title: The Blue Danube

text: When Strauss's stepdaughter, Alice von Meyszner-Strauss, asked the composer Johannes Brahms to sign her autograph-fan, he wrote down the first bars of "The Blue Danube", but added "Leider nicht von Johannes Brahms" ("Unfortunately not by Johannes Brahms").


title: The Blue Danube

text: The work commences with an extended introduction in the key of A major with shimmering (tremolo) violins and a horn spelling out the familiar waltz theme, answered by staccato wind chords, in a subdued mood. It rises briefly into a loud passage but quickly dies down into the same restful nature of the opening bars. A contrasting and quick phrase in D major anticipates the waltz before three quiet downward-moving bass notes "usher in" the first principal waltz melody.


title: The Blue Danube

text: The first waltz theme is a familiar gently rising triad motif played by cellos and horns in the tonic (D major), accompanied by the harp; the Viennese waltz beat is accentuated at the end of each 3-note phrase. The Waltz 1A triumphantly ends its rounds of the motif, and waltz 1B follows in the same key; the genial mood is still apparent.


title: The Blue Danube

text: Waltz 2A glides in quietly (still in D major) before a short contrasting middle section in B-flat major. The entire section is repeated.


title: The Blue Danube

text: A more dour waltz 3A is introduced in G major before a fleeting eighth-note melodic phrase (waltz 3B). A loud Intrada (introduction) in Gm is then played. Waltz 4A starts off in a romantic mood (it is in F major) before a more joyous waltz 4B in the same key.


title: The Blue Danube

text: After another short Intrada in A, cadencing in F-sharp minor, sonorous clarinets spell out the poignant melody of waltz 5A in A. Waltz 5B is the climax, punctuated by cymbal crashes. Each of these may be repeated at the discretion of the performer.


title: The Blue Danube

text: The coda recalls earlier sections (3A and 2A) before furious chords usher in a recap of the romantic Waltz 4A. The idyll is cut short as the waltz hurries back to the famous waltz theme 1A again. This statement is also cut short, however, by the final codetta: a variation of 1A is presented, connecting to a rushing eighth-note passage in the final few bars: repeated tonic chords underlined by a snare drum roll and a bright-sounding flourish.


title: The Blue Danube

text: A typical performance lasts around 10 minutes, with the seven-minute main piece, followed by a three-minute coda.


title: The Blue Danube

text: The "Beautiful Blue Danube" was first written as a song for a carnival choir (for bass and tenor), with rather satirical lyrics (Austria having just lost a war with Prussia). The original title was also referring to a poem about the Danube in the poet Karl Isidor Beck's hometown, Baja in Hungary, and not in Vienna. Later Franz von Gernerth wrote new, more "official-sounding" lyrics:


title: The Blue Danube

text: The specifically Viennese sentiment associated with Strauss's melody has made it an unofficial national anthem of Austria.


title: The Blue Danube

text: The piece was prominently used in Stanley Kubrick's 1968 film "". After a leap from humanity's prehistoric past to its spacefaring future, the first two-thirds of "The Blue Danube" are heard as a space plane approaches and docks with a space station; it concludes while another spacecraft travels from the station to the Moon. The piece is then reprised over the film's closing credits.


title: Tales of Arcadia

text: Tales of Arcadia is a trilogy of computer-animated science fantasy television series created for Netflix by Guillermo del Toro and produced by DreamWorks Animation and Double Dare You. The series comprising the trilogy follows the inhabitants of the small suburban town of Arcadia Oaks, which is secretly home to various supernatural creatures and the young heroes who fight against the forces of evil that lurk in the shadows.


title: Tales of Arcadia

text: Since its release, the franchise has been widely praised as an ambitious and boundary-pushing animated series, with Filmink's Travis Johnson calling it "the best children's animation to come along since ""." "Trollhunters" was nominated for nine Daytime Emmy Awards in 2017, winning more than any other animated or live-action television program that year, and the trilogy has been twice nominated for the Emmy for Outstanding Children's Animated Series. It has also received or been nominated for a BAFTA Award, several Annie Awards, Golden Reel Awards, a Saturn Award, and twice won the Kidscreen Award of "Best New Series" for the first and final chapters, "Trollhunters" and "Wizards." The franchise has been critically acclaimed for its high quality CGI animation, its dark emotional and mature tone and complex writing, voice acting, representation of Latin Americans and immigrants, themes of prejudice, music, humor, and characters.


title: Tales of Arcadia

text: The show has also spawned several original children's books and has been adapted into a series of graphic novels by Marc Guggenheim and Richard Hamilton released by Dark Horse, and a video game titled "", released on PlayStation 4, Xbox One, Nintendo Switch and Microsoft Windows.


title: Tales of Arcadia

text: In August 2020, it was announced the trilogy would be concluded with a full-length feature film titled "", which was released to Netflix on July 21, 2021.


title: Tales of Arcadia

text: Guillermo del Toro initially envisioned the idea of "" as a live-action television series. However, this was deemed impractical due to budgetary concerns of using computer generated monsters as main cast members in a live-action production, and as a result he instead turned the idea into a book he co-wrote alongside Daniel Kraus and published by Disney-Hyperion. DreamWorks Animation then optioned the book to develop as an animated feature film set to be directed by Pixar veteran Rodrigo Blaas, who stayed on as executive producer when Netflix greenlit the project as a CGI-animated television series. Marc Guggenheim was hired to pen the original screenplay for the film version, and went on to write pilot for "". Dan and Kevin Hageman were brought on as co-executive producers for the series, with Aaron Waltke, AC Bradley, and Chad Quandt joining the writers' room.


title: Tales of Arcadia

text: Production on the series and its subsequent sequels began in early 2014 and continued until the end of the franchise in 2021. The project attracted an all-star cast, including the voices of Anton Yelchin, Emile Hirsch, Mark Hamill, Kelsey Grammer, Ron Perlman, Glenn Close, Lena Headey, Steven Yeun, Anjelica Huston, Diego Luna, Nick Offerman, Tatiana Maslany, Nick Frost, Stephanie Beatriz, Alfred Molina, David Bradley, Colin O'Donoghue, John Rhys-Davies, and more throughout its six year run.


title: Tales of Arcadia

text: In November 2017, del Toro announced that "Trollhunters" would be expanded into a trilogy of interconnected animated series under the name "Tales of Arcadia." The two sequel series set to continue the story would be entitled "" and "", and would explore the secret worlds of extraterrestrials and wizards hidden in the same fictional town of "Trollhunters".


title: Tales of Arcadia

text: In April 2018, it was announced that despite the sudden passing of lead actor Anton Yelchin, the role of Jim Lake Jr. would incorporate both the voices of Yelchin and Emile Hirsch for the entirety of Part 3 of "Trollhunters" and future iterations of the series. Two characters introduced in the final season of "Trollhunters"—Aja and Krel (voiced by Tatiana Maslany and Diego Luna, respectively)—also reprised their roles and serve as the leads in "3Below". In May 2018, it was revealed that Steve Palchuk would also have his role extended into "Wizards" as well, making him and Toby Domzalski (voiced by Charlie Saxton) the first characters to encompass the entire trilogy. On July 7, 2020, it was revealed that the character of Douxie Casperan (voiced by Colin O'Donoghue) and his familiar Archie (voiced by Alfred Molina) would be introduced as the final main characters of "", rounding out the ensemble cast.


title: Tales of Arcadia

text: In 2017, Marc Guggenheim and Rodrigo Blaas continued their role as showrunners and executive producers for "3Below", with A.C. Bradley serving as story editor and head writer until her departure to work on "What If...?".


title: Tales of Arcadia

text: In 2018, Aaron Waltke and Chad Quandt returned as co-executive producers and co-showrunners with Marc Guggenheim for "," before departing to write and produce the forthcoming television series, "".


title: Tales of Arcadia

text: Dan and Kevin Hageman and Marc Guggenheim wrote the screenplay for the finale film, "", released on July 21, 2021.


title: Tales of Arcadia

text: "Tales of Arcadia" follows the inhabitants of the small suburban town of Arcadia Oaks (a fictionalized version of Arcadia, California), which is secretly home to various supernatural creatures and the young heroes who fight against the forces of evil that lurk in the shadows.


title: Tales of Arcadia

text: In "", a boy named James Lake Jr, becomes the first human to be a Trollhunter, carrying the duty of protecting both the trolls living in a secret realm known as Trollmarket and humans living in the surface world from an invasion of flesh-eating trolls known as Gumm-Gumms led by the vicious warlord, Gunmar the Skullcrusher.


title: Tales of Arcadia

text: In "", two royal siblings named Princess Aja and Crown Prince Krel Tarron, who live on the alien planet Akiridion-5, must escape to Earth when their home is taken over by an evil general named Val Morando.


title: Tales of Arcadia

text: In "", a sorcerer-in-training named Douxie Casperan must embark on a time-bending adventure to medieval Camelot in a battle with the Arcane Order to save the future of Arcadia Oaks and the world at large.


title: Tales of Arcadia

text: Finally, in "", all of the Guardians of Arcadia unite when the world is on the brink of an apocalyptic battle for the control of magic that will determine the fate of these supernatural worlds that have now converged as the Arcane Order reawakens the Titans.


title: Tales of Arcadia

text: "" is a video game based on "Trollhunters". It was released for PlayStation 4, Xbox One, Nintendo Switch and PC on September 25, 2020.


title: Tales of Arcadia

text: Following the release of "Trollhunters: Rise of the Titans", writer Marc Guggenheim said the film is meant to "wrap up the trilogy and for this really to be the final chapter in the story", but that it simultaneously "also opens the door for a whole host of new storytelling possibilities", and that it was "designed to be a cap, and [he suspects] it will remain that way for at least a little bit".


title: Carnage (2011 film)

text: Carnage is a 2011 black comedy film directed by Roman Polanski, based on the Tony Award-winning 2006 play "Le Dieu du carnage" by French playwright Yasmina Reza. The screenplay is by Reza and Polanski. The film is an international co-production of France, Germany, Poland, and Spain. It stars Jodie Foster, Kate Winslet, Christoph Waltz, and John C. Reilly.


title: Carnage (2011 film)

text: In this comedy of errors, two sets of parents try to resolve a situation in a civilised manner as their idiosyncrasies rise to the surface.


title: Carnage (2011 film)

text: "Carnage" premiered at the 2011 Venice International Film Festival on 1 September 2011, where it competed for the Golden Lion. It was theatrically released on 18 November 2011. The film received positive reviews, with critics praising the performances of Foster and Winslet and Polanski's direction.


