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Twenty Thousand Leagues Under the Seas

Twenty Thousand Leagues Under the Seas (Vingt Mille Lieues sous les mers) is a science fiction adventure novel by the French writer Jules Verne. It is often considered a classic within both its genres and world literature.

The novel was originally serialised from March 1869 to June 1870 in Pierre-Jules Hetzel's French fortnightly periodical, the Magasin d'éducation et de récréation. A deluxe octavo edition, published by Hetzel in November 1871, included 111 illustrations by Alphonse de Neuville and Édouard Riou. The book was widely acclaimed on its release, and remains so; it is regarded as one of the premier adventure novels and one of Verne's greatest works, along with Around the World in Eighty Days and Journey to the Center of the Earth. Its depiction of Captain Nemo's submarine, the Nautilus, is regarded as ahead of its time, since it accurately describes many features of modern submarines, which in the 1860s were comparatively primitive vessels.

Jules Verne saw a model of the French submarine Plongeur at the Exposition Universelle in 1867, which inspired him while writing the novel.

Title
The title refers to the distance travelled under the various seas: 20,000 metric leagues (80,000 km, over 40,000 nautical miles), nearly twice the circumference of the Earth.

Principal characters

 * Professor Pierre Aronnax, a French natural scientist and the narrator of the story.
 * Conseil, Aronnax's Flemish servant who is highly devoted to him and knowledgeable in biological classification.
 * Ned Land, a Canadian harpooner, described as having "no equal in his dangerous trade".
 * Captain Nemo, the designer and captain of the Nautilus.

Plot
During the year 1866, ships of various nationalities sight a mysterious sea monster, which is speculated to be a gigantic narwhal. The U.S. government assembles an expedition in New York City to find and destroy the monster. Professor Pierre Aronnax, a French marine biologist and the story's narrator, is in town at the time and receives a last-minute invitation to join the expedition. Canadian whaler and master harpooner Ned Land and Aronnax's faithful manservant Conseil are also among the participants.

The expedition leaves Brooklyn aboard the United States Navy frigate Abraham Lincoln, then travels south around Cape Horn into the Pacific Ocean. After a five-month search ending off Japan, the frigate locates and attacks the monster, which damages the ship's rudder. Aronnax and Land are hurled into the sea, and Conseil jumps into the water after them. They survive by climbing onto the "monster", which, they are startled to find, is a futuristic submarine. They wait on the deck of the vessel until morning, when they are captured and introduced to the submarine's mysterious constructor and commander, Captain Nemo.

The rest of the novel describes the protagonists' adventures aboard the Nautilus, which was built in secrecy and now roams the seas beyond the reach of land-based governments. In self-imposed exile, Captain Nemo seems to have a dual motivation — a quest for scientific knowledge and a desire to escape terrestrial civilization. Nemo explains that his submarine is electrically powered and can conduct advanced marine research; he also tells his new passengers that his secret existence means he cannot let them leave — they must remain on board permanently.

They visit many oceanic regions, some factual and others fictitious. The travelers view coral formations, sunken vessels from the Battle of Vigo Bay, the Antarctic ice barrier, the transatlantic telegraph cable, and the legendary underwater realm of Atlantis. They even travel to the South Pole and are trapped in an upheaval of an iceberg on the way back, caught in a narrow gallery of ice from which they are forced to dig themselves out. The passengers also put on diving suits, hunt sharks and other marine fauna with air guns in the underwater forests of Crespo Island, and attend an undersea funeral for a crew member who died during a mysterious collision experienced by the Nautilus. When the submarine returns to the Atlantic Ocean, a school of giant squid ("devilfish") attacks the vessel and kills another crewman.

The novel's later pages suggest that Captain Nemo went into undersea exile after his homeland was conquered and his family slaughtered by a powerful imperialist nation. Following the episode of the devilfish, Nemo largely avoids Aronnax, who begins to side with Ned Land. Ultimately, the Nautilus is attacked by a warship from the mysterious nation that has caused Nemo such suffering. Carrying out his quest for revenge, Nemo — whom Aronnax dubs an "archangel of hatred" — rams the ship below her waterline and sends her to the bottom, much to the professor's horror. Afterward, Nemo kneels before a portrait of his deceased wife and children, then sinks into a deep depression.

Circumstances aboard the submarine change drastically: watches are no longer kept, and the vessel wanders about aimlessly. Ned becomes so reclusive that Conseil fears for the harpooner's life. One morning, he announces that they are in sight of land and have a chance to escape. Professor Aronnax is more than ready to leave Captain Nemo, who now horrifies him, yet he is still drawn to the man. Fearing that Nemo's very presence could weaken his resolve, he avoids contact with the captain. Before their departure, the professor eavesdrops on Nemo and overhears him calling out in anguish, "O almighty God! Enough! Enough!". Aronnax immediately joins his companions as they carry out their escape plans, but as they board the submarine's skiff they realize that the Nautilus has seemingly blundered into the ocean's deadliest whirlpool, the Moskenstraumen (more commonly known as the "Maelstrom"). They escape and find refuge on an island off the coast of Norway. The submarine's ultimate fate remained unknown until the events of The Mysterious Island.

Themes and subtext
Captain Nemo's assumed name recalls Homer's Odyssey, when Odysseus encounters the monstrous Cyclops Polyphemus in the course of his wanderings. Polyphemus asks Odysseus his name, and Odysseus replies that it is Outis (Οὖτις) 'no one', translated into Latin as "Nemo". Like Captain Nemo, Odysseus wanders the seas in exile (though only for ten years) and similarly grieves the tragic deaths of his crewmen.

