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Whiteness studies

Whiteness studies is the study of the structures that produce white privilege, the examination of what whiteness is when analyzed as a race, a culture, and a source of systemic racism, and the exploration of other social phenomena generated by the societal compositions, perceptions and group behaviors of white people. It is an interdisciplinary arena of inquiry that has developed beginning in the United States from white trash studies and critical race studies, particularly since the late 20th century. It is focused on what proponents describe as the cultural, historical and sociological aspects of people identified as white, and the social construction of "whiteness" as an ideology tied to social status.

Pioneers in the field include W. E. B. Du Bois ("Jefferson Davis as a Representative of Civilization", 1890; Darkwater, 1920), James Baldwin (The Fire Next Time, 1963), Theodore W. Allen (The Invention of the White Race, 1976, expanded in 1995), historian David Roediger (The Wages of Whiteness, 1991), author and literary critic Toni Morrison (Playing in the Dark: Whiteness and the Literary Imagination, 1992), and Ruth Frankenberg (White Women, Race Matters: The Social Construction of Whiteness, 1993).

By the mid-1990s, numerous works across many disciplines analyzed whiteness, and it has since become a topic for academic courses, research and anthologies. Some syllabuses associate the dismantling of white supremacy as a stated aim in the understanding of whiteness, while other sources view the field of study as primarily educational and exploratory, such as in questioning the objectivity of generations of works produced in intellectual spheres dominated by white scholars.

A central tenet of whiteness studies is a reading of history and its effects on the present that is inspired by postmodernism and historicism. According to this reading, racial superiority was socially constructed in order to justify discrimination against non-whites. Since the 19th century, some writers have argued that the phenotypical significance attributed to specific races are without biological association, and that what is called "race" is therefore not a biological phenomenon. Many scientists have demonstrated that racial theories are based upon an arbitrary clustering of phenotypical categories and customs, and can overlook the problem of gradations between categories. Thomas K. Nakayama and Robert L. Krizek write about whiteness as a "strategic rhetoric," asserting, in the essay "Whiteness: A Strategic Rhetoric", that whiteness is a product of "discursive formation" and a "rhetorical construction". Nakayama and Krizek write, "there is no 'true essence' to 'whiteness': there are only historically contingent constructions of that social location." Nakayama and Krizek also suggest that by naming whiteness, one calls out its centrality and reveals its invisible, central position. Whiteness is considered normal and neutral, therefore, to name whiteness means that one identifies whiteness as a rhetorical construction that can be dissected to unearth its values and beliefs.

Major areas of research in whiteness studies include the nature of white privilege and white identity, the historical process by which a white racial identity was created, the relation of culture to white identity, and possible processes of social change as they affect white identity.

Definitions of whiteness
Zeus Leonardo defines whiteness as "a racial discourse, whereas the category 'white people' represents a socially constructed identity, usually based on skin color". Steve Garner notes that "whiteness has no stable consensual meaning" and that "the meanings attached to 'race' are always time- and place-specific, part of each national racial regime".

Development of the field
Studies of whiteness as a unique identity could be said to begin among black people, who needed to understand whiteness to survive, particularly in slave societies such as the American colonies and United States. An important theme in this literature is, beyond the general "invisibility" of blacks to whites, the unwillingness of white people to consider that black people study them anthropologically. American author James Weldon Johnson wrote in his 1912 novel The Autobiography of an Ex-Colored Man that "colored people of this country know and understand the white people better than the white people know and understand them". Author James Baldwin wrote and spoke extensively about whiteness, defining it as a central social problem and insisting that it was choice, not a biological identity. In The Fire Next Time (1963), a non-fiction book on race relations in the United States, Baldwin suggests that "'White people in this country will have quite enough to do in learning how to accept and love themselves and each other, and when they have achieved this—which will not be tomorrow and may very well be never—the Negro problem will no longer exist, for it will no longer be needed.'"A major black theory of whiteness connects this identity group with acts of terrorism—i.e., slavery, rape, torture, and lynching—against black people, who were treated as sub-human.

White academics in the United States and the United Kingdom (UK) began to study whiteness as early as 1983, creating a discipline called "whiteness studies". The "canon wars" of the late 1980s and 1990s, a term that refers to political controversy over the centrality of white authors and perspectives in United States culture, led the scholar Shelley Fisher Fishkin to ask "how the imaginative construction of 'whiteness' had shaped American literature and American history". The field developed a large body of work during the early 1990s, which, according to Fishkin, extends across the disciplines of "literary criticism, history, cultural studies, sociology, anthropology, popular culture, communication studies, music history, art history, dance history, humor studies, philosophy, linguistics, and folklore".

As of 2004, according to The Washington Post, at least 30 institutions in the United States including Princeton University, the University of California at Los Angeles, the University of New Mexico and University of Massachusetts Amherst offer, or have offered, courses in whiteness studies. Whiteness studies often overlaps with post-colonial theory, the study of orientalism, and anti-racist education.

One contribution to White Studies is Rich Benjamin's Searching for Whitopia: An Improbable Journey to the Heart of White America. The book examines white social beliefs and white anxiety in the contemporary United States, in the context of enormous demographic, cultural, and social change. The book explains how white privilege and segregation might flourish, even in the absence of explicit racial animus.

Another contribution to whiteness studies is Gloria Wekker's White Innocence: Paradoxes of Colonialism and Race, which discusses the immutability and fluidity of white identity and its relationship to innocence in the context of post-colonial Netherlands in the first decade of the twenty-first century. In Wekker's analysis, the process of separating Dutch from "Other" is facilitated through skin tone and non-Christian religious practices. According to Wekker, the process of racialization is reserved for mid-to-late twentieth century immigrant groups (Muslims, Black Surinamese, Black Antilleans), as a means of delineating groups outside the constructed immutable "norms" of Dutch society.

Sociologist Michael Eric Dyson contributed to the discussion of white identity in his 2017 book Tears We Cannot Stop: A Sermon to White America. Dyson's book specifically addresses "five dysfunctional ways that those regarded as white respond when confronted with the reality that whiteness is simultaneously artificial and powerful" as well as "dysfunctional ways that black people sometimes respond to white racism."

Whiteness
Whiteness studies draws on research into the definition of race, originating with the United States but applying to racial stratification worldwide. This research emphasizes the historically recent social construction of white identity. As stated by W. E. B. Du Bois in 1920: "The discovery of a personal whiteness among the world's peoples is a very modern thing,—a nineteenth and twentieth century matter, indeed." The discipline examines how white, Native, and African/black identities emerged in interaction with the institutions of slavery, colonial settlement, citizenship, and industrial labor. Scholars such as Winthrop Jordan have traced the evolution of the legally defined line between "blacks" and "whites" to colonial government efforts to prevent cross-racial revolts among unpaid laborers.

Princeton professor Nell Irvin Painter, in her 2010 book The History of White People, says the idea of whiteness is not just a matter of biology but also includes "concepts of labor, gender, class, and images of personal beauty".(p. xi) The earliest European societies, including the Greeks and Romans, had no concept of race and classified people by ethnicity and social class, with the lowest class being slaves, most of whom were European in origin.(p. xi) Race science, developed in Europe in the 1800s, included intense analysis of different groups of Europeans, who were classified as belonging to three or four different races, with the most admirable being from northern Europe.(pp. 215–6) From the early days of the United States, whiteness was a criterion for full citizenship and acceptance into society. The American definition of whiteness evolved over time; initially groups such as Jews and Southern Europeans were not regarded as white, but as skin color became the primary criterion, they were gradually accepted. Painter argues that in the 21st century the definition of whiteness – or more precisely the definition of "nonblackness" – has continued to expand, so that now "The dark of skin who happen to be rich ... and the light of skin from any (racial background) who are beautiful, are now well on their way to inclusion."(pp. 389–90.)

Academic Joseph Pugliese is among writers who have applied whiteness studies to an Australian context, discussing the ways that Australian Aboriginals were marginalized in the wake of the European colonization of Australia, as whiteness came to be defined as central to Australian identity, diminishing Aboriginal identity in the process. Pugliese discusses the 20th-century White Australia policy as a conscious attempt to preserve the "purity" of whiteness in Australian society. Likewise Stefanie Affeldt considers whiteness "a concept not yet fully developed at the time the first convicts and settlers arrived down under" which, as a social relation, had to be negotiated and was driven forward in particular by the labour movement. Eventually, with the Federation of Australia, "[o]verlaying social differences, the shared membership in the 'white race' was the catalyst for the consolidation of the Australian colonies as the Commonwealth of Australia".

White backlash
White backlash or white rage in association with or as a consequence of whiteness is an area of investigation in whiteness studies. Sociologist Matthew Hughey has described this examination of racially-based backlash within its historical context; "Another approach to the study of whiteness centres on the white "back-lash" against the advances born from the civil rights movement."

Political scientist Danielle Allen has analyzed the intersection of whiteness with North American demographic changes, stating how they can "provoke resistance from those whose well-being, status and self-esteem are connected to historical privileges of 'whiteness'". Discussing the method of this resistance, Veronica Strong-Boag's co-edited Rethinking Canada: The Promise of Women's History explores how white backlash in Canada attempts to frames the defending of white interests as a "defence of national identity", rather than an acknowledgement of the political action of whiteness.

Scholar George Yancy has explored the societal response to perceived loss of racial privilege in his 2018 book Backlash; how reactions derived from whiteness fluctuate between Robin DiAngelo's concept of white fragility versus the more extreme backlashes throughout history.

White education
The study of white education and its intersection with whiteness is a continuing area of research in whiteness studies. Scholarly investigation has critiqued white-derived education as inevitably for the benefit of, organized by, and oriented towards white people. Horace Mann Bond was one of the early scholars to identify bias and privilege operating in white education systems. Bond critiqued suggestions African Americans were not intelligent enough to participate in the same schools as white Americans and campaigned against calls for literacy tests for suffrage. He challenged the Southern Manifesto and identified bias for funding white education, rather than universal funding, even within the reformist movement for desegregated schools.

Whiteness and privilege have continued in US education after Jim Crow versions of the segregationist ideology have lost their legitimacy due to legal and political failures. Privacy and individualism discourses mask white fear and newer forms of exclusion in contemporary education according to scholar, Charles R. Lawrence III.

