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Mata Hari

Margaretha Geertruida MacLeod (, ; 7 August 1876 – 15 October 1917), better known by the stage name Mata Hari (, ; , lit. 'eye of the day'), was a Dutch exotic dancer and courtesan who was convicted of being a spy for Germany during World War I. She was executed by firing squad in France. The idea of a beautiful exotic dancer using her powers of seduction as a spy made her name synonymous with the femme fatale. Her story has served as an inspiration for books, films, and other works.

It has been said that she was convicted and condemned because the French Army needed a scapegoat, and that the files used to secure her conviction contained falsifications. Some have even stated that Mata Hari could not have been a spy and was innocent.

Early life
Margaretha Geertruida Zelle was born 7 August 1876 in Leeuwarden, Netherlands. She was the eldest of four children to Antje van der Meulen (1842–1891) and her husband, Adam Zelle (1840–1910). She had three younger brothers; Johannes Hendriks, Arie Anne, and Cornelis Coenraad. She was affectionately called "M'greet" by her family. Despite traditional assertions that Mata Hari was partly of Jewish, Malaysian, or Javanese, i.e., Indonesian descent, scholars conclude she had no Jewish or Asian ancestry, and both of her parents were Dutch. Her father owned a hat shop, made investments in the oil industry, and became affluent enough to give Margaretha and her siblings a lavish early childhood that included exclusive schools until the age of 13.

Soon after Margaretha's father went bankrupt in 1889, her parents divorced, and her mother died in 1891. Her father remarried in Amsterdam on 9 February 1893 to Susanna Catharina ten Hoove (1844–1913). The family fell apart, and Margaretha was sent to live with her godfather, Mr. Visser, in Sneek. She studied to be a kindergarten teacher in Leiden, but when the headmaster began to flirt with her conspicuously, she was removed from the institution by her godfather. A few months later, she fled to her uncle's home in The Hague.

Dutch East Indies
At 18, Margaretha answered an advertisement in a Dutch newspaper placed by Dutch colonial army captain Rudolf MacLeod (1856–1928), who was living in what was then the Dutch East Indies (now Indonesia) and was looking for a wife. Margaretha married MacLeod in Amsterdam on 11 July 1895. He was the son of Captain John Brienen MacLeod (a descendant of the Gesto branch of the MacLeods of Skye, hence his Scottish surname) and Dina Louisa, Baroness Sweerts de Landas. The marriage enabled Zelle to move into the Dutch upper class and placed her finances on a sound footing. She moved with her husband to Malang on the east side of the island of Java, travelling out on the SS Prinses Amalia in May 1897. They had two children, Norman-John MacLeod (1897–1899) and Louise Jeanne MacLeod (1898–1919).

The marriage was overall a disappointment. Rudolf was an alcoholic, physically abused Margaretha, and blamed her for his lack of promotion. He openly kept a concubine, a socially accepted practice in the Dutch East Indies. Margaretha abandoned him temporarily, moving in with Van Rheedes, another Dutch officer. She studied Indonesian culture intensely for several months and joined a local dance company. In correspondence to her relatives in the Netherlands in 1897, she revealed her artistic name of Mata Hari, the word for "sun" in the local Indonesian language (literally, "eye of the day").

At Rudolf's urging, Margaretha returned to him, but his behavior did not change. She sought escape from her circumstances by studying the local culture. In 1899, their children fell violently ill from complications relating to the treatment of syphilis contracted from their parents, though the family claimed an irate servant poisoned them. Jeanne survived, but Norman died. Some sources maintain that one of Rudolf's enemies may have poisoned their supper to kill both of their children. After moving back to the Netherlands, the couple officially separated on 30 August 1902. The divorce became final in 1906, and Margaretha was awarded custody of Jeanne. Rudolf was legally required to pay child support but never did. Once when Jeanne visited Rudolf, he did not return her to her mother. Margaretha did not have the resources to fight the situation and accepted it, believing that while Rudolf had been an abusive husband, he had been a good father. Jeanne later died at the age of 21, possibly from complications related to syphilis.

Paris

In 1903, Zelle moved to Paris, where she performed as a circus horse rider using the name Lady MacLeod, much to the disapproval of the Dutch MacLeods. Struggling to earn a living, she also posed as an artist's model.

By 1904, Mata Hari rose to prominence as an exotic dancer. She was a contemporary of dancers Isadora Duncan and Ruth St. Denis, leaders in the early modern dance movement, which around the turn of the 20th century, looked to Asia and Egypt for artistic inspiration. Gabriel Astruc became her personal booking agent.

Promiscuous, flirtatious, and openly flaunting her body, Mata Hari captivated her audiences and was an overnight success from the debut of her act at the Musée Guimet on 13 March 1905. She became the long-time mistress of the millionaire industrialist Émile Étienne Guimet, who had founded the Musée. Entertainers of her era commonly invented colourful stories about their origins, and she posed as a Javanese princess of priestly Hindu birth, pretending to have been immersed in the art of sacred Indian dance since childhood. She was photographed numerous times during this period, nude or nearly so. Some of these pictures were obtained by MacLeod and strengthened his case in keeping custody of their daughter.

Mata Hari brought a carefree provocative style to the stage in her act, which garnered wide acclaim. The most celebrated segment of her act was her progressive shedding of clothing until she wore just a jeweled breastplate and some ornaments upon her arms and head. She was never seen bare-chested as she was self-conscious about having small breasts. Early in her career, she wore a bodystocking for her performances that was similar in color to her skin, but that was later omitted.

Her act was successful because it elevated erotic dance to a more respectable status and broke new ground in a style of entertainment for which Paris was later world-famous. Her style and free-willed attitude made her popular, as did her eagerness to perform in exotic and revealing clothing. She posed for provocative photos and mingled in wealthy circles. Since most Europeans at the time were unfamiliar with the Dutch East Indies, Mata Hari was thought of as exotic, and her claims were accepted as genuine. One enthusiastic French journalist wrote in a Paris newspaper that Mata Hari was "so feline, extremely feminine, majestically tragic, the thousand curves and movements of her body trembling in a thousand rhythms." One journalist in Vienna wrote after seeing one of her performances that Mata Hari was "slender and tall with the flexible grace of a wild animal, and with blue-black hair" and that her face "makes a strange foreign impression."

By about 1910, myriad imitators had arisen. Critics began to opine that the success and dazzling features of the popular Mata Hari were due to cheap exhibitionism and lacked artistic merit. Although she continued to schedule important social events throughout Europe, she was disdained by serious cultural institutions as a dancer who did not know how to dance.

Mata Hari's career went into decline after 1912. On 13 March 1915, she performed in the last show of her career. She had begun her career relatively late as a dancer and had started putting on weight. However, by this time, she had become a successful courtesan, known more for her sensuality and eroticism than for her classical beauty. She had relationships with high-ranking military officers, politicians, and others in influential positions in many countries. Her relationships and liaisons with powerful men frequently took her across international borders. Before World War I, she was generally viewed as an artist and a free-spirited bohemian, but as war approached, she began to be seen by some as a wanton and promiscuous woman, and perhaps a dangerous seductress.

Espionage

During World War I, the Netherlands remained neutral. As a Dutch subject, Zelle was thus able to cross national borders freely. To avoid the battlefields, she traveled between France and the Netherlands via Spain and Britain, and her movements inevitably attracted attention. During the war, Zelle was involved in what was described as a very intense romantic-sexual relationship with Captain Vadim Maslov, a 23-year-old Russian Staff Captain of the 1st Special Infantry Regiment serving with the French, whom she called the love of her life. Maslov was part of the 50,000-strong Russian Expeditionary Force sent to the Western Front in the spring of 1916.

In the April 1917, Maslov was wounded fighting in the ill-fated Nivelles Offensive to capture the German controlled fortified Brimont mountain range, losing his sight in his left eye, which led Zelle to ask for permission to visit her wounded lover at the hospital where he was staying near the front. As a citizen of a neutral country, Zelle would not normally be allowed near the front. Zelle was met by agents from the Deuxième Bureau who told her that she would be allowed to see Maslov if she agreed to spy for France.

Before the war, Zelle had performed as Mata Hari several times before the Crown Prince Wilhelm, eldest son of Kaiser Wilhelm II and nominally a senior German general on the Western Front. The Deuxième Bureau believed she could obtain information by seducing the Crown Prince for military secrets. In fact, his involvement was minimal, and it was German government propaganda that promoted the image of the Crown Prince as a great warrior, the worthy successor to the Hohenzollern monarchs who had made Prussia strong and powerful. They wanted to avoid publicizing that the man expected to be the next Kaiser was a playboy noted for womanizing, partying, and indulging in alcohol, who spent another portion of his time associating with far right-wing politicians, with the intent to have his father declared insane and deposed. Unaware that the Crown Prince did not have much to do with the running of Army Group Crown Prince or the 5th Army, the Deuxième Bureau offered Zelle 1 million francs if she could seduce him and provide France with good intelligence about German plans. The fact that the Crown Prince had, before 1914, never commanded a unit larger than a regiment, and was now supposedly commanding both an army and an army group at the same time should have been a clue that his role in German decision-making was mostly nominal. Zelle's contact with the Deuxième Bureau was Captain Georges Ladoux, who later emerged as one of her principal accusers.

In November 1916 she was traveling from Spain aboard the steamship USS Zeelandia. When the ship called at the British port of Falmouth she was arrested and taken to London, where she was interrogated at length by Sir Basil Thomson, assistant commissioner at New Scotland Yard in charge of counter-espionage. He gave an account of this in his 1922 book Queer People, saying that she eventually admitted to working for the Deuxième Bureau. Initially detained in Canon Row police station, she was then released and stayed at the Savoy Hotel. A full transcript of the interview is in Britain's National Archives and was broadcast, with Mata Hari played by Eleanor Bron, on the independent station LBC in 1980. It is unclear if she lied on this occasion, believing the story made her sound more intriguing, or if French authorities were using her in such a way but would not acknowledge her due to the embarrassment and international backlash it could cause.

In late 1916, Zelle traveled to Madrid, where she met the German military attaché Major Arnold Kalle and asked if he could arrange a meeting with the Crown Prince. During this period, Zelle apparently offered to share French secrets with Germany in exchange for money, though whether this was because of greed or an attempt to set up a meeting with Crown Prince Wilhelm remains unclear.

In January 1917, Major Kalle transmitted radio messages to Berlin describing the helpful activities of a German spy code-named H-21, whose biography so closely matched Zelle's that it was obvious that Agent H-21 could only be Mata Hari. The Deuxième Bureau intercepted the messages and, from the information they contained, identified H-21 as Mata Hari. The messages were in a code that German intelligence knew had already been broken by the French, suggesting that the messages were contrived to have Zelle arrested by the French.