The novel repeatedly mentions the U.S. Naval Commander Matthew Fontaine Maury, an oceanographer who investigated the winds, seas, and currents, collected samples from the depths, and charted the world's oceans. Maury was internationally famous, and Verne may have known of his French ancestry.

The novel alludes to other Frenchmen, including Lapérouse, the celebrated explorer whose two sloops of war vanished during a voyage of global circumnavigation; Dumont d'Urville, a later explorer who found the remains of one of Lapérouse's ships; and Ferdinand de Lesseps, builder of the Suez Canal and nephew of the sole survivor of Lapérouse's ill-fated expedition. The Nautilus follows in the footsteps of these men: she visits the waters where Lapérouse's vessels disappeared; she enters Torres Strait and becomes stranded there, as did d'Urville's ship, the Astrolabe; and she passes beneath the Suez Canal via a fictitious underwater tunnel joining the Red Sea to the Mediterranean.

In possibly the novel's most famous episode, the above-described battle with a school of giant squid, one of the monsters captures a crew member. Reflecting on the battle in the next chapter, Aronnax writes: "To convey such sights, it would take the pen of our most renowned poet, Victor Hugo, author of The Toilers of the Sea." A bestselling novel in Verne's day, The Toilers of the Sea also features a threatening cephalopod: a laborer battles with an octopus, believed by critics to be symbolic of the Industrial Revolution. Certainly, Verne was influenced by Hugo's novel, and, in penning this variation on its octopus encounter, he may have intended the symbol to also take in the Revolutions of 1848.

Other symbols and themes pique modern critics. Margaret Drabble, for instance, argues that Verne's masterwork also anticipated the ecology movement and influenced French avant-garde imagery. As for additional motifs in the novel, Captain Nemo repeatedly champions the world's persecuted and downtrodden. While in Mediterranean waters, the captain provides financial support to rebels resisting Ottoman rule during the Cretan Revolt of 1866–1869, proving to Professor Aronnax that he had not severed all relations with terrestrial mankind. In another episode, Nemo rescues an Indian pearl diver from a shark attack, then gives the fellow a pouch full of pearls, more than the man could have gathered after years of his hazardous work. When asked why he would help a "representative of that race from which he'd fled under the seas", Nemo responds that the diver, as an "East Indian", "lives in the land of the oppressed".

Indeed, the novel has an under-the-counter political vision, hinted at in the character and background of Captain Nemo himself. In the book's final form, Nemo says to professor Aronnax, "That Indian, sir, is an inhabitant of an oppressed country; and I am still, and shall be, to my last breath, one of them!" In the novel's initial drafts, the mysterious captain was a Polish nobleman, whose family and homeland were slaughtered by Russian forces during the Polish January Uprising of 1863. These specifics were suppressed during the editing stages at the insistence of Verne's publisher Pierre-Jules Hetzel, believed responsible by today's scholars for many modifications of Verne's original manuscripts. At the time France was a putative ally of the Russian Empire, hence Hetzel demanded that Verne suppress the identity of Nemo's enemy, not only to avoid political complications but also to avert lower sales should the novel appear in Russian translation. Hence Professor Aronnax never discovers Nemo's origins.

Even so, a trace remains of the novel's initial concept, a detail that may have eluded Hetzel: its allusion to an unsuccessful rebellion under a Polish hero, Tadeusz Kościuszko, leader of the uprising against Russian and Prussian control in 1794; Kościuszko mourned his country's prior defeat with the Latin exclamation "Finis Poloniae!" ("Poland is no more!").

Five years later, and again at Hetzel's insistence, Captain Nemo was revived and revamped for another Verne novel, The Mysterious Island. The novel changes the captain's nationality from Polish to Indian; in the book's final chapters, Nemo reveals that he is an Indian prince named Dakkar who was a descendant of Tipu Sultan, a prominent ruler of the Kingdom of Mysore, and participated in the Indian Rebellion of 1857, an ultimately unsuccessful uprising against Company rule in India. After the rebellion, which led to the death of his family, Nemo fled beneath the seas, then made a final reappearance in the later novel's concluding pages.

Verne took the name "Nautilus" from one of the earliest successful submarines, built in 1800 by Robert Fulton, who also invented the first commercially successful steamboat. Fulton named his submarine after a marine mollusk, the chambered nautilus. As noted above, Verne also studied a model of the newly developed French Navy submarine Plongeur at the 1867 Exposition Universelle, which guided him in his development of the novel's Nautilus.

The diving gear used by passengers on the Nautilus is presented as a combination of two existing systems: 1) the surface-supplied hardhat suit, which was fed oxygen from the shore through tubes; 2) a later, self-contained apparatus designed by Benoit Rouquayrol and Auguste Denayrouze in 1865. Their invention featured tanks fastened to the back, which supplied air to a facial mask via the first-known demand regulator. The diver didn't swim but walked upright across the seafloor. This device was called an aérophore (Greek for "air-carrier"). Its air tanks could hold only thirty atmospheres, but Nemo claims that his futuristic adaptation could do far better: "The Nautilus's pumps allow me to store air under considerable pressure ... my diving equipment can supply breathable air for nine or ten hours."

English translations
The novel was first translated into English in 1872 by Reverend Lewis Page Mercier. Mercier cut nearly a quarter of Verne's French text and committed hundreds of translating errors, sometimes drastically distorting Verne's original (including uniformly mistranslating the French scaphandre — properly "diving suit" — as "cork-jacket", following a long-obsolete usage as "a type of lifejacket"). Some of these distortions may have been perpetrated for political reasons, such as Mercier's omitting the portraits of freedom fighters on the wall of Nemo's stateroom, a collection originally including Daniel O'Connell among other international figures. Mercier's text became the standard English translation, and some later retranslations continued to recycle its mistakes, including mistranslating the title as "... under the Sea", rather than "... under the Seas".

