title: Turkic languages

text: Empty cells do not necessarily imply that a particular language is lacking a word to describe the concept, but rather that the word for the concept in that language may be formed from another stem and is not cognate with the other words in the row or that a loanword is used in its place.


title: Turkic languages

text: Also, there may be shifts in the meaning from one language to another, and so the "Common meaning" given is only approximate. In some cases, the form given is found only in some dialects of the language, or a loanword is much more common (e.g. in Turkish, the preferred word for "fire" is the Persian-derived "ateş", whereas the native "od" is dead). Forms are given in native Latin orthographies unless otherwise noted.


title: Turkic languages

text: The Turkic language family is currently regarded as one of the world's primary language families. Turkic is one of the main members of the controversial Altaic language family. There are some other theories about an external relationship but none of them are generally accepted.


title: Turkic languages

text: The possibility of a genetic relation between Turkic and Korean, independently from Altaic, is suggested by some linguists. The linguist Kabak (2004) of the University of Würzburg states that Turkic and Korean share similar phonology as well as morphology. Li Yong-Sŏng (2014) suggest that there are several cognates between Turkic and Old Korean. He states that these supposed cognates can be useful to reconstruct the early Turkic language. According to him, words related to nature, earth and ruling but especially to the sky and stars seem to be cognates.


title: Turkic languages

text: The linguist Choi suggested already in 1996 a close relationship between Turkic and Korean regardless of any Altaic connections:


title: Turkic languages

text: Many historians also point out a close non-linguistic relationship between Turkic peoples and Koreans. Especially close were the relations between the Göktürks and Goguryeo.


title: Turkic languages

text: Some linguists suggested a relation to Uralic languages, especially to the Ugric languages. This view is rejected and seen as obsolete by mainstream linguists. Similarities are because of language contact and borrowings mostly from Turkic into Ugric languages. Stachowski (2015) states that any relation between Turkic and Uralic must be a contact one.


title: Raven's Home

text: Raven's Home is an American family sitcom television series developed by Jed Elinoff and Scott Thomas that premiered on Disney Channel on July 21, 2017. The series stars Raven-Symoné, Issac Ryan Brown, Navia Robinson, Jason Maybaum, Sky Katz, and Anneliese van der Pol for its first four seasons. Raven-Symoné and Issac Ryan Brown returned for the fifth season, alongside Mykal-Michelle Harris, Felix Avitia, Emmy Liu-Wang and Rondell Sheridan.


title: Raven's Home

text: Based on the characters created by Michael Poryes and Susan Sherman, the series is a spinoff of "That's So Raven", the second spinoff from that series after "Cory in the House". The series centers on Raven Baxter, a divorced mother of preteen twins Booker and Nia, living with her childhood best friend Chelsea and her son Levi in Chicago, Illinois.


title: Raven's Home

text: Best friends Raven and Chelsea, both divorced single mothers, are now raising their children in an apartment together in Chicago. Their house is turned upside down when they realize that Raven's son Booker has inherited the same psychic abilities as his mother.


title: Raven's Home

text: In the fifth season, Raven and Booker temporarily relocate to Raven's hometown of San Francisco to care for Raven's father Victor after he suffers a mild heart attack. While Raven tries to get her father back in shape, Booker must navigate his mother's old school with the help of some new friends and his younger cousin Alice.


title: Raven's Home

text: On August 14, 2015, Raven-Symoné and her former co-stars were reunited in an appearance on "The View". T'Keyah Crystal Keymáh and Rondell Sheridan were not present, but were mentioned by the cast. A pilot for the series was announced by Disney Channel on October 27, 2016, and Raven-Symoné also announced that she was departing as co-host of "The View" later in 2016 in order to work on the series full time. On November 14, 2016, it was announced that Anneliese van der Pol would reprise her role of Chelsea Daniels in the series as a divorced mother who is raising a son, Levi, and moves in with Raven. Disney Channel officially greenlit the series, with the title of "Ravens Home", on April 4, 2017. Executive producers Jed Elinoff and Scott Thomas serve as showrunners and head writers, with Raven-Symoné also on the writing team as an executive producer. The series is filmed at Hollywood Center Studios.


title: Raven's Home

text: Disney Channel renewed the series for a second season on October 10, 2017, which began filming in November 2017. Additionally, starting with the second season, Michael Feldman and Dava Savel replaced Jed Elinoff and Scott Thomas as showrunners. Both Savel and Feldman served as writers and producers on "That's So Raven". On September 28, 2018, it was announced that a musical episode of the series would premiere on October 12, 2018.


title: Raven's Home

text: Following a silent renewal, on November 28, 2018, it was announced that Eunetta T. Boone would be taking over as showrunner and executive producer for the third season. On March 21, 2019, it was announced that production on the third season was temporarily shut down, following the death of Eunetta T. Boone. On May 10, 2019, it was announced that the third season would premiere on June 17, 2019.


title: Raven's Home

text: On October 16, 2019, it was announced by Disney Channel that the series was renewed for a fourth season, with production scheduled to begin sometime in 2019. Additionally, Alison Taylor joined the series as an executive producer.


title: Raven's Home

text: On June 29, 2020, it was announced that "Raven's Home" and "Bunk'd" would have a special crossover event on July 24, 2020.


title: Raven's Home

text: On October 1, 2021, it was announced by Disney Channel that the series was renewed for a fifth season. Raven Symoné and Isaac Ryan Brown would return for the season; however, Navia Robinson, Jason Maybaum, Sky Katz, and Anneliese van der Pol would not return. Additionally, newcomers Mykal-Michelle Harris, Felix Avitia, and Emmy Liu-Wang joined as Alice, Neil and Ivy, respectively, and Rondell Sheridan would return as Raven's father Victor Baxter. Production of the fifth season commenced in fall 2021. Adrienne Bailon also returned as Alana Rivera, Raven's high school bully in the original series. On February 10, 2022, it was announced that the fifth season would premiere on March 11, 2022.


title: Raven's Home

text: On June 21, 2022, "Entertainment Tonight" announced that Keymáh would reprise her role as Tanya Baxter in the season five finale. This marks her first time portraying the character since 2005 in her final appearance in the season 3 "That's So Raven" episode, "Food For Thought".


title: Raven's Home

text: Raven-Symoné announced during a panel at Disney's D23 Expo on September 10, 2022, that the series was renewed for a sixth season.


title: Raven's Home

text: The world premiere of "Raven's Home" aired immediately after the premiere of "Descendants 2" on the Disney Channel on July 21, 2017. The first season concluded on October 20, 2017. The second season premiered on June 25, 2018, and concluded on November 30, 2018. The third season premiered on June 17, 2019, and concluded on May 3, 2020. The fourth season premiered on July 24, 2020, and concluded on May 21, 2021. The fifth season premiered on March 11, 2022.


title: Raven's Home

text: "Raven's Home" has received positive reviews. Writing for "The Post", Georgia Davis appreciated the pilot for "maintain[ing] the charm and energy" of the original, praising Raven and Chelsea's characterizations, as well as the performances of the child actors. Davis concluded, "It might be too early to tell, but it seems "Raven's Home" is on the right path for success." Emily Ashby of Common Sense Media wrote that ""That's So Raven" fans will find plenty more of what they loved about the original series in this sharply written sitcom that plays up the woes of adulting and tween trials in a surprisingly great balance."


title: Langston Hughes

text: James Mercer Langston Hughes (February 1, 1901 – May 22, 1967) was an American poet, social activist, novelist, playwright, and columnist from Joplin, Missouri. One of the earliest innovators of the literary art form called jazz poetry, Hughes is best known as a leader of the Harlem Renaissance. He famously wrote about the period that "the Negro was in vogue", which was later paraphrased as "when Harlem was in vogue."


title: Langston Hughes

text: Growing up in a series of Midwestern towns, Hughes became a prolific writer at an early age. He moved to New York City as a young man, where he made his career. He graduated from high school in Cleveland, Ohio, and soon began studies at Columbia University in New York City. Although he dropped out, he gained notice from New York publishers, first in "The Crisis" magazine and then from book publishers, and became known in the creative community in Harlem. He eventually graduated from Lincoln University. In addition to poetry, Hughes wrote plays and short stories. He also published several nonfiction works. From 1942 to 1962, as the civil rights movement was gaining traction, he wrote an in-depth weekly column in a leading black newspaper, "The Chicago Defender".


title: Langston Hughes

text: Like many African-Americans, Hughes had a complex ancestry. Both of Hughes' paternal great-grandmothers were enslaved Africans, and both of his paternal great-grandfathers were white slave owners in Kentucky. According to Hughes, one of these men was Sam Clay, a Scottish-American whiskey distiller of Henry County, said to be a relative of statesman Henry Clay. The other putative paternal ancestor whom Hughes named was Silas Cushenberry, a slave trader of Clark County. Hughes wrote that Cushenberry was a Jewish slave trader, but a study of the Cushenberry family genealogy in the nineteenth century has found no Jewish affiliation. Hughes's maternal grandmother Mary Patterson was of African-American, French, English and Native American descent. One of the first women to attend Oberlin College, she married Lewis Sheridan Leary, also of mixed-race descent, before her studies. In 1859, Lewis Leary joined John Brown's raid on Harpers Ferry in West Virginia, where he was fatally wounded.


title: Langston Hughes

text: Ten years later, in 1869, the widow Mary Patterson Leary married again, into the elite, politically active Langston family. (See The Talented Tenth.) Her second husband was Charles Henry Langston, of African-American, Euro-American and Native American ancestry. He and his younger brother John Mercer Langston worked for the abolitionist cause and helped lead the Ohio Anti-Slavery Society in 1858.


title: Langston Hughes

text: After their marriage, Charles Langston moved with his family to Kansas, where he was active as an educator and activist for voting and rights for African Americans. His and Mary's daughter Caroline (known as Carrie) became a schoolteacher and married James Nathaniel Hughes (1871–1934). They had two children; the second was Langston Hughes, by most sources born in 1901 in Joplin, Missouri (though Hughes himself claims in his autobiography to have been born in 1902).


title: Langston Hughes

text: Langston Hughes grew up in a series of Midwestern small towns. His father left the family soon after the boy was born and later divorced Carrie. The senior Hughes traveled to Cuba and then Mexico, seeking to escape the enduring racism in the United States.


