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Dornford Yates

Cecil William Mercer (7 August 1885 – 5 March 1960), known by his pen name Dornford Yates, was an English writer and novelist whose novels and short stories, some humorous (the Berry books), some thrillers (the Chandos books), were best-sellers during the Interwar Period.

The pen name Dornford Yates, first in print in 1910, resulted from combining the maiden names of his grandmothers – the paternal Eliza Mary Dornford, and the maternal Harriet Yates.

Early life
William (Bill) Mercer was born in Walmer, Kent, the son of Cecil John Mercer (1850–1921) and Helen Wall (1858–1918). His father was a solicitor whose sister, Mary Frances, married Charles Augustus Munro; their son was Hector Hugh Munro (the writer Saki); Bill Mercer is said to have idolised his elder cousin.

Mercer attended St Clare preparatory school in Walmer from 1894 to 1899. The family moved from Kent to London when he joined Harrow School as a day pupil in 1899, his father selling his solicitor's practice in Kent and setting up office in Carey Street. Leaving Harrow in 1903, he attended University College, Oxford in 1904, where he achieved a Third in Law.

At university, he was active in the Oxford University Dramatic Society (OUDS), becoming secretary in 1906 and president in 1907, his final year. He acted in the 1905 production of Aristophanes’ The Clouds, of which the Times reviewer said: "Among individual actors the best was Mr. C. W. Mercer, whose 'Strepsiades' was full of fun, and who possesses real comic talent." After a small part in the 1906 production of Measure for Measure, in his final year, he appeared as 'Demetrius' in A Midsummer Night's Dream, and as 'Pedant' in The Taming of the Shrew, a production which included the professional actresses Lily Brayton as 'Katherine', and her sister Agnes as 'Bianca'.

Among the many useful friends Mercer made in the OUDS were Gervais Rentoul, who asked him to be his best man, and Lily Brayton's husband, actor Oscar Asche, later producer of the play Kismet, and writer of Chu Chin Chow. After university, Mercer took a caravanning holiday in Hampshire, with Asche, Lily, Agnes, and another theatrical couple, Matheson Lang and his wife, Hutin Britton; both Asche and Lang recall that holiday in their memoirs.

Mercer's third-class Oxford law degree was insufficient to gain him traditional access to the bar. However, in 1908 his father obtained his son a post as pupil to a prominent barrister, H. G. Muskett, whose practice often required his appearing in court on behalf of the police commissioner. As Muskett's pupil, Mercer saw much of the seedy side of London life, some of which is evident in his novels.

In 1909, he was called to the Bar where he worked for several years. In his first memoirs, As Berry & I Were Saying, he recalls his involvement in the trial of the poisoner Hawley Harvey Crippen, when he returned from acting with the Old Stagers, at Canterbury, to have first look at the legal brief. Mercer is in a photograph of the Bow Street Court committal proceedings, published in the Daily Mirror of 30 August 1910.

In his spare time, he wrote short stories that were published in Punch, The Harmsworth RED Magazine, Pearson's Magazine, and the Windsor Magazine, maintaining a relationship with this last until the end of the 1930s; after it closed he wrote for the Strand Magazine. He also assisted in the writing of What I Know (Mills & Boon, 1913) - US title King Edward As I Knew Him - the memoirs of C. W. Stamper, who had been motor engineer to King Edward VII.

The Great War and afterwards
At the outbreak of the Great War in 1914, Mercer was commissioned as Second Lieutenant in the 3rd County of London Yeomanry (Sharpshooters), although his stories continued to appear in the Windsor until March 1915. In 1915, his regiment left for Egypt and, in November 1915 as part of the 8th Mounted Brigade, he was sent to the Salonika/Macedonian front where the war was in stalemate. Suffering severe muscular rheumatism he was sent home in 1917 and, although he was still in uniform, the War Office did not again post him. He eventually left the army in 1919. In June of that year the Windsor carried his first story since the end of the war.

Since 1914, the Mercer family home had been Elm Tree Road, behind the north-west side of Lord's Cricket Ground in St John's Wood, where his friends Oscar and Lily Asche were close neighbours. In autumn of 1919, he and Asche combined to write the stage show Eastward Ho!, but the production was not a great success and he did not again attempt to write for the stage. A frequent social – and then romantic – Elm Tree Road visitor was Bettine (Athalia) Stokes Edwards, an American girl who danced in Chu Chin Chow (and daughter of Robert Ewing Edwards of Philadelphia, Pennsylvania) who became Mercer's first wife. The New York Times announcement of their engagement (28 August 1919) states: "Mr & Mrs Glover Fitzhugh Perin of 57 West Fifty-eight street have announced the engagement of Mrs Perin’s oldest daughter Miss Bettine Stokes Edwards. . . ." suggesting that her father either was dead or divorced; her remarried mother then lived in New York City. Mercer and Bettine married at St James's, Spanish Place, in the Marylebone district of London, on 22 October 1919. The month of October also marked the appearance of a story in the Windsor called Valerie whose female lead made a living as a dancer; this story never appeared in book form.

Mercer decided not to return to the bar, and to concentrate on his writing. He and Bettine lived in Elm Tree Road, where their only child, Richard, was born on 20 July 1920. After the Great War, many ex-officers found that the rise in the cost of living in London precluded maintaining the style of life of a gentleman to which they had become accustomed; some looked beyond England. In 1922, the Mercers emigrated to France, where it was possible to live more cheaply, and where the climate was kinder to Mercer's muscular rheumatism.

French residence
They chose the resort town Pau, in the western Pyrenees, in the Basses–Pyrénées département (now Pyrénées-Atlantiques) – where lived a sizeable British expat colony, but when the Mercers moved in is unknown. In Dornford Yates – A Biography (1982), A.J. Smithers reports "exactly how he hit upon the place is not clear", but Pau figures several times in the memoirs he is presumed to have ghost-written for C.W. Stamper, and so that might be the answer – "anywhere good enough for King Edward VII was good enough for him".

They rented the Villa Maryland, on Rue Forster, where Mercer proved an exacting husband, while Bettine was a social woman, and by 1929, the failure of their marriage was evident. Bettine had been indiscreet in her extra-marital romantic liaisons, and Mercer sued for divorce. Bettine did not defend, and the divorce was made absolute in September 1933. In the event, she returned to her family in the U.S.

Less than a year later, on 10 February 1934, at Chertsey Register office, Mercer married Doreen Elizabeth Lucie Bowie, whom he met on a cruise in 1932. She was the daughter of London solicitor David Mather Bowie of Virginia Water. Elizabeth was twenty years younger than her new husband, who felt he had met the incarnation of his fictional "Jill Mansel", thus did he call her "Jill" for the rest of his life. For him, Villa Maryland had many memories of Bettine, so he and Elizabeth decided to build a new house, named "Cockade". They chose a spot twenty-seven miles south of Pau, a little north-west of Eaux-Bonnes, on the road to the hamlet of Aas; the project is related in The House That Berry Built, wherein the name of the house is "Gracedieu" (God's Grace). They did not enjoy long residence in Cockade.

With France falling to the Wehrmacht in June 1940, the Mercers hurriedly arranged caretakers for Cockade, and then escaped the country – in company of visiting friends, Matheson Lang and wife – and traversed Spain en route to Portugal. They subsequently took ship for South Africa, arriving in Salisbury, Southern Rhodesia, in 1941.

The Second World War and the Rhodesian years
C.W. Mercer was re-commissioned, this time in the Royal Rhodesian Regiment, and attained the rank of major. As the war concluded, the couple realised their plan of returning to Cockade – but were disappointed in the decrepitude of the house and the socially conscious, post-war attitude of their one-time servants. After some months, the Mercers obtained exit visas and returned to Umtali, Southern Rhodesia, (now Mutare, Zimbabwe), where they lived for the rest of his life. Mercer supervised the building of a replacement house for Cockade, another hillside venture, and, in 1948, they moved into "Sacradown", on Oak Avenue. The furniture in France was shipped to Rhodesia, as were the Waterloo Bridge balusters (see The House that Berry Built), which had never reached Cockade, but had been stored in England during the Second World War.

Cecil William Mercer died in March 1960.

Writings
Mercer originally wrote short stories for the monthly magazines. His first known published work, Temporary Insanity, appeared in Punch in May 1910 – this is the first known occasion of his use of his pen name – and his second, Like A Tale That is Told appeared in the Red Magazine in July 1910. The first known 'Berry' story to be published, Babes in the Wood, appeared in Pearson's Magazine in September 1910. None of these early stories was ever included in his books. Many of his works began as stories in The Windsor Magazine, before being collected in book form by the Windsor 's publishers, Ward Lock. Between September 1911 and September 1939 he had 123 stories published in the Windsor, and after it closed, the Strand Magazine carried three of his stories in 1940 and 1941. Four of his novels were serialised in Woman's Journal between 1933 and 1938. In the United States four of his novels were serialized in Woman's Home Companion between 1933 and 1939, while others appeared in The Saturday Evening Post and Blue Book.

His first story for The Windsor Magazine was "Busy Bees", in September 1911, and this and fourteen subsequent stories from that publication up to the July 1914 issue were republished in book form as The Brother of Daphne, in 1914. Some of the stories were edited for the book, to eliminate events, such as marriage, for the leading characters – which suggests that, originally, he had not planned on using the same characters for a story series. The narrator – later identified as "Boy Pleydell" – marries in "Babes in the Wood" and possibly in "Busy Bees", which became chapter VIII "The Busy Beers" in The Brother of Daphne, with the end of the story altered to remove the hint of marriage.

His second book, The Courts of Idleness, was published in 1920, containing material written before, during, and after the Great War. It was divided into three sections. In Book I Yates introduced a new set of characters similar to, but separate from, Berry & Co, in four stories that had appeared in the Windsor between December 1914 and March 1915, and a final story from the Windsor of June 1919 in which the male characters have their story lines resolved in Salonika, during the Great War. The Interlude has a story entitled "And The Other Left", from the November 1914 Windsor, which is set on the Western Front with a unique set of characters. Book II returns to the 'Berry' characters, with two pre-war stories from the August and September 1914 Windsor, and three post-war stories from the issues of July, August and September 1919. The book's final story, "Nemesis", was written for, but rejected by, Punch; subsequently, it appeared in the Windsor in November 1919, with the main character named "Jeremy"; for the book he became "Berry". "Nemesis" was written to the Punch length, and so is much shorter than most of the other stories in The Courts of Idleness.

