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Tody

The todies are a family, Todidae, of tiny Caribbean birds in the order Coraciiformes, which also includes the kingfishers, bee-eaters and rollers. The family has one living genus, Todus, and one genus known from the fossil record, Palaeotodus.

Taxonomy and systematics
The todies were originally placed in the kingfisher genus Alcedo before being placed in the genus Todus in 1760 by Mathurin Jacques Brisson. They have been linked to a large number of potential relatives since then, including nightjars, trogons, barbets, jacamars, puffbirds, kingfishers, motmots and even some passerine species such as broadbills, cotingas and flowerpeckers. The todies were placed in their own order, Todiformes, before being placed in the Coraciiformes.

Genetic analysis of the extant (living) species suggests that they diversified between 6-7 million years ago. The fossil record of the family is sparse, but three species of tody have been described from fossils found in North America, Germany and France, showing that the family was once more widespread than it is today. Species from the fossil genus, Palaeotodus, are larger than living species and may have been closer in size to the tody motmot.

The phylogenetic relationship between the six families that make up the order Coraciiformes is shown in the cladogram below. The number of species in each family is taken from the list maintained by Frank Gill, Pamela C. Rasmussen and David Donsker on behalf of the International Ornithological Committee (IOC).

Distribution and habitat
The todies are endemic to the islands of the Caribbean. These are small, near passerine species of forests of the Greater Antilles: Puerto Rico, Jamaica, and Cuba, with adjacent islands, have one species each, and Hispaniola has two: the broad-billed tody (Todus subulatus) in the lowlands (including Gonâve Island), and the narrow-billed tody (Todus angustirostris) in the highlands.

Description
Todies range in weight from 5 to 7 g and in length from 10 to 11.5 cm. They have colourful plumage, and resemble kingfishers in their general shape. They have green heads, backs and wings, red throats (absent in immature Puerto Rican, broad-billed, and narrow-billed todies) with a white and blue-grey stripe on each side, and yellow undertail coverts; the colour of the rest of the undersides is pale and varies according to species. The irises are pale grey. They have long, flattened bills (as do many flycatching birds) with serrated edges; the upper mandible is black and the lower is red with a little black. The legs, and especially the feet, are small. Todies are highly vocal, except that the Jamaican tody seldom calls in the non-breeding season (August to November); they give simple, unmusical buzzing notes, beeps, and guttural rattles, puffing their throats out with every call. Their wings produce a "strange, whirring rattle", though mostly when courting or defending territory in the Puerto Rican tody.

Diet
Todies eat small prey such as insects and lizards. Insects, from 50 families have been identified in their diet, particularly grasshoppers, crickets, beetles, bugs, butterflies, bees, wasps, and ants, form the greater part of the diet. Spiders and millipedes may also be taken, as is a small amount of fruit (2% of the diet).

Their preferred habitat for foraging is in the forest understory. Todies typically sit on a low, small branch, singly or in pairs, keeping still or stepping or hopping sideways. When they see prey moving on the lower surface of a leaf, they fly a short distance (averaging 2.2 m in the broad-billed tody and 1.0 m in the Puerto Rican tody), diagonally upward to glean it. They may also take prey from the ground, occasionally chasing it with a few hops. Todies are generally sedentary; the longest single flight known for the broad-billed tody is 40 m. Their activity is greatest in the morning when sunny weather follows rain, and in March and September.

Todies are highly territorial but will join mixed-species foraging flocks composed of resident species and migrants from North America, when they pass through their territories.

Breeding
Like most of the Coraciiformes, todies nest in tunnels, which they dig with their beaks and feet in steep banks or rotten tree trunks. The tunnel is 30 cm long in the Cuban and narrow-billed todies, 30 to 60 cm in the broad-billed tody, and ends in a nest chamber, generally not reused. They lay about four round white eggs in the chamber. Both parents incubate but are surprisingly inattentive to the eggs. The young are altricial and stay in the nest until they can fly. Both parents also care for the nestlings, much more attentively; they may feed each chick up to 140 times per day, the highest rate known among birds.

Species list

 * Todus
 * Broad-billed tody, Todus subulatus
 * Cuban tody, Todus multicolor
 * Jamaican tody, Todus todus
 * Narrow-billed tody, Todus angustirostris
 * Puerto Rican tody, Todus mexicanus

 * †Palaeotodus
 * †Palaeotodus emryi
 * †Palaeotodus escampsiensis
 * †Palaeotodus itardiensis

title: Tody


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James Halliwell-Phillipps

James Orchard Halliwell-Phillipps (born James Orchard Halliwell; 21 June 1820 – 3 January 1889) was an English Shakespearean scholar, antiquarian, and a collector of English nursery rhymes and fairy tales.

Life
The son of Thomas Halliwell, he was born in London and was educated privately and at Jesus College, Cambridge. He devoted himself to antiquarian research, particularly of early English literature. Beginning at the age of 16, between 1836 and 1837, he contributed 47 articles to ''The Parthenon. A Weekly Journal of English and Foreign Literature, the Arts, and Sciences; in 1839 he edited Sir John Mandeville's Travels; in 1842 published an Account of the European manuscripts in the Chetham Library, besides a newly discovered metrical romance of the 15th century (Torrent of Portugal'').

In 1841, while at Cambridge, Halliwell dedicated his book Reliquae Antiquae to Sir Thomas Phillipps, the noted bibliomaniac. Phillipps invited Halliwell to stay at his estate, Middle Hill. There Halliwell met Phillipps's daughter, Henrietta, to whom he soon proposed marriage. However, also around this time, Halliwell was accused of stealing manuscripts from Trinity College, Cambridge. Although no prosecution was brought, Phillipps's suspicions were aroused and he refused to consent to the marriage. This led to the couple's elopement in 1842. Phillipps refused ever to see his daughter or Halliwell again.

In 1842, Halliwell published the first edition of Nursery Rhymes of England followed by Nursery Rhymes and Nursery Tales, containing the first printed version of the Three Little Pigs and a version of the Christmas carol The Twelve Days of Christmas.

From 1845 Halliwell was excluded from the library of the British Museum on account of the suspicion concerning his possession of some manuscripts which had been removed from the library of Trinity College, Cambridge. He published privately an explanation of the matter in 1845. Halliwell also had a habit, detested by bibliophiles, of cutting up seventeenth-century books and pasting parts he liked into scrapbooks. During his life he destroyed 800 books and made 3,600 scraps. In 1848 he published his Life of Shakespeare, illustrated by John Thomas Blight (1835–1911), which had several editions; in 1853–1865 a sumptuous edition, limited to 150 copies, of Shakespeare in folio, with full critical notes. After 1870 he entirely gave up textual criticism, and devoted his attention to elucidating the particulars of Shakespeare's life. He collated all the available facts and documents in relation to it, and exhausted the information to be found in local records in his Outlines of the Life of Shakespeare. He was instrumental in the purchase of New Place for the corporation of Stratford-on-Avon, and in the formation there of the Shakespeare museum.

He assumed the name of Phillipps in 1872, under the will of the grandfather of his first wife, Henrietta Phillipps. He took an active interest in the Camden Society, the Percy Society and the Shakespeare Society, for which he edited many early English and Elizabethan works. He died on 3 January 1889, and was buried in Patcham churchyard, near Hollingbury in East Sussex.

His house, Hollingbury Copse, near Brighton, was full of rare and curious works, and he generously gave many of them to Chetham's Library, Manchester, to the Morrab Library of Penzance, to the Smithsonian Institution, and to the library of the University of Edinburgh.

Works
His publications in all numbered more than sixty volumes, including:

 * (1840). The Connexion of Wales with the early Science of England.
 * (1840). A Few Notes on the History of the Discovery of the Composition of Water.
 * (1841). Shakespeariana. J. R. Smith (reissued by Cambridge University Press, 2009; ISBN 978-1-108-00002-4)
 * (1842). Cambridge Jokes: From the Seventeenth to the Twentieth Century. Thomas Stevenson, Tilt and Bogue (reissued by Cambridge University Press, 2009; ISBN 978-1-108-00122-9)
 * (1842). An Account of the European Manuscripts in the Chetham Library, Manchester.
 * (1843). The Nursery Rhymes of England, obtained principally from oral tradition.
 * (1843). A Collection of Pieces in the Dialect of Zummerzet.
 * (1846). A Dictionary of Archaic & Provincial Words, Obsolete Phrases, Proverbs & Ancient Customs, From the Fourteenth Century, Volume I A-I
 * (1847). A Dictionary of Archaic & Provincial Words, Obsolete Phrases, Proverbs & Ancient Customs, From the Fourteenth Century, Volume II J-Z
 * (1847). An historical sketch of the Provincial Dialects of England, illustrated by numerous examples.
 * (1848). Some account of the Vernon Manuscript, a volume of early English poetry preserved in the Bodleian Library.
 * (1849). Notices of the History and Antiquities of Islip.
 * (1849). Popular Rhymes and Nursery Tales: a sequel to The Nursery Rhymes of England.
 * (1851). Notes on Ascertaining the Value, and Directions for the Preservation, of Old Books, Manuscripts, Deeds and Family Papers.
 * (1854). Brief Observations on some Ancient Systems of Notation.
 * (1855). Contributions to English Lexicography.
 * (1856). A Catalogue of an Unique Collection of Ancient English Broadside Ballads, with notes of the tunes and imprints.
 * (1859). An Introduction to the Evidences of Christianity.
 * (1860). Notes of Family Excursions in North Wales, taken chiefly from Rhyl, Abergele, Llandudno, and Bangor.
 * (1860). A Skeleton Hand-List of the Early Quarto editions of the Plays of Shakespeare; with notices of the old impressions of the Poems.
 * (1861). Rambles in Western Cornwall by the Footsteps of the Giants; with notes on the Celtic remains of the Land's End district and the Islands of Scilly.
 * (1863). A Calendar of the Records at Stratford-on-Avon
 * (1864). An Historical Account of the New Place, Stratford-Upon-Avon, the Last Residence of Shakespeare
 * (1866). A Hand-Book Index to the Works of Shakespeare: Including References to the Phrases, Manners, Customs, Proverbs, Songs, Particles, &c., Which Are Used or Alluded to by the Great Dramatist. J.E. Adlard (reissued by Cambridge University Press, 2009; ISBN 978-1-108-00121-2)
 * (1884). The Stratford Records and the Shakespeare Autotypes. A brief review of singular delusions that are current at Stratford-on-Avon

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

title: James Halliwell-Phillipps


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The Firm (album)

The Firm is the first studio album by British rock band the Firm, released by Atlantic Records on 11 February 1985. Its tracks range from the epic "Midnight Moonlight", based on a previously unreleased song by Led Zeppelin called "Swan Song" – first tinkered with during the Physical Graffiti sessions – to the commercially successful "Radioactive". "Closer" employs a horn section to subtle effect. The album also includes a version of the Righteous Brothers' hit "You've Lost That Lovin' Feelin'".

