometown of Indianapolis. The Library of America published a compendium of Vonnegut's compositions between 1963 and 1973 the following April, and another compendium of his earlier works in 2012. Late 2011 saw the release of two Vonnegut biographies: Gregory Sumner's Unstuck in Time and Charles J. Shields's And So It Goes. Shields's biography of Vonnegut created some controversy. According to The Guardian, the book portrays Vonnegut as distant, cruel and nasty. "Cruel, nasty and scary are the adjectives commonly used to describe him by the friends, colleagues, and relatives Shields quotes", said The Daily Beast's Wendy Smith. "Towards the end he was very feeble, very depressed and almost morose", said Jerome Klinkowitz of the University of Northern Iowa, who has examined Vonnegut in depth.

Like Mark Twain, Mr. Vonnegut used humor to tackle the basic questions of human existence: Why are we in this world? Is there a presiding figure to make sense of all this, a god who in the end, despite making people suffer, wishes them well?

Dinitia Smith, The New York Times, 2007

Vonnegut's works have evoked ire on several occasions. His most prominent novel, Slaughterhouse-Five, has been objected to or removed at various institutions in at least 18 instances. In the case of Island Trees School District v. Pico, the United States Supreme Court ruled that a school district's ban on Slaughterhouse-Five—which the board had called "anti-American, anti-Christian, anti-Semitic, and just plain filthy"—and eight other novels was unconstitutional. When a school board in Republic, Missouri, decided to withdraw Vonnegut's novel from its libraries, the Kurt Vonnegut Memorial Library offered a free copy to all the students of the district.

Tally, writing in 2013, suggests that Vonnegut has only recently become the subject of serious study rather than fan adulation, and much is yet to be written about him. "The time for scholars to say 'Here's why Vonnegut is worth reading' has definitively ended, thank goodness. We know he's worth reading. Now tell us things we don't know." Todd F. Davis notes that Vonnegut's work is kept alive by his loyal readers, who have "significant influence as they continue to purchase Vonnegut's work, passing it on to subsequent generations and keeping his entire canon in print—an impressive list of more than twenty books that [Dell Publishing] has continued to refurbish and hawk with new cover designs." Donald E. Morse notes that Vonnegut "is now firmly, if somewhat controversially, ensconced in the American and world literary canon as well as in high school, college and graduate curricula". Tally writes of Vonnegut's work:

Vonnegut's 14 novels, while each does its own thing, together are nevertheless experiments in the same overall project. Experimenting with the form of the American novel itself, Vonnegut engages in a broadly modernist attempt to apprehend and depict the fragmented, unstable, and distressing bizarreries of postmodern American experience ... That he does not actually succeed in representing the shifting multiplicities of that social experience is beside the point. What matters is the attempt, and the recognition that ... we must try to map this unstable and perilous terrain, even if we know in advance that our efforts are doomed.

Kurt Vonnegut Museum and Library in Indianapolis in 2022

The Science Fiction and Fantasy Hall of Fame inducted Vonnegut posthumously in 2015. The asteroid 25399 Vonnegut is named in his honor. A crater on the planet Mercury has also been named in his honor. In 2021, the Kurt Vonnegut Museum and Library in Indianapolis was designated a Literary Landmark by the Literary Landmarks Association. In 1986, the University of Evansville library located in Evansville, Indiana, where he spoke during the dedication ceremony, was named after Vonnegut.

Views

The beliefs I have to defend are so soft and complicated, actually, and, when vivisected, turn into bowls of undifferentiated mush. I am a pacifist, I am an anarchist, I am a planetary citizen, and so on.

— Kurt Vonnegut

War

In the introduction to Slaughterhouse-Five, Vonnegut recounts meeting the film producer Harrison Starr at a party, who asked him whether his forthcoming book was an anti-war novel—"Yes, I guess", replied Vonnegut. Starr responded: "Why don't you write an anti-glacier novel?" In the novel, Vonnegut's character continues: "What he meant, of course, is that there would always be wars, that they were as easy to stop as glaciers. I believe that, too. And even if wars didn't keep coming like glaciers, there would still be plain old death". Vonnegut was a pacifist.

A large painting of Vonnegut on Massachusetts Avenue, Indianapolis, blocks away from the Kurt Vonnegut Museum and the Athenæum (Das Deutsche Haus), which was designed by his family's architecture firm

In 2011, NPR wrote, "Kurt Vonnegut's blend of anti-war sentiment and satire made him one of the most popular writers of the 1960s." Vonnegut stated in a 1987 interview, "My own feeling is that civilization ended in World War I, and we're still trying to recover from that", and that he wanted to write war-focused works without glamorizing war itself. Vonnegut had not intended to publish again, but his anger against the George W. Bush administration led him to write A Man Without a Country.

Slaughterhouse-Five is the Vonnegut novel best known for its antiwar themes, but the author expressed his beliefs in ways beyond the depiction of the destruction of Dresden. One character, Mary O'Hare, opines that "wars were partly encouraged by books and movies" starring "Frank Sinatra or John Wayne or some of those other glamorous, war-loving, dirty old men". Vonnegut made a number of comparisons in Slaughterhouse-Five between Dresden and the bombing of Hiroshima and wrote in Palm Sunday (1991), "I learned how vile that religion of mine could be when the atomic bomb was dropped on Hiroshima".

Nuclear war, or at least deployed nuclear arms, is mentioned in almost all of Vonnegut's novels. In Player Piano, the computer EPICAC is given control of the nuclear arsenal and is charged with deciding whether to use high-explosive or nuclear arms. In Cat's Cradle, John's original purpose in setting pen to paper was to write an account of what prominent Americans had been doing as Hiroshima was bombed.

Religion

Some of you may know that I am neither Christian nor Jewish nor Buddhist, nor a conventionally religious person of any sort. I am a humanist, which means, in part, that I have tried to behave decently without any expectation of rewards or punishments after I'm dead. ... I myself have written, "If it weren't for the message of mercy and pity in Jesus' Sermon on the Mount, I wouldn't want to be a human being. I would just as soon be a rattlesnake."

Kurt Vonnegut, God Bless You, Dr. Kevorkian, 1999

Vonnegut was an atheist, a humanist and a freethinker, serving as the honorary president of the American Humanist Association. In an interview for Playboy, he stated that his forebears who came to the United States did not believe in God, and he learned his atheism from his parents. Vonnegut did not, however, disdain those who seek the comfort of religion, hailing church associations as a type of extended family. He occasionally attended a Unitarian church, but with little consistency. In his autobiographical work Palm Sunday, Vonnegut says that he is a "Christ-worshipping agnostic". During a speech to the Unitarian Universalist Association, he called himself a "Christ-loving atheist". However, he was keen to stress that he was not a Christian.