The Berry books are semi-autobiographical, humorous romances, often in short story form, and, in particular, feature Bertram "Berry" Pleydell ("of White Ladies, in the County of Hampshire") and his family – his wife and cousin, Daphne, her brother, Boy Pleydell (the narrator), and their cousins Jonathan "Jonah" Mansel, and his sister, Jill. Collectively, they are "Berry & Co." Although all five appear in "Babes in the Wood", their precise relationships there are unstated, and Berry and Daphne are referred to as second cousins as late as Jonah & Co; later stories feature a simple family tree, showing them to be first cousins descended from two brothers and a sister.

"Berry & Co." capture the English upper classes of the Edwardian era, still self-assured, but affected by changing social attitudes and the decline of their fortunes. As in many of Yates' books, grand houses, powerful motor cars, and foreign travel feature prominently in the 'Berry' stories. In the 1950s, C.W. Mercer wrote two books of fictionalized memoirs, As Berry and I Were Saying and B-Berry and I Look Back, written as conversations between Berry and his family. They contain many anecdotes about his experiences as a lawyer, but are, in the main, an elegy for a past upper-class way of life.

The 'Chandos' books, starting with Blind Corner, in 1927, marked a change in style and content, being thrillers set mainly in Continental Europe (often in Carinthia, Austria), wherein the hero–narrator, Richard Chandos, and colleagues, including George Hanbury and Jonathan Mansel (who also featured in the 'Berry' books), tackle criminals, protect the innocent, woo beautiful ladies, and hunt for treasure. These were originally published by Hodder and Stoughton although later they were re-issued by Ward Lock. It is the 'Chandos' novels to which Alan Bennett especially refers in naming Dornford Yates in the play Forty Years On (1972): "Sapper, Buchan, Dornford Yates, practitioners in that school of Snobbery with Violence that runs like a thread of good-class tweed through twentieth-century literature." Yates also wrote other thrillers in the same style, but with different characters.

Besides these two genres, some of Yates' novels do not easily fall into either the humorous or the thriller category.

Anthony Lyveden was Dornford Yates's first novel, telling the story of an impoverished ex-officer. Originally, it was published in monthly instalments in The Windsor Magazine,

Valerie French, the sequel to Anthony Lyveden features mostly the same cast. At the start of the book Lyveden is suffering amnesia, and cannot recall the events of the previous book, leading to romantic complications.

The Stolen March is a fantasy set in a lost realm, between Spain and France, where travellers encounter characters from nursery rhymes and fairy tales. A planned sequel, The Tempered Wind, is referred to in the quasi-autobiography, B-Berry and I Look Back, where Yates mentions abandoning the book as it failed to "take charge".

This Publican features a scheming woman and her hen-pecked husband. Some critics have suggested that the portrayal of the villainess represented a thinly-veiled attack on Mercer's first wife, although that could imply that the husband was a self-portrait, and as Smithers' states, "...he would hardly have held himself out in a character so feeble and flaccid."

Lower than Vermin is a novel in which the author defends his views on social class, and criticises the path Britain was following under the post-war Labour government; the title derives from a description of members of the Conservative Party given in a 1948 speech by Labour Party MP and government minister Aneurin Bevan.

Ne'er-Do-Well is a murder story narrated by Richard Chandos, with whom the investigating detective is staying.

Wife Apparent was Yates's last novel, set in 1956.

Stage, cinema, and other media
The 1919 musical play Eastward Ho! was written by Oscar Asche (author) with lyrics by Dornford Yates and music by Grace Torrens and John Ansell. It was produced by Edward Laurillard and George Grossmith Jr., and opened at the Alhambra Theatre in London on 9 September and ran for 124 performances.

The BBC produced an adaptation of She Fell Among Thieves in 1977, featuring Malcolm McDowell as Chandos, Michael Jayston as Mansel, and Eileen Atkins as Vanity Fair. This adaptation was also used as the first episode of the US TV series Mystery! in 1980.

An episode of the ITV Hannay series, "A Point of Honour", was based on the eponymous short story published in The Brother of Daphne, but the source was uncredited. An audiobook edition of Blind Corner, read by Alan Rickman, was produced by Chivers Audio Books.

Related works
In 1948 Richard Usborne wrote an article entitled Ladies and Gentlemen v. Cads and Rotters about the works of Dornford Yates in Volume 3, Number 11 of The Windmill, a literary magazine. Yates was not pleased by the article, but nevertheless Usborne went on to write Clubland Heroes (1953; reprinted 1974 and 1983) in which he examined the work of Yates and two contemporary thriller writers, John Buchan and Sapper.

The 1973 novel Indecent Exposure by Tom Sharpe plays up the 'Englishman' that Dornford Yates created in his novels. There is a group of characters in the satirical novel who style themselves as the 'Dornford Yates' club and who try to emulate the 'Master' in avoiding reality and a changing world. Sharpe was later hired by the BBC to adapt She Fell Among Thieves for television, and used the same satirical approach.

In 1983 Sharpe wrote an introduction to a reprint of Yates' first Chandos thriller Blind Corner, one of a series issued by J.M.Dent & Sons under the title Classic Thrillers. Further Yates' books in the series were Perishable Goods, with an introduction by Richard Usborne; Blood Royal, with an introduction by A.J.Smithers; Fire Below; She Fell Among Thieves, with an introduction by Ion Trewin; Gale Warning; Cost Price; Red in the Morning; An Eye For a Tooth; and The Best of Berry, with an introduction by Jack Adrian.

Following the publication of Dornford Yates - A Biography in 1982, Smithers went on to write Combined Forces in 1983, subtitled "Being the Latter-Day adventures of Maj-Gen Sir Richard Hannay, Captain Hugh 'Bulldog' Drummond and Berry and Co", which has the heroes (and some villains) of Buchan, Sapper and Yates meeting up after World War Two and having further adventures together.

In 2015, Kate Macdonald published Novelists Against Social Change: Conservative Popular Fiction, 1920–1960, which examines the work of Buchan, Yates and Angela Thirkell.

title: Dornford Yates


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Frederick Herzberg

Frederick Irving Herzberg (April 18, 1923 – January 19, 2000 ) was an American psychologist who became one of the most influential names in business management. He is most famous for introducing job enrichment and the Motivator-Hygiene theory. His 1968 publication "One More Time, How Do You Motivate Employees?" had sold 1.2 million reprints by 1987 and was the most requested article from the Harvard Business Review.

Personal life
Herzberg was born in 1923 in Lynn, Massachusetts, to Gertrude and Lewis Herzberg, who were Jewish Lithuanian immigrants. He was brought up in New York City, and enrolled at the City College of New York in 1939. He did not finish his studies as he enlisted in the army. In 1944 he married Shirley Bedell, who later became a pediatrician.

During his military service Herzberg was involved in the relocation of internees from the Dachau Concentration Camp. His experience with this work, where he "realized that a society goes insane when the sane are driven insane", has been seen as central to the development of his working philosophy.

He finally finished his studies and graduated from the City College of New York in 1946. He then decided to move to the University of Pittsburgh where he earned a master's degree in science and public health. He completed a Ph.D. at Pittsburgh focused on electric shock therapy.

Research
Herzberg started his research on organizations in the 1950s. He worked at the University of Utah, where he remained until he retired. Prior to his move to Utah, Herzberg was professor of management at Case Western Reserve University, where he established the Department of Industrial Mental Health.

In his lifetime, Herzberg had consulted for many organizations as well as for the United States and other foreign governments. He has a son, Mark, who currently lives in West New York.

Herzberg's papers, coverning his work from the 1950s to the 1990s, are held in the special collections archive at the University of Utah. The bulk of the material in the collection dates from the 1970s and 1980s.

Motivator-Hygiene Theory
Herzberg proposed the motivator-hygiene theory, also known as the two-factor theory of job satisfaction. According to his theory, people are influenced by two sets of factors.

The idea is that hygiene factors will not motivate, but if they are not there, they can lower motivation. These factors could be anything from clean toilets and comfortable chairs, to a reasonable level of pay and job security. The theory deals with satisfaction and dissatisfaction in jobs which are not affected by the same set of needs, but instead occur independently of each other. Herzberg's theory challenged the assumption that "dissatisfaction was a result of an absence of factors giving rise to satisfaction".

Motivational factors will not necessarily lower motivation, but can be responsible for increasing motivation. These factors could involve job recognition, potential for promotion or even the work in itself.

Herzberg (1987) describes the growth factors (or motivators) as "achievement, recognition for achievement, the work itself, responsibility, and growth or advancement", which are intrinsic. Intrinsic factors include "orientations toward money, recognition, competition, and the dictates of other people, and the latter includes challenge, enjoyment, personal enrichment, interest, and self-determination". The hygiene factors (or dissatisfaction-avoidance), which are extrinsic to the job, are "company policy and administration, supervision, interpersonal relationships, working conditions, salary, status, and security". This extrinsic factor "refers to doing something because it leads to a distinct outcome, something external you expect to receive, and the latter refers to doing something because it is inherently interesting or enjoyable, an internal reward."

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

title: Frederick Herzberg


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High-level equilibrium trap

The high-level equilibrium trap is a concept developed by environmental historian Mark Elvin to explain why China never underwent an indigenous Industrial Revolution despite its wealth, stability, and high level of scientific achievement. Essentially, he claims that the Chinese pre-industrial economy had reached an equilibrium point where supply and demand were well-balanced. Late imperial production methods and trade networks were so efficient and labor was so cheap that investment in capital to improve efficiency would not be profitable.

At the same time, an intellectual paradigm shift from Taoism to Confucianism among the intelligentsia moved the focus of academic inquiry from natural science and mathematics, which were conceived of under Taoism as investigations into the mystical nature of the universe, to studies of social philosophy and morality under Confucianism. According to Elvin, this produced an intellectual climate that was not conducive to technical innovation.

By comparison, the economy of Great Britain at the time of the Industrial Revolution was vastly smaller and less efficient than the late imperial Chinese economy. Labor was comparatively more expensive, and internal trade far less efficient than in China. This produced large imbalances in the forces of supply and demand, leading to economic problems which provided a large financial incentive for the creation of scientific and engineering advances designed to address them. At the same time, the Enlightenment had shifted the focus of academic inquiry towards natural sciences, providing the basis for many technical innovations.