General Walter Nicolai, the chief IC (intelligence officer) of the German Army, had grown very annoyed that Mata Hari had provided him with no intelligence worthy of the name, instead selling the Germans mere Paris gossip about the sex lives of French politicians and generals, and decided to terminate her employment by exposing her as a German spy to the French.

Trial
In December 1916, the Second Bureau of the French War Ministry let Mata Hari obtain the names of six Belgian agents. Five were suspected of submitting fake material and working for the Germans, while the sixth was suspected of being a double agent for Germany and France. Two weeks after Mata Hari had left Paris for a trip to Madrid, the Germans executed the double agent while the five others continued their operations. This development proved to the Second Bureau that Mata Hari had communicated the names of the six spies to the Germans.

On 13 February 1917, Mata Hari was arrested in her room at the Hotel Elysée Palace on the Champs Elysées in Paris. She was tried on 24 July, accused of spying for Germany and consequently causing the deaths of at least 50,000 soldiers. Although the French and British intelligence suspected her of spying for Germany, neither could produce definite evidence against her.

"A harlot? Yes, but a traitoress, never!"

Zelle's principal interrogator, who grilled her relentlessly, was Captain Pierre Bouchardon; he later prosecuted her at trial. Bouchardon established that much of the Mata Hari persona was invented. Far from being a Javanese princess, Zelle was Dutch, which he used as evidence of her dubious and dishonest character at her trial. Zelle admitted to Bouchardon that she had accepted 20,000 francs from a German diplomat and former lover as reimbursement for belongings taken from her by German authorities. Bouchardon claimed that this was, in fact, payment to her for spying for Germany. In the meantime, Ladoux had been preparing a case against his former agent by casting all of her activities in the worst possible light, going so far as to engage in evidence tampering.

Scapegoat
In 1917, France had been badly shaken by the Great Mutinies of the French Army in the spring of 1917 following the failure of the Nivelle Offensive and massive strikes. France might have collapsed from war exhaustion. Having one German spy on whom everything that went wrong with the war could be blamed was convenient for the French government. Mata Hari seemed the perfect scapegoat. The case against her received maximum publicity in the French press and led to her importance being greatly exaggerated. The Canadian historian Wesley Wark stated in a 2014 interview that Mata Hari was never an important spy but a scapegoat for French military failures that had nothing to do with her. Wark stated: "They needed a scapegoat, and she was a notable target for scapegoating." The British historian Julie Wheelwright stated: "She really did not pass on anything that you couldn't find in the local newspapers in Spain." Wheelwright described Zelle as "an independent woman, a divorcée, a citizen of a neutral country, a courtesan, and a dancer, which made her a perfect scapegoat for the French, who were then losing the war. She was ... held up as an example of what might happen if your morals were too loose."

Claiming her innocence, Zelle wrote letters to the Dutch Ambassador in Paris. "My international connections are due [to] my work as a dancer, nothing else .... Because I really did not spy, it is terrible that I cannot defend myself." The most terrible and heartbreaking moment for Mata Hari during the trial occurred when her lover Maslov—by now deeply embittered as a result of losing his eye in combat—declined to testify for her and told her that he did not care whether she was convicted. When Zelle learned that Maslov had abandoned her, she fainted.

Her defense counsel, veteran international lawyer Édouard Clunet, faced impossible odds; he was denied permission to cross-examine the prosecution's witnesses or to examine his witnesses directly. Bouchardon used the fact that Zelle was a woman as evidence of her guilt, saying: "Without scruples, accustomed to making use of men, she is the type of woman who is born to be a spy." Zelle has often been portrayed as a femme fatale, the dangerous, seductive woman who uses her sexuality to manipulate men effortlessly, but others view her differently: in the words of the American historians Norman Polmer and Thomas Allen she was "naïve and easily duped", a victim of men rather than a victimizer.

Although news reports following her execution claimed she had admitted to spying for Germany, Mata Hari made no such admission. She maintained throughout her ordeal that she had never been a German spy. At her trial, Zelle vehemently insisted that her sympathies were with the Allies and declared her passionate love of France, her adopted homeland. In October 2001, documents released from the archives of MI5 (British counter-intelligence) were used by a Dutch group, the Mata Hari Foundation, to ask the French government to exonerate Zelle as they argued that the MI5 files proved she was not guilty of the charges she was convicted of. A spokesperson from the Mata Hari Foundation argued that at most, Zelle was a low-level spy who provided no secrets to either side, stating: "We believe that there are sufficient doubts concerning the dossier of information that was used to convict her to warrant re-opening the case. Maybe she wasn't entirely innocent, but it seems clear she wasn't the master-spy whose information sent thousands of soldiers to their deaths, as has been claimed."

Execution
Zelle was executed by a firing squad consisting of 12 French soldiers just before dawn on 15 October 1917. She was 41. According to an eyewitness account by British reporter Henry Wales, she was not bound and refused a blindfold. She defiantly blew a kiss to the firing squad.

A 1934 New Yorker article reported that at her execution, she wore "a neat Amazonian tailored suit, especially made for the occasion, and a pair of new white gloves", though another account indicates she wore the same suit, low-cut blouse, and tricorn hat ensemble which had been picked out by her accusers for her to wear at trial, and which was still the only full, clean outfit which she had in prison. Neither description matches photographic evidence. Wales recorded her death, saying that after the volley of shots rang out, "Slowly, inertly, she settled to her knees, her head up always, and without the slightest change of expression on her face. For the fraction of a second it seemed she tottered there, on her knees, gazing directly at those who had taken her life. Then she fell backward, bending at the waist, with her legs doubled up beneath her." A non-commissioned officer then walked up to her body, pulled out his revolver, and shot her in the head to make sure she was dead.

Remains and 2017 French declassification
Mata Hari's body was not claimed by any family members and was accordingly used for medical study. Her head was embalmed and kept in the Museum of Anatomy in Paris. In 2000, archivists discovered that it had disappeared, possibly as early as 1954, according to curator Roger Saban, during the museum's relocation. Her head remains missing. Records dated 1918 show that the museum also received the rest of the body, but none of the remains could later be accounted for.

Mata Hari's sealed trial and other related documents, a total of 1,275 pages, were declassified by the French Army in 2017, one hundred years after her execution.

Museum exhibition
The Frisian museum (Dutch: Fries Museum) in Leeuwarden, Netherlands, contains a "Mata Hari Room". Included in the exhibit are two of her personal scrapbooks and an oriental rug embroidered with the footsteps of her fan dance. Located in Mata Hari's native town, the museum is well known for researching the life and career of Leeuwarden's world-famous citizen. The largest-ever Mata Hari exhibition was opened in the Museum of Friesland on 14 October 2017, one hundred years after her death.

Mata Hari's birthplace is located in the building at Kelders 33. The building suffered smoke and water damage during a fire in 2013 but was later restored. Architect Silvester Adema studied old drawings of the storefront to reconstruct it as it appeared when Adam Zelle, the father of Mata Hari, had a hat shop there. In 2016, an information centre (belevingscentrum) was created in the building displaying mementos of Mata Hari.

In popular culture
The idea of an exotic dancer working as a lethal double agent using her powers of seduction to extract military secrets from her many lovers made Mata Hari an enduring archetype of the femme fatale.

Her life inspired several films, including:
 * Mata Hari (1920)
 * Mata Hari (1927), a German production
 * Mata Hari (1931), a Hollywood motion picture starring Greta Garbo
 * In the 1939 romantic comedy Cafe Society, Mattie Harriett is hired by Allyn Joslyn's gossip columnist to spy on the film's two protagonists, Fred MacMurray and Madeleine Carroll.
 * Mata Hari, Agent H21 (1964) with Jeanne Moreau as Mata-Hari, Jean-Louis Trintignant, Claude Rich, Jean-Pierre Leaud, Marie Dubois, and Charles Denner, directed by Jean-Louis Richard
 * In the 1967 James Bond spoof Casino Royale, Joanna Pettet played Mata Bond, said to be the daughter of James Bond and Mata Hari.
 * In the 1968 Spanish comedy Operación Mata Hari, Mata Hari (Carmen de Lirio) retires with an accountant and her Spanish maid Guillermina (Gracita Morales) impersonates her in an espionage imbroglio.
 * In the 1970 American series Lancelot Link, Secret Chimp, a chimpanzee named "Mata Hairi" plays the role of a secret agent, voiced by Joan Gerber.
 * In the 1972 British comedy film Up the Front, Zsa Zsa Gabor portrays Mata Hari.
 * Mata Hari (1981), television series
 * "Mata Hari; The Magic Camera", an episode of Fantasy Island (1982)
 * Mata Hari, a 1985 film
 * In "Paris, October 1916", a 1993 episode of The Young Indiana Jones Chronicles, she is portrayed by Domiziana Giordano. Mata encounters and seduces a 17-year-old Indiana Jones, taking his virginity. "Paris, October 1916" was later re-edited into the second half of the film Demons of Deception.
 * Mata Hari (2016)
 * Mata Hari (2017), short film
 * Mata Hari: The Naked Spy (2017)
 * Mata Hari (2017), a 12-episode Russian-Portuguese TV series, stars Vahina Giocante in the title role.
 * In the 2021 movie The King's Man Mata Hari is portrayed by Austrian actress Valerie Pachner.

Mata Hari's life also inspired at least five stage musicals:
 * Mata Hari in 1967, starring Pernell Roberts and Marisa Mell
 * Mata Hari by Lene Lovich, Judge Smith, and Les Chappell, premiered in 1982 at the Lyric Theatre, Hammersmith.
 * Mata!, with words and music by Stuart Brayson, premiered at Blackpool Grand Theatre in June 1995.
 * Mata Hari at the Moulin Rouge by Frank Wildhorn debuted in Seoul, South Korea in March 2016.
 * One Last Night with Mata Hari, written by Craig Walker with music by John Burge, debuted at the Isabel Bader Centre for the Performing Arts in Kingston, Ontario, in January 2017.
 * In 2022, its musical adaptation by director Kim Moon Jeong and performed by the South Korean singer Solar from Mamamoo.

Two songs named after Mata Hari have appeared at the Eurovision Song Contest:

 * In 1976, Norway participated with the song "Mata Hari", performed by Anne-Karine Strøm.
 * In 2021, Azerbaijan participated with the song "Mata Hari", performed by Samira Efendi.

In 1931 Mata Hari, an American thoroughbred racehorse, was foaled. She twice won championship honors as the top filly in the sport. In 1943, when in foal to fellow champion Balladier, she produced Spy Song.