title: Carnage (2011 film)

text: At the 69th Golden Globe Awards, Foster and Winslet received nominations for Best Actress – Motion Picture Musical or Comedy. As of 2022, it is Polanski's last film to be shot in English until his upcoming film "The Palace".


title: Carnage (2011 film)

text: When two grade-school boys get into a fight in the park that results in one boy, Zachary Cowan, hitting the other, Ethan Longstreet, in the face with a stick, their parents meet in a Brooklyn apartment to discuss the matter. Zachary's parents, Alan (Christoph Waltz) and Nancy Cowan (Kate Winslet), visit the home of Michael (John C. Reilly) and Penelope Longstreet (Jodie Foster), Ethan's parents. Their meeting is initially intended to be short, but due to various circumstances, the conversation continues to draw out.


title: Carnage (2011 film)

text: In fact, Alan and Nancy begin to leave the apartment on two occasions, but are drawn back in to further discussion.


title: Carnage (2011 film)

text: At first, the couples are friendly to each other, but their respective comments start to hurt feelings, making everyone argue with one another. Apart from fighting amongst themselves, the couples blame each other about who is responsible for the fight between their sons. Nancy calls the Longstreets "superficially fair-minded" and Penelope and Michael complain about Alan's arrogant and dull attitude. Everyone also gets irritated with Alan when he accepts endless business phone calls on his BlackBerry, interrupting the discussion, and showing he has more interest in his business problems than the matter at hand. Michael also receives many phone calls from his ailing mother, to his frustration.


title: Carnage (2011 film)

text: Nancy accuses Michael of being a murderer because he, annoyed by the constant noise it made during the night, had earlier turned his daughter Courtney's pet hamster loose in the street. Penelope becomes emotional about the hamster and with everyone arguing with each other. Other issues include a risky drug Alan is working to defend and Michael's mother has been prescribed, and the question of idealism and responsibility that is part of Penelope's current work.


title: Carnage (2011 film)

text: Michael offers everyone a glass of fine scotch. Penelope claims she doesn't "get drunk" and Nancy drinks way too many and finally stops Alan's phone calls by dropping his cellphone in Penelope's flower vase full of tulips and water. Penelope and Nancy both laugh uproariously while Michael and Alan try to blow-dry the BlackBerry.


title: Carnage (2011 film)

text: The conversation continues to decay into personal attacks and opinionated statements and, eventually, epithets are uttered. Penelope is ranting, calling Nancy's son a 'snitch', and Nancy's true colors are revealed when she destroys the tulips and drunkenly and vulgarly states she is glad that her son beat up Penelope's and Michael's son. The couples realize the conversation is going nowhere. Alan's BlackBerry, lying on the coffee table, vibrates, and all four stare at it.


title: Carnage (2011 film)

text: The film cuts to the hamster, alive and well in the park, where Ethan and Zachary are reconciling on their own.


title: Carnage (2011 film)

text: Although set in Brooklyn, New York, the film was shot in Paris, because of Polanski's fugitive status. The opening and closing scenes, ostensibly filmed in Brooklyn Bridge Park, were shot in France against a green screen. Polanski's son Elvis, seen only in long shots in the opening and closing scenes, portrays the Cowans' son. Actress Julie Adams (famous for "Creature from the Black Lagoon") voices Alan Cowan's secretary on the phone, and was a dialect coach for Waltz.


title: Carnage (2011 film)

text: The apartment, in which almost the whole film takes place, was designed in a sound studio on the outskirts of Paris. Production designer Dean Tavoularis placed a priority on making the set look authentically American, having numerous products and appliances shipped from the US, and renting American ironmongery for the doors.


title: Carnage (2011 film)

text: The film premiered at the 68th Venice International Film Festival. The film was released in the United States on 16 December 2011 by Sony Pictures Classics.


title: Carnage (2011 film)

text: "Carnage" received generally positive reviews from critics. It holds "fresh" rating on Rotten Tomatoes, which notes that "it isn't as compelling on the screen as it was on the stage, but "Carnage" makes up for its flaws with Polanski's smooth direction and assured performances from Winslet and Foster." On Metacritic, which uses an average of the critics' reviews, the film holds a 61/100, indicating "Generally favorable reviews".


title: Carnage (2011 film)

text: John Anderson of "Newsday" compared the film to "Who's Afraid of Virginia Woolf?" and said: "The astonishing Waltz steals the picture, possibly because he's the one with a rational perspective (despite his telephonic obsessiveness). He sees the whole exercise as pointless. Ultimately, so do we." Giuseppe Sedia of the "Krakow Post" remarked that the descent of four adults to a thuggish level has been featured as well in Polanski's short film "Rozbijemy zabawę". He added that "it is interesting to speculate on what Hitchcock might have made of Reza's oeuvre".


title: Carnage (2011 film)

text: "Carnage" grossed $2.5 million at the U.S. box office after twenty weeks in theaters, with another $25 million in foreign countries, for a worldwide gross of $27,603,069.


title: Number 17A

text: Number 17A is an abstract expressionist painting by Jackson Pollock. It is owned by hedge fund manager Kenneth C. Griffin, who purchased it in September 2015 from David Geffen for $200 million, a then record-breaking price, at which time it was lent to the Art Institute of Chicago. , it is ranked 5th on the list of most expensive paintings.


title: Number 17A

text: The painting is oil paint on fiberboard and is a drip painting, created by splashing paint onto a horizontal surface. It was painted a year after Jackson Pollock introduced his drip technique. The piece was featured in the August 1949 edition of "Life" that made Jackson Pollock a celebrity.


title: Claire Saffitz

text: Claire Saffitz (born 1986) is an American food writer, chef, and YouTube personality. Until mid-2020, she was a contributing editor at "Bon Appétit" magazine and starred in several series on the "Bon Appétit" YouTube channel, including "Gourmet Makes", in which she created gourmet versions of popular snack foods by reverse engineering them. Since leaving the company, she has published two cookbooks, "Dessert Person" and "What's for Dessert?", which both became "New York Times" Best Sellers. She has continued work as a video host on her own YouTube channel and as a freelance recipe developer, including for "New York Times" Cooking.


title: Claire Saffitz

text: Saffitz was born in St. Louis, Missouri, to an Ashkenazi Jewish family. In the early 1900s, her great-grandfather emigrated to the United States from what was then Russia but is now Ukraine; before emigrating, he worked as a baker.


title: Claire Saffitz

text: She attended Captain Elementary and graduated from Clayton High School in 2005. She went on to attend Harvard University, graduating in 2009 with an AB in U.S. history and literature, then studied French cuisine and pastry at École Grégoire-Ferrandi in Paris, France. After a four-month externship at Spring Restaurant, Saffitz moved to Montreal, Québec, where she received a master's degree in history at McGill University in 2013, with a focus on French culinary history in the early modern era.


title: Claire Saffitz

text: Saffitz joined "Bon Appétit" in 2013, starting as a recipe tester and working her way up to being a senior food editor, where she remained until August 2018, when she left her full-time position at the magazine. She returned in November 2018 as a freelance recipe developer and video host.


title: Claire Saffitz

text: In July 2017, "Gourmet Makes" debuted, in which Saffitz attempted to recreate or elevate popular snack foods such as Doritos, Twinkies, and Gushers. "Gourmet Makes" consistently trended on YouTube and developed a cult following on social media. Saffitz's work has been described as taking "junk food staples and...elevating them from their humble processed beginnings into wonders of gastronomy."


title: Claire Saffitz

text: In February 2019, "Bon Appétit" launched two new series that featured Saffitz: "Bon Appétit’s Baking School" and "Making Perfect".


title: Claire Saffitz

text: On January 22, 2020, Saffitz appeared on a cooking segment on "The Tonight Show Starring Jimmy Fallon".


title: Claire Saffitz

text: On June 8, 2020, Adam Rapoport resigned as editor-in-chief of "Bon Appétit" after a photo of him in brownface resurfaced online and sparked widespread criticism. The company as a whole also received criticism after food editor Sohla El-Waylly accused the magazine and Condé Nast Entertainment, which produces the videos on the "Bon Appétit" YouTube channel, of discriminating against employees of color, claiming they were subject to lesser pay than their non-minority counterparts. Amidst these circumstances, Saffitz announced she had not been under contract with the company since May 2020 and that she would be reevaluating her relationship with "Bon Appétit". In October 2020, she formally announced she would not be renewing her contract.


title: Claire Saffitz

text: Saffitz's debut cookbook, "Dessert Person: Recipes and Guidance for Baking with Confidence", was published by Clarkson Potter, an imprint of Penguin Random House, on October 20, 2020. The book became a "New York Times" Best Seller, debuting at No. 2 on the "Advice, How-To & Miscellaneous" list for the week of November 8, 2020. In June 2021, the "Dessert Person" cookbook was nominated by the International Association of Culinary Professionals as a finalist in the annual IACP Cookbook Awards in the "Baking Sweet & Savory, Confections & Desserts" category and a nominee for the IACP Julia Child First Book Award, winning the latter in October 2021.


title: Claire Saffitz

text: In December 2020, Saffitz launched her own YouTube channel, beginning with a focus on demonstrating recipes from her book, "Dessert Person". The channel is produced by Vincent Cross, formerly of "Bon Appétit", who also worked on the Binging with Babish YouTube channel.


title: Claire Saffitz

text: In January 2021, Saffitz started contributing to NYT Cooking, including being featured on their YouTube channel. In May 2021, Saffitz made another appearance on "The Tonight Show".


title: Claire Saffitz

text: Claire's second cookbook, titled "What's for Dessert: Simple Recipes for Dessert People" was released on November 8, 2022. It also became a "New York Times" Best Seller.


title: Claire Saffitz

text: Saffitz lives with her husband, fellow chef Harris Mayer-Selinger, in the Upper West Side neighborhood of New York City. The couple also own a cabin in upstate New York, which they purchased in late 2020.


title: Marxist feminism

text: Marxist feminism is a philosophical variant of feminism that incorporates and extends Marxist theory. Marxist feminism analyzes the ways in which women are exploited through capitalism and the individual ownership of private property. According to Marxist feminists, women's liberation can only be achieved by dismantling the capitalist systems in which they contend much of women's labor is uncompensated. Marxist feminists extend traditional Marxist analysis by applying it to unpaid domestic labor and sex relations.