The Firm peaked at No. 17 on the Billboard 200 chart, and reached No. 15 on the UK Albums Chart. The song "Radioactive" topped Billboard's Top Rock Tracks chart for one week.

Track listing
All tracks are written by Jimmy Page and Paul Rodgers except where noted

The Firm

 * Paul Rodgers – lead vocals, acoustic and electric guitars, production
 * Jimmy Page – acoustic and electric guitars, production
 * Tony Franklin – fretless bass, keyboards, synthesizer, backing vocals
 * Chris Slade – drums and percussion

Additional musicians

 * Steve Dawson – trumpet on "Closer"
 * Paul "Shilts" Weimar – baritone saxophone on "Closer"
 * Willie Garnett – tenor saxophone on "Closer"
 * Don Weller – tenor saxophone solo on "Closer"
 * Sam Brown, Helen Chappelle & Joy Yates – backing vocals on "You've Lost That Lovin' Feeling" & "Midnight Moonlight"

Production personnel

 * Stuart Epps – engineering
 * Gordon Vicary – mastering
 * Steve Maher – cover artwork
 * Steve Privett – tape operation; supplier of tea, gin and tonics

title: The Firm (album)


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Rapid City (disambiguation)

Rapid City is a city in South Dakota

Rapid City may also refer to:

Canada

 * Rapid City, Manitoba

United States

 * Rapids City, Illinois
 * Rapid City, Michigan, an unincorporated community of Clearwater Township, Michigan

title: Rapid City (disambiguation)


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Stevensville

Stevensville, the name of several places, may refer to:

 * Australia
 * Stevensville, Victoria

 * Canada
 * Stevensville, Ontario

 * United States
 * Stevensville, Maryland
 * Stevensville, Michigan
 * Stevensville, Montana
 * Stevensville, Pennsylvania
 * Stevensville, Vermont
 * Stevensville, Virginia

title: Stevensville


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Ernst Heinkel

Dr. Ernst Heinkel (24 January 1888 – 30 January 1958) was a German aircraft designer, manufacturer, Wehrwirtschaftsführer in Nazi Germany, and member of the Nazi party. His company Heinkel Flugzeugwerke produced the Heinkel He 178, the world's first turbojet-powered aircraft, and the Heinkel He 176, the first rocket aircraft.

Early life
Heinkel was born in Grunbach, today a part of Remshalden. As a young man he became an apprentice machinist at a foundry. Heinkel studied at the Technical Academy of Stuttgart, where he initially became interested in aviation through a fascination with Zeppelins, and in 1909 attended an international airshow in Frankfurt am Main. He decided that flight was the future of transportation, and the following year he built his first aircraft, working from a set of plans by Henri Farman. Heinkel crashed it in 1911 and suffered severe injuries.

Albatros Flugzeugwerke
Soon afterwards, he got a job at Luft-Verkehrs Gesellschaft (LVG), who were building Farman aircraft. From there, he went to Albatros. after the war Heinkel claimed to have designed the Albatros B.II, a successful reconnaissance and trainer aircraft used during the early stages of the First World War, but its main designer was in fact Robert Thelen. His aircraft were used by the Austro-Hungarian army and Germany's Kaiserliche Marine during the war. After leaving Albatros, Heinkel designed several land- and seaplanes for the Hansa-Brandenburg company starting in 1914.

Heinkel-Flugzeugwerke
In 1921, Heinkel was appointed head designer of the recently re-established Caspar-Werke, but soon left after a dispute over ownership of a design. In 1922 he established the Heinkel-Flugzeugwerke company at Warnemünde. Due to the restrictions placed on German aircraft manufacturing by the Treaty of Versailles, Heinkel looked overseas for contracts, with some seaplane designs being licence-built in Sweden and working on catapult-launched seaplanes for the Imperial Japanese Navy. He installed a similar catapult on the ocean liner Bremen for launching mail planes.

Versailles Treaty violations
Between 1921 and 1924, the Japanese government placed several orders with Heinkel's company, and helped him skirt the Versailles Treaty, which banned the construction of military aircraft in Germany, by informing the company of facility inspections by allied commissions in advance. Japan was part of the inspection commission. Heinkel hid his aircraft in dunes behind his plant and they were never discovered during inspections. Heinkel noted in his memoirs that his company's relationship with Japan in the 1920s led to decades of cooperation.

1933-1945
After Adolf Hitler came to power, designs by Heinkel's firm formed a vital part of the Luftwaffe's growing strength in the years leading up to the Second World War. This included the Heinkel He 59, the Heinkel He 115 and the Heinkel He 111. He was designated a Wehrwirtschaftführer (~ defence industry leader) by the German government for his commitment to rearmament.

Heinkel was passionate about high-speed flight, and was keen on exploring alternative forms of aircraft propulsion. He donated aircraft to Wernher von Braun who was investigating rocket propulsion for aircraft, as well as sponsoring the research of Hans von Ohain into turbojet engines, leading to the flight of the Heinkel He 178, the first aircraft to fly solely under turbojet power, on August 27, 1939.

Heinkel had been a critic of Hitler's regime, having been forced to fire Jewish designers and staff in 1933; he was, however, a member of the Nazi party, and was awarded the German National Prize for Art and Science in 1938, one of the rarest honors of the German government. Heinkel Flugzeugwerke used forced Jewish labor, starting in 1941.

In 1942 the government "nationalised" the Heinkel works. In practice, this meant that Heinkel was detained until he sold his controlling interest in his factories to Hermann Göring. Heinkel moved to Vienna and started a new design bureau and corporate offices in Vienna's Schwechat suburb, establishing manufacturing facilities in Zwölfaxing and Floridsdorf as the Heinkel-Sud complex for his firm, the original Rostock-"Marienehe" plant (today's Rostock-Schmarl neighborhood) becoming the Heinkel-Nord facility. It was at the Heinkel-Sud offices that Dr. Heinkel worked on the Heinkel He 274 four-engined high-altitude heavy bomber design - as one of the trio of proposals for aircraft designs to succeed his firm's failed Heinkel He 177A heavy bomber — including an unbuilt Amerikabomber design - until the war's end concluded the production of the firm's Spatz single-seat jet fighter.

Post-war
In July 1945 Heinkel was captured by American troops and held for possible exploitation and/or possible trial under Operation Dustbin, and was held for a time at Kransberg Castle, near Frankfurt.

With Germany forbidden from manufacturing aircraft by the Allies, Heinkel used his company's facilities to build private transportation. In 1953 Heinkel began production of the Tourist scooter, followed by the Perle moped in 1954. In 1956 he introduced the Heinkel Kabine bubble car. Bubble car and moped production ceased shortly after the restriction on aircraft manufacture was lifted, but scooter production continued until 1965. In 1959, Heinkel's company was sued by Edmund Bartl for being enriched by slave labour during World War II; however, the German Supreme Court dismissed his claims for filing too late, and ordered Bartl to pay court costs and attorney's fees.

Death and legacy
Ernst Heinkel died in 1958 in Stuttgart. His autobiography, Stürmisches Leben, was published in 1956 and translated into English as He1000 in its British edition and Stormy Life: Memoirs of a Pioneer of the Air Age in its US edition.

In 1981, Heinkel was inducted into the International Air & Space Hall of Fame at the San Diego Air & Space Museum.

title: Ernst Heinkel


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Plachutta

The Plachutta is a device found in chess problems wherein a piece is sacrificially positioned in blockade to deny coverage of multiple distant squares required by the opposition. For example, two of an opponent's bishops, queen, or rooks are defending locations through an intersection square, and an enemy unit moved into that square blocks disrupts coverage in such a way that, even if captured, the previous defensive situation cannot be restored.

The Plachutta is named after Joseph Plachutta (1827–1883), and related to a number of other problem themes: it can be regarded as a Würzburg–Plachutta brought about by a sacrifice on the critical square (a Würzburg-Plachutta itself being a pair of Holzhausen interferences); or it can be thought of as a Novotny with similarly moving (rather than differently moving) black pieces involved (a Novotny itself being a Grimshaw brought about by a white sacrifice on the critical square). It can also be compared to the anti-Bristol, in which two similarly moving black pieces interfere with each other along the same line.

1.
The problem to the right is a relatively simple example by William Shinkman, published in White Rooks, 1910. It is a mate in three (white moves first and must checkmate black in three moves against any defence). The (first move of the solution) is 1.d5. Examining the initial position reveals why this works: white would like to play either 1.Ra8 or 1.Rg8, but the former is prevented by black's bishop and the latter is prevented by black's queen. 1.d5 blocks the paths of both black pieces to these squares, and whichever black piece takes the pawn interferes with the other and has to defend against both threats itself (to use chess jargon, it becomes overloaded). So, if 1...Qxd5 white can play 2.Ra8+ Qxa8, when the queen is deflected from her defence of g8, allowing 3.Rg8#, while if 1...Bxd5 white can play 2.Rg8+ Bxg8, deflecting the bishop from defence of a8, allowing 3.Ra8#.

2.
To the right is another relatively simple example, but this time it is two rooks, rather than bishop and queen, involved in the interferences. The problem, by D. J. Densmore, published in the Gazette-Times, 1916, is another mate in three. The key is 1.Nb7, which interferes with both rooks and so threatens both 2.Rh7# and 2.Rb1#. Black can defend with Raxb7, but this overloads the capturing rook, so white can play 2.Rb1+ Rxb1 3.Rh7#. The other capture is similar: 1...Rbxb7 2.Rh7+ Rxh7 3.Rb1#. Whichever rook captures, it interferes with the other and becomes overloaded, having to defend against two threats on its own.

3.
A more sophisticated modern example is the award-winning mate-in-four problem to the right by Aleksandr N. Pankrat'ev and Josip Varga, which was published in Sahovski Glasnik in 1991 and won 1st prize. White begins with 1.e3, adding protection to d4 and threatening 2.Rc5#. Black's two main defenses are the two captures on e3, but each one allows a different Plachutta interference by White on move 2. If 1...Rxe3, White plays 2.f4!, a Plachutta interference with the queen and bishop: 2...Qxf4 allows 3.Nxe3+ Qxe3 4.Nxe5# and 2...Bxf4 allows 3.Nxe5+ Bxe5 4.Nxe3#. If 1...Bxe3, White plays 2.Bb3+!, a Plachutta interference with the two black rooks: 2...Rbxb3 allows 3.Nxe3+ Rxe3 4.Nb6# and 2...Raxb3 allows 3.Nb6+ Rxb6 4.Nxe3#.