Background
According to Elvin, Chinese knowledge of science, mathematics, and engineering in the 14th century was far more advanced than anywhere else in the world. He presents the case study of the spinning wheel, a device used to assist in the production of yarn from plant fibers which increased the efficiency of a worker by orders of magnitude. An automatic, water-powered spinning wheel for hemp fiber was described in Chinese scientific manuals by the early 14th century; comparable devices would not be invented in Europe until the 18th century.

Despite providing an enormous gain in worker productivity, the Chinese spinning wheel fell into disuse over the subsequent centuries and was completely unknown by the 17th century, whereas the mechanical automation of spinning in Europe in the 18th century (from manual spinning wheel precursors of the 13th century ultimately sourced from Asia Minor) led directly to a process of technical refinement and engineering improvements that resulted in the Industrial Revolution and widespread mechanization of production of goods beyond yarn.

Decline of the mechanical spinning wheel in China
Elvin says that cotton began replacing hemp as the main fiber crop shortly after the mechanical spinning wheel was invented. Cotton produced far higher fiber yields per unit of land than hemp, and was thus far more profitable, so it largely replaced hemp. As hemp fibers are much longer than cotton fibers, existing mechanical spinning wheels designed for hemp could not be used to spin cotton fibers without substantial mechanical modifications to the apparatus. Apparently, no such modifications were ever made. All spinning in China reverted to far less efficient hand-spinning, and the automatic spinning wheel was forgotten. Elvin proposes several factors whose confluence prevented any further technical development of the automatic spinning wheel.

Cheap labor
Elvin says that substantially all extant arable land in China was already under cultivation by the 17th century. Prior to that, food production was expanded by simply cultivating new areas rather than through technical improvements in production methods, which was possible only because of China's vast size. Once all arable land was under cultivation, the lack of technical progress meant that crop yields were relatively flat, whereas the population continued to grow. This led to a large labor surplus, which drove down wages substantially. He suggests that this abundance of cheap labor rendered the capital investment required for ongoing engineering research and improvements simply not cost-effective compared to hiring laborers to do the work by hand.

Further, the wealthy merchants who financed cotton production wielded effective political control over government officials. They had the trade laws written broadly in their favor in such a way as to prevent any significant accumulation of wealth by the independent peasant contractors who were actually doing the spinning, rendering it less likely that one of the spinners would be in a position to develop efficiency-improving technology.

Well-developed trade network
By the cotton period, Elvin says that China's trade network had reached an advanced and highly efficient state. As the Chinese economy was enormous, local shortages and crop failures were no longer a major problem as local shortages were quickly alleviated through internal trade with some other part of the vast economy. This removed much of the local economic pressure to increase production efficiency.

Shift from Taoism to Confucianism
Elvin says that the Chinese intelligentsia gradually abandoned Taoism in favor of Confucianism around the 14th century. Whereas the Taoist philosophical paradigm had promoted scientific and mathematical investigation as a kind of mystical exploration of the workings of the universe, the Confucian paradigm focused far more on social philosophy and morality, which prompted a general lack of further research in mathematics and natural sciences.

Decline of serfdom
During the period when hemp was the dominant fiber crop, many Chinese peasants still lived as serfs and worked under the direct control and supervision of an aristocratic manor lord. Elvin says that this direct supervision of their work by well-educated lords who had broad knowledge of the latest scientific and engineering principles may have contributed to the invention of the automatic spinning wheel as a means of improving their work efficiency. In the cotton-dominant period, however, the practice of serfdom had died out and much spinning was organized as a cottage industry; peasant spinners typically worked at home as independent contractors with no direct supervision. He suggests that their lack of access to education may have helped to prevent the development of technical improvements in the spinning process.

The high-level equilibrium trap
Elvin says that these factors in combination produced what he calls a "high-level equilibrium trap." He says that widespread technical progress results from some large disequilibrium between supply and demand in the economy, which prompts people to find creative new ways to address the difficulties produced by the change.

The late imperial Chinese economy had reached an equilibrium point. It had become stable, efficient, and well organized. The rapidly growing population but slowly growing amount of agricultural land largely prevented any significant capital surplus from developing, as almost all production was required for basic sustenance.

The growing population also provided a ready pool of cheap labor. The Chinese economy was enormous and well integrated. The dense and well-developed network of canals yielded a relatively large amount of profit to the upper classes and alleviated local supply shortages. Thus, there was no incentive for further technical refinement, and technical progress stagnated.

Contrast with Britain
By contrast, the British economy at the time of the Industrial Revolution was much smaller than China's. Local shortages could not be readily alleviated by internal trade; besides being far smaller than China, Britain lacked an efficient internal water-based trade network, which prompted the development of the steam engine and railroads. The early paucity of arable farmland in Britain encouraged technical refinements to improve crop yields at an early date, whereas the vast size of China permitted production to be increased simply by cultivating more land until late in the imperial period. Although overseas colonies provided cheap labor during the Industrial Revolution, local labor in Britain itself was more expensive than in China, providing the capitalist class an incentive to improve worker efficiency.

title: High-level equilibrium trap


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Leif Garrett

Leif Garrett (born Leif Per Nervik; November 8, 1961) is an American actor, singer, and television personality. He worked as a child actor, then in the 1970s became famous as a teen idol in music. He later received much publicity for his drug abuse and legal troubles.

Early life
Garrett was born in Hollywood, California, to Rik Nervik and actress Carolyn Stellar, and started his entertainment career at age five. His father was absent for most of his life. He graduated from high school aged 15.

Acting career
Garrett and his sister Dawn Lyn worked a variety of acting jobs. They co-starred in the horror movie Devil Times Five as juvenile mental patients who go on a murder spree at an isolated ski resort. Dawn and Leif also guest-starred in an episode of Gunsmoke as well as Wonder Woman.

Garrett's more notable performances include the breakthrough role of Jimmy Henderson in Bob & Carol & Ted & Alice (1969); the protagonist's son Mike Pusser from the Walking Tall movies (1973, 1975, 1977) and the recurring role of Zack Russell on the ABC TV series Family. He also played the role of Leonard Unger, the son of Felix Unger (Tony Randall), on the ABC series The Odd Couple, a part that had been previously played by Willie Aames.

In late 1975, Garrett appeared in the role of Endy Karras in a 12-week CBS drama series Three for the Road, with Alex Rocco as his father, Peter Karras, and Vincent Van Patten as his older brother, John Karras. Garrett's appearance in the program triggered a response from teenage girls and led to his first appearances in teenage magazines, such as Tiger Beat. Garrett also played alongside Lee Van Cleef in two Spaghetti Westerns shot mainly in Israel:  and God's Gun. He played the title role in the television film Peter Lundy and the Medicine Hat Stallion and also starred in the film Skateboard.

In the early 1980s, Garrett returned to acting, appearing in a small role as Bob Sheldon in the 1983 Francis Ford Coppola film The Outsiders. In 1985, he starred in Thunder Alley as the lead singer of a pop band that is torn apart by drugs, and in Shaker Run as a mechanic. Other notable Garrett movies from the decade include Delta Fever and the horror film Cheerleader Camp. He played a deranged murderer who was in love with his sister in Party Line.

Music career
In late 1976, Garrett signed a five-album recording contract with Atlantic Records. In early 1977, he released a single called "Come Back When You Grow Up", and recorded his first album, Leif Garrett. The album was released in July 1977, and his first four singles charted modestly on the US Billboard Hot 100. All of these hits were covers of late 1950s and early 1960s hits such as the Dion covers "Runaround Sue" and "The Wanderer". In mid-1978, he signed with Scotti Brothers Records and recorded his second album, Feel the Need. Its first single, "I Was Made for Dancin'", reached number 10 on the US Hot 100 and number 4 on the UK Singles Chart early in 1979. It became his greatest hit in the US and the UK.

Subsequent singles failed to crack the Top 20 in either country, but he continued to record, releasing the albums Same Goes For You (1979), Can't Explain (1980) and My Movie of You (1981) in quick succession. In May 1979, he hosted a TV special, Leif, with guest stars Brooke Shields, Marie Osmond, Bob Hope and Flip Wilson.

In 1981, Garrett recorded "I Am a Rebel", words and music expressly composed for him by Victorio Pezzolla and produced by Richard Finch of KC and the Sunshine Band which became the theme song for an Italian TV program entitled Il Barattolo. He mostly stopped recording music in the early 1980s and concentrated on acting for the rest of the decade. He later claimed the producers would not allow him to make music aimed at an adult audience when he reached his early twenties. In 1986, he provided lead vocals to the song "The Way to Happiness", and backing vocals to the title track of the L. Ron Hubbard album The Road to Freedom.

1990–2005
In the mid-1990s, Garrett returned to acting and singing, appearing in the 1995 low-budget horror film Dominion, touring with the Melvins and recording vocals for their cover of "Smells Like Teen Spirit" on The Crybaby (2000). In 1998, a greatest hits compilation, The Leif Garrett Collection, was released. Garrett, however, has stated: "My former record label was bought out. The label was started by me … meaning my music started it, funded it. And then it was bought out by some company that released the Greatest Hits Collection. Not only have I not seen any royalties from that, but they wanted me to promote it—the compensation being a couple of CDs."

In the late 1990s, Garrett hosted the series 8-Track Flashback on the cable music channel VH-1, replacing fellow teen idol David Cassidy. VH-1 went on to feature Garrett in a 1999 episode of its Behind the Music series.

In 1999, he formed the band Godspeed with Christopher Wade Damerst and Michael Scott (the Distortions, Deadtime Stories). They recorded a three-song EP on Garrett's own label, Tongue and Groove Records.

Garrett's stage work includes playing the title role in Joseph and the Amazing Technicolor Dreamcoat and, in late 2000, appearing in the National Theatre of the Deaf's production of A Child's Christmas in Wales. He also appeared in summer stock at The Barn Theatre's production of Old Timer in 2001. In the same year, he voiced himself in the animated television series Family Guy episode "The Thin White Line".

In 2003, Garrett appeared as himself in the David Spade film Dickie Roberts: Former Child Star. He co-wrote and sang "Former Child Star" for the film's soundtrack and was one of the singers of "Child Stars on Your Television", which played over the ending credits. He appeared with Aaron Carter in the 2005 film Popstar.

2006–present
In September 2006, Garrett appeared on the celebrity edition of Fear Factor. He won the grand prize of $50,000. On New Year's Eve 2006, Garrett first appeared in Las Vegas with retro act Original Idols Live!, hosted by Barry Williams. The show also featured the Bay City Rollers, Bo Donaldson and the Heywoods, and the Cowsills, with selected appearances by Merrill Osmond, Tony DeFranco, and Danny Bonaduce.