Vonnegut was an admirer of Jesus' Sermon on the Mount, particularly the Beatitudes, and incorporated it into his own doctrines. He also referred to it in many of his works. In his 1991 book Fates Worse than Death, Vonnegut suggests that during the Reagan administration, "anything that sounded like the Sermon on the Mount was socialistic or communistic, and therefore anti-American". In Palm Sunday, he wrote that "the Sermon on the Mount suggests a mercifulness that can never waver or fade". However, Vonnegut had a deep dislike for certain aspects of Christianity, often reminding his readers of the bloody history of the Crusades and other religion-inspired violence. He despised the televangelists of the late 20th century, feeling that their thinking was narrow-minded.

Religion features frequently in Vonnegut's work, both in his novels and elsewhere. He laced a number of his speeches with religion-focused rhetoric and was prone to using such expressions as "God forbid" and "thank God". He once wrote his own version of the Requiem Mass, which he then had translated into Latin and set to music. In God Bless You, Dr. Kevorkian, Vonnegut goes to heaven after he is euthanized by Dr. Jack Kevorkian. Once in heaven, he interviews 21 deceased celebrities, including Isaac Asimov, William Shakespeare, and Kilgore Trout—the last a fictional character from several of his novels. Vonnegut's works are filled with characters founding new faiths, and religion often serves as a major plot device, for example, in Player Piano, The Sirens of Titan and Cat's Cradle. In The Sirens of Titan, Rumfoord proclaims The Church of God the Utterly Indifferent. Slaughterhouse-Five sees Billy Pilgrim, lacking religion himself, nevertheless become a chaplain's assistant in the military and display a large crucifix on his bedroom wall.^[] In Cat's Cradle, Vonnegut invented the religion of Bokononism.

Politics

Vonnegut's thoughts on politics were shaped in large part by Robert Redfield, an anthropologist at the University of Chicago, co-founder of the Committee on Social Thought, and one of Vonnegut's professors during his time at the university. In a commencement address, Vonnegut remarked that "Dr. Redfield's theory of the Folk Society ... has been the starting point for my politics, such as they are". Vonnegut did not particularly sympathize with liberalism or conservatism. Vonnegut also mused on the specious simplicity of American politics, saying facetiously: "If you want to take my guns away from me, and you're all for murdering fetuses, and love it when homosexuals marry each other ... you're a liberal. If you are against those perversions and for the rich, you're a conservative. What could be simpler?" Regarding political parties, Vonnegut said: "The two real political parties in America are the Winners and the Losers. The people don't acknowledge this. They claim membership in two imaginary parties, the Republicans and the Democrats, instead."

Vonnegut disdained more mainstream American political ideologies in favor of socialism, which he thought could provide a valuable substitute for what he saw as social Darwinism and a spirit of "survival of the fittest" in American society, believing that "socialism would be a good for the common man". Vonnegut often returned to a quote by socialist and five-time presidential candidate Eugene V. Debs: "As long as there is a lower class, I am in it. As long as there is a criminal element, I'm of it. As long as there is a soul in prison, I am not free." Vonnegut expressed disappointment that communism and socialism seemed to be unsavory topics to the average American and believed that they offered beneficial substitutes to contemporary social and economic systems.

Technology

In A Man Without a Country, Vonnegut quipped, "I have been called a Luddite. I welcome it. Do you know what a Luddite is? A person who hates newfangled contraptions." The negative effects of the progress of technology are a constant theme throughout Vonnegut's works, from Player Piano to his final essay collection, A Man Without a Country. Political theorist Patrick Deneen has identified this skepticism about technological progress as a theme of Vonnegut novels and stories, including Player Piano, "Harrison Bergeron", and "Tomorrow and Tomorrow and Tomorrow". Scholars who position Vonnegut as a critic of liberalism reference his pessimism toward technological progress. Vonnegut described Player Piano some years after its publication as "a novel about people and machines, and machines frequently got the best of it, as machines will." Loss of jobs due to machine innovation, and thus loss of meaning or purpose in life, is a key plot point in the novel. The "newfangled contraptions" Vonnegut hated included the television, which he critiqued often throughout his nonfiction and fiction. In Timequake, for example, Vonnegut tells the story of "Booboolings", human analogs who develop morally through their imaginative formation. However, one evil sister on the planet of the Booboolings learns from lunatics how to build televisions. He writes:

When the bad sister was a young woman, she and the nuts worked up designs for television cameras and transmitters and receivers. Then she got money from her very rich mom to manufacture these satanic devices, which made imaginations redundant. They were instantly popular because the shows were so attractive and no thinking was involved ... Generations of Booboolings grew up without imaginations ... Without imaginations, though, they couldn't do what their ancestors had done, which was read interesting, heartwarming stories in the faces of one another. So ... Booboolings became among the most merciless creatures in the local family of galaxies.

Against imagination-killing devices like televisions, and against electronic substitutes for embodied community, Vonnegut argued that "Electronic communities build nothing. You wind up with nothing. We are dancing animals. How beautiful it is to get up and go out and do something."

Writing

Influences

Vonnegut's writing was inspired by an eclectic mix of sources. When he was younger, Vonnegut stated that he read works of pulp fiction, science fiction, fantasy, and action-adventure. He also read the classics, such as the plays of Aristophanes—like Vonnegut's works, humorous critiques of contemporary society. Vonnegut's life and work also share similarities with that of Adventures of Huckleberry Finn writer Mark Twain. Both shared pessimistic outlooks on humanity and a skeptical take on religion and, as Vonnegut put it, were both "associated with the enemy in a major war", as Twain briefly enlisted in the South's cause during the American Civil War, and Vonnegut's German name and ancestry connected him with the United States' enemy in both world wars. He also cited Ambrose Bierce as an influence, calling "An Occurrence at Owl Creek Bridge" the greatest American short story and deeming any who disagreed or had not read the story "twerps".