In 1962, Anthony Bonner published a translation of the novel with Bantam Classics. This edition included an introduction by Ray Bradbury, comparing Captain Nemo to Captain Ahab of Moby-Dick.

A significant modern revision of Mercier's translation appeared in 1966, prepared by Walter James Miller and published by Washington Square Press. Miller addressed many of Mercier's errors in the volume's preface and restored a number of his deletions in the text. In 1976, Miller published "The Annotated Jules Verne, Twenty Thousand Leagues under the Sea" at the suggestion of the Thomas Y. Crowel Company editorial staff. The cover declared it "The only completely restored and annotated edition". In 1993, Miller collaborated with his fellow Vernian Frederick Paul Walter to produce "The Completely Restored and Annotated Edition", published in 1993 by the Naval Institute Press. Its text took advantage of Walter's unpublished translation, which Project Gutenberg later made available online.

In 1998, William Butcher issued a new, annotated translation with the title Twenty Thousand Leagues under the Seas, published by Oxford University Press (ISBN 978-0-19-953927-7). Butcher includes detailed notes, a comprehensive bibliography, appendices and a wide-ranging introduction studying the novel from a literary perspective. In particular, his original research on the two manuscripts studies the radical changes to the plot and to the character of Nemo urged on Verne by Hetzel, his publisher.

In 2010, Frederick Paul Walter issued a fully revised, newly researched translation, 20,000 Leagues Under the Seas: A World Tour Underwater. Complete with an extensive introduction, textual notes, and bibliography, it appeared in an omnibus of five of Walter's Verne translations titled Amazing Journeys: Five Visionary Classics and published by State University of New York Press (ISBN 978-1-4384-3238-0).

In 2017, David Coward issued a new translation published by Penguin Classics (ISBN 9780141394930) with the title Twenty Thousand Leagues Under the Sea, including a new introduction, notes, and a note on the text, using the 1871 Christian Chelebourg edition of the text as the basis for his translation. Coward also included 42 illustrations, which were published for the first time in the 'Collection Hetzel' in 1901.

Reception
The science fiction writer Theodore L. Thomas criticized the novel in 1961, claiming that "there is not a single bit of valid speculation" in the book and that "none of its predictions has come true". He described its depictions of Nemo's diving gear, underwater activities, and the Nautilus as "pretty bad, behind the times even for 1869 ... In none of these technical situations did Verne take advantage of knowledge readily available to him at the time." The notes to the 1993 translation point out that the errors Thomas notes were in Mercier's translation, not the original.

Despite his criticisms, Thomas conceded: "Put them all together with the magic of Verne's story-telling ability, and something flames up. A story emerges that sweeps incredulity before it".

In 2023, Malaurie Guillaume presented Nemo as the first eco-terrorist or first figure of ecologic radicality.

title: Twenty Thousand Leagues Under the Seas


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M551 Sheridan

The M551 "Sheridan" AR/AAV (Armored Reconnaissance/Airborne Assault Vehicle) was a light tank developed by the United States and named after General Philip Sheridan, of American Civil War fame. It was designed to be landed by parachute and to swim across rivers. It was armed with the technically advanced but troublesome M81/M81 Modified/M81E1 152 mm gun/launcher, which fired both conventional ammunition and the MGM-51 Shillelagh guided anti-tank missile.

The M551 Sheridan entered service with the United States Army in 1967. At the urging of General Creighton Abrams, the U.S. Commander, Military Assistance Command Vietnam, at the time, the M551 was rushed into combat service to South Vietnam in January 1969. Later that year, M551s were deployed to units in Europe and South Korea. The Sheridan saw extensive combat in the Vietnam War from 1969 to 1973. However, problems with the platform became evident, particularly its poor survivability and reliability.

Based on its experiences in Vietnam, the Army realized the shortcomings of the Sheridan, and after the war in 1975 began to eliminate the vehicle from its units in 1979. A modest fleet of vehicles remained in the 82nd Airborne Division and the National Guard. Various improvement programs were successfully undertaken to improve the Sheridan's reliability. Problems persisted with the 152 mm gun/launcher, and various efforts explored to replace it with a more conventional model. The Sheridan went on to serve in the invasion of Panama and the Gulf War. The Army sought to replace the Sheridan with the M8 Armored Gun System, but this was canceled in 1996, late in its development. The Sheridan was retired without a designated replacement in 1996. The Army acquired the M1128 Mobile Gun System to fulfill a similar requirement, but this is being retired in 2022. The Army's current light tank acquisition program is Mobile Protected Firepower.

A large number of Sheridans were retained in service at the National Training Center (NTC) at Fort Irwin, California and as Armor Officer Basic training at Armor Training Center, then located at Fort Knox, Kentucky. They worked as simulated Soviet armored opposition force (OPFOR) to train U.S. military units on simulated tank on tank armored combat to test on combat effectiveness in a desert environment. They were retired from the NTC in 2003.

Development
In the immediate post-World War II era, the U.S. Army introduced the M41 Walker Bulldog into service to fill the role of a light tank. The lifespan of the M41 was fairly short. At 25 tons it was considered too heavy to be a true light tank, and had a rather short cruising range. Plans were started to build an even lighter replacement mounting the same gun, the T71 and T92. The T92 appeared to be the more promising of the two. As the prototypes were entering testing, information about the new Soviet PT-76 light tank became available. The PT-76 was amphibious, and soon there were demands that any U.S. light tank should be able to swim as well. The T92 could not be easily refitted for this role, so the Army canceled the program in 1958.