In August 2007, Country Music Television (CMT) cast Garrett in the short-lived Ty Murray's Celebrity Bull Riding Challenge, among nine celebrities appearing on the show. However, he quit after one episode, citing soreness and lack of desire to continue.

In November 2007, Garrett released the album Three Sides of..., which constituted songs he recorded with his current band F8 and his 1990s band Godspeed as well as some new songs.

In 2008, the producers of TruTV's The Smoking Gun Presents: World's Dumbest... added Garrett to their cast, which features comedic commentary from celebrities like Garrett who have had brushes with the law. Garrett has frequently spoofed his troubled past and participates in a wide variety of sketches and skits written specially for him by the show's producers. In a 2010 episode, Garrett reenacted his recent arrest with two actors, including Todd Bridges, another show regular, portraying police officers.

Garrett toured South Korea in May 2010, with shows in Seoul and Busan. This marked the 30th anniversary of Garrett's first performance in Korea in June 1980. He embarked on another tour of the country in 2013.

Garrett was a cast member in the fourth season of Celebrity Rehab with Dr. Drew, which documented Garrett's struggle with addiction to heroin. The season premiered December 1, 2010. Garrett's sister, Dawn Lyn, and mother, Carolyn Stellar (November 6, 1934 – September 2, 2022), who was battling Stage 4 lung cancer, both appeared in Episode 7, which was filmed during Family Day, when the recovering addicts were visited by their loved ones to discuss how their addiction affected their family relationship. In the early 2010s, Garrett began collaborating with punk rock artist and songwriter Craig Else. He released two singles on the Internet, sharing Else's credits, "Everything" (released in 2010) and "Help You, Make You" (released in 2012). The two also recorded a cover of Neil Young's "Old Man".

He published an autobiography entitled Idol Truth in 2019. In the biography and related interviews, Garrett explained that in multiple tracks in his earlier albums, Jim Haas, actually replaced his vocals entirely. The producers had wanted him to "smooth" Garrett's uneven vocals, but made the choice sometimes to replace Garrett entirely on his own albums. In some cases, Garrett's producers even brought in Haas to sing for Garrett behind a curtain during some live concert tour performances.

Personal life
Garrett and actress Nicollette Sheridan dated on and off for five years until 1985. Garrett also dated celebrities such as his former Family co-star Kristy McNichol, Tatum O'Neal, and Justine Bateman. In the 1990s, he was in a long-term relationship with actress Elaine Bilstad, who died in 1999 of a heart ailment.

In October 2001, Garrett was in a personal bankruptcy proceeding in a federal court in Los Angeles. Court papers stated his only regular income was a $1,000 monthly gift from his mother. His only listed possessions were his clothes, some household goods and about $350 in cash. Garrett had accumulated a $76,198 debt in unpaid credit card bills over a four-year period.

Legal troubles
Garrett admitted that he started using drugs when he was 14. On November 3, 1979, five days before his 18th birthday, he crashed a Porsche 914 that was being leased to his mother after a midnight party while he was driving to buy more cocaine. His blood alcohol level was three times over the legal limit of that time and place, and he was high on quaaludes. The accident left his passenger and friend, Roland Winkler, a paraplegic. Garrett had only met Winkler about a month earlier. Neither Garrett nor Winkler was wearing a seatbelt. Garrett was later tried as a juvenile on drunk-driving charges; his driver's license was suspended for a year and he was placed on a year's probation. Winkler sued in January 1980, claiming Garrett was at fault in the accident.

In December 1984, Los Angeles Superior Court ordered Garrett's insurers, Transamerica Insurance Co., to pay $3.9 million to Winkler. Jurors assessed total damages in the civil negligence case at $4,215,500, but subtracted 8% of that amount, or $337,240, on the grounds that Winkler contributed to his own injuries by agreeing to ride in a car with a driver who he knew was drunk. Both Garrett and Winkler admitted in court that they were drunk and had taken depressant drugs; the court heard they had each taken equal amounts of alcohol and drugs that night. The panel ordered Garrett to pay $15,000 in punitive damages, which was not diminished by Winkler's partial responsibility. Winkler's attorney, Edward Steinbrecher, attributed the relatively small punitive damage award to Garrett's testimony that his net worth was only $50,000 to $100,000. In 1987, Winkler settled for $6 million with the Premier Insurance Co., which had insured the firm leasing the Porsche to Garrett's mother. Garrett and Winkler were reunited in 1999 for an episode of Behind the Music, where Garrett was relieved to learn that Winkler had no bad feelings towards him and even said that Garrett's actions following the accident had actually saved his life.

Garrett was arrested for possession of cocaine in 1997.

On June 29, 1999, Los Angeles police arrested Garrett in the MacArthur Park area after he allegedly tried to buy heroin and cocaine from undercover officers. In March 2001, a Los Angeles judge issued a warrant for his arrest when he failed to attend court for a progress report required by his 1999 conviction. Two days later, the judge lifted the warrant and dropped the 1999 charges after Garrett submitted evidence that he had completed a rehab program.

In 2004, Garrett was arrested for possession of cocaine. He pleaded guilty in March 2005 to attempted possession of cocaine-based narcotics and was placed on probation. When he failed to appear in court in December 2005 for a status report, a warrant was issued for his arrest.

On January 14, 2006, when Garrett was arrested on a Los Angeles Metro Rail platform for not having a ticket, police found heroin in his possession. Because of the outstanding warrant for violating probation in a cocaine-related arrest, he was held without bail. He agreed to join a strict drug-diversion program, and his release from jail was ordered.

Garrett dropped out of the rehabilitation program and was taken into custody again on March 30 after a Superior Court commissioner determined he failed several drug tests while staying in a live-in drug diversion program. Garrett acknowledged he needed more help. On May 11, after failing to complete court-ordered drug rehabilitation, he was sentenced to 90 days in jail and three years' probation. He was given credit for the jail time he had already served since March 30.

On February 1, 2010, Garrett was arrested again for possession of narcotics. After denying having any drugs in his possession, he finally admitted to police that he had black tar heroin in his shoe. He posted $10,000 bail and was charged with a felony count of heroin possession. On October 18, 2010, he pleaded no contest to heroin possession in Los Angeles and entered a court-ordered rehabilitation program.

Other recording appearances
Garrett has also sung on releases by the Melvins (The Crybaby), the Crush Ups ("Betty Ford for X-Mas") and Liberty n' Justice ("Sight Unseen" on Soundtrack of a Soul), among others.

Filmography

 * Bob & Carol & Ted & Alice (1969)
 * Walking Tall (1973)
 * Peopletoys (Devil Times Five) (1974)
 * Macon County Line (1974)
 * Walking Tall Part 2 (1975)
 * God's Gun (1976)
 * Paper Tigers (1977)
 * Kid Vengeance (1977)
 * Walking Tall: Final Chapter (1977)
 * Peter Lundy and the Medicine Hat Stallion (1977)
 * Skateboard (1978)
 * Sgt. Pepper's Lonely Hearts Club Band (1978)
 * Longshot (1981)
 * The Outsiders (1983)
 * Shaker Run (1985)
 * Thunder Alley (1985)
 * Delta Fever (1987)
 * Cheerleader Camp (1987)
 * Party Line (1988)
 * The Banker (1989)
 * The Spirit of '76 (1990)
 * Dominion (1995)
 * The Whispering (1996)
 * The Next Tenant (1998)
 * I Woke Up Early the Day I Died (1998)
 * The Art of a Bullet (1999)
 * Dickie Roberts: Former Child Star (2003)
 * Popstar (2005)
 * Circumstances of Fate (2006)
 * Fish Mich (2009)

Television work

 * Nanny and the Professor ("The Human Element") (1970)
 * Black Noon (1971)
 * Cannon ("Death Is a Double-Cross") (1971)
 * Family Affair ("Heroes Are Born") (1971)
 * The F.B.I. ("The Deadly Species") (1972 season 7 episode 24)
 * Circle of Fear (1973)
 * Strange Homecoming (1974)
 * The Odd Couple ("The Frog") (1974)
 * The Last Survivors (1975)
 * Three for the Road (1975)
 * Flood! (1976)
 * Peter Lundy and the Medicine Hat Stallion (1977)
 * The Hanna-Barbera Happy Hour (1978)
 * Family (1978)
 * Wonder Woman ("My Teenage Idol is Missing") (1978 season 3 episode 1)
 * CHiPs (two-part episode "Roller Disco") (1979)
 * Superboy ("Bringing Down The House") (1988)
 * VH1's 8-Track Flashback (1995–1996)
 * Family Guy ("The Thin White Line") (2001)
 * The Weakest Link (2001)
 * American Black Beauty (2005)
 * Celebrity Fear Factor (2005)
 * Ty Murray's Celebrity Bull Riding Challenge (2007)
 * truTV Presents: World's Dumbest... (2008–2013)
 * Celebrity Rehab with Dr. Drew (2010)

title: Leif Garrett


text:
Montel Williams

Montel Brian Anthony Williams (born July 3, 1956) is an American television host, actor and motivational speaker. He is known for hosting the daytime tabloid talk show The Montel Williams Show, which ran in syndication from 1991 to 2008. He currently hosts Military Makeover: Operation Career on Lifetime. Williams founded the Montel Williams MS Foundation after being diagnosed with multiple sclerosis in 1999. He is noted for his service in both the United States Marine Corps and the United States Navy, from which he retired after 22 years of service.

Early life and education
Born in Baltimore, Maryland, on July 3, 1956, Williams attended Andover High School in neighboring Linthicum, Maryland, where he was elected president of his class in both his junior and senior years. He was a good student, athlete, and musician, and he was active in countywide student government issues in Annapolis, Maryland.

Williams was raised as a Roman Catholic and served as an altar server in the Catholic Church.

Montel's father, Herman Williams Jr., was a firefighter who in 1992 became Baltimore's first African American Fire Chief. Montel's mother is biracial.

Military
Williams enlisted in the United States Marine Corps in 1974. He completed the one-year Naval Academy Preparatory School course and then in 1975, he was accepted as the first black Marine into the four-year officer training program at the U.S. Naval Academy.

