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Culture of Canada

The culture of Canada embodies the artistic, culinary, literary, humour, musical, political and social elements that are representative of Canadians. Throughout Canada's history, its culture has been influenced firstly by its indigenous cultures, and later by European culture and traditions, mostly by the British and French. Over time, elements of the cultures of Canada's immigrant populations have become incorporated to form a Canadian cultural mosaic. Certain segments of Canada's population have, to varying extents, also been influenced by American culture due to shared language (in English-speaking Canada), significant media penetration and geographic proximity.

Canada is often characterized as being "very progressive, diverse, and multicultural". Canada's federal government has often been described as the instigator of multicultural ideology because of its public emphasis on the social importance of immigration. Canada's culture draws from its broad range of constituent nationalities, and policies that promote a just society are constitutionally protected. Canadian policies—such as abortion, euthanasia, same-sex marriage, and cannabis; an emphasis on cultural diversity; large-scale immigration; abolishing capital punishment; publicly funded health care; higher and more progressive taxation; efforts to eliminate poverty; and strict gun control are social indicators of the country's political and cultural values. Canadians identify with the country's institutions of health care, military peacekeeping, the national park system, and the Canadian Charter of Rights and Freedoms.

The Canadian government has influenced culture with programs, laws and institutions. It has created crown corporations to promote Canadian culture through media, such as the Canadian Broadcasting Corporation (CBC) and the National Film Board of Canada (NFB), and promotes many events which it considers to promote Canadian traditions. It has also tried to protect Canadian culture by setting legal minimums on Canadian content in many media using bodies like the Canadian Radio-television and Telecommunications Commission (CRTC).

Influences
For thousands of years, Canada has been inhabited by indigenous peoples from a variety of different cultures and of several major linguistic groupings. Although not without conflict and bloodshed, early European interactions with First Nations and Inuit populations in what is now Canada were arguably peaceful. First Nations and Métis peoples played a critical part in the development of European colonies in Canada, particularly for their role in assisting European coureur des bois and voyageurs in the exploration of the continent during the North American fur trade. Over the course of three centuries, countless North American Indigenous words, inventions, concepts, and games have become an everyday part of Canadian language and use. Many places in Canada, both natural features and human habitations, use indigenous names. The name "Canada" itself derives from the St. Lawrence Huron-Iroquoian word "Kanata" meaning "village" or "settlement". The name of Canada's capital city Ottawa comes from the Algonquin language term "adawe" meaning "to trade".

In the 17th-century, French colonials settled New France in Acadia, in the present-day Maritimes, and in Canada, along the Saint Lawrence River in present-day Quebec and Ontario. These regions were under French control from 1534 to 1763. However, the British conquered Acadia in 1710 and conquered Canada in 1760. The British were able to deport most of the Acadians, but they were unable to deport the Canadiens of Canada because they severely outnumbered the British forces. The British therefore had to make deals with Canadiens and hope they would one day become assimilated. The American Revolution, from 1775 to 1783, provoked the migration of 40,000 to 50,000 United Empire Loyalists from the Thirteen Colonies to the newly conquered British lands, which brought American influences to Canada for the first time. Following the War of 1812, many Scottish and English people settled in Upper Canada and Lower Canada. Many Irish people fleeing the Great Famine also arrived between 1845 and 1852.

The Canadian Forces and overall civilian participation in the First World War and Second World War helped to foster Canadian nationalism; however, in 1917 and 1944, conscription crises highlighted the considerable rift along ethnic lines between Anglophones and Francophones. As a result of the First and Second World Wars, the Government of Canada became more assertive and less deferential to British authority. Canada, until the 1940s, was often described as "binational", with the 2 components being the cultural, linguistic and political identities of English Canadians and of French Canadians.

Legislative restrictions on immigration (such as the Continuous journey regulation and Chinese Immigration Act) that had favoured British, American and other European immigrants (such as Dutch, German, Italian, Polish, Swedish and Ukrainian) were amended during the 1960s, resulting in an influx of people of many different ethnicities. By the end of the 20th century, immigrants were increasingly Chinese, Indian, Vietnamese, Jamaican, Filipino, Lebanese, Pakistani and Haitian. By the 21st century Canada had thirty four ethnic groups with at least one hundred thousand members each, of which eleven have over 1,000,000 people and numerous others are represented in smaller numbers. , 16.2% of the population self-identify as a visible minority.

Development of popular culture
Themes and symbols of pioneers, trappers, and traders played an important part in the early development of Canadian culture. Modern Canadian culture as it is understood today can be traced to its time period of westward expansion and nation building. Contributing factors include Canada's unique geography, climate, and cultural makeup. Being a cold country with long winter nights for most of the year, certain unique leisure activities developed in Canada during this period including ice hockey and embracement of the summer indigenous game of lacrosse.

By the 19th century, Canadians came to believe themselves possessed of a unique "northern character," due to the long, harsh winters that only those of hardy body and mind could survive. This hardiness was claimed as a Canadian trait, and sports that reflected this, such as snowshoeing and cross-country skiing, were asserted as characteristically Canadian. During this period, the churches tried to influence leisure activities by preaching against drinking, and scheduling annual revivals and weekly club activities. In a society in which most middle-class families now owned a harmonium or piano, and standard education included at least the rudiments of music, the result was often an original song. Such stirrings frequently occurred in response to noteworthy events, and few local or national excitements were allowed to pass without some musical comment.

By the 1930s, radio played a major role in uniting Canadians behind their local or regional teams. Rural areas were especially influenced by sports coverage and the propagation of national myths. Outside the sports and music arena, Canadians expressed a national character of being hard working, peaceful, orderly and polite.

Cultural legislation
French Canada's early development was relatively cohesive during the 17th and 18th centuries, and this was preserved by the Quebec Act of 1774, which allowed Roman Catholics to hold offices and practice their faith. In 1867, the Constitution Act was thought to meet the growing calls for Canadian autonomy while avoiding the overly strong decentralization that contributed to the Civil War in the United States. The compromises reached during this time between the English- and French-speaking Fathers of Confederation set Canada on a path to bilingualism which in turn contributed to an acceptance of diversity. The English and French languages have had limited constitutional protection since 1867 and full official status since 1969. Section 133 of the Constitution Act of 1867 (BNA Act) guarantees that both languages may be used in the Parliament of Canada. Canada adopted its first Official Languages Act in 1969, giving English and French equal status in the government of Canada. Doing so makes them "official" languages, having preferred status in law over all other languages used in Canada.

Prior to the advent of the Canadian Bill of Rights in 1960 and its successor the Canadian Charter of Rights and Freedoms in 1982, the laws of Canada did not provide much in the way of civil rights and this issue was typically of limited concern to the courts. Canada since the 1960s has placed emphasis on equality and inclusiveness for all people. Multiculturalism in Canada was adopted as the official policy of the Canadian government and is enshrined in Section 27 of the Canadian Charter of Rights and Freedoms. In 1995, the Supreme Court of Canada ruled in Egan v. Canada that sexual orientation should be "read in" to Section Fifteen of the Canadian Charter of Rights and Freedoms, a part of the Constitution of Canada guaranteeing equal rights to all Canadians. Following a series of decisions by provincial courts and the Supreme Court of Canada, on July 20, 2005, the Civil Marriage Act (Bill C-38) became law, legalizing same-sex marriage in Canada. Furthermore, sexual orientation was included as a protected status in the human-rights laws of the federal government and of all provinces and territories.

Contemporary politics
Canadian governments at the federal level have a tradition of liberalism, and govern with a moderate, centrist political ideology. Canada's egalitarian approach to governance emphasizing social justice and multiculturalism, is based on selective immigration, social integration, and suppression of far-right politics that has wide public and political support. Peace, order, and good government are constitutional goals of the Canadian government.

Canada has a multi-party system in which many of its legislative customs derive from the unwritten conventions of and precedents set by the Westminster parliament of the United Kingdom. The country has been dominated by two parties, the centre-left Liberal Party of Canada and the centre-right Conservative Party of Canada. The historically predominant Liberals position themselves at the centre of the political scale, with the Conservatives sitting on the right and the New Democratic Party occupying the left. Smaller parties like the Quebec nationalist Bloc Québécois and the Green Party of Canada have also been able to exert their influence over the political process by representation at the federal level.

Nationalism and protectionism
In general, Canadian nationalists are concerned about the protection of Canadian sovereignty and loyalty to the Canadian State, placing them in the civic nationalist category. It has likewise often been suggested that anti-Americanism plays a prominent role in Canadian nationalist ideologies. A unified, bi-cultural, tolerant and sovereign Canada remains an ideological inspiration to many Canadian nationalists. Alternatively Quebecois nationalism and support for maintaining French Canadian culture many of whom were supporters of the Quebec sovereignty movement during the late-20th century.

Cultural protectionism in Canada has, since the mid-20th century, taken the form of conscious, interventionist attempts on the part of various Canadian governments to promote Canadian cultural production. Sharing a large border, a common language (for the majority), and being exposed to massive diffusions of American media makes it difficult for Canada to preserve its own culture versus being assimilated to American culture. While Canada tries to maintain its cultural differences, it also must balance this with responsibility in trade arrangements such as the General Agreement on Tariffs and Trade (GATT) and the United States–Mexico–Canada Agreement (USMCA).

Foreign relations
The notion of peacekeeping is deeply embedded in Canadian culture and a distinguishing feature that Canadians feel sets their foreign policy apart from its closest ally, the United States. Canada's foreign policy of peacekeeping, peace enforcement, peacemaking, and peacebuilding has been intertwined with its tendency to pursue multilateral and international solutions since the end of World War II.

Canada's central role in the development of peacekeeping in the mid 1950s gave it credibility and established it as a country fighting for the "common good" of all nations. Canada has since been engaged with the United Nations, NATO and the European Union (EU) in promoting its middle power status into an active role in world affairs.

Canada has long been reluctant to participate in military operations that are not sanctioned by the United Nations, such as the Vietnam War or the 2003 Invasion of Iraq. Canada has participated in US-led, UN-sanctioned operations such as the first Gulf War, in Afghanistan and Libya. The country also participates with its NATO allies in UN-sanctioned missions, such as the Kosovo Conflict and in Haiti.

Values
Canadian values are the perceived commonly shared ethical and human values of Canadians. The major political parties have claimed explicitly that they uphold Canadian values, but use generalities to specify them. Historian Ian MacKay argues that, thanks to the long-term political impact of "Rebels, Reds, and Radicals", and allied leftist political elements, "egalitarianism, social equality, and peace... are now often simply referred to...as 'Canadian values.'" Canada ranks among the highest in international measurements of government transparency, civil liberties, quality of life, economic freedom, education, and gender equality.