In January 1959, the first concept studies were initiated for the armored reconnaissance/airborne assault vehicle that would replace both the M41 and M56 Scorpion self-propelled gun. By October 1959, 12 proposals had been received by the Ordnance Tank Automotive Command. Two proposals were downselected in December: One from Cadillac Motor Car Division of General Motors Corporation, and a joint venture of AAI Corporation and Allis-Chalmers Manufacturing Company. Mockups of both proposals were evaluated in May 1960.

The AAI candidate had three crewmen, and weighed the closest to the 10-ton weight limit specified in the requirements. The Cadillac design was only slightly heavier, with four crew. The three-man turret of the Cadillac proposal was considered more effective than the two-man turret proposed by AAI. The weight limit was reset at 15 tons. In June 1960, Cadillac Motor Car Division signed a contract to develop their concept further, which was designated as the AR/AAV XM551. In August 1961, the Secretary of the Army approved the name "Sheridan," after Major General Philip Sheridan.

A test bed underwent operations at Cleveland Tank Plant in December 1961. The decision to use the 152 mm caliber XM81 gun-launcher instead of a more conventional gun was driven by the desire to save weight. The XM81 weighed about half as much as the 105 mm caliber M68, and could fire both conventional and missile rounds. Testing of the XM81 began at Erie Army Depot in late 1961.

By 1962, the Army realized that the MGM-51 Shillelagh missile system would not immediately be ready for the Sheridan, and so considered several alternative gun systems. These including conventional 76 mm, 90 mm and 105 mm options, as well as missile systems such as ENTAC and TOW. In March 1967, a 105 mm howitzer XM103E7 and then a 76 mm gun was installed in the turret of an M551 at Rock Island Arsenal. Neither configuration was adopted. The Army ultimately decided to arm the Sheridan with just 152 mm conventional rounds until the Shillelagh was more mature.

The first of 12 pilots was delivered in June 1962. Pilots 1–3 comprised the first generation. With the second-generation pilots 4–6, the band track was replaced with single-pin, link type tracks. An XM551 test bed turret with gun-launcher was mated to an M41 chassis, which began firing tests in August 1962 at Aberdeen Proving Ground. The third generation of pilots, starting with pilot 7, eliminated the water jet propulsion. Pilots 9–11 were delivered in 1964, and pilot 12 was delivered in February 1965.

In the 1960s the Army was also developing the MBT-70 main battle tank with West Germany. The U.S. Army no longer used the heavy, medium, and light tank classifications. In 1960, with the deactivation of its last (M103) heavy tank battalion, and the fielding of the new M60 series tank, the U.S. Army had adopted a main battle tank (MBT) doctrine; a single tank filling all combat roles. The U.S. Army still retained the M41 Walker Bulldog light tank in the Army National Guard, but other than the units undergoing the transitional process, the regular army consisted of MBTs. Fearing Congress would balk at funding two developmental tank programs, the Army chose to designate the Sheridan as an armored reconnaissance vehicle rather than a light tank. The Army also believed "tank" too much evoked the main battle tank, a different role altogether, so the new project was instead officially classified as an "Armored Reconnaissance/Airborne Assault Vehicle."

Production
In April 1965 the Army awarded a four-year $114.5 million contract to the Cadillac Gage division of the General Motors (GM) for the production of the M109 howitzer and the XM551 General Sheridan. Limited production was approved in May, and then classified as "Standard A" in May 1966. Production took place at the Cleveland Army Tank Automotive Plant. The first two production units were delivered to the Army in July. During development, the Marine Corps evaluated the Sheridan as a possible replacement for the M50 Ontos. The Corps determined that the Sheridan would be too costly.

The Sheridan entered service in June 1967 with 1st Battalion, 63rd Armor Regiment at Fort Riley. 2,426 Sheridans were planned. In the end, 1,662 Sheridans were built between 1966 and November 1970. The total cost of the M551 program was $1.3 billion.

The M81 gun had problems with cracks developing near the breech after repeated firing, a problem that was later tracked to the "key" on the missiles that ran in a slot cut into the barrel. Most field units were modified to help address the problem, but later the modified M81E1 was introduced with a shallower slot, along with a matching modification to the missile, that cured the problem.

In March 1969, after the Army invoked secrecy in declining to disclose program costs, a Government Accounting Office (GAO) official said that development costs had reached $1.3 billion. Congressman Samuel S. Stratton criticized Army officials for the program's high costs, and accused officials of concealing cost figures to cover up for their own "bumbling ineptness". A GAO report leaked in May 1969 revealed the Army had fast-tracked the program to avoid budgetary scrutiny, despite indications by May 1966 that the tank's caseless ammunition was prone to cooking off. The problem had since then been resolved by a compressed-air system that forced hot ammunition residue from the breech, the Army told Congress. The Army said the Sheridan had performed well enough that it was planning to send hundreds more. A Congressional report in July 1969 identified $1.2 billion wasted on the M60 and Sheridan. The report attributed several Vietnam War casualties to Sheridan design faults, and said that the tank had been wholly unready for combat there "without extensive and costly retrofits."

In 1971, Frankford Arsenal awarded Hughes Aircraft Corporation a contract to begin producing the AN/VVG-1 laser rangefinder for the M551A1 upgrade.

Vietnam War
The U.S. Army staff in Washington had been recommending since 1966 to the commander of U.S. forces in South Vietnam, General Westmoreland, that the Sheridan should be used there. Since the main gun ammunition was not available, he argued that it was simply a $300,000 machine gun platform. By 1968, the new, or soon to be, U.S. commander in South Vietnam, General Creighton Abrams, had been notified that the 152 mm rounds were now available for the Sheridan. However, as General Abrams began to make preparations for the equipping of U.S. cavalry squadrons for the vehicle, the affected squadrons expressed their concerns that the new aluminum tanks were not only highly vulnerable to mines and anti-tank rocket fire, but they would not be as capable of "jungle busting" as the M48A3 medium tanks.