White identity
Analyzing whiteness to forge new understandings of white identity has been a field of exploration for academics since the publications which largely founded modern whiteness studies in the mid-1990s. In exploring Ruth Frankenberg's works, and her interchanging use of the two concepts, the separation has been examined by scholars attempting to intellectually "disengtangle each from the other".

Sociologist Howard Winant, favoring a deconstructionist (rather than abolitionist) study of whiteness, suggests this methodology can help redefine and reorient understanding of white identity. In biological examination, whiteness studies has sought to expose how "white identity is neither pure nor unchanging – that its genealogy is mixed" in order to unearth biases within the white racial identity.

White privilege
In 1965, drawing from insights from Du Bois and inspired by the Civil Rights Movement, Theodore W. Allen began a 40-year analysis of "white skin privilege", "white race" privilege, and "white" privilege. In a piece he drafted for a "John Brown Commemoration Committee", he urged that "White Americans who want government of the people" and "by the people" to "begin by first repudiating their white skin privileges". From 1967 to 1969 various versions of the pamphlet, "White Blindspot", containing pieces by Allen and Noel Ignatin (Noel Ignatiev), focused on the struggle against "white skin privilege" and significantly influenced Students for a Democratic Society (SDS) and sectors of the New Left. By June 15, 1969, The New York Times was reporting that the National Office of SDS was calling "for an all-out fight against 'white skin privileges'".

In 1974–1975, Allen extended his analysis of "white privilege", racial oppression, and social control to the colonial period with his ground-breaking Class Struggle and the Origin of Racial Slavery: The Invention of the White Race. With continued research, he developed his ideas as his seminal two-volume The Invention of the White Race published in 1994 and 1997.

For almost forty years, Allen offered a detailed historical analysis of the origin, maintenance, and functioning of "white-skin privilege" and "white privilege" in such writings as: "White Supremacy in U.S. History" (1973); "Class Struggle and the Origin of Racial Slavery: The Invention of the White Race" (1975); "The Invention of the White Race," Vol. 1: "Racial Oppression and Social Control" (1994, 2012); "The Invention of the White Race," Vol. 2: "The Origin of Racial Oppression in Anglo-America" (1997, 2012); "Summary of the Argument of 'The Invention of the White Race'" Parts 1 and 2 (1998); "In Defense of Affirmative Action in Employment Policy" (1998); "'Race' and 'Ethnicity': History and the 2000 Census" (1999); and "On Roediger's Wages of Whiteness" (Revised Edition)";

In his historical work, Allen asserted that:
 * the "white race" was invented as a ruling class social control formation in the late 17th-/early-18th century Anglo-American plantation colonies (principally Virginia and Maryland);
 * central to this process was the ruling-class plantation bourgeoisie conferring "white race" privileges on European-American working people;
 * these privileges were not only against the interests of African Americans, they were also "poison", "ruinous", a baited hook, to the class interests of working people;
 * white supremacy, reinforced by "white skin privilege", has been the main retardant of working-class consciousness in the US; and
 * struggle for radical social change should direct principal efforts at challenging white supremacy and "white skin privileges". Allen's work influenced Students for a Democratic Society (SDS) and sectors of the "new left" and paved the way for "white privilege", "race as social construct", and "whiteness studies". He also raised important questions about developments in those areas, and he avoided using the term "whiteness", using quotation marks when he did.

Laura Pulido writes about the relation of white privilege to racism. "'White privilege [is] a highly structural and spatial form of racism ... I suggest that historical processes of suburbanization and decentralization are instances of white privilege and have contributed to contemporary patterns of environmental racism.'"Pulido defines environmental racism as "the idea that nonwhites are disproportionately exposed to pollution".

Writers such as Peggy McIntosh say that social, political, and cultural advantages are accorded to whites in global society. She argues that these advantages seem invisible to white people, but obvious to non-whites. McIntosh argues that whites utilize their whiteness, consciously or unconsciously, as a framework to classify people and understand their social locations. In addition, even though many white people understand that whiteness is associated with privilege, they do not acknowledge their privilege because they view themselves as average and non-racist. Essentially, whiteness is invisible to white people.

For instance, "'I think whites are carefully taught not to recognize white privilege, as males are taught not to recognize male privilege. So I have begun in an untouched way to ask what it is like to have white privilege. I have come to see white privilege as an invisible package of unearned assets which I can count on cashing in each day, but about which I was 'meant' to remain oblivious' (188)."McIntosh calls for Americans to acknowledge white privilege so that they can more effectively attain equality in American society. She argues, "'To redesign social systems we need first to acknowledge their colossal unseen dimensions. The silences and denials surrounding privilege are the key political tool here. They keep the thinking about equality or equity incomplete, protecting unearned advantage and conferred dominance by making these taboo subjects' (192)."

White privilege is also related to white guilt. As Shannon Jackson writes in the article, "White Noises: On Performing White, On Writing Performance" (1998), "The rhetorics of white guilt are tiresome, cliche, disingenuous, and everywhere. And now that the stereotype of 'the guilty white' is almost entrenched in its negativity as 'the racist white', people actively try to dis-identify from both."

White shift
White racial shift or decline, which has been abbreviated to the phrase whiteshift, and its intersection or connectedness to whiteness, has been a source of study and academic research within the field of whiteness studies. In relation to demographic decline of white people, the phenomenon has been analyzed as producing "a formal re-articulation of whiteness as a social category" in relation to fear-based politics with the US. Academic Vron Ware has examined this fear-based element in the sociology of resentment, and its intersection with class and whiteness. Ware analyzed how white decline, and its portrayal in British media, facilitated a victim or grievance culture, particularly among white British working-class communities.

Political scientist Charles King has proposed that, in the context of the numerical decline of white Americans, whiteness is progressively revealed to be driven by social power, rather than biology.

White socialization
White socialization or white-ethnic socialization is an emerging area of research in whiteness studies. Scholar Julia Carmen Rodil has analyzed the role that non-Hispanic white parents play in the racial socialization of white children, arguing that colorblindness as an ideology in upbringing leads to unchecked racism. Research suggests that white people are socialized to perceive race as a zero-sum game and a black-white binary and this informs the beliefs in reverse racism and prejudice plus power. For white youth, parents play a role in conversations around race and racism and this influences racial perceptions and biases into adulthood. Social media has also been found to play a role in the racial socialization of white adolescents.

Critical whiteness studies
An offshoot of critical race theory, theorists of critical whiteness studies seek to examine the construction and moral implications of whiteness, in order to reveal and deconstruct its assumed links to white privilege and white supremacy. Barbara Applebaum defines it as the "field of scholarship whose aim is to reveal the invisible structures that produce and reproduce white supremacy and privilege", and "presumes a certain conception of racism that is connected to white supremacy". Anoop Nayak describes it as underpinned by the belief that whiteness is "a modern invention [which] has changed over time and place", "a social norm and has become chained to an index of unspoken privileges", and that "the bonds of whiteness can yet be broken/deconstructed for the betterment of humanity". There is a great deal of overlap between critical whiteness studies and critical race theory, as demonstrated by focus on the legal and historical construction of white identity, and the use of narratives (whether legal discourse, testimony or fiction) as a tool for exposing systems of racial power.

Whiteness and architecture
In the early 21st century, architectural historians have published studies related to the construction of whiteness in the built environment. Studies have grappled with the exclusionary nature of the architectural profession, which erected barriers for nonwhite practitioners, the ways in which architects and designers have employed motifs, art programs, and color schemes that reflected the aspirations of European-Americans and, most recently, with the racialization of space.

Criticisms
Writers David Horowitz and Douglas Murray draw a distinction between whiteness studies and other analogous disciplines. Writes Horowitz, "Black studies celebrates blackness, Chicano studies celebrates Chicanos, women's studies celebrates women, and white studies attacks white people as evil." Dagmar R. Myslinska, an adjunct associate professor of law at Fordham University, argues that whiteness studies overlooks the heterogeneity of whites' experience, be it due to class, immigrant status, or geographical location. Alastair Bonnett argues that whiteness studies treated "white" culture as a homogenous and stable "racial entity" – for example, Bonnett observes that whiteness researchers in Britain argued that white British people lived in a homogenous "white culture" (which Bonnett observed was never clearly described), with the researchers completely ignoring British culture's regional diversity, despite having ample opportunity to study it.

Barbara Kay, a columnist for the National Post, has sharply criticized whiteness studies, writing that it "points to a new low in moral vacuity and civilizational self-loathing" and is an example of "academic pusillanimity." According to Kay, whiteness studies "cuts to the chase: It is all, and only, about white self-hate."

Kay noted the leanings of the field by quoting Jeff Hitchcock, co-founder and executive director of the Center for the Study of White American Culture (CSWAC) who stated in a 1998 speech: There is no crime that whiteness has not committed against people of colour.... We must blame whiteness for the continuing patterns today... which damage and prevent the humanity of those of us within it....We must blame whiteness for the continuing patterns today that deny the rights of those outside of whiteness and which damage and pervert the humanity of those of us within it.

In addition to such criticism in the mass media, whiteness studies has earned a mixed reception from academics in other fields. In 2001, historian Eric Arnesen wrote that "whiteness has become a blank screen onto which those who claim to analyze it can project their own meanings" and that the field "suffers from a number of potentially fatal methodological and conceptual flaws." First, Arnesen writes that the core theses of whiteness studies—that racial categories are arbitrary social constructs without definite biological basis, and that some white Americans benefit from racist discrimination of non-whites—have been common wisdom in academia for many decades and are hardly as novel or controversial as whiteness studies scholars seem to believe. Additionally, Arnesen accuses whiteness studies scholars of sloppy thinking; of making claims not supported by their sources; of overstating supporting evidence; and of cherry picking to neglect contrary information.

He notes that a particular datum almost entirely ignored by whiteness studies scholars is religion, which has played a prominent role in conflicts among various American classes. He says that a type of "keyword literalism" persists in whiteness studies, where important words and phrases from primary sources are taken out of their historical context. Whiteness has so many different definitions that the word is "nothing less than a moving target." Arnesen notes that whiteness studies scholars are entirely on the far left of the political spectrum, and suggests that their apparent vitriol towards white Americans is due in part to white workers not fulfilling the predictions of Marxist theory that the proletariat would overcome racial, national and class distinctions to unite and overthrow capitalism. He cites, as an example, David Roediger's afterword to the seminal Wages of Whiteness, which asserts that the book was written as a reaction to "the appalling extent to which white male workers voted for Reaganism in the 1980s." Arnesen argues that in the absence of supporting evidence, whiteness studies often rely on amateurish Freudian speculation about the motives of white people: "The psychoanalysis of whiteness here differs from the 'talking cure' of Freudianism partly in its neglect of the speech of those under study." Without more accurate scholarship, Arnesen writes that "it is time to retire whiteness for more precise historical categories and analytical tools."

