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Vita Sackville-West

Victoria Mary, Lady Nicolson, CH (née Sackville-West; 9 March 1892 – 2 June 1962), usually known as Vita Sackville-West, was an English author and garden designer.

Sackville-West was a successful novelist, poet and journalist, as well as a prolific letter writer and diarist. She published more than a dozen collections of poetry and 13 novels during her life. She was twice awarded the Hawthornden Prize for Imaginative Literature: in 1927 for her pastoral epic, The Land, and in 1933 for her Collected Poems. She was the inspiration for the protagonist of Orlando: A Biography, by her friend and lover Virginia Woolf. She wrote a column in The Observer from 1946 to 1961 and is remembered for the celebrated garden at Sissinghurst in Kent, created with her husband, Sir Harold Nicolson.

Antecedents

Victoria Mary Sackville-West — called Vita, to distinguish her from her mother — was born on 9 March 1892 at Knole, the Kent home of Sackville-West's aristocratic ancestors. She was the only child of cousins Victoria Sackville-West and Lionel Sackville-West, 3rd Baron Sackville. Vita's mother, the illegitimate daughter of Lionel Sackville-West, 2nd Baron Sackville and the Spanish dancer Pepita (Josefa de Oliva, née Durán y Ortega), had been raised in a Parisian convent.

Although the marriage of Sackville-West's parents was initially happy, the couple drifted apart shortly after her birth. Lionel took a mistress, an opera singer who came to live with them at Knole.

Knole had been given to Thomas Sackville by Elizabeth I, in the sixteenth century. The Sackville-West family followed the English aristocracy's inheritance customs, preventing Vita from inheriting Knole upon the death of her father; this was a source of life-long bitterness for her. The house followed the title, and was bequeathed instead by her father to his brother Charles, who became the 4th Baron.

Early life
Sackville-West was initially taught at home by governesses and later attended Helen Wolff's school for girls, an exclusive day school in Mayfair, where she met first loves Violet Keppel and Rosamund Grosvenor. She did not befriend local children and found it hard to make friends at school. Her biographers characterise her childhood as one filled by loneliness and isolation. She wrote prolifically at Knole, penning eight full-length (unpublished) novels between 1906 and 1910, ballads and many plays, some in French. Her lack of formal education led to later shyness with her peers, such as those in the Bloomsbury Group. She felt herself to be sluggish of mind and she was never at the intellectual heart of her social group.

Sackville-West's apparently Roma lineage introduced a passion for "gypsy" ways, a culture she perceived to be hot-blooded, heart-led, dark, and romantic. It informed the stormy nature of many of her later love affairs and was a strong theme in her writing. Sackville-West visited Roma camps and felt herself to be at one with them.

Vita's mother had a wide array of famous lovers, including financier J. P. Morgan and Sir John Murray Scott (from 1897 until his death in 1912). Scott, secretary to the couple who inherited and developed the Wallace Collection, was a devoted companion and Lady Sackville and he were rarely apart during their years together. During her childhood, Vita spent a great deal of time in Scott's apartments in Paris, perfecting her already fluent French.

First loves
Sackville-West debuted in 1910. She was wooed by Orazio Pucci, son of a distinguished Florentine family; by Lord Granby (later 9th Duke of Rutland); and by Lord Lascelles (later 6th Earl of Harewood), among others. In 1924 she had a passionate affair with historian Geoffrey Scott. Scott's marriage collapsed shortly thereafter, as was often the fallout with Sackville-West's affairs, all with women after this point (as most of them had been beforehand).

Sackville-West fell in love with Rosamund Grosvenor (1888–1944), who was four years her senior. In her journal, Vita wrote "Oh, I dare say I realized vaguely that I had no business to sleep with Rosamund, and I should certainly never have allowed anyone to find it out," but she saw no real conflict. Lady Sackville, Vita's mother, invited Rosamund to visit the family at their villa in Monte Carlo (1910). Rosamund also stayed with Vita at Knole House, at Murray Scott's pied-à-terre on the Rue Laffitte in Paris, and at Sluie, Scott's shooting lodge in the Scottish Highlands, near Banchory. Their secret relationship ended in 1913 when Vita married.

Sackville-West was more deeply involved with Violet Keppel, daughter of the Hon. George Keppel and his wife, Alice Keppel. The sexual relationship began when they were both in their teens and strongly influenced them for years. Both later married and became writers.

Marriage to Harold Nicolson
Sackville-West was courted for 18 months by young diplomat Harold Nicolson, whom she found to be a secretive character. She writes that the wooing was entirely chaste and throughout they did not so much as kiss. In 1913, at age 21, Vita married him in the private chapel at Knole. Vita's parents were opposed to the marriage on the grounds that "penniless" Nicolson had an annual income of only £250. He was the third secretary at the British Embassy in Constantinople at the time. Another of Sackville-West's suitors, Lord Granby, had an annual income of £100,000, owned vast acres of land and was heir to an old title, Duke of Rutland.

The couple had an open marriage. Both Sackville-West and her husband had same-sex relationships before and during their marriage, as did some of the Bloomsbury Group of writers and artists, with whom they had connections. Sackville-West saw herself as psychologically divided into two: one side of her personality was more feminine, soft, submissive, and attracted to men while the other side was more masculine, hard, aggressive, and attracted to women. Following the pattern of his father's career, Harold Nicolson was at various times a diplomat, journalist, broadcaster, Member of Parliament, and author of biographies and novels. After the wedding the couple lived in Cihangir, a suburb of Constantinople (now Istanbul), the capital of the Ottoman Empire. Sackville-West loved Constantinople, but the duties of a diplomat's wife did not appeal to her. It was only during this time that she attempted to don, with good grace, the part of a "correct and adoring wife of the brilliant young diplomat", as she sarcastically wrote. When she became pregnant, in the summer of 1914, the couple returned to England to ensure that she could give birth in a British hospital.

The family lived at 182 Ebury Street, Belgravia and bought Long Barn in Kent as a country house (1915–1930). They employed the architect Edwin Lutyens to make improvements to the house. The British declaration of war on the Ottoman Empire in November 1914, following Ottoman naval attacks on Russia, precluded any return to Constantinople.

The couple had two children: Benedict (1914–1978), an art historian, and Nigel (1917–2004), a well-known editor, politician, and writer. Another son was stillborn in 1915.

Relationship with Violet Keppel

Sackville-West continued to receive devoted letters from her lover Violet Keppel. She was deeply upset to read of Keppel's engagement to Major Denys Trefusis. Her response was to travel to Paris to see Keppel and persuade her to honour their commitment. Keppel, depressed and suicidal, did eventually marry her fiancé, under pressure from her mother, though Keppel made it clear that she did not love her husband. Sackville-West called the marriage her own greatest failure.

Sackville-West and Keppel disappeared together several times from 1918 on, mostly to France. One day in 1918 Vita writes that she experienced a radical 'liberation', where her male aspect was unexpectedly freed. She writes: "I went into wild spirits; I ran, I shouted, I jumped, I climbed, I vaulted over gates, I felt like a schoolboy let out on a holiday... that wild irresponsible day".

The mothers of both women joined forces to sabotage the relationship and force their daughters back to their husbands. But they were unsuccessful. Sackville-West often dressed as a man, styled as Keppel's husband. The two women made a bond to remain faithful to one another, pledging that neither would engage in sexual relations with their husbands.

Keppel continued to pursue her lover to great lengths, until Sackville-West's affairs with other women finally took their toll. In November 1919, while staying at Monte Carlo, Sackville-West wrote that she felt very low, entertaining thoughts of suicide, believing that Nicolson would be better off without her. In 1920 the lovers ran off again to France together and their husbands chased after them in a small two-seater aeroplane. Sackville-West heard allegations that Keppel and her husband Trefusis had been involved sexually, and she broke off the relationship as the lesbian oath of fidelity had been broken. Despite the rift, the two women stayed devoted to one another.

Persia
From 1925 to 1927, Nicolson lived in Tehran where Sackville-West often visited him. Sackville-West's book A Passenger to Tehran recounts her time there. The couple were involved in planning the coronation of Rezā Khan and got to know the six-year old Crown Prince Mohammad Reza well. She also visited and wrote about the former capital of Isfahan to see the Safavid palaces.

Relationship with Virginia Woolf

Sackville-West's relationship with the prominent writer Virginia Woolf began in 1925 and ended in 1935, reaching its height between 1925 and 1928. The American scholar Louise DeSalvo wrote that the ten years while they were together were the artistic peak of both women's careers, owing to the positive influence they had on one another: "neither had ever written so much so well, and neither would ever again reach this peak of accomplishment".

In December 1922, Sackville-West first met Virginia Woolf at a dinner party in London. Though Sackville-West came from an aristocratic family that was far richer than Woolf's own, the women bonded over their confined childhoods and emotionally absent parents. Woolf knew about Sackville-West's relationship with Keppel and was impressed by her free spirit.

Sackville-West greatly admired Woolf's writings, considering her to be the better author. She told Woolf in one letter: "I contrast my illiterate writing with your scholarly one, and I am ashamed". Though Woolf envied Sackville-West's ability to write quickly, she was inclined to believe that the volumes were written too much in haste: "Vita's prose is too fluent".

As the two grew close, Woolf disclosed that as a child she had been abused by her step-brother. It was largely due to Sackville-West's support that Woolf began to heal from the trauma, allowing her for the first time to have a satisfying erotic relationship. Woolf purchased a mirror during a trip to France with Sackville-West, saying she felt she could look in a mirror for the first time in her life. Sackville-West's support gave Woolf greater confidence and helped her cast off her self-image of a sickly semi-recluse. She persuaded Woolf that her nervous ailments had been misdiagnosed, and that she should focus on her own varied intellectual projects; that she must learn to rest.

To help the Woolfs, Sackville-West chose their Hogarth Press to be her publisher. Seducers in Ecuador, the first Sackville-West novel to be published by Hogarth, sold only 1,500 copies in its first year. The Edwardians, published next, sold 30,000 copies in its first six months. The boost helped Hogarth financially, though Woolf did not always value the books' romantic themes. The increased security of the Press's fortunes allowed Woolf to write more experimental novels such as The Waves. Though contemporary critics consider Woolf a better writer, critics in the 1920s viewed Sackville-West as more accomplished, with her books outselling Woolf's by a large margin.

Sackville-West loved to travel, frequently going to France, Spain and to visit Nicolson in Persia. These trips were emotionally draining for Woolf, who missed Sackville-West intensely. Woolf's novel To the Lighthouse, noteworthy for its theme of longing for someone absent, was partly inspired by Sackville-West's frequent absences. Sackville-West inspired Woolf to write one of her most famous novels, Orlando, featuring a protagonist who changes sex over the centuries. This work was described by Sackville-West's son Nigel Nicolson as "the longest and most charming love-letter in literature."