In 1977, Bally Manufacturing released an electromechanical pinball machine named after Mata Hari, and a solid-state version in 1978.

In the 1982 release of Birds & Bees by the Belgian band Telex (band), the tenth track on the album is dedicated to Mata Hari.

In 1995, Israeli singer Ofra Haza released a single titled "Mata Hari".

In February 2016, the Dutch National Ballet premiered a two-act ballet entitled Mata Hari, with Anna Tsygankova dancing the role of Mata Hari, choreography by Ted Brandsen and music by Tarik O'Regan.

In 2017, the opera Mata Hari by librettist Peter Peers and composer Matt Marks premiered at New York's Prototype Festival. In August 2018, it was also produced by West Edge Opera, with Tina Mitchell reprising her starring role.

In 2018, French nu-disco band L'Impératrice released their album titled 'Matahari' containing a song of the same name.

In 2019, English singer-songwriter Frank Turner released a song about Mata Hari entitled "Eye of the Day" on his album No Man's Land.

In 2020, the Dutch singer Kovacs released a single titled “Mata Hari”.

In 2022, she was referenced in episode 4 of the second season of Apple TV show Slow Horses.

title: Mata Hari


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Dr. Feelgood (band)

Dr. Feelgood are an English pub rock band formed in 1971. Hailing from Canvey Island, Essex, they are best known for early singles such as "She Does It Right", "Roxette", "Back in the Night" and "Milk and Alcohol". Their original and distinctively British R&B sound was centred on Wilko Johnson's choppy guitar style. Along with Johnson, the initial band line-up included singer Lee Brilleaux and the rhythm section of John B. Sparks, known as "Sparko", on bass guitar and John Martin, known as "The Big Figure", on drums. Although their most commercially productive years were the mid to late-1970s, and in spite of Brilleaux's death in 1994 of lymphoma, a version of the band (featuring none of the original members) continue to tour and record.

Early years
The band were formed on Canvey Island in 1971 by Johnson, Brilleaux and Sparks, who had all been members of existing R&B bands, and soon added drummer John Martin. They took their name from a 1962 record by the American blues pianist and singer Willie Perryman (also known as "Piano Red") called "Dr. Feel-Good", which Perryman recorded under the name of Dr. Feelgood & the Interns. The song was covered by several British beat groups in the 1960s, including Johnny Kidd & the Pirates. The term is also a slang term for heroin or for a physician who is willing to over-prescribe drugs.

By late 1973, the band's driving R&B influence had made them one of the most popular bands on the growing London pub rock circuit, which included regular appearances at the Lord Nelson music pub venue. They soon recorded their debut album, Down by the Jetty, for United Artists in 1974. Like many pub rock acts, Dr. Feelgood built up a dedicated following and were known primarily for their high energy and intense live performances constantly honed through their touring and regular performances. Their studio albums such as Down by the Jetty and Malpractice (1975) added significantly to their rising popularity.

Their breakthrough 1976 live album, Stupidity, reached number one in the UK Albums Chart (their only chart-topper). But after the 1977 follow-up Sneakin' Suspicion, Johnson left the group because of conflicts with Lee Brilleaux. He was replaced by Gypie Mayo. The band with Mayo were never as popular as when Johnson was in the line-up, yet they went on to enjoy their only top ten hit single in 1979 with "Milk and Alcohol". Johnson, who died in 2022, went on to form the group Solid Senders before joining Ian Dury and the Blockheads in 1980.

Later years
Despite Mayo's departure in 1981, and various subsequent line-up changes which left Brilleaux the only remaining original member, Dr. Feelgood continued touring and recording through the 1980s. The band then suffered an almost career-finishing blow when Brilleaux died of cancer on 7 April 1994.

As Brilleaux had insisted prior to his death, Dr. Feelgood reunited in May 1995, initially with vocalist Pete Gage (not to be confused with guitarist Pete Gage of Geno Washington and Vinegar Joe), and recommenced touring in 1996. Though the band contained no original members at this point, the musicians backing Gage had all previously played as members of Dr. Feelgood for at least five years, and in some cases for over a decade. In 1999, Gage was replaced by Robert Kane, formerly of the Animals II and the Alligators, who celebrated his 1,000th gig as the frontman of Dr. Feelgood in April 2007.

Every year after Brilleaux's death, a special concert known as the Lee Brilleaux Birthday Memorial was held on Canvey Island, where former and current Feelgoods celebrated the music of Dr. Feelgood, and raised money for The Fair Havens Hospice in Westcliff-on-Sea. Fans attended from all over the globe, and the 20th and final event was held on 9 May 2014. Still based in the UK, Dr. Feelgood continue to play across the world, with concerts in 2010 in Austria, Bahrain, Belgium, Finland, France, the Netherlands, Italy, Spain and Switzerland.

Band manager Chris Fenwick organises an annual walk around Canvey to commemorate Brilleaux's life, as well as additional walking tours during which he points out landmarks from the band's career. These include the jetty featured in the photograph on the band's first album cover, and venues where they played early in their career, such as The Lobster Smack inn, The Monico Nightclub and The Canvey Club (disguised as 'The Alibi Club' on the sleeve of the album Sneakin' Suspicion).

A film by Julien Temple about the early days of the band, Oil City Confidential, premiered at the London Film Festival on 22 October 2009, and received a standing ovation. Guest of honour was Lee Brilleaux's mother Joan Collinson, along with his widow Shirley and children Kelly and Nick. All the surviving members of the original band were present along with manager Chris Fenwick, former tour manager and Stiff Records boss Jake Riviera and other friends and colleagues of the band. The film has its own Facebook page. Reviewing the film for The Independent, Nick Hasted concluded: "Feelgood are remembered in rock history, if at all, as John the Baptists to punk's messiahs". On general release from 1 February 2010, the film was critically well received, with Peter Bradshaw of The Guardian describing it as "...a vivid study of period, music and place". The film was first broadcast on BBC Four in April 2010.

A major exhibition of memorabilia celebrating the band's career ran at The Canvey Club between May and July 2013, having been extended several times.

On 16 June 2021, it was announced that Walwyn was "unavailable to play live shows for the foreseeable future", due to family holiday commitments and the fact that his son has a possible compromised immune system. Later concerts were played by former guitarist Gordon Russell, whom Walwyn had replaced 32 years before.

In April 2024 the band's van was stolen, leaving them without any instruments and equipment, a week before a forthcoming tour of Germany. The theft took place outside the home of bassist Phil Mitchell in Hockley, Essex, between the night of 15 April and the morning of 16 April.

Members
Current members
 * Phil H. Mitchell – bass, acoustic guitar, backing vocals (1983–1991, 1995–present)
 * Kevin Morris – drums, percussion, backing vocals (1983–1994, 1995–present)
 * Gordon Russell – lead and slide guitars, backing vocals (1983–1989, 2021–present)
 * Robert Kane – lead vocals, harmonica (1999–present)

Discography

 * Down by the Jetty (1975)
 * Malpractice (1975)
 * Stupidity (1976)
 * Sneakin' Suspicion (1977)
 * Be Seeing You (1977)
 * Private Practice (1978)
 * Let It Roll (1979)
 * A Case of the Shakes (1980)
 * Fast Women & Slow Horses (1982)
 * Doctor's Orders (1984)
 * Mad Man Blues (1985)
 * Brilleaux (1986)
 * Classic (1987)
 * Primo (1991)
 * The Feelgood Factor (1993)
 * On the Road Again (1996)
 * Chess Masters (2000)
 * Repeat Prescription (2006)

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

title: Dr. Feelgood (band)


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Talk:Hausdorff dimension

Talk 2003 -2006
"If M is a metric space, and d > 0 is a real number, then the d-dimensional Hausdorff measure Hd(M) is defined to be the infimum of all m > 0 such that for all r > 0, M can be covered by countably many closed sets of diameter < r and the sum of the d-th powers of these diameters is less than or equal to m."

I read infimium, so I'm clear on that, but this definition is still opaque to me. Please clarify. --BlackGriffen

The box-counting dimension is not the same thing as the Housdorff dimension! -- Miguel

 * Thanks, I changed that. Now all we need is an article on the box-counting dimension... :) -- Schnee 23:22, 13 Aug 2003 (UTC)

Hausdorff dimension isn't the only fractal dimension...it should have its own entry, and fractal dimension to talk about fractal dimensions collectively, it seems.

 * Done. -- Jheald 22:01, 19 January 2006 (UTC).

Banner
The banner is ridiculous and I am going to remove it. CSTAR 17:43, 25 Nov 2004 (UTC)

Doubling property
I put in a condition at the beginning which is basically the doubling property (which is of course much weaker). I'm not even sure I stated it correctly. Will the experts object? I perhaps should do my homework and consult my copy of Gromov-Semmes et-al. But hey, I'll let Tosha do that.CSTAR 17:49, 26 Nov 2004 (UTC)

Haha, ironic for the page-doubling bug to strike here. X) -- 21:24, 26 Nov 2004 (UTC)

Name change
It's called Hausdorff dimension. Policy is that usual names should be used. This page should be moved back. Charles Matthews 19:31, 26 Nov 2004 (UTC)

 * It's moved back. Do you happen to know what the point of the name change was? CSTAR 19:43, 26 Nov 2004 (UTC)

It's User:Eequor on a stampede. See Besicovitch. Charles Matthews 20:08, 26 Nov 2004 (UTC)

 * I see; so because the two of you agree with each other, you must be correct? --[[User:Eequor| η  [[Image:Venus symbol (blue).gif|♀]] [ υωρ ]]] 20:39, 26 Nov 2004 (UTC)

 * Charles Matthews and I do agree, and either we're correct or we're not. Whether we're correct or not ideally should be determined by a discussion of the relevant linguistic facts in this case (as I've tried to do below). If no consensus emerges, than some other mediation procedure is needed.  That mediation procedure may reduce to some less desirable criteria for selection of the ultimate name.

 * Please note that neither of us is suggesting Besicovitch not be mentioned. BTW, Besicovitch's contribution in this area is in obtaining fairly precise bounds on the growth properties of coverings. Besicovith wrote all his papers mre than 20 years after Felix Hausdorff introduced Hausdorff measure. I don't see how you can even argue fairness here! CSTAR 21:13, 26 Nov 2004 (UTC)

 * Ah, that helps. Do you happen to have the dates of their publications, or where they were published?  It would be nice to have the details of Besicovitch's contribution.  --[[User:Eequor| η  [[Image:Venus symbol (blue).gif|♀]] [ υωρ ]]] 21:21, 26 Nov 2004 (UTC)

 * Besicovitch indeed has a long list (in the 100s) of reputable publications, which is much longer than Haudorff's (although as I said, came much later than Hausdorff). Partly because Besicovitch lived much longer than Hausdorff he was much more prolific.  Probably the most relevant one is

 * A. S. Besicovitch and H. D. Ursell, Sets of Fractional Dimensions, 1937, Journal of the London Mathematical Society, v12.