title: Langston Hughes

text: After the separation, Hughes's mother traveled, seeking employment. Langston was raised mainly in Lawrence, Kansas, by his maternal grandmother, Mary Patterson Langston. Through the black American oral tradition and drawing from the activist experiences of her generation, Mary Langston instilled in her grandson a lasting sense of racial pride. Imbued by his grandmother with a duty to help his race, Hughes identified with neglected and downtrodden black people all his life, and glorified them in his work. He lived most of his childhood in Lawrence. In his 1940 autobiography "The Big Sea", he wrote: "I was unhappy for a long time, and very lonesome, living with my grandmother. Then it was that books began to happen to me, and I began to believe in nothing but books and the wonderful world in books—where if people suffered, they suffered in beautiful language, not in monosyllables, as we did in Kansas."


title: Langston Hughes

text: After the death of his grandmother, Hughes went to live with family friends, James and Auntie Mary Reed, for two years. Later, Hughes lived again with his mother Carrie in Lincoln, Illinois. She had remarried when he was an adolescent. The family moved to the Fairfax neighborhood of Cleveland, Ohio, where he attended Central High School and was taught by Helen Maria Chesnutt, whom he found inspiring.


title: Langston Hughes

text: His writing experiments began when he was young. While in grammar school in Lincoln, Hughes was elected class poet. He stated that in retrospect he thought it was because of the stereotype about African Americans having rhythm.


title: Langston Hughes

text: I was a victim of a stereotype. There were only two of us Negro kids in the whole class and our English teacher was always stressing the importance of rhythm in poetry. Well, everyone knows, except us, that all Negroes have rhythm, so they elected me as class poet.


title: Langston Hughes

text: During high school in Cleveland, Hughes wrote for the school newspaper, edited the yearbook, and began to write his first short stories, poetry, and dramatic plays. His first piece of jazz poetry, "When Sue Wears Red", was written while he was in high school.


title: Langston Hughes

text: Hughes had a very poor relationship with his father, whom he seldom saw when a child. He lived briefly with his father in Mexico in 1919. Upon graduating from high school in June 1920, Hughes returned to Mexico to live with his father, hoping to convince him to support his plan to attend Columbia University. Hughes later said that, prior to arriving in Mexico, "I had been thinking about my father and his strange dislike of his own people. I didn't understand it, because I was a Negro, and I liked Negroes very much." His father had hoped Hughes would choose to study at a university abroad and train for a career in engineering. On these grounds, he was willing to provide financial assistance to his son but did not support his desire to be a writer. Eventually, Hughes and his father came to a compromise: Hughes would study engineering, so long as he could attend Columbia. His tuition provided, Hughes left his father after more than a year.


title: Langston Hughes

text: While at Columbia in 1921, Hughes managed to maintain a B+ grade average. He published poetry in the "Columbia Daily Spectator" under a pen name. He left in 1922 because of racial prejudice among students and teachers. He was denied a room on campus because he was black. Eventually he settled in Hartley Hall, but he still suffered from racism among his classmates, who seemed hostile to anyone who did not fit into a WASP category. He was attracted more to the African-American people and neighborhood of Harlem than to his studies, but he continued writing poetry. Harlem was a center of vibrant cultural life.


title: Langston Hughes

text: Hughes worked at various odd jobs before serving a brief tenure as a crewman aboard the S.S. "Malone" in 1923, spending six months traveling to West Africa and Europe. In Europe, Hughes left the S.S. "Malone" for a temporary stay in Paris. There he met and had a romance with Anne Marie Coussey, a British-educated African from a well-to-do Gold Coast family; they subsequently corresponded, but she eventually married Hugh Wooding, a promising Trinidadian lawyer. Wooding later served as chancellor of the University of the West Indies.


title: Langston Hughes

text: During his time in England in the early 1920s, Hughes became part of the black expatriate community. In November 1924, he returned to the U.S. to live with his mother in Washington, D.C. After assorted odd jobs, he gained white-collar employment in 1925 as a personal assistant to historian Carter G. Woodson at the Association for the Study of African American Life and History. As the work demands limited his time for writing, Hughes quit the position to work as a busboy at the Wardman Park Hotel. Hughes's earlier work had been published in magazines and was about to be collected into his first book of poetry when he encountered poet Vachel Lindsay, with whom he shared some poems. Impressed, Lindsay publicized his discovery of a new black poet.


title: Langston Hughes

text: The following year, Hughes enrolled in Lincoln University, a historically black university in Chester County, Pennsylvania. He joined the Omega Psi Phi fraternity.


title: Langston Hughes

text: After Hughes earned a B.A. degree from Lincoln University in 1929, he returned to New York. Except for travels to the Soviet Union and parts of the Caribbean, he lived in Harlem as his primary home for the remainder of his life. During the 1930s, he became a resident of Westfield, New Jersey for a time, sponsored by his patron Charlotte Osgood Mason.


title: Langston Hughes

text: Some academics and biographers believe that Hughes was homosexual and included homosexual codes in many of his poems, as did Walt Whitman, who, Hughes said, influenced his poetry. Hughes's story "Blessed Assurance" deals with a father's anger over his son's effeminacy and "queerness". The biographer Aldrich argues that, in order to retain the respect and support of black churches and organizations and avoid exacerbating his precarious financial situation, Hughes remained closeted.


title: Langston Hughes

text: Arnold Rampersad, the primary biographer of Hughes, determined that Hughes exhibited a preference for African-American men in his work and life. But, in his biography Rampersad denies Hughes's homosexuality, and concludes that Hughes was probably asexual and passive in his sexual relationships. Hughes did, however, show a respect and love for his fellow black man (and woman). Other scholars argue for his homosexuality: his love of black men is evidenced in a number of reported unpublished poems to an alleged black male lover.


title: Langston Hughes

text: On May 22, 1967, Hughes died in the Stuyvesant Polyclinic in New York City at the age of 66 from complications after abdominal surgery related to prostate cancer. His ashes are interred beneath a floor medallion in the middle of the foyer in the Schomburg Center for Research in Black Culture in Harlem. It is the entrance to an auditorium named for him. The design on the floor is an African cosmogram entitled "Rivers". The title is taken from his poem "The Negro Speaks of Rivers". Within the center of the cosmogram is the line: "My soul has grown deep like the rivers".


title: Langston Hughes

text: First published in 1921 in "The Crisis"—official magazine of the National Association for the Advancement of Colored People (NAACP)—"The Negro Speaks of Rivers" became Hughes's signature poem and was collected in his first book of poetry, "The Weary Blues" (1926). Hughes's first and last published poems appeared in "The Crisis"; more of his poems were published in "The Crisis" than in any other journal. Hughes' life and work were enormously influential during the Harlem Renaissance of the 1920s, alongside those of his contemporaries, Zora Neale Hurston, Wallace Thurman, Claude McKay, Countee Cullen, Richard Bruce Nugent, and Aaron Douglas. Except for McKay, they worked together also to create the short-lived magazine "Fire!! Devoted to Younger Negro Artists".


title: Langston Hughes

text: Hughes and his contemporaries had different goals and aspirations than the black middle class. Hughes and his fellows tried to depict the "low-life" in their art, that is, the real lives of blacks in the lower social-economic strata. They criticized the divisions and prejudices within the black community based on skin color. Hughes wrote what would be considered their manifesto, "The Negro Artist and the Racial Mountain", published in "The Nation" in 1926:


title: Langston Hughes

text: The younger Negro artists who create now intend to express our individual dark-skinned selves without fear or shame. If white people are pleased we are glad. If they are not, it doesn't matter. We know we are beautiful. And ugly, too. The tom-tom cries, and the tom-tom laughs. If colored people are pleased we are glad. If they are not, their displeasure doesn't matter either. We build our temples for tomorrow, strong as we know how, and we stand on top of the mountain free within ourselves.


title: Langston Hughes

text: His poetry and fiction portrayed the lives of the working-class blacks in America, lives he portrayed as full of struggle, joy, laughter, and music. Permeating his work is pride in the African-American identity and its diverse culture. "My seeking has been to explain and illuminate the Negro condition in America and obliquely that of all human kind", Hughes is quoted as saying. He confronted racial stereotypes, protested social conditions, and expanded African America's image of itself; a "people's poet" who sought to reeducate both audience and artist by lifting the theory of the black aesthetic into reality.


title: Langston Hughes

text: Hughes stressed a racial consciousness and cultural nationalism devoid of self-hate. His thought united people of African descent and Africa across the globe to encourage pride in their diverse black folk culture and black aesthetic. Hughes was one of the few prominent black writers to champion racial consciousness as a source of inspiration for black artists. His African-American race consciousness and cultural nationalism would influence many foreign black writers, including Jacques Roumain, Nicolás Guillén, Léopold Sédar Senghor, and Aimé Césaire. Along with the works of Senghor, Césaire, and other French-speaking writers of Africa and of African descent from the Caribbean, such as René Maran from Martinique and Léon Damas from French Guiana in South America, the works of Hughes helped to inspire the Négritude movement in France. A radical black self-examination was emphasized in the face of European colonialism. In addition to his example in social attitudes, Hughes had an important technical influence by his emphasis on folk and jazz rhythms as the basis of his poetry of racial pride.


title: Langston Hughes

text: In 1930, his first novel, "Not Without Laughter", won the Harmon Gold Medal for literature. At a time before widespread arts grants, Hughes gained the support of private patrons and he was supported for two years prior to publishing this novel. The protagonist of the story is a boy named Sandy, whose family must deal with a variety of struggles due to their race and class, in addition to relating to one another.


title: Langston Hughes

text: In 1931, Hughes helped form the "New York Suitcase Theater" with playwright Paul Peters, artist Jacob Burck, and writer (soon-to-be underground spy) Whittaker Chambers, an acquaintance from Columbia. In 1932, he was part of a board to produce a Soviet film on "Negro Life" with Malcolm Cowley, Floyd Dell, and Chambers.


title: Langston Hughes

text: In 1931 Prentiss Taylor and Langston Hughes created the Golden Stair Press, issuing broadsides and books featuring the artwork of Prentiss Taylor and the texts of Langston Hughes. In 1932 they issued The Scottsboro Limited based on the trial of the Scottsboro Boys.