 * 1.e3 anything-else 2. Rc5#
 * 1.e3 Rxe3 2.f4 Qxf4 allows 3.Nxe3+ Qxe3 4.Nxe5#.
 * 1.e3 Rxe3 2.f4 Bxf4 allows 3.Nxe5+ Bxe5 4.Nxe3#.
 * 1.e3 Bxe3 2.Bb3+ Rbxb3 allows 3.Nxe3+ Rxe3 4.Nb6#.
 * 1.e3 Bxe3 2.Bb3+ Raxb3 allows 3.Nb6+ Rxb6 4.Nxe3#

4.
Although the term Plachutta is confined to the world of chess problems, not being used in a wider chess context, the underlying Plachutta pattern does occasionally (though rarely) appear in an actual game. One example is to the right, a position which occurred in a 1914 game between Siegbert Tarrasch (with white) and a team of opponents consisting of Davide Marotti (who became the champion of Italy in 1921), E. Napoli, de Simone, and del Giudice. In the diagrammed position, the black queen defends against Qb7 and the rook on c8 defends against Rxc5. Tarrasch played 31.Bc7!, a Plachutta interference after which black cannot maintain control over both b7 and c5 (Black actually resigned after this move). If 31...Rxc7 the rook is overloaded, having to look after both the key squares: 32.Qb7+ Rxb7 and the rook is deflected from defence of c5, allowing 33.Rxc5#. If instead 31...Qxc7 it is the queen which is overloaded: 32.Rxc5+ Qxc5 deflects the queen from defence of b7, allowing 33.Qb7+ Kxa5 34.Ra1#.

title: Plachutta


text:
Corvallis

Corvallis may refer to:

Places

 * Corvallis, Montana, USA
 * Corvallis, Oregon, USA

Education

 * Corvallis High School (California)
 * Corvallis High School (Montana)
 * Corvallis High School (Oregon)

Others

 * Cessna 350 Corvalis light aircraft
 * Cessna 400 Corvalis light aircraft
 * Corvallis Gazette-Times
 * Corvallis Knights, baseball team
 * Corvallis Municipal Airport
 * Corvallis Pride, women's football team

title: Corvallis


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Alphabet Synthesis Machine

The Alphabet Synthesis Machine (2002) is a work of interactive art which makes use of genetic algorithms to "evolve" a set of glyphs similar in appearance to a real-world alphabet. Users create initial glyphs and the program takes over. As the creators of the project put it, their goal was "to bring about the specific feeling of semi-sense one experiences when one recognizes—- but cannot read—- the unfamiliar writing of another culture." The project was developed by Golan Levin, a new-media artist, in collaboration with Cassidy Curtis and Jonathan Feinberg.

title: Alphabet Synthesis Machine


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Jymie Merritt

Jymie Merritt (May 3, 1926 – April 10, 2020) was an American jazz double-bassist, Ampeg Baby Bass and bass guitar pioneer, band leader and composer. Merritt was a member of Art Blakey's Jazz Messengers group from 1957 until 1962. The same year he left Blakey's band, Merritt formed his own group, The Forerunners, which he led sporadically until his death in 2020. Merritt also worked as a sideman for blues and jazz musicians such as Bull Moose Jackson, B. B. King, Chet Baker, Max Roach, Dizzy Gillespie, and Lee Morgan.

Early life
Raised in Philadelphia, Pennsylvania, Jymie, born James Raleigh Merritt, was the son of Agnes Merritt (née Robinson), a choral director, voice and piano teacher, and Raleigh Howard "RH" Merritt, a businessman and author. After serving in the U.S. Army during World War II from 1944 to 1946 Jymie returned home to work for a short time in his father's real estate business, and after a brief flirtation with the clarinet he was inspired by a Duke Ellington recording featuring bassist Jimmy Blanton. Encouraged by his mother he studied with Carl Torello, double bassist for the Philadelphia Orchestra, and at the Ornstein School of Music in Philadelphia.

Career highlights
Jymie Merritt worked in jazz, R&B, and blues. In the early 1950s he toured with rock and roll musicians Bull Moose Jackson and Chris Powell moving on to work with bluesman BB King from 1955 to 1957.

In 1957, Merritt moved to Manhattan, New York, to work with Art Blakey and the Jazz Messengers. The Messenger ensemble Merritt joined featured his friend Benny Golson as well as Bobby Timmons and Lee Morgan. Merritt's touring and recording with Blakey extended until 1962, when an unknown ailment forced him to stop touring.

By 1964, Merritt was back, working with the trumpeter and vocalist Chet Baker, and is featured prominently in Baker's unfinished autobiography published under the title As Though I Had Wings: The Lost Memoir.

From 1965 to 1968, Merritt worked with the drummer, composer and activist Max Roach, not only in the rhythm section but as a composer, recording "Nommo" on Roach's Atlantic album Drums Unlimited (1966). "Nommo" would earn Merritt a nomination for Best Jazz Composer in DownBeat magazine's Critics Poll.

Merritt left Max Roach in the late 1960s to work with trumpeter Dizzy Gillespie, appearing with Gillespie's band on The Dick Cavett Show.

One of Jymie Merritt's most productive showcases as a composer was when he reunited with his former Jazz Messenger Lee Morgan. Morgan's Blue Note album Live at the Lighthouse (1970) featuring Merritt's composition "Absolutions" (recorded earlier by Max Roach).

In 1962, Jymie Merritt formed and fronted the Forerunners in Philadelphia, Pennsylvania. The band, which evolved into a music cooperative exploring Merritt's own system of chord inversions, harmonics, and unique approaches to composition and rehearsals, produced a lexicon of its own known as the "Forerunner system" or concept. The Forerunner concept in its early days culminated in Merritt's expansive composition "Visions of the Ghost Dance". Among the original members of the Forerunner band were Odean Pope, Kenny Lowe, Donald Bailey, and September Wrice. This group performed regularly in and around Philadelphia for five years, until Merritt joined Max Roach's band. Pope also joined Roach's band, playing with him into the 1970s. Forerunner was on and off periodically from the 1960s through the 1980s, depending on what band Merritt was playing with at the time as well as how his health was. Saxophonist Bobby Zankel was a member of the second incarnation of the band when he joined in 1982, which also included Alan Nelson, Odean Pope, Julian Pressley, Colmore Duncan, and Warren McLendon. Zankel is primarily known as an alto saxophonist, but played baritone sax with the band, and described the role of the sax section over solos as taking on an accompanying role, where they would always play under the soloist, comparing it to the typical role of the bassist but in the sax section." Approaching his 90th birthday Merritt continued to rehearse and perform with the current incarnation of The Forerunners, some of whom had been with the ensemble from its inception.

Pioneer of the electric bass
Merritt joined the Bull Moose Jackson band in 1949, and was an early adopter of the Ampeg Baby bass (a hybrid acoustic-electric instrument). Merritt recalls when he first bought a Fender bass guitar:

"Now all this time, I had been playing electric bass, from about the first year of service with the Bull Moose band. We were out in Oklahoma somewhere, when Benny Golson saw this Western band, what you call a hillbilly band, with a fellow playing what looked like a guitar and sounded like a bass. Benny got me over to hear this and we later saw one in a music store. Benny went in for some reeds or something, so I tried a Fender electric bass and that night I took it to work. The owner let me take it and I tried it out working and nobody raised any objection. I had been having trouble with my own bass, one of the assembly line types, so I was in the market for a new bass. Anyway, I got curious and bought the thing and played it for the next seven years or so. I guess at the time I was the only one in jazz playing an electric bass. Certainly, I’m pretty sure Monk Montgomery wasn’t playing one because we used to see him in Minneapolis and he was always interested to see the instrument."

Awards and honors
In November 2013, along with friend and fellow bassist Reggie Workman, Jymie Merritt received the Clef Club of Philadelphia's Living Legend, Jazz Award.

At the 2009 Philadelphia Jazz Fair, produced by musician and professor Don Glanden, Philadelphia's University of the Arts and the Jazz Heritage Project honored Jymie Merritt and the jazz organist Trudy Pitts with the Jazz Heritage Award. Merritt's award was presented to him by another great Philadelphia bassist, the late Charles Fambrough.

In addition, Jymie Merritt was honored with the Don Redman Heritage Award in June 2008 at a ceremony and concert in Harper's Ferry, West Virginia at the annual event sponsored by the Harpers Ferry Historical Association and the Jefferson County NAACP in cooperation with the Don Redman Heritage Society of Piedmont, West Virginia.

Personal life
Merritt's marriage to Dorothy Viola Small (d. 2008) produced five children: Mharlyn Merritt, a writer and vocalist who received a National Endowment for the Arts Fellowship for Jazz Performance in 1988; Marlon Merritt, an accomplished guitarist and retired career Army veteran of the Iraqi War; Martyn Merritt (deceased), world traveler, bon vivant and classical pianist who studied with internationally acclaimed pianist Leon Bates; Marvon Merritt, percussionist and drummer, and Mike Merritt, a renowned bassist in his own right who has performed and recorded with Levon Helm, Phoebe Snow, Johnny Copeland, B. B. King and many other world-class musicians. Mike is best known as the bassist for the Basic Cable Band on Conan O'Brien's TBS talk-show. Continuing the family's musical heritage in 2005 Mike co-produced along with his sister Mharlyn an independent CD on the EMerrittus label featuring brother Marlon on guitar, Uri Caine, Al Kooper, Lew Soloff and the Vivino Brothers entitled "Alone Together".

Merritt had a younger brother, LeRoy Merritt, an amateur artist and arts and crafts enthusiast who lived in West Philadelphia, Pennsylvania.

Merritt lived in Center City, Philadelphia, with his wife Ave and his cat Jazzie. He died on April 10, 2020, of liver cancer in Philadelphia, aged 93.

As sideman
With Art Blakey and the Jazz Messengers With Chet Baker With Sonny Clark With Curtis Fuller With Benny Golson With Lee Morgan With Max Roach
 * Moanin' (Blue Note, 1958)
 * 1958 – Paris Olympia (Fontana, 1958)
 * Des Femmes Disparaissent (Soundtrack) (Fontana, 1958)
 * At the Jazz Corner of the World (Blue Note, 1959)
 * Just Coolin' (Blue Note, 1959)
 * Les Liaisons Dangereuses 1960 (Fontana, 1959) – Original Soundtrack with Barney Wilen
 * Africaine (Blue Note, 1959)
 * Paris Jam Session (1959)
 * The Big Beat (Blue Note, 1960)
 * Like Someone in Love (Blue Note, 1960)
 * A Night in Tunisia (Blue Note, 1960)
 * Mosaic (Blue Note, 1961)
 * A Day with Art Blakey and the Jazz Messengers (1961)
 * Pisces (1961)
 * The Freedom Rider (1961)
 * Roots & Herbs (1961)
 * Three Blind Mice (1962)
 * Buhaina's Delight (1963)
 * The Most Important Jazz Album of 1964/65 (Colpix, 1964)
 * Standards (Blue Note, 1959)
 * South American Cookin' (Epic, 1961)
 * Soul Trombone (Impulse!, 1961)
 * The Other Side of Benny Golson (Riverside, 1958)
 * Live at the Lighthouse (Blue Note, 1969)
 * The Last Session (Blue Note, 1972)
 * Drums Unlimited (Atlantic, 1965)
 * Members, Don't Git Weary (Atlantic, 1968)
 * With Jimmy Witherspoon
 * The Blues Is Now (1967)
 * With Wayne Shorter
 * Wayning Moments (1962)

title: Jymie Merritt


text:
Winch

A winch is a mechanical device that is used to pull in (wind up) or let out (wind out) or otherwise adjust the tension of a rope or wire rope (also called "cable" or "wire cable").