There were, however, tensions in the relationship. Woolf was often bothered by what she viewed as Sackville-West's promiscuity, charging that Sackville-West's great need for sex led her to take up with anyone who struck her fancy. In A Room of One's Own (1929), Woolf attacks patriarchal inheritance laws. This was an implicit criticism of Sackville-West, who never questioned the leading social and political position of the aristocracy to which she belonged. She felt that Sackville-West was unable to critique the system she was both a part of and, to a certain extent, a victim of. In the 1930s they clashed over Nicolson's "unfortunate" involvement with Oswald Mosley and the New Party (later renamed the British Union of Fascists), and they were at odds over the imminent war. Sackville-West supported rearmament while Woolf remained loyal to her pacifism; this contributed to the distancing of their relationship in 1935.

"My friendship to Vita is over. Not with a quarrel, not with a bang, but as ripe fruit falls. But her voice saying 'Virginia?' outside the tower room was as enchanting as ever. Only then nothing happened."

However, the two women reconnected in 1937 and remained close until Woolf's death in 1941.

"Your friendship means so much to me. In fact it is one of the major things in my life"

Other lovers
One of Sackville-West's male suitors, Henry Lascelles, would later marry the Princess Royal and become the 6th Earl of Harewood.

In 1927, Sackville-West had an affair with Mary Garman, a member of the Bloomsbury Group; between 1929 and 1931, she maintained a relationship with Hilda Matheson, head of the BBC Talks Department. In 1931, Sackville-West was in a ménage à trois with journalist Evelyn Irons and Irons's lover, Olive Rinder. Irons had interviewed Sackville-West after her novel The Edwardians had become a best-seller.

Sissinghurst

In 1930 the family acquired and moved to Sissinghurst Castle, near Cranbrook, Kent. It had once been owned by Vita's ancestors. This gave it a dynastic attraction as she was excluded from inheriting Knole and a title. Sissinghurst was an Elizabethan ruin and the creation of the gardens would be a joint labour of love that would last many decades, first entailing years of clearing debris from the land. Nicolson provided the architectural structure, with strong classical lines, which would frame his wife's innovative informal planting schemes. She created a new and experimental system of enclosures or rooms, such as the White Garden, Rose Garden, Orchard, Cottage Garden and Nuttery. She also innovated single colour-themed gardens and design principles orientating the visitors' experience to discovery and exploration. Her first garden at Long Barn (Kent, 1915–1930) was experimental, a place of learning by trial and error and she carried over her ideas and projects to Sissinghurst, using her hard won experience. Sissinghurst was first opened to the public in 1938.

Sackville-West took up writing again in 1930 after a six-year break as she needed money to pay for Sissinghurst. Nicolson, having left the Foreign Office, no longer had a diplomat's salary to draw upon. She also had to pay tuition for her two sons to attend Eton College. She felt she had become a better writer thanks to the mentorship of Woolf. In 1947 she began a weekly column in The Observer called "In your Garden", although she was not a trained horticulturist or designer. She continued the very popular column until a year before her death, and writing helped to make Sissinghurst one of the most famous and visited gardens in England. In 1948 she became a founder member of the National Trust's garden committee. The grounds are now run by the National Trust. She was awarded the Veitch Memorial Medal from the Royal Horticultural Society.

Portrait of a Marriage
In the early 1920s Sackville-West wrote a memoir of her relationships. In it she sought to explain both why she had chosen to stay with Nicolson and why she had fallen in love with Violet Keppel. The work, titled Portrait of a Marriage, was not published until 1973. In the book she uses metaphors from nature to present her account as truthful and honest, describing her life as a "bog" and a "swamp", suggesting that her personal life was naturally unappealing and unpleasant. Sackville-West stated that she wanted to explain her sexuality, which she presented as being at the core of her personality. She wrote that in the future "it will be recognized that many more people of my type do exist than under the present-day system of hypocrisy is commonly admitted".

Reflecting a certain ambivalence about her sexuality, Sackville-West presented her sexual desires for Keppel as both "deviant" and "natural", as if she herself was uncertain of whether her sexuality was normal or not, though the American scholar Georgia Johnston has argued that Sackville-West's confusion on this point was due to her wish to have this memoir published one day. In this regard, Sackville-West wrote of her deep desire and love for Keppel while at same time declaring her "shame" about this "duality with which I was too weak and too self-indulgent to struggle". At various times, Sackville-West called herself a "pariah" with a "perverted nature" and "unnatural" feelings for Keppel, who was portrayed as a tempting, if degrading, object of her desire. Sackville-West called for a "spirit of candor" in society that would allow for tolerance of gay and bisexual people. Much influenced by the theories promoted by sexologists like Magnus Hirschfeld, Edward Carpenter, Richard von Krafft-Ebing, Havelock Ellis and Sigmund Freud, Sackville-West sometimes wrote of her sexuality as abnormal and wrong and due to some psychological flaw she was born with, portraying heterosexuality as the norm that she wanted, but failed to live up to.

Several times, Sackville-West stated that she wrote Portrait of a Marriage for scientific purposes so people would be able to understand bisexual people, which would thus allow her, despite her self-condemnation, to present her sexuality as in some way normal. Several of the sexologists Sackville-West cited, most notably Carpenter and Ellis, had argued that homosexuality and bisexuality were in fact normal, and despite her condemning herself, her use of a "scientific" approach backed up with quotes from Ellis and Carpenter allowed her to present her bisexuality as implicitly normal. Writing in the third person, Sackville-West declared "she regrets that the person Harold married wasn't entirely and wholly what he had thought of her, and that the person who loves and owns Violet isn't a second person, because each suits each other". Sackville-West presented her sexuality as part of the personality she had been born with, portraying herself as an accursed woman who should be the object of sympathy, not condemnation.

In 1973, when her son Nigel Nicolson published Portrait of a Marriage, he was uncertain if he was going to be charged with obscenity, going to considerable lengths to stress the legitimacy of a love for a person of the same sex in his introduction. Despite portraying herself as in some way "deviant" because of her feelings for women, Sackville-West also wrote in Portrait of a Marriage of the discovery and acceptance of her bisexuality as a teenager as the joyous "liberation of half my personality", suggesting that she did not really see herself as a woman with "deviant" sexuality, as this statement contradicted what she had written at the beginning of the book about her "perverted" sexuality. Johnson wrote that Sackville-West, in presenting the lesbian side of herself in terms that depicted Keppel as evil and Nicolson as good, was the only way possible at the time to express this side of her personality, writing "even if annihilating herself seemed the only way she could present any type of acceptable self."

The memoir was dramatised by the BBC (and PBS in North America) in 1990, starring Janet McTeer as Vita, and Cathryn Harrison as Violet. The series won four BAFTAs.

Challenge
Sackville-West's novel Challenge (1923) also bears witness to her affair with Keppel: Sackville-West and Keppel had started writing this book as a collaborative endeavour. It was published in America but banned in the UK until 1974.

The male character's name, Julian, had been Sackville-West's nickname when passing as a man. Challenge (first entitled Rebellion, then Enchantment, then Vanity and at some point Foam), is a roman à clef with the character of Julian being a male version of Sackville-West and Eve, the woman he desires so passionately is Keppel. Notably, Sackville-West in Challenge defends Keppel against several of the insults Nicolson had applied to her in his letters to her; for example Nicolson often called Keppel a "swine" and a "pig", and in the book Julian goes out of his way to say that Eve is neither a swine nor a pig. In the book, Julian says that "Eve is not a 'little swine', she just has the weaknesses and faults of femininity carried to the 9th degree, but is also redeemed by a self-sacrifice, which is very feminine".

Reflecting her obsession with the Romani people, Eve is portrayed as a seductive Romani woman with an "insinuating femininity" that Julian cannot resist, calling him away from his political mission of winning independence on a fictional Greek island during the Greek war of independence. Nicolson wrote in a letter to his wife: "Don't please dedicate it to Violet, it would kill me if you did". When Challenge was published in 1924, the dedication was written in Romani reading: "This book is yours, honoured witch. If you read it, you will find your tormented soul changed and free". Throughout their relationship, Keppel was given to threatening suicide if Sackville-West left her, a character trait shared by Eve, who finally drowns herself by walking in the sea when Julian is aboard a boat and too far off to hear her calling for him. The book's ending reflected Sackville-West's guilt about breaking her relationship with Keppel.

Her mother, Lady Sackville, found the portrayal obvious enough to refuse to allow publication of the novel in England; but Vita's son Nigel Nicolson praises his mother: "She fought for the right to love, men and women, rejecting the conventions that marriage demands exclusive love, and that women should love only men, and men only women. For this she was prepared to give up everything ... How could she regret that the knowledge of it should now reach the ears of a new generation, one so infinitely more compassionate than her own?"

Sackville-West was fascinated with and often wrote about the Roma people. As the British scholar Kirstie Blair noted, for her: "Gypsies represent liberation, excitement, danger and the free expression of sexuality". In particular, the Roma women, especially Spanish Romani women, served as a symbol for female homosexuality in her writings. As with many other female writers in this period, for Sackville-West, the Romani represented a social element both familiar and strange; a people perceived and admired as flamboyant romantics while at the same time viewed and hated as shifty, dishonest types; a rootless people who belonged nowhere yet could be found everywhere in Europe, serving as a symbol for a sort of unconventional femininity. The picture Sackville-West held of the Romani was much influenced by orientalism, as the Romani were believed to have originated from India. The idea of a people who belonged nowhere, existing outside of the values of "civilization", held genuine appeal to her as it offered up the possibility of gender roles different from those held in the West. Sackville-West was English, but she invented Romani ancestry for herself on the Spanish side of her family, explaining her bohemian behaviour as due to her alleged "Gypsy" descent.

Orlando
Woolf was inspired by Sackville-West to write her novel Orlando (1928), featuring a protagonist who changes sex over the centuries. Reflecting Sackville-West's interest in the Romani, when Orlando goes to bed as a man and mysteriously wakes up as a woman in Constantinople (which is implied might have been the result of a spell cast by a Romani witch whom he married), it is at a Romani camp in the Balkans that Orlando is first welcomed and accepted as a woman, as the Romani in the novel make no distinctions between the sexes. Ultimately Woolf satirizes Sackville-West's Romani fetish, as Orlando, an English aristocrat, prefers not to live in poverty as part of wandering Romani caravan in the Balkans, because the call of a settled life of the aristocracy at a country house in England proves too strong for her, just as in real life Sackville-West fantasised about living the nomadic life of a Romani, but in reality preferred the settled life in the English countryside. Orlando, which was intended as a fantasy where the character of Orlando (a stand-in for Sackville-West) inherits an estate, not unlike Knole (which Sackville-West would have inherited as the eldest child if she had been a man), ironically marked the beginning of a tension between the two women. Sackville-West often complained in her letters that Woolf was more interested in writing a fantasy about her than in returning her gestures of affection in the real world.

Family History
Sackville-West's 1932 novel Family History tells the story of Evelyn Jarrold, a rich widow who married into a family which owes its recent wealth and social position to the ownership of coal mines, and her ill-fated love affair with Miles Vane-Merrick, a much younger man with progressive social ideas. Evelyn Jarrold's husband, Tommy, died in the Great War, and she has nothing to occupy her apart from her son Dan (the Jarrolds' heir, who is away at Eton), social events, and visits to her dressmaker. Vane-Merrick is a farming landowner and Member of Parliament, and is writing a book on economics. He represents new, progressive values and the male world of work and economic activity, and Evelyn Jarrold represents traditional values and the female world of family ties and social engagements.