Vonnegut called George Orwell his favorite writer and admitted that he tried to emulate Orwell. "I like his concern for the poor, I like his socialism, I like his simplicity", Vonnegut said. Vonnegut also said that Orwell's Nineteen Eighty-Four and Brave New World by Aldous Huxley heavily influenced his debut novel, Player Piano, in 1952. The novel also included ideas from mathematician Norbert Wiener's book Cybernetics: Or Control and Communication in the Animal and the Machine. Vonnegut commented that Robert Louis Stevenson's stories were emblems of thoughtfully put together works that he tried to mimic in his own compositions. Vonnegut also hailed playwright and socialist George Bernard Shaw as "a hero of [his]" and an "enormous influence". Within his own family, Vonnegut stated that his mother, Edith, had the greatest influence on him. "[My] mother thought she might make a new fortune by writing for the slick magazines. She took short-story courses at night. She studied writers the way gamblers study horses."

Early on in his career, Vonnegut decided to model his style after that of Henry David Thoreau, who wrote as if from the perspective of a child, allowing Thoreau's works to be widely comprehensible. Using a youthful narrative voice allowed Vonnegut to deliver concepts in a modest and straightforward way. Other influences on Vonnegut include The War of the Worlds author H. G. Wells and satirist Jonathan Swift. Vonnegut credited American journalist and critic H. L. Mencken for inspiring him to become a journalist.

Style and technique

The book Pity the Reader: On Writing with Style by Kurt Vonnegut and his longtime friend and former student Suzanne McConnell, published posthumously by Rosetta Books and Seven Stories Press in 2019, delves into the style, humor, and methodologies Vonnegut employed, including his belief that one should "Write like a human being. Write like a writer."

I've heard the Vonnegut voice described as "manic depressive", and there's certainly something to this. It has an incredible amount of energy married to a very deep and dark sense of despair. It's frequently over-the-top, and scathingly satirical, but it never strays too far from pathos—from an immense sympathy for society's vulnerable, oppressed and powerless. But, then, it also contains a huge allotment of warmth. Most of the time, reading Kurt Vonnegut feels more like being spoken to by a very close friend. There's an inclusiveness to his writing that draws you in, and his narrative voice is seldom absent from the story for any length of time. Usually, it's right there in the foreground—direct, involving and extremely idiosyncratic.

Gavin Extence, The Huffington Post, 2013

In his book Popular Contemporary Writers, Michael D. Sharp describes Vonnegut's linguistic style as straightforward, his sentences concise, his language simple, his paragraphs brief, and his ordinary tone conversational. Vonnegut uses this style to convey normally complex subject matter in a way that is intelligible to a large audience. He credited his time as a journalist for his ability and pointed to his work with the Chicago City News Bureau, which required him to convey stories in telephone conversations. Vonnegut's compositions include distinct references to his own life, notably in Slaughterhouse-Five and Slapstick.

Vonnegut believed that ideas and the convincing communication of those ideas to the reader were vital to literary art. He did not always sugarcoat his points; much of Player Piano leads to the moment when Paul, on trial and hooked to a lie detector, is asked to tell a falsehood. Paul says, "Every new piece of scientific knowledge is a good thing for humanity". Robert T. Tally Jr., in his volume on Vonnegut's novels, wrote, "Rather than tearing down and destroying the icons of twentieth-century, middle-class American life, Vonnegut gently reveals their basic flimsiness". Vonnegut did not simply propose utopian solutions to the ills of American society but showed how such schemes would not allow ordinary people to live lives free from want and anxiety. The large, artificial U.S. families in Slapstick soon serve as an excuse for tribalism. People give no help to those not part of their group; the extended family's place in the social hierarchy becomes vital.

In the introduction to their essay "Kurt Vonnegut and Humor", Tally and Peter C. Kunze suggest that Vonnegut was not a "black humorist", but a "frustrated idealist" who used "comic parables" to teach the reader absurd, bitter or hopeless truths, with his grim witticisms serving to make the reader laugh rather than cry. "Vonnegut makes sense through humor, which is, in the author's view, as valid a means of mapping this crazy world as any other strategies." Vonnegut resented being called a black humorist, feeling that, as with many literary labels, it allowed readers to disregard aspects of a writer's work that did not fit the label.

Vonnegut's works have been labeled science fiction, satire and postmodern. He resisted such labels, but his works do contain common tropes in those genres. In his books, Vonnegut imagines alien societies and civilizations, as is common in science fiction. He emphasizes or exaggerates absurdities and idiosyncrasies. Furthermore, Vonnegut makes fun of problems, as satire does. However, literary theorist Robert Scholes noted in Fabulation and Metafiction that Vonnegut "reject[s] the traditional satirist's faith in the efficacy of satire as a reforming instrument. [He has] a more subtle faith in the humanizing value of laughter."

Postmodernism entails a response to the theory that science will reveal truths. Postmodernists contend that truth is subjective rather than objective. Truth includes bias toward individual beliefs and outlooks on the world. Postmodernist writers use unreliable, first-person narration, and narrative fragmentation. One critic has argued that Vonnegut's most famous novel, Slaughterhouse-Five, features a metafictional, Janus-headed outlook and seeks to represent historical events while doubting the ability to represent history. Doubt is evident in the opening lines of the novel: "All this happened, more or less. The war parts, anyway, are pretty much true." The bombastic opening—"All this happened"—"reads like a declaration of complete mimesis," which is radically called into question in the rest of the quote and "[t]his creates an integrated perspective that seeks out extratextual themes [like war and trauma] while thematizing the novel's textuality and inherent constructedness at one and the same time." Although Vonnegut does use fragmentation and metafiction in some of his works, he more distinctly focuses on the peril of individuals who find subjective truths, mistake them for objective truths, and proceed to impose these truths on other people.

Themes

Economy

Vonnegut was a vocal critic of American society, and this was reflected in his writings. Several key social themes recur in Vonnegut's works, such as wealth, the lack of it, and its unequal distribution among a society. In The Sirens of Titan, the novel's protagonist, Malachi Constant, is exiled to Saturn's moon Titan as a result of his vast wealth, which has made him arrogant and wayward. In God Bless You, Mr. Rosewater, readers may find it difficult to determine whether the rich or the poor are in worse circumstances, as the lives of both groups' members are ruled by their wealth or their poverty. Further, in Hocus Pocus, the protagonist is named Eugene Debs Hartke, a homage to the famed socialist Eugene V. Debs and Vonnegut's socialist views.