title: Marxist feminism

text: Because of its foundation in historical materialism, Marxist feminism is similar to socialist feminism and, to a greater degree, materialist feminism. The latter two place greater emphasis on what they consider the "reductionist limitations" of Marxist theory but, as Martha E. Gimenez notes in her exploration of the differences between Marxist and materialist feminism, "clear lines of theoretical demarcation between and within these two umbrella terms are somewhat difficult to establish."


title: Marxist feminism

text: Marxism follows the development of oppression and class division in the evolution of human society through the development and organization of wealth and production, and concludes the evolution of oppressive societal structure to be relative to the evolution of oppressive family structures, i.e., the normalization of oppressing the female sex marks or coincides to the birth of oppressive society in general.


title: Marxist feminism

text: In "The Origin of the Family, Private Property, and the State" (1884), Friedrich Engels writes about the earliest origins of the family structure, social hierarchy, and the concept of wealth, drawing from both ancient and contemporary study. He concludes that women originally had a higher social status and equal consideration in labor, and particularly, only women were sure to share a family name. As the earliest men did not even share the family name, Engels says, they did not know for sure who their children were or benefit from inheritance.


title: Marxist feminism

text: When agriculture first became abundant and the abundance was considered male wealth, as it was sourced from the male work environment away from the home, a deeper wish for male lineage and inheritance was founded. To achieve that wish, women were not only granted their long-sought monogamy but forced into it as part of domestic servitude, while males pursued a hushed culture of "hetaerism". Engels describes this situation as coincidental to the beginnings of forced servitude as a dominant feature of society, leading eventually to a European culture of class oppression, where the children of the poor were expected to be servants of the rich.


title: Marxist feminism

text: Engels rewrites a quote in this book, by himself and Marx from 1846, "The first division of labor is that between man and woman for the propagation of children", to say, "The first class opposition that appears in history coincides with the development of the antagonism between man and woman in monogamous marriage, and the first class oppression coincides with that of the female sex by the male."


title: Marxist feminism

text: Gender oppression is reproduced culturally and maintained through institutionalized inequality. By privileging men at the expense of women and refusing to acknowledge traditional domestic labor as equally valuable, the working-class man is socialized into an oppressive structure which marginalizes the working-class woman.


title: Marxist feminism

text: Marxist feminist authors in the 1970s, such as Margaret Benston and Peggy Morton, relied heavily on analysis of productive and unproductive labor in an attempt to shift the perception of the time that consumption was the purpose of a family, presenting arguments for a state-paid wage to homemakers, and a cultural perception of the family as a productive entity. In capitalism, the work of maintaining a family has little material value, as it produces no marketable products. In Marxism, the maintenance of a family is productive, as it has a service value, and is used in the same sense as a commodity.


title: Marxist feminism

text: Focusing on exclusion from productive labor as the most important source of female oppression, some Marxist feminists advocated for the inclusion of domestic work within the waged capitalist economy. The idea of compensating reproductive labor was present in the writing of socialists such as Charlotte Perkins Gilman (1898) who argued that women's oppression stemmed from being forced into the private sphere. Gilman argued that conditions for women would improve when their work was located, recognized, and valued in the public sphere.


title: Marxist feminism

text: Perhaps the most influential effort to compensate reproductive labor was the International Wages for Housework Campaign, an organization launched in Italy in 1972 by members of the International Feminist Collective. Many of these women, including Selma James, Mariarosa Dalla Costa, Brigitte Galtier, and Silvia Federici published a range of sources to promote their message in academic and public domains. Despite beginning as a small group of women in Italy, the Wages for Housework Campaign was successful in mobilizing on an international level. A Wages for Housework group was founded in Brooklyn, New York, with the help of Federici. As Heidi Hartmann acknowledges (1981), the efforts of these movements, though ultimately unsuccessful, generated important discourse regarding the value of housework and its relation to the economy.


title: Marxist feminism

text: Many Marxist feminist scholars analyzing modes of oppression at the site of production note the effect that housework has on women in a capitalist system. In Angela Davis' "Women, Race and Class", the concept of housework is utilized to deconstruct the capitalist construct of gendered labor within the home and to show the ways in which women are exploited through "domestic slavery". To address this, Davis concludes that the "socialisation of housework – including meal preparation and child care – presupposes an end to the profit-motive's reign over the economy." In this manner, domestic slavery upholds the structural inequities faced by women in all capitalist economies.


title: Marxist feminism

text: Other Marxist feminist have noted the concept of domestic work for women internationally and the role it plays in buttressing global patriarchy. In Paresh Chattopadhyay's response to Custer's "Capital Accumulation and Women's Labor in Asian Economies", Chattopadhyay notes the ways in which Custer analyzes "women's labor in the garments industry in West Bengal and Bangladesh as well as in Bangladesh's agricultural sector, labor management methods of the Japanese industrial bourgeoisie and, finally, the mode of employment of the women laborers in Japanese industry" in demonstrating the ways in which the domestic sphere exhibits similar gender-based exploitation of difference. In both works, the gendered division of labor, specifically within the domestic sphere, is shown to illustrate the methods the capitalist system exploits women globally.


title: Marxist feminism

text: Another solution proposed by Marxist feminists is to liberate women from their forced connection to reproductive labor. In her critique of traditional Marxist feminist movements such as the Wages for Housework Campaign, Heidi Hartmann (1981) argues that these efforts "take as their question the relationship of women to the economic system, rather than that of women to men, apparently assuming the latter will be explained in their discussion of the former." Hartmann believes that traditional discourse has ignored the importance of women's oppression as women, and instead focused on women's oppression as members of the capitalist system. Similarly, Gayle Rubin, who has written on a range of subjects including sadomasochism, prostitution, pornography, and lesbian literature, first rose to prominence through her 1975 essay "", in which she coins the phrase "sex/gender system" and criticizes Marxism for what she claims is its incomplete analysis of sexism under capitalism, without dismissing or dismantling Marxist fundamentals in the process.


title: Marxist feminism

text: More recently, many Marxist feminists have shifted their focus to the ways in which women are now potentially in worse conditions as a result of gaining access to productive labor. Nancy Folbre proposes that feminist movements begin to focus on women's subordinate status to men both in the reproductive (private) sphere, as well as in the workplace (public sphere). In an interview in 2013, Silvia Federici urges feminist movements to consider the fact that many women are now forced into productive "and" reproductive labor, resulting in a double day. Federici argues that the emancipation of women cannot occur until they are free from the burden of unwaged labor, which she proposes will involve institutional changes such as closing the wage gap and implementing child care programs in the workplace. Federici's suggestions are echoed in a similar interview with Selma James (2012) and have even been touched on in recent presidential elections.


title: Marxist feminism

text: Scholars and sociologists such as Michael Hardt, Antonio Negri, Arlie Russell Hochschild and Shiloh Whitney discuss a new form of labor that transcends the traditional spheres of labor and which does not create product, or is byproductive. Affective labor focuses on the blurred lines between personal life and economic life. Whitney states, "The daily struggle of unemployed persons and the domestic toil of housewives no less than the waged worker are thus part of the production and reproduction of social life, and of the biopolitical growth of capital that valorizes information and subjectivities."


title: Marxist feminism

text: The concept of emotional labor, particularly the emotional labor that is present and required in pink collar jobs, was introduced by Arlie Russell Hochschild in her book "The Managed Heart: Commercialization of Human Feeling" (1983) in which she considers the affective labor of the profession as flight attendants smile, exchange pleasantries and banter with customers.


title: Marxist feminism

text: In 1977 the British feminist sociologist Veronica Beechey published 'Some Notes on Female Wage Labour', which argued that women should be understood as an unrecognised 'reserve arm of labour'. In response, Floya Anthias published 'Woman and the Reserve Army of Labour: A Critique of Veronica Beechy', to query Beechey's arguments, while also recognising that it Beechey's was "the most sophisticated and influential attempt to analyse women's wage labour by using or reconstituting the categories of Marx's Capital". In 1987 Verso published Beechey's collected essays on women's participation in labour as the book "Unequal Work".


title: Marxist feminism

text: With the emergence of intersectionality as a widely popular theory of current feminism, Marxist feminists remain critical of its reliance on bourgeois identity politics. Intersectionality operates in Marxist feminism as a lens to view the interaction of different aspects of identity as a result of structured, systematic oppression.


title: Marxist feminism

text: The nature of Marxist feminists and their ability to mobilize to promote social change has enabled them to engage in important activism. As activist, Marxist feminists insist "on developing politics that put women's oppression and liberation, class politics, anti-imperialism, antiracism, and issues of gender identity and sexuality together at the heart of the agenda." Though their advocacy often receives criticism, Marxist feminists challenge capitalism in ways that facilitate new discourse and shed light on the status of women. These women throughout history have used a range of approaches in fighting hegemonic capitalism, which reflect their different views on the optimal method of achieving liberation for women.


title: Marxist feminism

text: A few women that contributed to the development of Marxist Feminism as a theory were Chizuko Ueno, Anuradha Ghandy, Claudia Jones, and Angela Davis. Chizuko Ueno is well known for being one of the first women to introduce Marxist Feminism in Japan. Additionally, Chizuko Ueno was also one of the primary developers of feminist theories across Japan. Among other renowned Marxists Feminists, their influence impacted nations such as Ukraine, India, Russia, United States, and Trinidad and Tobago.


title: Marxist feminism

text: Clara Zetkin and Alexandra Kollontai were opposed to forms of feminism that reinforce class status. They did not see a true possibility to unite across economic inequality because they argue that it would be extremely difficult for an upper-class woman to truly understand the struggles of the working class. For instance, Kollontai wrote in 1909: For what reason, then, should the woman worker seek a union with the bourgeois feminists? Who, in actual fact, would stand to gain in the event of such an alliance? Certainly not the woman worker.Kollontai avoided associating herself with the term "feminism" as she deemed the term to be too closely related to that of the bourgeois feminism that shut out the capability of other classes to benefit from the term.