He graduated in 1980 with a degree in general engineering and a minor in international security affairs. He completed Naval Cryptologic Officer training, and spent 18 months in Guam as a cryptologic officer for naval intelligence. He was later supervising cryptologic officer with the Naval Security Fleet Support Division at Fort Meade, Maryland. It was there Williams worked for the National Security Agency, where he was involved in the U.S. invasion of Grenada in 1983, known as Operation Urgent Fury. On several occasions, he worked to secure the release of United States citizens — typically military personnel who had been captured in foreign lands — returned to U.S. soil. After 17 years of active duty and 5 more as a reservist, Williams retired in 1996 from the Naval Reserve at the rank of lieutenant commander after 22 years of service. His awards include two Meritorious Service Medals, two Navy Commendation Medals, the National Defense Service Medal, the Navy Achievement Medal, two Navy Expeditionary Medals, the Armed Forces Expeditionary Medal and two Humanitarian Service Medals.

As a civilian, Willams was again honored in 2008 with a Navy Superior Public Service Award for his "continuous support and recognition of Sailors, Marines and their families throughout his 17 years on television".

The Montel Williams Show
Williams began The Montel Williams Show (syndicated by CBS Paramount Television) in 1991. In 1996, Williams received a Daytime Emmy Award for Outstanding Talk Show Host. Ratings for the show peaked during the 1996–97 season, with a 4.4 average rating. He was again nominated for Outstanding Talk Show Host in 2002, and the Montel Williams Show was nominated for Outstanding Talk Show in 2001 and 2002.

On January 30, 2008, Variety reported that CBS TV Distribution had terminated The Montel Williams Show when key Fox-owned stations chose not to renew it for the 2008–09 season. On May 16, 2008, the last episode of The Montel Williams Show aired. Speculation followed the end of The Montel Williams Show, which was cancelled immediately after Williams criticized mainstream news media's preference for stories about Hollywood stars over those about military personnel and events. Commentators felt his statements may have alienated the Fox TV Network.

On November 10, 2010, Oprah Winfrey invited Williams, along with former talk show hosts Phil Donahue, Geraldo Rivera, Ricki Lake, and Sally Jessy Raphael as guests on her show. This was the first time that the fellow talkers had appeared together since their programs left the air.

Williams work has been criticized by the Independent Investigations Group, which declared The Montel Williams Show to be noteworthy Truly Terrible Television with its satirical TTTV award (for similar reasons, awarded to "every episode featuring Sylvia Browne").

Controversial self-declared psychic Sylvia Browne featured frequently on The Montel Williams Show from 1991 until its finale in 2008. Williams described Browne as "the most-appearing guest on a talk show in the history of television" and "the longest-running guest in daytime television", and her appearances included particularly controversial incidents relating to kidnap victims Shawn Hornbeck and Amanda Berry. Williams was criticized for allowing his high-profile show to serve as a channel for Browne, notably by fellow retired military officer Hal Bidlack, with Bidlack publicly asking, "Commander Williams, have you lost your honor?" In February 2019, an episode of Last Week Tonight with John Oliver featured a segment on television psychics and Williams' association with Browne was criticized.

Acting
Williams has also guest-starred in episodic television and off-Broadway plays. Among other roles, he portrayed a Navy SEAL, Lieutenant Curtis Rivers, in three episodes of the television series JAG. He also produced and starred in a short-lived television series called Matt Waters, which appeared on CBS in 1996. He played an ex-Navy SEAL turned inner-city high school teacher. In 1997 he played Lt Col Northrop, a USAF nuclear missile silo commander, in the fictional movie The Peacekeeper. In 2002, he played the judge presiding over Erica Kane's (Susan Lucci) murder trial on the ABC soap opera All My Children. In 2003 he made a guest appearance on the soap as himself to promote an episode of his own show on which several AMC stars were scheduled to appear. In 2004 he hosted American Candidate, a political reality show on Showtime. Williams has also guest-starred on The New Adventures of Robin Hood and Guiding Light.

Williams also appeared in a Perry Mason movie in 1993 titled The Case Of The Telltale Talk Show Host. His character, Boomer Kelly, was a former football player who was appearing on a radio talk show whose owner was found murdered. He was also a voice actor in 2008 in the political satire film War, Inc., providing the voice of the main character's GPS tracking device/counselor.

On October 1, 2019, Williams appeared in an episode of the Fox drama The Resident entitled, "Flesh of My Flesh". Williams played himself, as a TV personality covering a nearly impossible cancer surgery being performed on an adoptive mother of seven.

Production
Williams produced and narrated the Starline Films documentary film 4CHOSEN: The Documentary, which tells the story about the New Jersey Turnpike shooting in 1998, and the racial profiling case that followed the incident. In 1999, Williams directed the film, Little Pieces, starring Grace Morley and Amy Acton.

Spokesman
Williams was a national spokesman of the Partnership for Prescription Assistance (PPA), a patient assistance program clearinghouse that helps low-income patients apply for free or reduced-price prescription drugs. On November 30, 2007, while in Savannah, Georgia, to promote PPA, he threatened reporters following an earlier interview at which Courtney Scott, a 17-year-old high school intern reporter for the Savannah Morning News, had asked him whether restriction of pharmaceutical profits would discourage research and development of new drugs. Angered by the question, Williams retorted, "I'm trying to figure out exactly why you are here and what the interview is about,” and subsequently terminated that videotaped interview; Williams later ran into Scott in his hotel and approached her, reportedly saying,” ‘Don't look at me like that. Do you know who I am? I'm a big star, and I can look you up, find where you live and blow you up".

Williams's public relations representatives later apologized for his hostile outburst in an issued statement: "I mistakenly thought the reporter and photographer in question were at the hotel to confront me about some earlier comments. I was wrong, and I apologize for my overreaction". In 2010 Williams became chief spokesman for the Poker Training Network, now Card Geniuses, a MLM-based poker instruction and playing website.

Payday loan controversy
Williams was a paid spokesperson for MoneyMutual, a lead generator for a payday lending service. In early 2015, a controversy around this position erupted when an education activist, André-Tascha Lammé, accused Williams on Twitter of supporting a company that harms African-American consumers. Williams denied the allegations, stating that Lammé was fundamentally incorrect in his assessment of the loans and their terms. The New York State Department of Financial Services then investigated the claims and Benjamin Lawsky issued a statement on March 10 that it "made no finding of a violation of law by Mr. Williams". He added that the department had found that "Using Mr. Williams's reputation as a trusted celebrity endorser, MoneyMutual marketed loans to struggling consumers with sky-high interest rates - sometimes in excess of 1,300 percent". SellingSource, the parent company, was fined $2.1 million and ordered to stop advertising to New Yorkers.

Campaigning
Williams is an outspoken advocate for US military veterans. He has publicly lobbied for government action to promptly resolve the Veterans Affairs scandal.

Other work
On April 6, 2009, Williams began hosting a daily radio show, Montel Across America, on Air America Media. On January 21, 2010, Air America ceased broadcasting, leaving Williams without a radio outlet.

As of May 2009, he started hosting an infomercial for the Living Well Healthmaster, a blender product. It is presented under the title Living Well with Montel; the infomercial is structured similarly to his old talk show, featuring guests talking about their health problems, with the Healthmaster mixer being the solution. Later episodes of Living Well with Montel advertised a home pressure cooker and an identity theft protection service. In June 2010, Williams began doing infomercials for LifeLock, a security fraud company.

On October 1, 2014, Williams spoke in front of a Congressional committee in support of Marine Sgt. Andrew Tahmooressi, who was arrested in Tijuana, Baja California, for carrying guns across the U.S.-Mexican border.

Williams was once a Republican, leaving the political party in 1993 and registering as an independent. He is a supporter of LGBT rights. He endorsed Hillary Clinton for president as the superior choice, writing that Donald Trump posed a "clear and present danger" to the nation.

On September 2, 2021, Williams was appointed as a Director on the Board of Better For You Wellness, Inc.

CBD oil
Williams has marketed cannabidiol (also known as CBD oil) products. According to Forbes, Williams "spent years working to develop medicinal-quality CBD to treat his own multiple sclerosis".

Personal life
Williams has two daughters, Ashley Williams (b. 1984) and Maressa Williams (b. 1988), with his first wife, Rochele See. Williams married Grace Morley, an exotic dancer on June 6, 1992. They have a son, Montel Brian Hank Williams (b. 1993), and a daughter, Wyntergrace Williams (b. 1994). The couple divorced in 2000.

In 2001, Williams briefly dated Kamala Harris, who later went on to become Vice President of the United States after winning the 2020 election. Williams tweeted in 2020 that he had "'great respect'" for Harris.

In July 2006, Williams proposed to girlfriend Tara Fowler, an American Airlines flight attendant. They married before friends and family on a beach in Bermuda on October 6, 2007.

Williams participated in the 2007 World Series of Poker main event, and planned to donate any potential winnings to American families affected by the Iraq War. He was eliminated in Day 2. During the event Williams also spoke out about the port security bill signed in 2006 that banned online gaming sites from accepting money transactions from the U.S.

Four months after making a guest appearance in an episode of Touched by an Angel, Williams was diagnosed with multiple sclerosis in 1999. In the following year, Williams created the MS Foundation, a nonprofit organization with a focus on research and education. Williams has openly stated that he uses medical cannabis, stating it helps to ease his multiple sclerosis-caused neuropathic pain. Williams has become a vocal advocate of cannabis, supporting efforts to pass medical cannabis laws in the United States, as well as calling for full legalization. He has also said that snowboarding is his "best therapy" for multiple sclerosis, commenting that "When I stand up I need first to hold on to something and think about the positioning of my legs. If I were to just start walking I would fall. I have to get my brain to find my legs and then I will usually take a test step, but I say something at the time to anyone who might be watching to distract from what I'm really doing. Then I'll find places to grab as I walk and talk, sometimes even walking backwards because I have more control that way. People have no idea that I'm doing this. But when I'm snowboarding and my feet are strapped in, my brain seems to have a direct connection to my legs. After snowboarding it's night and day for my balance and walking. There's a real physical change before I get up the mountain and when I come down. The benefits last for days. ".

Williams was hospitalized on May 30, 2018, when he had a cerebellar hemorrhagic stroke while working out at a gym.

title: Montel Williams


text:
Arado Ar 234

The Arado Ar 234 Blitz (English: lightning) is a jet-powered bomber designed and produced by the German aircraft manufacturer Arado. It was the world's first operational turbojet-powered bomber, seeing service during the final years of the Second World War.