A 2013 Statistics Canada survey found that an "overwhelming majority" of Canadians shared the values of human rights (with 92% of respondents agreeing that they are a shared Canadian value), respect for the law (92%) and gender equality (91%). Universal access to publicly funded health services "is often considered by Canadians as a fundamental value that ensures national health care insurance for everyone wherever they live in the country." The Canadian Charter of Rights and Freedoms, was intended to be a source for Canadian values and national unity. The 15th Prime Minister Pierre Trudeau wrote in his Memoirs that:"Canada itself could now be defined as a 'society where all people are equal and where they share some fundamental values based upon freedom', and that all Canadians could identify with the values of liberty and equality."

Numerous scholars, beginning in the 1940s with American sociologist Seymour Martin Lipset; have tried to identify, measure and compare them with other countries, especially the United States. However, there are critics who say that such a task is practically impossible.

Denis Stairs a professor of political Science at Dalhousie University; links the concept of Canadian values with nationalism. [Canadians typically]...believe, in particular, that they subscribe to a distinctive set of values - Canadian values - and that those values are special in the sense of being unusually virtuous.

Identity

Canada's large geographic size, the presence of a significant number of indigenous peoples, the conquest of one European linguistic population by another and relatively open immigration policy have led to an extremely diverse society. As a result, the issue of Canadian identity remains under scrutiny.

Canada has constitutional protection for policies that promote multiculturalism rather than cultural assimilation or a single national myth. In Quebec, cultural identity is strong, and many commentators speak of a French Canadian culture as distinguished from English Canadian culture. However, as a whole, Canada is in theory, a cultural mosaic—a collection of several regional, and ethnic subcultures.

As Professor Alan Cairns noted about the  Canadian Charter of Rights and Freedoms , "the initial federal government premise was on developing a pan-Canadian identity"'. Pierre Trudeau himself later wrote in his Memoirs (1993) that "Canada itself" could now be defined as a "society where all people are equal and where they share some fundamental values based upon freedom", and that all Canadians could identify with the values of liberty and equality.

Political philosopher Charles Blattberg suggests that Canada is a "multinational country"; as all Canadians are members of Canada as a civic or political community, a community of citizens, and this is a community that contains many other kinds within it. These include not only communities of ethnic, regional, religious, and civic (the provincial and municipal governments) sorts, but also national communities, which often include or overlap with many of the other kinds.

Journalist and author Richard Gwyn has suggested that "tolerance" has replaced "loyalty" as the touchstone of Canadian identity. Journalist and professor Andrew Cohen wrote in 2007: "The Canadian Identity, as it has come to be known, is as elusive as the Sasquatch and Ogopogo. It has animated—and frustrated—generations of statesmen, historians, writers, artists, philosophers, and the National Film Board ... Canada resists easy definition."

Canada's 15th prime minister Pierre Trudeau in regards to uniformity stated:

"Uniformity is neither desirable nor possible in a country the size of Canada. We should not even be able to agree upon the kind of Canadian to choose as a model, let alone persuade most people to emulate it. There are few policies potentially more disastrous for Canada than to tell all Canadians that they must be alike. There is no such thing as a model or ideal Canadian. What could be more absurd than the concept of an 'all-Canadian' boy or girl? A society which emphasizes uniformity is one which creates intolerance and hate."

In 2015, Prime Minister Justin Trudeau defined the country as the world's first postnational state: "There is no core identity, no mainstream in Canada".

The question of Canadian identity was traditionally dominated by three fundamental themes: first, the often conflicted relations between English Canadians and French Canadians stemming from the French Canadian imperative for cultural and linguistic survival; secondly, the generally close ties between English Canadians and the British Empire, resulting in a gradual political process towards complete independence from the imperial power; and finally, the close proximity of English-speaking Canadians to the United States. Much of the debate over contemporary Canadian identity is argued in political terms, and defines Canada as a country defined by its government policies, which are thought to reflect deeper cultural values.

In 2013, more than 90% of Canadians believed that the Canadian Charter of Rights and Freedoms and the national flag were the top symbols of Canadian identity. Next highest were the national anthem, the Royal Canadian Mounted Police and hockey.

Inter-provincial interactions
Western alienation is the notion that the western provinces have historically been alienated, and in extreme cases excluded, from mainstream Canadian political affairs in favour of Eastern Canada or more specifically the central provinces. Western alienation claims that these latter two are politically represented, and economically favoured, more significantly than the former, which has given rise to the sentiment of alienation among many western Canadians. Likewise; the Quebec sovereignty movement that lead to the Québécois nation and the province of Quebec being recognized as a "distinct society" within Canada, highlights the sharp divisions between the Anglo and Francophone population.

Though more than half of Canadians live in just two provinces (Ontario and Quebec), each province is largely self-contained due to provincial economic self-sufficiency. Only 15 percent of Canadians live in a different province from where they were born, and only 10 percent go to another province for university. Canada has always been like this, and stands in sharp contrast to the United States' internal mobility which is much higher. For example 30 percent live in a different state from where they were born, and 30 percent go away for university. Scott Gilmore in Maclean's argues that "Canada is a nation of strangers", in the sense that for most individuals, the rest of Canada outside their province is little-known. Another factor is the cost of internal travel. Intra-Canadian airfares are high—it is cheaper and more common to visit the United States than to visit another province. Gilmore argues that the mutual isolation makes it difficult to muster national responses to major national issues.

Humour
Canadian humour is an integral part of the Canadian Identity. There are several traditions in Canadian humour in both English and French. While these traditions are distinct and at times very different, there are common themes that relate to Canadians' shared history and geopolitical situation in the Western Hemisphere and the world. Various trends can be noted in Canadian comedy. One trend is the portrayal of a "typical" Canadian family in an ongoing radio or television series. Other trends include outright absurdity, and political and cultural satire. Irony, parody, satire, and self-deprecation are arguably the primary characteristics of Canadian humour.

The beginnings of Canadian national radio comedy date to the late 1930s with the debut of The Happy Gang, a long-running weekly variety show that was regularly sprinkled with corny jokes in between tunes. Canadian television comedy begins with Wayne and Shuster, a sketch comedy duo who performed as a comedy team during the Second World War, and moved their act to radio in 1946 before moving on to television. Second City Television, otherwise known as SCTV, Royal Canadian Air Farce, This Hour Has 22 Minutes, The Kids in the Hall, Trailer Park Boys, Corner gas  and more recently Schitt's Creek are regarded as television shows which were very influential on the development of Canadian humour. Canadian comedians have had great success in the film industry and are amongst the most recognized in the world.

Humber College in Toronto and the École nationale de l'humour in Montreal offer post-secondary programmes in comedy writing and performance. Montreal is also home to the bilingual (English and French) Just for Laughs festival and to the Just for Laughs Museum, a bilingual, international museum of comedy. Canada has a national television channel, The Comedy Network, devoted to comedy. Many Canadian cities feature comedy clubs and showcases, most notable, The Second City branch in Toronto (originally housed at The Old Fire Hall) and the Yuk Yuk's national chain. The Canadian Comedy Awards were founded in 1999 by the Canadian Comedy Foundation for Excellence, a not-for-profit organization.

Symbols
Predominant symbols of Canada include the maple leaf, beaver, and the Canadian horse. Many official symbols of the country such as the Flag of Canada have been changed or modified over the past few decades to Canadianize them and de-emphasise or remove references to the United Kingdom. Other prominent symbols include the sports of hockey and lacrosse, the Canada goose, the Royal Canadian Mounted Police, the Canadian Rockies, and more recently the totem pole and Inuksuk; material items such as Canadian beer, maple syrup, tuques, canoes, nanaimo bars, butter tarts and the Quebec dish of poutine have also been defined as uniquely Canadian. Symbols of the Canadian monarchy continue to be featured in, for example, the Arms of Canada, the armed forces, and the prefix His Majesty's Canadian Ship. The designation Royal remains for institutions as varied as the Royal Canadian Armed Forces, Royal Canadian Mounted Police and the Royal Winnipeg Ballet.

Visual arts
Indigenous artists were producing art in the territory that is now called Canada for thousands of years prior to the arrival of European settler colonists and the eventual establishment of Canada as a nation state. Like the peoples that produced them, indigenous art traditions spanned territories that extended across the current national boundaries between Canada and the United States. The majority of indigenous artworks preserved in museum collections date from the period after European contact and show evidence of the creative adoption and adaptation of European trade goods such as metal and glass beads. Canadian sculpture has been enriched by the walrus ivory, muskox horn and caribou antler and soapstone carvings by the Inuit artists. These carvings show objects and activities from the daily life, myths and legends of the Inuit. Inuit art since the 1950s has been the traditional gift given to foreign dignitaries by the Canadian government.

The works of most early Canadian painters followed European trends. During the mid-19th century, Cornelius Krieghoff, a Dutch-born artist in Quebec, painted scenes of the life of the habitants (French-Canadian farmers). At about the same time, the Canadian artist Paul Kane painted pictures of indigenous life in western Canada. A group of landscape painters called the Group of Seven developed the first distinctly Canadian style of painting, inspired by the works of the legendary landscape painter Tom Thomson. All these artists painted large, brilliantly coloured scenes of the Canadian wilderness.

Since the 1930s, Canadian painters have developed a wide range of highly individual styles. Emily Carr became famous for her paintings of totem poles in British Columbia. Other noted painters have included the landscape artist David Milne, the painters Jean-Paul Riopelle, Harold Town and Charles Carson and multi-media artist Michael Snow. The abstract art group Painters Eleven, particularly the artists William Ronald and Jack Bush, also had an important impact on modern art in Canada. Government support has played a vital role in their development enabling visual exposure through publications and periodicals featuring Canadian art, as has the establishment of numerous art schools and colleges across the country.

Literature
Canadian literature is often divided into French- and English-language literatures, which are rooted in the literary traditions of France and Britain, respectively. Canada's early literature, whether written in English or French, often reflects the Canadian perspective on nature, frontier life, and Canada's position in the world, for example the poetry of Bliss Carman or the memoirs of Susanna Moodie and Catherine Parr Traill. These themes, and Canada's literary history, inform the writing of successive generations of Canadian authors, from Leonard Cohen to Margaret Atwood.

By the mid-20th century, Canadian writers were exploring national themes for Canadian readers. Authors were trying to find a distinctly Canadian voice, rather than merely emulating British or American writers. Canadian identity is closely tied to its literature. The question of national identity recurs as a theme in much of Canada's literature, from Hugh MacLennan's Two Solitudes (1945) to Alistair MacLeod's No Great Mischief (1999). Canadian literature is often categorized by region or province; by the socio-cultural origins of the author (for example, Acadians, indigenous peoples, LGBT, and Irish Canadians); and by literary period, such as "Canadian postmoderns" or "Canadian Poets Between the Wars".