title: Marxist feminism

text: Kollontai was a prominent leader in the Bolshevik party in Russia, defending her stance on how capitalism had shaped a rather displeasing and oppressing position for females that are part of its system. She recognized and emphasized the difference between the proletariat and bourgeoise women in society, though it has been expressed by Kollontai's thought that all women under a capitalist economy were those of oppression. One of the reasons Kollontai had a strict opposition of the bourgeois women and proletariat or working-class women to have an alliance is because the bourgeois was still inherently using the women of the working class to their advantage, and therefore prolonging the injustice that women in a capitalist society are treated. She theorized that a well-balanced economic utopia was ingrained in the need for gender equality, but never identified as a feminist, though she greatly impacted the feminist movement within the ideology of feminism within and throughout socialism. Kollontai had a harsh stance on the feminist movement and believed feminists to be naïve in only addressing gender as the reason inequality was happening under a capitalist rule. She believed that the true issue of inequality was that of the division of classes that led to the immediate production of gender struggles, just how men in the structure of the classes shown a harsh divide as well. Kollontai analyzed the theories and historical implications of Marxism as a background for her ideologies, which she addressed the most profound obstacle for society to address be that of the gender inequality, which could never be eradicated under a capitalist society. As capitalism is inherently for private profit, Kollontai's argument toward the eradication of women suffrage within society under a capitalist rule also delved into how women cannot and will not be abolished under a capitalist society because of the ways in which women's "free labor" has been utilized. Kollontai criticized the feminist movement as also neglecting to emphasize how the working class, while trying to care and provide for a family and being paid less than that of men, was still expected to cater to and provide for the bourgeois or upper-class women who were still oppressing the working-class women by utilizing their stereotypical type of work. Kollontai also faced harsh scrutiny in being a woman leader in a time of a male dominated political stance during the Bolshevik movement. In keeping with her unusual position during her time, she also kept diaries of her plans and ideas on moving towards a more "modern" society where socialism would help uproot that of capitalism and the oppression that different groups of gender and class had been facing. Kollontai was a great example of a woman who was indeed still oppressed by the times and was removed from her own ideologies and progress for the mere fact she was a woman in times where being so in a powerful position was frowned upon and "great women" were only allowed to be placed alongside "great men" in history. Kollontai's most pertinent presence in feminist socialism was her stance on reproductive rights and her view on women being allowed the same luxuries that men have in finding love not only to be stable and supported, and to also be able to make their own money and be secure on their own two feet. She focused her attention on opening up society's allowance of women's liberation from a capitalist and bourgeois control and emphasizing women's suffrage in the working-class.


title: Marxist feminism

text: Critics like Kollontai believed liberal feminism would undermine the efforts of Marxism to improve conditions for the working class. Marxists supported the more radical political program of liberating women through socialist revolution, with a special emphasis on work among women and in materially changing their conditions after the revolution. Additional liberation methods supported by Marxist feminists include radical "Utopian Demands", coined by Maria Mies. This indication of the scope of revolution required to promote change states that demanding anything less than complete reform will produce inadequate solutions to long-term issues.


title: Gunpowder empires

text: The gunpowder empires, or Islamic gunpowder empires, is a collective term coined by Marshall G. S. Hodgson and William H. McNeill at the University of Chicago, referring to three Muslim empires: the Ottoman Empire, Safavid Empire and the Mughal Empire, in the period they flourished from the 16th to the 18th century. These three empires were among the strongest and most stable economies of the early modern period, leading to commercial expansion, and greater patronage of culture, while their political and legal institutions were consolidated with an increasing degree of centralization. The empires underwent a significant increase in per capita income and population, and a sustained pace of technological innovation. They stretched from Central Europe and North Africa in the west to Bengal and Arakan in the east. Hodgson's colleague William H. McNeill expanded on the history of gunpowder use across multiple civilizations including East Asian, South Asian and European powers in his "The Age of Gunpowder Empires". Vast amounts of territory were conquered by the Islamic gunpowder empires with the use and development of the newly invented firearms, especially cannon and small arms, in the course of imperial expansion. Like in Europe, the introduction of gunpowder weapons prompted changes such as the rise of centralized monarchical states.


title: Gunpowder empires

text: According to G. S. Hodgson, in the gunpowder empires these changes went well beyond military organisation.


title: Gunpowder empires

text: The Mughals, based in the Indian subcontinent, inherited in part the Timurid Renaissance, and are recognised for their lavish architecture and for having heralded in Bengal an era of what some describe as proto-industrialization. The Safavids created an efficient and modern state administration for Iran and sponsored major developments in the fine arts. The sultans of the Ottoman Empire, also known as the "Kaysar-i Rûm", controlled the holy cities of Mecca and Medina, and hence were the recognised Caliphs of Islam; their powers, wealth, architecture, and various contributions significantly influenced the course of Eurasian history. Hodgson's colleague William H. McNeill expanded on the history of gunpowder use across multiple civilizations including East Asian, European, and South Asian powers in his 1993 work ""The Age of Gunpowder Empires"".


title: Gunpowder empires

text: The phrase was coined by Marshall G. S. Hodgson and his colleague William H. McNeill at the University of Chicago. Hodgson used the phrase in the title of Book 5 ("The Second Flowering: The Empires of Gunpowder Times") of his highly influential three-volume work, "The Venture of Islam" (1974). Hodgson saw gunpowder weapons as the key to the "military patronage states of the Later Middle Period" which replaced the unstable, geographically limited confederations of Turkic clans that prevailed in post-Mongol times. Hodgson defined a "military patronage state" as one having three characteristics:


title: Gunpowder empires

text: first, a legitimization of independent dynastic law; second, the conception of the whole state as a single military force; third, the attempt to explain all economic and high cultural resources as appanages of the chief military families.


title: Gunpowder empires

text: Such states grew "out of Mongol notions of greatness," but "[s]uch notions could fully mature and create stable bureaucratic empires only after gunpowder weapons and their specialized technology attained a primary place in military life."


title: Gunpowder empires

text: McNeill argued that whenever such states "were able to monopolize the new artillery, central authorities were able to unite larger territories into new, or newly consolidated, empires." Monopolization was key. Although Europe pioneered the development of new artillery in the fifteenth century, no state monopolized it. Gun-casting know-how had been concentrated in the Low Countries near the mouths of the Scheldt and Rhine rivers. France and the Habsburgs divided those territories among themselves, resulting in an arms standoff. By contrast, such monopolies allowed states to create militarized empires in Western Asia, Russia, and India, and "in a considerably modified fashion" in China, Korea, and Japan.


title: Gunpowder empires

text: More recently, the Hodgson–McNeill "gunpowder empire" hypothesis has been called into disfavour as a neither "adequate [n]or accurate" explanation, although the term remains in use. Reasons other than (or in addition to) military technology have been offered for the nearly simultaneous rise of three centralized military empires in contiguous areas dominated by decentralized Turkic tribes. One explanation, called "Confessionalization" by historians of fifteenth century Europe, invokes examination of how the relation of church and state "mediated through confessional statements and church ordinances" lead to the origins of absolutist polities. Douglas Streusand uses the Safavids as an example:


title: Gunpowder empires

text: One problem of the Hodgson–McNeill theory is that the acquisition of firearms does not seem to have preceded the initial acquisition of territory constituting the imperial critical mass of any of the three early modern Islamic empires, except in the case of the Mughal empire. Moreover, it seems that the commitment to military autocratic rule pre-dated the acquisition of gunpowder weapons in all three cases. Nor does it seem to be the case that the acquisition of gunpowder weapons and their integration into the military was influenced by which variety of Islam the particular empire promoted. Whether or not gunpowder was inherently linked to the existence of any of these three empires, it cannot be questioned that each of the three acquired artillery and firearms early in their history and made such weapons an integral part of their military tactics.


title: Gunpowder empires

text: Michael Axworthy has pointed out that the label is misleading in the case of the Safavids, as unlike contemporary European armies, the Safavid military mostly used swords, lances, and bows well into the mid-18th century. It was not until the rule of Nader Shah's Afsharid dynasty that the majority of Iran's troops would be equipped with firearms for the first time.


title: Gunpowder empires

text: The first of the three empires to acquire gunpowder weapons was the Ottoman Empire. By the 14th century, the Ottomans had adopted gunpowder artillery. The adoption of the gunpowder weapons by the Ottomans was so rapid that they "preceded both their European and Middle Eastern adversaries in establishing centralized and permanent troops specialized in the manufacturing and handling of firearms." But it was their use of artillery that shocked their adversaries and impelled the other two Islamic empires to accelerate their weapons programs. The Ottomans had artillery at least by the reign of Bayezid I and used them in the sieges of Constantinople in 1399 and 1402. They finally proved their worth as siege engines in the successful siege of Salonica in 1430. The Ottomans employed Middle-Eastern as well as European foundries to cast their cannons, and by the siege of Constantinople in 1453, they had large enough cannons to batter the walls of the city, to the surprise of the defenders.


title: Gunpowder empires

text: The Ottoman military's regularized use of firearms proceeded ahead of the pace of their European counterparts. The Janissaries had been an infantry bodyguard using bows and arrows. During the rule of Sultan Mehmed II they were drilled with firearms and became "perhaps the first standing infantry force equipped with firearms in the world." The Janissaries are thus considered the first modern standing armies. The combination of artillery and Janissary firepower proved decisive at Varna in 1444 against a force of Crusaders, Başkent in 1473 against the Aq Qoyunlu, and Mohács in 1526 against Hungary. But the battle which convinced the Safavids and the Mughals of the efficacy of gunpowder was Chaldiran.


title: Gunpowder empires

text: The matchlock arquebus began to be used by the Janissary corps by the 1440s. The musket later appeared in the Ottoman Empire by 1465. Damascus steel was later used in the production of firearms such as the musket from the 16th century. At the Battle of Mohács in 1526, the Janissaries equipped with 2000 "tüfenks" (usually translated as musket) "formed nine consecutive rows and they fired their weapons row by row," in a "kneeling or standing position without the need for additional support or rest." The Chinese later adopted the Ottoman kneeling position for firing. In 1598, Chinese writer Zhao Shizhen described Turkish muskets as being superior to European muskets. The Chinese "Wu Pei Chih" (1621) later described Turkish muskets that used a rack-and-pinion mechanism, which was not known to have been used in any European or Chinese firearms at the time.


title: Gunpowder empires

text: The Dardanelles Gun was designed and cast in bronze in 1464 by Munir Ali. The Dardanelles Gun was still present for duty more than 340 years later in 1807, when a Royal Navy force appeared and commenced the Dardanelles Operation. Turkish forces loaded the ancient relics with propellant and projectiles, then fired them at the British ships. The British squadron suffered 28 casualties from this bombardment.