In Kurt Vonnegut: A Critical Companion, Thomas F. Marvin states: "Vonnegut points out that, left unchecked, capitalism will erode the democratic foundations of the United States." Marvin suggests that Vonnegut's works demonstrate what happens when a "hereditary aristocracy" develops, where wealth is inherited along familial lines: the ability of poor Americans to overcome their situations is greatly or completely diminished. Vonnegut also often laments social Darwinism and a "survival of the fittest" view of society. He points out that social Darwinism leads to a society that condemns its poor for their own misfortune and fails to help them out of their poverty because "they deserve their fate".

Ethics in science

Science and the ethical obligations of scientists are also a common theme in Vonnegut's works. His first published story, "Report on the Barnhouse Effect", like many of his early stories, centered on a scientist concerned about the uses of his own invention. Player Piano and Cat's Cradle explore the effects on humans of scientific advances. In 1969, Vonnegut gave a speech to the American Association of Physics Teachers called "The Virtuous Physicist". Asked afterwards what a virtuous scientist was, Vonnegut replied, "one who declines to work on weapons."

Life

Vonnegut also confronts the idea of free will in a number of his pieces. In Slaughterhouse-Five and Timequake the characters have no choice in what they do; in Breakfast of Champions, characters are very obviously stripped of their free will and even receive it as a gift; and in Cat's Cradle, Bokononism views free will as heretical.

The majority of Vonnegut's characters are estranged from their actual families and seek to build replacement or extended families. For example, the engineers in Player Piano called their manager's spouse "Mom". In Cat's Cradle, Vonnegut devises two separate methods for loneliness to be combated: A "karass", which is a group of individuals appointed by God to do his will, and a "granfalloon", defined by Marvin as a "meaningless association of people, such as a fraternal group or a nation". Similarly, in Slapstick, the US government codifies that all Americans are a part of large extended families.

Fear of losing one's purpose in life is a theme in Vonnegut's works. During the Great Depression Vonnegut witnessed the devastation many people felt when they lost their jobs, and while at General Electric he witnessed machines being built to take the place of human labor. He confronts these things in his works through references to the growing use of automation and its effects on human society. This is most starkly represented in his first novel, Player Piano, where many Americans are left purposeless and unable to find work, as machines replace human workers. Loss of purpose is also depicted in Galápagos, where a florist rages at her spouse for creating a robot able to do her job, and in Timequake, where an architect kills himself when replaced by computer software.

Suicide by fire is another common theme in Vonnegut's works; the author often returns to the theory that "many people are not fond of life". He uses this as an explanation for why humans have so severely damaged their environment and made devices such as nuclear weapons that can make their creators extinct. In Deadeye Dick Vonnegut features the neutron bomb, which is designed to kill people but leave buildings and structures untouched. He also uses this theme to demonstrate the recklessness of those who put powerful, apocalypse-inducing devices at the disposal of politicians.

"What is the point of life?" is a question Vonnegut often pondered in his works. When one of his characters, Kilgore Trout, finds the question "What is the purpose of life?" written in a bathroom, his response is, "To be the eyes and ears and conscience of the Creator of the Universe, you fool." Marvin finds Trout's theory curious, given that Vonnegut was an atheist and thus for him, there is no Creator to report back to, and comments that, "[as] Trout chronicles one meaningless life after another, readers are left to wonder how a compassionate creator could stand by and do nothing while such reports come in". In the epigraph to Bluebeard, Vonnegut quotes his son Mark and gives an answer to what he believes is the meaning of life: "We are here to help each other get through this thing, whatever it is."

Tralfamadore

A fictional planet called Tralfamadore is a recurring motif in Vonnegut's works. A planet by that name is referenced in The Sirens of Titan; God Bless You, Mr. Rosewater; Slaughterhouse-Five; Hocus Pocus; and Timequake. It is variously depicted as being located outside the Milky Way galaxy or being fictional within the fiction itself; in Slaughterhouse-Five, it is implied to be imaginary as a result of the protagonist losing his grip on reality. A recurring characteristic of the inhabitants of Tralfamadore is their low esteem of humanity. According to Julia A. Whitehead, Vonnegut used the concept of an imagined planet inhabited by beings more enlightened than humans as an outlet for escapism. By contrast, Lawrence R. Boer rejects the notion that the pessimism and fatalism of the Tralfamadorians in Slaughterhouse-Five reflect the views of the author, and Brian Stableford characterizes the different Tralfamadorian races in that book and The Sirens of Titan as "tiny-minded smartasses".

Awards and nominations

Award	Year	Category	Book	Result	Ref.
International Fantasy Award	1953	-	Player Piano	Nominated	-
Writers Guild of America Award	1960	Television script	"Auf Wiedersehen"	Won	-
Hugo Award	1960	Best Novel	The Sirens of Titan	Nominated
Hugo Award	1964	Best Novel	Cat's Cradle	Nominated
Nebula Award	1970	Best Novel	Slaughterhouse-Five	Nominated
Hugo Award	1970	Best Novel	Slaughterhouse-Five	Nominated
Drama Desk Award	1971	Outstanding New Play	Happy Birthday, Wanda June	Won	-
Seiun Award	1973	Foreign Novel	The Sirens of Titan	Won	-
Hugo Award for Best Dramatic Presentation	1973	Best Dramatic Presentation	Slaughterhouse-Five	Won	-
John W. Campbell Award	1986	Best Science Fiction Novel	Galápagos	Nominated
Audie Award	2009	Short Stories/Collections	Armageddon in Retrospect	Won	-
Science Fiction and Fantasy Hall of Fame	2015	-	-	Inducted	-
Prometheus Hall of Fame award of the Libertarian Futurist Society	2019	-	Harrison Bergeron	Inducted	-

Works

Main article: Kurt Vonnegut bibliography

Unless otherwise cited, items in this list are taken from Thomas F. Marvin's 2002 book Kurt Vonnegut: A Critical Companion, and the date in parentheses is the date the work was published:

Novels

• Player Piano (1952)
• The Sirens of Titan (1959)
• Mother Night (1962)
• Cat's Cradle (1963)
• God Bless You, Mr. Rosewater (1965)
• Slaughterhouse-Five (1969)
• Breakfast of Champions (1973)
• Slapstick (1976)
• Jailbird (1979)
• Deadeye Dick (1982)
• Galápagos (1985)
• Bluebeard (1987)
• Hocus Pocus (1990)
• Timequake (1997)