 * However, I freely admit I am not a historian of mathematics, so among the 100s of papers he wrote there may be other more relevant ones. The main point is that Besicovitch was a very accomplished analyst who developed many powerful techniques to compute many things, including Hausdorff measures.  So I don't want to err in the other direction and not give him due credit.CSTAR 21:40, 26 Nov 2004 (UTC)

Historical accuracy
If you really want to be accurate, you should say something like

 * Though most authors use the term Hausdorff dimension, and indeed Hausdorff was the first to explicitly introduce this concept, some authors (notably Mandelbrot) also refer to it as Hausdorff-Besicovitch dimension, particularly since Besicovotch developed many techniques for determining sizes of coverings of sets, which in turn are useful for calculating Hausdorff measures of highly irregular sets.

ALso Hausdorff dimension is not a measurement and it also would be misleading to call it a measure. It's just a number assigned to  a set. CSTAR 22:07, 26 Nov 2004 (UTC)

 * How is it not a measurement? What measure is not just a number assigned to a set?
 * JumpDiscont (talk) 02:50, 3 October 2009 (UTC)

Hausdorff dimension
Why the name change? Virtually every authoritative work on the subject refers to the concept as Hausdorff dimension. For example

 * H. Federer Geometric Measure Theory, Springer -Verlag, 1969
 * K. J. Falconer, The Geometry of Fractal Sets, Cambridge University Press, 1985
 * M. Gromov with M. Katz, P. Pansu and S. Semmes, Metric Structures for Riemannian and Non-Riemannian Surfaces, Birkauser, 2001

CSTAR 19:56, 26 Nov 2004 (UTC)

 * On the other hand, Mandelbrot uses Hausdorff-Besicovitch dimension. It would be unfair to credit Felix Hausdorff but not Abram Samoilovitch Besicovitch, wouldn't it?  --[[User:Eequor| η  [[Image:Venus symbol (blue).gif|♀]] [ υωρ ]]] 20:01, 26 Nov 2004 (UTC)

Firstly, Mandelbrot is much more of a publicist than a serious mathematician. I'm not prepared to take that book as an authority on mathematics. We use fractal the way he does (for better or for worse), because it's his term.

Second point: Wikipedia naming policy is (generally) to use the most usual name. The article can discuss credit where due; the title should be the normal way of naming anything. Charles Matthews 20:19, 26 Nov 2004 (UTC)

 * Mandelbrot I'm afraid is much in the minority here. The list of sources calling it Hausdorff dimension is really very long. In addition to the three I mentioned above, one can also add:

 * * W. Hurewicz and Wallman, Dimension Theory, Princeton Univrsity Press, 1941
 * * F. Morgan Geometric Meaasure Theory, Academic Press, 1988

 * Whether or not it's unfair to give it a name is an entirely different matter, and is not Wikipedia's responsibility to assign names based on fairness or any other criteria. If you want to do a historical study to determine who invented the concept, then by all means do so. I will support your writing such an article and it will be useful. However, in this instance the overwhelming evidence is that it's called Hausdorff dimension by authorities in the area. The Wikipedia policy on the matter is quite clear.CSTAR 20:22, 26 Nov 2004 (UTC)

 * I am aware that the metric is often referred to as the Hausdorff dimension; however, to dismiss one researcher because "everybody else does" is POV. --[[User:Eequor| η  [[Image:Venus symbol (blue).gif|♀]] [ υωρ ]]] 20:33, 26 Nov 2004 (UTC)

 * The discussion is in relation to how something, in this case a technical concept, is named. Concepts often are assigned names in a haphazard way, completely unrelated to who may have first discovered them. Buy using a name, no one is making a determination about credit. Bezout's theorem is one example.  It is almost universally agreed that he had little to do with it.

 * Wikipedia should not be in the business of assigning names or creating extensions or modification of existing language (except in very limited cases, such as providing an auxiliary explanatory or as a temporary notational artifice). Moreover, I have presented many academically respected references showing that indeed "everybody else" (other than Mandelbrot) assigns this name to the dimensionality concept in question. How is relying on the fact that "everybody else" (other than Mandelbrot) uses a particular name an insatnce of POV? Language is a social phenomenon. It's the collective result of everybody's behavior.

 * It may unfair but that's the way linguistic behavior works.CSTAR 20:57, 26 Nov 2004 (UTC)

 * Names are area where "absolute NPOV" is hardly possible. Be it a mathemathical concept, Polish city or anything where various POVs may exist. Wikipedia policy to use the name the reader would most propably use is reasonable. Frequency of usage is decidable and factual. Historical justice is not. Best what can be done about NPOV is to note various names in the article and create redirects. (See Prim-Jarnik's algorithm) --Wikimol 22:31, 26 Nov 2004 (UTC)

 * That's right - mathematical names are full of incorrect history. The history is properly in the article, not the title. The argument offered does not, in my view, have much to recommend it. Charles Matthews 22:39, 26 Nov 2004 (UTC)

 * I agree with Charles and CSTAR and I moved it back -Lethe | Talk

 * I think it should be Hausdorff dimension. That's the term commonly used. As such it is the appropriate title. Whether justified or fair, most people call it this, and Wikipedia policy is to use the common title. CheeseDreams 23:39, 2 Dec 2004 (UTC)

Hausdorff dimension/Hausdorff measure
I think to split it.Tosha 06:09, 28 Dec 2004 (UTC)

 * Do uou mean you think you think are going to split the article? What are the advantages of doing so? Particularly, since the two subjects are tied so closely together.CSTAR 06:38, 28 Dec 2004 (UTC)

They are not tied, one is defined using the other Tosha 21:39, 28 Dec 2004 (UTC)

 * They are not tied

 * That's certainly a new viewpoint.

 * I'm certainly aware that one is defined using the other. But maybe I should have asked how you propose to split them up, particularly, as I'm sure you agree,  logical order may have no relation to expository order.  Note that the introductory paragraphs refer to Hausdorff's idea of using measure to determine some kind of dimension as opposed to some more naive box counting dimension. CSTAR 22:10, 28 Dec 2004 (UTC)

 * P.S. I don't oppose splitting them up, it's just that I don't see the expository advantages. But I'm convincible. CSTAR 22:23, 28 Dec 2004 (UTC)

I think it is a good idea to split them. The simplest definition of Hausdorff dimension does not involve the Hausdorff measure, but involves the Hausdorff content. Anyway, the Hausdorff content should be discussed somewhere. I think there is a lot to say about Hausdorff measure and it would not be good to put all this stuff here. Oded (talk) 19:52, 9 May 2008 (UTC)
 * Related material which should be discussed somewhere are doubling, Ahlfors regularity and Roger's generalizations of Hausdorff measure.  Trying to find a rational way of organizing and subdividing all this stuff is difficult.  If you want to have at it, go ahead.--CSTAR (talk) 20:37, 9 May 2008 (UTC)

 * I'm far from an expert about H-measure. I will probably start out by splitting H-measure away from here, put here the definition of H-dim in terms of H-content, create a page with the basic definition of H-measure. But then I would leave it to people more knowledgeble to write the rest. Oded (talk) 21:20, 9 May 2008 (UTC)

Does this really work? or?
I think this does not work correctly! Take a look at the image at right, there you can see three examples of Hausdorff dimensions. The first is a 2D Cantor set, four main attractors and scale factor $$1:2$$, no rotation. This gives a dimension of 2.0 and the result is also a two dimensional, 45º tilted square. The second image are the same but here a rotation of 45º is also used. From the Hausdorff method point of view this is still 2.0 dimensions but it's far from a two dimensional surface we see. Now if one choose to use a scale factor of $$1:sqrt(2)$$ then we vill get 4.0 dimensions and a perfec two dimensional surface. Is the Hausdorff method of counting dimensions wrong? Or did I miss something? ;-) // Solkoll 12:35, 1 Mar 2005 (UTC)

 * When you say "I think this does not work correctly!" what "this" are you referring to? CSTAR 12:44, 1 Mar 2005 (UTC)

 * This = the method of counting dimensions. The rotaion changes the dimesion from what I can see, (but I'm no pro, jus a guy who likes to make fractals and thinks a lot about how to do this, scale ratios and such). This is not taken in count using the Hausdorff method. // S

 * Rotating is a Lipschitz map. Read the the theorem on Lipschitz invariance! CSTAR 15:58, 6 Mar 2005 (UTC)

 * Why not try this: $$ln ( points ) / ln ( | cos ( angle ) * scale | + | sin ( angle ) * scale | )$$. For the three images above this makes 2.0, 1.333..., 2.0 dimensions. (More like the looks of the pictures than 2.0, 2.0, 4.0 I say =) See also: the metric of the taxicab geometry: |x| + |y|, is this the same?. // Solkoll 11:59, 6 Mar 2005 (UTC)

 * [[Image:SimDim.jpg|thumb|300px|Drawn with Fractal Attraction]]

Well, you are computing the similarity dimension (for an iterated function system), not the Hausdorff dimension. There is a theorem that says you get the Hausdorff dimension when you do this, provided the Open Set Condition (OSC) holds. Basically, this means there is not too much overlap of the images. In the first case, the OSC is true. You get a solid square, and it does have dimension 2. In the other two cases, the OSC is not true. In the second case, because of the overlap, the Hausdorff dimension could be less than 2. From the picture, it looks like it is. In the third case, the image is a solid square, but there is overlap again (can you see it in the picture?)... so the Hausdorff dimension (2) could be less than the similarity dimension (4).