Development of the Ar 234 can be traced back to the latter half of 1940 and the request to tender from the Ministry of Aviation to produce a jet-powered high-speed reconnaissance aircraft. Arado was the only respondent with their E.370 design. While its range was beneath that of the Ministry's specification, an initial order for two prototypes was promptly issued to the company, designated Ar 234. While both of the prototypes had been mostly completed prior to the end of 1941, the Junkers Jumo 004 turbojet engines were not available prior to February 1943. Due to engine unreliability, the maiden flight of the Ar 234 V1 was delayed until 30 July 1943. In addition to the original reconnaissance-orientated Ar 234A, the fast bomber Ar 234B model was developed in response to a request by the Ministry of Aviation. Due to a lack of internal space in the relatively slender fuselage, bombloads of up to 1500 kg had to be carried on external racks rather than in internal bomb bays.

The Ar 234 was produced only in small numbers, despite plans for production of 500 per month by late 1945. This was partly due to a lack of available jet engines and other critical materials, for which the aircraft had to compete with other types, such as the Messerschmitt Me 262. Several models were proposed, with alternative engines, cockpit improvements, and adaptations for other roles, including as a night fighter. In late 1944, aerial reconnaissance missions over enemy territory commenced. The Ar 234 was almost entirely used to perform such reconnaissance missions and it was in this capacity that it became the last Luftwaffe aircraft to overfly the United Kingdom during the war, in April 1945. In its capacity as a bomber, the most prominent use of the Ar 234 was the repeated attempts to destroy the Ludendorff Bridge at Remagen between 7 and 17 March 1945. Many airframes were destroyed or captured on the ground due to a lack of serviceable engines or fuel.

Background
During the closing months of 1940, the Nazi German Ministry of Aviation offered a tender for a jet-powered high-speed reconnaissance aircraft with a range of 2156 km. Arado was the only company to respond, offering their E.370 project, led by Professor Walter Blume. The design was of a high-wing mostly conventional-looking aircraft that was powered by a pair of Junkers Jumo 004 turbojet engines, one being located underneath each wing.

Arado estimated that the E.370 would possess a maximum speed of 780 km/h at 6000 m, an operating altitude of 11000 m and a range of 1995 km. While the range was short of the Ministry's specification, it decided to order a pair of prototypes, which were designated as the Ar 234. These were largely complete before the end of 1941, but the Jumo 004 engines were not ready until February 1943. When they did arrive, Junkers considered the engines too unreliable for in-flight use and were only cleared for ground tests. Months later, flight-ready engines were finally delivered and on 30 July 1943, the Ar 234 V1 performed its first flight from Rheine airfield.

The second prototype, V2, crashed on 2 October 1943 at Rheine near Münster after suffering a fire in its port wing, the failure of both engines, and instrumentation failures. The aircraft dived into the ground from 1200 m, killing the pilot. That same year, the third prototype, V3, was displayed to Adolf Hitler at Insterberg, who was enthusiastic about the aircraft and authorised Arado to obtain factory personnel, raw materials, and the funds necessary to build two hundred by the end of 1944. The eight prototype aircraft were fitted with the trolley-and-skid landing gear intended for the never produced Ar 234A version.

The sixth and eighth in the series were powered by four BMW 003 jet engines instead of two Jumo 004s; the sixth had the four engines in individual nacelles, while the eighth had the engines in "twinned" nacelles underneath each wing. A 1942 engineering drawing of the E 370 showed a 1430 L forward tank, a 830 L mid-fuselage tank, and an rear tank with a 1540 L capacity. These were the first four-engined jet aircraft to fly. The twin-Jumo 004 powered Ar 234 V7 prototype was the first jet aircraft used for a reconnaissance mission, on 2 August 1944.

Landing gear design
The projected weight for the aircraft was approximately 8 t. To reduce weight and maximize the internal fuel, Arado did not use retractable landing gear. Instead, the aircraft was to take off from a jettisonable tricycle gear-style trolley, referred to as a nosewheel takeoff-carriage in English, as described in an Ar 234A Typenblatt factory drawing for the V8 prototype, and land on three retractable skids, one under the central section of the fuselage and one under each engine nacelle. The main skid, beneath the fuselage, was originally intended to fully retract, and was originally shown in a 1942-dated engineering drawing, under the E 370 airframe factory development designation, as intended to be made from a three-sided channel-section component, featuring a set of nine triple-beaded wooden rollers within the channel-section main skid. However, this landing gear did not allow aircraft to move after the landing run, which would have left aircraft scattered over an airfield, unable to taxi off the runway. Erich Sommer said that landing the skid-equipped prototypes on a wet grass airstrip "was like greased lightning" and "like [landing on] soap", due to the complete lack of braking capability.

Ar 234B
At the request of the Ministry of Aviation, Arado also produced a pair of prototypes configured as fast bombers, as the Ar 234B. On 12 March 1944, the first of these, Ar 234 V9, performed its first flight. It was the first to feature a fully retractable tricycle landing gear, with the main gear retracting forward into the mid-fuselage, and the nose gear retracted rearwards.

The Ar 234's slender fuselage was largely filled with fuel tanks, leaving no room for an internal bomb bay, which was carried on external racks. The forward-set cockpit did not provide the pilot with any visibility to the rear, thus the rear firing guns it was fitted with were aimed through a periscope, mounted on the cockpit roof. This periscope could also be flipped forwards for dive-bombing however, its usefulness was impaired by the scope's image being flipped upside down. The defensive fixed rear gun system was found to be useless by the pilots, and was omitted in the Ar 234B. The aircraft was widened slightly at mid-fuselage and the central fuel tank was omitted to fit in the main landing gear, while enlarged forward (1800 L) and aft (2000 L) fuel tanks compensated for its removal.

During flight testing, while carrying its maximum bombload of three SC 500 bombs, the Ar 234 V9 could reach 672 km/h at 5000 m, faster than any other Luftwaffe bomber at the time. The normal bomb load consisted of a pair of 500 kg bombs suspended from the engines or one large 1000 kg bomb semi-recessed in the underside of the fuselage, while the maximum bombload was 1500 kg. It could also carry the heavier BT 1400 (1510 kg unpowered bomb-torpedo), although the ground clearance was limited. If this munition was deployed, the aircraft's fuel capacity was noticeably reduced while rocket assistance was needed for takeoff. The pilot would engage the autopilot while using the bomb sight, which was interfaced with the autopilot to adjust the aircraft's flight path directly.

Production lines were being set up while the 20 B-0 pre-production aircraft were being delivered, by the end of June. Production was slow, as Arado was to maintain production to compensate for other factories bombed during the USAAF's "Big Week",(20-25 February 1944), in addition to an ongoing license-construction of the Heinkel He 177 heavy bomber. Between mid-1944 and the end of the conflict, only 210 aircraft were built. During February 1945, production switched to the C variant. German plans were for production to reach 500 per month by November 1945.

In addition, some Ar 234 B-2 airframes were modified to serve as night fighters. Designated Ar 234B-2/N and code named Nachtigall (Nightingale), these were fitted with FuG 218 "Neptun" VHF-band radar, with a reduced-dipole length version of the standard Hirschgeweih eight-dipole element, VHF-band transceiving AI radar antenna system, and carried a pair of forward-firing 20mm MG 151/20 autocannon within a Magirusbombe conformal gun pod on the rear fuselage hardpoint. The radar system was operated by a second crew member in a cramped compartment in the rear. Two of these served with Kommando Bonow, a Luftflotte Reich experimental test unit. Operations began in March 1945, but the aircraft was unsuitable for night fighting and no kills were made.

Ar 234C
The Ar 234C was equipped with four lighter (625 kg apiece) BMW 003A engines mounted in a pair of twin-engine nacelles based on those from the eighth prototype. The primary reason for this switch was to free up Junkers Jumo 004s for the Me 262, but it also improved takeoff power to nearly (7040 lbf). An improved cockpit, with a slightly bulged outline in the upper contour, and integrating a swept-back fairing for the periscope, and a simplified window design with 13 glazed panels reduced to 8. The BMW jet engines improved top speed by about 20% over the B series airframes.

The C-1 was intended for reconnaissance, the C-2 for bombing, and the C-3 for bombing, ground attack (using anti-personnel bombs) or night fighting (with two additional 20mm MG 151/20s in a forward firing ventral pack).

During October 1944, the prototype Ar 234 V19 performed its first flight. Although an operational test squadron was being prepared, only 14 C-series airframes were completed by the end of the war, with fewer than half having engines. Some were found at the end of the war sitting in the open, complete but for empty engine nacelles.. Flight testing of the new sub-type hadn't started yet when Germany surrendered. Three basic variants of the C-series were planned, with several more laid out as detailed proposals. Some of these would have had a pair of the higher thrust, but 950 kg heavier Heinkel HeS 011 jet engines, while others were to have swept or "crescent"-type wings.

Ar 234D
The D model was intended to be a two-seat aircraft based on the B-series fuselage, but with an enlarged cockpit using fewer glazing panels than the C version, powered by a pair of more powerful Heinkel HeS 011 turbojet engines. The HeS 011 powerplant never reached quantity production, but only 10 examples had been started

Ar 234P
The P model was intended to be a two-seat night fighter version with a variant of the D-series cockpit, differing in powerplant options and several options of radar. Several were in the planning stage, but none were produced.

Operational history
By 1944, the Luftwaffe's bombing capability had been severely reduced from attrition across multiple fronts, and despite the advance offered by the pending arrival of production Ar 234s, there was a shortage of experienced pilots. The first unit-level type conversion orders were issued to III/KG 76 in May 1944 and personnel had to be pulled from the front lines and brought to central Germany for aircraft and engine familiarisation, which was facilitated with two-seat Messerschmitt Me 262s.

Challenges were encountered getting the Ar 234 operational, including poor quality of worksmanship, and severe shortages of certain resources, such as fuel. The reliability of the Jumo 004 engines would worsen over time, a trend attributed to using ill-suited fuels. The engines suffered from frequent flameouts and had to be overhauled or replaced after roughly ten hours of operation, although as ground crews became more skilled, the time needed to swap engines was reduced. The aircraft's lengthy takeoff runs were responsible for several accidents and attempts at resolution included improvements to pilot training and the use of jettisonable liquid fuel Starthilfe rocket-assisted takeoff units, mounted under each outer wing. Accidents would often be fatal due to the lack of an ejection seat, the pilot instead having to exit via a highly impractical hatch in the floor.

During August 1944, several of Ar 234 prototypes - including six surviving Ar 234A-series prototypes were dispatched on aerial reconnaissance missions. The seventh prototype would perform the first reconnaissance mission over the United Kingdom by a Luftwaffe jet. These reconnaissance flights helped assess the potential for an Allied naval invasion of the Netherlands. Allied piston-engine fighters proved unable to intercept them, being incapable of matching their speed and altitude.