Canadian authors have accumulated numerous international awards. In 1992, Michael Ondaatje became the first Canadian to win the Booker Prize for The English Patient. Margaret Atwood won the Booker in 2000 for The Blind Assassin and Yann Martel won it in 2002 for the Life of Pi. Carol Shields's The Stone Diaries won the Governor General's Awards in Canada in 1993,  the 1995 Pulitzer Prize for Fiction, and the 1994 National Book Critics Circle Award. In 2013, Alice Munro was the first Canadian to be awarded the Nobel Prize in Literature for her work as "master of the modern short story". Munro is also a recipient of the Man Booker International Prize for her lifetime body of work, and three-time winner of Canada's Governor General's Award for fiction.

Theatre
Canada has had a thriving stage theatre scene since the late 1800s. Theatre festivals draw many tourists in the summer months, especially the Stratford Shakespeare Festival in Stratford, Ontario, and the Shaw Festival in Niagara-on-the-Lake, Ontario. The Famous People Players are only one of many touring companies that have also developed an international reputation. Canada also hosts one of the largest fringe festivals, the Edmonton International Fringe Festival.

Canada's largest cities host a variety of modern and historical venues. The Toronto Theatre District is Canada's largest, as well as being the third largest English-speaking theatre district in the world. In addition to original Canadian works, shows from the West End and Broadway frequently tour in Toronto. Toronto's Theatre District includes the venerable Roy Thomson Hall; the Princess of Wales Theatre; the Tim Sims Playhouse; The Second City; the Canon Theatre; the Panasonic Theatre; the Royal Alexandra Theatre; historic Massey Hall; and the city's new opera house, the Sony Centre for the Performing Arts. Toronto's Theatre District also includes the Theatre Museum Canada.

Montreal's theatre district ("Quartier des Spectacles") is the scene of performances that are mainly French-language, although the city also boasts a lively anglophone theatre scene, such as the Centaur Theatre. Large French theatres in the city include Théâtre Saint-Denis and Théâtre du Nouveau Monde.

Vancouver is host to, among others, the Vancouver Fringe Festival, the Arts Club Theatre Company, Carousel Theatre, Bard on the Beach, Theatre Under the Stars and Studio 58.

Calgary is home to Theatre Calgary, a mainstream regional theatre; Alberta Theatre Projects, a major centre for new play development in Canada; the Calgary Animated Objects Society; and One Yellow Rabbit, a touring company.

There are three major theatre venues in Ottawa; the Ottawa Little Theatre, originally called the Ottawa Drama League at its inception in 1913, is the longest-running community theatre company in Ottawa. Since 1969, Ottawa has been the home of the National Arts Centre, a major performing-arts venue that houses four stages and is home to the National Arts Centre Orchestra, the Ottawa Symphony Orchestra and Opera Lyra Ottawa. Established in 1975, the Great Canadian Theatre Company specializes in the production of Canadian plays at a local level.

Television
Canadian television, especially supported by the Canadian Broadcasting Corporation, is the home of a variety of locally produced shows. French-language television, like French Canadian film, is buffered from excessive American influence by the fact of language, and likewise supports a host of home-grown productions. The success of French-language domestic television in Canada often exceeds that of its English-language counterpart. In recent years nationalism has been used to prompt products on television. The I Am Canadian campaign by Molson beer, most notably the commercial featuring Joe Canadian, infused domestically brewed beer and nationalism.

Canada's television industry is in full expansion as a site for Hollywood productions. Since the 1980s, Canada, and Vancouver in particular, has become known as Hollywood North. The American TV series Queer as Folk was filmed in Toronto. Canadian producers have been very successful in the field of science fiction since the mid-1990s, with such shows as The X-Files, Stargate SG-1, Highlander: The Series, the new Battlestar Galactica, My Babysitter's a Vampire, Smallville, and The Outer Limits all filmed in Vancouver.

The CRTC's Canadian content regulations dictate that a certain percentage of a domestic broadcaster's transmission time must include content that is produced by Canadians, or covers Canadian subjects. These regulations also apply to US cable television channels such as MTV and the Discovery Channel, which have local versions of their channels available on Canadian cable networks. Similarly, BBC Canada, while showing primarily BBC shows from the United Kingdom, also carries Canadian output.

Film
A number of Canadian pioneers in early Hollywood significantly contributed to the creation of the motion picture industry in the early days of the 20th century. Over the years, many Canadians have made enormous contributions to the American entertainment industry, although they are frequently not recognized as Canadians.

Canada has developed a vigorous film industry that has produced a variety of well-known films and actors. In fact, this eclipsing may sometimes be creditable for the bizarre and innovative directions of some works, such as auteurs Atom Egoyan (The Sweet Hereafter, 1997) and David Cronenberg (The Fly, Naked Lunch, A History of Violence) and the avant-garde work of Michael Snow and Jack Chambers. Also, the distinct French-Canadian society permits the work of directors such as Denys Arcand and Denis Villeneuve, while First Nations cinema includes the likes of Atanarjuat: The Fast Runner. At the 76th Academy Awards, Arcand's The Barbarian Invasions became Canada's first film to win the Academy Award for Best Foreign Language Film.

The National Film Board of Canada is a public agency that produces and distributes films and other audiovisual works which reflect Canada to Canadians and the rest of the world'. Canada has produced many popular documentaries such as The Corporation, Nanook of the North, Final Offer, and Canada: A People's History. The Toronto International Film Festival (TIFF) is considered by many to be one of the most prevalent film festivals for Western cinema. It is the première film festival in North America from which the Oscars race begins.

Music
The music of Canada has reflected the multi-cultural influences that have shaped the country. Indigenous, the French, and the British have all made historical contributions to the musical heritage of Canada. The country has produced its own composers, musicians and ensembles since the mid-1600s. From the 17th century onward, Canada has developed a music infrastructure that includes church halls; chamber halls; conservatories; academies; performing arts centres; record companies; radio stations, and television music-video channels. The music has subsequently been heavily influenced by American culture because of its proximity and migration between the two countries. Canadian rock has had a considerable impact on the development of modern popular music and the development of the most popular subgenres.

Patriotic music in Canada dates back over 200 years as a distinct category from British patriotism, preceding the first legal steps to independence by over 50 years. The earliest known song, "The Bold Canadian", was written in 1812. The national anthem of Canada, "O Canada" adopted in 1980, was originally commissioned by the Lieutenant Governor of Quebec, the Honourable Théodore Robitaille, for the 1880 Saint-Jean-Baptiste Day ceremony. Calixa Lavallée wrote the music, which was a setting of a patriotic poem composed by the poet and judge Sir Adolphe-Basile Routhier. The text was originally only in French, before English lyrics were written in 1906.

Music broadcasting in the country is regulated by the Canadian Radio-television and Telecommunications Commission (CRTC). The Canadian Academy of Recording Arts and Sciences presents Canada's music industry awards, the Juno Awards, which were first awarded in a ceremony during the summer of 1970.

Media
Canada's media is highly autonomous, uncensored, diverse, and very regionalized. The Broadcasting Act declares "the system should serve to safeguard, enrich, and strengthen the cultural, political, social, and economic fabric of Canada". Canada has a well-developed media sector, but its cultural output—particularly in English films, television shows, and magazines—is often overshadowed by imports from the United States. As a result, the preservation of a distinctly Canadian culture is supported by federal government programs, laws, and institutions such as the Canadian Broadcasting Corporation (CBC), the National Film Board of Canada (NFB), and the Canadian Radio-television and Telecommunications Commission (CRTC).

Canadian mass media, both print and digital, and in both official languages, is largely dominated by a "handful of corporations". The largest of these corporations is the country's national public broadcaster, the Canadian Broadcasting Corporation, which also plays a significant role in producing domestic cultural content, operating its own radio and TV networks in both English and French. In addition to the CBC, some provincial governments offer their own public educational TV broadcast services as well, such as TVOntario and Télé-Québec.

Non-news media content in Canada, including film and television, is influenced both by local creators as well as by imports from the United States, the United Kingdom, Australia, and France. In an effort to reduce the amount of foreign-made media, government interventions in television broadcasting can include both regulation of content and public financing. Canadian tax laws limit foreign competition in magazine advertising.

Sports
Sports in Canada consists of a variety of games. Although there are many contests that Canadians value, the most common are ice hockey, box lacrosse, Canadian football, basketball, soccer, curling, baseball and ringette. All but curling and soccer are considered domestic sports as they were either invented by Canadians or trace their roots to Canada.

Ice hockey, referred to as simply "hockey", is Canada's most prevalent winter sport, its most popular spectator sport, and its most successful sport in international competition. It is Canada's official national winter sport. Lacrosse, a sport with indigenous origins, is Canada's oldest and official summer sport. Canadian football is Canada's second most popular spectator sport, and the Canadian Football League's annual championship, the Grey Cup, is the country's largest annual sports event.

While other sports have a larger spectator base, association football, known in Canada as soccer in both English and French, has the most registered players of any team sport in Canada, and is the most played sport with all demographics, including ethnic origin, ages and genders. Professional teams exist in many cities in Canada – with a trio of teams in North America's top pro league, Major League Soccer – and international soccer competitions such as the FIFA World Cup, UEFA Euro and the UEFA Champions League attract some of the biggest audiences in Canada. Other popular team sports include curling, street hockey, cricket, rugby league, rugby union, softball and Ultimate frisbee. Popular individual sports include auto racing, boxing, karate, kickboxing, hunting, sport shooting, fishing, cycling, golf, hiking, horse racing, ice skating, skiing, snowboarding, swimming, triathlon, disc golf, water sports, and several forms of wrestling.

As a country with a generally cool climate, Canada has enjoyed greater success at the Winter Olympics than at the Summer Olympics, although significant regional variations in climate allow for a wide variety of both team and individual sports. Great achievements in Canadian sports are recognized by Canada's Sports Hall of Fame, while the Lou Marsh Trophy is awarded annually to Canada's top athlete by a panel of journalists. There are numerous other Sports Halls of Fame in Canada.

Cuisine
Canadian cuisine varies widely depending on the region. The former Canadian prime minister Joe Clark has been paraphrased to have noted: "Canada has a cuisine of cuisines. Not a stew pot, but a smorgasbord." While there are considerable overlaps between Canadian food and the rest of the cuisine in North America, many unique dishes (or versions of certain dishes) are found and available only in the country. Common contenders for the Canadian national food include poutine   and butter tarts. Other popular Canadian made foods include indigenous fried bread  bannock, French tourtière, Kraft Dinner, ketchup chips,  date squares, nanaimo bars, back bacon, the caesar cocktail and many many more. The Canadian province of Quebec is the birthplace and world's largest producer of maple syrup, The Montreal-style bagel and Montreal-style smoked meat are both food items originally developed by Jewish communities living in Quebec

The three earliest cuisines of Canada have First Nations, English, and French roots. The indigenous population of Canada often have their own traditional cuisine. The cuisines of English Canada are closely related to British and American cuisine. Finally, the traditional cuisines of French Canada have evolved from 16th-century French cuisine because of the tough conditions of colonial life and the winter provisions of Coureur des bois. With subsequent waves of immigration in the 18th and 19th century from Central, Southern, and Eastern Europe, and then from Asia, Africa and Caribbean, the regional cuisines were subsequently affected.