title: Gunpowder empires

text: At Chaldiran, the Ottomans met the Safavids in battle for the first time. Sultan Selim I moved east with his field artillery in 1514 to confront what he perceived as a Shia threat instigated by Shah Ismail in favor of Selim's rivals. Ismail staked his reputation as a divinely-favored ruler on an open cavalry charge against a fixed Ottoman position. The Ottomans deployed their cannons between the carts that carried them, which also provided cover for the armed Janissaries. The result of the charge was devastating losses to the Safavid cavalry. The defeat was so thorough that the Ottoman forces were able to move on and briefly occupy the Safavid capital, Tabriz. Only the limited campaign radius of the Ottoman army prevented it from holding the city and ending the Safavid rule.


title: Gunpowder empires

text: Although the Chaldiran defeat brought an end to Ismail's territorial expansion program, the shah nonetheless took immediate steps to protect against the real threat from the Ottoman sultanate by arming his troops with gunpowder weapons. Within two years of Chaldiran, Ismail had a corps of musketeers ("tofangchi") numbering 8,000, and by 1521, possibly 20,000. After Abbas the Great reformed the army (around 1598), the Safavid forces had an artillery corps of 500 cannons as well as 12,000 musketeers.


title: Gunpowder empires

text: The Safavids first put their gunpowder arms to good use against the Uzbeks, who had invaded eastern Persia during the civil war that followed the death of Ismail I. The young shah Tahmasp I headed an army to relieve Herat and encountered the Uzbeks on 24 September 1528 at Jam, where the Safavids decisively beat the Uzbeks. The shah's army deployed cannons (swivel guns on wagons) in the center protected by wagons with cavalry on both flanks. Mughal emperor Babur described the formation at Jam as "in the Anatolian fashion." The several thousand gun-bearing infantry also massed in the center as did the Janissaries of the Ottoman army. Although the Uzbek cavalry engaged and turned the Safavid army on both flanks, the Safavid center held (because it was not directly engaged by the Uzbeks). Rallying under Tahmasp's personal leadership, the infantry of the center engaged and scattered the Uzbek center and secured the field.


title: Gunpowder empires

text: By the time he was invited by the Lodi governor of Lahore Daulat Khan to support his rebellion against Lodi Sultan Ibrahim Khan, Babur was familiar with gunpowder firearms and field artillery and a method for deploying them. Babur had employed Ottoman expert Ustad Ali Quli, who showed Babur the standard Ottoman formation—artillery and firearm-equipped infantry protected by wagons in the center, and mounted archers on both wings. Babur used this formation at the First Battle of Panipat in 1526, where the Afghan and Rajput forces loyal to the Delhi sultanate, though superior in numbers but without the gunpowder weapons, were defeated. The decisive victory of the Timurid forces is one reason opponents rarely met Mughal princes in pitched battle over the course of the empire's history. The reigns of Akbar The Great, Shah Jahan and Aurangzeb have been described as a major height of Indian history. The Mughal Empire became a powerful geopolitical entity with at times, 16.1% of the world population. The Mughals inherited elements of Persian culture and art, as did the Ottomans and Safavids.


title: Gunpowder empires

text: The three Islamic gunpowder empires are known for their quickly gained success in dominating the battle fields using their newly acquired firearms and techniques. East Asian powers and their military success are commonly overlooked in this subject due to the success of not only the Islamic empires, but also European empires. The success and innovation of gunpowder combat in East Asia, however, are worth mentioning in the same context as that of the Islamic gunpowder empires for their military advancements.


title: Gunpowder empires

text: There were various ways that small firearms came to China. During the golden age of East Asian Piracy between the 1540s and 1560s, it was most likely that through their battles and other encounters with these pirates, the Ming dynasty forces inevitably got hold of the weapons and copied them. It was also likely that a powerful mariner Wang Zhi, who controlled thousands of armed men eventually surrendered to the Ming in 1558 and they replicated his weapons. This particular account on arquebus technology was the first to spark the interest of Ming officials for the Chinese to broaden their use of these weapons.


title: Gunpowder empires

text: Turkish arquebuses may have reached China before Portuguese ones. In Zhao Shizhen's book of 1598, the "Shenqipu", there were illustrations of Ottoman Turkish musketmen with detailed illustrations of their muskets, alongside European musketeers with detailed illustrations of their muskets. There was also illustration and description of how the Chinese had adopted the Ottoman kneeling position in firing. Zhao Shizhen described the Turkish muskets as being superior to the European muskets. The "Wu Pei Chih" (1621) later described Turkish muskets that used a rack-and-pinion mechanism, which was not known to have been used in any European or Chinese firearms at the time.


title: Gunpowder empires

text: The Chinese intensively practiced tactical strategies based on firearm use which resulted in military success. Qi Jiguang, a revered Ming military leader, drilled his soldiers to extremes so that their performance in battle would be successful. In addition, Qi Jiguang also used innovative battle techniques like the volley, counter march, dividing into teams, and even encouraged having a flexible formation to adapt to the battle field.


title: Gunpowder empires

text: During the Sino-Dutch War beginning in 1661, Southern Ming commander Zheng Chenggong (Koxinga) used similar tactics to Qi Jiguang effectively in battle. While the Dutch may have had superior weapons, the Chinese were able to defeat Dutch forces through their strict adherence to discipline and their ability to stay in formation. Ultimately, it was their technique and training that defeated the Dutch weapons.


title: Gunpowder empires

text: In 1631, "Heavy Troops" that could build and operate European-style cannon, The imported cannons in the Qing dynasty had a high reputation such as 'Great General in Red'. The Manchu elite did not concern themselves directly with guns and their production, preferring instead to delegate the task to Han-Chinese craftsmen, who produced for the Qing a similar composite metal cannon known as the "Shenwei grand general." Cannons and muskets are also widely used in wars known as 'Ten Great Campaigns'. However, after the Qing gained hegemony over East Asia in the mid-18th century, the practice of casting composite metal cannons fell into disuse until the dynasty faced external threats once again in the Opium War of 1840, at which point smoothbore cannons were already starting to become obsolete as a result of rifled barrels.


title: Gunpowder empires

text: The Japanese adopted the use of the Portuguese arquebus in the middle of the 16th century. Multiple accounts have said that Portuguese men working for Chinese pirates ended up in Japan by chance and impressed the local ruler with the weapons. Soon after, the Japanese started mass-producing the Portuguese style weapon for themselves. In other accounts, this firearm technology may have trickled in to Japan as early as 1540 from the constant in and out flow of Japanese mercenaries who could have picked up firearms in their travels. Soon, Japanese soldiers carrying firearms would greatly outnumber those with other weapons.


title: Gunpowder empires

text: Tonio Andrade cited that the Military Revolution Model that gave the Europeans so much military success included the use of superior drilling techniques. The drilling technique he was speaking of was the musketeer volley technique. The volley technique was said to have been invented by Japanese Warlord Oda Nobunaga. He used the same technique that Japanese archers used, but the effect that the technique had to allow soldiers to reload at the same time others could fire was devastating to their enemies.


title: Gunpowder empires

text: Koreans had been using Chinese and self made firearms as early as the late 14th century. They were also quite adept and innovative with their strategies on the battle field. In fact, there were accounts of Koreans using a type of volley technique in 1447. But a war between the Japanese against the Koreans and the Ming starting in 1592 and ending in 1598 would change the Korean's perspective on warfare. While it was a devastating defeat to the Koreans, this war forced the Koreans to realize that they needed to adopt the use of the musket as well as Japanese and Chinese methods. The Koreans quickly issued the musket as the base of their military tactic, and their musketeers became more than 50 percent of the military by 1594. They trained using manuals based on Qi Jiguang's techniques such as the volley, while incorporating their own methods too. These events marked the beginning of a Korean military revolution in which the Koreans could combat their enemies using modern equipment and methods of warfare.


title: Gunpowder empires

text: There were many instances where the Korean military used their new techniques effectively. In 1619, the Koreans aided the Ming against the Manchus, a great military force. While the Koreans and Ming lost, a Korean unit did exhibit their techniques successful in battle. Then, in 1627 and 1636, the Koreans faced the Manchus alone, again showing their competency in battle by using their musket tactics. Again, they lost in battle to the Manchus in both battles. In 1654 and 1658, the Koreans aided the Qing in battle against the Russians for control over land in Manchuria. In these instances, the Koreans showed their superior tactics and were the reason for the Russians' defeat.


title: Gunpowder empires

text: Comparatively little attention has been made to the use and innovation of gunpowder in the expansion of Vietnam. There is, in fact, a widespread belief that the Vietnamese introduced firearms to China, although other scholars disagree. Regardless, the use of gunpowder technology has left an undeniable mark in Vietnamese history, allowing the "southward march" and significant expansion of Vietnamese territory.


title: Gunpowder empires

text: Europeans are said to have pushed gunpowder technology to its limits, improving the formulas that existed and devising new uses of the substance after it was introduced to Europe via the Silk Road in the thirteenth century. Europeans were improving gunpowder a century after the first gun was invented in China.


title: Gunpowder empires

text: Roger Bacon, a renowned early European alchemist (1214 – 1292), set forth the marvels of the world; key among them was the ingredients of gunpowder. With these ingredients available, European scientists, inventors and alchemists went on to create corned gunpowder, which had a different refinement process. It entailed adding a wet substance to the gunpowder and then drying it as a mixture. With this improved gunpowder technology, German friar Berthold Schwarz invented the first European cannon in 1353.


title: Gunpowder empires

text: Europeans also improved the gunpowder firearms which had been made in China and the Middle East, creating stronger and more durable rifles using advanced European metalworking techniques. They learned how to calculate the amount of force exerted by the gas contained in a gun's chamber, which led to guns with the power to fire greater distances.


title: Gunpowder empires

text: Improved gunpowder from Europe later, in 1520, reached China on a Portuguese ship, though Turkish arquebuses may have reached China before Portuguese ones. The Ottomans and Portuguese introduced the cannon, improved rifles and other advancements to China, hundreds of years after gunpowder's original invention in China, bringing gunpowder's journey through Asia full circle.


title: BCS National Championship Game

text: The BCS National Championship Game, or BCS National Championship, was a postseason college football bowl game, used to determine a national champion of the NCAA Division I Football Bowl Subdivision (FBS), first played in the 1998 college football season as one of four designated bowl games, and beginning in the 2006 season as a standalone event rotated among the host sites of the aforementioned bowls.