In 2002, historian Peter Kolchin offered a more positive assessment and declared that, at its best, whiteness studies has "unfulfilled potential" and offers a novel and valuable means of studying history. Particularly, he praises scholarship into the development of the concept of whiteness in the United States, and notes that the definition and implications of a white racial identity have shifted over the decades. Yet Kolchin describes a "persistent sense of unease" with certain aspects of whiteness studies. There is no consensus definition of whiteness, and thus the word is used in vague and contradictory ways, with some scholars even leaving the term undefined in their articles or essays." Kolchin also objects to "a persistent dualism evident in the work of the best whiteness studies authors," who often claim that whiteness is a social construct while also arguing, paradoxically, that whiteness is an "omnipresent and unchanging" reality existing independent of socialization. Kolchin agrees that entering a post-racial paradigm might be beneficial for humanity, but he challenges the didactic tone of whiteness studies scholars who single out a white racial identification as negative, while praising a black or Asian self-identification. Scholars in whiteness studies sometimes seriously undermine their arguments by interpreting historical evidence independent of its broader context (e.g., Karen Brodkin's examination of American anti-semitism largely neglects its roots in European anti-semitism). Finally, Kolchin categorically rejects the argument—common amongst many whiteness scholars—that racism and whiteness are intrinsically and uniquely American, and he expresses concern at the "belief in the moral emptiness of whiteness [...] there is a thin line between saying that whiteness is evil and saying that whites are evil."

Theodore W. Allen, pioneering writer on "white skin privilege" and "white privilege" from the 1960s until his death in 2005, offered a critical review "On Roediger's Wages of Whiteness" (Revised Edition). He personally put "whiteness" in quotes because he shied away from using the term. As Allen explained, "'it's an abstract noun, it's an abstraction, it's an attribute of some people, it's not the role they play. And the white race is an actual objective thing. It's not anthropologic, it's a historically developed identity of European Americans and Anglo-Americans and so it has to be dealt with. It functions... in this history of ours and it has to be recognized as such. . . .to slough it off under the heading of 'whiteness,' to me seems to get away from the basic white race identity trauma.'"In a scholarly debate with whiteness studies pioneer David Roediger, Eric Kaufmann, a scholar of political demography and identity politics and the author of Whiteshift (which was criticised for defending white identity politics ), criticizes the field as a whole, arguing :"'White Studies suffers from a number of serious flaws which should lead us to question whether this approach can continue to advance the frontiers of knowledge in the wider sphere of ethnic and racial studies'.. These flaws include: 1) a constructivism which fails to recognise the cognitive and social processes that underpin social 'reality'; 2) an excessive emphasis on ethnic boundaries as opposed to ethnic narratives, thereby overstating the degree of malleability possible in ethnic identity; 3) a tacit belief in white exceptionalism, which overemphasises the ideological character of whiteness and deifies whites; 4) an elision of dominant ethnicity and race; and 5) a threefold parochialism in terms of place, time horizon and the role of race in ethnic studies.'"Kaufmann then proposes, as an alternative approach to the study of white identity, the emerging concept of "dominant ethnicity", using Anthony D. Smith's definition of "ethnic group" as a "named, imagined, human community, many of whose members believe in a myth of shared ancestry and place of origin."

List of courses

 * U.S. Race Theory & the Problem of Whiteness, Arizona State University.

Books

 * With an "Introduction" by Jeffrey B. Perry.
 * (Introduction here)
 * With an "Introduction" by Jeffrey B. Perry.
 * (Introduction here)
 * (Introduction here)
 * (Introduction here)
 * (Introduction here)
 * (Introduction here)
 * (Introduction here)
 * (Introduction here)

Book chapters

 * Reproduction of two pamphlets:
 * Reproduction of two pamphlets:
 * Reproduction of two pamphlets:
 * Reproduction of two pamphlets:
 * Reproduction of two pamphlets:

 * CD Rom publication.
 * CD Rom publication.
 * CD Rom publication.
 * CD Rom publication.

Journal articles

 * Pdf.
 * Pdf.
 * Pdf.
 * Pdf.
 * Pdf.
 * Pdf.
 * Pdf.
 * Pdf.

Other

 * Allen, Theodore W. "White Supremacy in U.S. History". Speech delivered at a Guardian Forum on the National Question, April 28, 1973, rpt. in "White Supremacy a Collection", Chicago: Sojourner Truth Organization, 1976.

title: Whiteness studies


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User:Divadiane

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DivaDiane Singer (soprano), Teacher of Singing

Diane currently resides in Frankfurt, Germany, and has been living in Germany for 12 years. She has a Bachelor of Music in Vocal Performance from the University of Wisconsin-Madison. She studied Early Music in Bremen, Germany, and has continued her education with seminars by such experts as Cornelius Reid, Barbara Thornton, Emma Kirkby, Anthony Rooley and Christoph Pregardien. She performs with the group "The Lady Chapel Singers" based in Philadelphia and with the group "Elysium" based in Berlin, Germany.

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

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Mount Vernon, Glasgow

Mount Vernon is a residential area in the east end of the city of Glasgow, Scotland. It directly borders Sandyhills and Foxley to the west, while Barlanark is the closest neighbourhood to the north, Barrachnie and Baillieston to the east and Carmyle to the south, although Mount Vernon is separated from these by areas of open land, including Early Braes public park and the former Kenmuir farm.

History
The area was originally part of the Parish of Old Monkland, and also of the Barony and Regality of Glasgow. From at least the Middle Ages, the rental book of the Diocese of Glasgow records it as Windy Edge or variations thereof – AD 1526, Jame Browyn rentalit in vs xd land in the Wyndy Hege. In 1742 a Glasgow merchant named Robert Boyd purchased the 'Old Extent of Windyedge' and renamed it Mount Vernon, in honour of Admiral Edward Vernon of the Royal Navy who was famous at that time for his expedition against the Spanish Main. Another Glasgow merchant, George Buchanan, whose family had extensive interests in tobacco trade purchased the land in 1758 and built an extension to the existing house re-modelling it as a country mansion.

The Mount Vernon of the early 21st century is generally affluent and suburban in character; administratively, the area forms part of the Shettleston ward of Glasgow City Council.

Mount Vernon Old Railway, This railway run through Mount Vernon Park and along Carrick Drive, Picture of Map Old Monkland 1950s from National Library of Scotland

Landfill site
To the south of Mount Vernon is Greenoakhill Quarry, one of Europe's largest urban landfill sites, operated by Paterson Quarries Ltd. The landfill has been operational since 1955 and receives an assortment of high level waste from all over Scotland. The site covers 230 acres and is licensed to take up to 500,000 tonnes of waste per year. Landfill gas from the site is collected to fuel gas turbines generating electricity which is fed back into the National Grid.

Greenoakhill Forest is an ongoing project to transform parts of the landfill site no longer in use into public parkland. The first phase of the restored site is open, with newly planted trees, paths and benches.

Transport
Mount Vernon railway station is on the Glasgow – Whifflet Line. Services to Glasgow Central depart at xx19 and xx49; services to Whifflet depart xx26 and xx56.

The M74 motorway runs to the south of Mount Vernon, with Junction 3 the nearest with access to the network in both directions.

Buildings

 * Mount Vernon House was situated on the high ground approximately 125 m to the west of Mount Vernon Avenue. It was demolished in the early part of the 20th century.
 * Mount Vernon Community Hall is located within Mount Vernon Park. It is operated as a registered charity and has been serving the community since October 1971; the building is owned by Glasgow City Council. The day-to-day running of the community hall is run by a group of Mount Vernon Community Volunteers. Regular community events and activities take part at the community hall. The Centre Playgroup is also based there.
 * Mount Vernon Bowling and Tennis Club, established in the 1890s, is located on Central Grove.

 * Kenmuir Mount Vernon Church (merged with Carmyle's congregation in the 2010s) is located on London Road (A74) at the southern end of the neighbourhood.

Notable people
Celebrities living there include Elaine C. Smith and Cameron McKenna.

John Barrowman and Sir John William McNee were born in Mount Vernon.

Parks

 * Mount Vernon Park: has a play park, MUGA pitch football pitches, community Garden, woodland nature trail
 * Barrachnie Park: has a Skate park, rugby pitches, running track
 * Early Braes Park: has large grass areas for nature with Tollcross burn running through it.

title: Mount Vernon, Glasgow


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Lists of United States state symbols

U.S. states, districts, and territories have representative symbols that are recognized by their state legislatures, territorial legislatures, or tradition. Some, such as flags, seals, and birds have been created or chosen by all U.S. polities, while others, such as state crustaceans, state mushrooms, and state toys have been chosen by only a few.

Insignia

 * Insignia
 * Coats of arms
 * Colors
 * Flags
 * Governor standards
 * Mottos
 * Nicknames
 * Seals
 * Governor seals

Flora and fauna

 * Amphibians
 * Bats
 * Birds
 * Crustaceans
 * Dinosaurs
 * Dog breeds
 * Fish
 * Flowers
 * Grasses
 * Horse breeds
 * Insects
 * Mammals
 * Microbes
 * Mushrooms
 * Plants
 * Reptiles
 * Seashells
 * Trees

Geology

 * Fossils
 * Minerals, rocks, stones, and gemstones
 * Soils

Other

 * Dances
 * Firearms
 * Foods
 * Beverages
 * Musical instruments
 * Poems
 * Ships
 * Songs
 * Sports
 * Tartans
 * Theaters
 * Toys

Lists by state, territory, and district

 * Alabama
 * Alaska
 * American Samoa
 * Arizona
 * Arkansas
 * California
 * Colorado
 * Connecticut
 * Delaware
 * District of Columbia
 * Florida
 * Georgia
 * Guam
 * Hawaii
 * Idaho
 * Illinois
 * Indiana
 * Iowa
 * Kansas
 * Kentucky
 * Louisiana
 * Maine
 * Maryland
 * Massachusetts
 * Michigan
 * Minnesota
 * Mississippi
 * Missouri
 * Montana
 * Nebraska
 * Nevada
 * New Hampshire
 * New Jersey
 * New Mexico
 * New York
 * North Carolina
 * North Dakota
 * Northern Mariana Islands
 * Ohio
 * Oklahoma
 * Oregon
 * Pennsylvania
 * Puerto Rico
 * Rhode Island
 * South Carolina
 * South Dakota
 * Tennessee
 * Texas
 * U.S. Virgin Islands
 * Utah
 * Vermont
 * Virginia
 * Washington
 * West Virginia
 * Wisconsin
 * Wyoming

title: Lists of United States state symbols


text:
Verger

A verger (or virger, so called after the staff of the office, or wandsman in British English, though archaic) is a person, usually a layperson, who assists in the ordering of religious services, particularly in Anglican churches.