The characters of Viola and Leonard Anquetil in Family History are socialists, pacifists and feminists, thinly veiled versions of Virginia and Leonard Woolf. In Orlando, Woolf allowed Vita to finally "own" Knole, and in Family History, Vita returns the gesture, as the Anquetils have children who turned out to be intelligent and decent people. Woolf had never had children and was afraid that she would have been a bad mother. In casting her fictional alter-ego as an excellent mother she was offering a "gift" to Woolf.

Other work and achievements
Most of the novels were an immediate success (except Dark Island, Grand Canyon and La Grande Mademoiselle). All Passion Spent (1931) and Seducers in Ecuador (1924) sold especially well. Somewhat ironically Seducers overtook her mentor's novel Mrs Dalloway at the top of the sales charts.

The Edwardians (1930) and All Passion Spent are perhaps her best-known novels today. In the latter, the elderly Lady Slane courageously embraces a long-suppressed sense of freedom and whimsy after a life-time of following convention. This novel was dramatised by the BBC in 1986 starring Dame Wendy Hiller. All Passion Spent appears to reflect Woolf's influence. The character of Lady Slane begins to truly live only after the death of her husband, a former prime minister. She befriends the servants of her estate, discovering the lives of people she had previously ignored. At the end of the novel Lady Slane persuades her granddaughter to break off an arranged marriage in order to pursue her career as a musician.

Grand Canyon (1942) is a science fiction "cautionary tale" (as she termed it) about a Nazi invasion of an unprepared United States. The book takes an unsuspected twist, however, that makes it something more than a typical invasion yarn.

A recently rediscovered work from 1922 "A Note of Explanation" was written specifically to be a part of the miniature collection of books within the doll's House, and tells the story of a sprite that inhabits the doll's house and re-tells several fairy tales from the point of view of the sprite, indicating how they had influenced the story. The book was adapted for the stage by Emily Ingram under the title "A Sprite in the Doll's House" in 2019 and was performed in Edinburgh, at the Palace of Holyrood House as part of their Christmas festivities.

The poetry remains the least known of Sackville-West's work. It encompassed epics and translations of volumes such as Rilke's Duino Elegies. Her epic poems The Land (1926) and The Garden (1946) reflect an enduring passion for the earth and family tradition.The Land may have been written in response to the central work of Modernist poetry The Waste Land (also published by Hogarth Press). She dedicated her poem to her lover Dorothy Wellesley. A recording of Sackville-West reading it was released by the British Columbia label. Her poem won the Hawthornden Prize in 1927. She won it again in 1933 with her Collected Poems, becoming the only writer to do so twice. The Garden won the Heinemann Award for literature.

Her epic poem Solitude, published by the Hogarth Press in October 1938 contains references to the Bible, Paracelsus, Ixion, Catullus, Andromeda, the Iliad and a Sabine bride, all of which were quite acceptable in the early 20th century, but were seen as anachronistic by 1938. The narrator of Solitude has an ardent love of the English countryside. Though the sex of the narrator is left ambiguous, implied at various points to be a man or a woman, it is made clear the narrator loved intensely a woman who is no longer present and who is deeply missed. At one point, the narrator's horror and disgust at Ixion, a brutal rapist, implies that she is a woman. At another point in the poem, her desire to free Andromeda from her chains and to make love suggests that she is a lesbian. The narrator compares the love of nature to the love of books, as both cultivate her mind. She thinks of herself as superior to the farmers who merely work the land without the time or the interest for poetry, all of which make it possible for her to have a deeper appreciation of nature.

She is not well known as a biographer. The most famous of those works is her biography of Saint Joan of Arc in the work of the same name. Additionally, she composed a dual biography of Saint Teresa of Ávila and Thérèse of Lisieux entitled The Eagle and the Dove, a biography of the author Aphra Behn, and a biography of her maternal grandmother, the Spanish dancer known as Pepita.

Despite being a shy woman, Sackville-West often forced herself to participate in literary readings before book clubs and on the BBC in order to feel a sense of belonging. Her love of the classical traditions in literature put her out of favour with modernist critics and by the 1940s, she was often dismissed as a dated writer, much to her chagrin. In 1947 Sackville-West was made a Fellow of the Royal Society of Literature and a Member of the Order of the Companions of Honour.

Death and legacy

Vita Sackville-West died at Sissinghurst in June 1962, aged 70, from abdominal cancer. She was cremated and ashes buried in the family crypt within the church at Withyham, eastern Sussex.

Sissinghurst Castle is owned by the National Trust. Her son Nigel Nicolson lived there after her death, and following his death in 2004 his own son Adam Nicolson, Baron Carnock, came to live there with his family. With his wife, the horticulturalist Sarah Raven, they committed to restore the mixed working farm and growing food on the property for residents and visitors, a function that had withered under the aegis of the Trust.

The film Vita and Virginia, with Gemma Arterton as Vita and Elizabeth Debicki as Virginia, had its world premiere at the 2018 Toronto International Film Festival. It is directed by Chanya Button and based on a play by Eileen Atkins, created from the love letters between Sackville-West and Woolf. The play was first performed in London in October 1993 and off Broadway in November 1994.

Poetry
In her poetry, she often engaged themes of natural life and romantic love. She published more than a dozen collections of poetry during her life, listed here:
 * Timgad: [a poem] (1900)
 * Constantinople: eight poems (1915)
 * Poems of West & East (1917) (also credited as Mrs. Harold Nicolson)
 * The Land (1926)
 * King's daughter (1929)
 * Invitation to cast out care (1931)
 * Sissinghurst (1931)
 * Collected poems (1933)
 * Solitude: a poem (1938)
 * The Garden (1946)
 * Lost poem (or A Madder Caress) (2013)

Novels

 * Heritage (1919)
 * The dragon in shallow waters (1920)
 * Challenge (1920)
 * Grey Wethers: a romantic novel (1923)
 * Seducers in Ecuador (Hogarth Press, 1924)
 * The Edwardians (1930)
 * All Passion Spent (1931)
 * Family History (1932)
 * The Dark Island (1934)
 * Grand Canyon: A Novel (1942)
 * Devil at Westease: the story as related by Roger Liddiard (1947)
 * The Easter party (1953)
 * No Signposts in the Sea (1961)

Children's books

 * A Note of Explanation (written for Queen Mary's Dolls' House in 1924, published posthumously in 2017)

Short stories and novellas

 * Orchard and vineyard (1892)
 * The heir: a love story (1922)
 * To be let or sold (1930)
 * Thirty Clocks Strike the Hour, and other stories (1932)
 * The death of Noble Godavary and Gottfried Künstler (1932)
 * Another world than this ..: an anthology (1945)
 * Nursery rhymes (1947)

Plays

 * Chatterton: a drama in three acts (1909)

Letters

 * Dearest Andrew: letters from V. Sackville-West to Andrew Reiber, 1951-1962 (1979)
 * The Letters of Vita Sackville-West to Virginia Woolf (edited by Louise A. DeSalvo and Mitchell A. Leaska, Arrow, 1984)
 * Vita and Harold: The Letters of Vita Sackville-West and Harold Nicolson (1992)
 * Violet to Vita: The Letters of Violet Trefusis to Vita Sackville-West 1910–1921 (edited by Mitchell A. Leaska and John Phillips, 1991)
 * Portrait of a Marriage: Vita Sackville-West and Harold Nicolson by Nigel Nicolson, Vita Sackville-West (compiled by her son Nigel Nicolson from her journals and letters, Weidenfeld & Nicolson, 1973)
 * Love Letters: Vita and Virginia by Virginia Woolf and Vita Sackville-West (introduction by Alison Bechdel Vintage Classics, 2021)

Biographies

 * Aphra Behn, the incomparable Astrea (Gerald Howe, 1927)
 * Andrew Marvell (1929)
 * Saint Joan of Arc (Doubleday 1936, reprinted M. Joseph 1969)
 * Pepita (Doubleday, 1937, reprinted Hogarth Press 1970)
 * The eagle and the dove, a Study in Contrasts: St. Teresa of Avila and St. Thérèse of Lisieux (M. Joseph, 1943)
 * Daughter of France: the life of Anne Marie Louise d'Orléans, duchesse de Montpensier, 1627-1693, La Grande Mademoiselle (1959)

Guides

 * Knole and the Sackvilles (1922) - a history of her ancestral home
 * Passenger to Teheran (Hogarth Press 1926, reprinted Tauris Parke Paperbacks 2007, ISBN 978-1-84511-343-8)
 * Twelve Days: an account of a journey across the Bakhtiari Mountains of South-western Persia (first published UK 1927; Doubleday Doran 1928; M. Haag 1987, reprinted Tauris Parke Paperbacks 2009 as Twelve Days in Persia)
 * How does your garden grow? (1935) (Beverley Nichols, Compton Mackenzie, Marion Dudley Cran, Vita Sackville-West)
 * Some flowers (1937)
 * Country notes (1939)
 * Country Notes in Wartime (Hogarth Press, 1940)
 * English country houses (William Collins, 1941, illustrated)
 * The Women's Land Army (M. Joseph / Ministry of Agriculture and Fisheries, 1944)
 * Exhibition Catalogue: Elizabethan portraits (1947)
 * Knole, Kent (1948)
 * In Your Garden (1951)
 * In your garden again (1953)
 * Walter de la Mare and The traveller (1953)
 * More for your garden (1955)
 * Even more for your garden (1958)
 * Joy of Gardening: a selection for Americans (1958)
 * Berkeley Castle (1960)
 * Faces: profiles of dogs (Harvill Press, 1961, photographs by Laelia Goehr)
 * Garden Book (1975)
 * Hidcote Manor Garden, Gloucestershire (1976)
 * Une Anglaise en Orient (1993)

Translations

 * Duineser Elegien: Elegies from the Castle of Duino, translated from the German of Rainer Maria Rilke by V. and Edward Sackville-West (1931)

In 1931, Virginia and Leonard Woolf's Hogarth Press published in London a small run of a beautiful edition of Rainer Maria Rilke's Duino Elegies. This marked the English debut of Rilke's masterpiece, which would eventually be rendered in English over 20 times, influencing countless poets, musicians and artists across the English-speaking world.

Influences

 * Orlando: A Biography by Virginia Woolf (Hogarth Press, 1928)
 * Behind the Mask: The Life of Vita Sackville-West by Matthew Dennison (2014)

title: Vita Sackville-West


text:
User talk:IMSoP/Archive 1

If you are replying to a comment I left on your  page: Please leave a signature below, so I know you've been here, but leave the actual response next to my comment - that way, the conversation will continue to make sense, without me having to watch'' your  page. I get notified, but the conversation stays "over there".''

(This is just an experiment, to see if this is in fact any better than doing one or the other. Plus, no-one seems to have read this instruction in the time it's been here, so I guess it's pretty much a failed experiment!)