In its simplest form, it consists of a spool (or drum) attached to a hand crank. Traditionally, winches on ships accumulated wire or rope on the drum; those that do not accumulate, and instead pass on the wire/rope (see yacht photo above), are called capstans. Despite this, sailboat capstans are most often referred to as winches. Winches are the basis of such machines as tow trucks, steam shovels and elevators. More complex designs have gear assemblies and can be powered by electric, hydraulic, pneumatic or internal combustion drives. It might include a solenoid brake and/or a mechanical brake or ratchet and pawl which prevents it unwinding unless the pawl is retracted. The rope may be stored on the winch. When trimming a line on a sailboat, the crew member turns the winch handle with one hand, while tailing (pulling on the loose tail end) with the other to maintain tension on the turns. Some winches have a "stripper" or cleat to maintain tension. These are known as "self-tailing" winches.

In the Ancient World
The earliest literary reference to a winch can be found in the account of Herodotus of Halicarnassus on the Persian Wars (Histories 7.36), where he describes how wooden winches were used to tighten the cables for a pontoon bridge across the Hellespont in 480 BCE. Winches may have been employed even earlier in Assyria.

By the 4th century BCE, winch and pulley hoists were regarded by Aristotle as common for architectural use (Mech. 18; 853b10-13).

In the 20th Century
The yacht Reliance, American defender of the 1903 America's Cup, was the first racing boat to be fitted with modern winches below decks. The Reliance's competitors relied on muscle power using topside mounted capstans and windlasses, which would soon be replaced in most applications by winches, including on fishing boats, where they are used to bring in the fishing nets.

Vehicle recovery
The main feature that legally distinguishes a tow truck from a conventional truck in many jurisdictions is the presence of a winch, which is used to either extract disabled or immobilized vehicles, or to load them onto flatbed/tilt and load type tow trucks. These may be electrically or hydraulically powered from a power take-off, and is wound with a wire cable and equipped with a hook. Snatch blocks may be used to change direction or increase the pulling power and a variety of specialized hooks may be attached to the main hook, including hooks which attach to specific parts of the car. J-hooks, which look somewhat like blunt meat hooks are used to hook around axles. Mini-J hooks can be used if there is a tow loop provided, and R and T hooks are designed to hook into slots cut by the manufacturer in the underside of the frame on many cars. Axle straps may also be used, when there are few other places to attach.

Off-road vehicles
Off-road vehicles may be equipped with recovery tools such as winches on the front and back bumpers, usually mounted to a winch bar or frame mounted metal bumper. Less commonly it is mounted on a specialised metal plate "hidden winch mount" behind the vehicle's stock bumper, this is referred to as a "hidden winch" as the hook and fairlead hides behind a flip-up front number plate, the winch itself is not visible. The snubbing winch is used to pull vehicles out of mud, snow, sand, rocks, and water, and to pull vehicles through or over obstacles. The winch is made of cable made up of a braided synthetic rope, or a steel cable wrapped around a motorized drum. Each is controlled electronically, allowing the operator to control the winch speed. Modern vehicles typically use electric winches running off the car's 12V starter or 24V secondary battery. The winch is either controlled with a detachable cable, a button inside the car or wireless remote. Older vehicles may have a PTO winch, controlled via the car's transmission, a secondary clutch maybe used so the vehicle does not need to be moving while winching. Some winches are powered by the pressure generated in the hydraulic steering system. The high lift jack or come-along is used for manual winching.

Aircraft use
Gliders are often launched using a winch mounted on a trailer or heavy vehicle. This method is widely used at many European gliding clubs, as an inexpensive alternative to aerotowing. The engine is usually a gas/petrol, LPG or diesel, though hydraulic fluid engines and electrical motors are also used. The winch pulls in 1000 to 1600 m of high-tensile steel wire or a synthetic fibre cable, attached at the other end to the glider. The cable is released at a height of about 400 to 700 m after a short, steep climb.

Search and Rescue helicopters are often equipped with winches to avoid having to get the helicopter dangerously close to obstacles, or into ocean troughs, allowing rescue teams to be lowered and evacuees to be extricated while the helicopter hovers overhead. Helicopter winches are also used for heli-logging and for airlifting oversized cargo, such as vehicles and other aircraft, although the winch in these cases is only used to reduce the hazards to flying with an loose cable hanging below the helicopter.

Stationary balloons, such as the barrage balloons used during the Second World War to discourage marauding aircraft, and the Kite balloons used during the First World War for artillery spotting are usually tethered with a winch, which can be used to lower the balloon, either to relocate it, or to bring it down quickly to prevent it being shot down by enemy aircraft. Larger man carrying kites often used winches to raise and lower them.

Towed gunnery targets, used to train anti-aircraft gunners, and both fighter pilots and aircraft gunners, are run out behind the target tug aircraft for practice, and winched in for take-off and landing.

Before advances were made in antennas in the 1950s, radio aerials were quite long, and needed to be winched out for use, and winched back in for landing. Failure to do so would then damage the aerial, as happened to Amelia Earhart on one of the legs of her last flight.

Theatre

Winches are frequently used as elements of backstage mechanics to move scenery in large theatrical productions. They are often embedded in the stage floor and used to move large set pieces on and off.

Wakeskate winch
Wakeskate winching is a sport where a person on a waterski or snowboard is propelled across the water with a winch. The winch consists of a gas-powered engine, spool, rope, frame, and sometimes a simple transmission. The person being towed walks (or swims) away from the winch, while extending the rope. When the winch is engaged, it pulls the boarder in at a speed ranging from 25 to 40 km/h. The winch may be mounted to a vehicle, set into the ground by stakes, or tied to a tree. The cable may also be run through pulleys mounted offshore so that it pulls the person away from where the winch is located, and multiple pulleys may be used to multiply the force applied by a small but high revving motor instead of using a transmission.

Lever winch
Lever winches are winches that use self-gripping jaws instead of spools to move rope or wire through the winch. Powered by moving a handle back and forth, they allow one person to move objects several tons in weight.

Snubbing winch
This is a vertical spool with a ratchet mechanism similar to a conventional winch, but with no crank handle or other form of drive. The line is wrapped around the spool and can be tightened or reeled in by pulling the tail line. The winch takes the load once the pull is stopped with little operator tension needed to hold it. These also allow controlled release of the tension by the operator using the friction of the line around the ratcheted spool. They are used on small sailing boats and dinghies to control sheets and other lines, and in larger applications to supplement and relieve tension on the primary winches.

Air winch
An air winch, sometimes known as an air hoist or air tugger, is an air-powered version of a winch. It is commonly used for the lifting and the suspension of materials. In the oil and gas, construction, and maritime industries, air winches are frequently preferred to electric, diesel, and hydraulic winches because of their durability, versatility, and safety.

title: Winch


text:
Gaspare Spontini

Gaspare Luigi Pacifico Spontini (14 November 1774 – 24 January 1851) was an Italian opera composer and conductor from the classical era. During the first two decades of the 19th century, Spontini was an important figure in French opera, and composed over twenty works.

Biography
Born in Maiolati, Papal State (now Maiolati Spontini, Province of Ancona), he spent most of his career in Paris and Berlin, but returned to his place of birth at the end of his life. During the first two decades of the 19th century, Spontini was an important figure in French opera. In his more than twenty operas, Spontini strove to adapt Gluck's classical tragédie lyrique to the contemporary taste for melodrama, for grander spectacle (in Fernand Cortez for example), for enriched orchestral timbre, and for melodic invention allied to idiomatic expressiveness of words.

As a youth, Spontini studied at the Conservatorio della Pietà de' Turchini, one of four active music conservatories of Naples. Working his way from Italian city to city, he got his first break in Rome, with his successful comedy Li Puntigli delle Donne (Carnival 1793). In 1803, he went to Paris, where, on 11 February 1804, debuted his comic opera La Finta Filosofa, his Neapolitan success of 1799. In part on the recommendation of the comte de Rémusat and his literary countess, a dame du palais, Spontini circulated in the Imperial court, was made a member of the Académie Impériale de Musique and gained a court position as compositeur particulier de la chambre of the Empress in 1805.

Though Spontini's earlier successes were comedies, with the encouragement of Empress Joséphine in 1807, Spontini wrote his greatest success, the tragédie lyrique La Vestale, which has remained his best-known work. Its premiere at the Opéra in Paris established Spontini as one of the greatest Italian composers of his age. His contemporaries Cherubini, Beethoven, Weber, Rossini and Meyerbeer all considered it a masterpiece, and later composers such as Berlioz, Verdi, and Wagner admired it.

During the Peninsular War, Napoleon promoted works such as Gasparo Spontini's Fernand Cortez (1809), which concerned the Spanish conquest of Mexico under the reign of Charles V. In 1811, Spontini married Celeste Érard, the niece of the Parisian maker of pianos and harps Sébastien Érard; it was a happy marriage, though childless. He was made a chevalier of Napoleon's Legion of Honor; its Maltese cross hangs round his neck in the portrait by Nicolas-Eustache Maurin (illustration).

Under the changed political climate of the Bourbon Restoration, Spontini, closely identified with the former Empire, saw his opera Olimpie (1819, revised 1821, 1826) meet with indifference, leading him to leave Paris for Berlin, where his operas had already achieved success. There he became Kapellmeister and chief conductor at the Königliches Opernhaus, and in this period he composed the Prussian National Anthem "Borussia". There he also met the young Mendelssohn, but deprecated the 17-year old's opera Die Hochzeit des Camacho.

In 1842, a disillusioned Spontini, chagrined at the success of Giacomo Meyerbeer and others in Germany, returned to Italy, where he died in 1851.