In late 1968, General Abrams met with Colonel George S. Patton IV – the son of World War II General Patton – commander of the 11th Armored Cavalry Regiment (11th ACR), the only full regiment of cavalry in South Vietnam. When Abrams mentioned the cavalry's concerns over the new vehicle, Patton recommended that the Sheridans be combat tested by a divisional cavalry squadron as well as a squadron from his own regiment, as the squadrons had completely different missions.

First deployment
The first Sheridans arrived in South Vietnam in January 1969 and were accompanied by their factory representatives, instructors and evaluators as the new vehicles were issued to the 3rd Squadron, 4th Cavalry Regiment, and the 1st Squadron of the 11th ACR. By the end of 1970, there were more than 200 Sheridans in South Vietnam. They stayed in the field until the last U.S. armored cavalry unit, the 1st Squadron, 1st Cavalry Regiment prepared for re-deployment back to the United States in April 1972. By the end of its combat debut in 1972, the Sheridan had seen extensive action in the Vietnam War, being assigned to nearly all armored cavalry squadrons involved in that conflict.

In 1969, armored cavalry units (minus the 11th ACR, which retained its M48 tank companies) began replacing their M48 Patton tanks, which were normally transferred to the Army of South Vietnam. The opinions of crews on Vietnam-era M551s were mixed at best and assessments from senior commanders were often negative. This was due largely to the high loss rate of Sheridans and casualty rates among crews. Landmines and RPGs that would damage an M48 Patton tank, tended to destroy a Sheridan and either kill or wound most of its crew.

A 1969 evaluation of the vehicles found that the M551 was employed in reconnaissance, night patrol and road clearing, accumulating 39,455 road miles and 520 combat missions, with a ready rate of 81.3 percent. Despite vulnerability to rockets and mines, it was judged worthy of applying modifications and equipping all cavalry squadrons with the Sheridan.

First combat/first losses
In addition to the problems presented by aluminum construction, the Sheridan had a defect that no other common armored vehicle possessed: it fired combustible-cased 152 mm main gun rounds. These rounds were "fixed", meaning that the projectile was firmly attached to the combustible-cased propellant charge, and if the projectile separated from the combustible-case during loading, which was not uncommon, the crewmen were instructed not to load the round. Sometimes, the combustible-cases and their charges remained on the turret floor due to the emergencies at the time, and additionally, all of the remaining serviceable 152 mm rounds were combustible-cased, and sleeved into a re-usable white nine-ply nylon bag, which was form-fitted to hold the combustible-case portion of the round. The white/silver-colored bag had a strap attached to the bottom, which the loader would grab and pull off prior to gently inserting the round into the breech. Once a mine or RPG-type weapon created an ignition source, smoke and fire became imminent, and it became a matter of Standing Operating Procedure to abandon the tank immediately. On 15 February 1969, just one month after the Sheridan's arrival in South Vietnam, an M551 from the 3/4th Cavalry detonated a 25-pound pressure-activated land mine, which ruptured its hull and ignited the combustible-case charges of the 152 mm rounds, resulting in a secondary explosion that destroyed the tank. In late 1969, nine Sheridans from the 4th Squadron, 12th Cavalry Regiment were fording a river near the DMZ, when three of the M551s triggered mines, completely destroying them. In March 1971, five Sheridans from the 11th ACR were lost in one day to RPG fire; all five vehicles burst into flames and were totally destroyed.

Performance
Over 200 Sheridans were shipped to Vietnam. The Sheridan was unpopular with American soldiers in Vietnam, mainly because of its perceived vulnerability. While the Sheridan brought superior firepower where it was used in lieu of the M113 ACAV, the Sheridan was a poor substitute for the better armored M48 Patton.

The Sheridan had several advantages: it did not get stuck in the mud as often as the 52-ton M48 did, nor did it throw its track off as often. The reliability of the engine system and gun of the tank was, however, not fully up to the task. Of 74 M551 sent to Vietnam in February 1969, by May there were recorded 16 serious mechanical faults, 41 failed shots, 140 defective ammunitions and 25 burned engines; the turret itself had 125 electric faults, several recoil system faults and instances of blown up guns. An additional problem was that much of the carried machine-gun ammunition had to be stored outside the turret as the internal space was extremely limited.

Although an average M48 crew could fire as many as seventeen 90 mm rounds during a "mad minute" (60 seconds with all guns firing on command), the Sheridan was known to put out only two 152 mm rounds during the same time frame. The caseless rounds needed air vents to clear the gun tube and breech prior to loading another round, while the M48 breech block opened as the used case was ejected and closed as the new round was shoved in. The faster the loader, the faster the Patton's gun could be fired. For the Sheridan, the loader had to wait for the mechanism. After firing, the loader would have to wait, as the breech slowly opened rearward then turned downward. After another instrument indicated that all turret systems were still operational, the loader would gently push the 152 mm fixed round into the breech and watch the breech block slowly rotate upward, then forward into the breech, then again, wait for the lights.

Combat field modifications
A common field modification was to mount a large steel shield, from the M113 Armored Cavalry Assault Vehicle, around the commander's 50-cal. (12.7 mm) gun, allowing it to be fired with some level of protection. This evolved into an "armored birdcage". Anti-mine armor kits composed of spaced aluminum and steel plates were applied to the hull bottom, although only covering from the front to halfway to the end. Later, steel plates were applied to hull sides above the front road wheels.

Chain-link fencing was applied over the front of the hull in Vietnam to counter rocket-propelled grenades.