title: Langston Hughes

text: In 1932, Hughes and Ellen Winter wrote a pageant to Caroline Decker in an attempt to celebrate her work with the striking coal miners of the Harlan County War, but it was never performed. It was judged to be a "long, artificial propaganda vehicle too complicated and too cumbersome to be performed."


title: Langston Hughes

text: Maxim Lieber became his literary agent, 1933–45 and 1949–50. (Chambers and Lieber worked in the underground together around 1934–35.)


title: Langston Hughes

text: Hughes' first collection of short stories was published in 1934 with "The Ways of White Folks". He finished the book at a Carmel, California cottage provided for a year by Noel Sullivan, another patron. These stories are a series of vignettes revealing the humorous and tragic interactions between whites and blacks. Overall, they are marked by a general pessimism about race relations, as well as a sardonic realism. He also became an advisory board member to the (then) newly formed San Francisco Workers' School (later the California Labor School).


title: Langston Hughes

text: In 1935, Hughes received a Guggenheim Fellowship. The same year that Hughes established his theatre troupe in Los Angeles, he realized an ambition related to films by co-writing the screenplay for "Way Down South". Hughes believed his failure to gain more work in the lucrative movie trade was due to racial discrimination within the industry.


title: Langston Hughes

text: In Chicago, Hughes founded "The Skyloft Players" in 1941, which sought to nurture black playwrights and offer theatre "from the black perspective." Soon thereafter, he was hired to write a column for the "Chicago Defender", in which he presented some of his "most powerful and relevant work", giving voice to black people. The column ran for twenty years. Hughes also mentored writer Richard Durham who would later produce a sequence about Hughes in the radio series "Destination Freedom". In 1943, Hughes began publishing stories about a character he called Jesse B. Semple, often referred to and spelled "Simple", the everyday black man in Harlem who offered musings on topical issues of the day. Although Hughes seldom responded to requests to teach at colleges, in 1947 he taught at Atlanta University. In 1949, he spent three months at the University of Chicago Laboratory Schools as a visiting lecturer. Between 1942 and 1949, Hughes was a frequent writer and served on the editorial board of "Common Ground", a literary magazine focused on cultural pluralism in the United States published by the Common Council for American Unity (CCAU).


title: Langston Hughes

text: He wrote novels, short stories, plays, poetry, operas, essays, and works for children. With the encouragement of his best friend and writer, Arna Bontemps, and patron and friend, Carl Van Vechten, he wrote two volumes of autobiography, "The Big Sea" and "I Wonder as I Wander", as well as translating several works of literature into English. With Bontemps, Hughes co-edited the 1949 anthology "The Poetry of the Negro", described by "The New York Times" as "a stimulating cross-section of the imaginative writing of the Negro" that demonstrates "talent to the point where one questions the necessity (other than for its social evidence) of the specialization of 'Negro' in the title".


title: Langston Hughes

text: From the mid-1950s to the mid-1960s, Hughes' popularity among the younger generation of black writers varied even as his reputation increased worldwide. With the gradual advance toward racial integration, many black writers considered his writings of black pride and its corresponding subject matter out of date. They considered him a racial chauvinist. He found some new writers, among them James Baldwin, lacking in such pride, over-intellectual in their work, and occasionally vulgar.


title: Langston Hughes

text: Hughes wanted young black writers to be objective about their race, but not to scorn it or flee it. He understood the main points of the Black Power movement of the 1960s, but believed that some of the younger black writers who supported it were too angry in their work. Hughes's work "Panther and the Lash", posthumously published in 1967, was intended to show solidarity with these writers, but with more skill and devoid of the most virulent anger and racial chauvinism some showed toward whites. Hughes continued to have admirers among the larger younger generation of black writers. He often helped writers by offering advice and introducing them to other influential persons in the literature and publishing communities. This latter group, including Alice Walker, whom Hughes discovered, looked upon Hughes as a hero and an example to be emulated within their own work. One of these young black writers (Loften Mitchell) observed of Hughes:


title: Langston Hughes

text: Langston set a tone, a standard of brotherhood and friendship and cooperation, for all of us to follow. You never got from him, 'I am "the" Negro writer,' but only 'I am "a" Negro writer.' He never stopped thinking about the rest of us.


title: Langston Hughes

text: Hughes was drawn to Communism as an alternative to a segregated America. Many of his lesser-known political writings have been collected in two volumes published by the University of Missouri Press and reflect his attraction to Communism. An example is the poem "A New Song".


title: Langston Hughes

text: In 1932, Hughes became part of a group of black people who went to the Soviet Union to make a film depicting the plight of African Americans in the United States. The film was never made, but Hughes was given the opportunity to travel extensively through the Soviet Union and to the Soviet-controlled regions in Central Asia, the latter parts usually closed to Westerners. While there, he met Robert Robinson, an African American living in Moscow and unable to leave. In Turkmenistan, Hughes met and befriended the Hungarian author Arthur Koestler, then a Communist who was given permission to travel there.


title: Langston Hughes

text: As later noted in Koestler's autobiography, Hughes, together with some forty other Black Americans, had originally been invited to the Soviet Union to produce a Soviet film on "Negro Life", but the Soviets dropped the film idea because of their 1933 success in getting the US to recognize the Soviet Union and establish an embassy in Moscow. This entailed a toning down of Soviet propaganda on racial segregation in America. Hughes and his fellow Blacks were not informed of the reasons for the cancelling, but he and Koestler worked it out for themselves.


title: Langston Hughes

text: Hughes's poetry was frequently published in the CPUSA newspaper and he was involved in initiatives supported by Communist organizations, such as the drive to free the Scottsboro Boys. Partly as a show of support for the Republican faction during the Spanish Civil War, in 1937 Hughes traveled to Spain as a correspondent for the "Baltimore Afro-American" and other various African-American newspapers. In August 1937, he broadcast live from Madrid alongside Harry Haywood and Walter Benjamin Garland. When Hughes was in Spain a Spanish Republican cultural magazine, "El Mono Azul", featured Spanish translations of his poems. In November 1937 Hughes departed Spain for which "El Mono Azul" published a brief farewell message entitled “el gran poeta de raza negra” (“the great poet of the black race”).


title: Langston Hughes

text: Hughes was also involved in other Communist-led organizations such as the John Reed Clubs and the League of Struggle for Negro Rights. He was more of a sympathizer than an active participant. He signed a 1938 statement supporting Joseph Stalin's purges and joined the American Peace Mobilization in 1940 working to keep the U.S. from participating in World War II.


title: Langston Hughes

text: Hughes initially did not favor black American involvement in the war because of the persistence of discriminatory U.S. Jim Crow laws and racial segregation and disfranchisement throughout the South. He came to support the war effort and black American participation after deciding that war service would aid their struggle for civil rights at home. The scholar Anthony Pinn has noted that Hughes, together with Lorraine Hansberry and Richard Wright, was a humanist "critical of belief in God. They provided a foundation for nontheistic participation in social struggle." Pinn has found that such writers are sometimes ignored in the narrative of American history that chiefly credits the civil rights movement to the work of affiliated Christian people.


title: Langston Hughes

text: Hughes was accused of being a Communist by many on the political right, but he always denied it. When asked why he never joined the Communist Party, he wrote, "it was based on strict discipline and the acceptance of directives that I, as a writer, did not wish to accept." In 1953, he was called before the Senate Permanent Subcommittee on Investigations led by Senator Joseph McCarthy. He stated, "I never read the theoretical books of socialism or communism or the Democratic or Republican parties for that matter, and so my interest in whatever may be considered political has been non-theoretical, non-sectarian, and largely emotional and born out of my own need to find some way of thinking about this whole problem of myself." Following his testimony, Hughes distanced himself from Communism. He was rebuked by some on the Radical Left who had previously supported him. He moved away from overtly political poems and towards more lyric subjects. When selecting his poetry for his "Selected Poems" (1959) he excluded all his radical socialist verse from the 1930s. These critics on the Left were unaware of the secret interrogation that took place days before the televised hearing.


title: Langston Hughes

text: Hughes was featured reciting his poetry on the album "Weary Blues" (MGM, 1959), with music by Charles Mingus and Leonard Feather, and he also contributed lyrics to Randy Weston's "Uhuru Afrika" (Roulette, 1960).


title: Langston Hughes

text: Hughes' life has been portrayed in film and stage productions since the late 20th century. In "Looking for Langston" (1989), British filmmaker Isaac Julien claimed him as a black gay icon—Julien thought that Hughes' sexuality had historically been ignored or downplayed. Film portrayals of Hughes include Gary LeRoi Gray's role as a teenage Hughes in the short subject film "Salvation" (2003) (based on a portion of his autobiography "The Big Sea"), and Daniel Sunjata as Hughes in the "Brother to Brother" (2004). "Hughes' Dream Harlem", a documentary by Jamal Joseph, examines Hughes' works and environment.


title: Langston Hughes

text: "Paper Armor" (1999) by Eisa Davis and "Hannibal of the Alps" (2005) by Michael Dinwiddie are plays by African-American playwrights that address Hughes's sexuality. Spike Lee's 1996 film "Get on the Bus", included a black gay character, played by Isaiah Washington, who invokes the name of Hughes and punches a homophobic character, saying: "This is for James Baldwin and Langston Hughes."


title: Langston Hughes

text: Hughes was also featured prominently in a national campaign sponsored by the Center for Inquiry (CFI) known as African Americans for Humanism.


title: Langston Hughes

text: Hughes' "Ask Your Mama: 12 Moods for Jazz", written in 1960, was performed for the first time in March 2009 with specially composed music by Laura Karpman at Carnegie Hall, at the "Honor" festival curated by Jessye Norman in celebration of the African-American cultural legacy. "Ask Your Mama" is the centerpiece of "The Langston Hughes Project", a multimedia concert performance directed by Ron McCurdy, professor of music in the Thornton School of Music at the University of Southern California. The European premiere of The Langston Hughes Project, featuring Ice-T and McCurdy, took place at the Barbican Centre, London, on November 21, 2015, as part of the London Jazz Festival mounted by music producers Serious.


title: Langston Hughes

text: The novel "Harlem Mosaics" (2012) by Whit Frazier depicts the friendship between Langston Hughes and Zora Neale Hurston, and tells the story of how their friendship fell apart during their collaboration on the play "Mule Bone".


title: Langston Hughes

text: On September 22, 2016, his poem "I, Too" was printed on a full page of "The New York Times" in response to the riots of the previous day in Charlotte, North Carolina.