Hello, ...
and a slightly belated welcome to Wikipedia! You probably don't need it at this point, but we do have a Guide for h2g2 Researchers. Cheers! -- Stephen Gilbert 10:59 23 Jun 2003 (UTC)

Hi, thanks for that lightening-fast fix up of my spelling on Subversion. I'm notorious for leaving little errors in things. --Ejrh 05:38, 18 Dec 2003 (UTC)

 * No problem. I have a habit of going round copyediting when I should be going to bed (UTC == local time for me!).  [And now I understand what was meant on the pump about  You have new messages message.  Never seen it before!] - IMSoP 05:50, 18 Dec 2003 (UTC)

I have seen color in parts of other user's signatures, but I have obviously implemented it incorrectly. I think I will ask on the village pump. Sennheiser ! 01:22, 6 Feb 2004 (UTC) --- Thanks for spotting the double-redirect on Vitamin-S and amending accordingly. I haven't yet mastered doing redirects, but your vigilance should act as a suitable goad! Stan 20:00, 6 Feb 2004 (UTC)

Hi! I was wondering why the, etc., was deprecated, but I added that third method (the one that you enabled in How to edit a page) just in case, to make it easy on whoever decided that there was a problem with he 2nd method. Whenever I find a few moments elsewhere (probably later in the week), I'll go hunt down other such cases (if someone else hasn't done so already by then) and change them to make them consistent, along with a note on why not to use the other 2 methods, to keep someone else from "fixing" them. Scott McNay 05:48, 2004 Feb 20 (UTC)

 * I was just going to remove the old code entirely, so that the only concern is whether or not there's a problem with the third version. Was going to just add a note on the old ways and the problem with them.  Scott McNay 04:35, 2004 Feb 21 (UTC)

--- Hi, I added some replies in Talk:cycle agreeing with some of your points and I also invited a couple of other people to make some comments to help resolve the outstanding issues. RayTomes 10:30, 21 Mar 2004 (UTC)

I'll try to add some necessary Wiki links to my user page soon. Yaohua2000 16:46, 21 Mar 2004 (UTC)

On the Three Character Classic that you corrected : My sentence is incorrect but your change looses the meaning (in Chinese scholls, this book was the very first one studied, before any others, that's what I tried to say), if you have an idea on how to write that. gbog 13:21, 6 Apr 2004 (UTC)

Thank you :) Angela. 00:58, Apr 8, 2004 (UTC)

-- The train on platform 3 is for Didcot, Swindon, Bath Spa, Bristol Temple Meads............Oh great update on Sterkfontein thanks, a BIG improvement, but really you SHOULD BE WORKING!

 * Heheh. Well, yes I should; yes I should... :-D IMSoP 20:57, 23 Apr 2004 (UTC)

Duplication of vfd talk
Are you going through to check for conversations that have been accidentally deleted now? A convo I was taking part in has now completely disappeared... :-( -- Graham :) | Talk 16:44, 24 Apr 2004 (UTC)

Sits/Lies
lol. I'm not that sensitive. :) moink 19:23, 25 Apr 2004 (UTC)

Empire of Atlantium
Hi there. Apologies for the intrusion, but as you have been a positive contributor to the ongoing review of the Empire of Atlantium article recently I thought you might be interested to note that this article has been listed for deletion for the second time in several months, by a user who appears to have targeted it in some sort of POV-push. If you believe this article is worthy of continued inclusion I'd encourage you read my comments in response on the VFD page, and place a vote accordingly. --Gene_poole 08:31, 27 Apr 2004 (UTC)

Evidence in the matter of Wik2
The material you presented in Wikipedia talk:Requests for arbitration/Wik2 should go to Requests for arbitration/Wik2/Evidence with examples of of such edits. Fred Bauder 13:04, Apr 27, 2004 (UTC)

Talk: Mr Benn
Goodness! I feel guilty for being lazy now - I sort of left it cos I thought, "Oh God, how many times am I going to press save when I should be previewing, I'll leave it." Anyway, thanks, I appreciate that. It's like when my mum picks up my dirty socks ;o) Now: Get on with your work!  Or go to bed! --bodnotbod 21:39, May 2, 2004 (UTC)

Nemetschek on Vfd
Hello, I'd like to point out that I did not ever list Nemetschek. I listed Nemetscheck (note the spelling) before you turned it into a redirect. Later I commented on Template:VfD-Nemetscheck that it was a superfluous duplicate anyway, but that should not be construed to mean that I wanted Nemetschek to be deleted! If I had wanted that, I would have listed it separately. If you feel that Nemetschek was a VfD candidate, you could at least have given your own reasons instead of making it appear as if I had listed it. Lupo 09:26, 3 May 2004 (UTC)

 * You wrote:

 * >Oh dear, that whole Nemetscheck/Nemetschek thing is more of a mess than I thought it was

 * Indeed. Well, no harm done, and I'd like to apologize as well — I didn't check the VfD history either (as you put it so succintly: *shudder*) and thought you had created that listing. Oh well... if only I had thought of just redirecting the misspelled version, this whole mess could have been avoided. Lupo 06:23, 4 May 2004 (UTC)

Tnx...
...for the kind words & quote on the VP. –Hajor

Peer Review Please
Hi, you were kind enough the other week to give comment on the Manual of Style : Talk page; could you review the article that John & Wik keep reverting over at Papua (Indonesian province) : Page history -- My version speaks for itself; different maps, more content, and honest facts not twisted racist non-sense. THeir version paints Papuans as dumb blackmen lead around by a Reverend with a sing-song (please compare that paragraph to mine). Their version also removes the vital links to the US State Dept. document & the letter from JFK, without which US readers may have difficultly understanding why their government did what it did at that time.

Also they keep reverting over West Papuan Genocide - a perfectly good article that they apparently hate because the Yale University uses the term West Papua which they have expunged from their version at Human rights violations in western New Guinea. I'm hoping some peer review may stop Wik and friend.

They accuse me of POV, which I feel their article is loaded with where-as my article avoids any POV by simply listing known facts and allowing readers to form their own thoughts. Even Tannin explained that to them but it goes in one ear & out the other apparantly. Also English language users can really only search the Internet for the country title "West Papua", as Papua would only return PNG & New Guinea pages. The current Indonesian name of the region is actually Propinsi Papua. THe name issue is discussed on the talk page for a waste of time, and the meaning of Papua is even in dictionaries, sometimes even West Papua is.Daeron 15:01, 8 May 2004 (UTC)

You had an extra in the middle, so you were inadvertently telling it that the maths typesetting should stop there! (I've taken it out so you can copy-and-paste the new version, in case anyone's about to say "looks fine to me"). You had ...{\Gamma(1+y)} \frac{\... - easy to miss in amongst all that TeX; it might be a good idea to split it onto multiple lines to make it easier to edit (a single newline within the TeX markup doesn't make any difference to its display).

What a thoroughly scary equation, by the way - keep that thing away from me! - IMSoP 22:37, 8 May 2004 (UTC)

math typesetting help
Hi IMSoP

thanks for this. I would have sworn that I'd checked that equation with a fine toothed comb...must be the Wiki gremlin, I guess.

The reason that the equation was one line was that I thought the linebreaking was causing the problem...heigh ho.

I know you won't want to know this, but the equation (see unified neutral theory of biodiversity) is actually a massive simplification of earlier methods! take a look at the page!

cheers

Robinh 08:08, 10 May 2004 (UTC)

IRC
As a complete IRC novice, I've found mIRC to be pretty good (I don't know what you're looking for, but just thought I'd say :) -- sannse (talk) 19:10, 22 Jun 2004 (UTC)

wtf's an entiomer?
your shoes are entiomers of each other. 3d mirror images. the same but different. -- Rick
 * what do you think of working that analogy/metaphor/whatever into the text of the enantiomer article
 * DONE! Rick Boatright 19:44, 2 Jul 2004 (UTC)

Malicious Deletion Attempt
Hello. Sorry for the imposition, but I thought you might be interested to note that an article you supported in the past on vfd has been listed again under malicious circumstances - the 3rd such attempt in 7 months. Please feel free to review the discussion and cast your vote as you feel appropriate: http://en.wikipedia.org/wiki/Wikipedia:Votes_for_deletion/Atlantium --Gene_poole 10:38, 10 Aug 2004 (UTC)

Categories for deletion
Hi. Can I ask you to revisit Wikipedia_talk:Categories_for_deletion, in particular the section headed Frustration - deletion without discussion - I still think there's a lot needing to be talked out and some kind of way forward found. At the moment category deletion seems to be controlled as a fiefdom. --[[User:Bodnotbod| bodnotbod »  .....TALK Q uietly ) ]] 02:20, Aug 26, 2004 (UTC)

beta Systemic Bias section
Hi, if you wish to help contribute to a beta version of a Wikipedia page section designed to counter-act Wikipedia's systematic bias, please sign the bottom of this section on the Village pump - Village_pump. If not, no worries.--Xed 03:33, 22 Sep 2004 (UTC)

Adminship?
Are you interested in becoming an administrator? You've been here for quite a while now (longer than me) and seem to understand our policies pretty well. I would like to nominate you if you are willing - please let me know. --Michael Snow 01:47, 30 Sep 2004 (UTC)

Official invitation
Hi!

This is a message to let you know that there is now a UK-specific Wikipedia community page at UK wikipedians' notice board. It would be great if you could come and get involved! -- Graham ☺ | Talk 23:02, 1 Oct 2004 (UTC)

multiple redirects
Dear IMSoP, I have seen that you have changed the redirect of the last but one link from. This was a double redirect. Maybe the wording and the title of 661 where misleading but it points to a problem of both (automaticaly) detecting and handling the multiple redirects. Are multiple redirects corrected manualy until now? Where to report them if seen accidentaly and not familiar with a specific subject? Regards Gangleri 00:35, 2004 Oct 8 (UTC)

underlines in firefox
I said : ''Hello, this is probably not the right place to ask that. I recently downloaded Firefox and am happy with it. I only have problems with few sites, and especially with wikipedia : links are underlined with a stroke that is touching the bottom of letters, and the result is ugly ang hard to read. Do I have to correct this myself in a personalized css or shall the GUI developpers be warned that a kind of bug has to be fixed ? gbog 15:27, 2004 Oct 17 (UTC)''

You answered : ''Hi; it seems you're not the only one to have this problem, but I can't seem to reproduce it myself. Clear your cache, and if the problem's still there, perhaps you could give some more details: What version of Windows/MacOS// are you using? Does anything other than the skin make a difference (e.g. logging in/out)? Please respond on my talk page so I'll spot it; thanks. - IMSoP 17:49, 17 Oct 2004 (UTC) ''

 * Well, I reloaded some pages but I don't want to really clear all my cache, for other reasons. I think the problem is not coming from an old version of a cached css, because I installed Firefox only few days ago. In those wikipedias where links aren't underlined except when mouse is over, I have the same problem, but links are easier to read when mouse is not over them. This problem may be linked to the font chosen for the new GUI of most wikipedias, as I don't see anything wrong in other websites, using Times or Arial. I'm using Windows 2000 Pro SP3, English, OS Version is 5.0.2195 (thanks Aida) gbog 05:38, 2004 Oct 18 (UTC)

 * Hi, me again. I tried the code you gave me and it worked well (no underlining problem). I tried to change the font to Times and, again, links where correctly underlined. I tried on a test page at home to display both Arial links and Times links, both where ok. Therefore I'm suspecting a kind of mess somewhere in the .css of wikipedia. If you had other ideas, please tell me. gbog 02:38, 2004 Oct 22 (UTC)

Ogg files
Hi, Imsop.