--G A Edgar 15:19, 17 Mar 2005 (UTC)

 * Thank you for that professor Edgar =) this clears things out. And yes the overlaps is clearly shown in your picture. // Solkoll 16:42, 17 Mar 2005 (UTC)

New picture
I don't want to get into an discussion of the merits of pictures, but I don't particularly like the new SIrepinski image.CSTAR 12:49, 1 Mar 2005 (UTC)

 * Too kitschy I guess? too many colours? =) The old image was not good either, too pixly for my taste. I can make a softer Hi-res anti-anilise = no pixels - just lines, if you like? Mono-colour? B&W? RGB-fade as the current image but a clear backgrund? Make a wish =) // Solkoll 20:56, 1 Mar 2005 (UTC)

 * Two colour, uniform background. (BTW I made the previous one with XFIG). CSTAR 22:52, 1 Mar 2005 (UTC)

 * Better now? I'm using C/C++ under win32 & DirectX to create my images. This means a lot of work but also full control over the situation. If you, as I do, like kitschy fractal images? then take a look at commons:Category:Images of fractals or sv:Kategori:Bilder av fraktaler, (same sentens but in Swedish). All images are from my tools, (and all of them are not kitchy either =) // Solkoll 11:22, 2 Mar 2005 (UTC)

Additivity
"The Hausdorff outer measure Hs is defined for all subsets of X. However, we can in general assert additivity properties, that is

 * $$   H^s(A \cup B) = H^s(A) + H^s(B)$$

for disjoint A, B, only when A and B are both Borel sets. From the perspective of assigning measure and dimension to sets with unusual metric properties such as fractals, however, this is not a restriction."

This is wrong, it is for measurable A, B, not only Borel. The set of all measurable sets is strictly larger than the set of all Borel sets. This is true for at least Hausdorff and Lebesgue measure (proof can be by construction using inverse images of the Cantor ternary function, or by cardinality).220.245.178.131 05:37, 28 February 2006 (UTC)

 * It is certainly true for Borel sets. The intent of the claim is that some additional restriction is necessary on the sets A, B. I will fix the statement so it is fully accurate.

 * BTW one cannot conclude that in general if $$ H^s(A \cup B) = H^s(A) + H^s(B)$$ THEN both A, B are measurable. In fact,  a set is E measurable in the Caratheodory sense iff it splits every set Ainto two parts so that the outer measures add up, that is for all A

 * $$ \mu^*(A) = \mu^*(A \cap E) + \mu^*(A \setminus E) $$
 * --CSTAR 05:58, 28 February 2006 (UTC)

Recent edits
Why are these recent edits an improvement? Any subset of a metric space is a metric space. Moreover, it's thge behavior of the measure which is unintuitive, not the values. I think the article should be reverted to version of August 26 .--CSTAR 14:44, 12 October 2006 (UTC)

 * After rereading my changes I agree. I am reverting as you suggested. —Tobias Bergemann 18:03, 12 October 2006 (UTC)

finite hausdorff dimension for compact sets?
"For instance R has dimension 1 and its 1-dimensional Hausdorff measure is infinite." The first reason I would imagine that R is able to have infinite Hausdorff measure is that it is not compact. Is there a compact set whose Hausdorff measure is infinite, or a proof that such a set cannot exist? It would be a nice little comment to add after the quoted sentence either way.69.215.17.209 16:21, 31 March 2007 (UTC)

 * Sure. Just take your favorite countable, compact metric space (e.g. 1/n with 0).  Being countable, it has Hausdorff dimension 0, but the d=0 Hausdorff measure is just the counting measure, so it has infinite measure.  —Preceding unsigned comment added by 72.33.108.253 (talk) 17:51, 26 November 2008 (UTC)

Hey
Hausdorff dimension eh, has anyone got a fractal with a hausdorff dimension = golden ratio? 83.70.46.38 06:21, 23 April 2007 (UTC)

Yes: Beardon (1965, On the Hausdorff dimension of general Cantor sets) showed that generalised Cantor sets with arbitrary dimension can be generated. Colin Rowat (talk) 07:07, 24 October 2011 (UTC)

About Hausdorff dimension and Hausdorff measure
The two concepts are related but are not the same: Hausdorff measure of smooth sets coincides with Lebesgue measure, while the Hausdorff dimension coincides with the "algebraic" dimension (very rougly, it is the cardinality of the set of linearly independent unit vectors needed to span the smallest linear subspace enclosing the given set). The confusion derives from the fact that in classical references, Hausdorff dimension is also called Hausdorff dimension measure: I have reported two links from the online Springer Enciclopedya of Mathematics clarifyng the two conceps. I also remember that the fundamental reference in the field, i.e. Herb Federer's masterpiece, clearly states the two concepts and their difference (I'm quite sure and I will check later). In my opinion it is necessary to give rise to two separate voices. Daniele.tampieri (talk) 14:43, 7 April 2008 (UTC)
 * Hausdorff measure
 * Hausdorff dimension
 * Hausdorff measure is a (a family of) countably additive measures Hλ on Borel sets, indexed by a real parameter λ . Hausdorff dimension is a real number defined in terms of Hausdorff dimension (measure Note Correction --CSTAR (talk) 03:17, 28 April 2008 (UTC)). All Hausdorff measures on Rn defined in terms of continuous metrics on Rn which are invariant under translation, are identical up to  a nonzero scaling constant.  In some instances, determining the value of this constant can be very important and Federer does a very careful job of computing these values.  Determining the scaling constants is tantamount to computing volumes of spheres, and for some problems in mathematics the asymptotic behavior of these volumes as n goes to infinity is very interesting and important.  However, for determining the Hausdorff dimension of sets, the value of the scaling constant is of no interest. --CSTAR (talk) 15:42, 7 April 2008 (UTC)
 * This is wrong, e.g. the metric d(x,y)^s for d Euclidean distance 0<s<1 is invariant under translation and continuous but the Hausdorff measures aren't the same. Oh well.--CSTAR (talk) 20:57, 5 May 2008 (UTC)

Date of introduction
As far as I can see the earliest reference was published in 1919. The fact that Hausdorff submitted the paper in 1918 doesn't mean the theory was "introduced" then, as the introduction currently states. The current text could be retained if Hausdorff was presenting his work at conferences in 1918 before publication of the article. —DIV (128.250.80.15 (talk) 02:44, 28 April 2008 (UTC))

Informal discussion
Whoa. The "Informal Discussion" is anything but. Someone needs to bring this down to a level where someone who isn't a math major can understand. Or perhaps consider changing the name. Timothyjwood (talk) 04:37, 7 July 2008 (UTC)

 * I think Timothy is right. This informal discussion discusses too many things (e.g. topological dimension) that are not essential to the main point. We should rewrite the informal discussion to motivate the definition of Hausdorff dimension (going through Minkowski dimension). I envision something similar to an expanded version of what is currently the third paragraph. Oded (talk) 05:43, 7 July 2008 (UTC)

 * It's three years later, and the informal discussion is not clear to me: "But you can easily take a single real number, one parameter, and split its digits to make two real numbers."  What does "split lll digits" mean?  What is the grammar here:  Is "one parameter" an appositive of "single real number"?  If not, then should it read "single real number and one parameter and split"?  I don't know. 211.225.34.164 (talk) 10:16, 28 June 2011 (UTC)

 * Another ~4 yrs, and still no progress in the lede and mentioned informal section. Perhaps in maths this is the equivalent of a secret handshake, that we simply are not intended to understand or enter this rarified realm. 165.20.108.150 (talk) 23:34, 5 March 2015 (UTC)

 * I can explain what "split its digits" means: take a number like 3.14159..., and split it into two numbers: one whose digits are those corresponding to even powers of 10 in the original number (3.45...) and one whose digits are those corresponding to odd powers of 10 in the original number (0.119...). Obviously, if you start with two different numbers and split them up this way (assuming you're careful about picking your decimal expansions) you'll get different pairs of numbers at the end; and any pair of numbers can be generated this way (since you can just take the two decimal expansions and interleave them).  I don't know how to explain it more simply than just giving an example, though.  68.113.159.26 (talk) 04:08, 7 October 2016 (UTC)

Minkowski dimension, rather than Hausdorff?
[In the Section entitled "Informal discussion," i]s the construction given in the paragraph beginning, "Consider the number N(r) of balls of radius at most r ..." not that used in deriving Minkowski dimension, rather than Hausdorff? The key detail is the use of regular elements, the r-balls. If so, this gives an upper bound for Hausdorff dimension, which is typically much more easily derived than the Hausdorff dimension itself. 147.188.129.99 (talk) 20:30, 27 October 2011 (UTC)

Product inequality
Anyone have a proof (or sketch) that the dimension of a product is at least the sum of the dimensions?

Formal definition is wrong
I'm not an expert in this area, but I'm pretty sure the given definition of Hausdorff content is incorrect. It disagrees with the books I've looked at, and moreover does not make sense. The given definition places no restriction on the balls used to cover the set. The typical definition of Hausdorff content is to say something like: H^d_delta is the infimum of sums of (r_i)^d, where the set can be covered by balls B_i of radius r_i LESS THAN DELTA. Then define H^d of the set to be the limit of H^d_delta as delta goes to 0. Otherwise, for instance you get that the 1-dimensional Hausdorff content of the unit ball in R^3 is finite. Kier07 (talk) 16:36, 6 February 2009 (UTC)

Never mind, sorry. Though the words "content" and "measure" are very similar, so I think the article should be clearer about the fact that these are different ideas. Kier07 (talk) 16:44, 6 February 2009 (UTC)

Hausdorff content (defined here without delta) and Hausdorff measure (defined in many sources with delta) are, indeed, different. For example, the unit ball in Euclidean space R^n is covered by some ball of some radius, so the d-dimensional content is finite for all d. But of course the d-dimensional Hausdorff measure is finite only if d >= n.G A Edgar (talk) 11:21, 26 July 2009 (UTC)

Furthermore, defining Hausdorff dimension using the Hausdorff content is wrong. It must be defined from the Hausdorff measure.G A Edgar (talk) 11:21, 26 July 2009 (UTC)

OK, the definition of Hausdorff dimension is not wrong. Although the Hausdorff content and the Hausdorff measure are different, when one is zero so is the other. G A Edgar (talk) 13:34, 30 July 2009 (UTC)

Formal Definition
From the definitions at the beginning at the paragraph, it seems clear that we are interested in the Hausforff dimension of S. However, the definition at the end is given with X, which is the enclosing metric space and not what we were interested in in the first place. Wouldn't it be clearer and more correct to give it with S instead? Joelthelion (talk) 10:22, 17 August 2010 (UTC)

"Every space filling curve hits some points multiple times"
This assertion appears in the article. I can't tell if it's wrong or just confusing. None of the space-filling curves listed on the Space-filling curves page intersect themselves and the ones pictured have a Hausdorff dimension of 2.

I suggest removing or clarifying this assertion, but I don't have the mathematical expertise to know which is appropriate.

-

That statement is correct and here's why: A space filling curve maps a line to a filled square or cube or hypercube. The definition gives us that the curve is both continuous and onto. If it were to not intersect itself, then the curve would also be 1-1, which in turn become an isomorphism. Since a line and a square are not isomorphic, the curve should hit some points multiple times.