Short fiction collections

• Canary in a Cat House (1961)
• Welcome to the Monkey House (1968)
• Bagombo Snuff Box (1997)
• God Bless You, Dr. Kevorkian (1999)
• Armageddon in Retrospect (2008) – short stories and essays
• Look at the Birdie (2009)
• While Mortals Sleep (2011)
• We Are What We Pretend to Be (2012)
• Sucker's Portfolio (2013)
• Complete Stories (2017)

Plays

• The First Christmas Morning (1962)
• Fortitude (1968)
• Happy Birthday, Wanda June (1970)
• Between Time and Timbuktu (1972)
• Stones, Time and Elements (A Humanist Requiem) (1987)
• Make Up Your Mind (1993)
• L'Histoire du Soldat (1997)

Nonfiction

• Wampeters, Foma and Granfalloons (1974)
• Palm Sunday (1981)
• Nothing Is Lost Save Honor: Two Essays (1984)
• Fates Worse Than Death (1991)
• A Man Without a Country (2005)^[32]
• Kurt Vonnegut: The Cornell Sun Years 1941–1943 (2012)
• If This Isn't Nice, What Is?: Advice to the Young (2013)
• Vonnegut by the Dozen (2013)
• Kurt Vonnegut: Letters (2014)
• Pity the Reader: On Writing With Style (2019) with Suzanne McConnell
• Love, Kurt: The Vonnegut Love Letters, 1941–1945 (2020) Editor Edith Vonnegut

Interviews

• Conversations with Kurt Vonnegut (1988) with William Rodney Allen
• Like Shaking Hands with God: A Conversation About Writing (1999) with Lee Stringer
• Kurt Vonnegut: The Last Interview: And Other Conversations (2011)

Children's books

• Sun Moon Star (1980)

Art

• Kurt Vonnegut Drawings (2014)

Best, worst and average case

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Best,_worst_and_average_case

In computer science, best, worst, and average cases of a given algorithm express what the resource usage is at least, at most and on average, respectively. Usually the resource being considered is running time, i.e. time complexity, but could also be memory or some other resource. Best case is the function which performs the minimum number of steps on input data of n elements. Worst case is the function which performs the maximum number of steps on input data of size n. Average case is the function which performs an average number of steps on input data of n elements.

In real-time computing, the worst-case execution time is often of particular concern since it is important to know how much time might be needed in the worst case to guarantee that the algorithm will always finish on time.

Average performance and worst-case performance are the most used in algorithm analysis. Less widely found is best-case performance, but it does have uses: for example, where the best cases of individual tasks are known, they can be used to improve the accuracy of an overall worst-case analysis. Computer scientists use probabilistic analysis techniques, especially expected value, to determine expected running times.

The terms are used in other contexts; for example the worst- and best-case outcome of an epidemic, worst-case temperature to which an electronic circuit element is exposed, etc. Where components of specified tolerance are used, devices must be designed to work properly with the worst-case combination of tolerances and external conditions.

Best-case performance for algorithm

The term best-case performance is used in computer science to describe an algorithm's behavior under optimal conditions. For example, the best case for a simple linear search on a list occurs when the desired element is the first element of the list.

Development and choice of algorithms is rarely based on best-case performance: most academic and commercial enterprises are more interested in improving average-case complexity and worst-case performance. Algorithms may also be trivially modified to have good best-case running time by hard-coding solutions to a finite set of inputs, making the measure almost meaningless.

Worst-case versus amortized versus average-case performance

Further information: average-case complexity, amortized analysis, and worst-case complexity

Worst-case performance analysis and average-case performance analysis have some similarities, but in practice usually require different tools and approaches.

Determining what typical input means is difficult, and often that average input has properties which make it difficult to characterise mathematically (consider, for instance, algorithms that are designed to operate on strings of text). Similarly, even when a sensible description of a particular "average case" (which will probably only be applicable for some uses of the algorithm) is possible, they tend to result in more difficult analysis of equations.

Worst-case analysis gives a safe analysis (the worst case is never underestimated), but one which can be overly pessimistic, since there may be no (realistic) input that would take this many steps.

In some situations it may be necessary to use a pessimistic analysis in order to guarantee safety. Often however, a pessimistic analysis may be too pessimistic, so an analysis that gets closer to the real value but may be optimistic (perhaps with some known low probability of failure) can be a much more practical approach. One modern approach in academic theory to bridge the gap between worst-case and average-case analysis is called smoothed analysis.

When analyzing algorithms which often take a small time to complete, but periodically require a much larger time, amortized analysis can be used to determine the worst-case running time over a (possibly infinite) series of operations. This amortized cost can be much closer to the average cost, while still providing a guaranteed upper limit on the running time. So e.g. online algorithms are frequently based on amortized analysis.

The worst-case analysis is related to the worst-case complexity.

Practical consequences

Many algorithms with bad worst-case performance have good average-case performance. For problems we want to solve, this is a good thing: we can hope that the particular instances we care about are average. For cryptography, this is very bad: we want typical instances of a cryptographic problem to be hard. Here methods like random self-reducibility can be used for some specific problems to show that the worst case is no harder than the average case, or, equivalently, that the average case is no easier than the worst case.

On the other hand, some data structures like hash tables have very poor worst-case behaviors, but a well written hash table of sufficient size will statistically never give the worst case; the average number of operations performed follows an exponential decay curve, and so the run time of an operation is statistically bounded.

Examples

Sorting algorithms

See also: Sorting algorithm § Comparison of algorithms

 

Algorithm	Data structure	Time complexity:Best	Time complexity:Average	Time complexity:Worst	Space complexity:Worst
Quick sort	Array	O(n log(n))	O(n log(n))	O(n2)	O(n)
Merge sort	Array	O(n log(n))	O(n log(n))	O(n log(n))	O(n)
Heap sort	Array	O(n log(n))	O(n log(n))	O(n log(n))	O(1)
Smooth sort	Array	O(n)	O(n log(n))	O(n log(n))	O(1)
Bubble sort	Array	O(n)	O(n2)	O(n2)	O(1)
Insertion sort	Array	O(n)	O(n2)	O(n2)	O(1)
Selection sort	Array	O(n2)	O(n2)	O(n2)	O(1)
Bogo sort	Array	O(n)	O(n n!)	O(∞)	O(1)

Graphs of functions commonly used in the analysis of algorithms, showing the number of operations N versus input size n for each function