Post–Vietnam War service
The Army began to phase out the Sheridan in 1978, although at the time there was no real replacement. Nevertheless, the 82d Airborne Division was able to keep them until 1996. The Sheridan was the only "rapidly" air-deployable tank in the inventory. Their units were later upgraded to the M551A1 TTS model, including a thermal sighting system for the commander and gunner.

In the early 1980s, the M551A1 was fitted with a visual modification kit to resemble Warsaw Pact vehicles from Soviet BMP-1, ZSU-23, T-55 to T-80s, at the National Training Center at Fort Irwin, California. These modified vehicles were used in part of the U.S. Army's Soviet opposition forces (OPFOR) by providing realistic ground training to U.S. military units about Soviet combat doctrine in a desert environment. The OPFOR Sheridans no longer fulfill that role, having been retired at the end of 2003 and subsequently scrapped or made available as "hard targets" or, in a few cases, as museum pieces. Many were dumped to create artificial reefs.

Panama
The Sheridan's only air drop in combat occurred during the United States invasion of Panama (Operation Just Cause) in 1989, when 14 M551s were deployed with C Company, 3/73rd Armor, 82nd Airborne Division. Four M551s were secretly delivered to Howard Air Force Base in Panama aboard a C-5 Galaxy in November 1989, days before the invasion. They were attached to TF Bayonet (193rd Infantry Brigade), and attached down further to TF Gator. These Sheridans took part in the attack on the Comandancia, initially supported by fire from Quarry Heights, and later displacing forward into the city. As part of Team Armor, these Sheridans later provided support to JSOC elements as they secured high-value targets throughout Panama City. The remaining 10 Sheridans were delivered via C-141 low-velocity airdrop (LVAD) to Torrijos-Tocumen Airport some hours after H-hour. One of these was destroyed after its parachutes failed to deploy, while another was damaged. As of 2009, this marked the first and only combat air-drop of tanks in history.

The Sheridan was praised for its performance in Panama. A U.S. after-action report noted the Sheridan's "extreme psychological effect on enemy forces", who were apparently deterred from firing at U.S. forces reinforced by tanks.

Gulf War
In the early days of Desert Shield, Sheridans were airlanded in Saudi Arabia before coalition heavy armor arrived by ship. The first Sheridans sent were the M551A1 model. The Army hastily sent 60 M551A1 TTS models with the thermal sight upgrade to replace the older models. The 3/73rd used the Sheridan as part of a flanking force in Operation Desert Storm, and saw tank-on-tank combat. Their role was limited to reconnaissance due to their age and light armor. It is likely that no more than six Shillelagh missiles were fired at Iraqi anti-tank guns or T-55s; this was the only occasion in which Shillelagh missiles were fired in anger, from the inventory of 88,000 missiles produced. Other than some overheating problems in the summer months of the buildup, the Sheridan suffered no mechanical breakdowns in combat and performed extremely well.

Australian trials
During 1967 and 1968 the Australian Army trialed two Sheridans to determine if the type met a requirement for light armored fighting vehicles to serve with the Royal Australian Armoured Corps newly formed cavalry regiments. The main trials took place in the tropical Innisfail area of north Queensland between January and June 1968. In January 1969 the Minister for the Army announced that Australia would not purchase any Sheridans as the tanks did not meet the Army's requirements. The main shortcoming revealed in the trials concerned the safety of the combustible case. The two Sheridans were returned to the U.S. Army in early 1969, and the Australian Army met its requirement by fitting turrets from Alvis Saladin armored cars to M113 armored personnel carriers.

Replacement
In 1977, TRADOC commander General Donn A. Starry met with Army Chief of Staff General Edward C. Meyer to convince him that the service should retire the Sheridan. Starry had commanded the 11th ACR in Vietnam, and knew the vehicle's shortcomings. Starry's arguments prevailed over those of Army Material Command commander General John R. Guthrie, a Sheridan defender, and Meyer agreed the Sheridan would be retired. The Army decided on the M60A1 as the service's interim successor until the M3 Bradley was ready. At the time, 567 Sheridans existed in USAREUR, 535 in the continental U.S., and 41 in the Pacific. The Army began converting units in Europe in 1978, and in the rest of the service by 1980. The Army sustained 140 Sheridans in the 82nd Airborne Division and the National Guard. Some Sheridans were kept in pre-positioned reserve.

Several attempts to improve or replace the Sheridan have been made over the years since it was introduced. In 1976, DARPA (followed by TACOM) initiated the High Mobility/Agility (HIMAG) program. Several concepts were pursued, including the High Survivability Test Vehicle (Lightweight) and the Elevated Kinetic Energy (ELKE) gun system. The latter was trialed on a Sheridan hull in 1982. Following the Iran hostage crisis, the Rapid Deployment Force concept was pursued by both the Army and the Marine Corps. The Marine Corps initiated the Mobile Protected Weapon System (MPWS) program. In 1983, the Naval Surface Weapons Research Center Laboratory mounted a 105 mm caliber gun onto a Sheridan chassis. The Army initiated the Mobile Protected Gun program, and announced plans to modify Sheridans with 105 mm or 120 mm caliber guns. Neither program was pursued further; The Army project was canceled in 1985.

From 1978 to 1980, under the joint Army–Marine Corps Advanced Antiarmor Vehicle Evaluation (ARMVAL), TACOM rebuilt 10 Sheridans with the General Motors 8V53T diesel engine and improved suspension. The vehicle's armament and some armor was removed. The uprated engine and improved suspension improved the power-to-weight ratio and cross-country mobility. The Army also evaluated a fully stabilized Staget sighting system.