It seems counter-intuitive; but it's correct nonetheless. 212.175.32.133 (talk) 09:26, 7 April 2015 (UTC)

Article tag added
Yet another mathematical encyclopedia completely inaccessible to a lay reader? Tag added because not even the lede is approachable. This is a typical maths article problem, that mathematicians are writing for themselves. I challenge contributing editors to write a lede and figure legends (if not the whole of the introductory portions of the article) that any high school-educated reader can read—without chasing every wikilink that appears. Wikilinks and citations are intended to allow interested readers to go deeper in particular subject areas, not to replace the need for good, understandable exposition. 165.20.108.150 (talk) 23:20, 5 March 2015 (UTC)
 * Lede rewritten from other Wikipedia article content and new sources, making at least opening more readable. See how this fits. 71.239.87.100 (talk) 04:57, 6 March 2015 (UTC)
 * Tagger let me suggest reading the whole Wikipedia article on Mathematics. If after doing that you still come back expecting mathematicians to write their Wikipedia articles on the subject in such a way that anyone with a high school diploma can instantly understand them, then sorry, I can't help you.  By the way, if this particular subject didn't happen to have the loaded term "dimension" in its name, you likely would have never added the tag.  (Would you have added it to any page with a title like "Diophantine equation" or "Kuratowski closure-complement problem" instead?  I doubt it.)  Tag removed. Mathematrucker (talk) 13:06, 13 July 2017 (UTC)

Citations inappropriate moved here for discussion
Given the WP:PSTS policy strictures on use of primary sources, the following two bits of text and their sources are moved here for discussion. In my view they add nothing to the article, and begin a pattern of dumping of trivial results here that will in long run, move the article to a status even further from GA than it currently is:
 * The bond system of an amorphous solid changes its Hausdorff dimension from Euclidean 3 below glass transition temperature Tg (where the amorphous material is solid), to fractal 2.55±0.05 above Tg, where the amorphous material is liquid.
 * REF:
 * [objection: very narrow primary research result, of questionable general importance, not further supported by a secondary source, and not integrated into any clear theme of the overall article (i.e., a stray related research result that lacks notability for inclusion)]

 * SECTION: The Hausdorff Dimension Theorem. For any given r ≥ 0, and integer n  ≥ r, there are at least continuum-many fractals  $$ A \subset \mathbb{R}^n$$ of Hausdorff dimension r.
 * REF: Soltanifar, M. (2006). On A Sequence of Cantor Fractals, Rose Hulman Undergraduate Mathematics Journal, Vol 7, No 1, paper 9.
 * [objection: very narrow primary research result, of questionable general importance, not further supported by a secondary source, and not integrated into any clear theme of the overall article (i.e., a stray related research result that lacks notability for inclusion); moreover, a publication of primary results in an undergraduate university journal, and not a standard, high quality venue, even for primary results, so clearly in need of substantiation before reintroduction]

Le Prof 71.239.87.100 (talk) 04:56, 6 March 2015 (UTC)

Examples section
Why is the examples section flooded with "citation needed"s? These examples aren't some hard problems which took hundreds of years to solve, at maximum they would take an average person ten minutes to verify with a pen and paper. 212.175.32.133 (talk) 11:28, 6 April 2015 (UTC)
 * I reacted in the same way to-day (more than 18 months later, with nothing really having happened since that time). Here are the edits where they were introduced.  can you confirm that they are your edits?
 * The edits not only cluttered this and other sections with "unsourced" tags (for both sections and sentences), it also made some re-labeling at the references. Before these edits, the reflist appeared under the heading Notes, and references more comprehensive literature under the heading References.  This was changed to References and Further reading, respectively.
 * My personal opinion is that the article was better before than after these edits. However, Leprof 7272, or whoever else the editor was, was at least formally following some WP standard.  The question more is if this really is a good standard, or a good interpretation of the standards.  At least for math articles, I think that more general references for whole sections are better than sourcing each and every fact separately - and especially so, when a subject is treated, where indeed there are numerous interesting but fairly immediate consequences of the definitions, as in this case.  If you have understood the definitions, then you also should understand the consequences, which now are individually tagged as unsourced, with reasonably little trouble.  (If you never in your life have met similar subjects, and still on a theoretical level understand the definitions, then it may take a little longer than 10 minutes to verify them; but with a general reference provided, you also just might try to look them up.)
 * Actually, I have the impression that WP editors with more mathematical experience in general tend to be a bit more flexible about referencing each and every obvious consequence of the definitions separately. However, it is possible that this flexibility deviates from WP standards, at least as these are interpreted by a non-ignorable fraction of the experienced editors with mostly non-mathematical main interests.
 * In this case, I'd like to remove a number of the tags; but not if there is a strong dissent. JoergenB (talk) 20:12, 27 October 2016 (UTC)
 * As I mentioned above in my justification for removing the inappropriate "too technical" tag (how it remained for over two years is a mystery to me), I suspect that all the tag clutter here may be partly attributable to the cachet the word "dimension" has in ordinary English. Mathematrucker (talk) 13:41, 13 July 2017 (UTC)

Important omission
The famous formula $$D=\frac{log(P)}{-log(\frac{1}{\epsilon})}$$ is absent!

If the article should be reduced to one formula, it would be that formula, and is not clearly and explicitly exposed. — Preceding unsigned comment added by 206.132.109.103 (talk) 14:07, 5 January 2017 (UTC)

"Balls" misleading?
In the "Formal Definition" section, I'm assuming that the "balls" are balls under the supremum measure? I don't think that would be at all obvious to the average reader... Twin Bird (talk) 03:26, 5 April 2020 (UTC)

Adding a Generalized Hausdorff Dimension Theorem to the Page
Hi Editors; I suggest adding this Theorem to the page for readers' reference. It shows the existence of deterministic fractals for given Hausdorff dimension and Lebesgue measure. Thanks\\

P.S.\\

Theorem 6 (The Generalized Hausdorff Dimension Theorem). For any real r>0 and l≥0, there are aleph-two (symmetric) fractals with the Hausdorff dimension r.1{0}(l)+n.1(0,∞)(l) and Lebesgue measure l in Rn where (⌈r⌉≤n).

Link:

https://www.mdpi.com/2227-7390/9/13/1546 https://doi.org/10.3390/math9131546 — Preceding unsigned comment added by MohsenSoltanifarNA (talk • contribs) 02:21, 9 July 2021 (UTC)

British Coast Line
The approximation of the British Coast Line looks like an approximation of the Minkowski dimension (that often coincides with the Hausdorff dimension). For Hausdorff dimension balls of different size < delta are allowed. Maybe that should be clarified. — Preceding unsigned comment added by 2A02:908:621:3520:FFDE:36A8:F977:BA99 (talk) 18:47, 16 April 2022 (UTC)

title: Talk:Hausdorff dimension


text:
Lagged Fibonacci generator

A Lagged Fibonacci generator (LFG or sometimes LFib) is an example of a pseudorandom number generator. This class of random number generator is aimed at being an improvement on the 'standard' linear congruential generator. These are based on a generalisation of the Fibonacci sequence.

The Fibonacci sequence may be described by the recurrence relation:

 * $$S_n = S_{n-1} + S_{n-2}$$

Hence, the new term is the sum of the last two terms in the sequence. This can be generalised to the sequence:

 * $$S_n \equiv S_{n-j} \star S_{n-k} \pmod{m},   0 < j < k$$

In which case, the new term is some combination of any two previous terms. m is usually a power of 2 (m = 2M), often 232 or 264. The $$\star$$ operator denotes a general binary operation. This may be either addition, subtraction, multiplication, or the bitwise exclusive-or operator (XOR). The theory of this type of generator is rather complex, and it may not be sufficient simply to choose random values for j and k. These generators also tend to be very sensitive to initialisation.

Generators of this type employ k words of state (they 'remember' the last k values).

If the operation used is addition, then the generator is described as an Additive Lagged Fibonacci Generator or ALFG, if multiplication is used, it is a Multiplicative Lagged Fibonacci Generator or MLFG, and if the XOR operation is used, it is called a Two-tap generalised feedback shift register or GFSR. The Mersenne Twister algorithm is a variation on a GFSR. The GFSR is also related to the linear-feedback shift register, or LFSR.

Properties of lagged Fibonacci generators
The maximum period of lagged Fibonacci generators depends on the binary operation $$\star$$. If addition or subtraction is used, the maximum period is (2k − 1) × 2M−1. If multiplication is used, the maximum period is (2k − 1) × 2M−3, or 1/4 of period of the additive case. If bitwise xor is used, the maximum period is 2k − 1.

For the generator to achieve this maximum period, the polynomial:

 * y = xk + xj + 1

must be primitive over the integers mod 2. Values of j and k satisfying this constraint have been published in the literature.

Another list of possible values for j and k is on page 29 of volume 2 of The Art of Computer Programming:

 * (24, 55), (38, 89), (37, 100), (30, 127), (83, 258), (107, 378), (273, 607), (1029, 2281), (576, 3217), (4187, 9689), (7083, 19937), (9739, 23209)

Note that the smaller number have short periods (only a few "random" numbers are generated before the first "random" number is repeated and the sequence restarts).

If addition is used, it is required that at least one of the first k values chosen to initialise the generator be odd. If multiplication is used, instead, it is required that all the first k values be odd, and further that at least one of them is ±3 mod 8.

It has been suggested that good ratios between j and k are approximately the golden ratio.

Problems with LFGs
In a paper on four-tap shift registers, Robert M. Ziff, referring to LFGs that use the XOR operator, states that "It is now widely known that such generators, in particular with the two-tap rules such as R(103, 250), have serious deficiencies. Marsaglia observed very poor behavior with R(24, 55) and smaller generators, and advised against using generators of this type altogether.  ... The basic problem of two-tap generators R(a, b) is that they have a built-in three-point correlation between $$x_{n}$$, $$x_{n-a}$$, and $$x_{n-b}$$, simply given by the generator itself ... While these correlations are spread over the size $$p = max(a, b, c, \ldots )$$ of the generator itself, they can evidently still lead to significant errors.". This only refers to the standard LFG where each new number in the sequence depends on two previous numbers. A three-tap LFG has been shown to eliminate some statistical problems such as failing the Birthday Spacings and Generalized Triple tests.