Public opinion data on culture
A 2022 web survey by the Association for Canadian Studies found that an absolute majority of respondents in all provinces except Alberta disagreed with the statement that "there is only one Canadian culture". Most respondents didn't choose what music to listen to based on whether or not the artist was Canadian. While half of Quebeckers and more than one third of respondents in the rest of Canada agreed that "I worry about preserving my culture" at the same time 60% of respondents agreed that "If a Canadian artist is good enough, they will become discovered without the need for specific Canadian content rules". Forty-six percent of respondents had no favourite Canadian musical artist. Rock, pop, and country music were the most popular genres of music, with above twenty percent fan bases in all age categories, but with hip-hop also appealing to more than twenty percent in the youngest cohort (18–35 years old). Film genre preferences were largely as the same across age categories, with comedies and action films the most popular, except that only one percent of older people (>55 years old) were fans of animated movies compared to eleven percent in young adults, while older adults showed a strong preference for dramas compared to younger people. Three out of four respondents could not name a single Canadian visual artist, living or dead.

Outside views
In a 2002 interview with the Globe and Mail, Aga Khan, the 49th Imam of the Ismaili Muslims, described Canada as "the most successful pluralist society on the face of our globe", citing it as "a model for the world". A 2007 poll ranked Canada as the country with the most positive influence in the world. 28,000 people in 27 countries were asked to rate 12 countries as either having a positive or negative worldwide influence. Canada's overall influence rating topped the list with 54 per cent of respondents rating it mostly positive and only 14 per cent mostly negative. A global opinion poll for the BBC saw Canada ranked the second most positively viewed nation in the world (behind Germany) in 2013 and 2014.

The United States is home to a number of perceptions about Canadian culture, due to the countries' partially shared heritage and the relatively large number of cultural features common to both the US and Canada. For example, the average Canadian may be perceived as more reserved than his or her American counterpart. Canada and the United States are often inevitably compared as sibling countries, and the perceptions that arise from this oft-held contrast have gone to shape the advertised worldwide identities of both nations: the United States is seen as the rebellious child of the British Crown, forged in the fires of violent revolution; Canada is the calmer offspring of the United Kingdom, known for a more relaxed national demeanour.

title: Culture of Canada


text:
List of companies of Canada

Canada is a country in the northern part of North America. Canada is the world's eighth-largest economy, with a nominal GDP of approximately US$2.2 trillion. It is a member of the Organisation for Economic Co-operation and Development (OECD) and the Group of Seven (G7), and is one of the world's top ten trading nations, with a highly globalized economy. Canada is a mixed economy, ranking above the US and most western European nations on The Heritage Foundation's index of economic freedom, and experiencing a relatively low level of income disparity. The country's average household disposable income per capita is over US$23,900, higher than the OECD average. Furthermore, the Toronto Stock Exchange is the seventh-largest stock exchange in the world by market capitalization, listing over 1,500 companies with a combined market capitalization of over US$2 trillion.

For further information on the types of business entities in this country and their abbreviations, see "Business entities in Canada".

Largest firms
This list shows firms in the Fortune Global 500, which ranks firms by total revenues reported before March 31, 2022. Only the top five firms (if available) are included as a sample.

Notable firms
This list includes notable companies with primary headquarters located in the country. The industry and sector follow the Industry Classification Benchmark taxonomy. Organizations which have ceased operations are included and noted as defunct.

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

title: List of companies of Canada


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Cauchy distribution

The Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as the Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution. The Cauchy distribution $$f(x; x_0,\gamma)$$ is the distribution of the $x$-intercept of a ray issuing from $$(x_0,\gamma)$$ with a uniformly distributed angle. It is also the distribution of the ratio of two independent normally distributed random variables with mean zero.

The Cauchy distribution is often used in statistics as the canonical example of a "pathological" distribution since both its expected value and its variance are undefined (but see below). The Cauchy distribution does not have finite moments of order greater than or equal to one; only fractional absolute moments exist. The Cauchy distribution has no moment generating function.

In mathematics, it is closely related to the Poisson kernel, which is the fundamental solution for the Laplace equation in the upper half-plane.

It is one of the few stable distributions with a probability density function that can be expressed analytically, the others being the normal distribution and the Lévy distribution.

History
A function with the form of the density function of the Cauchy distribution was studied geometrically by Fermat in 1659, and later was known as the witch of Agnesi, after Agnesi included it as an example in her 1748 calculus textbook. Despite its name, the first explicit analysis of the properties of the Cauchy distribution was published by the French mathematician Poisson in 1824, with Cauchy only becoming associated with it during an academic controversy in 1853. Poisson noted that if the mean of observations following such a distribution were taken, the mean error did not converge to any finite number. As such, Laplace's use of the central limit theorem with such a distribution was inappropriate, as it assumed a finite mean and variance. Despite this, Poisson did not regard the issue as important, in contrast to Bienaymé, who was to engage Cauchy in a long dispute over the matter.

Constructions
Here are the most important constructions.

Rotational symmetry
If one stands in front of a line and kicks a ball with a direction (more precisely, an angle) uniformly at random towards the line, then the distribution of the point where the ball hits the line is a Cauchy distribution.

More formally, consider a point at $$(x_0, \gamma)$$ in the x-y plane, and select a line passing the point, with its direction (angle with the $$x$$-axis) chosen uniformly (between -90° and +90°) at random. The intersection of the line with the x-axis is the Cauchy distribution with location $$x_0$$ and scale $$\gamma$$.

This definition gives a simple way to sample from the standard Cauchy distribution. Let $$ u $$ be a sample from a uniform distribution from $$[0,1]$$, then we can generate a sample, $$x$$ from the standard Cauchy distribution using

 * $$ x = \tan\left(\pi(u-\frac{1}{2})\right) $$

When $$U$$ and $$V$$ are two independent normally distributed random variables with expected value 0 and variance 1, then the ratio $$U/V$$ has the standard Cauchy distribution.

More generally, if $$(U, V)$$ is a rotationally symmetric distribution on the plane, then the ratio $$U/V$$ has the standard Cauchy distribution.

Probability density function (PDF)
The Cauchy distribution is the probability distribution with the following probability density function (PDF)
 * $$f(x; x_0,\gamma) = \frac{1}{\pi\gamma \left[1 + \left(\frac{x - x_0}{\gamma}\right)^2\right]} = { 1 \over \pi } \left[ { \gamma \over (x - x_0)^2 + \gamma^2 } \right], $$

where $$x_0$$ is the location parameter, specifying the location of the peak of the distribution, and $$\gamma$$ is the scale parameter which specifies the half-width at half-maximum (HWHM), alternatively $$2\gamma$$ is full width at half maximum (FWHM). $$\gamma$$ is also equal to half the interquartile range and is sometimes called the probable error. Augustin-Louis Cauchy exploited such a density function in 1827 with an infinitesimal scale parameter, defining what would now be called a Dirac delta function.

Properties of PDF
The maximum value or amplitude of the Cauchy PDF is $$\frac{1}{\pi \gamma}$$, located at $$x=x_0$$.

It is sometimes convenient to express the PDF in terms of the complex parameter $$\psi= x_0 + i\gamma$$

f(x;\psi)=\frac{1}{\pi}\,\textrm{Im}\left(\frac{1}{x-\psi}\right)=\frac{1}{\pi}\,\textrm{Re}\left(\frac{-i}{x-\psi}\right) $$

The special case when $$x_0 = 0$$ and $$\gamma = 1$$ is called the standard Cauchy distribution with the probability density function
 * $$ f(x; 0,1) = \frac{1}{\pi (1 + x^2)}. \!$$

In physics, a three-parameter Lorentzian function is often used:
 * $$f(x; x_0,\gamma,I) = \frac{I}{\left[1 + \left(\frac{x-x_0}{\gamma}\right)^2\right]} = I \left[ { \gamma^2 \over (x - x_0)^2 + \gamma^2 } \right], $$

where $$I$$ is the height of the peak. The three-parameter Lorentzian function indicated is not, in general, a probability density function, since it does not integrate to 1, except in the special case where $$I = \frac{1}{\pi\gamma}.\!$$

Cumulative distribution function (CDF)
The Cauchy distribution is the probability distribution with the following cumulative distribution function (CDF):
 * $$F(x; x_0,\gamma)=\frac{1}{\pi} \arctan\left(\frac{x-x_0}{\gamma}\right)+\frac{1}{2}$$

and the quantile function (inverse cdf) of the Cauchy distribution is
 * $$Q(p; x_0,\gamma) = x_0 + \gamma\,\tan\left[\pi\left(p-\tfrac{1}{2}\right)\right].$$

It follows that the first and third quartiles are $$(x_0 - \gamma, x_0 + \gamma)$$, and hence the interquartile range is $$2\gamma$$.

For the standard distribution, the cumulative distribution function simplifies to arctangent function $$\arctan(x)$$:
 * $$F(x; 0,1)=\frac{1}{\pi} \arctan\left(x\right)+\frac{1}{2}$$

Other constructions
The standard Cauchy distribution is the Student's t-distribution with one degree of freedom, and so it may be constructed by any method that constructs the Student's t-distribution.

If $$\Sigma$$ is a $$p\times p$$ positive-semidefinite covariance matrix with strictly positive diagonal entries, then for independent and identically distributed $$X,Y\sim N(0,\Sigma)$$ and any random $$p$$-vector $$w$$ independent of $$X$$ and $$Y$$ such that $$w_1+\cdots+w_p=1$$ and $$w_i\geq 0, i=1,\ldots,p,$$ (defining a categorical distribution) it holds that
 * $$\sum_{j=1}^p w_j\frac{X_j}{Y_j}\sim\mathrm{Cauchy}(0,1).$$

Properties
The Cauchy distribution is an example of a distribution which has no mean, variance or higher moments defined. Its mode and median are well defined and are both equal to $$x_0$$.

The Cauchy distribution is an infinitely divisible probability distribution. It is also a strictly stable distribution.

Like all stable distributions, the location-scale family to which the Cauchy distribution belongs is closed under linear transformations with real coefficients. In addition, the Cauchy distribution is closed under linear fractional transformations with real coefficients. In this connection, see also McCullagh's parametrization of the Cauchy distributions.

Sum of Cauchy distributions
If $$X_1, X_2, ..., X_n$$ are IID samples from the standard Cauchy distribution, then their sample mean $$\bar X = \frac 1n \sum_i X_i$$ is also standard Cauchy distributed. In particular, the average does not converge to the mean, and so the standard Cauchy distribution does not follow the law of large numbers.