Etymology

The title of verger arises from the ceremonial rod they traditionally carried known as a virge (from the Latin virga, "branch, staff, rod"; see virgule). The Maces of State used in the House of Lords and the House of Commons of the British Parliament are examples of another modern use of the medieval virge. In former times, a verger might have needed to use his virge to keep back animals or an overenthusiastic crowd from the personage he was escorting or even to discipline unruly choristers.

History
The office of verger has its roots in the early days of the Church of England's history. The Order shares certain similarities with the former Minor Orders of Porter and Acolyte. Historically, vergers were responsible for the order and upkeep of a house of worship, including the care of the church buildings, its furnishings, and sacred relics, preparations for liturgy, conduct of the laity, and grave-digging responsibilities. Although there is no definitive historical examination of the office of verger, evidence from Rochester, Lincoln, Exeter, and Salisbury Cathedrals points to the existence of vergers even in the 16th century. Koster is the Dutch word for 'sexton' or 'verger' (the equivalent German word is Küster), derived from the Latin custos ('guard'). The symbol of a guild of cathedral vergers is the crossed keys.

Duties
During the service itself, a verger's main duty is ceremonially to precede the religious participants as they move about the church; they do not typically take any speaking part in the service itself. It could be argued that a verger's main pride during a service lies in their inconspicuousness; vergers often play a very prominent role "behind the scenes"—helping to plan the logistical details of service and discreetly shepherding the clergy through it (in some churches these latter duties are handled by a Master of Ceremonies, while the verger functions as a sort of marshal in the procession).

Robes
The typical robes of a verger are a black gown worn over a black cassock. The gown is somewhat like an academic gown and is open-fronted in the English tradition. It is common for a verger's gown to bear the arms of the church, usually on one or both sleeves. It can be trimmed with velvet, which may be in another colour (a colour prominently associated with the cathedral, for instance). Formally, a jabot may be worn at the neck.

Less formally, a verger may wear a gown without a cassock below, or, conversely, a cassock without the gown. In more modern settings, a verger might wear a scapular instead of a gown.

If a verger also serves at the altar during divine worship, the gown is often replaced with a surplice.

Modern function
Some vergers see their role as one of welcoming or hospitality, encompassing duties such as arranging weddings and funerals or meeting important visitors such as bishops. Vergers at Westminster Abbey, for example, also lead guided tours.

In small churches, the office of the verger is often combined with that of the sexton, who is responsible for maintaining church buildings and grounds. In some organizations the functions of the sexton and the verger are performed by the same person. Equally, many churches have neither a verger nor a sexton and these duties fall to the churchwardens.

In 20th-century debates in the Anglican Church in Australia, some clergy argued that women should be allowed to serve as churchwardens because their experience in housekeeping would lead them to check up on the work of the vergers, indicating that many vergers performed maintenance.

Catholic Church
The office of the verger has, for the most part, disappeared in the Catholic tradition, the closest function being that of the sexton or the head or senior usher, particularly in those churches (usually large establishments, like St. Patrick's Cathedral in New York City or the Basilica of the National Shrine of the Immaculate Conception in Washington, DC) that have a formal, organized corps of ushers.

Cultural references
Perhaps the best-known portrait of an Anglican verger in fiction is in Somerset Maugham's short story, "The Verger". In British popular culture, the BBC sitcom Dad's Army featured a bumbling caricature of a verger named Maurice Yeatman, played by Edward Sinclair. The sitcom The Vicar of Dibley, whose title character is among the Church of England's first female vicars, also featured a female verger, the dim-witted but well-intentioned Alice Tinker (Emma Chambers).

title: Verger


text:
User talk:Soilguy5

Talk with me about philosophy

Subway
As far as I know, the Maharashtra government still has a long way to go before all the formalities are completed, before even the construction of the Bombay subway is started. I don't think that this will see the light of day so soon, the costs of the subway are exhorbitant. A cheaper transport system such as the elevated railway, as promoted by the Konkan Railways, is more likely to materialise than the subway. Let us stick to present modes of transports. Once the subway hurdles are cleared, then we can put it down. Nichalp 20:23, Jun 9, 2004 (UTC)

title: User talk:Soilguy5


text:
Morvern Callar

Morvern Callar is a 1995 experimental novel by Scottish author Alan Warner. Published as his first novel, its first-person narrative—mainly written in Scots—explores the social life and cultural interests of the titular character following the sudden death of her boyfriend.

The novel was a winner of the Somerset Maugham Award in 1996, and a critically acclaimed adaptation directed by Scottish film director Lynne Ramsay was released in 2002.

Development
Warner initially developed the narrative of Morvern Callar from the perspective of the titular character's boyfriend. He became frustrated with the rigidity of the perspective and reworked the novel to be from Callar's perspective, and to begin with her boyfriend's suicide; he commented that "I was very, very uncomfortable and nervous about it – I didn't think it was convincing. I thought the rhythm was very strange. I didn't think it was any good. And I didn't show it to anyone."

Analysis
Morvern Callar has been analyzed as dealing with "the neoliberalization of working conditions from within" in the British Isles, using a polyphonic style of narrative depicting the overlapping yet abruptly changing lives of its characters to convey precarity; hence, "the absence of any collective organization in the novel further emphasizes the divisions that precarity creates".

Reviews

 * Dunn, Angus, review of Morvern Callar by Alan Warner, in Bryan, Tom, Northwords, Issue 7, Ross and Cromarty District Council, 1996, p. 33,

title: Morvern Callar


text: User talk:68.115.164.159

title: User talk:68.115.164.159


text:
Talk:Duality of categories

This page should redirect to equivalence of categories, an article which explicitly uses the title of this page (which dual (category theory) does not). It might be good to cross link both articles to avoid confusion of "duality of categories" and "duality in category theory".

Most importantly, note that all articles currently linking to this page really mean an equivalence. --Markus Krötzsch 22:21, 12 May 2004 (UTC)

title: Talk:Duality of categories


text: User talk:66.167.235.171

title: User talk:66.167.235.171


text:
List of languages by number of native speakers in India

The Republic of India is home to several hundred languages. Most Indians speak a language belonging to the families of the Indo-Aryan branch of Indo-European (c. 77%), the Dravidian (c. 20.61%), the Austroasiatic (precisely Munda and Khasic) (c. 1.2%), or the Sino-Tibetan (precisely Tibeto-Burman) (c. 0.8%), with some languages of the Himalayas still unclassified. The SIL Ethnologue lists 424 living languages in India.

Overview
India has not had a national language since its independence in 1947. However, Rule 1976 (As Amended, 1987) of the Constitution of India, mandates Hindi and English as the "Official Languages" required "for Official Purpose of the Union." Business in the Indian parliament is transacted in either Hindi or in English. English is allowed for official purposes such as parliamentary proceedings, judiciary, communications between the Central Government and a State Government.

States within India have the liberty and powers to select their own official language(s) through legislation. In addition to the two Official Languages, the constitution recognizes 22 regional languages, named in a specific list as "Scheduled Languages". (Hindi is but English is not.) India's Constitution includes provisions detailing the languages used for the official purposes of the union, the languages used for the official purposes of each state and union territory and the languages used for communication between the union and the states.

Hindi is the most widely spoken language, mostly prevalent in the northern parts of India. The Indian census takes the widest possible definition of "Hindi" as a broad variety of the "Hindi Belt". According to 2001 Census, 53.6% of the Indian population declared that they speak Hindi as either their first or second language, in which 41% of them have declared it as their native language. 12% of Indians declared that they can speak English as a second language.

Hindi is the fastest growing language of India, followed by Kashmiri in the second place, with Meitei (officially called Manipuri) as well as Gujarati, in the third place, and Bengali in the fourth place, according to the 2011 census of India.

Thirteen languages account for more than 1% of Indian population each, and between themselves for over 95%; all of them are "scheduled languages of the constitution". Scheduled languages spoken by fewer than 1% of Indians are Santali (0.63%), Kashmiri (0.54%), Nepali (0.28%), Sindhi (0.25%), Konkani (0.24%), Dogri (0.22%), Meitei (0.14%), Bodo (0.13%) and Sanskrit (In the 2001 census of India, 14,135 people reported Sanskrit as their native language). The largest language that is not "scheduled" is Bhili (0.95%), followed by Gondi (0.27%), Khandeshi (0.21%), Tulu (0.17%) and Kurukh (0.10%).

As per 2011 census, 26% of Indians are bilingual and 7% are trilingual.

India has a Greenberg's diversity index of 0.914—i.e. two people selected at random from the country will have different native languages in 91.4% of cases.

As per the 2011 Census of India, languages by highest number of speakers are as follows: Hindi, Bengali, Marathi, Telugu, Tamil, Gujarati, Urdu, Kannada, Odia, Malayalam.

List of languages by number of native speakers
Ordered by number of speakers as first language.

More than one million speakers
The 2011 census recorded 31 individual languages as having more than 1 million native speakers (0.1% of total population). The languages in bold are scheduled languages (the only scheduled language with less than 1 million native speakers is Sanskrit). The first table is restricted to only speaking populations for scheduled languages.

* Excludes figures of Paomata, Mao-Maram and Purul sub-divisions of Senapati district of Manipur for 2001.

** The percentage of speakers of each language for 2001 has been worked out on the total population of India excluding the population of Mao-Maram, Paomata and Purul subdivisions of Senapati district of Manipur due to cancellation of census results.