Usage

 * Freeciv uses a lagged Fibonacci generator with {j = 24, k = 55} for its random number generator.
 * The Boost library includes an implementation of a lagged Fibonacci generator.
 * Subtract with carry, a lagged Fibonacci generator engine, is included in the C++11 library.
 * The Oracle Database implements this generator in its DBMS_RANDOM package (available in Oracle 8 and newer versions).

title: Lagged Fibonacci generator


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Psychopharmacology

Psychopharmacology (from Greek ψῡχή; φάρμακον; and -λογία) is the scientific study of the effects drugs have on mood, sensation, thinking, behavior, judgment and evaluation, and memory. It is distinguished from neuropsychopharmacology, which emphasizes the correlation between drug-induced changes in the functioning of cells in the nervous system and changes in consciousness and behavior.

The field of psychopharmacology studies a wide range of substances with various types of psychoactive properties, focusing primarily on the chemical interactions with the brain. The term "psychopharmacology" was likely first coined by David Macht in 1920. Psychoactive drugs interact with particular target sites or receptors found in the nervous system to induce widespread changes in physiological or psychological functions. The specific interaction between drugs and their receptors is referred to as "drug action", and the widespread changes in physiological or psychological function is referred to as "drug effect". These drugs may originate from natural sources such as plants and animals, or from artificial sources such as chemical synthesis in the laboratory.

Early psychopharmacology
Not often mentioned or included in the field of psychopharmacology today are psychoactive substances not identified as useful in modern mental health settings or references. These substances are naturally occurring, but nonetheless psychoactive, and are compounds identified through the work of ethnobotanists and ethnomycologists (and others who study the native use of naturally occurring psychoactive drugs). However, although these substances have been used throughout history by various cultures, and have a profound effect on mentality and brain function, they have not always attained the degree of scrutinous evaluation that lab-made compounds have. Nevertheless, some, such as psilocybin and mescaline, have provided a basis of study for the compounds that are used and examined in the field today. Hunter-gatherer societies tended to favor hallucinogens, and today their use can still be observed in many surviving tribal cultures. The exact drug used depends on what the particular ecosystem a given tribe lives in can support, and are typically found growing wild. Such drugs include various psychoactive mushrooms containing psilocybin or muscimol and cacti containing mescaline and other chemicals, along with myriad other plants containing psychoactive chemicals. These societies generally attach spiritual significance to such drug use, and often incorporate it into their religious practices. With the dawn of the Neolithic and the proliferation of agriculture, new psychoactives came into use as a natural by-product of farming. Among them were opium, cannabis, and alcohol derived from the fermentation of cereals and fruits. Most societies began developing herblores, lists of herbs which were good for treating various physical and mental ailments. For example, St. John's wort was traditionally prescribed in parts of Europe for depression (in addition to use as a general-purpose tea), and Chinese medicine developed elaborate lists of herbs and preparations. These and various other substances that have an effect on the brain are still used as remedies in many cultures.

Modern psychopharmacology
The dawn of contemporary psychopharmacology marked the beginning of the use of psychiatric drugs to treat psychological illnesses. It brought with it the use of opiates and barbiturates for the management of acute behavioral issues in patients. In the early stages, psychopharmacology was primarily used for sedation. With the 1950s came the establishment of lithium for mania, chlorpromazine for psychoses, and then in rapid succession, the development of tricyclic antidepressants, monoamine oxidase inhibitors, and benzodiazepines, among other antipsychotics and antidepressants. A defining feature of this era includes an evolution of research methods, with the establishment of placebo-controlled, double-blind studies, and the development of methods for analyzing blood levels with respect to clinical outcome and increased sophistication in clinical trials. The early 1960s revealed a revolutionary model by Julius Axelrod describing nerve signals and synaptic transmission, which was followed by a drastic increase of biochemical brain research into the effects of psychotropic agents on brain chemistry. After the 1960s, the field of psychiatry shifted to incorporate the indications for and efficacy of pharmacological treatments, and began to focus on the use and toxicities of these medications. The 1970s and 1980s were further marked by a better understanding of the synaptic aspects of the action mechanisms of drugs. However, the model has its critics, too – notably Joanna Moncrieff and the Critical Psychiatry Network.

Neurotransmitters
Psychoactive drugs exert their sensory and behavioral effects almost entirely by acting on neurotransmitters and by modifying one or more aspects of synaptic transmission. Neurotransmitters can be viewed as chemicals through which neurons primarily communicate; psychoactive drugs affect the mind by altering this communication. Drugs may act by 1) serving as a precursor to a neurotransmitter; 2) inhibiting neurotransmitter synthesis; 3) preventing storage of neurotransmitters in the presynaptic vesicle; 4) stimulating or inhibiting neurotransmitter release; 5) stimulating or blocking post-synaptic receptors; 6) stimulating autoreceptors, inhibiting neurotransmitter release; 7) blocking autoreceptors, increasing neurotransmitter release; 8) inhibiting neurotransmission breakdown; or 9) blocking neurotransmitter reuptake by the presynaptic neuron.

Hormones
The other central method through which drugs act is by affecting communications between cells through hormones. Neurotransmitters can usually only travel a microscopic distance before reaching their target at the other side of the synaptic cleft, while hormones can travel long distances before reaching target cells anywhere in the body. Thus, the endocrine system is a critical focus of psychopharmacology because 1) drugs can alter the secretion of many hormones; 2) hormones may alter the behavioral responses to drugs; 3) hormones themselves sometimes have psychoactive properties; and 4) the secretion of some hormones, especially those dependent on the pituitary gland, is controlled by neurotransmitter systems in the brain.

Alcohol
Alcohol is a depressant, the effects of which may vary according to dosage amount, frequency, and chronicity. As a member of the sedative-hypnotic class, at the lowest doses, the individual feels relaxed and less anxious. In quiet settings, the user may feel drowsy, but in settings with increased sensory stimulation, individuals may feel uninhibited and more confident. High doses of alcohol rapidly consumed may produce amnesia for the events that occur during intoxication. Other effects include reduced coordination, which leads to slurred speech, impaired fine-motor skills, and delayed reaction time. The effects of alcohol on the body's neurochemistry are more difficult to examine than some other drugs. This is because the chemical nature of the substance makes it easy to penetrate into the brain, and it also influences the phospholipid bilayer of neurons. This allows alcohol to have a widespread impact on many normal cell functions and modifies the actions of several neurotransmitter systems. Alcohol inhibits glutamate (a major excitatory neurotransmitter in the nervous system) neurotransmission by reducing the effectiveness at the NMDA receptor, which is related to memory loss associated with intoxication. It also modulates the function of GABA, a major inhibitory amino acid neurotransmitter. Abuse of alcohol has also been correlated with thiamine deficiencies within the brain, leading to lasting neurological conditions that affect primarily the ability of the brain to effectively store memories. One such neurological condition is called Korsakoff's syndrome, for which very few effective treatment modalities have been found. The reinforcing qualities of alcohol leading to repeated use – and thus also the mechanisms of withdrawal from chronic alcohol use – are partially due to the substance's action on the dopamine system. This is also due to alcohol's effect on the opioid systems, or endorphins, that have opiate-like effects, such as modulating pain, mood, feeding, reinforcement, and response to stress.

Antidepressants
Antidepressants reduce symptoms of mood disorders primarily through the regulation of norepinephrine and serotonin (particularly the 5-HT receptors). After chronic use, neurons adapt to the change in biochemistry, resulting in a change in pre- and postsynaptic receptor density and second messenger function. The Monoamine Theory of Depression and Anxiety, which states that the disruption of the activity of nitrogen containing neurotransmitters (i.e. serotonin, norepinephrine, and dopamine) is strongly correlated with the presence of depressive symptoms. Despite its longstanding prominence in pharmaceutical advertising, the myth that low serotonin levels cause depression is not supported by scientific evidence.

Monoamine oxidase inhibitors (MAOIs) are the oldest class of antidepressants. They inhibit monoamine oxidase, the enzyme that metabolizes the monoamine neurotransmitters in the presynaptic terminals that are not contained in protective synaptic vesicles. The inhibition of the enzyme increases the amount of neurotransmitter available for release. It increases norepinephrine, dopamine, and 5-HT, thus increasing the action of the transmitters at their receptors. MAOIs have been somewhat disfavored because of their reputation for more serious side effects.

Tricyclic antidepressants (TCAs) work through binding to the presynaptic transporter proteins and blocking the reuptake of norepinephrine or 5-HT into the presynaptic terminal, prolonging the duration of transmitter action at the synapse.

Selective serotonin reuptake inhibitors (SSRIs) selectively block the reuptake of serotonin (5-HT) through their inhibiting effects on the sodium/potassium ATP-dependent serotonin transporter in presynaptic neurons. This increases the availability of 5-HT in the synaptic cleft. The main parameters to consider in choosing an antidepressant are side effects and safety. Most SSRIs are available generically and are relatively inexpensive. Older antidepressants such as TCAs and MAOIs usually require more visits and monitoring, which may offset the low expense of the drugs. SSRIs are relatively safe in overdoses and better tolerated than TCAs and MAOIs for most patients.

Antipsychotics
All proven antipsychotics are postsynaptic dopamine receptor blockers (dopamine antagonists). For an antipsychotic to be effective, it generally requires a dopamine antagonism of 60%–80% of dopamine D2 receptors.

First generation (typical) antipsychotics: Traditional neuroleptics modify several neurotransmitter systems, but their clinical effectiveness is most likely due to their ability to antagonize dopamine transmission by competitively blocking the receptors or by inhibiting dopamine release. The most serious and troublesome side effects of these classical antipsychotics are movement disorders that resemble the symptoms of Parkinson's disease, because the neuroleptics antagonize dopamine receptors broadly, also reducing the normal dopamine-mediated inhibition of cholinergic cells in the striatum.

Second-generation (atypical) antipsychotics: The concept of "atypicality" is from the finding that second generation antipsychotics (SGAs) have a greater serotonin/dopamine ratio than earlier drugs, and might be associated with improved efficacy (particularly for the negative symptoms of psychosis) and reduced extrapyramidal side effects. Some of the efficacy of atypical antipsychotics may be due to 5-HT2 antagonism or the blockade of other dopamine receptors. Agents that purely block 5-HT2 or dopamine receptors other than D2 have often failed as effective antipsychotics.

Benzodiazepines
Benzodiazepines are often used to reduce anxiety symptoms, muscle tension, seizure disorders, insomnia, symptoms of alcohol withdrawal, and panic attack symptoms. Their action is primarily on specific benzodiazepine sites on the GABAA receptor. This receptor complex is thought to mediate the anxiolytic, sedative, and anticonvulsant actions of the benzodiazepines. Use of benzodiazepines carries the risk of tolerance (necessitating increased dosage), dependence, and abuse. Taking these drugs for a long period of time can lead to severe withdrawal symptoms upon abrupt discontinuation.