• Insertion sort applied to a list of n elements, assumed to be all different and initially in random order. On average, half the elements in a list A₁ ... A_j are less than element A_j+1, and half are greater. Therefore, the algorithm compares the (j + 1)^th element to be inserted on the average with half the already sorted sub-list, so t_j = j/2. Working out the resulting average-case running time yields a quadratic function of the input size, just like the worst-case running time.
• Quicksort applied to a list of n elements, again assumed to be all different and initially in random order. This popular sorting algorithm has an average-case performance of O(n log(n)), which contributes to making it a very fast algorithm in practice. But given a worst-case input, its performance degrades to O(n²). Also, when implemented with the "shortest first" policy, the worst-case space complexity is instead bounded by O(log(n)).
• Heapsort has O(n) time when all elements are the same. Heapify takes O(n) time and then removing elements from the heap is O(1) time for each of the n elements. The run time grows to O(nlog(n)) if all elements must be distinct.
• Bogosort has O(n) time when the elements are sorted on the first iteration. In each iteration all elements are checked if in order. There are n! possible permutations; with a balanced random number generator, almost each permutation of the array is yielded in n! iterations. Computers have limited memory, so the generated numbers cycle; it might not be possible to reach each permutation. In the worst case this leads to O(∞) time, an infinite loop.

Data structures

See also: Search data structure § Asymptotic worst-case analysis

 

Data structure	Time complexity								Space complexity
	Avg: Indexing	Avg: Search	Avg: Insertion	Avg: Deletion	Worst: Indexing	Worst: Search	Worst: Insertion	Worst: Deletion	Worst
Basic array	O(1)	O(n)	O(n)	O(n)	O(1)	O(n)	O(n)	O(n)	O(n)
Dynamic array	O(1)	O(n)	O(n)	—	O(1)	O(n)	O(n)	—	O(n)
Stack	O(n)	O(n)	O(1)	O(1)	O(n)	O(n)	O(1)	O(1)	O(n)
Queue	O(n)	O(n)	O(1)	O(1)	O(n)	O(n)	O(1)	O(1)	O(n)
Singly linked list	O(n)	O(n)	O(1)	O(1)	O(n)	O(n)	O(1)	O(1)	O(n)
Doubly linked list	O(n)	O(n)	O(1)	O(1)	O(n)	O(n)	O(1)	O(1)	O(n)
Skip list	O(log (n))	O(log (n))	O(log (n))	O(log (n))	O(n)	O(n)	O(n)	O(n)	O(nlog (n))
Hash table	—	O(1)	O(1)	O(1)	—	O(n)	O(n)	O(n)	O(n)
Binary search tree	O(log (n))	O(log (n))	O(log (n))	O(log (n))	O(n)	O(n)	O(n)	O(n)	O(n)
Cartesian tree	—	O(log (n))	O(log (n))	O(log (n))	—	O(n)	O(n)	O(n)	O(n)
B-tree	O(log (n))	O(log (n))	O(log (n))	O(log (n))	O(log (n))	O(log (n))	O(log (n))	O(log (n))	O(n)
Red–black tree	O(log (n))	O(log (n))	O(log (n))	O(log (n))	O(log (n))	O(log (n))	O(log (n))	O(log (n))	O(n)
Splay tree	—	O(log (n))	O(log (n))	O(log (n))	—	O(log (n))	O(log (n))	O(log (n))	O(n)
AVL tree	O(log (n))	O(log (n))	O(log (n))	O(log (n))	O(log (n))	O(log (n))	O(log (n))	O(log (n))	O(n)
K-d tree	O(log (n))	O(log (n))	O(log (n))	O(log (n))	O(n)	O(n)	O(n)	O(n)	O(n)

• Linear search on a list of n elements. In the absolute worst case, the search must visit every element once. This happens when the value being searched for is either the last element in the list, or is not in the list. However, on average, assuming the value searched for is in the list and each list element is equally likely to be the value searched for, the search visits only n/2 elements.

Randomized algorithm

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Randomized_algorithm

A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random determined by the random bits; thus either the running time, or the output (or both) are random variables.

There is a distinction between algorithms that use the random input so that they always terminate with the correct answer, but where the expected running time is finite (Las Vegas algorithms, for example Quicksort), and algorithms which have a chance of producing an incorrect result (Monte Carlo algorithms, for example the Monte Carlo algorithm for the MFAS problem) or fail to produce a result either by signaling a failure or failing to terminate. In some cases, probabilistic algorithms are the only practical means of solving a problem.

In common practice, randomized algorithms are approximated using a pseudorandom number generator in place of a true source of random bits; such an implementation may deviate from the expected theoretical behavior and mathematical guarantees which may depend on the existence of an ideal true random number generator.

Motivation

As a motivating example, consider the problem of finding an ‘a’ in an array of n elements.

Input: An array of n≥2 elements, in which half are ‘a’s and the other half are ‘b’s.

Output: Find an ‘a’ in the array.

We give two versions of the algorithm, one Las Vegas algorithm and one Monte Carlo algorithm.

Las Vegas algorithm:

findingA_LV(array A, n)
begin
    repeat
        Randomly select one element out of n elements.
    until 'a' is found
end

This algorithm succeeds with probability 1. The number of iterations varies and can be arbitrarily large, but the expected number of iterations is

${\displaystyle \underset{n\to \mathrm{\infty }}{lim}\sum _{i=1}^n\frac{i}{2^i}=2}$

Since it is constant, the expected run time over many calls is ${\displaystyle \mathrm{\Theta }(1)}$. (See Big Theta notation)

Monte Carlo algorithm:

findingA_MC(array A, n, k)
begin
    i := 0
    repeat
        Randomly select one element out of n elements.
        i := i + 1
    until i = k or 'a' is found
end

If an ‘a’ is found, the algorithm succeeds, else the algorithm fails. After k iterations, the probability of finding an ‘a’ is:

${\displaystyle Pr[\mathrm{f}\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{a}]=1-(1/2{)}^k}$

This algorithm does not guarantee success, but the run time is bounded. The number of iterations is always less than or equal to k. Taking k to be constant the run time (expected and absolute) is ${\displaystyle \mathrm{\Theta }(1)}$.

Randomized algorithms are particularly useful when faced with a malicious "adversary" or attacker who deliberately tries to feed a bad input to the algorithm (see worst-case complexity and competitive analysis (online algorithm)) such as in the Prisoner's dilemma. It is for this reason that randomness is ubiquitous in cryptography. In cryptographic applications, pseudo-random numbers cannot be used, since the adversary can predict them, making the algorithm effectively deterministic. Therefore, either a source of truly random numbers or a cryptographically secure pseudo-random number generator is required. Another area in which randomness is inherent is quantum computing.