In 1987, the Army tested a version of the LAV-25, classified as the M1047. The Army determined that these were unsuitable for LAPES, and could not match the firepower of the Sheridan. Congress did not favor the M1047, though a few were deployed with the 3/73rd Armor in the Gulf War. The Marine Corps also developed the LAV-105 to meet its requirements, but later canceled that project as well. In 1992, the Army selected FMC Corporation to produce the Armored Gun System (AGS), later type classified as the M8 Armored Gun System. The AGS was canceled in 1996 by the Pentagon before it could enter production. United Defense proposed the AGS as its mobile gun system variant in the Interim Armored Vehicle program. In 2000, the Army instead selected a variant of the General Dynamics LAV III, later type-classified as the M1128 Mobile Gun System. The Mobile Gun System's problematic service history led to the vehicle's planned retirement in 2022.

The Army initiated development of a light tank acquisition program called Mobile Protected Firepower, selecting the General Dynamics Land Systems Griffin II in June 2022.. The U.S. Army took delivery of the first production vehicle in February 2024, and the vehicle has been type classified as the M10 Booker.

Armament

The 152 mm M81 gun-launcher that came to be used in the Sheridan was developed by Ford-Aeronutronic under a contract awarded by the Army in 1959. The gun's primary purpose was to fire the Shillelagh missile, but it could also fire more conventional combustible case ammunition. Two factors contributed to the selection of such a large-caliber gun. The Army desired a gun that would be capable of penetrating 150 mm of armor at 60 degrees, more than the 76 mm guns of the M41 or T92 were capable of. Secondly, the Shillelagh missile housed complicated electronics in addition to its warhead. As a consequence of the pairing of a large caliber gun and relatively lightweight vehicle, only low-velocity rounds would be compatible with the gun.
 * Primary armament

A number of existing vehicles already mounted only ATGMs, or alternately recoilless rifles like the M50 Ontos, but these typically had limited utility in the infantry support role, or in the case of Ontos could not be reloaded from within the vehicle. The XM551 appeared to offer a superior balance between anti-tank and infantry support. The gun was ideal for infantry support. The large, low velocity gun could fire a large high explosive projectile or canister shot. In comparison, high-velocity anti-tank guns over-penetrated soft targets, while smaller caliber weapons could not carry as great a payload.

The Shillelagh missile system experienced problems with its missile guidance system early in its development. Two problems were identified. First, smoke from the rocket motor disrupted the infrared signal, necessary for guidance, between the tank and missile. A similar issue was identified during conditions where the sun was behind the turret. The first issue was resolved by changing the propellant to a composition that produced less smoke. This and other fixes were successful in resolving the problems with the missile guidance. In a year-long test that concluded in 1964, 58 out of 63 launches were successful.

The M81 fired combustible case conventional ammunition in addition to the Shillelagh missile. This solution was chosen rather than a conventional metal case because the Army desired that the Sheridan use the same ammunition as the MBT-70. In theory the combustible nitrocellulose case would be completely consumed during the firing of the ammunition. In practice, as often as 39 percent of the time, the case could absorb moisture from the air and only be partially consumed. This was dangerous to the crew as the smoldering case could prematurely detonate the next loaded round, as happened three times during five months of testing from November 1966 to March 1967. The cases could also break open, or swell so much with moisture that they could not be chambered. The Army started packaging the rounds in Neoprene bags to reduce the impact of moisture on the combustible case rounds. These were removed by the loader before the round was used. The combustible case was made more durable, and less likely to break, in subsequent generations of ammunition. An open-breach scavenging system using compressed air to blow any debris out of the gun was installed to resolve the issue of smoldering debris in the breach. This created problems of its own as the system could blow smoldering debris into the crew compartment. Recognizing the danger, the Army canceled production of this system. A closed breach system that solved the problem was put into production in 1968. Vehicles without this system, the first 700 off the production line were waylayed in storage pending the installation of this system. The gun with this new system installed was called the M81E1. Sheridans with this system installed carried 29 rounds of ammunition instead of 30 due to space constraints.

The second and even third road wheels could clear off the ground when the main gun fired high-explosive anti-tank rounds. The recoil was so violent that components such as the commander's birdcage armor and the searchlight were liable to come off. In the Vietnam War, firing the gun often adversely affected the delicate electronics, which were at the early stages of the transition to solid state devices, so the missile and its guidance system was omitted from vehicles deployed to South Vietnam. The expensive missile was fired in anger only in the Persian Gulf War's Operation Desert Storm, despite a production run of 88,000 units.

Ammunition:
 * MGM-51 Shillelagh missile.
 * MTM-51 Shillelagh missile training round.
 * M409, high-explosive anti-tank multipurpose (HEAT-MP).
 * HE-T XM657E2 Shell, high explosive. Never standardized.
 * Canister M625, beehive anti-personnel round launching 10,000 13-grain flechettes from the muzzle. Could be used to clear foliage or against personnel.
 * XM617, anti-personnel round firing 8,200 fléchettes.
 * XM410-WP, white phosphorous smoke round. Never standardized.
 * M411A1 Shell (TP-T), training round.

The commander's cupola was armed with a .50 caliber M2HB in a flexible anti-aircraft mount on the turret. Stowage capacity was for 1000 rounds
 * Secondary armament

Early production Sheridans were armed with the 7.62 mm M73 coaxial machine gun. These were soon replaced with the M73E1 model and then the 7.62 mm M219 variant. The M73 and M219 were problematic designs and were replaced by the 7.62 mm M240 machine gun. Stowage capacity was for 3,000 rounds.

Early XM551 pilots had a .50 caliber spotting rifle, and pilot #7 had a 15mm XM122 spotting rifle. Development of spotting rifles was ended when it was decided to eventually install laser rangefinders on the production vehicle.