I'm sorry I was rude to you. It just shows one should never edit in haste.

Here's a quick take on How to play Ogg files.

As a classical music editor, my sole interest in Ogg files on the Wikipedia is to enable a reader--no matter how amateurish a computer user he may be--to hear them. In my workplace I have spent a fair amount of time helping computer-challenged people, and my experience leads me to believe that they will best be served by a message that is very short and to the point.

The problem with a large "resource page" on sound files, such as Sound, is that it will be edited collaboratively, mostly by computer geeks (please--no ethnic slur intended). This will rapidly produce a long, complex page that--although useful for other reasons--will fully intimidate the computer-challenged and thus defeat the original purpose I had in posting How to play Ogg files. That's why I want to make How to play Ogg files the link that people will see first when they visit Ogg looking for help.

I've now added a link from How to play Ogg files to Sound, so that technically adept readers will not be limited to the very brief information provided in How to play Ogg files. I hope you will consider this as an appropriate way of serving all of our readers, both technically non-adept and technically adept.

Yours very truly, Opus33 00:46, 22 Oct 2004 (UTC)

More on Ogg
Hi again, Imsop. I'm sorry to be so aggravating, and thanks for fixing my link format.

Just to try and make my intentions clear, it's the following scenario that I'm worried about:

 * Elderly user visits Chester (song), wants to hear the sound file, can't hear it, clicks Ogg hoping for help.
 * Doesn't get help, but rather endless stuff about the Ogg project. Gives up and watches TV instead.

It doesn't have to be this way.

It's true that linking to a help page is slightly self-referential, but we ought to have our priorities. I think the goal of serving our readers vastly outranks the rather obscure reasons that people want the Wikipedia not to be self-referential.

I've added a bit to the Meta discussion page you mentioned.

Yours very truly, Opus33 16:33, 22 Oct 2004 (UTC)

Janus Lists of dog breeds

 * Dear IMSoP, Special credits for your help, your work at Bugzilla and all the "wiki" projects. I am evaluating your wonderful inputs and come back later with further comments. Regards Gangleri 20:30, 2004 Nov 8 (UTC)

appendix 1
'''. This gives a very strange behaviour: ,       and so on at any level of the "nested" templates, also Talk''' at User:Gangleri/tests/breed discussion, User:Gangleri/tests/breed discussion IMSoP and so on.
 * Dear IMSoP, I was puzzeled by a new issue. At some point in time it should be possible to "transfer" complex templates to another projects.
 * Thinking about this (and beeing around in dozens of Wikipedias) I tried to replace project related words as User with '''
 * Tray to change the first line of User:Gangleri/tests/list (maintenance) IMSoP actualy looking as
 * to this
 * You may see, that the template will not work any more.
 * To my opinion it should be possible to change / replace the keywords as User, Talk, Special and all others with      , '''
 * What do you think about this?
 * If you support the idea of portability, I would kindly ask you to make the appropriate wording for a (new) feature request or make it as an addition to a related existing one. Best regards Gangleri 00:41, 2004 Nov 9 (UTC)

 * Wow! It works already at test:User Talk:Gangleri/tests#04:53, 11 Nov 2004 (UTC) Thanks!
 * Please delete test:User:TalkGangleri/tests. Thanks! [[   :Gangleri|Gangleri | T | [ Th]]] 05:12, 2004 Nov 11 (UTC)

appendix 2

 * At the end of User:Gangleri/tests/list (template) (in the line starting with Last update) you will see that in order to reference this template I could not use : I was forced to use    :Gangleri/tests/list (template) . This makes additional work, if templates are moved from one place to another and can be the source of errors.
 * I assume that it hase been a long discussion how these variables should work:
 * a) to have the values from the target
 * b) to have the values from the source
 * It is a pity that only one alternative is available now. What do you think about a switsch as  ,    and so on? Best regards Gangleri 00:41, 2004 Nov 9 (UTC)

 * I think, that wath happens at "appendix 1" is exactly the behaviour a). I can not see (at this moment) a need to handle namespace variables like this.
 * Combining the issues from "appendix 1" with those from "appendix 2" and having in mind, that at some point in time templates could be shared between projects as well, there might be a third requirement too:
 * c) to have as values for the namespace variables those from the change / translation to the last project (because the translation may be done over many projects). Regards Gangleri 01:05, 2004 Nov 9 (UTC)

appendix 3

 * Regarding Usefull new variables I identified three unti this moment:
 * domain name as wikipedia.org here
 * subdomain name as en here
 * random, min, max,
 * Regards Gangleri 02:23, 2004 Nov 9 (UTC)
 * last change could be more interesting then
 * last author
 * Regards Gangleri 18:19, 2004 Nov 9 (UTC)

 * See 876. Gangleri | [ Th] | T 02:24, 2004 Nov 14 (UTC)

 * Only "wording" of "the main namespace" is known, not the "technical"     ==     . Should this be changed? Regards Gangleri | [ Th] | T 01:54, 2004 Nov 16 (UTC)

appendix 4

 * Dear IMSoP, You are very close to the development of WikiMedia software and the "insiders". I read a lot of documentation pages but until now I did not find a "complete" list of all the parameters for the different normal and special pages.
 * I could see a lot of the parameters used for url's starting with  http://en.wikipedia.org/w/wiki.phtml?  as
 * title=...
 * &action=edit, &edit&section=new, &action=purge, &action=submit, action=history, &action=watch, &action=unwatch, &oldid=..., &diff=0, &diff=...&oldid=...
 * title=Special:
 * title=Special:Watchlist&days=0 Watchlist&days=0.5 Watchlist&days=7, days
 * http://en.wikipedia.org/w/wiki.phtml?title=Special:Watchlist&magic=yes, magic
 * title=Special:Emailuser&target=...
 * title=Special:Movepage&target=...
 * title=Special:Categories&limit=500&offset=0
 * title=Special:Categories&feed=rss
 * title=Special:Categories&feed=atom&feed=rss
 * http://en.wikipedia.org/w/wiki.phtml?title=Special:Contributions&target=Gangleri
 * http://en.wikipedia.org/w/wiki.phtml?title=Special:Contributions&hideminor=0&target=Gangleri&limit=500&offset=0
 * http://en.wikipedia.org/wiki/Special:Search?ns2=1&search=gangleri&searchx=Search gives Additional pages
 * You made several examples using :
 * http://en.wikipedia.org/
 * http://en.wikipedia.org
 * http://en.wikipedia.org
 * or used direct InterWiki links:
 * Special:Whatlinkshere/Pug
 * Special:Recentchangeslinked/Pug
 * Some of the parameters you used together with:
 * The following seems invalid:
 * localurl
 * localurl:
 * localurl
 * localurl:
 * There is a very wide range of combining them. Are there some simple roles when to use InterWiki links and when to use ?
 * Are there other ways to reference (these) pages too?
 * But I have to stop at some point in time. Thanks again in advance whenever you answer. There is no hurry. Regards Gangleri 03:27, 2004 Nov 9 (UTC)

More notes:
 * For Special:Contributions (this link shows "No target") the parameter "&magic=yes" is allowed but would not make (much) sense. Maybe only in connection with (minor) contributions, you would not like to follow / watch, but this is already available at Special:Watchlist.
 * You probably know how to see "your" "[ magic]" contributions:
 * [ magic]
 * What will [ this] show if placed on somebody elses page?
 * [ this]
 * It is OK, "minimal privacy" is preserved, also with [ "magic"] parameter ;-) Regards Gangleri | [ Th] | T 03:15, 2004 Nov 16 (UTC)
 * See 891. 05:37, 2004 Nov 16 (UTC)

Information managment

 * Dear IMSoP, I want to drop a few lines about the "articles from a category" feature request(s) at 827 (marked as a dupplicate of 144, refered also at 844). The principles are quite simple and come from the database world:
 * what to select (WHERE ...)
 * how to display (SELECT ... probably attributes, fields)
 * how to order (ORDER BY ...)
 * how to limit, how to move the window over all (selected and ordered) objects
 * how flexible the implementation is / how many (powerfull) options user can choose from are available
 * combine whatever usefull combination of existing WikiMedia code
 * If WikiMedia software is able to show the Contributions or Watchlist with the links to changed objects (what), timestamp (when), user (who), additional fields as new, minor change, comment (more) then this code could be used also
 * for the category list
 * for the magic watchlist
 * for the list of categories Special:Categories
 * for the Project namespace
 * for the Template namespace
 * for the Wikipedia namespace
 * for the WP shortcuts
 * In many cases this would be a "parallel approch" to the lists. Some users prefer categories, some other lists and some other prefer to search or to go from one article to a linked one.
 * Example: If I have found an interesting articel and want to contact someone, I look at the history and then at the last timestamp of the users contribution (to see if he is still "active" or not). Then I decide to e-mail that user or search another person. The bottom line is that it would be possible to show the users list by last contribution too. I would not require it should, but it is possible to make it.

 * I am very confident that together the changes with the highest priority and largest acceptency will be implemented. This is why it is not up to me to specify this. Regards Gangleri 04:23, 2004 Nov 9 (UTC)

Addendum made at 02:53, 2004 Nov 16 (UTC):
 * Preliminary: Many improvements are made already at test: in Version 1.4-cvs. Thank you all!
 * I want to explain some issues related to "waste of time" / "efficiency". Maybe I will repead what I pointed out already "here and there".
 * It happens to me (and I assume also to other users) that I work more intensively at one project / some projects or have to make a break. If I come back later to another project and take a look there at Special:Contributions (also with the "[ magic] keyword") or at Special:Watchlist I can not change the sort order and / or "what is displayed". For the later "Contributions" how many "history" records are displayed, (personaly) I realy am interested only to see the last one not all.
 * I will be diverted / distracted to "how to find it" from my original taughts "what I want to do now". The "rigid" way imposed (sometimes) at Wikipedia now (please excuse these words) is not the way how "you drive a car", "find directions" in a town or on a highway.
 * Bottom line: (Personaly due to time constraints) I talke a look only at some of the "objects" (articles, talks, etc.) and I know that (doing so) I will not follow all "objects" of my areas of interest, not respond to some talks ...
 * "Felxibility" is the ability to choose from what is the most suitable way for "you". To my understanding this taughs deal with "consistent" options == "same" options, you should find at all the special pages. Thanks for reading so far. Regards Gangleri | [ Th] | T 02:53, 2004 Nov 16 (UTC)

other open issues / bugs

 * Dear IMSoP, Please take a look at Invalid article names. Regards Gangleri 01:47, 2004 Nov 10 (UTC)

 * Dear IMSoP, I am not shure if
 * 563 Broken Unicode links to Wikipedia at Commons
 * 579 trying to create page on en with special characters in the title
 * 670 usage of characters as "(", ")", ... in anchor of InterWiki links
 * needs to be changed from "WikiMedia web site" to "MediaWiki" or not.