title: Langston Hughes

text: The Beinecke Rare Book and Manuscript Library at Yale University holds the Langston Hughes papers (1862–1980) and the Langston Hughes collection (1924–1969) containing letters, manuscripts, personal items, photographs, clippings, artworks, and objects that document the life of Hughes. The Langston Hughes Memorial Library on the campus of Lincoln University, as well as at the James Weldon Johnson Collection within the Yale University also hold archives of Hughes' work. The Moorland-Spingarn Research Center at Howard University includes materials acquired from his travels and contacts through the work of Dorothy B. Porter.


title: Charles de Gaulle Airport

text: Paris Charles de Gaulle Airport (, ) or Roissy Airport, is the principal airport serving the French capital, Paris, and the largest international airport in France. Opened in 1974, it is in Roissy-en-France, northeast of Paris and is named after statesperson Charles de Gaulle (1890–1970).


title: Charles de Gaulle Airport

text: Charles de Gaulle Airport serves as the principal hub for Air France and a destination for other legacy carriers (from Star Alliance, Oneworld and SkyTeam), as well as a focus city for low-cost carriers easyJet and Vueling. It is operated by Groupe ADP under the brand Paris Aéroport.


title: Charles de Gaulle Airport

text: In 2019, the airport handled 76,150,007 passengers and 498,175 aircraft movements, thus making it the world's ninth busiest airport and Europe's second busiest airport (after Heathrow) in terms of passenger numbers. Charles de Gaulle is also the busiest airport within the European Union. In terms of cargo traffic, the airport is the eleventh busiest in the world and the busiest in Europe, handling of cargo in 2019. It is also the airport that is served by most number of airlines, with more than 105 airlines operating at the airport.


title: Charles de Gaulle Airport

text: , the airport offers direct flights to the most countries and hosts the most airlines in the world. Marc Houalla has been the director of the airport since 12 February 2018.


title: Charles de Gaulle Airport

text: Paris Charles de Gaulle Airport covers of land. The airport area, including terminals and runways, spans over three "départements" and six "communes":


title: Charles de Gaulle Airport

text: The choice of constructing an international aviation hub outside of central Paris was made due to a limited prospect of potential relocations or expropriations and the possibility of further expanding the airport in the future.


title: Charles de Gaulle Airport

text: Management of the airport lies solely on the authority of "Groupe ADP", which also manages Orly (south of Paris), Le Bourget (to the immediate southwest of Charles de Gaulle Airport, now used for general aviation and Paris Air Shows), several smaller airfields in the suburbs of Paris, and other airports directly or indirectly worldwide.


title: Charles de Gaulle Airport

text: The planning and construction phase of what was known then as "Aéroport de Paris Nord" (Paris North Airport) began in 1966. On 8 March 1974 the airport, renamed Charles de Gaulle Airport, opened. Terminal 1 was built in an avant-garde design of a ten-floors-high circular building surrounded by seven satellite buildings, each with six gates allowing sunlight to enter through apertures. The main architect was Paul Andreu, who was also in charge of the extensions during the following decades.


title: Charles de Gaulle Airport

text: Following the introduction of the brand Paris Aéroport to all its Parisian airports, Groupe ADP also announced major changes for the Charles de Gaulle Airport: Terminals of the Satellite 1 will be merged, as well as terminals 2B and 2D. A new luggage automated sorting system and conveyor under Terminal 2E Hall L was installed to speed luggage delivery time for airlines operating Paris-Charles de Gaulle's hub. The CDG Express, the direct express rail link from Paris to Charles de Gaulle Airport, is planned for completion by 2023.


title: Charles de Gaulle Airport

text: The Frutiger typeface was commissioned for use in the airport and implemented on signs throughout the building in 1975. Initially called "Roissy", it was renamed after its designer Adrian Frutiger.


title: Charles de Gaulle Airport

text: Until 2005, every PA announcement made at Terminal 1 was preceded by a distinctive chime, nicknamed "Indicatif Roissy" and composed by Bernard Parmegiani in 1971. The chime can be heard in the Roman Polanski film "Frantic". The chime was officially replaced by the "Indicatif ADP" chime.


title: Charles de Gaulle Airport

text: On 14 April 2016, the Groupe ADP rolled out the "Connect 2020" corporate strategy and the commercial brand Paris Aéroport was applied to all Parisian airports, including Le Bourget airport.


title: Charles de Gaulle Airport

text: Charles de Gaulle Airport has three terminals: Terminal 1 is the oldest and situated opposite to Terminal 3. It was closed for renovation during the pandemic and reopened on 1 December 2022 and will house all Star Alliance, Oneworld members and some non-aligned airlines; Terminal 2 is located at another side with 7 sub-terminal buildings (2A to 2G). Terminal 2 was originally built exclusively for Air France; since then it has been expanded significantly and now houses all SkyTeam members, a few Star Alliance and Oneworld members, and most non-aligned airlines. Terminals 2A to 2F are interconnected by elevated walkways and situated next to each other. Terminal 2G is a satellite building connected by shuttle bus.


title: Charles de Gaulle Airport

text: Terminal 3 (formerly known as "Terminal 9") hosts charter and low-cost airlines. The CDGVAL light-rail shuttle connects Terminal 2 to Terminals 1/3 and their parking lots.


title: Charles de Gaulle Airport

text: The first terminal, designed by Paul Andreu, was built in the image of an octopus. It consists of a circular terminal building which houses key functions such as check-in counters and baggage claim conveyors. Seven satellites with boarding gates are connected to the central building by underground walkways.


title: Charles de Gaulle Airport

text: The central building, with a large skylight in its centre, dedicates each floor to a single function. The first floor is reserved for technical operations and not accessible to the public. The second floor contains shops and restaurants, the CDGVAL inter-terminal shuttle train platforms (for Terminal 2 and trains to central Paris) and check-in counters from a recent renovation. The majority of check-in counters, however, are located on the third floor, which also has access to taxi stands, bus stops and special pick-up vehicles. Departing passengers with valid boarding passes can reach the fourth floor, which houses duty-free stores and border control posts, for the boarding gates. The fifth floor contains baggage claim conveyors for arriving passengers. All four upper floors have assigned areas for parking and airline offices.


title: Charles de Gaulle Airport

text: Passages between the third, fourth and fifth floors are provided by a tangle of escalators arranged through the centre of the building. These escalators are suspended over the central court. Each escalator is covered with a transparent tube to shelter from all weather conditions. These escalators were often used in film shootings (e.g. "The Last Gang of Ariel Zeitoun"). The Alan Parsons Project album "I Robot" features these escalators on its cover.


title: Charles de Gaulle Airport

text: Terminal 1 was closed in 2020 for two years as several terminals were made redundant during the COVID-19 pandemic. It remained closed for renovation work and reopened on 1 December 2022. It will be used by all Star Alliance and Oneworld members (with the exception of those who operate from Terminal 2) that serve Charles de Gaulle Airport along with Aer Lingus, Bulgaria Air, Emirates, Etihad Airways, Eurowings, Icelandair, Kuwait Airways, Oman Air and some other non-aligned airlines along with SkyTeam member Saudia. Before the renovation, Terminal 1 was used by all Star Alliance members that served CDG except those at Terminal 2.


title: Charles de Gaulle Airport

text: Terminal 2 is spread across seven sub-terminals: 2A to 2G. Terminals 2A to 2F are connected by inter-terminal walkways, but Terminal 2G is a satellite building away. Terminal 2G can only be accessed by shuttle bus from Terminals 1, 2A to 2F and 3. The CDGVAL inter-terminal shuttle train, Paris RER Regional-Express and high-speed TGV rail station, Aéroport Charles de Gaulle 2 TGV, is located within the Terminal 2 complex and between 2C and 2E (on one side) or 2D and 2F (on the opposite side).


title: Charles de Gaulle Airport

text: Terminal 2F was used for the filming of the music video for the U2 song "Beautiful Day". The band also had their picture taken inside Terminal 2F for the album artwork of their 2000 album "All That You Can't Leave Behind".


title: Charles de Gaulle Airport

text: From 14 January 2023, Terminal 2 will be used by Air France, all SkyTeam members with the exception of Saudia, Oneworld (American Airlines, British Airways, Finnair, Japan Airlines, Royal Air Maroc, and Royal Jordanian), Star Alliance (Air China, Croatia Airlines, Ethiopian Airlines, EVA Air and Thai Airways International), easyJet and all other airlines.


title: Charles de Gaulle Airport

text: On 23 May 2004, shortly after the inauguration of terminal 2E, a portion of it collapsed near Gate E50, killing four people. Two of the dead were reported to be Chinese citizens, one Czech and the other Lebanese. Three other people were injured in the collapse. Terminal 2E had been inaugurated in 2003 after some delays in construction and was designed by Paul Andreu. Administrative and judicial enquiries were started. Andreu also designed Terminal 3 at Dubai International Airport, which collapsed while under construction on 28 September 2004.


title: Charles de Gaulle Airport

text: Before this accident, ADP had been planning for an initial public offering in 2005 with the new terminal as a major attraction for investors. The partial collapse and indefinite closing of the terminal just before the beginning of summer seriously hurt the airport's business plan.


title: Charles de Gaulle Airport

text: In February 2005, the results from the administrative inquiry were published. The experts pointed out that there was no single fault, but rather a number of causes for the collapse, in a design that had little margin for safety. The inquiry found the concrete vaulted roof was not resilient enough and had been pierced by metallic pillars and some openings weakened the structure. Sources close to the inquiry also disclosed that the whole building chain had worked as close to the limits as possible, so as to reduce costs. Paul Andreu denounced the building companies for having not correctly prepared the reinforced concrete.


title: Charles de Gaulle Airport

text: On 17 March 2005, ADP decided to tear down and rebuild the whole part of Terminal 2E (the "jetty") of which a section had collapsed, at a cost of approximately €100 million. The reconstruction replaced the innovative concrete tube style of the jetty with a more traditional steel and glass structure. During reconstruction, two temporary departure lounges were constructed in the vicinity of the terminal that replicated the capacity of 2E before the collapse. The terminal reopened completely on 30 March 2008.