title: BCS National Championship Game

text: The game was organized by a group known as the Bowl Championship Series, consisting of the Rose Bowl, Sugar Bowl, Fiesta Bowl, and Orange Bowl, which sought to match the two highest-ranked teams in a championship game to determine the best team in the country at the end of the season. The participating teams were determined by averaging the results of the final weekly Coaches' Poll, the Harris Poll of media, former players and coaches, and the average of six computer rankings. The Coaches' Poll was contractually required to name the winner of the game as its No. 1 team on the final postseason ranking; hence, the AFCA National Championship Trophy was presented to the winning team during a post-game ceremony.


title: BCS National Championship Game

text: The methodologies of the BCS system and its selections proved to be controversial. Although in most years the winner of the BCS National Championship would also be designated as the national champion by other organizations and polls (such as the Associated Press poll), the 2003 season was a major exception, as the BCS rankings chose the AP's No. 3-ranked team, the University of Oklahoma, over the No. 1-ranked team in that poll, the University of Southern California, to participate in the national title game (the Sugar Bowl) despite Oklahoma's loss to Kansas State University in the 2003 Big 12 Championship Game. That was the only season during the BCS era when the national championship was split, with Louisiana State University winning the BCS national championship and the University of Southern California winning the AP national championship, plus the football writers' national championship.


title: BCS National Championship Game

text: The BCS National Championship Game was played for the final time in 2013 after the same organizing group established a new system, the College Football Playoff, a four-team single elimination tournament, as the successor to the BCS.


title: BCS National Championship Game

text: The first BCS Championship was played at the conclusion of the 1998 college football season in accordance with an agreement by the Big Ten Conference, the Pac-10 Conference, and the Rose Bowl Game to join the "Bowl Alliance" system. The expanded format was called the Bowl Championship Series.


title: BCS National Championship Game

text: The Bowl Alliance and its predecessor, the Bowl Coalition, featured championship games in the 1992–1997 seasons. However, these could not always ensure a matchup between the top two ranked teams because of the lack of participation by the Big Ten and Pac-10.


title: BCS National Championship Game

text: The BCS National Championship Game was initially rotated among the four participating bowl games: the Fiesta Bowl, Sugar Bowl, Orange Bowl, and Rose Bowl. However, beginning with the 2006 season, the BCS National Championship Game was added as a separate contest, played after New Year's Day. The game rotated its location among the Fiesta, Sugar, Orange, and Rose venues.


title: BCS National Championship Game

text: Note: Conference affiliations are contemporaneous with the game, which may differ from the current alignment.


title: BCS National Championship Game

text: <nowiki>*</nowiki> The American Athletic Conference was known as the Big East during the 1991–2012 seasons. Because of a split between the non-FBS schools and FBS schools, the conference adopted its present name for the 2013 season.


title: BCS National Championship Game

text: <nowiki>**</nowiki> Alabama defeated fellow SEC member LSU in the 2012 BCS Championship Game, resulting in both a win and loss for the conference.


title: BCS National Championship Game

text: Critics of the BCS National Championship argued against the internal validity of a so-called "national championship" being awarded to the winner of a single postseason game. Critics lamented that the participants were selected based upon polls, computer rankings, popularity and human biases, and not by on-field competition, as in other major sports and all other levels of college football, which employed tournament-format championships. Often, the BCS system led to controversies in which multiple teams finished the season with identical records, and voters distinguished the worthiness of their participation in the BCS National Championship with no set of formal criteria or standards. The end of the 2010 season was one of the best examples of this. Without any objective criteria for evaluation of the teams, the BCS forced voters to impose their own standards and tiebreakers. Critics noted that the system inherently fostered selection bias, and therefore lacked both internal validity and external validity.


title: BCS National Championship Game

text: Controversies surrounding teams' inclusion in the BCS National Championship Game were numerous. In 2001, Oregon, ranked second in the AP poll, was bypassed in favor of Nebraska despite Nebraska's 62-36 blowout to Colorado in its final regular season game. In 2003, USC was not included in the championship game, but beat Michigan in the Rose Bowl and ended up No. 1 in the final AP poll. The following season, undefeated Auburn, Boise State, and Utah teams were left out of the national title game (the Orange Bowl). In 2008, Utah was excluded from the BCS championship for a second time despite being the only undefeated FBS team and finished second in the final AP poll behind Florida. In 2009, five schools finished the regular season undefeated: Alabama, Texas, Cincinnati, TCU, and Boise State; however, the BCS formula selected traditional powers Alabama and Texas to participate in the BCS National Championship Game.


title: BCS National Championship Game

text: In 2010, three teams, Oregon, Auburn, and TCU, all finished the year with undefeated records. While TCU statistically led the other two teams in all three major phases of the game (1st in defense, 14th in offense and 13th in special teams ) the teams from the two automatic qualifying conferences, Oregon (Pac-12) and Auburn (SEC), were selected over the Horned Frogs for the 2011 national title game. Many voters cited TCU's membership in the non-automatic qualifying Mountain West Conference, perceived as having weaker teams, as one significant reason for their exclusion, despite TCU's undefeated regular-season records in both 2010 and the previous year. Adding to the controversy were comments made by the president of Ohio State University, Gordon Gee, who said that teams which played "the little sisters of the poor" instead of the "murderer's row" of teams in the automatic qualifier conferences did not deserve any national title game consideration. Gee retracted his statement and apologized after TCU defeated Wisconsin in the 2011 Rose Bowl (the Badgers had convincingly defeated Ohio State during the regular season).


title: BCS National Championship Game

text: Many critics of the Bowl Championship Series favored a tournament with eight to sixteen teams, similar to those administered by the NCAA for its Football Championship Subdivision (FCS), Division II, and Division III football championships. Others favored adopting the incremental step of adding a single post-bowl championship game between the winners of two BCS games among the top four ranked teams in the BCS standings, a so-called "plus one" option. On June 24, 2009, the BCS presidential oversight committee rejected the Mountain West Conference's proposed eight-team playoff plan.


title: BCS National Championship Game

text: In 2009, the NCAA ruled that former USC running back Reggie Bush was retroactively ineligible for the 2004 BCS National Championship, the 2005 Orange Bowl vs. Oklahoma, for receiving various illegal benefits. In May 2011, the NCAA rejected all appeals of USC's penalties, which included Bush's ineligibility and a two-year bowl ban. On June 6, 2011, USC became the first school to lose a Bowl Championship Series national title due to NCAA sanctions when the BCS presidential oversight committee stripped the school of its 2004 title. As a result, there is no 2004 BCS champion, although USC retained its 2004 AP national title. Additionally, the BCS also nullified USC's participation in the 2006 Rose Bowl. (See attributions 1 and 2.)


title: BCS National Championship Game

text: During 2012, the BCS actively considered changes to the format for the 2014 football season, to either to extend the season by one game by establishing a four-school semifinal round or by selecting the participants in the national championship game after the season's bowl games were completed. On June 26, 2012, the BCS presidential oversight committee approved a four-school playoff format, in which the participants are determined by a selection committee. The semifinals are played as existing bowl games on or around New Year's Eve and New Year's Day. The championship game is played approximately a week later at a neutral site selected through a competitive bidding process.


title: BCS National Championship Game

text: From 1999 through 2005, ABC broadcast eight BCS National Championship Games pursuant to broadcasting rights negotiated with the BCS and the Rose Bowl, whose rights were offered separately. Beginning with the 2006 season, FOX obtained the BCS package, consisting of the Orange Bowl, Fiesta Bowl, Sugar Bowl, and the BCS National Championship Games hosted by these bowls, with ABC retaining the rights to the Rose Bowl and BCS National Championship Games hosted by the Rose Bowl.


title: BCS National Championship Game

text: On November 18, 2008, the BCS announced that ESPN had won the television rights to the BCS National Championship Game, as well as the other four BCS bowls, for 2011–2014.


title: BCS National Championship Game

text: As part of ESPN's contract with the BCS, ESPN Deportes provided the first Spanish-language U.S. telecast of the BCS National Championship Game in 2012.


title: BCS National Championship Game

text: During the BCS era, there was no NCAA Division I FBS playoff, and the BCS National Championship Game was just one of several national championship selection processes in existence.


title: BCS National Championship Game

text: The American Football Coaches Association (AFCA) participated in a weekly Coaches' Poll published by "USA Today"; for its final poll of the season, the AFCA was contractually bound to select the BCS National Champion as its No. 1 team. Thus, the winner of the game was awarded the AFCA National Championship Trophy in a postgame ceremony.


title: BCS National Championship Game

text: The BCS National Champion was also automatically awarded the National Football Foundation's MacArthur Bowl.


title: BCS National Championship Game

text: The Associated Press and the Football Writers Association of America were independent of the BCS system; their national championship trophies could have been awarded to a school other than the BCS National Championship Game winner.


title: Lawrence Hilton-Jacobs

text: Lawrence Hilton-Jacobs (born September 4, 1953) is an American actor and singer. Best known for playing Freddie "Boom Boom" Washington in "Welcome Back Kotter" (1975–79), he has also appeared in a number of films and television shows, including "Claudine" (1974), "Cooley High" (1975), "Roots" (1977), "Bangers and Mash" (1983), "Alien Nation (TV series)" (1989–90), "" (1992), and "31" (2016).


title: Lawrence Hilton-Jacobs

text: Hilton-Jacobs was born in New York City, New York, the fifth of nine children of parents Hilton Jacobs (died 2000) and Clothilda Jacobs (died 2008). He began his acting career in the summer of 1969 and graduated from the High School of Art and Design in 1971. He attended Wilkes University for a short time before his acting career took off. Afterward, he studied acting with the Negro Ensemble Company and the Al Fann Theatrical Ensemble.


title: Lawrence Hilton-Jacobs

text: In 1975, he won the role of Freddie "Boom Boom" Washington on the ABC hit comedy series, "Welcome Back, Kotter". Hilton-Jacobs also starred in cult classic "Cooley High" in 1975, and two years later had a role in the block-buster ABC mini-series "Roots". Hilton-Jacobs starred in a few commercials over the years, including an early 1970s commercial for The United Negro College Fund. Later in his career, he appeared in the 1989-1990 science fiction TV series "Alien Nation" as Sgt. Dobbs, an LAPD detective. He portrayed Panda Thomas (#1) in Rob Zombie's slasher film "31".


title: Lawrence Hilton-Jacobs

text: Hilton-Jacobs portrayed Joseph Walter "Joe" Jackson, the father of the Jackson family, in the 1992 miniseries "". He also appeared in a commercial for Salon Selectives.


title: Lawrence Hilton-Jacobs

text: As a homage to him, the housing project in Eddie Murphy's television program "The PJs" is named the Hilton-Jacobs Projects.