 * To my knowledge version 1.4 should allow sharing of images between projects.
 * Could you make an example using the image is:Mynd:Ægishjálmur.jpg at test: without copying it? Or is this feature not available yet?
 * I placed a picture from at test:User:Gangleri. [[    :Gangleri|Gangleri | T | [ Th]]] 05:53, 2004 Nov 11 (UTC)
 * What bugs are related to image sharing? Regards Gangleri 16:29, 2004 Nov 10 (UTC)

bugzilla

 * Dear IMSoP, are you able to "edit " bugzilla bugs. I think that some links should be adjusted there as specified at 144 item #3. (I made another spelling error there too "underschores".)
 * I have not searched for some interwiki help at bugzilla. I supose it is not there.
 * References from bugzilla to en: should not include the starting colon.
 * en:User talk:IMSoP and en:User_talk:IMSoP will fail
 * All spaces Spaces in the anchors should be replaced with underscores.
 * en:User_talk:IMSoP would miss the anchor.
 * en: can be suppressed / omited.
 * User_talk:IMSoP 05:45, 2004 Nov 16 (UTC)
 * I just saw that spaces should be replaced with underscores else no clickable link would be generated. Or is this just a interfearence with "line wraping" ? 05:52, 2004 Nov 16 (UTC)
 * Suggestions:
 * id as 144 would be a "nice to have". Regards Gangleri | [ Th] | T 03:47, 2004 Nov 16 (UTC)
 * I support the idea to have a "preview" also at bugzilla. I saw this somewhere. Gangleri | [ Th] | T 06:26, 2004 Nov 16 (UTC)

 *  P.S. I did not expect that the section name would be generated as this:
 * a) User talk:IMSoP
 * User talk:IMSoP
 * the "link translation" is of course:
 * b) http://en.wikipedia.org/wiki/User_talk:IMSoP#bugzilla_.28http:.2F.2Fbugzilla.wikipedia.org.2F.29
 * http://en.wikipedia.org/wiki/User_talk:IMSoP#bugzilla_.28http:.2F.2Fbugzilla.wikipedia.org.2F.29
 * Oh! I should have used a piped link:
 * c) User talk:IMSoP#bugzilla
 * User talk:IMSoP#bugzilla
 * d) User talk:IMSoP#bugzilla
 * User talk:IMSoP#bugzilla
 * Oh! or combinations with underscore(s) (in the anchor):
 * e) (from c)) User talk:IMSoP#bugzilla
 * User talk:IMSoP#bugzilla
 * Comments: I must admit this is not a simple anchor ;-) No "normal" user would use this!
 * Detailed analysis should / will show what is a "primary" and what a "subsequent" error depending on how the parser interprets this.
 * I did not expect that a colon ":" at b) would "brake" the link.
 * I realise that for any "meta" language "escape" characters are needed too / required.
 * f) (from b)) http://en.wikipedia.org/wiki/User_talk:IMSoP#bugzilla_.28http.3A.2F.2Fbugzilla.wikipedia.org.2F.29
 * http://en.wikipedia.org/wiki/User_talk:IMSoP#bugzilla_.28http.3A.2F.2Fbugzilla.wikipedia.org.2F.29
 * Replacing colon ":" with ".3A" would preserve the link from braking; but the link will fail :-( Regards Gangleri | [ Th] | T 04:17, 2004 Nov 16 (UTC)

I want to let you know about:

 * meta:Talk:Interwiki map Regards Gangleri | [ Th] | T 01:12, 2004 Nov 16 (UTC)
 * Dear IMSoP, thank you for your answers and the time to spend for this. I will need some sleep and read them carefully. Best regards, Reinhardt - Gangleri | [ Th] | T 17:22, 2004 Nov 16 (UTC)

UTF-8 conversion issues
Hi, I was intrigued by your comment at WP:RfD about the difficulties encountered in French Wikipedia UTF-8 conversion. I'm assuming that part of the problems were the way that in the Latin-1 character set, the characters with diacrits added are in the xC0-xFF range - which is exactly the space used by UTF-8 to mark the start of multi-character sequences. So all instances of them have to be converted to their UTF-8 equivalents. Therefore, not only do articles with those characters in their titles have to be renamed, but in all pages which link to them, the links must be found and modified. Also redirects, etc, etc. Are there problems I missed? Noel (talk) 03:48, 23 Nov 2004 (UTC)

Pet skunk link
Hi, thanks for fixing that link on the pet skunk page. Is there any way to link it internally? Knowing how to do that would help me with other articles. Nathanlarson32767 04:57, 10 Dec 2004 (UTC)

Article Licensing
Hi, I've started a drive to get users to multi-license all of their contributions that they've made to either (1) all U.S. state, county, and city articles or (2) all articles, using the Creative Commons Attribution-Share Alike (CC-by-sa) v1.0 and v2.0 Licenses or into the public domain if they prefer. The CC-by-sa license is a true free documentation license that is similar to Wikipedia's license, the GFDL, but it allows other projects, such as WikiTravel, to use our articles. Since you are among the top 2000 Wikipedians by edits, I was wondering if you would be willing to multi-license all of your contributions or at minimum those on the geographic articles. Over 90% of people asked have agreed. For More Information:
 * Multi-Licensing FAQ - Lots of questions answered
 * Multi-Licensing Guide
 * Free the Rambot Articles Project

To allow us to track those users who muli-license their contributions, many users copy and paste the " " template into their user page, but there are other options at Template messages/User namespace. The following examples could also copied and pasted into your user page:

 * Option 1
 * I agree to multi-license all my contributions, with the exception of my user pages, as described below:

OR
 * Option 2
 * I agree to multi-license all my contributions to any U.S. state, county, or city article as described below:

Or if you wanted to place your work into the public domain, you could replace " " with "  ". If you only prefer using the GFDL, I would like to know that too. Please let me know what you think at my talk page. It's important to know either way so no one keeps asking. -- Ram-Man (comment| talk)

Eternal September
Acclimate and acclimatize (US spelling, remember? :-) are actually exactly synonymous, according to dictionary.com. It was my bit, but I'm not married to it. I did forget to check for an in-link, though; thanks. -- Baylink 21:40, 14 Dec 2004 (UTC)

Swami
Hi IMSoP; actually, "prepend" is computer jargon, not a word people are familiar with. No kidding, check our Webster friend. Actually, "append" has not the implict meaning of the insertion happening at the end, but common use made people think so, and when computer people needed to emphasize otherwise the word prepend came to be. I think we could wait before it becomes common outside of Ling 215 circles to use it in Wikipedia. The Swami page is as you left it, but I suggest you reconsider for the sake of clarity. Best, --Subramanian 06:19, 20 Jan 2005 (UTC)

out of sync

 * Hallo IMSoP, It's long time since my last message here. I mede some thousend edits at a community wiki and last at ro:. Regarding my work at ro: and eo: I placed some questions at User talk:Patrick. Please take a look at them. I think you may respond on Patricks talk page if you know answers for this and that. Thanks in advance. Regards Gangleri | [ Th] | T 22:39, 2005 Feb 4 (UTC)

Writing system
IMSoP, thanks for the reorg of the writing system page contents. The new structure has quite improved the article flow - cheers! --cjllw | TALK  07:44, 2005 Jun 17 (UTC)

Resolution for your problem
If you are soapy, then rinse off already. --Lord Voldemort 30 June 2005 19:31 (UTC)

 * You said, "IMSoP." "IM So P." "I'm Soapy." Nevermind. Dark Lords are not very funny. --Lord Voldemort 4 July 2005 14:56 (UTC)

What is a mask work?
Thanks for your comment on this article. The intro was indeed cryptic. I added a new definition. Does this make sense to you now? Your suggestions for improvements are welcome. --Edcolins 12:50, July 16, 2005 (UTC)

WikiKto
Tanks for your help ! Davidias 00:35, 6 August 2005 (UTC)

ASIN
Hi: I have removed my comment from Shimgray's ASIN discussion because your movement of it to the ==Deletion bad== section does not reflect my position. Although I prefer to see something else used in place of ASIN, I was advocating the replacement of ASINs rather than their deletion. Your movement of my comment changed its sense. I know that you meant no harm. Please give deeper consideration to the effects of such moves should you think of doing something similar again. —Theo (Talk) 23:02, 9 August 2005 (UTC)

Nice Edit summary
"haha bonk". Very funny ;) — Ilγαηερ   (Tαlκ)  16:00, 11 August 2005 (UTC)

Thanks
Thank you for forwarding me to the WikiProjects article. Johann Wolfgang 00:13, 23 August 2005 (UTC)

User Categorisation
You were listed on the Wikipedians/Europe page as living in or being associated with Europe. As part of the User categorisation project, these lists are being replaced with user categories. If you would like to add yourself to the category that is replacing the page, please visit Category:Wikipedians in Europe for instructions.--Rmky87 04:03, 12 October 2005 (UTC)

Sister Cities: List or Paragraph...???
User:Derek.cashman wants to change, and thinks, that all "Sister cities" lists in articles should be converted/changed to “paragraph” form. I don’t want to. Can you imagine a lists of 26 sister cities, like for Istanbul, and trying to read it in paragraph form? Please read my opinion and info and vote. I would like your input. WikiDon 02:54, 4 November 2005 (UTC)

failed experiment
I just re-viewed that 'graph on this page via (the Popups, by hovering) my lk to this page, in the " Cool Ideas (to consider adopting)" sec'n of my Wiki-bookmarks page. As it happens, i had just left this note, and was thinking abt whether a few templates to facilitate using this protocol, that you and others have introduced, would be a good idea one of the Cool Ideas to consider adopting. FWIW. I may send you further thots. --Jerzy•t 15:21, 15 February 2006 (UTC)

Please read
Talk:Feature extraction JKW 10:07, 23 April 2006 (UTC)

Test Wiki
I saw your comment on Wikipedia talk:About the Sandbox from over a year ago and just wanted to let you know the test wiki (test.wikipedia.org) is running again if you didn't know already. Timrem 18:36, 3 June 2006 (UTC)

Please contact me to continue a discussion
Please contact me at R Duggan 04:18, 26 November 2006 (UTC) to continue a discussion

Eastbourne
Lets make Eastbourne a Featured Article! MortimerCat 02:29, 21 December 2006 (UTC)

I don't know if you have been watching the Eastbourne article, but I have reorganised the sections. I feel it made an improvement as the page is now appears less disjointed. A what needs to be done section on the talk page has been set up that I am hoping will start a discussion on where to go from here. Some recent editors have been spammed drawing their attention to this. If you could pop along and break the ice with the comment please. MortimerCat 12:19, 7 January 2007 (UTC)

Re: Error in AWB edit
Woops, look at that, you're right. Sorry about that. (I fixed another similar one in the same article). Like you said, it's probably one of the meant-to-be-helpful features of AWB that could be turned off. I'll find out how to do that so the minimum editing gets done when I do post-move mass changes. —Wknight94 (talk) 18:43, 6 January 2007 (UTC)
 * By the way, I just did a successful test - if you wrap code like that in a  tag, AWB will ignore it.  If you run across more articles with heavy square bracket usage, you should keep that in mind.  I'll do the same.  I tested this out in URI scheme.  If you have a moment, please check to make sure my nowiki tags didn't break anything.  Thanks and sorry again for the mixup.  —Wknight94 (talk) 20:02, 6 January 2007 (UTC)

Orphaned non-free image (Image:MainPage-Mosaic1.0-IMSoP.png)
Thanks for uploading Image:MainPage-Mosaic1.0-IMSoP.png. The image description page currently specifies that the image is non-free and may only be used on Wikipedia under a claim of fair use. However, the image is currently orphaned, meaning that it is not used in any articles on Wikipedia. If the image was previously in an article, please go to the article and see why it was removed. You may add it back if you think that that will be useful. However, please note that images for which a replacement could be created are not acceptable for use on Wikipedia (see our policy for non-free media).