In the example above, the Las Vegas algorithm always outputs the correct answer, but its running time is a random variable. The Monte Carlo algorithm (related to the Monte Carlo method for simulation) is guaranteed to complete in an amount of time that can be bounded by a function the input size and its parameter k, but allows a small probability of error. Observe that any Las Vegas algorithm can be converted into a Monte Carlo algorithm (via Markov's inequality), by having it output an arbitrary, possibly incorrect answer if it fails to complete within a specified time. Conversely, if an efficient verification procedure exists to check whether an answer is correct, then a Monte Carlo algorithm can be converted into a Las Vegas algorithm by running the Monte Carlo algorithm repeatedly till a correct answer is obtained.

Computational complexity

Computational complexity theory models randomized algorithms as probabilistic Turing machines. Both Las Vegas and Monte Carlo algorithms are considered, and several complexity classes are studied. The most basic randomized complexity class is RP, which is the class of decision problems for which there is an efficient (polynomial time) randomized algorithm (or probabilistic Turing machine) which recognizes NO-instances with absolute certainty and recognizes YES-instances with a probability of at least 1/2. The complement class for RP is co-RP. Problem classes having (possibly nonterminating) algorithms with polynomial time average case running time whose output is always correct are said to be in ZPP.

The class of problems for which both YES and NO-instances are allowed to be identified with some error is called BPP. This class acts as the randomized equivalent of P, i.e. BPP represents the class of efficient randomized algorithms.

Early history

Sorting

Quicksort was discovered by Tony Hoare in 1959, and subsequently published in 1961. In the same year, Hoare published the quickselect algorithm, which finds the median element of a list in linear expected time. It remained open until 1973 whether a deterministic linear-time algorithm existed.

Number theory

In 1917, Henry Cabourn Pocklington introduced a randomized algorithm known as Pocklington's algorithm for efficiently finding square roots modulo prime numbers. In 1970, Elwyn Berlekamp introduced a randomized algorithm for efficiently computing the roots of a polynomial over a finite field. In 1977, Robert M. Solovay and Volker Strassen discovered a polynomial-time randomized primality test (i.e., determining the primality of a number). Soon afterwards Michael O. Rabin demonstrated that the 1976 Miller's primality test could also be turned into a polynomial-time randomized algorithm. At that time, no provably polynomial-time deterministic algorithms for primality testing were known.

Data structures

One of the earliest randomized data structures is the hash table, which was introduced in 1953 by Hans Peter Luhn at IBM. Luhn's hash table used chaining to resolve collisions and was also one of the first applications of linked lists. Subsequently, in 1954, Gene Amdahl, Elaine M. McGraw, Nathaniel Rochester, and Arthur Samuel of IBM Research introduced linear probing, although Andrey Ershov independently had the same idea in 1957. In 1962, Donald Knuth performed the first correct analysis of linear probing, although the memorandum containing his analysis was not published until much later. The first published analysis was due to Konheim and Weiss in 1966.

Early works on hash tables either assumed access to a fully random hash function or assumed that the keys themselves were random. In 1979, Carter and Wegman introduced universal hash functions, which they showed could be used to implement chained hash tables with constant expected time per operation.

Early work on randomized data structures also extended beyond hash tables. In 1970, Burton Howard Bloom introduced an approximate-membership data structure known as the Bloom filter. In 1989, Raimund Seidel and Cecilia R. Aragon introduced a randomized balanced search tree known as the treap. In the same year, William Pugh introduced another randomized search tree known as the skip list.

Implicit uses in combinatorics

Prior to the popularization of randomized algorithms in computer science, Paul Erdős popularized the use of randomized constructions as a mathematical technique for establishing the existence of mathematical objects. This technique has become known as the probabilistic method. Erdős gave his first application of the probabilistic method in 1947, when he used a simple randomized construction to establish the existence of Ramsey graphs. He famously used a more sophisticated randomized algorithm in 1959 to establish the existence of graphs with high girth and chromatic number.

Examples

Quicksort

Quicksort is a familiar, commonly used algorithm in which randomness can be useful. Many deterministic versions of this algorithm require O(n²) time to sort n numbers for some well-defined class of degenerate inputs (such as an already sorted array), with the specific class of inputs that generate this behavior defined by the protocol for pivot selection. However, if the algorithm selects pivot elements uniformly at random, it has a provably high probability of finishing in O(n log n) time regardless of the characteristics of the input.

Randomized incremental constructions in geometry

In computational geometry, a standard technique to build a structure like a convex hull or Delaunay triangulation is to randomly permute the input points and then insert them one by one into the existing structure. The randomization ensures that the expected number of changes to the structure caused by an insertion is small, and so the expected running time of the algorithm can be bounded from above. This technique is known as randomized incremental construction.

Min cut

Main article: Karger's algorithm

Input: A graph G(V,E)

Output: A cut partitioning the vertices into L and R, with the minimum number of edges between L and R.

Recall that the contraction of two nodes, u and v, in a (multi-)graph yields a new node u ' with edges that are the union of the edges incident on either u or v, except from any edge(s) connecting u and v. Figure 1 gives an example of contraction of vertex A and B. After contraction, the resulting graph may have parallel edges, but contains no self loops.

Figure 2: Successful run of Karger's algorithm on a 10-vertex graph. The minimum cut has size 3 and is indicated by the vertex colours.

Figure 1: Contraction of vertex A and B

Karger's basic algorithm:

begin
    i = 1
    repeat
        repeat
            Take a random edge (u,v) ∈ E in G
            replace u and v with the contraction u'
        until only 2 nodes remain
        obtain the corresponding cut result Ci
        i = i + 1
    until i = m
    output the minimum cut among C1, C2, ..., Cm.
end

In each execution of the outer loop, the algorithm repeats the inner loop until only 2 nodes remain, the corresponding cut is obtained. The run time of one execution is ${\displaystyle O(n)}$, and n denotes the number of vertices. After m times executions of the outer loop, we output the minimum cut among all the results. The figure 2 gives an example of one execution of the algorithm. After execution, we get a cut of size 3.

Lemma 1—Let k be the min cut size, and let C = {e₁, e₂, ..., e_k} be the min cut. If, during iteration i, no edge e ∈ C is selected for contraction, then C_i = C.