This can be proved by repeated integration with the PDF, or more conveniently, by using the characteristic function of the standard Cauchy distribution (see below):$$\varphi_X(t) = \operatorname{E}\left[e^{iXt} \right ] = e^{- |t|}.$$With this, we have $$\varphi_{\sum_i X_i}(t) = e^{-n |t|} $$, and so $$\bar X$$ has a standard Cauchy distribution.

More generally, if $$X_1, X_2, ..., X_n$$ are independent and Cauchy distributed with location parameters $$x_1, ..., x_n$$ and scales $$\gamma_1, ..., \gamma_n$$, and $$a_1, ..., a_n$$ are real numbers, then $$\sum_i a_iX_i$$ is Cauchy distributed with location $$\sum_i a_ix_i$$ and scale$$\sum_i |a_i|\gamma_i$$. We see that there is no law of large numbers for any weighted sum of independent Cauchy distributions.

This shows that the condition of finite variance in the central limit theorem cannot be dropped. It is also an example of a more generalized version of the central limit theorem that is characteristic of all stable distributions, of which the Cauchy distribution is a special case.

Central limit theorem
If $$X_1, X_2, ...$$ are IID samples with PDF $$\rho$$ such that $$\lim_{c \to \infty}\frac{1}{c} \int_{-c}^c x^2\rho(x) dx = \frac{2\gamma}{\pi} $$ is finite, but nonzero, then $$\frac 1n \sum_{i=1}^n X_i$$ converges in distribution to a Cauchy distribution with scale $$\gamma$$.

Characteristic function
Let $$X$$ denote a Cauchy distributed random variable. The characteristic function of the Cauchy distribution is given by

 * $$\varphi_X(t) = \operatorname{E}\left[e^{iXt} \right ] =\int_{-\infty}^\infty f(x;x_0,\gamma)e^{ixt}\,dx = e^{ix_0t - \gamma |t|}.$$

which is just the Fourier transform of the probability density. The original probability density may be expressed in terms of the characteristic function, essentially by using the inverse Fourier transform:

 * $$f(x; x_0,\gamma) = \frac{1}{2\pi}\int_{-\infty}^\infty \varphi_X(t;x_0,\gamma)e^{-ixt} \, dt \!$$

The nth moment of a distribution is the nth derivative of the characteristic function evaluated at $$t=0$$. Observe that the characteristic function is not differentiable at the origin: this corresponds to the fact that the Cauchy distribution does not have well-defined moments higher than the zeroth moment.

Kullback-Leibler divergence
The Kullback–Leibler divergence between two Cauchy distributions has the following symmetric closed-form formula:

\mathrm{KL}\left(p_{x_{0,1}, \gamma_{1}}: p_{x_{0,2}, \gamma_{2}}\right)=\log \frac{\left(\gamma_{1}+\gamma_{2}\right)^{2}+\left(x_{0,1}-x_{0,2}\right)^{2}}{4 \gamma_{1} \gamma_{2}}. $$

Any f-divergence between two Cauchy distributions is symmetric and can be expressed as a function of the chi-squared divergence. Closed-form expression for the total variation, Jensen–Shannon divergence, Hellinger distance, etc are available.

Entropy
The entropy of the Cauchy distribution is given by:

\begin{align} H(\gamma) & =-\int_{-\infty}^\infty f(x;x_0,\gamma) \log(f(x;x_0,\gamma)) \, dx \\[6pt] & =\log(4\pi\gamma) \end{align} $$

The derivative of the quantile function, the quantile density function, for the Cauchy distribution is:

 * $$Q'(p; \gamma) = \gamma\,\pi\,{\sec}^2\left[\pi\left(p-\tfrac 1 2 \right)\right].\!$$

The differential entropy of a distribution can be defined in terms of its quantile density, specifically:

 * $$H(\gamma) = \int_0^1 \log\,(Q'(p; \gamma))\,\mathrm dp = \log(4\pi\gamma)$$

The Cauchy distribution is the maximum entropy probability distribution for a random variate $$X$$ for which

 * $$\operatorname{E}[\log(1+(X-x_0)^2/\gamma^2)]=\log 4$$

Moments
The Cauchy distribution is usually used as an illustrative counterexample in elementary probability courses, as a distribution with no well-defined (or "indefinite") moments.

Sample moments
If we take IID samples $$X_1, X_2, ..$$ from the standard Cauchy distribution, then the sequence of their sample mean is $$S_n = \frac 1n \sum_{i=1}^n X_i$$, which also has the standard Cauchy distribution. Consequently, no matter how many terms we take, the sample average does not converge.

Similarly, the sample variance $$V_n = \frac 1n \sum_{i=1}^n (X_i - S_n)^2$$ also does not converge. A typical trajectory of $$S_1, S_2, ...$$ looks like long periods of slow convergence to zero, punctuated by large jumps away from zero, but never getting too far away. A typical trajectory of $$V_1, V_2, ...$$ looks similar, but the jumps accumulate faster than the decay, diverging to infinity. These two kinds of trajectories are plotted in the figure.

Moments of sample lower than order 1 would converge to zero. Moments of sample higher than order 2 would diverge to infinity even faster than sample variance.

Mean
If a probability distribution has a density function $$f(x)$$, then the mean, if it exists, is given by

We may evaluate this two-sided improper integral by computing the sum of two one-sided improper integrals. That is,

for an arbitrary real number $$a$$.

For the integral to exist (even as an infinite value), at least one of the terms in this sum should be finite, or both should be infinite and have the same sign. But in the case of the Cauchy distribution, both the terms in this sum ($$) are infinite and have opposite sign. Hence ($$) is undefined, and thus so is the mean. When the mean of a probability distribution function (PDF) is undefined, no one can compute a reliable average over the experimental data points, regardless of the sample’s size.

Note that the Cauchy principal value of the mean of the Cauchy distribution is $$\lim_{a\to\infty}\int_{-a}^a x f(x)\,dx $$ which is zero. On the other hand, the related integral $$\lim_{a\to\infty}\int_{-2a}^a x f(x)\,dx $$ is not zero, as can be seen by computing the integral. This again shows that the mean ($$) cannot exist.

Various results in probability theory about expected values, such as the strong law of large numbers, fail to hold for the Cauchy distribution.

Smaller moments
The absolute moments for $$p\in(-1,1)$$ are defined. For $$X\sim\mathrm{Cauchy}(0,\gamma)$$ we have
 * $$\operatorname{E}[|X|^p] = \gamma^p \mathrm{sec}(\pi p/2).$$

Higher moments
The Cauchy distribution does not have finite moments of any order. Some of the higher raw moments do exist and have a value of infinity, for example, the raw second moment:

\begin{align} \operatorname{E}[X^2] & \propto \int_{-\infty}^\infty \frac{x^2}{1+x^2}\,dx = \int_{-\infty}^\infty 1 - \frac{1}{1+x^2}\,dx \\[8pt] & = \int_{-\infty}^\infty dx - \int_{-\infty}^\infty \frac{1}{1+x^2}\,dx = \int_{-\infty}^\infty dx-\pi = \infty. \end{align} $$

By re-arranging the formula, one can see that the second moment is essentially the infinite integral of a constant (here 1). Higher even-powered raw moments will also evaluate to infinity. Odd-powered raw moments, however, are undefined, which is distinctly different from existing with the value of infinity. The odd-powered raw moments are undefined because their values are essentially equivalent to $$\infty - \infty$$ since the two halves of the integral both diverge and have opposite signs. The first raw moment is the mean, which, being odd, does not exist. (See also the discussion above about this.) This in turn means that all of the central moments and standardized moments are undefined since they are all based on the mean. The variance—which is the second central moment—is likewise non-existent (despite the fact that the raw second moment exists with the value infinity).

The results for higher moments follow from Hölder's inequality, which implies that higher moments (or halves of moments) diverge if lower ones do.

Moments of truncated distributions
Consider the truncated distribution defined by restricting the standard Cauchy distribution to the interval $[−10^{100}, 10^{100}]$. Such a truncated distribution has all moments (and the central limit theorem applies for i.i.d. observations from it); yet for almost all practical purposes it behaves like a Cauchy distribution.

Estimation of parameters
Because the parameters of the Cauchy distribution do not correspond to a mean and variance, attempting to estimate the parameters of the Cauchy distribution by using a sample mean and a sample variance will not succeed. For example, if an i.i.d. sample of size n is taken from a Cauchy distribution, one may calculate the sample mean as:

 * $$\bar{x}=\frac 1 n \sum_{i=1}^n x_i$$

Although the sample values $$x_i$$ will be concentrated about the central value $$x_0$$, the sample mean will become increasingly variable as more observations are taken, because of the increased probability of encountering sample points with a large absolute value. In fact, the distribution of the sample mean will be equal to the distribution of the observations themselves; i.e., the sample mean of a large sample is no better (or worse) an estimator of $$x_0$$ than any single observation from the sample. Similarly, calculating the sample variance will result in values that grow larger as more observations are taken.

Therefore, more robust means of estimating the central value $$x_0$$ and the scaling parameter $$\gamma$$ are needed. One simple method is to take the median value of the sample as an estimator of $$x_0$$ and half the sample interquartile range as an estimator of $$\gamma$$. Other, more precise and robust methods have been developed  For example, the truncated mean of the middle 24% of the sample order statistics produces an estimate for $$x_0$$ that is more efficient than using either the sample median or the full sample mean. However, because of the fat tails of the Cauchy distribution, the efficiency of the estimator decreases if more than 24% of the sample is used.

Maximum likelihood can also be used to estimate the parameters $$x_0$$ and $$\gamma$$. However, this tends to be complicated by the fact that this requires finding the roots of a high degree polynomial, and there can be multiple roots that represent local maxima. Also, while the maximum likelihood estimator is asymptotically efficient, it is relatively inefficient for small samples. The log-likelihood function for the Cauchy distribution for sample size $$n$$ is:

 * $$\hat\ell(x_1,\dotsc,x_n \mid \!x_0,\gamma ) = - n \log (\gamma \pi) - \sum_{i=1}^n \log \left(1 + \left(\frac{x_i - x_0}{\gamma}\right)^2\right)$$

Maximizing the log likelihood function with respect to $$x_0$$ and $$\gamma$$ by taking the first derivative produces the following system of equations:

 * $$ \frac{d \ell}{d x_{0}} = \sum_{i=1}^n \frac{2(x_i - x_0)}{\gamma^2 + \left(x_i - \!x_0\right)^2} =0$$
 * $$ \frac{d \ell}{d \gamma} = \sum_{i=1}^n \frac{2\left(x_i - x_0\right)^2}{\gamma (\gamma^2 + \left(x_i - x_0\right)^2)} - \frac{n}{\gamma} = 0$$

Note that

 * $$ \sum_{i=1}^n \frac{\left(x_i - x_0\right)^2}{\gamma^2 + \left(x_i - x_0\right)^2} $$

is a monotone function in $$\gamma$$ and that the solution $$\gamma$$ must satisfy

 * $$ \min |x_i-x_0|\le \gamma\le \max |x_i-x_0|. $$

Solving just for $$x_0$$ requires solving a polynomial of degree $$2n-1$$, and solving just for $$\,\!\gamma$$ requires solving a polynomial of degree $$2n$$. Therefore, whether solving for one parameter or for both parameters simultaneously, a numerical solution on a computer is typically required. The benefit of maximum likelihood estimation is asymptotic efficiency; estimating $$x_0$$ using the sample median is only about 81% as asymptotically efficient as estimating $$x_0$$ by maximum likelihood. The truncated sample mean using the middle 24% order statistics is about 88% as asymptotically efficient an estimator of $$x_0$$ as the maximum likelihood estimate. When Newton's method is used to find the solution for the maximum likelihood estimate, the middle 24% order statistics can be used as an initial solution for $$x_0$$.