List of mother tongues by number of speakers
Each of the languages of the 2001 census subsumes one or more mother tongues. Speaker numbers are available for these mother tongues and they are also included in the speaker numbers for their respective language. For example, the language Telugu (with a total of 81,127,740 speakers) includes the mother tongues of Telugu (with 80,912,459 speakers), Vadari (198,020 speakers) and "Others" (17,261 speakers). The General Notes from the 2001 census define "mother tongue" as "the language spoken in childhood by the person's mother to the person. If the mother died in infancy, the language mainly spoken in the person's home in childhood will be the mother tongue."

The following table lists those mother tongues that have more than one million speakers according to the 2011 census:

General references

 * Data table of Census of India, 2001
 * Language Maps from Central Institute of Indian Languages
 * Scheduled Languages in descending order of speaker's strength – 2001
 * Comparative ranking of scheduled languages in descending order of speaker's strength-1971, 1981, 1991 and 2001
 * Census data on Languages
 * C-16 Population By Mother Tongue – Town Level
 * C-16 Population By Mother Tongue


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Talk:Ostwind

Why call it "Ostwind (tank)" instead of just "Ostwind"? I think this is the primary Ostwind english readers would look up.

I also removed the note of discrepency. Considering that it's only off by one, and therefore more accurate then pretty much every other figure we have, I don't think it's really all that relevant. Oberiko 22:35, 12 May 2004 (UTC)

 * I have no objections to just calling it "Ostwind"...and the difference of one tank is indeed small enogh to let it slip by :p Ferkelparade 13:34, 13 May 2004 (UTC)

I am under the impression that this imagecould be considered fair use; but I'm a n00b to edits and not really sure how to go about it all, especially with regards to images. It comes from this site which also has other old pictures of several WWII armor which may be of use. ~Springfinger 21:00 19 Sept 2006

title: Talk:Ostwind


text:
User talk:81.5.140.5

March 2022
Hello, I'm Cutlass. I wanted to let you know that one or more of your recent contributions have been undone because they did not appear constructive. If you would like to experiment, please use the sandbox. If you have any questions, you can ask for assistance at the Teahouse. Thanks. Cutlass Ciera 19:17, 5 March 2022 (UTC)

title: User talk:81.5.140.5


text:
Cindy Cashdollar

Cindy Cashdollar (born May 25, 1956) is an American musician specializing in steel guitar and Dobro. She grew up in Woodstock, New York, where she perfected her skills by playing with bluegrass musician John Herald, blues musicians Paul Butterfield, and Levon Helm and Rick Danko of The Band. After residing in Austin, Texas, for 23 years, she has now returned to her native Woodstock, New York.

Cashdollar received five Grammy awards while playing for eight years with Asleep at the Wheel, and has also backed such noted performers as Bob Dylan, Leon Redbone, Redd Volkaert, Carla Olson and Ryan Adams as a member of his band The Cardinals. In August 2019, Cashdollar recorded dobro and lap steel on "Save Your Love For Me", the new Grayson Hugh record. In 2003, the Academy of Western Artists recognized Cashdollar as Instrumentalist of the Year Award in the Western Swing Music genre. She was inducted into The Austin Chronicle Hall of Fame in 2011–12.

She authored a series of instructional videos on her instruments and released her first solo album, Slide Show, in 2004. During the fall of 2004 she was a member of Ryan Adams's band The Cardinals playing the steel guitar live on stage. She also went into the studio with this band and played on the album Cold Roses, although she did not tour the album with Adams & The Cardinals and was replaced in 2005 by Jon Graboff.

From 2005 to 2008, Cashdollar played with Elana James, Redd Volkaert (and, sometimes, Nate Rowe), as The High Flyers, appearing on A Prairie Home Companion twice, as well as playing Austin area venues.

In 2006, she toured with Van Morrison promoting his country and western album, Pay the Devil. She appeared with him at the Austin City Limits Music Festival, on September 15, 2006 (subsequently released on Van Morrison's Live at Austin City Limits Festival limited edition recording), and on the television show Austin City Limits featuring Van Morrison, broadcast in November 2006. Cashdollar plays steel guitar on two of the tracks on Morrison's March 2008 studio album, Keep It Simple. She is an eponymous member of Dave Alvin's 2009 project, Dave Alvin and the Guilty Women.

title: Cindy Cashdollar


text:
Off side

The off side is a particular half of the field in cricket.

From the point of view of a right-handed batsman facing the bowler, it is the right-hand side of the field, or the half of the field in front of the right-handed batsman when he or she assumes the batting stance. The off side consists of the entire half of the field stretching from behind the batsman-end wicket, around third man, square of the wicket on the off side, the covers, and mid/long off, up to the opposite bowler-end wicket and, behind it, the straight field. To the opposing bowler facing a right-hand batsman, it is the left side of the field. The left-handed batsman's off side is to the batsman's left and to the opposing bowler's right.

In the diagram, fielding positions are shown for a right hand bowler approaching over-the-wicket to bowl to a right-handed batsman. Off side field positions in this diagram include the slips, gully, point, cover, mid-off, third man, and long off. Because of the typical line of attack of bowlers, the off side is usually more well-defended than the leg side, which in the diagram includes the fielding positions fine leg, square leg, mid-wicket, mid-on, and long on.

Some common batting strokes that are played through the off side include straight drive to long off, the cover drive, the square cut, the late cut, and the glance to third man. Batsmen skilled in strokeplay through these regions, particularly square of the wicket and through the covers, often become favorites for fans to watch because of the relative difficulty of mastering such shots. Various batsmen have distinguished their style and success through the off side, including such greats as Sachin Tendulkar, Brian Lara, Garfield Sobers, Kumar Sangakkara, Jacques Kallis, Rohit Sharma, Chris Gayle, Virender Sehwag, and Sourav Ganguly.

title: Off side


text: Template:Acorn computers, clones and compatibles


text:
Complete Heyting algebra

In mathematics, especially in order theory, a complete Heyting algebra is a Heyting algebra that is complete as a lattice. Complete Heyting algebras are the objects of three different categories; the category CHey, the category Loc of locales, and its opposite, the category Frm of frames. Although these three categories contain the same objects, they differ in their morphisms, and thus get distinct names. Only the morphisms of CHey are homomorphisms of complete Heyting algebras.

Locales and frames form the foundation of pointless topology, which, instead of building on point-set topology, recasts the ideas of general topology in categorical terms, as statements on frames and locales.

Definition
Consider a partially ordered set (P, ≤) that is a complete lattice. Then P is a complete Heyting algebra or frame if any of the following equivalent conditions hold:

 * P is a Heyting algebra, i.e. the operation $$(x\land\cdot)$$ has a right adjoint (also called the lower adjoint of a (monotone) Galois connection), for each element x of P.

 * For all elements x of P and all subsets S of P, the following infinite distributivity law holds:
 * $$x \land \bigvee_{s \in S} s = \bigvee_{s \in S} (x \land  s).$$

 * P is a distributive lattice, i.e., for all x, y and z in P, we have
 * $$x \land ( y \lor z ) = ( x \land  y ) \lor ( x \land  z )$$
 * and the meet operations $$(x\land\cdot)$$ are Scott continuous (i.e., preserve the suprema of directed sets) for all x in P.

The entailed definition of Heyting implication is $$a\to b=\bigvee\{c \mid a\land c\le b\}.$$

Using a bit more category theory, we can equivalently define a frame to be a cocomplete cartesian closed poset.

Examples
The system of all open sets of a given topological space ordered by inclusion is a complete Heyting algebra.

Frames and locales
The objects of the category CHey, the category Frm of frames and the category Loc of locales are complete Heyting algebras. These categories differ in what constitutes a morphism:

 * The morphisms of Frm are (necessarily monotone) functions that preserve finite meets and arbitrary joins.

 * The definition of Heyting algebras crucially involves the existence of right adjoints to the binary meet operation, which together define an additional implication operation. Thus, the morphisms of CHey are morphisms of frames that in addition preserves implication.

 * The morphisms of Loc are opposite to those of Frm, and they are usually called maps (of locales).

The relation of locales and their maps to topological spaces and continuous functions may be seen as follows. Let $$f: X\to Y$$ be any map. The power sets P(X) and P(Y) are complete Boolean algebras, and the map $$f^{-1}: P(Y)\to P(X)$$ is a homomorphism of complete Boolean algebras. Suppose the spaces X and Y are topological spaces, endowed with the topology O(X) and O(Y) of open sets on X and Y. Note that O(X) and O(Y) are subframes of P(X) and P(Y). If $$f$$ is a continuous function, then $$f^{-1}: O(Y)\to O(X)$$ preserves finite meets and arbitrary joins of these subframes. This shows that O is a functor from the category Top of topological spaces to Loc, taking any continuous map
 * $$f: X\to Y$$

to the map
 * $$O(f): O(X)\to O(Y)$$

in Loc that is defined in Frm to be the inverse image frame homomorphism
 * $$f^{-1}: O(Y)\to O(X).$$

Given a map of locales $$f: A\to B$$ in Loc, it is common to write $$f^*: B\to A$$ for the frame homomorphism that defines it in Frm. Using this notation, $$O(f)$$ is defined by the equation $$O(f)^* = f^{-1}.$$

Conversely, any locale A has a topological space S(A), called its spectrum, that best approximates the locale. In addition, any map of locales $$f: A\to B$$ determines a continuous map $$S(A)\to S(B).$$ Moreover this assignment is functorial: letting P(1) denote the locale that is obtained as the power set of the terminal set $$1=\{*\},$$ the points of S(A) are the maps $$p: P(1)\to A$$ in Loc, i.e., the frame homomorphisms $$p^*: A\to P(1).$$

For each $$a\in A$$ we define $$U_a$$ as the set of points $$p\in S(A)$$ such that $$p^*(a) =\{*\}.$$ It is easy to verify that this defines a frame homomorphism $$A\to P(S(A)),$$ whose image is therefore a topology on S(A). Then, if $$f: A\to B$$ is a map of locales, to each point $$p\in S(A)$$ we assign the point $$S(f)(q)$$ defined by letting $$S(f)(p)^*$$ be the composition of $$p^*$$ with $$f^*,$$ hence obtaining a continuous map $$S(f): S(A)\to S(B).$$ This defines a functor $$S$$ from Loc to Top, which is right adjoint to O.