Bibliography (French) Gaspare Spontini by Patrick Barbier, bleu nuit éditeur, 2017, 176 p. (ISBN 978-2-3588-4067-5)

For the opera

 * Li puntigli delle donne (1796)
 * L'eroismo ridicolo (1798)
 * Teseo riconosciuto (1798)
 * La fuga in maschera (1800)
 * Le metamorfosi di Pasquale (1802)
 * Milton (1804)
 * Julie, ou Le pot de fleurs (1805)
 * La vestale (1807)
 * Fernand Cortez (1809)
 * Olimpie (1819)
 * Nurmahal, oder das Rosenfest von Caschmir (1822)
 * Agnes von Hohenstaufen (1829)

Other compositions

 * L'eccelsa gara – Cantata, on a text by Luigi Balocchi (1806)
 * Tout le monde a tort – Vaudeville (1806)
 * Bacchanale des Danaïdes, for Antonio Salieri's Les Danaïdes (1817)
 * Borussia – Prussian anthem, on a text by Johann Friedrich Leopold Duncker (1818)
 * Tout deuil (1820)
 * Lalla Rûkh – Festspiel, on a text by S. H. Spicker, after Thomas Moore (1821)

Modern revivals
During the 20th century, Spontini's operas were only rarely performed, although several had their first revivals in years. Perhaps the most famous modern production was the revival of La vestale with Maria Callas at La Scala at the opening of the 1954 season, to mark the 180th anniversary of the composer's birth. The stage director was famed cinema director Luchino Visconti. That production was also the La Scala debut of tenor Franco Corelli. Callas recorded the arias "Tu che invoco" and "O Nume tutelar" from La vestale in 1955 (as did Rosa Ponselle in 1926). In 1969, conductor Fernando Previtali revived the opera, with soprano Leyla Gencer and baritone Renato Bruson. (An unofficial recording is in circulation.) In 1993, conductor Riccardo Muti recorded it in the original French language with Karen Huffstodt, Denyce Graves, Anthony Michaels-Moore and Dimitri Kavrakos.

Other revivals of Spontini include Agnes von Hohenstaufen in Italian as Agnese di Hohenstaufen at the Maggio Musicale festival in Florence in 1954, starring Franco Corelli and conducted by Vittorio Gui, and in Rome in 1970, with Montserrat Caballé and Antonietta Stella, conducted by Riccardo Muti, both recorded live. Fernand Cortez was revived in 1951, with a young Renata Tebaldi, at the San Carlo in Naples, conducted by Gabriele Santini. The premiere of the integral version of the work took place at the Erfurt (Germany) opera house (2006, Jean-Paul Penin, conductor).

title: Gaspare Spontini


text:
Talk:Knuth's up-arrow notation

Untitled
This could do with conversion to use TeX notation

I'll get right on it! Dysprosia

Can someone move this to "Knuth's up-arrow notation", please?

If it's gonna be moved, I'd vote for Knuth arrow. BTW I'd removed Ackermann function since Ackermann page no longer refers to it. Kwantus

use Knuth arrow for relatively small numbers LMAO! =) Kwantus

It was either that or relatively small large numbers! :) (Maybe smaller magnitude...) Dysprosia 05:49, 30 Aug 2003 (UTC)

I tried to set it so that 3(arrow arrow)5 was shown as also being equal to 3^(3^7625597484987), but couldn't get the notation right. Can someone fix that? DS 14:15, 7 May 2005 (UTC)

 * Done. - Gauge 23:03, 2 October 2005 (UTC)

327=273
Why is $$3^{3^3}$$ = 327, not 273? Thanks, --Abdull 23:12, 30 September 2005 (UTC)

 * 273 = (33)3 = 39 ≠ 327. Writing the exponentials as $$3^{3^3}$$ = pow(3, pow(3, pow(3, 1))), we see that we evaluate these functions from the inside out, so pow(3, pow(3, pow(3, 1))) = pow(3, pow(3, 3)) = pow(3, 27) = 327, rather than 273. - Gauge 22:59, 2 October 2005 (UTC)

 * Very big difference... 327 = 7,625,597,480,000 ≠ 273 = 19,683 Frozen Mists 21:59, 28 June 2007 (UTC)

Left-associative exponents and higher operators ARE used in some applications (although I can't site one offhand), but if you define higher operators based on left-association, you don't get essentially new operators, since in that case a^^b would = $$a^{(a-1)^b}$$, rather than a^a^...^a^a (b a's). —Preceding unsigned comment added by 24.165.184.37 (talk) 23:12, 11 March 2008 (UTC)

Study (generalization to non-integer arguments)
As I said in the article on the closely related Hyper Operator, I think it would beinteresting to investigate the notation for a non-natural number of arrows, equivalent to: $$a^{(n)}b|n\notin\mathbb{N}$$ I've already defined over all integers n, but I think it would be interesting to expand this to all reals, or possibly even all complex numbers. He Who Is 01:02, 23 April 2006 (UTC)

 * Sounds like hard work! I hope you can do it. Kaimiddleton 07:54, 22 April 2006 (UTC)

It can't be done unfortunately, at least not with any degree of rigour or consistency, because unlike addition and multiplication exponentiation is *neither associative nor commutative; hence in general a^^(b^^c) =/= (a^^b)^^c and a^^b =/= b^^a. Hence you get anomalies such as 2^^(1/3) < 2^^(2/7) even though 1/3 > 2/7.

A few people have worked on the problem and found partial solutions, and these may be worth looking into, but a definitive answer is always likely to prove elusive.
 * I am indebted to Dr. Roger Wheeler of Leicester University who pointed out to me a few years back that this is the reason any such attempts will fail.

Meltingpot (talk) 16:00, 6 September 2008 (UTC)

 * This argument against noninteger arguments (sic/lol) seems fallacious. Usual exponentiation does not obey the rule (a^b)^c =?= a^(b^c) nor a^b =?= b^a, yet exponentiation is well defined for all positive real numbers (and more, specifically: complex numbers that are not negative reals).
 * So, these apparent contradictions based on the premise that we have to have rules which we can't and therefore don't expect. I think various (e.g., "log-linear") interpolations could be possible - e.g.:
 * between 2^^2 = 4 = 2^2, 2^^3 = 16 = 2^4, 2^^4 = 65536 = 2^16 and 2^^5 = 2^65536, it seems quite natural to have
 * 2^^2.5 = 2^3, 2^^3.5 = 2^8 = 2^2^3 and 2^^4.5 = 2^256 = 2^2^8; with obvious generalisation
 * 2^^(2+x) = 2^(2+2x), 2^^(3+x) = 2^2^(2+2x), 2^^(4+x) = 2^2^2^(2+2x), etc., when 0 <= x <= 1.
 * (I don't particularly like this idea, which came first to my mind. But the fractional derivatives are defined similarly, by separating the integer part and the fractional part. I guess that it should not be difficult to find a slightly "smoother" generalisation...) — MFH:Talk 22:31, 20 June 2024 (UTC)
 * PS: a different, probably better generalisation comes to mind: append a final exponent 2^x where x is the fractional part: for x=0 it's 1 and does not change the value, for x=1 it's 2 and gives the next term in the series. This will obviously work for any other base (e.g., 3, 4, 5, ...) instead of 2. (It will *not* yield 2^^2.5 = 8 but rather 2^^2.5 = 2^2^sqrt(2) ≈ 6.3429... — MFH:Talk 22:46, 20 June 2024 (UTC)

Formal definition
Okay, what's the formal definition of $$ a \uparrow^n b $$ when $$ n = 0 $$? It was originally written as 1 in the formal notation, but as $$ ab $$ in the tables below. Now the line has been removed altogether, meaning the function is currently undefined for $$ n = 0 $$. It should be either

a\uparrow^n b= \left\{ \begin{matrix} a^b, & n \isin \{ 0, 1 \}; \\ a\uparrow^{n-1}(a\uparrow^n(b-1)), & \mbox{otherwise} \end{matrix} \right. $$

or

a\uparrow^n b= \left\{ \begin{matrix} ab, & n = 0; \\ a^b, & n = 1; \\ a\uparrow^{n-1}(a\uparrow^n(b-1)), & \mbox{otherwise} \end{matrix} \right. $$.

cBuckley (Talk • Contribs) 13:31, 21 May 2006 (UTC)

 * The article had b=0, not n = 0. As the article stands, the up-arrow is defined for n ≥ 1. Dysprosia 13:40, 21 May 2006 (UTC)

 * Okay, my mistake. So what's with the first line in each of the tables? cBuckley (Talk • Contribs) 14:26, 21 May 2006 (UTC)

I see no reason why it isn't defined for n = 0. The definition $$a\uparrow^n b = a^{(n-2)} b$$ gives a perfect definition for all n ≥ 2; n $$\in\mathbb{Z}$$He Who I s 20:24, 21 May 2006 (UTC)

 * Well, what would be the point of that? The arrow notation should be used when it should be used, so there's no practical need to make such a definition when one can resort to conventional notation. Dysprosia 22:35, 21 May 2006 (UTC)

I don't mean to say that there is a practical need for it, I merely mean to say that because of that definition, the Knuth up-arrow notation is defined for all n greater than of equal to -2.He Who Is 22:31, 22 May 2006 (UTC)

 * I think you mean to say that the up-arrow is defined for all n ≥ 2: as it stands, the hyper operator isn't defined for negative n. Dysprosia 22:38, 22 May 2006 (UTC)

Actually I did mean negative two, because the standard notation is defined for all n greater than or equal to zero (or depending on your point of view, all integers), and $$a\uparrow^n b = a^{n-2} b$$ . But, as you said, anyone can resort to the standard notation if they have to, so there's no reason to argue this point.He Who Is 19:45, 23 May 2006 (UTC)

I haven't come across a source with a definition for zero or less n arrows. There may be an inductive argument that $$a\uparrow^0 b = a$$ if b is non-zero. Unfortunately, this would need to be backed up by a citation. We need to avoid original research. --Ashawley (talk) 18:29, 28 March 2020 (UTC)

We currently have... - The general definition of the notation (by recursion) is as follows (for integer a, positive integer n and non-negative integer b):

a\uparrow^n b=  \begin{cases} a^b, & \text{if }n=1; \\ 1, & \text{if }b=0; \\ a\uparrow^{n-1}(a\uparrow^{n}(b-1)), & \text{otherwise } \end{cases} $$ -

I feel that this would look better as:

a\uparrow^n b=  \begin{cases} 1, & \text{if }b=0; \\ a^b, & \text{if }n=1; \\ a\uparrow^{n-1}(a\uparrow^{n}(b-1)), & \text{otherwise } \end{cases} $$ So that the three expressions $$ 1, a^b, a\uparrow^{n-1}(a\uparrow^{n}(b-1)) $$ are in order of 'increasing complexity'. Also, any tiny ambiguity about the value of $$ 0\uparrow 0 $$ would be immediately resolved. Clive tooth (talk) 17:14, 29 March 2020 (UTC)

Bogus table row?
The first row in "Tables of Values" is for m = 0, but the definition above says that that number must be greater than or equal to one. This seems inconsistent.