During the autumn of 1944, the first Ar 234Bs began entering service. Early missions included attacks in the Low Countries, at the Antwerp docks and a Brussels railway station. The type was used directly against Allied units during the Battle of the Bulge, and in January 1945, Ar 234s attacked artillery positions to the north of Bastogne. One month later, the Allies were able to capture a crashed Ar 234 after it had been forced down by a Republic P-47 Thunderbolt. The type also saw action in Northern Italy.

Perhaps the most notable use of the Ar 234 in the bomber role was the attempt to destroy the Ludendorff Bridge at Remagen. Between 7 March, when it was captured by the Allies, and 17 March, when it finally collapsed, the bridge was continually attacked by III/KG 76 Ar 234s carrying 1000 kg bombs. Most attacks missed the bridge, and heavy losses were experienced from ground-based anti-aircraft guns due to the low altitude these attacks were made from.

By 10 April 1945, 38 operational Ar 234s were reportedly on strength, including 24 reconnaissance aircraft, 12 bombers, and two night-fighters. However, most of these sat waiting for fuel and qualified personnel.

The Ar 234 continued to fly combat missions until the surrender of Germany on 8 May 1945. Several were recorded as having been lost, often destroyed by anti-aircraft guns, or "bounced" by Allied fighters either during takeoff or on landing when the jets were flying slow and straight, and were most vulnerable. This technique had already been used against Messerschmitt Me 262 jet. Numerous examples would be captured by the Allies.

Variants
Data from: Aircraft of the Third Reich Vol.1
 * Arado E 370:Draft proposal submitted to the Reichsluftfahrtministerium (RLM) for a fast jet reconnaissance bomber.

 * Ar 234 V1 to V5: Initial prototypes of the Ar 234A with skid landing gear, take-off tricycle gear trolley with trio of retractable landing skids, and two Jumo 004 engines.

 * Ar 234 V6 & V8:Prototypes for four-engined designs for the Ar 234, meant to use the alternative choice of the lower-thrust BMW 003 turbojet engines while retaining the A model skid/trolley undercarriage. The V6 was fitted with the quartet of BMW 003s in individual nacelles, unlike the V8 prototype which had the BMW jet engines in a pair of "twinned" nacelles, and essentially "prototyped" what would become the four-engined Ar 234C's engine installation.

 * Ar 234 V7:Development aircraft for the Ar 234B production aircraft, retaining the A-series' intended skid undercarriage, and saw active service.

 * Ar 234 V9 to V11:Representative prototypes of the Ar 234B production aircraft, with the V9 being the first airframe with retractable tricycle undercarriage.

 * Ar 234 V13 & V20
 * A pair of B-series prototypes fitted with four BMW 109-003 engines intended for the C-series aircraft, using the V8 prototype's "twinned" nacelle design, but without retractable wing-skids.

 * Ar 234 V15: A single B-series airframe fitted with 2 x BMW 003 engines for engine development testing, and rumored to have been considered for new wing planform tests.

 * Ar 234 V21 to V30:C-series development aircraft. V26 and V30 had experimental thick section wooden and thin section metal laminar flow wings.

 * Ar 234 V16:Intended to be fitted with an experimental crescent wing with sweep back lessening towards the tips, evolved by Rüdiger Kosin and Walther Lehmann. The wing was constructed but was destroyed before it could be fitted.

 * Ar 234 A:The first proposed production reconnaissance bomber fitted with skid undercarriage and take-off tricycle gear trolley, built only as the series of eight trolley-and-skid undercarriage V1 through V8 prototypes.

 * Ar 234 B-0: 20 pre-production aircraft.

 * Ar 234 B-1: Reconnaissance version, equipped with two Rb 50/30 or Rb 75/30 cameras. All reconnaissance variants were converted from B-2 aircraft with Rüstsatz b.

 * Ar 234 B-1 Berlin N: Two-engined aircraft, this was a wind tunnel test aircraft based on Ar 234 B-1 with FuG 244 Berlin N radar installed on top. The purpose of this plane was to be an early warning jet and also a fighter control jet.

 * Ar 234 B-2
 * Bomber version, with a maximum bombload of 1,500 kg (3,307 lb).

 * Ar 234 B-2/N: Night fighter version, two aircraft converted from B-2.

 * Ar 234 C-1: Four-engined aircraft – all C-series Ar 234s powered with a quartet of BMW 003 jet engines – as installed on the Ar 234 V8 prototype, otherwise similar to the Ar 234 B-1.

 * Ar 234 C-2: Four-engined aircraft similar to the Ar 234 B-2.

 * Ar 234 C-3: Multi-purpose version, armed with two 20 mm MG 151/20 cannons beneath the nose.

 * Ar 234 C-3/N: Proposed two-seat night fighter version, armed with two forward-firing 20 mm MG 151/20 and two 30 mm (1.18 in) MK 108 cannons, fitted with a mid-VHF band FuG 218 Neptun V radar.

 * Ar 234 C-4: Armed reconnaissance version, fitted with two cameras, armed with four 20 mm MG 151/20 cannon.

 * Ar 234 C-5: Proposed version with side-by-side seating for the crew. The 31st prototype was converted into this variant.

 * Ar 234 C-5 Berlin N: Proposed C-5 with a FuG 244 Berlin-N rotating radar dish on top of the plane, for early warning and fighter control role

 * Ar 234 C-6: Proposed two-seat reconnaissance aircraft. The 32nd prototype was converted into this variant.

 * Ar 234 C-7: Night fighter version, with side-by-side seating for the crew, fitted with an enhanced FuG 245 Bremen O cavity magnetron-based centimetric (30 GHz) radar.

 * Ar 234 C-8: Proposed single-seat bomber version, powered by two 1,080 kg (2,380 lb) Jumo 004D turbojet engines.

 * Ar 234 D-1: Proposed reconnaissance version. Not built.

 * Ar 234 D-2: Proposed bomber version. Not built.

 * Ar 234 P-1 : Two-seater with four BMW 003A-1 engines; one 20 mm MG 151/20 and one 30 mm (1.18 in) MK 108.

 * Ar 234 P-2 : Also a two-seater, with redesigned cockpit protected by a 13 mm (0.51 in) armour plate.

 * Ar 234 P-3: HeS 011A powered P-2, but with two cannon.

 * Ar 234P-4: as P-3 but with Jumo 004D engines.

 * Ar 234P-5: Three-seat version with HeS 011A engines, one 20 mm MG 151/20 and four 30 mm (1.18 in) MK 108 cannon.

 * Ar 234 R: Rocket-powered short range high-altitude reconnaissance version It had a rocket engine in its tail, while the turbojets had been discarded. It would be towed by a He 177 to 8 km altitude after which it would propel itself to 17 km altitude over the target after which it would glide back unpowered. Project only.

Operators

 * Nazi Germany
 * Luftwaffe
 * 1./Versuchsverband OKL, headquarters unit
 * Sonderkommando Götz, two prototype aircraft, was then increased in size and became;
 * Sonderkommando Sperling, carried reconnaissance on Western front and UK and helped to train crews of;
 * 1./Fernaufklärungsgruppe (FAGr) 123 (long distance reconnaissance unit)
 * Sonderkommando Hecht, carried out reconnaissance of southern portion of Western Front and also intended to train crews of;
 * 1./FAGr 100 (reconnaissance unit)
 * Sonderkommando Sommer, carried out reconnaissance in Italy and also intended to train crews of;
 * 1./FAGr 33 (reconnaissance unit)
 * Sonderkommando Bonow, (night fighter unit)
 * Kampfgeschwader 76 (bomber unit)

Surviving aircraft

Only one Ar 234 survives today, a B-2 bomber variant with manufacturer's serial number 140312. It was one of nine Ar 234s surrendered to British forces at Sola Airfield near Stavanger, Norway. The aircraft had been operating with ''8. Staffel III./Kampfgeschwader 76 (later reorganised as Einsatzstaffel) during the final weeks of the war, having operated previously with the 8th squadron, carrying the full-four-character Geschwaderkennung'' military code "F1+GS" on the fuselage sides, with the wing code "F1" painted in a much reduced size for sanctioned, late-war "low-visibility" requirements.

Teams of the USAAF's Operation Lusty were collecting examples of Luftwaffe technology for study. This aircraft and three others were traded to Operation Lusty by Eric "Winkle" Brown (test pilot and commanding officer of the Enemy Aircraft Flight at the Royal Aircraft Establishment) in exchange for an interview with Hermann Göring who was then being held by the Americans.

The aircraft was flown from Sola to Cherbourg in France on 24 June 1945 where it joined 34 other German aircraft to be shipped to the U.S. aboard the British aircraft carrier HMS Reaper (D82). Reaper departed from Cherbourg on 20 July and arrived at Newark, New Jersey eight days later. Upon arrival two of the Ar 234s were reassembled (including 140312) and flown by USAAF pilots to Freeman Army Airfield, Indiana for testing and evaluation. 140312 was assigned the foreign equipment number FE-1010. The fate of the second Ar 234 flown to Freeman Field remains a mystery. One of the remaining two was reassembled by the United States Navy at Naval Air Station Patuxent River, Maryland, for testing, but was found to be in unflyable condition and scrapped.

After receiving new engines, radio and oxygen equipment, 140312 was transferred to Wright Field near Dayton, Ohio and delivered to the Accelerated Service Test Maintenance Squadron of the Flight Test Division in July 1946. Flight testing was completed on 16 October 1946 though the aircraft remained at Wright Field until 1947. It was then transferred to Orchard Place Airport in Park Ridge, Illinois, and remained there until 1 May 1949 when it and several other aircraft stored at the airport were transferred to the Smithsonian Institution. During the early 1950s, the Ar 234 was moved to the Smithsonian's Paul Garber Restoration Facility at Suitland, Maryland for storage and eventual restoration.

The Smithsonian began restoring 140312 in 1984 and finished in February 1989. All paint had been stripped from the aircraft before the Smithsonian received it, so the aircraft was painted with the markings of an aircraft of 8./KG 76, the first operational unit to fly the "Blitz". The final Luftwaffe pilot who flew 140312 prior to Germany's surrender in World War II, Willi Kriessmann, was reunited with the aircraft in 1990; Kriessmann also donated his flight logs to the Smithsonian around that time. The restored aircraft was first displayed at the Smithsonian's main museum building in 1993 as part of a display titled "Wonder Weapon? The Arado Ar 234".