Proof

If G is not connected, then G can be partitioned into L and R without any edge between them. So the min cut in a disconnected graph is 0. Now, assume G is connected. Let V=L∪R be the partition of V induced by C : C = { {u,v} ∈ E : u ∈ L,v ∈ R} (well-defined since G is connected). Consider an edge {u,v} of C. Initially, u,v are distinct vertices. As long as we pick an edge ⁠${\displaystyle f\ne e}$⁠, u and v do not get merged. Thus, at the end of the algorithm, we have two compound nodes covering the entire graph, one consisting of the vertices of L and the other consisting of the vertices of R. As in figure 2, the size of min cut is 1, and C = {(A,B)}. If we don't select (A,B) for contraction, we can get the min cut.

Lemma 2—If G is a multigraph with p vertices and whose min cut has size k, then G has at least pk/2 edges.

Proof

Because the min cut is k, every vertex v must satisfy degree(v) ≥ k. Therefore, the sum of the degree is at least pk. But it is well known that the sum of vertex degrees equals 2|E|. The lemma follows.

Analysis of algorithm

The probability that the algorithm succeeds is 1 − the probability that all attempts fail. By independence, the probability that all attempts fail is $${\displaystyle \prod _{i=1}^{m}Pr(C_i\ne C)=\prod _{i=1}^m(1-Pr(C_i=C)).}$$

By lemma 1, the probability that C_i = C is the probability that no edge of C is selected during iteration i. Consider the inner loop and let G_j denote the graph after j edge contractions, where j ∈ {0, 1, …, n − 3}. G_j has n − j vertices. We use the chain rule of conditional possibilities. The probability that the edge chosen at iteration j is not in C, given that no edge of C has been chosen before, is ${\displaystyle 1-\frac{k}{|E(G_j)|}}$. Note that G_j still has min cut of size k, so by Lemma 2, it still has at least ${\displaystyle \frac{(n-j)k}{2}}$ edges.

Thus, ${\displaystyle 1-\frac{k}{|E(G_j)|}\ge 1-\frac{2}{n-j}=\frac{n-j-2}{n-j}}$.

So by the chain rule, the probability of finding the min cut C is $${\displaystyle Pr[C_i=C]\ge \left(\frac{n-2}{n}\right)\left(\frac{n-3}{n-1}\right)\left(\frac{n-4}{n-2}\right)\dots \left(\frac{3}{5}\right)\left(\frac{2}{4}\right)\left(\frac{1}{3}\right).}$$

Cancellation gives ${\displaystyle Pr[C_i=C]\ge \frac{2}{n(n-1)}}$. Thus the probability that the algorithm succeeds is at least ${\displaystyle 1-{\left(1-\frac{2}{n(n-1)}\right)}^m}$. For ${\displaystyle m=\frac{n(n-1)}{2}\ln n}$, this is equivalent to ${\displaystyle 1-\frac{1}{n}}$. The algorithm finds the min cut with probability ${\displaystyle 1-\frac{1}{n}}$, in time ${\displaystyle O(mn)=O(n^3\log n)}$.

Derandomization

Randomness can be viewed as a resource, like space and time. Derandomization is then the process of removing randomness (or using as little of it as possible). It is not currently known if all algorithms can be derandomized without significantly increasing their running time. For instance, in computational complexity, it is unknown whether P = BPP, i.e., we do not know whether we can take an arbitrary randomized algorithm that runs in polynomial time with a small error probability and derandomize it to run in polynomial time without using randomness.

There are specific methods that can be employed to derandomize particular randomized algorithms:

• the method of conditional probabilities, and its generalization, pessimistic estimators
• discrepancy theory (which is used to derandomize geometric algorithms)
• the exploitation of limited independence in the random variables used by the algorithm, such as the pairwise independence used in universal hashing
• the use of expander graphs (or dispersers in general) to amplify a limited amount of initial randomness (this last approach is also referred to as generating pseudorandom bits from a random source, and leads to the related topic of pseudorandomness)
• changing the randomized algorithm to use a hash function as a source of randomness for the algorithm's tasks, and then derandomizing the algorithm by brute-forcing all possible parameters (seeds) of the hash function. This technique is usually used to exhaustively search a sample space and making the algorithm deterministic (e.g. randomized graph algorithms)

Where randomness helps

When the model of computation is restricted to Turing machines, it is currently an open question whether the ability to make random choices allows some problems to be solved in polynomial time that cannot be solved in polynomial time without this ability; this is the question of whether P = BPP. However, in other contexts, there are specific examples of problems where randomization yields strict improvements.

• Based on the initial motivating example: given an exponentially long string of 2^k characters, half a's and half b's, a random-access machine requires 2^k−1 lookups in the worst-case to find the index of an a; if it is permitted to make random choices, it can solve this problem in an expected polynomial number of lookups.
• The natural way of carrying out a numerical computation in embedded systems or cyber-physical systems is to provide a result that approximates the correct one with high probability (or Probably Approximately Correct Computation (PACC)). The hard problem associated with the evaluation of the discrepancy loss between the approximated and the correct computation can be effectively addressed by resorting to randomization
• In communication complexity, the equality of two strings can be verified to some reliability using ${\displaystyle \log n}$ bits of communication with a randomized protocol. Any deterministic protocol requires ${\displaystyle \mathrm{\Theta }(n)}$ bits if defending against a strong opponent.
• The volume of a convex body can be estimated by a randomized algorithm to arbitrary precision in polynomial time. Bárány and Füredi showed that no deterministic algorithm can do the same. This is true unconditionally, i.e. without relying on any complexity-theoretic assumptions, assuming the convex body can be queried only as a black box.
• A more complexity-theoretic example of a place where randomness appears to help is the class IP. IP consists of all languages that can be accepted (with high probability) by a polynomially long interaction between an all-powerful prover and a verifier that implements a BPP algorithm. IP = PSPACE. However, if it is required that the verifier be deterministic, then IP = NP.
• In a chemical reaction network (a finite set of reactions like A+B → 2C + D operating on a finite number of molecules), the ability to ever reach a given target state from an initial state is decidable, while even approximating the probability of ever reaching a given target state (using the standard concentration-based probability for which reaction will occur next) is undecidable. More specifically, a limited Turing machine can be simulated with arbitrarily high probability of running correctly for all time, only if a random chemical reaction network is used. With a simple nondeterministic chemical reaction network (any possible reaction can happen next), the computational power is limited to primitive recursive functions.