The shape can be estimated using the median of absolute values, since for location 0 Cauchy variables $$X\sim\mathrm{Cauchy}(0,\gamma)$$, the $$\mathrm{median}(|X|) = \gamma$$ the shape parameter.

Multivariate Cauchy distribution
A random vector $$X=(X_1, \ldots, X_k)^T$$ is said to have the multivariate Cauchy distribution if every linear combination of its components $$Y=a_1X_1+ \cdots + a_kX_k$$ has a Cauchy distribution. That is, for any constant vector $$a\in \mathbb R^k$$, the random variable $$Y=a^TX$$ should have a univariate Cauchy distribution. The characteristic function of a multivariate Cauchy distribution is given by:

 * $$\varphi_X(t) = e^{ix_0(t)-\gamma(t)}, \!$$

where $$x_0(t)$$ and $$\gamma(t)$$ are real functions with $$x_0(t)$$ a homogeneous function of degree one and $$\gamma(t)$$ a positive homogeneous function of degree one. More formally:

 * $$x_0(at) = ax_0(t),$$
 * $$\gamma (at) = |a|\gamma (t),$$

for all $$t$$.

An example of a bivariate Cauchy distribution can be given by:
 * $$f(x, y; x_0,y_0,\gamma)= { 1 \over 2 \pi } \left[ { \gamma \over ((x - x_0)^2 + (y - y_0)^2 +\gamma^2)^{3/2} } \right] .$$

Note that in this example, even though the covariance between $$x$$ and $$y$$ is 0, $$x$$ and $$y$$ are not statistically independent.

We also can write this formula for complex variable. Then the probability density function of complex cauchy is :

 * $$f(z; z_0,\gamma)= { 1 \over 2 \pi } \left[ { \gamma \over (|z-z_0|^2 +\gamma^2)^{3/2} } \right] .$$

Like how the standard Cauchy distribution is the Student t-distribution with one degree of freedom, the multidimensional Cauchy density is the multivariate Student distribution with one degree of freedom. The density of a $$k$$ dimension Student distribution with one degree of freedom is:

 * $$f({\mathbf x}; {\mathbf\mu},{\mathbf\Sigma}, k)= \frac{\Gamma\left(\frac{1+k}{2}\right)}{\Gamma(\frac{1}{2})\pi^{\frac{k}{2}}\left|{\mathbf\Sigma}\right|^{\frac{1}{2}}\left[1+({\mathbf x}-{\mathbf\mu})^T{\mathbf\Sigma}^{-1}({\mathbf x}-{\mathbf\mu})\right]^{\frac{1+k}{2}}} .$$

The properties of multidimensional Cauchy distribution are then special cases of the multivariate Student distribution.

Transformation properties

 * If $$X \sim \operatorname{Cauchy}(x_0,\gamma)$$ then $$ kX + \ell \sim \textrm{Cauchy}(x_0 k+\ell, \gamma |k|)$$
 * If $$X \sim \operatorname{Cauchy}(x_0, \gamma_0)$$ and $$Y \sim \operatorname{Cauchy}(x_1,\gamma_1)$$ are independent, then $$ X+Y \sim \operatorname{Cauchy}(x_0+x_1,\gamma_0 +\gamma_1)$$ and $$ X-Y \sim \operatorname{Cauchy}(x_0-x_1, \gamma_0+\gamma_1)$$
 * If $$X \sim \operatorname{Cauchy}(0,\gamma)$$ then $$ \tfrac{1}{X} \sim \operatorname{Cauchy}(0, \tfrac{1}{\gamma})$$
 * McCullagh's parametrization of the Cauchy distributions: Expressing a Cauchy distribution in terms of one complex parameter $$\psi = x_0+i\gamma$$, define $$X \sim \operatorname{Cauchy}(\psi)$$ to mean $$X \sim \operatorname{Cauchy}(x_0,|\gamma|)$$. If $$X \sim \operatorname{Cauchy}(\psi)$$ then: $$\frac{aX+b}{cX+d} \sim \operatorname{Cauchy}\left(\frac{a\psi+b}{c\psi+d}\right)$$ where $$a$$, $$b$$, $$c$$ and $$d$$ are real numbers.
 * Using the same convention as above, if $$X \sim \operatorname{Cauchy}(\psi)$$ then: $$\frac{X-i}{X+i} \sim \operatorname{CCauchy}\left(\frac{\psi-i}{\psi+i}\right)$$where $$\operatorname{CCauchy}$$ is the circular Cauchy distribution.

Lévy measure
The Cauchy distribution is the stable distribution of index 1. The Lévy–Khintchine representation of such a stable distribution of parameter $$ \gamma $$ is given, for $$ X \sim \operatorname{Stable}(\gamma, 0, 0)\,$$ by:

 * $$\operatorname{E}\left( e^{ixX} \right) = \exp\left( \int_{ \mathbb{R} } (e^{ixy} - 1) \Pi_\gamma(dy) \right)$$

where

 * $$\Pi_\gamma(dy) = \left( c_{1, \gamma} \frac{1}{y^{1 + \gamma}} 1_{ \left\{y > 0\right\} } + c_{2,\gamma}  \frac{1}{|y|^{1 + \gamma}} 1_{\left\{ y < 0 \right\}} \right) \, dy

$$

and $$ c_{1, \gamma}, c_{2, \gamma} $$ can be expressed explicitly. In the case $$ \gamma = 1 $$ of the Cauchy distribution, one has $$ c_{1, \gamma} = c_{2, \gamma} $$.

This last representation is a consequence of the formula

 * $$\pi |x| = \operatorname{PV }\int_{\mathbb{R} \setminus\lbrace 0 \rbrace} (1 - e^{ixy}) \, \frac{dy}{y^2} $$

Related distributions

 * $$\operatorname{Cauchy}(0,1) \sim \textrm{t}(\mathrm{df}=1)\,$$ Student's t distribution
 * $$\operatorname{Cauchy}(\mu,\sigma) \sim \textrm{t}_{(\mathrm{df}=1)}(\mu,\sigma)\,$$ non-standardized Student's t distribution
 * If $$X, Y \sim \textrm{N}(0,1)\, X, Y$$ independent, then $$ \tfrac X Y\sim \textrm{Cauchy}(0,1)\,$$
 * If $$X \sim \textrm{U}(0,1)\,$$ then $$ \tan \left( \pi \left(X-\tfrac{1}{2}\right) \right) \sim \textrm{Cauchy}(0,1)\,$$
 * If $$X \sim \operatorname{Log-Cauchy}(0, 1)$$ then $$\ln(X) \sim \textrm{Cauchy}(0, 1)$$
 * If $$X \sim \operatorname{Cauchy}(x_0,\gamma)$$ then $$\tfrac1X \sim \operatorname{Cauchy}\left(\tfrac{x_0}{x_0^2+\gamma^2},\tfrac{\gamma}{x_0^2+\gamma^2}\right)$$
 * The Cauchy distribution is a limiting case of a Pearson distribution of type 4
 * The Cauchy distribution is a special case of a Pearson distribution of type 7.
 * The Cauchy distribution is a stable distribution: if $$X \sim \textrm{Stable}(1, 0, \gamma, \mu)$$, then $$X \sim \operatorname{Cauchy}(\mu, \gamma)$$.
 * The Cauchy distribution is a singular limit of a hyperbolic distribution
 * The wrapped Cauchy distribution, taking values on a circle, is derived from the Cauchy distribution by wrapping it around the circle.
 * If $$X \sim \textrm{N}(0,1)$$, $$Z \sim \operatorname{Inverse-Gamma}(1/2, s^2/2)$$, then $$Y = \mu + X \sqrt Z \sim \operatorname{Cauchy}(\mu,s)$$. For half-Cauchy distributions, the relation holds by setting $$X \sim \textrm{N}(0,1) I\{X>=0\}$$.

Relativistic Breit–Wigner distribution
In nuclear and particle physics, the energy profile of a resonance is described by the relativistic Breit–Wigner distribution, while the Cauchy distribution is the (non-relativistic) Breit–Wigner distribution.

Occurrence and applications

 * In spectroscopy, the Cauchy distribution describes the shape of spectral lines which are subject to homogeneous broadening in which all atoms interact in the same way with the frequency range contained in the line shape. Many mechanisms cause homogeneous broadening, most notably collision broadening. Lifetime or natural broadening also gives rise to a line shape described by the Cauchy distribution.
 * Applications of the Cauchy distribution or its transformation can be found in fields working with exponential growth. A 1958 paper by White derived the test statistic for estimators of $$\hat{\beta}$$ for the equation $$x_{t+1}=\beta{x}_t+\varepsilon_{t+1},\beta>1$$ and where the maximum likelihood estimator is found using ordinary least squares showed the sampling distribution of the statistic is the Cauchy distribution.
 * The Cauchy distribution is often the distribution of observations for objects that are spinning. The classic reference for this is called the Gull's lighthouse problem and as in the above section as the Breit–Wigner distribution in particle physics.
 * In hydrology the Cauchy distribution is applied to extreme events such as annual maximum one-day rainfalls and river discharges. The blue picture illustrates an example of fitting the Cauchy distribution to ranked monthly maximum one-day rainfalls showing also the 90% confidence belt based on the binomial distribution. The rainfall data are represented by plotting positions as part of the cumulative frequency analysis.
 * The expression for the imaginary part of complex electrical permittivity, according to the Lorentz model, is a Cauchy distribution.
 * As an additional distribution to model fat tails in computational finance, Cauchy distributions can be used to model VAR (value at risk) producing a much larger probability of extreme risk than Gaussian Distribution.

title: Cauchy distribution


text:
Talk:Chernobyl

Too many maps
The infobox has too many maps and some need to be removed. BigRed606 (talk) 02:37, 17 February 2022 (UTC)