Any locale that is isomorphic to the topology of its spectrum is called spatial, and any topological space that is homeomorphic to the spectrum of its locale of open sets is called sober. The adjunction between topological spaces and locales restricts to an equivalence of categories between sober spaces and spatial locales.

Any function that preserves all joins (and hence any frame homomorphism) has a right adjoint, and, conversely, any function that preserves all meets has a left adjoint. Hence, the category Loc is isomorphic to the category whose objects are the frames and whose morphisms are the meet preserving functions whose left adjoints preserve finite meets. This is often regarded as a representation of Loc, but it should not be confused with Loc itself, whose morphisms are formally the same as frame homomorphisms in the opposite direction.

Literature

 * P. T. Johnstone, Stone Spaces, Cambridge Studies in Advanced Mathematics 3, Cambridge University Press, Cambridge, 1982. (ISBN 0-521-23893-5)

 * Still a great resource on locales and complete Heyting algebras.

 * G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, and D. S. Scott, Continuous Lattices and Domains, In Encyclopedia of Mathematics and its Applications, Vol. 93, Cambridge University Press, 2003. ISBN 0-521-80338-1

 * Includes the characterization in terms of meet continuity.

 * Francis Borceux: Handbook of Categorical Algebra III, volume 52 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, 1994.

 * Surprisingly extensive resource on locales and Heyting algebras. Takes a more categorical viewpoint.

 * Steven Vickers, Topology via logic, Cambridge University Press, 1989, ISBN 0-521-36062-5.

title: Complete Heyting algebra


text:
Leg side

The leg side, or on side, is defined to be a particular half of the field used to play the sport of cricket. It is the side of the field that corresponds to the batsman's non-dominant hand, from their perspective.

From the point of view of a right-handed batsman facing the bowler, it is the left hand side of the cricket field (being to the bowler's right). With a left-handed batsman the on side is to the batsman's right (and to the bowler's left).

A cricket field is notionally divided into two halves, by an imaginary line running down the long axis of the pitch. In normal batting stance, the striking batsman stands side on to the bowler. The leg side is the half of the field behind the batsman. The half of the field in front of him is called the off side.

In the picture, the bowler is bowling from the bottom half of the image, the right-handed batsman (S), facing him sideways on, has his legs more on the right side of the picture, the leg-side. If the ball goes down that side of the pitch it will be "on" the batsman's legs, the on side.

The definition is relative to the batsman. If the batsman were to directly face the bowler, the leg side would be:
 * on the left side for a right-handed batsman, but
 * on the right side for a left-handed batsman.

The leg side is usually less well defended with fielders than the off side, because of the typical line of attack of the bowlers, which is frequently on or outside off stump. This makes it more difficult to hit the ball to the leg side because it involves swinging the bat across the line of the ball, which can lead to mishits and catches.

While the terms "leg side" and "on side" can refer to an entire half of the field, each term is often used to denote only part of this half. When the batsman plays the ball into this half in front of the wicket, it is usually said that the ball has been played to the on side. However, when the ball is played into the region level with or behind the wicket, it is said that the ball has been played to the leg side. The names of fielding positions often include the words "leg" or "on", and they reflect this convention. For example, fine leg is located behind the wicket, whereas mid on is located in front of it. When the batsman steps backwards from his normal batting stance on the crease as the ball is bowled, he is said to be moving towards the leg side.

Comparison with baseball
Since the leg side comprises the half of the field behind the batsman, with a right-handed batsman it is roughly analogous to the half of the baseball field that includes left field and third base. With a left-handed batsman, the leg side is analogous to the half that includes right field and first base. Thus hitting to the leg side is directly visually analogous to "pull" hitting in baseball (though since all fair territory in baseball is forward of the batter, "on" would more exactly match this area of the field). Conversely, off is analogous to baseball's "opposite-field" hitting.

title: Leg side


text:
Robert Williams

Robert, Rob, Robbie, Bob or Bobby Williams may refer to:

Film

 * Robert Williams (actor, born 1894) (1894–1931), American stage and film actor
 * Robert B. Williams (actor) (1904–1978), American film actor
 * Robert Guillaume (1927–2017), American film actor whose birth name is Robert Williams.
 * R. J. Williams (born 1978), American former child actor and later internet entrepreneur
 * Rob Williams (filmmaker), American film director

Music

 * Robert Pete Williams (1914–1980), American blues guitarist
 * Chocolate Williams (Robert Williams Jr., 1916–1984), jazz bassist and blues vocalist
 * Bob Williams (singer) (1918–2003), American singer and one of the Williams Brothers
 * Robert Williams (singer) (1949–2022), Greek singer and composer
 * Robert S. Williams (born 1949), bassoon player of the Detroit Symphony Orchestra
 * Robert Williams (drummer) (born 1955), Captain Beefheart, Hugh Cornwell, and solo
 * Robbie Williams (born 1974), British pop singer and former member of Take That
 * Rob Williams (1979–2009), partner of business Dolphin Music
 * Meek Mill (Robert Rihmeek Williams, born 1987), American rapper

Writers

 * Robert Williams (poet) (1744–1815), Welsh poet
 * Robert Williams (Robert ap Gwilym Ddu) (1767–1850), Welsh-language poet
 * Robert Williams (Trebor Mai) (1830–1877), Welsh-language poet
 * Robert Moore Williams (1907–1977), American science fiction novelist
 * Robert Williams (artist) (born 1943), cartoonist and painter
 * Rob Williams (comics), British comic writer

Military

 * Robert Williams (Royal Navy officer) (1765–1827) English rear-admiral in the Royal Navy
 * Robert Williams (adjutant general) (1829–1901), American brigadier general and Adjutant General of the US Army
 * Robert Williams (Medal of Honor) (1837–unknown), American sailor and Medal of Honor recipient
 * Robert B. Williams (general) (1901–1977), World War II major general in the United States Army Air Forces
 * Robert H. Williams (soldier) (1908–1983), American Marine brigadier general

UK

 * Sir Robert Williams, 2nd Baronet (c. 1627–1678), MP for Carnarvonshire, 1656–1658, and for Carnarvon Boroughs, 1659
 * Robert Williams (died 1763) (1695–1763), MP for Montgomeryshire, 1740–1741 and 1742–1747
 * Robert Williams (1735–1814) (1735–1814), MP for Dorchester, 1807–1812
 * Sir Robert Williams, 9th Baronet (1764–1830) of Penryn, MP for Carnarvonshire, 1790–1826, and for Beaumaris, 1826–1831
 * Robert Williams (1767–1847) (1767–1847), MP for Dorchester, 1812–1835
 * Robert Williams (1811–1890) (1811–1890), MP for Dorchester, 1835–1841
 * Sir Robert Williams, 1st Baronet, of Bridehead (1848–1943), Conservative MP for West Dorset, 1895–1922

US

 * Robert Williams (Mississippi politician) (1773–1836), Governor of the Mississippi Territory
 * Robert P. Williams (1841–1910), State Treasurer of Missouri, 1901–1905
 * Robert L. Williams (1868–1948), American politician, governor of Oklahoma
 * Robert R. Williams, mayor of Miami, 1937–1939
 * Bob Williams (West Virginia politician) (born 1951), American politician and state senator in West Virginia
 * Bob Williams (Washington politician), member of the Washington House of Representatives
 * Robert Q. Williams (born 1964), member of the South Carolina House of Representatives

Elsewhere

 * Robert Wynn Williams (1864–1929), member of the Queensland Legislative Assembly, Australia
 * Robert Williams (Victorian politician) (1870–1938), Australian politician
 * Robert Arthur Williams (born 1933), consultant and political figure in British Columbia, Canada
 * Robbie Williams (politician) (c. 1960–2007), Australian politician

Religion

 * Robert Williams (antiquary) (1810–1881), Welsh Anglican clergyman and Celtic scholar
 * Robert Williams (archdeacon of Carmarthen) (1863–1938), Welsh historian and Anglican priest
 * Robert Dewi Williams (1870–1955), Welsh schoolteacher, Presbyterian minister, and author
 * Robert Williams (archdeacon of Gower) (born 1951), Welsh Anglican priest
 * Robert Williams (American priest) (1955–1992), first openly gay male priest in the American Episcopal Church

Science

 * Robert Statham Williams (1859–1945), American bryologist
 * Sir Robert Williams, 1st Baronet, of Park (1860–1938), Scottish mining engineer, explorer, and railway developer
 * Robert R. Williams (1886–1965), American chemist who first synthesized vitamin B1
 * Robert Hardin Williams (1909–1979), American endocrinologist and diabetologist
 * Robert Williams (pathologist) (1916–2003), Welsh pathologist
 * Robin Williams (mathematician) (1919–2013), New Zealand mathematician, university administrator and civil servant
 * Robert Williams (English chemist) (1926–2015), Professor of Oxford University
 * Robert Williams (psychologist) (1930–2020), second president of the Association of Black Psychologists
 * Robert Williams (astronomer) (born 1940), director of STScI 1993–98; president of IAU, 2009–2012
 * Robin Williams (physicist) (Robert Hughes Williams, born 1941), Welsh physicist and academic
 * Robert H. Williams (physicist), environmental scientist at the Princeton Environmental Institute
 * Bobby G. Williams (born 1951), Jet Propulsion Laboratory engineer; namesake of asteroid 5642 Bobbywilliams

American football

 * Bob Williams (coach) (1877–1957), American college football coach
 * Bob Williams (quarterback) (1930–2016), football player for Notre Dame
 * Bobby Williams (defensive back) (1942–2012), American pro football player, St. Louis Cardinals and the Detroit Lions
 * Bob Williams (American football coach), at Livingston State Teachers College, now University of West Alabama, 1952
 * Robert Williams (quarterback), football player for Notre Dame, 1956–1958
 * Bobby Williams (born 1958), tight end, coach
 * Robert Williams (cornerback) (born 1962), former American football cornerback
 * Bobbie Williams (born 1976), American football guard
 * Robert Williams (defensive back) (born 1977), former American football cornerback

Baseball

 * Bob Williams (baseball) (1884–1962), baseball player for the New York Highlanders/Yankees
 * Bobby Williams (baseball) (1895–1978), American baseball shortstop and manager in the Negro leagues
 * Robert Williams (baseball) (1917–2000), American baseball pitcher and infielder in the Negro leagues