title: John T. Walton

text: John Thomas Walton (October 8, 1946 – June 27, 2005) was an American war veteran and a son of Walmart founder Sam Walton. He was also the chairman of True North Venture Partners, a venture capital firm. Walton cofounded the Children's Scholarship Fund, providing tuition scholarships for disadvantaged youth.


title: John T. Walton

text: Walton was born in Newport, Arkansas. He graduated from Bentonville High School where he was a star football player. Walton went on to attend the College of Wooster in Wooster, Ohio. He dropped out of college in 1968 to spend more time playing the flute and enlisted in the U.S. Army (after the Vietnamese Tet Offensive).


title: John T. Walton

text: During the Vietnam war, Walton served in the Green Berets as part of the Studies and Observations Group. He was involved in combat in the A Shau Valley and in Laos, where he was the medic and second-in-command of a unit named "Spike Team Louisiana". Walton later received a Silver Star for bravery in combat.


title: John T. Walton

text: After returning from Vietnam, Walton learned to fly and went to work as a pilot for Walmart. He later left the company to fly crop-dusters over cotton fields in several southern states and co-founded Satloc, an aerial application company that pioneered the use of GPS technology in agricultural crop-dusting. Walton then moved to San Diego where he founded Corsair Marine, a company that built trimaran sailboats. He also lived in Durango, Colorado, and was an enthusiastic skier, mountain biker, hiker, motorcycle rider, skydiver and scuba diver.


title: John T. Walton

text: In 1998, as part of the Philanthropy Roundtable, Walton and friend Ted Forstmann established the Children's Scholarship Fund to provide tuition assistance for low-income families to send their children to private schools. He was an advocate of school vouchers. For his achievements, he received the William E. Simon Prize for Philanthropic Leadership.


title: John T. Walton

text: Walton died on June 27, 2005, when the CGS Hawk Arrow home-built ultralight aircraft (registered as an "experimental aircraft" under FAA regulations) that he was piloting crashed in Jackson, Wyoming. Walton's plane crashed at 12:20 p.m. local time (1820 GMT) shortly after taking off from Jackson Hole Airport.


title: John T. Walton

text: The National Transportation Safety Board later reported that Walton had improperly reinstalled the rear locking collar on the elevator control torque tube. This allowed the torque tube to move rearward during his flight and loosened the elevator control cable tension. The outcome of the failed repair was an inflight loss of pitch control, without which Walton could not control the aircraft's altitude.


title: John T. Walton

text: Shortly before his death, "Forbes" magazine had estimated Walton's net worth to be billion, tied with his brother Jim as the 4th richest person in the United States and 11th-richest person in the world.


title: John T. Walton

text: Walton was survived by his wife Christy and their son Lukas. He was previously married to Mary Ann Gunn, who later became a judge in Arkansas. He had two brothers, S. Robson Walton and Jim Walton and a sister, Alice Walton.


title: German Emperor

text: The German Emperor (, ) was the official title of the head of state and hereditary ruler of the German Empire. A specifically chosen term, it was introduced with the 1 January 1871 constitution and lasted until the official abdication of Wilhelm II on 9 November 1918. The Holy Roman Emperor is sometimes also called "German Emperor" when the historical context is clear, as derived from the Holy Roman Empire's official name of "Holy Roman Empire of the German Nation" from 1512.


title: German Emperor

text: Following the revolution of 1918, the head of state was the president of the Reich (), beginning with Friedrich Ebert.


title: German Emperor

text: In the wake of the revolutions of 1848 and during the German Empire (1848–49), King Frederick Wilhelm IV of Prussia was offered the title "Emperor of the Germans" () by the Frankfurt Parliament in 1849, but declined it as "not the Parliament's to give". Frederick Wilhelm believed that only the German princes had the right to make such an offer, in accordance with the traditions of the Holy Roman Empire.


title: German Emperor

text: The title was carefully chosen by Otto von Bismarck, Minister President of Prussia and Chancellor of the North German Confederation, after discussion which continued until the proclamation of King Wilhelm I of Prussia as emperor at the Palace of Versailles during the Siege of Paris. Wilhelm accepted this title grudgingly on 18 January, having preferred "Emperor of Germany" (). However, that would have signaled a territorial sovereignty unacceptable to the South German monarchs, as well as a claim to lands outside his realm (Austria, Switzerland, Luxembourg, etc.).


title: German Emperor

text: "Emperor of the Germans", as had been proposed at the Frankfurt Parliament in 1849, was ruled out by Wilhelm as he considered himself a king who ruled by divine right and chosen "By the Grace of God", not by the people in a popular monarchy. But more in general, Wilhelm was unhappy about a crown that looked artificial (like Napoléon's), having been created by a constitution. He was afraid that it would overshadow the Prussian crown.


title: German Emperor

text: Since 1867, the presidency "(Bundespräsidium)" of the North German Confederation had been a hereditary office of the kings of Prussia. The new constitution of 1 January 1871, following Reichstag and Bundesrat decisions on 9/10 December, transformed the North German Confederation () into the German Empire (). This empire was a federal monarchy; the emperor was head of state and president of the federated monarchs (the kings of Bavaria, Württemberg, Saxony, the grand dukes of Baden, Mecklenburg-Schwerin, Hesse, among others, as well as the principalities, duchies and of the free cities of Hamburg, Lübeck and Bremen).


title: German Emperor

text: Under the imperial constitution, the empire was a federation of states under the permanent presidency of the king of Prussia. Thus, the imperial crown was directly tied to the Prussian crown—something Wilhelm II discovered in the aftermath of World War I. He erroneously believed that he ruled the empire in personal union with Prussia. With the war's end, he conceded that he could not remain emperor, but initially thought he could at least retain his Prussian crown. However, his last chancellor, Prince Max of Baden, knew this was legally impossible, and announced Wilhelm's abdication of both thrones on 9 November, two days before the Armistice. Realizing his situation was untenable, Wilhelm went into exile in the Netherlands later that night. It was not until 28 November that Wilhelm formally gave up all "rights to the crown of Prussia and to the rights to the German imperial crown connected therewith."


title: German Emperor

text: The German Emperors had an extensive list of titles and claims that reflected the geographic expanse and diversity of the lands ruled by the House of Hohenzollern.


title: German Emperor

text: His Imperial and Royal Majesty Wilhelm I, By the Grace of God, German Emperor and King of Prussia; Margrave of Brandenburg, Burgrave of Nuremberg, Count of Hohenzollern; sovereign and supreme Duke of Silesia and of the County of Glatz; Grand Duke of the Lower Rhine and of Posen; Duke of Saxony, of Westphalia, of Angria, of Pomerania, Lunenburg, Holstein and Schleswig, of Magdeburg, of Bremen, of Guelders, Cleves, Jülich and Berg, Duke of the Wends and the Kassubes, of Crossen, Lauenburg and Mecklenburg; Landgrave of Hesse and Thuringia; Margrave of Upper and Lower Lusatia; Prince of Orange; Prince of Rügen, of East Friesland, of Paderborn and Pyrmont, of Halberstadt, Münster, Minden, Osnabrück, Hildesheim, of Verden, Cammin, Fulda, Nassau and Moers; Princely Count of Henneberg; Count of Mark, of Ravensberg, of Hohenstein, Tecklenburg and Lingen, of Mansfeld, Sigmaringen and Veringen; Lord of Frankfurt.


title: German Emperor

text: His Imperial and Royal Majesty Frederick III, By the Grace of God, German Emperor and King of Prussia, Margrave of Brandenburg, Burgrave of Nuremberg, Count of Hohenzollern, Duke of Silesia and of the County of Glatz, Grand Duke of the Lower Rhine and of Posen, Duke of Saxony, of Angria, of Westphalia, of Pomerania and of Lunenburg, Duke of Schleswig, of Holstein and of Crossen, Duke of Magdeburg, of Bremen, of Guelderland and of Jülich, Cleves and Berg, Duke of the Wends and the Kashubians, of Lauenburg and of Mecklenburg, Landgrave of Hesse and in Thuringia, Margrave of Upper and Lower Lusatia, Prince of Orange, of Rugen, of East Friesland, of Paderborn and of Pyrmont, Prince of Halberstadt, of Münster, of Minden, of Osnabrück, of Hildesheim, of Verden, of Kammin, of Fulda, of Nassau and of Moers, Princely Count of Henneberg, Count of the Mark, of Ravensberg, of Hohenstein, of Tecklenburg and of Lingen, Count of Mansfeld, of Sigmaringen and of Veringen, Lord of Frankfurt.


title: German Emperor

text: His Imperial and Royal Majesty Wilhelm II, By the Grace of God, German Emperor and King of Prussia, Margrave of Brandenburg, Burgrave of Nuremberg, Count of Hohenzollern, Duke of Silesia and of the County of Glatz, Grand Duke of the Lower Rhine and of Posen, Duke of Saxony, of Angria, of Westphalia, of Pomerania and of Lunenburg, Duke of Schleswig, of Holstein and of Crossen, Duke of Magdeburg, of Bremen, of Guelderland and of Jülich, Cleves and Berg, Duke of the Wends and the Kashubians, of Lauenburg and of Mecklenburg, Landgrave of Hesse and in Thuringia, Margrave of Upper and Lower Lusatia, Prince of Orange, of Rugen, of East Friesland, of Paderborn and of Pyrmont, Prince of Halberstadt, of Münster, of Minden, of Osnabrück, of Hildesheim, of Verden, of Kammin, of Fulda, of Nassau and of Moers, Princely Count of Henneberg, Count of the Mark, of Ravensberg, of Hohenstein, of Tecklenburg and of Lingen, Count of Mansfeld, of Sigmaringen and of Veringen, Lord of Frankfurt.


title: Innocent (TV series)

text: Innocent is a British anthology television series, produced by TXTV productions, that was first broadcast on ITV for four consecutive nights between 14 and 17 May 2018. The first series stars Lee Ingleby as David Collins, Daniel Ryan as Phil Collins, David's faithful brother, Hermione Norris as Alice Moffatt and Adrian Rawlins as her husband, Rob Moffatt. The German TV broadcaster ARD produced a two-part adaptation, "", first broadcast in December 2019. The second series, aired in 2021, starred Katherine Kelly, Andrew Tiernan, Priyanga Burford and Jamie Bamber.