If you have uploaded other unlicensed media, please check whether they're used in any articles or not. You can find a list of 'image' pages you have edited by clicking on the "my contributions" link (it is located at the very top of any Wikipedia page when you are logged in), and then selecting "Image" from the dropdown box. Note that any non-free images not used in any articles will be deleted after seven days, as described on criteria for speedy deletion. Thank you. BetacommandBot 06:41, 21 June 2007 (UTC)

Orphaned non-free image (Image:MainPage-Netscape1.0N-IMSoP.png)
Thanks for uploading Image:MainPage-Netscape1.0N-IMSoP.png. The image description page currently specifies that the image is non-free and may only be used on Wikipedia under a claim of fair use. However, the image is currently orphaned, meaning that it is not used in any articles on Wikipedia. If the image was previously in an article, please go to the article and see why it was removed. You may add it back if you think that that will be useful. However, please note that images for which a replacement could be created are not acceptable for use on Wikipedia (see our policy for non-free media).

If you have uploaded other unlicensed media, please check whether they're used in any articles or not. You can find a list of 'image' pages you have edited by clicking on the "my contributions" link (it is located at the very top of any Wikipedia page when you are logged in), and then selecting "Image" from the dropdown box. Note that any non-free images not used in any articles will be deleted after seven days, as described on criteria for speedy deletion. Thank you. BetacommandBot 06:41, 21 June 2007 (UTC)

Orphaned non-free image (Image:MainPage-Mosaic1.0-IMSoP.png)
Thanks for uploading Image:MainPage-Mosaic1.0-IMSoP.png. The image description page currently specifies that the image is non-free and may only be used on Wikipedia under a claim of fair use. However, the image is currently orphaned, meaning that it is not used in any articles on Wikipedia. If the image was previously in an article, please go to the article and see why it was removed. You may add it back if you think that that will be useful. However, please note that images for which a replacement could be created are not acceptable for use on Wikipedia (see our policy for non-free media).

If you have uploaded other unlicensed media, please check whether they're used in any articles or not. You can find a list of 'image' pages you have edited by clicking on the "my contributions" link (it is located at the very top of any Wikipedia page when you are logged in), and then selecting "Image" from the dropdown box. Note that any non-free images not used in any articles will be deleted after seven days, as described on criteria for speedy deletion. Thank you. BetacommandBot 09:00, 22 June 2007 (UTC)

Orphaned non-free image (Image:MainPage-Netscape1.0N-IMSoP.png)
Thanks for uploading Image:MainPage-Netscape1.0N-IMSoP.png. The image description page currently specifies that the image is non-free and may only be used on Wikipedia under a claim of fair use. However, the image is currently orphaned, meaning that it is not used in any articles on Wikipedia. If the image was previously in an article, please go to the article and see why it was removed. You may add it back if you think that that will be useful. However, please note that images for which a replacement could be created are not acceptable for use on Wikipedia (see our policy for non-free media).

If you have uploaded other unlicensed media, please check whether they're used in any articles or not. You can find a list of 'image' pages you have edited by clicking on the "my contributions" link (it is located at the very top of any Wikipedia page when you are logged in), and then selecting "Image" from the dropdown box. Note that any non-free images not used in any articles will be deleted after seven days, as described on criteria for speedy deletion. Thank you. BetacommandBot 09:00, 22 June 2007 (UTC)

Eastbourne - Good Article Nomination
I don't know if you have been watching the Eastbourne article. If you have you would have seen I put it forward for a Good Article nomination. The results are back, and it has been put on hold pending some changes. It would be wonderful if you could pop back at some time, and see if you can help with some of the issues. MortimerCat 19:02, 23 June 2007 (UTC)

 * Thanks for your help, we succeeded in making Eastbourne an official Good Article. Next stop, Featured article status. MortimerCat 18:16, 1 July 2007 (UTC)

Agree on Trivia Issues
Hi, I just wanted to say that I def. agree with you on "trivia sections" such as the recent growing one in "Hexadecimal". If the line at the top stays as it is, that's OK with me too... just an example you could say, a pointer to another article showing that such things do exist. If I had my way, some of those audacious looking diagrams (too many bright colors ;-) ) wouldn't be in the article either. There was already some discussion in the past about that, but as someone else said, here they are back in again, but I'll leave that up to others... I don't know enough about WikiPedia policies -- having my own misgivings on some of them myself. Daniel B. Sedory 21:39, 3 December 2007 (UTC)

AfD nomination of RAS syndrome
I have nominated RAS syndrome, an article you created, for deletion. I do not feel that this article satisfies Wikipedia's criteria for inclusion, and have explained why at Articles for deletion/RAS syndrome. Your opinions on the matter are welcome at that same discussion page; also, you are welcome to edit the article to address these concerns. Thank you for your time. Do you want to opt out of receiving this notice? Ten Pound Hammer and his otters • (Chirps•Clams•Chowder) 00:38, 18 July 2008 (UTC)

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

authors: ಮಲ್ನಾಡಾಚ್ ಕೊಂಕ್ಣೊ

title: User talk:IMSoP/Archive 1


text:
Diophantine approximation

In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria.

The first problem was to know how well a real number can be approximated by rational numbers. For this problem, a rational number p/q is a "good" approximation of a real number α if the absolute value of the difference between p/q and α may not decrease if p/q is replaced by another rational number with a smaller denominator. This problem was solved during the 18th century by means of continued fractions.

Knowing the "best" approximations of a given number, the main problem of the field is to find sharp upper and lower bounds of the above difference, expressed as a function of the denominator. It appears that these bounds depend on the nature of the real numbers to be approximated: the lower bound for the approximation of a rational number by another rational number is larger than the lower bound for algebraic numbers, which is itself larger than the lower bound for all real numbers. Thus a real number that may be better approximated than the bound for algebraic numbers is certainly a transcendental number.

This knowledge enabled Liouville, in 1844, to produce the first explicit transcendental number. Later, the proofs that $\pi$ and e are transcendental were obtained by a similar method.

Diophantine approximations and transcendental number theory are very close areas that share many theorems and methods. Diophantine approximations also have important applications in the study of Diophantine equations.

The 2022 Fields Medal was awarded to James Maynard for his work on Diophantine approximation.

Best Diophantine approximations of a real number
Given a real number $α$, there are two ways to define a best Diophantine approximation of $α$. For the first definition, the rational number $p/q$ is a best Diophantine approximation of $α$ if
 * $$\left|\alpha -\frac{p}{q}\right | < \left|\alpha -\frac{p'}{q'}\right |,$$

for every rational number $p'/q'$ different from $p/q$ such that $0 < q′ ≤ q$.

For the second definition, the above inequality is replaced by
 * $$\left|q\alpha -p\right| < \left|q^\prime\alpha - p^\prime\right|.$$

A best approximation for the second definition is also a best approximation for the first one, but the converse is not true in general.

The theory of continued fractions allows us to compute the best approximations of a real number: for the second definition, they are the convergents of its expression as a regular continued fraction. For the first definition, one has to consider also the semiconvergents.

For example, the constant e = 2.718281828459045235... has the (regular) continued fraction representation

 * $$[2;1,2,1,1,4,1,1,6,1,1,8,1,\ldots\;].$$

Its best approximations for the second definition are
 * $$ 3, \tfrac{8}{3}, \tfrac{11}{4}, \tfrac{19}{7}, \tfrac{87}{32}, \ldots\, ,$$

while, for the first definition, they are
 * $$3, \tfrac{5}{2}, \tfrac{8}{3}, \tfrac{11}{4}, \tfrac{19}{7},

\tfrac{49}{18}, \tfrac{68}{25}, \tfrac{87}{32}, \tfrac{106}{39}, \ldots\, .$$

Measure of the accuracy of approximations
The obvious measure of the accuracy of a Diophantine approximation of a real number $α$ by a rational number $p/q$ is $\left|\alpha - \frac{p}{q}\right|.$ However, this quantity can always be made arbitrarily small by increasing the absolute values of $p$ and $q$; thus the accuracy of the approximation is usually estimated by comparing this quantity to some function $φ$ of the denominator $q$, typically a negative power of it.

For such a comparison, one may want upper bounds or lower bounds of the accuracy. A lower bound is typically described by a theorem like "for every element $α$ of some subset of the real numbers and every rational number $p/q$, we have $\left|\alpha - \frac{p}{q}\right|>\phi(q)$ ". In some cases, "every rational number" may be replaced by "all rational numbers except a finite number of them", which amounts to multiplying $φ$ by some constant depending on $α$.

For upper bounds, one has to take into account that not all the "best" Diophantine approximations provided by the convergents may have the desired accuracy. Therefore, the theorems take the form "for every element $α$ of some subset of the real numbers, there are infinitely many rational numbers $p/q$ such that $\left|\alpha - \frac{p}{q}\right|<\phi(q)$ ".

Badly approximable numbers
A badly approximable number is an x for which there is a positive constant c such that for all rational p/q we have

 * $$\left|{ x - \frac{p}{q} }\right| > \frac{c}{q^2} \ . $$

The badly approximable numbers are precisely those with bounded partial quotients.

Equivalently, a number is badly approximable if and only if its Markov constant is bounded.

Approximation of a rational by other rationals
A rational number $\alpha =\frac{a}{b}$ may be obviously and perfectly approximated by $\frac{p_i}{q_i} = \frac{i\,a}{i \,b}$  for every positive integer i.

If $\frac{p}{q} \not= \alpha = \frac{a}{b}\,,$ we have
 * $$\left|\frac{a}{b} - \frac{p}{q}\right| = \left|\frac{aq - bp}{bq}\right| \ge \frac{1}{bq},$$

because $$|aq - bp|$$ is a positive integer and is thus not lower than 1. Thus the accuracy of the approximation is bad relative to irrational numbers (see next sections).

It may be remarked that the preceding proof uses a variant of the pigeonhole principle: a non-negative integer that is not 0 is not smaller than 1. This apparently trivial remark is used in almost every proof of lower bounds for Diophantine approximations, even the most sophisticated ones.

In summary, a rational number is perfectly approximated by itself, but is badly approximated by any other rational number.

Approximation of algebraic numbers, Liouville's result
In the 1840s, Joseph Liouville obtained the first lower bound for the approximation of algebraic numbers: If x is an irrational algebraic number of degree n over the rational numbers, then there exists a constant c(x) > 0 such that

 * $$ \left| x- \frac{p}{q} \right| > \frac{c(x)}{q^n}$$

holds for all integers p and q where q > 0.