title: Charles de Gaulle Airport

text: Terminal 2G, dedicated to regional Air France and HOP! flights and its affiliates, opened in 2008. This terminal is to the east of all terminals and can only be reached by shuttle bus. Terminal 2G is used for passengers flying in the Schengen Area (and thus has no passport control) and handles Air France regional and European traffic and provides small-capacity planes (up to 150 passengers) with a faster turnaround time than is currently possible by enabling them to park close to the new terminal building and boarding passengers primarily by bus, or walking. A bus line called "navette orange" connects the terminal 2G inside the security check area with terminals 2E and 2F. Passengers transferring to other terminals need to continue their trip with other bus shuttles within the security check area if they do not need to get their bags.


title: Charles de Gaulle Airport

text: The completion of long Satellite 3 (or S3) to the immediate east of Terminals 2E and 2F provides further jetways for large-capacity airliners, specifically the Airbus A380. Check-in and baggage handling are provided by the existing infrastructure in Terminals 2E and 2F. Satellite 3 was opened in part on 27 June 2007 and fully operational in September 2007. It corresponds now to gates L of terminal 2E.


title: Charles de Gaulle Airport

text: The satellite S4, adjacent to the S3 and part of terminal 2E, officially opened on 28 June 2012. It corresponds now to gates M of terminal 2E. Dedicated to long-haul flights, it has the ability to handle 16 aircraft at the same time, with an expected capacity of 7.8 million passengers per year. Its opening has led to the relocation of all SkyTeam airlines to terminals 2E (for international carriers), 2F (for Schengen European carriers) and 2G.


title: Charles de Gaulle Airport

text: Air France has moved all of its operations previously located at 2C to 2E. In October 2012, 2F closed its international operations and became completely Schengen, allowing for all Air France flights currently operating in 2D to relocate to terminal 2F. Further, in April 2013, Terminal 2B closed for a complete renovation (all airlines relocated to 2D) and will receive upgrades including the addition of a second floor completely dedicated to arrivals. Once 2B is completed, 2D will close and receive similar upgrades, including the addition of a new floor. Low-cost carrier EasyJet has shown its interest in being the sole carrier at 2B. To facilitate connections, a new boarding area between 2A and 2C was opened in March 2012. It allows for all security and passport control to be handled in a single area, allows for many new shopping opportunities as well as new airline lounges, and eases transfer restrictions between 2A and 2C.


title: Charles de Gaulle Airport

text: According to "La Tribune", a new Terminal 4 was to be built around 2025, when Charles de Gaulle Airport's maximum capacity of 80 million would have been reached. This new Terminal 4, when constructed, would have been able to accommodate 30–40 million passengers per year and would have likely been built north of Terminal 2E. The Terminal 4 proposal was cancelled in 2021, after reduced traffic from the COVID-19 pandemic and new environmental regulations made it unfeasible.


title: Charles de Gaulle Airport

text: Terminal 3 is located 1 km (0.62 mi) away from Terminal 1. It consists of one single building for arrivals and departures. The walking distance between Terminals 1 and 3 is long, however, the rail station (named as "CDG Airport Terminal 1") for RER and CDGVAL trains are only at a distance of . Terminal 3 has no boarding gates constructed and all passengers are ferried via boarding buses to the aircraft stands.


title: Charles de Gaulle Airport

text: Roissypôle is a complex consisting of office buildings, shopping areas, hotels, and a bus coach and RER B station within Charles de Gaulle Airport. The complex includes the head office of Air France, Continental Square, the Hilton Paris Charles de Gaulle Airport, and le Dôme building. Le Dôme includes the head office of Air France Consulting, an Air France subsidiary. Continental Square has the head office of Air France subsidiary Servair and the Air France Vaccinations Centre.


title: Charles de Gaulle Airport

text: The airport's terminals are served by a free automated shuttle rail system, consisting of two lines (CDGVAL and LISA).


title: Charles de Gaulle Airport

text: CDGVAL ("Charles de Gaulle Véhicule Automatique Léger", English: "Charles de Gaulle light automatic vehicle") links Terminal 1, parking lot PR, Aéroport Charles de Gaulle 1 RER station (located inside Roissypôle and next to Terminal 3), Parking lot PX, and the Aéroport Charles de Gaulle 2 TGV and RER station located between Terminals 2C, 2D, 2E, and 2F


title: Charles de Gaulle Airport

text: LISA ("Liaison Interne Satellite Aérogare," English: "Connection internal satellite terminal)" links Terminal 2E to the Satellite S3 (L Gates) and Satellite S4 (M Gates).


title: Charles de Gaulle Airport

text: Charles de Gaulle Airport is connected to central Paris by the RER B, a hybrid suburban commuter and rapid transit line. The service has two stations on the airport grounds:


title: Charles de Gaulle Airport

text: During most times, there are two types of services that operate on the RER B between Charles de Gaulle airport and Paris:


title: Charles de Gaulle Airport

text: The express RER B service only stops at the Terminal 1 (also for Terminal 3) and Terminal 2 stations before Gare du Nord. Journey time is 30–35 minutes. The all-stops RER B service takes about 35–40 minutes and is sometimes overtaken by the express RER B trains.


title: Charles de Gaulle Airport

text: The RER B has historically suffered from slowness and overcrowding, so French authorities are building CDG Express, a train service that will operate non-stop from Charles de Gaulle Airport to Paris Gare de l'Est railway station (next to Gare du Nord) starting in 2025.


title: Charles de Gaulle Airport

text: Terminal 2 includes a TGV station on the LGV Interconnexion Est line. TGV inOui, Ouigo and Thalys high-speed services operate from the station offering services to stations across France and into Belgium and The Netherlands.


title: Charles de Gaulle Airport

text: BlaBlaBus, Eurolines, and Flixbus all offer services to international and domestic destinations from the bus station outside of the Aéroport Charles de Gaulle 1 RER station.


title: Charles de Gaulle Airport

text: The two other airports serving Paris are Orly Airport (south of Paris, the other major airport in Paris) and Paris-Le Bourget Airport (north-northeast of Paris, for general aviation and private jets).


title: Charles de Gaulle Airport

text: Several low-cost airlines also advertise Beauvais–Tillé Airport and Châlons Vatry Airport, respectively and from Paris proper, as serving "Paris" with "Paris–Beauvais" and "Paris–Vatry". Beauvais airport has no railway connections, but there is a shuttle bus to central Paris 15 times daily.


title: Infinity

text: Infinity is that which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol .


title: Infinity

text: Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions among philosophers. In the 17th century, with the introduction of the infinity symbol and the infinitesimal calculus, mathematicians began to work with infinite series and what some mathematicians (including l'Hôpital and Bernoulli) regarded as infinitely small quantities, but infinity continued to be associated with endless processes. As mathematicians struggled with the foundation of calculus, it remained unclear whether infinity could be considered as a number or magnitude and, if so, how this could be done. At the end of the 19th century, Georg Cantor enlarged the mathematical study of infinity by studying infinite sets and infinite numbers, showing that they can be of various sizes. For example, if a line is viewed as the set of all of its points, their infinite number (i.e., the cardinality of the line) is larger than the number of integers. In this usage, infinity is a mathematical concept, and infinite mathematical objects can be studied, manipulated, and used just like any other mathematical object.


title: Infinity

text: The mathematical concept of infinity refines and extends the old philosophical concept, in particular by introducing infinitely many different sizes of infinite sets. Among the axioms of Zermelo–Fraenkel set theory, on which most of modern mathematics can be developed, is the axiom of infinity, which guarantees the existence of infinite sets. The mathematical concept of infinity and the manipulation of infinite sets are used everywhere in mathematics, even in areas such as combinatorics that may seem to have nothing to do with them. For example, Wiles's proof of Fermat's Last Theorem implicitly relies on the existence of very large infinite sets for solving a long-standing problem that is stated in terms of elementary arithmetic.


title: Infinity

text: Ancient cultures had various ideas about the nature of infinity. The ancient Indians and the Greeks did not define infinity in precise formalism as does modern mathematics, and instead approached infinity as a philosophical concept.


title: Infinity

text: The earliest recorded idea of infinity in Greece may be that of Anaximander (c. 610 – c. 546 BC) a pre-Socratic Greek philosopher. He used the word "apeiron", which means "unbounded", "indefinite", and perhaps can be translated as "infinite".


title: Infinity

text: Aristotle (350 BC) distinguished "potential infinity" from "actual infinity", which he regarded as impossible due to the various paradoxes it seemed to produce. It has been argued that, in line with this view, the Hellenistic Greeks had a "horror of the infinite" which would, for example, explain why Euclid (c. 300 BC) did not say that there are an infinity of primes but rather "Prime numbers are more than any assigned multitude of prime numbers." It has also been maintained, that, in proving the infinitude of the prime numbers, Euclid "was the first to overcome the horror of the infinite". There is a similar controversy concerning Euclid's parallel postulate, sometimes translated:


title: Infinity

text: Other translators, however, prefer the translation "the two straight lines, if produced indefinitely ...", thus avoiding the implication that Euclid was comfortable with the notion of infinity. Finally, it has been maintained that a reflection on infinity, far from eliciting a "horror of the infinite", underlay all of early Greek philosophy and that Aristotle's "potential infinity" is an aberration from the general trend of this period.


title: Infinity

text: Zeno of Elea ( 495 –  430 BC) did not advance any views concerning the infinite. Nevertheless, his paradoxes, especially "Achilles and the Tortoise", were important contributions in that they made clear the inadequacy of popular conceptions. The paradoxes were described by Bertrand Russell as "immeasurably subtle and profound".


title: Infinity

text: Apparently, Achilles never overtakes the tortoise, since however many steps he completes, the tortoise remains ahead of him.


title: Infinity

text: Zeno was not attempting to make a point about infinity. As a member of the Eleatics school which regarded motion as an illusion, he saw it as a mistake to suppose that Achilles could run at all. Subsequent thinkers, finding this solution unacceptable, struggled for over two millennia to find other weaknesses in the argument.