title: Innocent (TV series)

text: This series tells the story of David Collins (Lee Ingleby), who was convicted of murdering his wife Tara. After serving seven years in prison he was acquitted on a legal technicality. The story revolves around attempts to reveal the truth of who actually killed Tara, with the plot involving the police, Tara's sister Alice (Hermione Norris), who now has custody of Tara and David's children, and David's brother Phil (Daniel Ryan).


title: Innocent (TV series)

text: Matthew Taylor, a 16-year-old school boy was brutally murdered in the quiet Lake District. Five years later the accused is found not guilty and released from prison.


title: Bias of an estimator

text: In statistics, the bias of an estimator (or bias function) is the difference between this estimator's expected value and the true value of the parameter being estimated. An estimator or decision rule with zero bias is called unbiased. In statistics, "bias" is an property of an estimator. Bias is a distinct concept from consistency: consistent estimators converge in probability to the true value of the parameter, but may be biased or unbiased; see bias versus consistency for more.


title: Bias of an estimator

text: All else being equal, an unbiased estimator is preferable to a biased estimator, although in practice, biased estimators (with generally small bias) are frequently used. When a biased estimator is used, bounds of the bias are calculated. A biased estimator may be used for various reasons: because an unbiased estimator does not exist without further assumptions about a population; because an estimator is difficult to compute (as in unbiased estimation of standard deviation); because a biased estimator may be unbiased with respect to different measures of central tendency; because a biased estimator gives a lower value of some loss function (particularly mean squared error) compared with unbiased estimators (notably in shrinkage estimators); or because in some cases being unbiased is too strong a condition, and the only unbiased estimators are not useful.


title: Bias of an estimator

text: Bias can also be measured with respect to the median, rather than the mean (expected value), in which case one distinguishes "median"-unbiased from the usual "mean"-unbiasedness property.


title: Bias of an estimator

text: Mean-unbiasedness is not preserved under non-linear transformations, though median-unbiasedness is (see ); for example, the sample variance is a biased estimator for the population variance. These are all illustrated below.


title: Bias of an estimator

text: Suppose we have a statistical model, parameterized by a real number "θ", giving rise to a probability distribution for observed data, formula_1, and a statistic formula_2 which serves as an estimator of "θ" based on any observed data formula_3. That is, we assume that our data follow some unknown distribution formula_4 (where "θ" is a fixed, unknown constant that is part of this distribution), and then we construct some estimator formula_2 that maps observed data to values that we hope are close to "θ". The bias of formula_2 relative to formula_7 is defined as


title: Bias of an estimator

text: where formula_9 denotes expected value over the distribution formula_4 (i.e., averaging over all possible observations formula_3). The second equation follows since "θ" is measurable with respect to the conditional distribution formula_4.


title: Bias of an estimator

text: An estimator is said to be unbiased if its bias is equal to zero for all values of parameter "θ", or equivalently, if the expected value of the estimator matches that of the parameter.


title: Bias of an estimator

text: In a simulation experiment concerning the properties of an estimator, the bias of the estimator may be assessed using the mean signed difference.


title: Bias of an estimator

text: The sample variance of a random variable demonstrates two aspects of estimator bias: firstly, the naive estimator is biased, which can be corrected by a scale factor; second, the unbiased estimator is not optimal in terms of mean squared error (MSE), which can be minimized by using a different scale factor, resulting in a biased estimator with lower MSE than the unbiased estimator. Concretely, the naive estimator sums the squared deviations and divides by "n," which is biased. Dividing instead by "n" − 1 yields an unbiased estimator. Conversely, MSE can be minimized by dividing by a different number (depending on distribution), but this results in a biased estimator. This number is always larger than "n" − 1, so this is known as a shrinkage estimator, as it "shrinks" the unbiased estimator towards zero; for the normal distribution the optimal value is "n" + 1.


title: Bias of an estimator

text: Suppose "X", ..., "X" are independent and identically distributed (i.i.d.) random variables with expectation "μ" and variance "σ". If the sample mean and uncorrected sample variance are defined as


title: Bias of an estimator

text: This can be seen by noting the following formula, which follows from the Bienaymé formula, for the term in the inequality for the expectation of the uncorrected sample variance above: formula_20.


title: Bias of an estimator

text: In other words, the expected value of the uncorrected sample variance does not equal the population variance "σ", unless multiplied by a normalization factor. The sample mean, on the other hand, is an unbiased estimator of the population mean "μ".


title: Bias of an estimator

text: Note that the usual definition of sample variance is formula_21, and this is an unbiased estimator of the population variance.


title: Bias of an estimator

text: where the transition to the second line uses the result derived above for the biased estimator. Thus formula_24, and therefore formula_25 is an unbiased estimator of the population variance, "σ". The ratio between the biased (uncorrected) and unbiased estimates of the variance is known as Bessel's correction.


title: Bias of an estimator

text: The reason that an uncorrected sample variance, "S", is biased stems from the fact that the sample mean is an ordinary least squares (OLS) estimator for "μ": formula_26 is the number that makes the sum formula_27 as small as possible. That is, when any other number is plugged into this sum, the sum can only increase. In particular, the choice formula_28 gives,


title: Bias of an estimator

text: The above discussion can be understood in geometric terms: the vector formula_31 can be decomposed into the "mean part" and "variance part" by projecting to the direction of formula_32 and to that direction's orthogonal complement hyperplane. One gets formula_33 for the part along formula_34 and formula_35 for the complementary part. Since this is an orthogonal decomposition, Pythagorean theorem says formula_36, and taking expectations we get formula_37, as above (but times formula_38).


title: Bias of an estimator

text: If the distribution of formula_39 is rotationally symmetric, as in the case when formula_40 are sampled from a Gaussian, then on average, the dimension along formula_34 contributes to formula_42 equally as the formula_43 directions perpendicular to formula_34, so that formula_45 and formula_46. This is in fact true in general, as explained above.


title: Bias of an estimator

text: A far more extreme case of a biased estimator being better than any unbiased estimator arises from the Poisson distribution. Suppose that "X" has a Poisson distribution with expectation "λ". Suppose it is desired to estimate


title: Bias of an estimator

text: with a sample of size 1. (For example, when incoming calls at a telephone switchboard are modeled as a Poisson process, and "λ" is the average number of calls per minute, then "e" is the probability that no calls arrive in the next two minutes.)


title: Bias of an estimator

text: To see this, note that when decomposing e from the above expression for expectation, the sum that is left is a Taylor series expansion of e as well, yielding ee = e (see Characterizations of the exponential function).


title: Bias of an estimator

text: If the observed value of "X" is 100, then the estimate is 1, although the true value of the quantity being estimated is very likely to be near 0, which is the opposite extreme. And, if "X" is observed to be 101, then the estimate is even more absurd: It is −1, although the quantity being estimated must be positive.


title: Bias of an estimator

text: is far better than this unbiased estimator. Not only is its value always positive but it is also more accurate in the sense that its mean squared error


title: Bias of an estimator

text: The bias of maximum-likelihood estimators can be substantial. Consider a case where "n" tickets numbered from 1 through to "n" are placed in a box and one is selected at random, giving a value "X". If "n" is unknown, then the maximum-likelihood estimator of "n" is "X", even though the expectation of "X" given "n" is only ("n" + 1)/2; we can be certain only that "n" is at least "X" and is probably more. In this case, the natural unbiased estimator is 2"X" − 1.


title: Bias of an estimator

text: Further properties of median-unbiased estimators have been noted by Lehmann, Birnbaum, van der Vaart and Pfanzagl. In particular, median-unbiased estimators exist in cases where mean-unbiased and maximum-likelihood estimators do not exist. They are invariant under one-to-one transformations.


title: Bias of an estimator

text: There are methods of construction median-unbiased estimators for probability distributions that have monotone likelihood-functions, such as one-parameter exponential families, to ensure that they are optimal (in a sense analogous to minimum-variance property considered for mean-unbiased estimators). One such procedure is an analogue of the Rao–Blackwell procedure for mean-unbiased estimators: The procedure holds for a smaller class of probability distributions than does the Rao–Blackwell procedure for mean-unbiased estimation but for a larger class of loss-functions.


title: Bias of an estimator

text: Any minimum-variance "mean"-unbiased estimator minimizes the risk (expected loss) with respect to the squared-error loss function (among mean-unbiased estimators), as observed by Gauss. A minimum-average absolute deviation "median"-unbiased estimator minimizes the risk with respect to the absolute loss function (among median-unbiased estimators), as observed by Laplace. Other loss functions are used in statistics, particularly in robust statistics.


title: Bias of an estimator

text: For univariate parameters, median-unbiased estimators remain median-unbiased under transformations that preserve order (or reverse order).


title: Bias of an estimator

text: Note that, when a transformation is applied to a mean-unbiased estimator, the result need not be a mean-unbiased estimator of its corresponding population statistic. By Jensen's inequality, a convex function as transformation will introduce positive bias, while a concave function will introduce negative bias, and a function of mixed convexity may introduce bias in either direction, depending on the specific function and distribution. That is, for a non-linear function "f" and a mean-unbiased estimator "U" of a parameter "p", the composite estimator "f"("U") need not be a mean-unbiased estimator of "f"("p"). For example, the square root of the unbiased estimator of the population variance is a mean-unbiased estimator of the population standard deviation: the square root of the unbiased sample variance, the corrected sample standard deviation, is biased. The bias depends both on the sampling distribution of the estimator and on the transform, and can be quite involved to calculate – see unbiased estimation of standard deviation for a discussion in this case.


title: Bias of an estimator

text: While bias quantifies the "average" difference to be expected between an estimator and an underlying parameter, an estimator based on a finite sample can additionally be expected to differ from the parameter due to the randomness in the sample.


title: Bias of an estimator

text: where formula_57 is the trace (diagonal sum) of the covariance matrix of the estimator and formula_58 is the square vector norm.


title: Bias of an estimator

text: If the variables "X" ... "X" follow a normal distribution, then "nS"/σ has a chi-squared distribution with "n" − 1 degrees of freedom, giving:


title: Bias of an estimator

text: With a little algebra it can be confirmed that it is "c" = 1/("n" + 1) which minimises this combined loss function, rather than "c" = 1/("n" − 1) which minimises just the square of the bias.


title: Bias of an estimator

text: More generally it is only in restricted classes of problems that there will be an estimator that minimises the MSE independently of the parameter values.


title: Bias of an estimator

text: However it is very common that there may be perceived to be a "bias–variance tradeoff", such that a small increase in bias can be traded for a larger decrease in variance, resulting in a more desirable estimator overall.