Basketball

 * Bob Williams (basketball, born 1931), American professional basketball player, played collegiately at Florida A&M
 * Bob Williams (basketball, born 1953), American basketball coach, most recently with UC Santa Barbara
 * Rob Williams (basketball) (1961–2014), American professional basketball player, played collegiately for Houston
 * Robert Williams III (born 1997), American professional basketball player, played collegiately for Texas A&M
 * Robert Williams (Grambling State basketball), American college basketball player for Grambling State

Cricket

 * Robert Williams (South African cricketer) (1912–1984), South African cricketer
 * Robert Williams (English cricketer) (born 1970), English former cricketer
 * Robbie Williams (cricketer) (born 1987), English cricketer for Middlesex

Football and rugby

 * Bobbie Williams (rugby union) (1865–1967), Welsh international rugby union player
 * Bobby Williams (Scottish footballer) (died 1916), Scottish footballer
 * Bob Williams (rugby) (1886–1969), Australian rugby league footballer
 * Bob Williams (Australian rules footballer) (1913–2004), Australian rules footballer with Hawthorn
 * Bobby Williams (footballer, born 1932), English footballer for Chester City
 * Bobby Williams (footballer, born 1940), English footballer
 * Robbie Williams (footballer, born 1979), English footballer for Warrington Town
 * Robbie Williams (footballer, born 1984), English footballer for Limerick
 * Robert Williams (footballer, born 1927), English footballer for Wrexham and Shrewsbury Town
 * Robert Williams (footballer, born 1932), English footballer for Mansfield Town

Other sports

 * Robert Williams (archer) (1841–1914), American archer
 * Bob Williams (rower) (1931–2017), Canadian rower
 * Robbie Williams (snooker player) (born 1986), English snooker player
 * Rob Williams (rower, born 1960), British rower
 * Rob Williams (rower, born 1985), British Olympian

Other

 * Robert A. Williams Jr., American lawyer and professor
 * Robert S. C. Williams, community service worker in Ontario, Canada
 * Robert C. Williams, the namesake of the Robert C. Williams Paper Museum
 * Robert F. Williams (1925–1996), American civil rights activist
 * Robert Wayne Williams (1952–1983), American murderer executed in Louisiana
 * Robert Williams (architect) (1848–1918), Welsh architect and social campaigner
 * Robert Williams (geometer) (born 1942), American designer, mathematician, and architect
 * Robert Williams (robot fatality) (1953–1979), the first person to be killed by a robot
 * Robert Williams (trade union leader) (1881–1936), British trade union organizer

title: Robert Williams


text:
Shoal Lake (Kenora District, Ontario)

Shoal Lake (Iskatewi-zaagaʼigan) is a lake that straddles the boundary between Ontario and Manitoba, Canada, northwest of the Lake of the Woods. Depending on the water level of Lake of the Woods, Shoal Lake runs both a tributary and distributary of Lake of the Woods and, for many practical purposes, is part of that lake.

There are two First Nations peoples, both Ojibwe, who  lay claim to much of Shoal Lake: Iskatewizaagegan 39 Independent First Nation (Shoal Lake First Nation #39) and Shoal Lake 40 First Nation.

Overview
Shoal Lake is in the Eastman Region of Manitoba and the Kenora District of Ontario, northwest of Lake of the Woods. It spans approximately 18 mi from north to south and 25 mi from east to west.

Smallmouth bass, northern pike, and walleye are its primary species of fish. At one time, it was a commercial fishery for walleye, but this was closed due to overfishing.

There are a number of private cabins in this area, and several commercial fishing lodges and resorts which offer housekeeping cabins and American-plan packages for tourists.

The lake has a history of gold mining and as gold prices rise so does the pressure to explore mining of the lake again. This pressure is being fought by local cottagers and the City of Winnipeg, which has used the lake as its main source of safe drinking water for almost 100 years. Shoal Lake falls under special and specific developmental guidelines in order to protect its water quality and unique wildlife.

Manitoba
In the Manitoba portion, Shoal Lake is a large isolated lake in the southeastern corner of the province.

Shoal Lake 40 First Nation, Ojibwe peoples, who are in the Eastman Region of Manitoba and the Kenora District of Ontario, is one of the First Nations that lays claim to the lake.

Shoal Lake is also home to Manitoba Pioneer Camp.

Winnipeg's drinking water
The City of Winnipeg has relied on the lake as its source for safe drinking water since 1919, supplied via the Greater Winnipeg Water District Aqueduct.

Before it is treated, water from Shoal Lake is stored in Deacon Reservoir, on the east side of the Winnipeg floodway, a few kilometres south of Highway 15.

Access by maintenance staff to the Aqueduct has been provided by the Greater Winnipeg Water District Railway, operated by the City, since 1916. The Railway formerly provided passenger and freight rail services to the public, from Winnipeg to the rail station at the Shoal Lake aqueduct intake.

Greater Winnipeg Water District
The Greater Winnipeg Water District (GWWD) was established in 1913 as a collaboration between the City of Winnipeg and its neighbouring municipalities, who decided to invest CA$13.5 million to access Shoal Lake.

Winnipeg Mayor Thomas R. Deacon spearheaded making Shoal Lake the city's water source, a project he had supported long before becoming mayor in 1913. In January 1913, a series of meetings was held between Winnipeg and the municipalities, who reached an agreement on draft legislation to form a water district.

On February 15 that year, An Act to incorporate the ‘Greater Winnipeg Water District,’ was passed by the Manitoba Legislature. The areas included in the district were the City of Winnipeg, City of St. Boniface, Town of Transcona, and Rural Municipality of St. Vital, as well as a part of the Rural Municipality of Fort Garry, the Rural Municipality of Assiniboia, and the Rural Municipality of Kildonan.

The GWWD was eventually succeeded by the City of Winnipeg Water and Waste Department.

title: Shoal Lake (Kenora District, Ontario)


text:
Lynne Ramsay

Lynne Ramsay (born 5 December 1969) is a Scottish film director, writer, producer, and cinematographer, best known for the feature films Ratcatcher (1999), Morvern Callar (2002), We Need to Talk About Kevin (2011), and You Were Never Really Here (2017). She has worked together with actors and actresses such as Tilda Swinton, Samantha Morton, Ezra Miller, Tommy Flanagan and Joaquin Phoenix. The latter of which she is working with on a second feature film. Ramsay was also slated to direct The Lovely Bones until she was replaced by the film's production company with director Peter Jackson. As of 2024, Ramsay is working on numerous feature films that have yet to be released.

Her works are marked by a fascination with children and young people and the recurring themes of grief, guilt, death, and its aftermath. They are low on dialogue and explicit story exposition, and instead use images, vivid details, music, and sound design to create their worlds.

Early life and education
Ramsay was born on 5 December 1969 in Glasgow. Her parents introduced her to movies at an early age through the work of Bette Davis, Nicolas Roeg, Alfred Hitchcock, and Michael Curtiz. She also credits the 1939 film The Wizard of Oz as an early inspiration.

Ramsay had an early passion for photography. She studied fine art and photography at Napier College, Edinburgh. In class she watched Maya Deren's film Meshes of the Afternoon and later cites it as a turning point in her career, inspiring her to apply to film school on a whim and encouraging her turn towards filmmaking.

In 1995, she graduated from the National Film and Television School in Beaconsfield, England, where she specialised in cinematography and direction.

Short films (1996–1998)
In 1996 Ramsay completed her debut short film Small Deaths as her graduating film at the UK's National Film and Television School. It is a series of three vignettes of children grappling with familial realities and the repercussions of their actions. Ramsay is the writer, director and cinematographer for this film. It won the 1996 Cannes Film Festival Short Film Prix du Jury. Later that same year Ramsay finished Kill the Day, her second short film. It captures a day in the life of a heroin addict recently released from jail, and tackles the theme of memory.

Gasman (1998), also written and directed by Ramsay, is about a brother and sister who attend a Christmas party with their father, and encounter two other children who are strangely familiar with him. This won her another Prix du Jury that year as well as a Scottish BAFTA for Best Short Film.

Ratcatcher and Morvern Callar (1999–2002)
Ramsay's short films impressed Ruth McCance of BBC Scotland, who approached Ramsay to write a treatment for a feature film. This movie turned into Ramsay's debut feature Ratcatcher which released in 1999 and was funded by BBC Scotland and Pathé. The film was entirely made by first-time filmmakers, as Ramsay enlisted the help of her film school colleagues. Ratcatcher is set in Maryhill, Glasgow during the binmen's strike of the 1970s and follows James (William Eadie), the child of a struggling working class family. The film received great critical success but stayed within the art house audience. It was screened at the 1999 Cannes Film Festival and opened the Edinburgh International Film Festival, winning her the BAFTA Award for Outstanding Debut by a British Writer, Director or Producer.

Morvern Callar (2002) is based on Alan Warner's existential 1995 novel of the same name. The film follows a young girl (Samantha Morton) adrift in Europe following the suicide of her boyfriend, which she doesn't report to the police. The movie has been desribed as a portrait of subversive grief and dissociation. The movie's soundtrack included acts like Can, Aphex Twin, Boards of Canada, Broadcast and The Mamas & the Papas.

The Lovely Bones debacle
In 2001, it was announced Ramsay was slated to direct the adaptation of Alice Sebolds The Lovely Bones, which she had read in a manuscript form prior to its publication. Her script told the story of the murder of a girl from her father's perspective. Shortly after the book turned into a global bestseller resulting in more pressure. Ramsay has said in interviews "People started to call it ‘The Lovely Money,’ they were getting greedy around it. And I could feel the vibes. It became like the Holy Bible, I kept handing in drafts and I thought they were good, but it was like ‘But that’s not exactly like the book, the book’s going to be a success.’ That was the mistake they made with the project." Then Film4, which had signed her onto the project, was massively downsized and the head of the company finally gave into the pressure coming from Hollywood big shots such as Steven Spielberg, and unceremoniously replaced Ramsay with Peter Jackson in 2004, when Jackson was fresh off The Lord Of The Rings saga. Ramsay has described dealing with Hollywood as a "David and Goliath situation". The Lovely Bones by Peter Jackson turned out to be a commercial and critical failure.

The loss of The Lovely Bones hurt Ramsay's self-confidence for a while, and the following year was made even more difficult for Ramsay, as both her father and her close friend, Liana Dognini, died. Dognini had been Ramsay's co-writer on Morvern Callar and the unrealized The Lovely Bones script.