-- Offby1 (talk) 00:05, 29 March 2010 (UTC)

 * I agree. Seems like there's no way to have zero arrows... --Ashawley (talk) 22:06, 19 March 2019 (UTC)

How much is $$a\uparrow\uparrow 0$$? 0 or 1 or another number? -- Athanatophobos August 4th 2016

 * Well as usual it is up to us to decide what we want it to mean, but the sensible choice would be 1 to preserve the equation $$a\uparrow\uparrow n=a\uparrow(a\uparrow\uparrow(n-1))$$. Kestrelsummer (talk) 23:10, 30 October 2016 (UTC)

OR for citation
I understand that this is WP:OR, but it's the "proof" for the citation (or an estimate).

let's define T=SQRT(10). (T is approximately equal to 3.16, which is close enough to 3 for something like "moderately sized hard drives"). Using T as a base, 10 (in decimal) would be expressed as 100T. 10010 is expressed as 10000T. The amount of space on a hard drive (d) it would take to store a number (using ASCII) on a hard drive is one byte per digit. For the powers of 10, let N be the power. the desired number to store is 10N. Expressed in N, the number of bytes it takes to store a number is N+1. If Expressed as base T, it would be 2N+1. Let's Examine T7625597484987. (I know it isn't equal to 37625597484987, but comparatively, they're close). Such a beast would have 7625597484988 digits when expressed in Base T. As a result, it would have approximately 3812798742494 digits when expressed in base 10. assuming each digit takes one byte, the number can be stored in 3 812 798 742 494 bytes, or approximately 4 Terabytes (hard drive manufacturers terabyte). If using a binary storage mechanism (as might be used to most efficiently store any number, say as in a twos compliment storage), 3 decimal digits, can approximately be stored in 10 binary digits. at 8 bits to a byte, this would take approximately 1 588 666 142 705 bytes, or 1.5 terabytes. Moderately large hard drives these days are about 300gb, (large ones at 500gb), which is 12ish (ascii) or 5ish (binary) "moderately large hard drives"? McKay 06:38, 19 January 2007 (UTC)

Error in table?
It seems to me that there is an error in the first table under table of values. First, we have $$2\uparrow\uparrow 6 = 2^{2^{65536}}\approx 10^{6.0 \times 10^{19,728}}$$

Then, in the very next table we have $$2\uparrow\uparrow 7 = 2^{2^{2^{65536}}}\approx 10^{10^{6.0 \times 10^{19,728}}}$$.

Assuming the first one is correct, shouldn't this be $$2\uparrow\uparrow 7 = 2^{2^{2^{65536}}}\approx 2^{10^{6.0 \times 10^{19,728}}}$$ since we are simply looking at 2 raised to the power in the previous column? I'm not sure which of these is incorrect, but I thought I would just bring this to the attention of someone who is more certain. GreekHouse 02:11, 12 October 2007 (UTC)

 * Compared to the effect of the rounding error in the 6.0, replacing 2 by 10 at the bottom has a negligible effect: a factor a little more than 3 at the second level, i.e. a term 0.5 at the third level.--Patrick 06:15, 12 October 2007 (UTC)

Small issue on convention
This article starts with the example of multiplication. Although I think that the example of 3x2 is the correct one, it is not consistent with the general example ab (a copies of b instead of b copies of a). However the general trend in this article is of course b copies of a. So should we make the first example ba or change the explicit example to two copies of three, which is counter-intuitive? Paul (talk) 08:15, 25 January 2008 (UTC)

→==Numeration systems based on the hierarchy (+, *, ^, ^^, ^^^, ...)==

Knuth arrows denote the 3rd and higher operations in the hierarchy $$( +, \ \times, \ \uparrow, \ \uparrow\uparrow, \ \uparrow\uparrow\uparrow, \ \dots)$$ which was introduced by Goodstein[1947] (he used other notation, but apparently also introduced the terms "tetration", "pentation", and so on). I wrote a description of Goodstein's base-b level-k system of uniquely representing any nonnegative integer (it uses digits 0,...,b-1 and the first k operators in the hierarchy), but I wasn't quite sure of the best WP article in which to enter it. Maybe it would be appropriate here (?), but because the family of hyper operations is precisely this hierarchy, I posted it over there, at Hyper_operator. Nevertheless, I used mostly Knuth arrow notation in the examples. --r.e.s. (talk) 21:23, 14 August 2008 (UTC)

Googolplex
The article claims "Note: (10\uparrow)^k denotes a functional power of the function f(n) = 10^n (the function also expressed by the suffix -plex as in googolplex)." Now, sorry to be picky, but this needs a citation. I know a googol is 10^100 and a googolplex is 10^10^100, but this alone does not imply that "-plex" generally means 10^n. And there are no other number names ending -plex to use as data points. The words "googol" and "googolplex" were introduced by Kasner as described in the googol article, and should be regarded as indivisible morphemes unless either (1) Kasner originally and explicitly intended "-plex" to be a generalisable suffix with this meaning, or (2) it has since come into widespread use with this meaning. Is either of those the case? I think not, but I'll put the question here in case anyone can answer more definitely. 91.105.25.16 (talk) 18:15, 14 January 2009 (UTC)

Incorrect Information
The base-2 representations at the end of the article seem to be wrong. Earlier in the same section it says that a base-b representation should only contain digits 0,1,...,b-1 and so a base-2 representation should only contain the digits 0 and 1 and yet all the representations contain a 2 digit. I do not understand the representations enough to fix them, but I was able to understand enough to see this was wrong. Could someone more knowledgeable fix this apparent inconsistency? --SurrealWarrior (talk) 17:01, 22 August 2009 (UTC)

 * I think it's a matter of terminology, in the sense that although the "complete hereditary representation" of an integer in base b does involve b, only {0,1,...,b-1} are called "digits". To some extent this can be compared to calling the expression 2*102 + 6*101 + 6*100 (which contains "10") the base-10 representation of the number usually written as 266. Probably this ought to be clarified in the article. — r.e.s. (talk) 13:27, 3 September 2011 (UTC)

Up-arrow notation defined on ordinals?
The ε₀ page uses Knuth's up-arrow notation extended to ordinals, but the definition for ordinals appears nowhere on this page, and perhaps it should. 75.22.201.232 (talk) 22:10, 24 April 2010 (UTC)

Graham's Number too large?
The article currently reads:

''"Some numbers are so large that multiple arrows of Knuth's up-arrow notation become too cumbersome; then an n-arrow operator is useful (and also for descriptions with a variable number of arrows), or equivalently, hyper operators.

''Some numbers are so large that even that notation is not sufficient. Graham's number is an example."''

To my non-mathematician eye, this means hyper operators describe bigger numbers than Knuth's notation does, and Graham's number is even beyond the conventional scope of hyper operators. This seems to contradict the Graham's number page, which states, "it can be easily described by recursive formulas using Knuth's up-arrow notation or the equivalent, as was done by Graham."

Maybe this makes sense at some level, but to a non-mathematician like me this appears contradictory, and at the very least isn't clear enough.--Atkinson (talk) 04:40, 27 July 2012 (UTC)

How do you say it?
What's the verbal way to express up-arrow notation?  K . Bog  20:08, 22 April 2014 (UTC)
 * There is a video of Ron Graham explaining Graham's (ie his) number, in which he pronounces it several different ways. But they are all quite close to things like "three four arrows three" for $$3\uparrow\uparrow\uparrow\uparrow 3$$. Kestrelsummer (talk) 18:20, 30 October 2016 (UTC)

The definition of up-arrow notation
Why $$a\uparrow^n b$$ is $$H_{n+2}(a,b)$$ instead of $$H_n(a,b)$$ ? — Preceding unsigned comment added by 140.113.136.218 (talk) 08:12, 13 May 2014 (UTC)

Here's a number for you: 10^10^10^100 ^(10^10^10^100) 10^10^10^100         10^10^10^100 layers

Severe error right at the beginning
before even the table of contents, we see https://wikimedia.org/api/rest_v1/media/math/render/svg/7bde1c371dfcf9daeaabd7284d046e92bebae399 which is soon followed by https://wikimedia.org/api/rest_v1/media/math/render/svg/7e2e1cbace2adb782550d7a5c3fffbc4e5add62d THESE ARE INCONSISTENT. If the first is correct, then we need to replace an 'n' with 'n-1' in the second. If the second is correct, then an extra arrow is needed in the first. I have added an ERROR remark. DO NOT REMOVE THE ERROR MARKER until the error is fixed.Jamesdowallen (talk) 12:41, 2 November 2017 (UTC)

Second definition is correct (note that the recursive definition works the same as the Ackermann function's recursive case). I have fixed the first definition to match the second. 70.72.216.53 (talk) 22:37, 23 November 2017 (UTC)

2^^^3 vs 2^^^4
I think it would be better to have the opening example show direct correlations to different examples of Arrows. Instead of using 2^4 2^^4 and 2^^^3 is it better to use 2 xUparrow 3 for all three to properly illustrate the difference between the 3 examples and to show the scale at which additional ^'s increase the results? Apriestofgix (talk) 18:43, 28 November 2017 (UTC)

associativity
The article claims that Knuth's arrow notation be right-associative, but I can't find any associativity rule in the cited links; they always use parentheses. Isn't it probably like exponentiation, where the writer has to specify the association (e.g. with parentheses or by using superscript notation)? Edit: In the first source right-associativity was used, but I'll check the source's sources.Ninjamin (talk) 16:29, 3 April 2019 (UTC)
 * I found Conway using right-associativity for Knuth's arrow notation, but most sources use parentheses, so there's no reason to see a general convention here. Also the article claims that the notation be defined to be associative, but Knuth's paper makes no mention of that, thus I'm going to remove that passage.141.99.250.138 (talk) 09:30, 4 April 2019 (UTC)

Down-arrow notation
There are a few sources on the internet, including Googology Wiki, for down-arrows which are a kind of inverse of Knuth's up-arrow. I'm not qualified to add it myself, but I think down-arrows merit a section in this article. Glumblebee (talk) 06:25, 25 June 2019 (UTC)

Definition
The formal definition in the first line uses parenthesis to define a right-associative operator. The last line says: "the operator is SOMETIMES used right-associatively". This is confusing. For a left associative operator the definition would have to be

a\uparrow^n b=(a\uparrow^n (b-1))\uparrow^{n-1} a $$ 2A02:A210:2142:6C00:D5BA:D812:1452:F501 (talk) 09:23, 12 November 2019 (UTC)

Where does the definition for b = 0 come from?
See title. Knuth's original article never said anything about what happens when either term is zero, and I find the definition of 0 \uparrow^n 0 particularly suspect -- after all, isn't 0^0 indeterminate? Arcorann (talk) 13:33, 19 May 2020 (UTC)

 * I've also raised the same concern. It doesn't come from anywhere.  See discussion under  above. --Ashawley (talk) 19:37, 30 June 2020 (UTC)

English syntax question
Shouldn't this sentence in the Definition section :
 * Remark however that Knuth did not define the "nil-arrow" ($$\uparrow^0$$).

more properly be
 * Note, however, that Knuth did not define the "nil-arrow" ($$\uparrow^0$$).