Russian occupation
News reports are stating that the city is now in the hands of the Russian military, as part of the invasion of Ukraine. 50.111.36.47 (talk) 18:06, 24 February 2022 (UTC)

russia.
russia. 2A02:C7F:7030:6E00:89E7:1523:8FE9:7419 (talk) 10:19, 25 February 2022 (UTC)

 * Whilst indeed captured, the city isn't annexed so far, so no, there is no way to change city's "Country" field. Seryo93 (talk) 10:27, 25 February 2022 (UTC)
 * so far? wtf?? Sergiwez (talk) 15:39, 17 June 2023 (UTC)
 * It won't change the country field even if annexed. 211.238.95.199 (talk) 14:31, 3 February 2024 (UTC)

Source and wording of "Jews were introduced to the city in the 16th century"?
Seems like this would benefit from a reference of the sort "see below" or "as discussed below" — Preceding unsigned comment added by 75.164.4.40 (talk) 08:43, 27 February 2022 (UTC)

There was no reference for when Jews moved into Chernobyl in the previous version of the article either though. Scott.Hayden.Walker (talk) 02:23, 5 July 2022 (UTC)

I apologize if I sounded combative on accident; I just don't know when the Jewish community of Chernobyl was founded. I just wanted to clean up the weird passive voice in the prior writing. Scott.Hayden.Walker (talk) 02:25, 5 July 2022 (UTC)

Requested Move 8 March 2022
Chernobyl → Chornobyl, as this is the proper Ukrainian spelling, as opposed to the Russian spelling. The city is in Ukraine. The article for Kyiv is spelled "Kyiv," rather than "Kiev." 69.116.147.54 (talk) 20:00, 8 March 2022 (UTC) Edit: People may also confuse "Chernobyl" with the power plant, or with Pripyat. 69.116.147.54 (talk) 01:54, 9 March 2022 (UTC)
 * Oppose: The Kiev → Kyiv move, while controversial, is backed up by a number of reliable sources who use that spelling in their English-language reporting. Many English-language sources still use the Russian spelling for Chernobyl, but the Ukrainian spelling for Kyiv (e.g. BBC News, CBS News, NPR, The New York Times, The Guardian, The Atlantic, Al Jazeera, New Scientist, ABC News). "Chernobyl" is by far the common spelling variant, and the one most reliable sources use, even if they have switched to saying "Kyiv" instead of "Kiev". Is this inconsistent? Possibly. But sources that have the "Chornobyl" spelling (IAEA press release, CNBC), are very few and far between. Our article on Odessa has not moved to the "Odesa" spelling, despite the latter appearing in more reliable sources recently – unlike "Chornobyl". It is unlikely this page is going to move to the Ukrainian spelling any time soon. —AFreshStart (talk) 23:35, 8 March 2022 (UTC)
 * Oppose for now. Agree with the above comment. The general switch to Kyiv across the board in English language sources is evident in various media outlets at the international, national, and local levels. For this, though, English language sources are still consistently referring to it as "Chernobyl" in reports, which have obviously been numerous these past few weeks. Eventually this may change, but for now, there doesn't appear to be evidence that "Chornobyl" is being widely or consistently used in English language sources. --JonRidinger (talk) 14:16, 16 March 2022 (UTC)

Requested move 16 March 2022

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

The result of the move request was: Not moved at this time. Politics and war crimes aside, WP:COMMONNAME predominates. It's entirely possible that this will change in the future, perhaps even in the near future! But ... consensus is clear that the sources do not back up the assertion that it's already changed. Red  Slash  21:46, 22 March 2022 (UTC)

Chernobyl → Chornobyl – The city is commonly known as Chernobyl in English, yet this name is derived from the Russian-language name Чернобыль. According to article 3.1 of the Ukrainian Toponimic Guidelines approved by the United Nations Group of Experts on Geographical Names, "Geographical names of the Ukrainian territory are formed and represented in writing according to the Ukrainian Spelling Rules in all spheres of their official use" (you can find the guidelines here https://unstats.un.org/unsd/ungegn/nna/toponymic/). According to the UN-approved rules of Ukrainian to English transliteration, Ukrainian name Чорнобиль is transliterated as Chornobyl (see the rules here https://unstats.un.org/unsd/geoinfo/ungegn/docs/26th-gegn-docs/WP/WP21_Roma_system_Ukraine%20_engl._.pdf). Besides, using transliterations of Ukrainian geographical names from Russian instead of Ukrainian is a relic of colonial past, not unlike using the name Bombay for the city of Mumbai in India. The usage of such names is especially offensive considering the ongoing fight for independence of Ukraine against Russia, the former colonizer, which wages the war trying to wipe the Ukrainian nation from the face of the Earth in the most brutal way. Leonidslupsky (talk) 11:05, 16 March 2022 (UTC)
 * — Leonidslupsky (talk • contribs) has made few or no other edits outside this topic.

 * Support - There are countless English language sources now using the spelling Chornobyl including Encyclopedia Britannica, the International Atomic Energy Agency, Power Technology and the National Post. JayAmber (talk) 13:42, 16 March 2022 (UTC)
 * Oppose per WP:COMMONNAME based on Google Ngrams. We should not be moving article titles based on international politics. Our article naming rules are very clear that the title of an article should be the most common name used in English for a subject. Rreagan007 (talk) 19:33, 16 March 2022 (UTC)
 * Support - per Leonidslupsky and JayAmber reasoning. - DownTownRich (talk) 20:15, 16 March 2022 (UTC)
 * Oppose - per the reasons listed by Rreagan007. This is the most common spelling of the location by English-language speakers. Chernobyl uses the spelling. News coverage of the recent takeover of the exclusion zone by Russian troops also utilize the Russian spelling. We should not alter the title of articles because of ongoing geopolitical turmoil, as it can have a chilling effect on viewership and can be confusing for the average person. JohnHawkinsBois (talk) 21:00, 16 March 2022 (UTC)
 * Strong oppose per Rreagan007 and JohnHawkinsBois above. The common name in English remains Chernobyl, and I suspect this move was requested for politically biased reasons.  O.N.R.  (talk) 21:42, 16 March 2022 (UTC)
 * Oppose per Rreagan007 and others. ♦ jaguar  00:42, 17 March 2022 (UTC)
 * Oppose WP:COMMONNAME applies here. Most people and reliably sourced media still refer their city as "Chernobyl", kinda like how Ganges still a common name against Ganga or Hanover is still common name against Hannover (double n). 180.254.171.93 (talk) 06:57, 17 March 2022 (UTC)
 * Oppose per WP:COMMONNAME.  Lugnuts  Fire Walk with Me 10:21, 17 March 2022 (UTC)
 * Oppose, sympathy for the people of Ukraine notwithstanding. Unlike "Kyiv", this is not the common name in contemporary English (recent sources such as the BBC and the NYT have both "Kyiv" and "Chernobyl" on the same page). Google is a very clumsy and imperfect tool, but on Scholar, "English-language" results are:
 * Chernobyl 2022, about 9210 results, page 99 has at least some hits
 * Chornobyl 2022, about 590 results
 * Justlettersandnumbers (talk) 12:01, 17 March 2022 (UTC)

 * Oppose for now, just as I said for the earlier move request. As of now, Kyiv has definitely emerged as the more common name in English language sources over Kiev, but Chernobyl still remains far more common over Chornobyl. That may very well change, but does not appear to be the case yet. --JonRidinger (talk) 14:01, 17 March 2022 (UTC)
 * Support – There are enough official reasons for that move, including the ones already mentioned here. The "commonly recognizable name" will not change itself into correct one until we support this change, in Wikipedia as well. Flipping Switches (talk) 16:15, 17 March 2022 (UTC)
 * This argument explicitly contradicts to our policies and must be discarded.--Ymblanter (talk) 07:52, 18 March 2022 (UTC)
 * Strong oppose. The English name is Chernobyl. What the Ukrainian government and the Ukrainian propaganda think about it is absolutely irrelevant in view of our policies.--Ymblanter (talk) 20:06, 17 March 2022 (UTC)
 * And, unsurprisingly, nominated by an obvious sock.--Ymblanter (talk) 20:07, 17 March 2022 (UTC)
 * Not Ukrainian government and Ukrainian propaganda but name of Ukrainian city in Ukrainian language, opposed to Russian name Chernobyl. Flipping Switches (talk) 02:55, 18 March 2022 (UTC)
 * What we must be interested in is the name of Ukrainian city in the English language, not in Ukrainian and not in Russian. This is what our policies say. The rest is pure propaganda.--Ymblanter (talk) 07:51, 18 March 2022 (UTC)
 * Propaganda? What do you think about Kyiv then? 211.238.95.199 (talk) 14:35, 3 February 2024 (UTC)
 * Strong Support "Chernobyl" is a post-colonial russian-soviet legacy that migrated to English. There is no self-sufficient name in the English language for a place name that is outside the United States, Great Britain or other countries outside Ukraine. There is a practice that is simply inherited from English by a foreign russian language. Today it is wrong and incorrect. It needs to change according to the current situation according to the Ukrainian pronunciation of "Chоrnobyl". The city has been a part of Ukraine since 1991, so it is appropriate to change the pronunciation in the English language to the correct one. There are no arguments to leave the old, incorrect and erroneous version of the pronunciation "Chernobyl". See at the Encyclopedia Britannica --Beznazvy (talk) 14:35, 19 March 2022 (UTC) — Beznazvy (talk • contribs) has made few or no other edits outside this topic.
 * Support – per the reasons listed by Leonidslupsky and JayAmber --ValeriySh (talk) 13:05, 19 March 2022 (UTC)
 * Strong Oppose many sources are adjusting how they name things for political reasons during the ongoing conflict. If they continue to use a different spelling once the political concerns are no longer pressing, we can consider it then.  The accepted spelling in English has been Chernobyl for 35 years. User:力 (powera,  π,  ν ) 18:18, 19 March 2022 (UTC)
 * Oppose - The common name is the current title. No need to make it harder to find or a redirect. --  Dane  talk  05:50, 20 March 2022 (UTC)
 * Support - To help standardize Ukrainian variants in English. Our decision here will also help popularize the name “Chornobyl” in media outlets. — Kostović (talk) 08:09, 20 March 2022 (UTC)
 * Oppose. The nom says, The city is commonly known as Chernobyl in English.  If that is the case then policy is quite clear that Chernobyl should be the preferred name.  The etymology of the term is not relevant.  It is not Wikipedia's job to try to change usage as several people have advocated, it is for us to reflect current usage. Kahastok talk 08:57, 20 March 2022 (UTC)
 * Support - Most postcolonial city names have been renamed, to better reflect local indigenous preferences. Ukrainian people have explicitly asked for their preferene to be recognised. I see no reason why this should be disallowed in this instance. Taavi5342 (talk) 11:58, 20 March 2022 (UTC) — Taavi5342 (talk • contribs) has made few or no other edits outside this topic.