We Need To Talk About Kevin and Jane Got a Gun dispute (2010–2015)
After a long hiatus Ramsay returned in 2011 with We Need to Talk About Kevin. The film, based on Lionel Shriver's novel, is about a mother (Tilda Swinton) dealing with the aftermath of a school massacre committed by her own son (Ezra Miller). It is again directed by Ramsay and this time co-written with her then-husband Rory Kinnear. Ramsay recalls working together with Jonny Greenwood for the soundtrack of the movie as an especially exciting part of the process.

Starting in 2011, Ramsay was sharing plans to direct a modern science-fiction adaptation of Herman Melville's Moby Dick called Mobius. The film was to be set in space, and deal with themes of psychology and claustrophobia. Ramsay explained, "So we're creating a whole new world, and a new alien. [It's] a very psychological piece, mainly taking place in the ship, a bit like Das Boot, so it's quite claustrophobic. It's another monster movie, cos the monster's Ahab." She secured funding for the project in 2012, but as of 2023 the film was still a future project.

The short film Swimmer (2012), was co-commissioned by BBC Films, Film4 and the London Organising Committee of the Olympic and Paralympic Games. It won a BAFTA Award for Best Short Film at the 66th British Academy Film Awards in 2013.

In 2012, Ramsay was slated to direct Jane Got a Gun, a movie about the farmer wife of an outlaw husband, who, after his gang turns on him, must defend herself with the help of an old lover. Natalie Portman signed on to star and produce the film. In March 2013, Ramsay abruptly left the project due to creative differences with producers and funders, including over the latter's demand for a happy ending. She was replaced by Gavin O'Connor. Actor Jude Law also left the production shortly after. In November 2013 news broke that the production company behind the movie was suing Ramsay for $750,000, claiming that she had not fulfilled her contractual obligations. The lawsuit also stated that Ramsay "was repeatedly under the influence of alcohol, was abusive to members of the cast and crew and was generally disruptive." Ramsay denied the allegations in a statement made shortly after. A year after parting ways, the lawsuit was resolved out of court. The public aspect of the dispute caused significant backlash against Ramsay. At the same time her marriage with Rory Kinnear came to an end. During the fallout she went to Santorini where she worked on the script that would become her next film, You Were Never Really Here. She ended up staying in Santorini for four years and in that time got pregnant with and gave birth to her daughter in Athens. In April 2013, she was selected as a member of the main competition jury at the 2013 Cannes Film Festival. In 2015, she was named as a member of the jury for the main competition at the 2015 Venice Film Festival.

You Were Never Really Here and upcoming projects (2016–present)
You Were Never Really Here, an adaptation of Jonathan Ames's novella of the same name, premiered to wide critical acclaim at the 70th Cannes Film Festival in 2017, where it received a standing ovation, and Ramsay won the Best Screenplay award. The film, starring Joaquin Phoenix as Joe, a war veteran and hitman saving young girls from sex trafficking, was picked up by Amazon Studios. It follows a "shattered [...] narrative structure" in trying to capture the effects of PTSD on the mind. The movie also marks the second collaboration with Jonny Greenwood. She later said she "found her soulmate in making movies" in Phoenix.

In 2018, she revealed she had started writing a script that she describes as an "epic environmental horror". In November 2020, it was announced Ramsay would be filming an adaptation of Stephen King's 1999 novel The Girl Who Loved Tom Gordon. The movie is co-written by Christy Hall, who co-created the Netflix series I Am Not Okay With This, and produced by Christine Romero and Roy Lee of Vertigo Entertainment among others.

Brigitte, a short documentary on Brigitte Lacombe, was released in 2019 after being commissioned as part of Miu Miu's Women's Tales series. The movie sees both women, who usually prefer being behind the camera, shooting each other.

At the Valencia International Film Festival in 2021 Ramsay revealed that she was working on another movie with Joaquin Phoenix called Polaris or Dark Slides. The film would also co-star Rooney Mara. As of August 2023, the production of the movie wrapped up.

In May 2022, Ramsay announced that she was working on a film adaptation of Margaret Atwood's Stone Mattress. The film, which is set to star Julianne Moore, Sandra Oh and Kyle Chandler, has been picked up by Amazon Studios. Ramsay says about the movie "regarding the overturning of Roe v Wade in America this story [...] feels more important than ever." The movie is set in the Arctic and Greenland.

Later that same year, it was announced that Ramsay would be directing an adaptation of Ariana Harwicz’s novel Die, My Love, which will be produced by Martin Scorsese and Jennifer Lawrence through Excellent Cadaver. Lawrence will additionally star as a woman who is driven to insanity by her marriage and childbirth. Ramsay said that Lawrence sent her a copy of the book, which is about postpartum depression and bipolar disorder, noting that the film itself would be funny, and that the movie would "probably" be her next film after the 2023 Hollywood strikes. As of June 2024, local news reported that the movie would begin production that summer.

In 2024, Variety reported Ramsay was writing yet another script with Townend, titled Hierarchies. No additional information about the scope of the project was released.

Personal life
Ramsay was previously married to Rory Stewart Kinnear, a writer and musician. Her niece, Lynne Ramsay Jr., has starred in multiple of her early short films.

Ramsay has one daughter. In an interview with The Guardian Ramsay shared that We Need To Talk About Kevin stars Tilda Swinton and John C. Reilly are the godparents of the child.

Influences and themes
In 1999, before the release of Ratcatcher, she cited Nan Goldin, Richard Billingham, Terrence Malick, Andrei Tarkovsky and John Cassavetes as her creative mentors. In that same interview she spoke about Robert Bresson's book Notes on the Cinematographer as "a little bible [...] in film school". Ramsay has also noted Rainer Werner Fassbinder's Fear Eats the Soul, David Lynch's Blue Velvet and Ingmar Bergman's The Virgin Spring as deeply moving movie-going experiences.

Ramsays films explore themes of death, rebirth, childhood, loss of innocence, guilt and memory. Many of her movies also deal with grief and its aftermath.

Critical response
Los Angeles Times columnist Mark Olsen considered Ramsay "one of the leading lights of young British cinema", describing her additionally as "among the most celebrated British filmmakers of her generation." The Harvard Film Archive describes Ramsay as "an uncompromising filmmaker fascinated by the tremendous power of cinema to appeal directly to the senses and awaken new depths in our audio-visual imagination. Immersive and at times almost overwhelming, Ramsay's films abound with uncommon imagery arresting for its remarkable use of texture, composition, color, music and sound." British film critic Jonathan Romney, wrote on the topic of We Need to Talk About Kevin, "Ramsay thinks not in concepts but in images. She doesn't make intellectual films, but ones that are close to music, taking visuals to the point of abstraction."

In 2007, Ramsay was rated number 12 in Guardian Unlimited's list of the world's 40 best directors working at the time.

Filmography
Feature films

Short films

Awards and nominations
On 8 October 2013, Ramsay was awarded an honorary doctorate by the University of Edinburgh for her contribution to British film.

title: Lynne Ramsay


text:
Viola arvensis

Viola arvensis is a species of violet known by the common name field pansy. It is native to Europe, western Asia, and North Africa, and it is known on other continents as an introduced species and a weed of disturbed and cultivated areas.

Viola arvensis was shown to contain cyclotides, a class of peptides found in plants. The peptide cycloviolacin O2 in particular has shown to possess cytotoxic activity against human cancer cells and is therefore looked at as a potential drug lead.

Description
It is an herbaceous annual plant with serrated leaves, and usually flowers with white all over, except the bottom petal (Although there are actually flowers with a tinge of purple at the top) and dehiscent capsules. It reproduces by seed. It grows 20 centimeters tall.

title: Viola arvensis


text:
Talk:Level set

revision
Hello fellow editors,

I have revised the article, since it lacked references and contained too much technical information that belongs elsewhere. Please comment.

Sasha (talk) 19:37, 28 August 2011 (UTC)

 * Then I would like to know wehere the technical information belongs to? I really liked the section []
 * 141.5.26.83 (talk) 15:56, 8 November 2011 (UTC)
 * It is possible that I erased too much, the picture is nice. But I do think the article should remain reasonably short. Sasha (talk) 20:07, 8 November 2011 (UTC)
 * I think you erased WAY too much, as the article borders on useless now to anyone who doesn't already know exactly what a level set is. As asked, if all that information doesn't belong here, then where does it belong? I definitely support a return to the version linked by the IP-user above. --Arvedui (talk) 21:03, 31 May 2012 (UTC)

 * I do not agree with your assessment of the content removed as "irrelevant". As for lacking sources, that should be very easy to correct.  The terms "isotherm", "isobar", and so on, are in standard use.  The proof of the gradient property can be found in any textbook on vector calculus.  I have restored most of the deleted content.   Sławomir Biały  (talk) 17:00, 5 December 2013 (UTC)

Graphic
How about a graphic representation? It's key to economic theory.

I will do it myself if I think of it again after finals. 128.193.8.98 (talk) 21:35, 28 February 2012 (UTC)

The July 2011 version was superior
The current article contains no didactic content whereas the July 2011 one did, plus it had an awesome picture. A sign of how bad the current page is, is that I direct my students to the July 2011 page. http://en.wikipedia.org/w/index.php?title=Level_set&oldid=441776585. I guess it finally annoyed me enough to tell you about it. I don't want to step on anyone's toes so I'm not going to make changes. But seriously, change it back, or make an effort to improve the content of this page. 139.80.48.109 (talk) 03:37, 15 February 2013 (UTC)

Other definition?
In Johannes Jahn's "Introduction to the Theory of Nonlinear Optimization" it's Looks like Jahn's level set is what's called "sublevel set" in this article. So maybe it should be mentioned that there are other definitions. -Quark8967 (talk) 22:08, 6 September 2014 (UTC)
 * (X, norm) a real normed space; S a nonempty subset of X; f: S \to |R a functional
 * Epigraph E(f) = { (x, a) \in S \times |R | f(x) <= a }
 * level set for a \in |R: S_a = { x \in S | f(x) <= a }

Isn't this just the preimage?
Should this be linked with https://en.wikipedia.org/wiki/Image_(mathematics)#Inverse_image? 160.39.247.132 (talk) 14:45, 18 October 2018 (UTC)

title: Talk:Level set