I would make that change, but I'm unsure whether the first version, using "Remark" is correct English as well and I'm just not aware of it. Thanks! -- ArglebargleIV (talk) 19:02, 23 March 2021 (UTC)

2↑↑4 and 2↑↑↑4 are bad examples because it is a coincidence that 2↑↑↑4 happens to be equal to 2^2^...^2 with 2↑↑4 2's
The examples for tetration and pentation used at the top of the article (2↑↑4 and 2↑↑↑4) are bad because they make it easy for a layperson like me trying to learn what pentation is from the article to come to a false conclusion about what pentation is.

Specifically, I saw that 2↑↑4=65536 and 2↑↑↑4=2^2^...^2 with 65536 2's and made the false assumption that the general version of this is true, i.e. that a↑↑↑b=a^a^...^a with a↑↑b a's (but this is false).

I highly doubt I'm the only person who came to this false conclusion about what pentation is when reading this example at the top of the article. I suggest a different example be used instead that doesn't have this coincidental feature, perhaps a=2 and b=3.

I leave it to a math person to make that judgment call and change it. Thank you! 70.123.9.81 (talk) 04:53, 5 March 2022 (UTC)

what is said here, if anything?

 * Since $$6\uparrow\uparrow4$$ = $$6^{6^{6^{6}}}$$ = $$6^{6^{46,656}}$$, Thus the result comes out with $$\underbrace{6^{6^{.^{.^{.^{6}}}}}}_{4}$$

If this is anything other than tautology, it is poorly phrased. —Tamfang (talk) 01:54, 23 December 2022 (UTC)

title: Talk:Knuth's up-arrow notation


text:
Mitchellville

Mitchellville is the name of several places:

Places

 * Australia
 * Mitchellville, South Australia, a locality in the District Council of Franklin Harbour
 * United States
 * Mitchellville, Arkansas
 * Mitchellsville, Illinois
 * Mitchellville, Iowa
 * Mitchellville, Maryland
 * Mitchellville, Missouri
 * Mitchellville, Tennessee

title: Mitchellville


text:
Wikipedia:Non-unique personal name

This page lists non-unique personal names in Wikipedia. There are references to two or more persons with the same name (homonymous or namesake).

Articles about these people are set in one of the following ways:
 * 1) The articles are all on the same page.
 * 2) A disambiguation block leads to the lesser known person(s).
 * 3) The name is a disambiguation page leading to pages for each person. These are also listed on Links to disambiguating pages.

It's these pages that are listed below.

 * See also: lists of people, Multiple-place names and how to best disambiguate per Naming conventions (people)

[Note: The list has now been removed (to avoid this page appearing in what-links-here lists for many pages and to make clear that the list no longer needs to be maintained). The list can be seen in older versions of this page (e.g. ).]

title: Wikipedia:Non-unique personal name


text:
Saarburg

Saarburg is a city of the Trier-Saarburg district, in the state of Rhineland-Palatinate, Germany, on the banks of the river Saar in the hilly country a few kilometers upstream from the Saar's junction with the Moselle. Now known as a tourist attraction, the river Leuk flows into the town centre and makes a spectacular drop of some 60 feet before joining the larger Saar that bisects the town. The waterfall is the result of a 13th-century project to redirect the Leuk through the city centre.

Saarburg is the seat of the Verbandsgemeinde ("collective municipality") Saarburg-Kell. The area around Saarburg is noted for the cultivation of Riesling grapes.

History
The history of the city begins with the construction of the now-ruined castle by Graf Siegfried of Luxembourg in 964. It received its town charter in 1291. The city has a bell foundry, the Glockengießerei Mabilion, which has been in operation since the 1770s, and the only one in Germany that produces bronze bells.

From 1945 to 1948 Saarburg was occupied by troops from Luxembourg. From 18 July 1946 to 6 June 1947 Onsdorf, in its then municipal boundary, formed part of the Saar Protectorate. French troops complemented the occupation until 1955.

Saarburg has a proud history with bells, being the producers of bells for many German cathedrals.

Twin towns — sister cities
Saarburg is twinned with:

 * 🇫🇷 Sarrebourg, France (1952)
 * 🇫🇷 Soulac-sur-Mer, France (1972)

Born in Saarburg

 * Marianne Baum (1912–1942), resistance fighter against Nazism
 * Erwin Menny (1893–1949), lieutenant general in the Second World War
 * Alexander von Warsberg (1836–1889), Austrian government official and travel writer

title: Saarburg


text:
Billy Eckstine

William Clarence Eckstine (July 8, 1914 – March 8, 1993) was an American jazz and pop singer and a bandleader during the swing and bebop eras. He was noted for his rich, almost operatic bass-baritone voice. In 2019, Eckstine was posthumously awarded the Grammy Lifetime Achievement Award "for performers who, during their lifetimes, have made creative contributions of outstanding artistic significance to the field of recording". His recording of "I Apologize" (MGM, 1951) was given the Grammy Hall of Fame Award in 1999. The New York Times described him as an "influential band leader" whose "suave bass-baritone" and "full-throated, sugary approach to popular songs inspired singers like Earl Coleman, Johnny Hartman, Joe Williams, Arthur Prysock, and Lou Rawls."

Early life and education
Eckstine was born in Pittsburgh, Pennsylvania, United States, the son of William Eckstein, a chauffeur, and Charlotte Eckstein, a seamstress. Eckstine's paternal grandparents were William F. Eckstein and Nannie Eckstein, a mixed-race, married couple who lived in Washington, D.C.; both were born in 1863. William was born in Prussia (now Germany), and Nannie in Virginia. Billy's sister, Maxine, was a high school teacher.

Eckstine attended Peabody High School in Pittsburgh. Other notables who attended there include the artist Romare Bearden, Gene Kelly, pianist Dodo Marmarosa and Lorin Maazel. During this time, he moved to Washington, D.C., attending Armstrong High School (where his sister taught), St. Paul Normal and Industrial School, and Howard University. In 1933, aged 19, he left Howard to start a music career, after winning first place and $10 in an amateur talent contest at Washington's Howard Theatre, where he imitated Cab Calloway singing a nursery rhyme with interpolated scatting.

Career
Heading to Chicago, Illinois, Eckstine joined Earl Hines' Grand Terrace Orchestra in 1939, staying with the band as vocalist and trumpeter until 1943. By that time, Eckstine had begun to make a name for himself through the Hines band's juke-box hits, such as "Stormy Monday Blues", and his own "Jelly, Jelly".

In 1944, Eckstine formed his own big band, and it became the finishing school for adventurous young musicians who would shape the future of jazz including Charlie Parker, Dizzy Gillespie, Dexter Gordon, Gene Ammons, Miles Davis, Art Blakey, Cecil Payne, Fats Navarro, Lucky Thompson, John Malachi, Sarah Vaughan, Pearl Bailey, and Lena Horne. Tadd Dameron, Gil Fuller and Jerry Valentine were among the band's arrangers. The Billy Eckstine Orchestra is considered to be the first bebop big-band, and had Top Ten chart entries that included "A Cottage for Sale" and "Prisoner of Love". Both were awarded a gold disc by the RIAA.

Dizzy Gillespie, in reflecting on the band in his 1979 autobiography To Be or Not to Bop, gives this perspective: "There was no band that sounded like Billy Eckstine's. Our attack was strong, and we were playing bebop, the modern style. No other band like this one existed in the world." In 1946 Eckstine starred as the hero in the musical film Rhythm in a Riff, which also starred Ann Baker and Lucky Millinder.

Eckstine became a solo performer in 1947, with records featuring lush, sophisticated orchestrations. Even before folding his band, Eckstine had recorded solo to support it, scoring two million-sellers in 1945 with "Cottage for Sale" and a revival of "Prisoner of Love". Far more successful than his band recordings, these prefigured Eckstine's future career. Eckstine would go on to record over a dozen hits during the late 1940s. He signed with the newly established MGM Records, and had immediate hits with revivals of "Everything I Have Is Yours" (1947), Rodgers and Hart's "Blue Moon" (1948), and Juan Tizol's "Caravan" (1949).

Eckstine had further success in 1950 with Victor Young's theme song to "My Foolish Heart", and the next year with a revival of the 1931 Bing Crosby hit, "I Apologize".

According to The New York Times, his 1950 appearance at the Paramount Theatre in New York City drew a larger audience than Frank Sinatra had done at his performance there. He was even called "the sepia Sinatra" for his rivalry of the country's most popular vocalist.

Eckstine was the subject of a three-page profile in the April 24, 1950 issue of Life magazine, in which the photographer Martha Holmes accompanied Eckstine and his entourage during a week in New York City. One photograph taken by Holmes and published in Life showed Eckstine with a group of white female admirers, one of whom had her hand on his shoulder and her head on his chest while she was laughing. Eckstine's biographer, Cary Ginell, wrote of the image that Holmes "...captured a moment of shared exuberance, joy, and affection, unblemished by racial tension". Holmes would later describe the photograph as the favorite of the many she had taken in her career, because it "...told just what the world should be like". The photograph was considered so controversial that an editor at Life sought personal approval from Henry Luce, the magazine's publisher, who said it should be published. The publication of the image caused letters of protest to be written to the magazine, and singer Harry Belafonte subsequently said of the publication that "When that photo hit, in this national publication, it was if a barrier had been broken". The controversy that resulted from the photograph had a severe effect on the trajectory of Eckstine's career. Tony Bennett would recall that "It changed everything...Before that, he had a tremendous following...and it just offended the white community", a sentiment shared by pianist Billy Taylor who said that the "coverage and that picture just slammed the door shut for him".

In 1951, Eckstine performed at the seventh Cavalcade of Jazz concert held on July 8 at Wrigley Field in Los Angeles, produced by Leon Hefflin, Sr. Also featured were Lionel Hampton and his Revue, Percy Mayfield, Jimmy Witherspoon, Joe Liggins and The Honeydrippers and Roy Brown.

Among Eckstine's recordings of the 1950s was a 1957 duet with Sarah Vaughan, "Passing Strangers", a minor hit for them in 1957, but an initial No. 22 success in the UK Singles Chart.