In 2005, 140312 became one of the first aircraft moved to the new Steven F. Udvar-Hazy Center near Dulles International Airport. Today, 140312 is displayed next to the last surviving Dornier Do 335, one of the other aircraft that accompanied it on its voyage across the Atlantic Ocean aboard the Reaper. 140312 is displayed with a pair of Starthilfe RATO units mounted under its wings. These may be the only surviving examples to be mounted on an aircraft design that actually used them during the conflict.

title: Arado Ar 234


text:
De Finetti's theorem

In probability theory, de Finetti's theorem states that exchangeable observations are conditionally independent relative to some latent variable. An epistemic probability distribution could then be assigned to this variable. It is named in honor of Bruno de Finetti.

For the special case of an exchangeable sequence of Bernoulli random variables it states that such a sequence is a "mixture" of sequences of independent and identically distributed (i.i.d.) Bernoulli random variables.

A sequence of random variables is called exchangeable if the joint distribution of the sequence is unchanged by any permutation of the indices. In general, while the variables of the exchangeable sequence are not themselves independent, only exchangeable, there is an underlying family of i.i.d. random variables. That is, there are underlying, generally unobservable, quantities that are i.i.d. – exchangeable sequences are mixtures of i.i.d. sequences.

Background
A Bayesian statistician often seeks the conditional probability distribution of a random quantity given the data. The concept of exchangeability was introduced by de Finetti. De Finetti's theorem explains a mathematical relationship between independence and exchangeability.

An infinite sequence

 * $$X_1, X_2, X_3, \dots $$

of random variables is said to be exchangeable if for any natural number n and any finite sequence i1, ..., in and any permutation of the sequence π:{i1, ..., in } → {i1, ..., in },

 * $$(X_{i_1},\dots,X_{i_n}) \text{ and } (X_{\pi(i_1)},\dots,X_{\pi(i_n)}) $$

both have the same joint probability distribution.

If an identically distributed sequence is independent, then the sequence is exchangeable; however, the converse is false—there exist exchangeable random variables that are not statistically independent, for example the Pólya urn model.

Statement of the theorem
A random variable X has a Bernoulli distribution if Pr(X = 1) = p and Pr(X = 0) = 1 − p for some p ∈ (0, 1).

De Finetti's theorem states that the probability distribution of any infinite exchangeable sequence of Bernoulli random variables is a "mixture" of the probability distributions of independent and identically distributed sequences of Bernoulli random variables. "Mixture", in this sense, means a weighted average, but this need not mean a finite or countably infinite (i.e., discrete) weighted average: it can be an integral over a measure rather than a sum.

More precisely, suppose X1, X2, X3, ... is an infinite exchangeable sequence of Bernoulli-distributed random variables. Then there is some probability measure m on the interval [0, 1] and some random variable Y such that
 * The probability measure of Y is m, and
 * The conditional probability distribution of the whole sequence X1, X2, X3, ... given the value of Y is described by saying that
 * X1, X2, X3, ... are conditionally independent given Y, and
 * For any i ∈ {1, 2, 3, ...}, the conditional probability that Xi = 1, given the value of Y, is Y.

Another way of stating the theorem
Suppose $$X_1,X_2,X_3,\ldots$$ is an infinite exchangeable sequence of Bernoulli random variables. Then $$X_1,X_2,X_3,\ldots$$ are conditionally independent and identically distributed given the exchangeable sigma-algebra (i.e., the sigma-algebra consisting of events that are measurable with respect to $$X_1,X_2,\ldots$$ and invariant under finite permutations of the indices).

Example
Here is a concrete example. We construct a sequence

 * $$X_1, X_2, X_3, \dots $$

of random variables, by "mixing" two i.i.d. sequences as follows.

We assume p = 2/3 with probability 1/2 and p = 9/10 with probability 1/2. Given the event p = 2/3, the conditional distribution of the sequence is that the Xi are independent and identically distributed and X1 = 1 with probability 2/3 and X1 = 0 with probability 1 − 2/3. Given the event p = 9/10, the conditional distribution of the sequence is that the Xi are independent and identically distributed and X1 = 1 with probability 9/10 and X1 = 0 with probability 1 − 9/10.

This can be interpreted as follows: Make two biased coins, one showing "heads" with 2/3 probability and one showing "heads" with 9/10 probability. Flip a fair coin once to decide which biased coin to use for all flips that are recorded. Here "heads" at flip i means Xi=1.

The independence asserted here is conditional independence, i.e. the Bernoulli random variables in the sequence are conditionally independent given the event that p = 2/3, and are conditionally independent given the event that p = 9/10. But they are not unconditionally independent; they are positively correlated.

In view of the strong law of large numbers, we can say that

 * $$\lim_{n\rightarrow\infty} \frac{X_1+\cdots+X_n}{n} = \begin{cases}

2/3 & \text{with probability }1/2, \\ 9/10 & \text{with probability }1/2. \end{cases} $$

Rather than concentrating probability 1/2 at each of two points between 0 and 1, the "mixing distribution" can be any probability distribution supported on the interval from 0 to 1; which one it is depends on the joint distribution of the infinite sequence of Bernoulli random variables.

The definition of exchangeability, and the statement of the theorem, also makes sense for finite length sequences

 * $$X_1,\dots, X_n,$$

but the theorem is not generally true in that case. It is true if the sequence can be extended to an exchangeable sequence that is infinitely long. The simplest example of an exchangeable sequence of Bernoulli random variables that cannot be so extended is the one in which X1 = 1 − X2 and X1 is either 0 or 1, each with probability 1/2. This sequence is exchangeable, but cannot be extended to an exchangeable sequence of length 3, let alone an infinitely long one.

Extensions
Versions of de Finetti's theorem for finite exchangeable sequences,  and for Markov exchangeable sequences have been proved by Diaconis and Freedman and by Kerns and Szekely. Two notions of partial exchangeability of arrays, known as separate and joint exchangeability lead to extensions of de Finetti's theorem for arrays by Aldous and Hoover.

The computable de Finetti theorem shows that if an exchangeable sequence of real random variables is given by a computer program, then a program which samples from the mixing measure can be automatically recovered.

In the setting of free probability, there is a noncommutative extension of de Finetti's theorem which characterizes noncommutative sequences invariant under quantum permutations.

Extensions of de Finetti's theorem to quantum states have been found to be useful in quantum information,  in topics like quantum key distribution and entanglement detection. A multivariate extension of de Finetti’s theorem can be used to derive Bose–Einstein statistics from the statistics of classical (i.e. independent) particles.

title: De Finetti's theorem


text:
Oswine of Deira

Oswine, Oswin or Osuine (died 20 August 651) was a King of Deira in northern England.

Life
Oswine succeeded King Oswald of Northumbria, probably around the year 644, after Oswald's death at the Battle of Maserfield. Oswine was the son of Osric. His succession, perhaps the choice of the people of Deira, split the Kingdom of Northumbria. Oswiu was the successor of Bernicia to the north.

After seven years of peaceful rule, Oswiu declared war on Oswine. Oswine refused to engage in battle, instead retreating to Gilling and the home of his friend, Earl Humwald. Humwald betrayed Oswine, delivering him to Oswiu's soldiers by whom Oswine was put to death, probably at Diddersley Hill in North Yorkshire.

Bede recounted the death of King Oswine in 651 and mentioned a place called "Wilfaresdun," which he explained to mean "Wilfar's Hill". According to Bede, this location was located approximately ten miles away from the village called Cataract, towards the northwest. King Oswin sought refuge in the house of Earl Hunwald, whom he believed to be his loyal friend, along with only one trusted soldier named Tonhere. However, Earl Hunwald betrayed him, and King Oswin was ultimately killed by Ethilwin, Oswy's commander, in a treacherous manner" Bede provides us with the following account of the events:

"Remisit exercitum quem congregaverat, ac singulos domum redire praecepit, a loco qui vocatur Vilfaraesdun, id est Mons Vilfari, et set a vico Cataractone decem ferme millibus passum contra solistitialem occasum secretus: divertitque ipse cum uno tantum milite sibi fidelissimo, nomine Tondheri, celandus in domo comitis Hunualdi, quem etiam ipsum sibi amicissimum autumabat. Sed, heu, proh dolor! longe aliter erat: nam ab eodem comite proditum eum Osuiu, eum praefato ipsius milite per praefectum suum Ediluinum detestanda omnibus morte interfecit. Quod factum est die decima tertia Kalendarum Septembrium, anno regni eius nono, in loco qui dicitur Ingetlingum."

Understanding this to describe a prominent hill located ten Roman miles (i.e. about 9 imperial miles along the old Roman road) northwest of Catterick, then we are left with one possible location for Wilfar's Hill: Diddersley Hill.

Veneration
In Anglo-Saxon culture, it was assumed that the nearest kinsmen to a murdered person would seek to avenge the death or require some other kind of justice on account of it (such as the payment of wergild: a sum of money paid to the relatives of a slain man on account of the killing). However, Oswine's nearest kinsman was Oswiu's own wife. Oswiu was also related to the slain. In order to confront the justice that was seen to be owed for the murder, Oswiu founded Gilling Abbey, a monastery partly staffed by the relatives of both of their families, and this monastery was given the task of offering prayers for both Oswiu's salvation and Oswine's departed soul. It was from the same monastery, many years later, that Oswine was later claimed to be a saint.

Oswine is one of many Anglo-Saxon royals who were honoured in monasteries and developed cults as saints. Another example is Edward the Martyr.

Oswine was buried at Tynemouth, but the place of burial was later forgotten. It is said that his burial place was made known by an apparition to a monk named Edmund, and his relics were translated to an honorable place in Tynemouth Priory in 1065. According to Alban Butler, in 1103, Ranulf Flambard, Bishop of Durham, translated the remains from the chapel at Tynemouth, which had fallen into disrepair, to St Alban's Abbey in Hertfordshire.

There was a cult of Saint Oswin as a Christian martyr because he had died "if not for the faith of Christ, at least for the justice of Christ".

St Oswin's Church, Wylam
The Church of England parish church of Wylam, Northumberland, England is dedicated to Saint Oswin. The church was built in 1886 and currently has a congregation of about 150. The church has a peal of 6 bells (in the tower) and has regular Sunday services with ringing.

Our Lady & St Oswin's Church, Tynemouth
St Oswin is co-patron (with Our Lady) of the Catholic parish of Tynemouth with a church at the end of Front Street not far from the ruins of the priory where Oswin was buried.

title: Oswine of Deira