title: Infinity

text: Finally, in 1821, Augustin-Louis Cauchy provided both a satisfactory definition of a limit and a proof that, for ,


title: Infinity

text: Suppose that Achilles is running at 10 meters per second, the tortoise is walking at 0.1 meters per second, and the latter has a 100-meter head start. The duration of the chase fits Cauchy's pattern with and . Achilles does overtake the tortoise; it takes him


title: Infinity

text: The Jain mathematical text Surya Prajnapti (c. 4th–3rd century BCE) classifies all numbers into three sets: enumerable, innumerable, and infinite. Each of these was further subdivided into three orders:


title: Infinity

text: In the 17th century, European mathematicians started using infinite numbers and infinite expressions in a systematic fashion. In 1655, John Wallis first used the notation formula_3 for such a number in his "De sectionibus conicis", and exploited it in area calculations by dividing the region into infinitesimal strips of width on the order of formula_4 But in "Arithmetica infinitorum" (also in 1655), he indicates infinite series, infinite products and infinite continued fractions by writing down a few terms or factors and then appending "&c.", as in "1, 6, 12, 18, 24, &c."


title: Infinity

text: In 1699, Isaac Newton wrote about equations with an infinite number of terms in his work "De analysi per aequationes numero terminorum infinitas".


title: Infinity

text: The infinity symbol formula_3 (sometimes called the lemniscate) is a mathematical symbol representing the concept of infinity. The symbol is encoded in Unicode at and in LaTeX as codice_1.


title: Infinity

text: It was introduced in 1655 by John Wallis, and since its introduction, it has also been used outside mathematics in modern mysticism and literary symbology.


title: Infinity

text: Gottfried Leibniz, one of the co-inventors of infinitesimal calculus, speculated widely about infinite numbers and their use in mathematics. To Leibniz, both infinitesimals and infinite quantities were ideal entities, not of the same nature as appreciable quantities, but enjoying the same properties in accordance with the Law of continuity.


title: Infinity

text: In real analysis, the symbol formula_3, called "infinity", is used to denote an unbounded limit. The notation formula_7 means that "formula_8" increases without bound, and formula_9 means that "formula_8" decreases without bound. For example, if formula_11 for every "formula_12", then


title: Infinity

text: In addition to defining a limit, infinity can be also used as a value in the extended real number system. Points labeled formula_25 and formula_26 can be added to the topological space of the real numbers, producing the two-point compactification of the real numbers. Adding algebraic properties to this gives us the extended real numbers. We can also treat formula_25 and formula_26 as the same, leading to the one-point compactification of the real numbers, which is the real projective line. Projective geometry also refers to a line at infinity in plane geometry, a plane at infinity in three-dimensional space, and a hyperplane at infinity for general dimensions, each consisting of points at infinity.


title: Infinity

text: In complex analysis the symbol formula_3, called "infinity", denotes an unsigned infinite limit. formula_7 means that the magnitude formula_31 of "formula_8" grows beyond any assigned value. A point labeled formula_3 can be added to the complex plane as a topological space giving the one-point compactification of the complex plane. When this is done, the resulting space is a one-dimensional complex manifold, or Riemann surface, called the extended complex plane or the Riemann sphere. Arithmetic operations similar to those given above for the extended real numbers can also be defined, though there is no distinction in the signs (which leads to the one exception that infinity cannot be added to itself). On the other hand, this kind of infinity enables division by zero, namely formula_34 for any nonzero complex number "formula_35". In this context, it is often useful to consider meromorphic functions as maps into the Riemann sphere taking the value of formula_3 at the poles. The domain of a complex-valued function may be extended to include the point at infinity as well. One important example of such functions is the group of Möbius transformations (see Möbius transformation § Overview).


title: Infinity

text: The original formulation of infinitesimal calculus by Isaac Newton and Gottfried Leibniz used infinitesimal quantities. In the second half of the 20th century, it was shown that this treatment could be put on a rigorous footing through various logical systems, including smooth infinitesimal analysis and nonstandard analysis. In the latter, infinitesimals are invertible, and their inverses are infinite numbers. The infinities in this sense are part of a hyperreal field; there is no equivalence between them as with the Cantorian transfinites. For example, if H is an infinite number in this sense, then H + H = 2H and H + 1 are distinct infinite numbers. This approach to non-standard calculus is fully developed in .


title: Infinity

text: A different form of "infinity" are the ordinal and cardinal infinities of set theory—a system of transfinite numbers first developed by Georg Cantor. In this system, the first transfinite cardinal is aleph-null (ℵ), the cardinality of the set of natural numbers. This modern mathematical conception of the quantitative infinite developed in the late 19th century from works by Cantor, Gottlob Frege, Richard Dedekind and others—using the idea of collections or sets.


title: Infinity

text: Dedekind's approach was essentially to adopt the idea of one-to-one correspondence as a standard for comparing the size of sets, and to reject the view of Galileo (derived from Euclid) that the whole cannot be the same size as the part. (However, see Galileo's paradox where Galileo concludes that positive integers cannot be compared to the subset of positive square integers since both are infinite sets.) An infinite set can simply be defined as one having the same size as at least one of its proper parts; this notion of infinity is called Dedekind infinite. The diagram to the right gives an example: viewing lines as infinite sets of points, the left half of the lower blue line can be mapped in a one-to-one manner (green correspondences) to the higher blue line, and, in turn, to the whole lower blue line (red correspondences); therefore the whole lower blue line and its left half have the same cardinality, i.e. "size".


title: Infinity

text: Cantor defined two kinds of infinite numbers: ordinal numbers and cardinal numbers. Ordinal numbers characterize well-ordered sets, or counting carried on to any stopping point, including points after an infinite number have already been counted. Generalizing finite and (ordinary) infinite sequences which are maps from the positive integers leads to mappings from ordinal numbers to transfinite sequences. Cardinal numbers define the size of sets, meaning how many members they contain, and can be standardized by choosing the first ordinal number of a certain size to represent the cardinal number of that size. The smallest ordinal infinity is that of the positive integers, and any set which has the cardinality of the integers is countably infinite. If a set is too large to be put in one-to-one correspondence with the positive integers, it is called "uncountable". Cantor's views prevailed and modern mathematics accepts actual infinity as part of a consistent and coherent theory. Certain extended number systems, such as the hyperreal numbers, incorporate the ordinary (finite) numbers and infinite numbers of different sizes.


title: Infinity

text: One of Cantor's most important results was that the cardinality of the continuum formula_37 is greater than that of the natural numbers formula_38; that is, there are more real numbers than natural numbers . Namely, Cantor showed that formula_39.


title: Infinity

text: The continuum hypothesis states that there is no cardinal number between the cardinality of the reals and the cardinality of the natural numbers, that is, formula_40.This hypothesis cannot be proved or disproved within the widely accepted Zermelo–Fraenkel set theory, even assuming the Axiom of Choice.


title: Infinity

text: Cardinal arithmetic can be used to show not only that the number of points in a real number line is equal to the number of points in any segment of that line, but also that this is equal to the number of points on a plane and, indeed, in any finite-dimensional space.


title: Infinity

text: The first of these results is apparent by considering, for instance, the tangent function, which provides a one-to-one correspondence between the interval () and.The second result was proved by Cantor in 1878, but only became intuitively apparent in 1890, when Giuseppe Peano introduced the space-filling curves, curved lines that twist and turn enough to fill the whole of any square, or cube, or hypercube, or finite-dimensional space. These curves can be used to define a one-to-one correspondence between the points on one side of a square and the points in the square.


title: Infinity

text: Until the end of the 19th century, infinity was rarely discussed in geometry, except in the context of processes that could be continued without any limit. For example, a line was what is now called a line segment, with the proviso that one can extend it as far as one wants; but extending it "infinitely" was out of the question. Similarly, a line was usually not considered to be composed of infinitely many points, but was a location where a point may be placed. Even if there are infinitely many possible positions, only a finite number of points could be placed on a line. A witness of this is the expression "the locus of "a point" that satisfies some property" (singular), where modern mathematicians would generally say "the set of "the points" that have the property" (plural).


title: Infinity

text: One of the rare exceptions of a mathematical concept involving actual infinity was projective geometry, where points at infinity are added to the Euclidean space for modeling the perspective effect that shows parallel lines intersecting "at infinity". Mathematically, points at infinity have the advantage of allowing one to not consider some special cases. For example, in a projective plane, two distinct lines intersect in exactly one point, whereas without points at infinity, there are no intersection points for parallel lines. So, parallel and non-parallel lines must be studied separately in classical geometry, while they need not to be distinguished in projective geometry.


title: Infinity

text: Before the use of set theory for the foundation of mathematics, points and lines were viewed as distinct entities, and a point could be "located on a line". With the universal use of set theory in mathematics, the point of view has dramatically changed: a line is now considered as "the set of its points", and one says that a point "belongs to a line" instead of "is located on a line" (however, the latter phrase is still used).


title: Infinity

text: The vector spaces that occur in classical geometry have always a finite dimension, generally two or three. However, this is not implied by the abstract definition of a vector space, and vector spaces of infinite dimension can be considered. This is typically the case in functional analysis where function spaces are generally vector spaces of infinite dimension.


title: Infinity

text: In topology, some constructions can generate topological spaces of infinite dimension. In particular, this is the case of iterated loop spaces.


title: Infinity

text: The structure of a fractal object is reiterated in its magnifications. Fractals can be magnified indefinitely without losing their structure and becoming "smooth"; they have infinite perimeters, and can have infinite or finite areas. One such fractal curve with an infinite perimeter and finite area is the Koch snowflake.


title: Infinity

text: Leopold Kronecker was skeptical of the notion of infinity and how his fellow mathematicians were using it in the 1870s and 1880s. This skepticism was developed in the philosophy of mathematics called finitism, an extreme form of mathematical philosophy in the general philosophical and mathematical schools of constructivism and intuitionism.


title: Infinity

text: In physics, approximations of real numbers are used for continuous measurements and natural numbers are used for discrete measurements (i.e., counting). Concepts of infinite things such as an infinite plane wave exist, but there are no experimental means to generate them.


title: Infinity

text: The first published proposal that the universe is infinite came from Thomas Digges in 1576. Eight years later, in 1584, the Italian philosopher and astronomer Giordano Bruno proposed an unbounded universe in "On the Infinite Universe and Worlds": "Innumerable suns exist; innumerable earths revolve around these suns in a manner similar to the way the seven planets revolve around our sun. Living beings inhabit these worlds."


title: Infinity

text: Cosmologists have long sought to discover whether infinity exists in our physical universe: Are there an infinite number of stars? Does the universe have infinite volume? Does space "go on forever"? This is still an open question of cosmology. The question of being infinite is logically separate from the question of having boundaries. The two-dimensional surface of the Earth, for example, is finite, yet has no edge. By travelling in a straight line with respect to the Earth's curvature, one will eventually return to the exact spot one started from. The universe, at least in principle, might have a similar topology. If so, one might eventually return to one's starting point after travelling in a straight line through the universe for long enough.