The 1960 Las Vegas live album, No Cover, No Minimum, featured Eckstine taking a few trumpet solos and showcasing his nightclub act. He recorded albums for Mercury and Roulette in the early 1960s and appeared on Motown albums during the mid to late years of the decade. After recording sparingly during the 1970s for Al Bell's Stax/Enterprise imprint, the international touring Eckstine made his last recording, the Grammy-nominated Billy Eckstine Sings with Benny Carter in 1986.

Eckstine made numerous appearances on television variety shows, including on The Ed Sullivan Show, The Nat King Cole Show, The Tonight Show with Steve Allen, Jack Paar, and Johnny Carson, The Merv Griffin Show, The Art Linkletter Show, The Joey Bishop Show, The Dean Martin Show, The Flip Wilson Show, and Playboy After Dark. He also performed as an actor in the TV sitcom Sanford and Son, and in such films as Skirts Ahoy, Let's Do It Again, and Jo Jo Dancer. He performed "The Star-Spangled Banner" prior to Game 4 of the 1979 World Series at Three Rivers Stadium in his native Pittsburgh.

Culturally Eckstine was a fashion icon. He was famous for his "Mr. B. Collar" – a high roll collar that formed a "B" over a Windsor-knotted tie (or without a tie at all). The collars were worn by many a hipster in the late 1940s and early 1950s.

In 1984, Eckstine recorded his penultimate album, I Am a Singer, arranged and conducted by Angelo DiPippo and featuring Toots Thielemans on harmonica. In November 1986, Eckstine recorded with saxophonist Benny Carter for his 1987 album Billy Eckstine Sings with Benny Carter. Eckstine made his final recordings for Motorcity Records, a label for ex-Motown artists founded by Ian Levine.

Personal life
He married his first wife June in 1942. After their divorce in 1952, he married actress and model Carolle Drake in 1953, and they remained married until his death. He was the father of four children by his second marriage including Ed Eckstine, a president of Mercury Records; Guy Eckstine, a Columbia and Verve Records A&R executive and record producer; international singer Charlotte Eckstine; and singer Gina Eckstine.

Illness and death
Eckstine suffered a stroke while performing in Salina, Kansas, in April 1992, and never performed again. Though his speech improved in the hospital, Eckstine had a heart attack and died nearly a year later on March 8, 1993, in Pittsburgh, aged 78. In the weeks leading up to his death, his family members played music for him in his room. His final word was "Basie".

A State Historical Marker was placed at 5913 Bryant Street in Pittsburgh's Highland Park neighborhood to mark the house where Eckstine grew up.

Tributes
His friend Duke Ellington recalled Eckstine's artistry in his 1973 autobiography Music is My Mistress: "Eckstine-style love songs opened new lines of communication for the man in the man-woman merry-go-round, and blues a la B were the essence of cool. When he made a recording of 'Caravan', I was happy and honored to watch one of our tunes help take him into the stratosphere of universal acclaim. And, of course, he hasn't looked back since. A remarkable artist, the sonorous B. ... His style and technique have been extensively copied by some of the neocommercial singers, but despite their efforts, he remains out front to show how and what should have been done."

Sammy Davis, Jr. made several live appearances and impersonated Eckstine. Eckstine was a pallbearer at Davis' funeral in 1990.

And, in Billboard, Quincy Jones stated: "I looked up to Mr. B as an idol. I wanted to dress like him, talk like him, pattern my whole life as a musician and as a complete person in the image of dignity that he projected.... As a black man, Eckstine was not immune to the prejudice that characterized the 1950s."

Jones is quoted in The Pleasures of Jazz as also saying of Eckstine: "If he'd been white, the sky would have been the limit. As it was, he didn't have his own radio or TV show, much less a movie career. He had to fight the system, so things never quite fell into place.'"

Lionel Hampton said: He was one of the greatest singers of all time.... We were proud of him because he was the first Black popular singer singing popular songs in our race. We, the whole music profession, were so happy to see him achieve what he was doing. He was one of the greatest singers of that era... He was our singer."

10" LP releases

 * 1940: Earl Hines – Billy Eckstine [Record 1: "Stormy Monday Blues" // "Water Boy"; Record 2: "I Got It Bad (And That Ain't Good)" // "Somehow"; Record 3: "Jelly, Jelly" // "Skylark"] (RCA Victor) 3x78rpm album set
 * 1949: Billy Eckstine Sings (National) – recorded 1945–1947
 * 1950: Songs By Billy Eckstine (MGM)
 * 1951: Billy Eckstine Favorites (MGM)
 * 1952: Love Songs By Rodgers and Hammerstein (MGM)
 * 1953: Billy Eckstine Sings Tenderly (MGM)
 * 1953: Earl Hines – Billy Eckstine: A Treasury Of Immortal Performances (RCA Victor) – recorded 1940–1942
 * 1953: The Great Mr. B: Billy Eckstine and His All-Star Band (DeLuxe/King) – recorded 1944
 * 1954: I Let a Song Go Out of My Heart: Billy Eckstine Sings 8 Great Duke Ellington Songs (MGM)
 * 1954: Blues For Sale (EmArcy)
 * 1954: The Love Songs of Mr. B (EmArcy)

12" LP releases

 * 1955: I Surrender, Dear (EmArcy)
 * 1955 Mr. B With a Beat (MGM) – with George Shearing Quintet, Woody Herman Orchestra, and The Metronome All Stars.
 * 1955: Rendezvous (MGM)
 * 1955: That Old Feeling (MGM)
 * 1957: Prisoner of Love (Regent)
 * 1957: The Duke, The Blues and Me! (Regent)
 * 1957: My Deep Blue Dream (Regent)
 * 1958: You Call It Madness (Regent)
 * 1958: Billy Eckstine's Imagination (EmArcy)
 * 1958: Billy Eckstine & Sarah Vaughan Sing Irving Berlin (Mercury)
 * 1958: Billy's Best! (Mercury)
 * 1959: Basie and Eckstine, Inc. with Count Basie Orchestra (Roulette)
 * 1960: No Cover, No Minimum (Roulette)
 * 1960: Once More With Feeling (Roulette)
 * 1961: Mr. B In Paris (Felsted/Decca [UK]; Barclay [France]) rec. 1957–1958; all 12 songs sung in French
 * 1961: Broadway, Bongos and Mr. B (Mercury)
 * 1962: At Basin St. East with Quincy Jones (Mercury)
 * 1962: Don't Worry 'Bout Me (Mercury)
 * 1963: The Golden Hits of Billy Eckstine (Mercury) – compilation
 * 1963: Now Singing In 12 Great Movies (Mercury)
 * 1964: The Modern Sound of Mr. B (Mercury)
 * 1965: The Prime of My Life (Motown)
 * 1966: My Way (Motown)
 * 1969: For Love of Ivy [also released as Gentle On My Mind] (Motown)
 * 1971: Stormy (Enterprise/Stax)
 * 1971: Feel the Warm (Enterprise/Stax)
 * 1971: Moment (Capitol)
 * 1972: Senior Soul (Enterprise/Stax)
 * 1974: If She Walked Into My Life (Enterprise/Stax)
 * 1979: Momento Brasiliero (Portuguese import release on Som Livre label)
 * 1984: I Am a Singer (Kimbo)
 * 1986: Billy Eckstine Sings with Benny Carter with special guest: Helen Merrill (Verve)

LP/CD compilations of note

 * 1960: Mr. B: The Great Billy Eckstine and His Orchestra (Audio Lab) – 12" LP reissue of The Great Mr. B from DeLuxe/King.
 * 1963: Billy & Sarah – with Sarah Vaughan (Lion) – compilation
 * 1971: Billy Eckstine Together (Spotlite) – 1945 live "radio broadcast" recordings
 * 1979: Billy Eckstine Sings (Savoy Jazz) – compilation
 * 1986: Mister B. and the Band: The Savoy Sessions (Savoy Jazz) – compilation
 * 1986: I Want To Talk About You (Xanadu) – this compilation features Eckstine's earliest recordings, 13 selections taken from his 1940–1942 Bluebird sides with the Earl Hines Orchestra; album is rounded out by 3 ballads taken from a 1945 live "radio broadcast" with his own big band.
 * 1991: Everything I Have Is Yours: The Best Of The MGM Years (Verve) – 2CD anthology with 42 tracks (note: the original 2-LP set was issued in 1985 with just 30 tracks)
 * 1991: Compact Jazz: Billy Eckstine (Verve) – compilation
 * 1994: Jazz 'Round Midnight: Billy Eckstine (Verve) – compilation
 * 1994: Verve Jazz Masters (Volume 22): Billy Eckstine (Verve) – compilation
 * 1996: Air Mail Special (Drive Archive) – reissue of the 1945 live "radio broadcast" recordings.
 * 1996: The Magnificent Mr. B (Flapper/Pearl) – anthology/compilation of material recorded with Earl Hines (for the Bluebird label), and Eckstine's recordings with his orchestra (for the DeLuxe and National labels).
 * 1997: The Chronological Billy Eckstine and His Orchestra 1944–1945 (Classics) – anthology/compilation
 * 1999: The Chronological Billy Eckstine and His Orchestra 1946–1947 (Classics) – anthology/compilation
 * 2001: Mr. B (ASV/Living Era) – anthology/compilation
 * 2002: Timeless Billy Eckstine (Savoy Jazz) – compilation
 * 2002: The Legendary Big Band 1943–1947 (Savoy Jazz) – 2CD anthology (all of Eckstine's recordings for the DeLuxe and National labels).
 * 2003: Kiss of Fire (Sepia) – compilation (contains 25 tracks recorded 1947–1952 for the MGM label).
 * 2003: The Motown Years (Motown/UMe) – 2CD anthology
 * 2004: Love Songs (Savoy Jazz) – compilation
 * 2004: A Proper Introduction To Billy Eckstine: Ballads, Blues and Bebop (Proper) – anthology/compilation
 * 2005: Jukebox Hits 1943–1953 (Acrobat) – anthology/compilation
 * 2005: Early Mr. B: 1940–1953 (Jazz Legends) – anthology/compilation of material recorded with Earl Hines (for the Bluebird label), and Eckstine's recordings with his orchestra (for the DeLuxe, National and MGM labels).
 * 2006: Prisoner of Love: The Romantic Billy Eckstine (Savoy Jazz) – this is a reissue of Timeless Billy Eckstine.
 * 2008: All of My Life (Jasmine) – 2CD anthology (contains 35 tracks recorded for the MGM label; also includes all 10 of his 1956 RCA recordings; and 10 of his 1957–1958 Mercury recordings).

Archives

 * "Musical arrangements for Billy Eckstine, 1950–1957" at Library of Congress

title: Billy Eckstine