This result allowed him to produce the first proven example of a transcendental number, the Liouville constant

\sum_{j=1}^\infty 10^{-j!} = 0.110001000000000000000001000\ldots\,, $$ which does not satisfy Liouville's theorem, whichever degree n is chosen.

This link between Diophantine approximations and transcendental number theory continues to the present day. Many of the proof techniques are shared between the two areas.

Approximation of algebraic numbers, Thue–Siegel–Roth theorem
Over more than a century, there were many efforts to improve Liouville's theorem: every improvement of the bound enables us to prove that more numbers are transcendental. The main improvements are due to, , , and , leading finally to the Thue–Siegel–Roth theorem: If $x$ is an irrational algebraic number and $ε > 0$, then there exists a positive real number $c(x, ε)$ such that

\left| x- \frac{p}{q} \right|>\frac{c(x, \varepsilon)}{q^{2+\varepsilon}} $$ holds for every integer $p$ and $q$ such that $q > 0$.

In some sense, this result is optimal, as the theorem would be false with ε = 0. This is an immediate consequence of the upper bounds described below.

Simultaneous approximations of algebraic numbers
Subsequently, Wolfgang M. Schmidt generalized this to the case of simultaneous approximations, proving that: If $x_{1}, ..., x_{n}$ are algebraic numbers such that $1, x_{1}, ..., x_{n}$ are linearly independent over the rational numbers and $ε$ is any given positive real number, then there are only finitely many rational $n$-tuples $(p_{1}/q, ..., p_{n}/q)$ such that
 * $$\left|x_i - \frac{p_i}{q}\right| < q^{-(1 + 1/n + \varepsilon)},\quad i = 1, \ldots, n.$$

Again, this result is optimal in the sense that one may not remove $ε$ from the exponent.

Effective bounds
All preceding lower bounds are not effective, in the sense that the proofs do not provide any way to compute the constant implied in the statements. This means that one cannot use the results or their proofs to obtain bounds on the size of solutions of related Diophantine equations. However, these techniques and results can often be used to bound the number of solutions of such equations.

Nevertheless, a refinement of Baker's theorem by Feldman provides an effective bound: if x is an algebraic number of degree n over the rational numbers, then there exist effectively computable constants c(x) > 0 and 0 < d(x) < n such that

 * $$\left| x- \frac{p}{q} \right|>\frac{c(x)}{|q|^{d(x)}} $$

holds for all rational integers.

However, as for every effective version of Baker's theorem, the constants d and 1/c are so large that this effective result cannot be used in practice.

General upper bound
The first important result about upper bounds for Diophantine approximations is Dirichlet's approximation theorem, which implies that, for every irrational number $α$, there are infinitely many fractions $$\tfrac{p}{q}\;$$ such that
 * $$\left|\alpha-\frac{p}{q}\right| < \frac{1}{q^2}\,.$$

This implies immediately that one cannot suppress the $ε$ in the statement of Thue-Siegel-Roth theorem.

Adolf Hurwitz (1891) strengthened this result, proving that for every irrational number $α$, there are infinitely many fractions $$\tfrac{p}{q}\;$$ such that
 * $$\left|\alpha-\frac{p}{q}\right| < \frac{1}{\sqrt{5}q^2}\,.$$

Therefore, $$\frac{1}{\sqrt{5}\, q^2}$$ is an upper bound for the Diophantine approximations of any irrational number. The constant in this result may not be further improved without excluding some irrational numbers (see below).

Émile Borel (1903) showed that, in fact, given any irrational number $α$, and given three consecutive convergents of $α$, at least one must satisfy the inequality given in Hurwitz's Theorem.

Equivalent real numbers
Definition: Two real numbers $$x,y$$ are called equivalent if there are integers $$a,b,c,d\;$$ with $$ad-bc = \pm 1\;$$ such that:
 * $$y = \frac{ax+b}{cx+d}\, .$$

So equivalence is defined by an integer Möbius transformation on the real numbers, or by a member of the Modular group $$\text{SL}_2^{\pm}(\Z)$$, the set of invertible 2 × 2 matrices over the integers. Each rational number is equivalent to 0; thus the rational numbers are an equivalence class for this relation.

The equivalence may be read on the regular continued fraction representation, as shown by the following theorem of Serret:

Theorem: Two irrational numbers x and y are equivalent if and only if there exist two positive integers h and k such that the regular continued fraction representations of x and y
 * $$\begin{align}

x &= [u_0; u_1, u_2, \ldots]\,, \\ y &= [v_0; v_1, v_2, \ldots]\, , \end{align}$$

satisfy
 * $$u_{h+i} = v_{k+i}$$

for every non negative integer i.

Thus, except for a finite initial sequence, equivalent numbers have the same continued fraction representation.

Equivalent numbers are approximable to the same degree, in the sense that they have the same Markov constant.

Lagrange spectrum
As said above, the constant in Borel's theorem may not be improved, as shown by Adolf Hurwitz in 1891. Let $$\phi = \tfrac{1+\sqrt{5}}{2}$$ be the golden ratio. Then for any real constant c with $$c > \sqrt{5}\;$$ there are only a finite number of rational numbers $p/q$ such that
 * $$\left|\phi-\frac{p}{q}\right| < \frac{1}{c\, q^2}.$$

Hence an improvement can only be achieved, if the numbers which are equivalent to $$\phi$$ are excluded. More precisely: For every irrational number $$\alpha$$, which is not equivalent to $$\phi$$, there are infinite many fractions $$\tfrac{p}{q}\;$$ such that

 * $$\left|\alpha-\frac{p}{q}\right| < \frac{1}{\sqrt{8} q^2}.$$

By successive exclusions — next one must exclude the numbers equivalent to $$\sqrt 2$$ — of more and more classes of equivalence, the lower bound can be further enlarged. The values which may be generated in this way are Lagrange numbers, which are part of the Lagrange spectrum. They converge to the number 3 and are related to the Markov numbers.

Khinchin's theorem on metric Diophantine approximation and extensions
Let $$\psi$$ be a positive real-valued function on positive integers (i.e., a positive sequence) such that $$q \psi(q)$$ is non-increasing. A real number x (not necessarily algebraic) is called $$\psi$$-approximable if there exist infinitely many rational numbers p/q such that

 * $$\left| x- \frac{p}{q} \right| < \frac{\psi(q)}{|q|}.$$

Aleksandr Khinchin proved in 1926 that if the series $\sum_{q} \psi(q) $ diverges, then almost every real number (in the sense of Lebesgue measure) is $$\psi$$-approximable, and if the series converges, then almost every real number is not $$\psi$$-approximable. The circle of ideas surrounding this theorem and its relatives is known as metric Diophantine approximation or the metric theory of Diophantine approximation (not to be confused with height "metrics" in Diophantine geometry) or metric number theory.

proved a generalization of Khinchin's result, and posed what is now known as the Duffin–Schaeffer conjecture on the analogue of Khinchin's dichotomy for general, not necessarily decreasing, sequences $$\psi$$. proved that a Hausdorff measure analogue of the Duffin–Schaeffer conjecture is equivalent to the original Duffin–Schaeffer conjecture, which is a priori weaker. In July 2019, Dimitris Koukoulopoulos and James Maynard announced a proof of the conjecture.

Hausdorff dimension of exceptional sets
An important example of a function $$\psi$$ to which Khinchin's theorem can be applied is the function $$\psi_c(q) = q^{-c}$$, where c > 1 is a real number. For this function, the relevant series converges and so Khinchin's theorem tells us that almost every point is not $$\psi_c$$-approximable. Thus, the set of numbers which are $$\psi_c$$-approximable forms a subset of the real line of Lebesgue measure zero. The Jarník-Besicovitch theorem, due to V. Jarník and A. S. Besicovitch, states that the Hausdorff dimension of this set is equal to $$1/c$$. In particular, the set of numbers which are $$\psi_c$$-approximable for some $$c > 1$$ (known as the set of very well approximable numbers) has Hausdorff dimension one, while the set of numbers which are $$\psi_c$$-approximable for all $$c > 1$$ (known as the set of Liouville numbers) has Hausdorff dimension zero.

Another important example is the function $$\psi_\varepsilon(q) = \varepsilon q^{-1}$$, where $$\varepsilon > 0$$ is a real number. For this function, the relevant series diverges and so Khinchin's theorem tells us that almost every number is $$\psi_\varepsilon$$-approximable. This is the same as saying that every such number is well approximable, where a number is called well approximable if it is not badly approximable. So an appropriate analogue of the Jarník-Besicovitch theorem should concern the Hausdorff dimension of the set of badly approximable numbers. And indeed, V. Jarník proved that the Hausdorff dimension of this set is equal to one. This result was improved by W. M. Schmidt, who showed that the set of badly approximable numbers is incompressible, meaning that if $$f_1,f_2,\ldots$$ is a sequence of bi-Lipschitz maps, then the set of numbers x for which $$f_1(x),f_2(x),\ldots$$ are all badly approximable has Hausdorff dimension one. Schmidt also generalized Jarník's theorem to higher dimensions, a significant achievement because Jarník's argument is essentially one-dimensional, depending on the apparatus of continued fractions.

Uniform distribution
Another topic that has seen a thorough development is the theory of uniform distribution mod 1. Take a sequence a1, a2, ... of real numbers and consider their fractional parts. That is, more abstractly, look at the sequence in $$\mathbb{R}/\mathbb{Z}$$, which is a circle. For any interval I on the circle we look at the proportion of the sequence's elements that lie in it, up to some integer N, and compare it to the proportion of the circumference occupied by I. Uniform distribution means that in the limit, as N grows, the proportion of hits on the interval tends to the 'expected' value. Hermann Weyl proved a basic result showing that this was equivalent to bounds for exponential sums formed from the sequence. This showed that Diophantine approximation results were closely related to the general problem of cancellation in exponential sums, which occurs throughout analytic number theory in the bounding of error terms.

Related to uniform distribution is the topic of irregularities of distribution, which is of a combinatorial nature.

Algorithms
Grotschel, Lovasz and Schrijver describe algorithms for finding approximately-best diophantine approximations, both for individual real numbers and for set of real numbers. The latter problem is called simultaneous diophantine approximation.

Unsolved problems
There are still simply stated unsolved problems remaining in Diophantine approximation, for example the Littlewood conjecture and the lonely runner conjecture. It is also unknown if there are algebraic numbers with unbounded coefficients in their continued fraction expansion.

Recent developments
In his plenary address at the International Mathematical Congress in Kyoto (1990), Grigory Margulis outlined a broad program rooted in ergodic theory that allows one to prove number-theoretic results using the dynamical and ergodic properties of actions of subgroups of semisimple Lie groups. The work of D. Kleinbock, G. Margulis and their collaborators demonstrated the power of this novel approach to classical problems in Diophantine approximation. Among its notable successes are the proof of the decades-old Oppenheim conjecture by Margulis, with later extensions by Dani and Margulis and Eskin–Margulis–Mozes, and the proof of Baker and Sprindzhuk conjectures in the Diophantine approximations on manifolds by Kleinbock and Margulis. Various generalizations of the above results of Aleksandr Khinchin in metric Diophantine approximation have also been obtained within this framework.

title: Diophantine approximation