title: Infinity

text: The curvature of the universe can be measured through multipole moments in the spectrum of the cosmic background radiation. To date, analysis of the radiation patterns recorded by the WMAP spacecraft hints that the universe has a flat topology. This would be consistent with an infinite physical universe.


title: Infinity

text: However, the universe could be finite, even if its curvature is flat. An easy way to understand this is to consider two-dimensional examples, such as video games where items that leave one edge of the screen reappear on the other. The topology of such games is toroidal and the geometry is flat. Many possible bounded, flat possibilities also exist for three-dimensional space.


title: Infinity

text: The concept of infinity also extends to the multiverse hypothesis, which, when explained by astrophysicists such as Michio Kaku, posits that there are an infinite number and variety of universes. Also, cyclic models posit an infinite amount of Big Bangs, resulting in an infinite variety of universes after each Big Bang event in an infinite cycle.


title: Infinity

text: In logic, an infinite regress argument is "a distinctively philosophical kind of argument purporting to show that a thesis is defective because it generates an infinite series when either (form A) no such series exists or (form B) were it to exist, the thesis would lack the role (e.g., of justification) that it is supposed to play."


title: Infinity

text: The IEEE floating-point standard (IEEE 754) specifies a positive and a negative infinity value (and also indefinite values). These are defined as the result of arithmetic overflow, division by zero, and other exceptional operations.


title: Infinity

text: Some programming languages, such as Java and J, allow the programmer an explicit access to the positive and negative infinity values as language constants. These can be used as greatest and least elements, as they compare (respectively) greater than or less than all other values. They have uses as sentinel values in algorithms involving sorting, searching, or windowing.


title: Infinity

text: In languages that do not have greatest and least elements, but do allow overloading of relational operators, it is possible for a programmer to "create" the greatest and least elements. In languages that do not provide explicit access to such values from the initial state of the program, but do implement the floating-point data type, the infinity values may still be accessible and usable as the result of certain operations.


title: Infinity

text: In programming, an infinite loop is a loop whose exit condition is never satisfied, thus executing indefinitely.


title: Infinity

text: Perspective artwork uses the concept of vanishing points, roughly corresponding to mathematical points at infinity, located at an infinite distance from the observer. This allows artists to create paintings that realistically render space, distances, and forms. Artist M.C. Escher is specifically known for employing the concept of infinity in his work in this and other ways.


title: Infinity

text: Cognitive scientist George Lakoff considers the concept of infinity in mathematics and the sciences as a metaphor. This perspective is based on the basic metaphor of infinity (BMI), defined as the ever-increasing sequence <1,2,3...>.


title: Croissant

text: A croissant is a buttery, flaky, Austrian viennoiserie pastry inspired by the shape of the Austrian kipferl but using the French yeast-leavened laminated dough. Croissants are named for their historical crescent shape, the dough is layered with butter, rolled and folded several times in succession, then rolled into a thin sheet, in a technique called laminating. The process results in a layered, flaky texture, similar to a puff pastry.


title: Croissant

text: Crescent-shaped breads have been made since the Renaissance, and crescent-shaped cakes possibly since antiquity but using brioche dough. Kipferls have long been a staple of Austrian, and French bakeries and pâtisseries. The modern croissant was developed in the early 20th century when French bakers replaced the brioche dough of the kipferl with a yeast-leavened laminated dough. In the late 1970s, the development of factory-made, frozen, preformed but unbaked dough made them into a fast food that could be freshly baked by unskilled labor. The croissant bakery, notably the "La Croissanterie" chain, was a French response to American-style fast food, and as of 2008, 30–40% of the croissants sold in French bakeries and patisseries were baked from frozen dough.


title: Croissant

text: The kipferl, the origin of croissant, can be dated back to at least the 13th century in Austria, and came in various shapes. The kipferl can be made plain or with nuts or other fillings (some consider the rugelach a form of kipferl).


title: Croissant

text: The birth of the croissant itself—that is, its adaptation from the plainer form of kipferl, before the invention of viennoiseries—can be dated to at least 1839 (some say 1838) when an Austrian artillery officer, August Zang, founded a Viennese bakery ("Boulangerie Viennoise") at 92, rue de Richelieu in Paris. This bakery, which served Viennese specialties including the kipferl and the Vienna loaf, quickly became popular and inspired French imitators (and the concept, if not the term, of "viennoiserie", a 20th-century term for supposedly Vienna-style pastries). The French version of the kipferl was named for its crescent ("croissant") shape and has become a universally identifiable shape across the world.


title: Croissant

text: Sylvain Claudius Goy, a French chef, was the first to make croissant with yeast leavened laminated dough.


title: Croissant

text: Alan Davidson, editor of the "Oxford Companion to Food", found no printed recipe for the present-day croissant in any French recipe book before the early 20th century; the earliest French reference to a croissant he found was among the "fantasy or luxury breads" in Payen's "Des substances alimentaires", 1853. However, early recipes for non-laminated croissants can be found in the 19th century and at least one reference to croissants as an established French bread appeared as early as 1850.


title: Croissant

text: Zang himself returned to Austria in 1848 to become a press magnate, but the bakery remained popular for some time afterwards, and was mentioned in several works of the time: "This same M. Zank ...founded around 1830 [sic], in Paris, the famous Boulangerie viennoise". Several sources praise this bakery's products: "Paris is of exquisite delicacy; and, in particular, the succulent products of the Boulangerie Viennoise"; "which seemed to us as fine as if it came from the Viennese bakery on the rue de Richelieu".


title: Croissant

text: By 1869, the croissant was well established enough to be mentioned as a breakfast staple, and in 1872, Charles Dickens wrote (in his periodical "All the Year Round") of "the workman's "pain de ménage" and the soldier's "pain de munition", to the dainty croissant on the boudoir table"


title: Croissant

text: The puff pastry technique that now characterizes the croissant was already mentioned in the late 17th century, when La Varenne's "Le Cuisinier françois" gave a recipe for it in the 1680 - and possibly earlier - edition. It was typically used not on its own but for shells holding other ingredients (as in a vol-au-vent). It does not appear to be mentioned in relation to the croissant until the 20th century.


title: Croissant

text: Stories of how the Kipferl — and so, ultimately, the croissant — was created are widespread and persistent culinary legends, going back to the 19th century. However, there are no contemporary sources for any of these stories, and an aristocratic writer, writing in 1799, does not mention the Kipferl in a long and extensive list of breakfast foods.


title: Croissant

text: The legends include tales that it was invented in Europe to celebrate the defeat of the Umayyad forces by the Franks at the Battle of Tours in 732, with the shape representing the Islamic crescent; that it was invented in Buda; or, according to other sources, in Vienna in 1683 to celebrate the defeat of the Ottomans by Christian forces in the siege of the city, as a reference to the crescents on the Ottoman flags, when bakers staying up all night heard the tunneling operation and gave the alarm.


title: Croissant

text: The above mentioned Alan Davidson proposed that the Islamic origin story originated with 20th-century writer Alfred Gottschalk, who gave two versions, one in the "Larousse Gastronomique" and the other in his "History of Food and Gastronomy":


title: Croissant

text: Uncooked croissant dough can also be wrapped around any praline, almond paste, or chocolate before it is baked (in the last case, it becomes like "pain au chocolat", which has a different, non-crescent, shape), or sliced to include sweet or savoury fillings. It may be flavored with dried fruit such as sultanas or raisins, or other fruits such as apples. In France and Spain, croissants are generally sold without filling and eaten without added butter, but sometimes with almond filling.


title: Croissant

text: In the United States, sweet fillings or toppings are sometimes used, and warm croissants may be filled with ham and cheese, or feta cheese and spinach. In the Levant, croissants are sold plain or filled with chocolate, cheese, almonds, or zaatar. In Germany, croissants are sometimes filled with Nutella or persipan; in southern Germany, there is also a popular variety of a croissant glazed with lye ("Laugencroissant"). In the German-speaking part of Switzerland, the croissant is typically called a "Gipfeli"; this usually has a crisper crust and is less buttery than the French-style croissant.


title: Croissant

text: Croissants are commonly served alongside coffee for breakfast, "aperitivo" (a light mid-morning meal), or "merienda" (a mid-afternoon meal). They are referred to as "medialunas" ("half moons") because of their shape and are typically coated with a sweet glaze ("medialunas de manteca", "half moons of butter"). Another variant is a "medialuna de grasa" ("half moon of lard"), which is not always sweet.


title: Croissant

text: A cousin of the croissant is the Italian "cornetto" (in the Center and South) or "brioche" (in the North). These variants are often considered to be the same, but that is not completely true: the French version tends to be crispy and contains a lot of butter, whereas an Italian cornetto or brioche is usually softer. Furthermore, the "cornetto vuoto" (Italian: "empty cornetto") is commonly accompanied by variants with filling, which include "crema pasticciera" (custard), apricot jam or chocolate cream. They often come covered with powdered sugar or other toppings. "Cornetto" with cappuccino at the bar is one of the most common breakfasts in Italy.


title: Croissant

text: On 11 November, St. Martin's Day is celebrated in the Polish region of Greater Poland, mainly in its capital city Poznań. On this day, the people of Poznań purchase and eat considerable amounts of sweet, crescent-shaped pastries called "rogale świętomarcińskie" ("St. Martin's croissants"). They are made specially for this occasion from puff pastry with a filling made of ground white poppy seeds, almonds, raisins, and nuts.


title: Croissant

text: The first type of Portuguese croissant is similar to the French, and can be plain or filled with custard, chocolate, fruit jam, or a typical Portuguese cream made of egg yolk and sugar, "doce de ovo". It is customary for these to also have powdered sugar on top. The second version has a similar consistency to brioche and is commonly eaten with ham and cheese. Sometimes this type is also served like toast, with a spread of butter. While the first type of croissant is considered sweet and is eaten during breakfast or tea, the second type is a more filling meal and is usually considered a sandwich and often prepared for picnics or as travel food. Both types share the same name (French/Portuguese: "croissant") but are typically found in different bakeries: the sweet croissant is more commonly found in Portuguese pâtisseries and the brioche croissant is usually found in coffeehouses.