Classical serotonergic psychedelics
Psychedelics cause perceptual and cognitive distortions without delirium. The state of intoxication is often called a "trip". Onset is the first stage after an individual ingests (LSD, psilocybin, ayahuasca, and mescaline) or smokes (dimethyltryptamine) the substance. This stage may consist of visual effects, with an intensification of colors and the appearance of geometric patterns that can be seen with one's eyes closed. This is followed by a plateau phase, where the subjective sense of time begins to slow and the visual effects increase in intensity. The user may experience synesthesia, a crossing-over of sensations (for example, one may "see" sounds and "hear" colors). These outward sensory effects have been referred to as the "mystical experience", and current research suggests that this state could be beneficial to the treatment of some mental illnesses, such as depression and possibly addiction. In instances where some patients have seen a lack of improvement from the use of antidepressants, serotonergic hallucinogens have been observed to be rather effective in treatment. In addition to the sensory-perceptual effects, hallucinogenic substances may induce feelings of depersonalization, emotional shifts to a euphoric or anxious/fearful state, and a disruption of logical thought. Hallucinogens are classified chemically as either indolamines (specifically tryptamines), sharing a common structure with serotonin, or as phenethylamines, which share a common structure with norepinephrine. Both classes of these drugs are agonists at the 5-HT2 receptors; this is thought to be the central component of their hallucinogenic properties. Activation of 5-HT2A may be particularly important for hallucinogenic activity. However, repeated exposure to hallucinogens leads to rapid tolerance, likely through down-regulation of these receptors in specific target cells. Research suggests that hallucinogens affect many of these receptor sites around the brain and that through these interactions, hallucinogenic substances may be capable of inducing positive introspective experiences. The current research implies that many of the effects that can be observed occur in the occipital lobe and the frontomedial cortex; however, they also present many secondary global effects in the brain that have not yet been connected to the substance's biochemical mechanism of action.

Dissociative hallucinogens
Another class of hallucinogens, known as dissociatives, includes drugs such as ketamine, phencyclidine (PCP), and Salvia divinorum. Drugs such as these are thought to interact predominantly with glutamate receptors within the brain. Specifically, ketamine is thought to block NMDA receptors that are responsible for signalling in the glutamate pathways. Ketamine's more tranquilizing effects can be seen in the central nervous system through interactions with parts of the thalamus by inhibition of certain functions. Ketamine has become a major drug of research for the treatment of depression. These antidepressant effects are thought to be related to the drug's action on the glutamate receptor system and the relative spike in glutamate levels, as well as its interaction with mTOR, which is an enzymatic protein involved in catabolic processes in the human body. Phencyclidine's biochemical properties are still mostly unknown; however, its use has been associated with dissociation, hallucinations, and in some cases seizures and death. Salvia divinorum, a plant native to Mexico, has strong dissociative and hallucinogenic properties when the dry leaves are smoked or chewed. The qualitative value of these effects, whether negative or positive, has been observed to vary between individuals with many other factors to consider.

Hypnotics
Hypnotics are often used to treat the symptoms of insomnia or other sleep disorders. Benzodiazepines are still among the most widely prescribed sedative-hypnotics in the United States today. Certain non-benzodiazepine drugs are used as hypnotics as well. Although they lack the chemical structure of the benzodiazepines, their sedative effect is similarly through action on the GABAA receptor. They also have a reputation of being less addictive than benzodiazepines. Melatonin, a naturally-occurring hormone, is often used over the counter (OTC) to treat insomnia and jet lag. This hormone appears to be excreted by the pineal gland early during the sleep cycle and may contribute to human circadian rhythms. Because OTC melatonin supplements are not subject to careful and consistent manufacturing, more specific melatonin agonists are sometimes preferred. They are used for their action on melatonin receptors in the suprachiasmatic nucleus, responsible for sleep-wake cycles. Many barbiturates have or had an FDA-approved indication for use as sedative-hypnotics, but have become less widely used because of their limited safety margin in overdose, their potential for dependence, and the degree of central nervous system depression they induce. The amino-acid L-tryptophan is also available OTC, and seems to be free of dependence or abuse liability. However, it is not as powerful as the traditional hypnotics. Because of the possible role of serotonin in sleep patterns, a new generation of 5-HT2 antagonists are in current development as hypnotics.

Cannabis and the cannabinoids
Cannabis consumption produces a dose-dependent state of intoxication in humans. There is commonly increased blood flow to the skin, which leads to an increased heart rate and sensations of warmth or flushing. It also frequently induces increased hunger. Iversen (2000) categorized the subjective and behavioral effects often associated with cannabis into three stages. The first is the "buzz", a brief period of initial responding where the main effects are lightheadedness or slight dizziness, in addition to possible tingling sensations in the extremities or other parts of the body. The "high" is characterized by feelings of euphoria and exhilaration characterized by mild psychedelia as well as a sense of disinhibition. If the individual has taken a sufficiently large dose of cannabis, the level of intoxication progresses to the stage of being "stoned", and the user may feel calm, relaxed, and possibly in a dreamlike state. Sensory reactions may include the feeling of floating, enhanced visual and auditory perception, visual illusions, or the perception of the slowing of time passage, which are somewhat psychedelic in nature.

There exist two primary CNS cannabinoid receptors, on which marijuana and the cannabinoids act. Both the CB1 and CB2 receptor are found in the brain. The CB2 receptor is also found in the immune system. CB1 is expressed at high densities in the basal ganglia, cerebellum, hippocampus, and cerebral cortex. Receptor activation can inhibit cAMP formation, inhibit voltage-sensitive calcium ion channels, and activate potassium ion channels. Many CB1 receptors are located on axon terminals, where they act to inhibit the release of various neurotransmitters. In combination, these chemical actions work to alter various functions of the central nervous system, including the motor system, memory, and various cognitive processes.

Opioids
The opioid category of drugs – including drugs such as heroin, morphine, and oxycodone – belong to the class of narcotic analgesics, which reduce pain without producing unconsciousness but do produce a sense of relaxation and sleep, and at high doses may result in coma and death. The ability of opioids (both endogenous and exogenous) to relieve pain depends on a complex set of neuronal pathways at the spinal cord level, as well as various locations above the spinal cord. Small endorphin neurons in the spinal cord act on receptors to decrease the conduction of pain signals from the spinal cord to higher brain centers. Descending neurons originating in the periaqueductal gray give rise to two pathways that further block pain signals in the spinal cord. The pathways begin in the locus coeruleus (noradrenaline) and the nucleus of raphe (serotonin). Similar to other abused substances, opioid drugs increase dopamine release in the nucleus accumbens. Opioids are more likely to produce physical dependence than any other class of psychoactive drugs, and can lead to painful withdrawal symptoms if discontinued abruptly after regular use.

Stimulants
Cocaine is one of the more common stimulants and is a complex drug that interacts with various neurotransmitter systems. It commonly causes heightened alertness, increased confidence, feelings of exhilaration, reduced fatigue, and a generalized sense of well-being. The effects of cocaine are similar to those of amphetamines, though cocaine tends to have a shorter duration of effect. In high doses or with prolonged use, cocaine can result in a number of negative effects, including irritability, anxiety, exhaustion, total insomnia, and even psychotic symptomatology. Most of the behavioral and physiological actions of cocaine can be explained by its ability to block the reuptake of the two catecholamines, dopamine and norepinephrine, as well as serotonin. Cocaine binds to transporters that normally clear these transmitters from the synaptic cleft, inhibiting their function. This leads to increased levels of neurotransmitter in the cleft and transmission at the synapses. Based on in-vitro studies using rat brain tissue, cocaine binds most strongly to the serotonin transporter, followed by the dopamine transporter, and then the norepinephrine transporter.

Amphetamines tend to cause the same behavioral and subjective effects of cocaine. Various forms of amphetamine are commonly used to treat the symptoms of attention deficit hyperactivity disorder (ADHD) and narcolepsy, or are used recreationally. Amphetamine and methamphetamine are indirect agonists of the catecholaminergic systems. They block catecholamine reuptake, in addition to releasing catecholamines from nerve terminals. There is evidence that dopamine receptors play a central role in the behavioral responses of animals to cocaine, amphetamines, and other psychostimulant drugs. One action causes the dopamine molecules to be released from inside the vesicles into the cytoplasm of the nerve terminal, which are then transported outside by the mesolimbic dopamine pathway to the nucleus accumbens. This plays a key role in the rewarding and reinforcing effects of cocaine and amphetamine in animals, and is the primary mechanism for amphetamine dependence.

Psychopharmacological research
In psychopharmacology, researchers are interested in any substance that crosses the blood–brain barrier and thus has an effect on behavior, mood, or cognition. Drugs are researched for their physiochemical properties, physical side effects, and psychological side effects. Researchers in psychopharmacology study a variety of different psychoactive substances, including alcohol, cannabinoids, club drugs, psychedelics, opiates, nicotine, caffeine, psychomotor stimulants, inhalants, and anabolic–androgenic steroids. They also study drugs used in the treatment of affective and anxiety disorders, as well as schizophrenia.

Clinical studies are often very specific, typically beginning with animal testing and ending with human testing. In the human testing phase, there is often a group of subjects: one group is given a placebo, and the other is administered a carefully measured therapeutic dose of the drug in question. After all of the testing is completed, the drug is proposed to the concerned regulatory authority (e.g. the U.S. FDA), and is either commercially introduced to the public via prescription, or deemed safe enough for over-the-counter sale.

Though particular drugs are prescribed for specific symptoms or syndromes, they are usually not specific to the treatment of any single mental disorder.

A somewhat controversial application of psychopharmacology is "cosmetic psychiatry": persons who do not meet criteria for any psychiatric disorder are nevertheless prescribed psychotropic medication. The antidepressant bupropion is then prescribed to increase perceived energy levels and assertiveness while diminishing the need for sleep. The antihypertensive compound propranolol is sometimes chosen to eliminate the discomfort of day-to-day anxiety. Fluoxetine in nondepressed people can produce a feeling of generalized well-being. Pramipexole, a treatment for restless leg syndrome, can dramatically increase libido in women. These and other off-label lifestyle applications of medications are not uncommon. Although occasionally reported in the medical literature, no guidelines for such usage have been developed. There is also a potential for the misuse of prescription psychoactive drugs by elderly persons, who may have multiple drug prescriptions.

Peer-reviewed journals

 * Experimental and Clinical Psychopharmacology, American Psychological Association
 * Journal of Clinical Psychopharmacology, Lippincott Williams & Wilkins
 * Journal of Psychopharmacology, British Association for Psychopharmacology, SAGE Publications
 * Psychopharmacology, Springer Berlin/Heidelberg

title: Psychopharmacology