 * Strong oppose, and suggest SNOW close (WP:SNOW), albeit with a heavy heart. Chernobyl has always been the WP:COMMONNAME, and User:Justlettersandnumbers's evidence that this has not been changed by the recent (and in my view important) shift towards Ukrainian names in English-language sources is persuasive.  User:AFreshStart provides several more instances at the 8 March discussion of authoritative media sources which have switched to Kyiv but have not switched to Chornobyl.  Turning to the arguments in favour of the change, User:JayAmber's is the only one based in WP's policies and practice.  However, the sources they cite have made the change only very recently and constitute a small proportion of the overall field, so whilst we might observe that a shift is happening (or coming), I think it is WP:TOOSOON to declare that one has taken place—again, see Justlettersandnumbers and AFreshStart's examples.  The moral argument that Wikipedia should use Ukrainian names in order to be on the right side of history is persuasive, at least to me, but this is not the forum for it—consensus should be sought at an RfC for a wiki-wide decision to override COMMONNAME.  —Kilopylae (talk) 19:09, 20 March 2022 (UTC)
 * Support - Whether a spelling is common or not is not written in stone — it's defined by how often it's used. Nothing wrong with intentionally making something more common. This is the will of the Ukrainian-speaking community. Sunny Daelos (talk) 19:12, 20 March 2022 (UTC) — Sunny Daelos (talk • contribs) has made few or no other edits outside this topic.
 * We likely have the same person voting multiple times. Anyway, the argument explicitly contradicts to the Wikipedia policies.--Ymblanter (talk) 22:23, 20 March 2022 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
 * @Ymblanter Can somebody get a checkuser to check them. We can not have that in the community. -DownTownRich (talk) 22:27, 20 March 2022 (UTC)
 * Oppose per sentiment and reasoning laid out by Kilopylae. Instaurare (talk) 09:06, 21 March 2022 (UTC)
 * Oppose per common name. Also, Wikipedia is not here to change national policies or to enact world change. Natg 19 (talk) 19:01, 21 March 2022 (UTC)

Semi-protected edit request on 17 March 2022
There 90000 death in total till today, not fewer than 100 2409:4041:2CB6:9D05:C694:EF0A:D2C1:FA6F (talk) 10:51, 17 March 2022 (UTC)
 * Red information icon with gradient background.svg Not done: please provide reliable sources that support the change you want to be made. ScottishFinnishRadish (talk) 11:04, 17 March 2022 (UTC)

Semi-protected edit request on 27 March 2022
Change the page title from “Chernobyl” to “Chornobyl”. The city is an Ukrainian city, therefore I believe Ukrainian spelling is appropriate (like for Kyiv or Lviv). Fairediting (talk) 06:51, 27 March 2022 (UTC)

 * Red information icon with gradient background.svg Not done: Moving the article would require an WP:RM. We had an RM on this precise move that closed less than a week ago with consensus not to move, so a new RM now would likely be speedy-closed. Kahastok talk 08:14, 27 March 2022 (UTC)

It's Chornobyl, not Chernobyl
The name of the article is not right. IhorInki (talk) 20:13, 21 April 2022 (UTC)

 * Stop russian chauvinism. IhorInki (talk) 20:14, 21 April 2022 (UTC)
 * Stop Ukrainian nationalism. The English name of the city if Chernobyl. Ymblanter (talk) 20:36, 21 April 2022 (UTC)
 * Looks like some social media campaign again. May be they should stop financing this and channel money into recovery of the economy. Ymblanter (talk) 20:37, 21 April 2022 (UTC)
 * Yeah, we need to use the common English-language spelling, but your comment is pretty weird, as it would be a pretty neat trick for them to finance an economic recovery while being invaded by Russia and prevented from exporting their grain by a blockade in the Black Sea. Ikan Kekek (talk) 21:09, 11 June 2022 (UTC)
 * Why aren't you banned yet? 211.238.95.199 (talk) 14:36, 3 February 2024 (UTC)
 * User:Ymblanter please try to WP:assume good faith and WP:don't bite the newcomers. Your comments trying to denigrate a new editor by associating them with “nationalism” and the “they” boogeyman violate WP:no personal attacks. In case you’re unaware, both spellings are used in English, for example, Chornobyl is in references like the World Factbook and NGA Geo Names Server, so the supposed factual rationale is false. —Michael Z. 15:09, 12 June 2022 (UTC)
 * User:IhorInki, the Wikipedia guidelines about WP:article titles say we usually use the most commonly used name in English-language sources, and not the official or correct name. To change it, we would have to demonstrate to editors that the spelling meets the huideline and get consensus for the change. Right now, energy is better invested in enlarging and improving articles. —Michael Z. 15:14, 12 June 2022 (UTC)
 * Mzajac, I have no motivation to start contributing to articles while there are mistakes in names of Ukrainian cities blocked by perverted rules and toxic community like @Ymblanter. IhorInki (talk) 11:08, 13 June 2022 (UTC)
 * Which is to say that you are not here to to build an encyclopedia. Ymblanter (talk) 11:40, 13 June 2022 (UTC)
 * Outside perspective, theres 2 options here, one is the Russian spelling, one is the Ukrainian spelling, since it is in Ukraine, shouldn't we use the native name, do we use the Ukrainian spelling for any cities in Russia? Although the more common name is the Russian one. I should point out there is a campaign in Ukraine to change Russian names of buildings and streets and cities to Ukrainian ones. To me this seems to be a debate between; common name and native name. The native name is VERY similar to the common name except for a one letter difference. Would people no longer know what we're talking about if we change one letter? I highly doubt it. I support keeping the Russian version for the CNPP page, and the page about the 1986 incident. But for the city itself? I support the native name. 2603:7000:3B40:B500:642A:F29F:796B:1E73 (talk) 22:19, 2 January 2023 (UTC)
 * I agree it seems absurd to refer to it by the Russian name, although I suppose it mostly gained international attention when the Russian name was used. It's a tricky one, but I would vote for Chornobyl, for several reasons. It seems destined to become the predominant way to write it, just as Kyiv has become the default one. Media (and many people) don't find it in good taste to use the Russian variant of a place-name in Ukraine in these times, and for good reason, and I can't see any rationale why anyone would revert to using Russian spellings after the conflict is over. Although I know there will be a lot of partisans against it, as evidenced above.--Euor (talk) 21:19, 26 April 2023 (UTC)

Semi-protected edit request on 18 May 2022
Delete russian names of the city 188.163.113.131 (talk) 12:52, 18 May 2022 (UTC)
 * Red information icon with gradient background.svg Not done for now: please establish a consensus for this alteration before using the template. ScottishFinnishRadish (talk) 13:02, 18 May 2022 (UTC)

Semi-protected edit request on 12 April 2023
In the last sentence of paragraph one, change Pripyat to Chernobyl. Legofan42 (talk) 14:38, 12 April 2023 (UTC)
 * Red information icon with gradient background.svg Not done for now: please establish a consensus for this alteration before using the template. Izno (talk) 17:30, 12 April 2023 (UTC)

Chornobyl v Chernobyl
In the English version of the Ukrainian constitution article 16 spells the city as Chornobyl. I would hope that the Ukrainian government is aware of the spelling of their one of, if not the, most famous city in Ukraine.

here's the link to the website I found the constitution on Caucasianhamburger (talk) 14:23, 21 April 2023 (UTC)

 * 45 edits in total, again. Ymblanter (talk) 16:35, 21 April 2023 (UTC)

2022 Speculation
It’s important to note that it was speculation and not confirmed that radiation levels were rising after the Russian military took control of the city. This makes it sound like western propaganda the way it’s worded. 2601:441:8301:8000:CCBE:EAFE:794C:2C50 (talk) 18:32, 3 June 2023 (UTC)

 * What "western propaganda" are you talking about here? 185.113.36.98 (talk) 19:04, 14 June 2023 (UTC)

Semi-protected edit request on 17 June 2023
It is not Chernomyl it is Chornobyl. It is a Ukrainian city and Chernobyl is a transliteration from the Russian terrorist language. Sergiwez (talk) 15:36, 17 June 2023 (UTC)

 * Thank you for your personal opinion, which, however, it at variance with the policies of the English Wikipedia. Ymblanter (talk) 15:52, 17 June 2023 (UTC)
 * Red question icon with gradient background.svg Not done: it's not clear what changes you want to be made. Please mention the specific changes in a "change X to Y" format and provide a reliable source if appropriate. M.Bitton (talk) 17:26, 17 June 2023 (UTC)

Rename the article "Chernobyl" to "Chornobyl".
I propose to rename this article and to use in future the variant of writing "Chornobyl" instead of "Chernobyl". Because the variant of writing through "o" is the only correct variant and is regulated by the spelling of the Ukrainian language and enshrined in the law of Ukraine. Elvstrem (talk) 15:50, 13 July 2023 (UTC)

 * See the FAQ at the top of the page. MrOllie (talk) 15:52, 13 July 2023 (UTC)
 * Chornobyl is Ukrainian name of Ukrainian town. I can't understand why Wikipedia would use rusified version of the name created by our former colonizers and current invadors 193.19.254.207 (talk) 14:06, 25 December 2023 (UTC)
 * We renamed the articles on Kyiv and Odesa when it was clear that most WP:reliable sources used those spellings (see the relevant talk page discussions). We will do so when it’s the case for Chornobyl as well. A quick search of sources in Google Books and Scholar shows it’s not the case at this time. —Michael Z. 03:41, 27 December 2023 (UTC)

Vladimir Ilyich Lenin Nuclear Power Plant
It wasn’t officially named the Vladimir Ilyich Lenin Nuclear Power Plant. That was the official title of the Leningrad Nuclear Power Plant. YakovlevWK (talk) 17:21, 23 November 2023 (UTC)

Cancel the spelling "Chernobyl" and leave only "Chornobyl"
I believe that using an outdated transliteration from the Russian language is not correct. Because the city was created in the Ukrainian SSR and named in the Ukrainian language, it is worth using Ukrainian Transliteration 45.10.90.10 (talk) 00:35, 2 March 2024 (UTC)
 * As you can see on this talk page, this comes up frequently. Western media outlets predominantly use Chernobyl and it doesn't look like there is a consensus to change it at this time. Wikipedia follows the usage of common words and not dictate them. Hope this helps answer your question. soetermans . ↑↑↓↓←→←→ B A TALK 00:47, 2 March 2024 (UTC)

Incorrect title of the article
This Wikipedia article spreads the incorrect name of the city of Chornobyl. Please we need to stop the practice of incorrect transliteration of the names of settlements from the Ukrainian language. Renaming the article will help users learn the correct title faster and prevent this error from spreading across the Internet. Mr Amsterdam (talk) 02:47, 9 March 2024 (UTC)
 * And how is the Ukrainian language relevant to an article on the history of the Soviet Union? Dimadick (talk) 17:37, 9 March 2024 (UTC)

title: Talk:Chernobyl