title: Croissant

text: Besides of the regular croissant, a variation called Xuixos () is sold. It is half of a croissant stuffed usually with cream.


title: Croissant

text: A remote similarity of the croissant shape is the Turkish "ay çöreği". It is filled with cinnamon, walnut, hazelnut, cacao and raisin. Its rectangular shape variant is known as "pastiç" or "İzmir çöreği". It is generally eaten during breakfast or with tea.


title: Croissant

text: The first step of manufacturing croissants is the "predough" formation. To prepare predough, flour, water, in-dough fat, yeast, salt, and sugar are mixed together in a single step. Typically, croissant predough is mixed in a relatively cool environment, for a longer time than other pastries. The ideal temperature of the dough should be around 19 °C, to best hydrate the ingredients. In comparison to the mixing of bread dough ingredients, pastry predough is considered underdeveloped in that mixing is stopped as soon as the dough appears homogeneous, to allow for further dough development in the next step.


title: Croissant

text: The second step is the lamination process. Lamination is necessary to produce multilayered dough with alternating layers of predough and fat. Generally, there are two methods for folding fat into the dough: the English method and the French method. In the English method, one fold results in two fat layers and three dough layers. After spreading out predough, roll-in fat is flattened to a similar thickness as the predough and spread over two-thirds of the surface of the laminated predough. The exposed third of predough is then folded over half of the roll-in fat, while the other end (one predough and one fat layer) is folded on top. In the French method, one fold results in one fat layer and two dough layers. After spreading out the predough and putting a layer of roll-in fat over the center surface of the dough, the corners of the predough are folded toward the middle of the fat. Croissant dough is typically laminated until 16–50 fat layers are obtained. The optimal number of layers can be determined by balancing certain crumb properties with specific volume. On one hand, a low number of layers yields large specific heights as well as irregular crumb structure with large voids. On the other hand, a large number of relatively thin layers leads to interconnections between different dough layers as well as less dough lift.


title: Croissant

text: After lamination, the dough is formed into its famous crescent shape. First, the laminated dough is cut into triangles of the desired size. The triangles are then rolled with three-and-a-half to four full turns, and finally, the ends of the roll are curved inwards to form a crescent.


title: Croissant

text: The third step is the fermentation process. Croissants are different from other puff pastries in that they include yeast, which, during proofing, increases the dough volume. Ideally, the optimum croissant quality is achieved at a yeast level of 7.5%, with a proof time of 60 minutes at 31 °C. The croissants are finished proofing when the dough has expanded two-and-a-half times its original volume.


title: Croissant

text: The fourth step is the baking process. Also known as "pastry lift" or "dough lift", the dough expands as water is converted to steam, thus increasing the pressure between each dough layer. As a result, the croissant dough rises up to yield its characteristic flaky texture. Depending on the type of oven used and specific size of the croissant, the baking time can range from 10 to 20 minutes and the oven temperature can be set anywhere from 165 °C to 205 °C.


title: Croissant

text: The final steps are the cooling and storage of the croissant. Croissants are generally not stored for very long and are typically consumed soon after baking.


title: Croissant

text: Gluten proteins affect the water absorption and viscoelastic properties of the predough. The role of proteins can be divided into two stages of dough formation: hydration and deformation. In the hydration stage, gluten proteins absorb water up to two times their own weight. In the deformation or kneading stage, the action of mixing causes the gluten to undergo a series of polymerization and depolymerization reactions, forming a viscoelastic network. Hydrated glutenin proteins in particular help form a polymeric protein network that makes the dough more cohesive. On the other hand, hydrated gliadin proteins do not directly form the network, but do act as plasticizers of the glutenin network, thus imparting fluidity to the dough’s viscosity.


title: Croissant

text: Starch also affects the viscosity of predough. At room temperature and in a sufficient amount of water, intact starch granules can absorb water up to 50% of their own dry weight, causing them to swell to a limited extent. The slightly swollen granules are found in the spaces between the gluten network, thus contributing to the consistency of the dough. The granules may not be intact, as the process of milling wheat into flour damages some of the starch granules. Given that damaged starch granules have the capacity to absorb around three times as much water as undamaged starch, the use of flour with higher levels of damaged starch requires the addition of more water to achieve optimal dough development and consistency.


title: Croissant

text: Water content affects the mechanical behavior of predough. As previously discussed, water is absorbed by gluten and starch granules to increase the viscosity of the dough. The temperature of the water is also important as it determines the temperature of the predough. In order to facilitate processing, cold water should be used for two main reasons. First, chilled water provides a desirable environment for gluten development, as the temperature at which mixing occurs impacts the dough’s hydration time, consistency, and required amount of mixing energy. Secondly, cold water is comparable to the temperature of the roll-in fat to be added later, which better facilitates the latter’s incorporation.


title: Croissant

text: In-dough fat affects the texture and lift of predough. Although higher levels of dough fat may lower dough lift during baking, it also correlates with a softer end product. As such, the main function of in-dough fat is to produce a desirable softness in the final croissant.


title: Croissant

text: In laminated croissant dough, the gluten network is not continuous. Instead, the gluten proteins are separated as thin gluten films between dough layers. The formation of thin, well-defined layers affects the height of dough lift. Generally, laminated croissant dough contains fewer layers than other puff pastry doughs that do not contain yeast, due to the presence of small bubbles in the gluten sheets. Upon proofing, these bubbles expand and destroy the integrity of the dough layers. The resulting interconnections between different dough layers would over-increase dough strength and allow water vapor to escape through micropores during baking, consequently decreasing dough lift. The role of fat also influences the separation of layers, as will be discussed next.


title: Croissant

text: Roll-in fat affects the flakiness and flavor of the croissant. In laminated dough, fat layers alternate with dough layers. As such, the most important function of roll-in fat is to form and maintain a barrier between the different dough layers during sheeting and folding. As previously stated, the ability for fat to maintain separation between folded dough layers ensures proper dough lift.


title: Croissant

text: The type of roll-in fat used is typically butter or margarine. Butter and margarine are both water-in-oil emulsions, composed of stabilized water droplets dispersed in oil. While butter is appealing due to its high consumer acceptance, its low melting point, 32 °C, actually makes it undesirable for production purposes. The use of butter as roll-in fat during the lamination step will cause problems of oiling out during sheeting and fermentation if the temperature is not tightly controlled, thus disrupting the integrity of the layers. On the other hand, kinds of margarine are commonly used as roll-in fat because they facilitate dough handling. Generally, roll-in margarine should have a melting point between 40 °C and 44 °C, at least 3 °C higher than the fermentation temperature to prevent oiling out prior to baking. It is also important to consider the plasticity and firmness of the roll-in fat, which is largely determined by its solid fat content. Generally, a greater proportion of solid fat coincides with larger croissant lift. At the same time, the roll-in fat should have plasticity comparable to that of the dough, such that the fat layers do not break during sheeting and folding. If the fat is firmer than the dough, then the dough can rupture. If the fat is softer than the dough, then it will succumb to the mechanical stress of sheeting and potentially migrate into the dough.


title: Croissant

text: Croissants contain yeast, "Saccharomyces cerevisiae", which is incorporated during predough formation. When oxygen is abundant, the yeast breaks down sugar into carbon dioxide and water through the process of respiration. This process releases energy that is used by the yeast for growth. After consuming all of the oxygen, the yeast switches to anaerobic fermentation. At this point, the yeast partially breaks down sugar into ethanol and carbon dioxide. Once saturates the dough’s aqueous phase, the gas begins to leaven the dough by diffusing to preexisting gas cells that were incorporated into the predough during mixing. Yeast action does not produce new gas cells, as the immense pressure required for a single molecule to create a new gas bubble is not physically attainable


title: Croissant

text: In order to ensure the flaky texture of the croissant, it is important to balance the yeast activity with steam production. If the yeast overproduces , then the well-defined layers may collapse. During the baking process, this would cause steam to escape too early from the bread, reducing dough lift and flakiness of the final product. Thus, to offset the negative effects of yeast on layer integrity and dough lift, croissants usually contain fewer layers than other puff pastries.


title: Croissant

text: During baking, the transient gluten network turns into a permanent network. At higher temperatures, intermolecular disulfide bonds form between glutenin molecules, as well as between gliadin and glutenin. With more bonds being made, the gluten network becomes more rigid, strengthening the croissant’s crumb texture. Additionally, the baking process significantly stretches the dough layers due to the large macroscopic deformation that occurred during fermentation’s dough lift.


title: Croissant

text: Starch undergoes gelatinization as a result of baking. Prior to baking, starch granules absorb a small amount of water at room temperature as it is mixed with water to form predough. As long as the dough’s temperature stays under the gelatinization temperature, this granule swelling is limited and reversible. However, once the baking process begins and the dough is exposed to temperatures above the gelatinization temperature, amylopectin crystallites become more disordered inside the starch granules and cause an irreversible destruction of molecular order. At the same time, starch gelatinization actively draws water from the gluten network, further decreasing the flexibility of the gluten. Currently, the extent of amylose leaching and granular structure distortion during the baking of croissants is still unknown.


title: Croissant

text: Roll-in fat gradually melts as the temperature in the oven increases. Some of the melting fat can migrate into the dough, which could then interfere with gluten protein crosslinking. The fat phase also contributes to dough lift through gas inflation, which will be described next.


title: Croissant

text: Water is converted to steam during the baking process, which is the main factor behind the leavening of the dough. The water for steam production comes from both the dough layers and the roll-in fat. As the fat melts, the continuous oil phase is no longer able to stabilize the water droplets, which are then released and converted to steam. Although the exact mechanism of steam entrapment is still unclear, it is likely a result of both steam expanding inside each dough layer and steam migrating to oil layers, where it inflates gas bubbles. The steam migration to oil phase is likely due to the smaller pressure differential required to inflate a bubble of steam in liquid fat than in solid dough. As the concentration of steam increases between dough layers, the increased pressure causes the dough to lift. It is important to note that during the entire baking process, only half of the water vapor contributes to dough lift, as the other half is lost through micropores and capillaries of interconnected dough layers.


title: Croissant

text: The effect of gluten proteins during cooling and storage is still unclear. It is possible that gluten proteins influence croissant firming through the loss of plasticizing water, which increases the stiffness of the gluten network.