Armor
The vehicle had a steel turret and aluminum hull. Although the hull could deflect heavy machine gun fire of up to 12.7 mm AP, it was easily penetrated by rocket-propelled grenades (RPGs), which could destroy the vehicle if the spalling contacted the caseless main gun rounds. Like the M113 armored personnel carrier, it was vulnerable to mines.

Tactical mobility

The Sheridan was powered by a large 300-hp (224 kW) Detroit Diesel 6V53T diesel engine, and a flat track (no support rollers). The XM551 thus had an excellent power-to-weight ratio and mobility, able to run at speeds up to 72 km/h (45 mph). However, the vehicle proved to be very noisy and early Sheridans were unreliable under combat conditions.

Swimming capability was provided by a flotation screen. The front armor was overlain by folding "surfboard". This could be opened up into a sloping vertical surface in front of the driver, providing a bow of a boat hull, about level with the top of the turret. Fabric formed the rest of the water barrier, folding up from compartments lining the upper corner where the side met the top of the hull, and held up at the back with poles. The front of the "hull" was provided with a plastic window, but in practice it was found that water splashing onto it made it almost useless, and the driver instead usually had to take steering directions from the vehicle commander. The M2 Bradley adopted a similar solution, but dropped it with upgraded armor. The Sheridan could swim across a river that was about 46 m (50 yards) wide. Tanks in the Patton series (M46, M47, M48), as well as the M60 tank could not perform these operations; they would have to crawl along the river bottoms using snorkels. Not by design, it was found that the swimming hardware acted to reduce the effectiveness of RPG hits. Although it was rarely used in Vietnam, fording was frequently used during Reforger exercises in Europe.

Strategic mobility

The Sheridan can be rigged for low-velocity airdrop from C-130 (19,000 kg, 42,000 lb max load), C-141 aircraft (17,460 kg, 38,500 lb max load), and the C-5. Many films exist showing the Sheridan being pulled out of a C-130 Hercules transport by brake chutes and skidding to a stop. The Low Altitude Parachute Extraction System (LAPES) is a somewhat risky maneuver that allows accurate delivery onto a field when landing is not possible, and the practice was stopped in the late 1990s. The tank is strapped down to a special pallet which absorbs most of the landing impact. The crew does not ride in the tank during extraction, but parachutes from another plane. On landing, they go to their tank, release the lines, and drive it away.

Variants

 * XM551/M551 - The M551 was the basic production model, beginning production in 1967. The XM551 had been a limited run pre-production model produced in 1965.
 * "Two Box" M551 - With the obvious shortcomings of the Shillelagh missile, all but two of the guidance and fire control components of the missile system were removed (the power supply and rate sensor were retained. These were needed for stabilized turret operation.). The resulting additional space was filled with two separate boxes, one for 7.62×51mm NATO ammunition (coaxial machine gun), and one for 12.7×99mm NATO (.50 BMG) ammunition, and the missile stowage was redesigned to accept conventional rounds.
 * M551A1 - Upgraded M551 with AN/VVG-1 laser rangefinder.
 * M551A1 TTS - Tank Thermal Sight, fitted with the AN/VSG-2B thermal sight unit, similar to the unit used on the M60A3 MBT. This later became standard to all M551A1s.
 * M551 NTC - National Training Center. Using M551 hulls, the NTC created a number of mock vehicles for training exercises resembling common Soviet/Warsaw pact types. They were also known as 'vismods', short for Visually Modified. They have since been retired in favor of similarly converted M113s and M1 Abrams.
 * Armored Tracked Recovery Vehicle (ATRV) - Prototype.

Users

 * Former
 * U.S. Army

Considered but rejected to replace the M50 Ontos under the Light Armored Combat Vehicleprogram. A Sheridan was evaluated from 1967 to 1968, but was rejected because the Australia believed would fare poorly in "Vietnam-type" conflicts.
 * Prospective users
 * U.S. Marine Corps
 * Australian Army

Display vehicles

 * Airborne & Special Operations Museum, Fayetetteville, NC
 * American Armoured Foundation's Tank and Ordnance War Memorial Museum, Danville, VA. M551A1 deployed in Desert Shield/Storm. Markings: 3rd Battalion 73 Regiment, Co. B, 2nd platoon, attached to the 82nd Airborne Division.
 * American Heritage Museum, Stow, Massachusetts has an M551 that is in operating condition.
 * American Society of Military History and Museums, South El Monte, Ca. 2 non running exhibits and a running, ex-vismod unit.
 * Antioch, Illinois has a veterans monument displaying a M551A1 across the street from the police station.
 * Camp Joseph T. Robinson, Arkansas National Guard Museum
 * Camp Perry, near Port Clinton, Ohio, has an M551 on display as part of a static display.
 * Columbia, MO Outdoor display at American Legion Park, off East Broadway, 602 Legion Ln, Columbia, MO 65201, United States.
 * First Division Museum at Cantigny, an example of the M551A1 is on display in the tank park outside the museum in Wheaton, Illinois.
 * Fort Bliss, static display at Sheridan Gate entrance.
 * Fort Hunter Liggett on static display at the entrance.
 * Fort Irwin/NTC, has one vehicle on display at the 11th Cavalry Regiment museum.
 * Fort Johnson, a "T-72" VISMOD is on display on Mississippi Avenue near the headquarters of 1st Battalion, 509th Parachute Infantry Regiment.
 * Fort Knox, Kentucky. Static display at Wilson Road entrance.
 * Fort Liberty, NC Outdoor exhibit at the 82d Airborne Division War Memorial Museum.
 * Fort Moore, static display on Tower Branch of U.S. Army Airborne School across from Maneuver Center of Excellence.
 * Fort Richardson, Camp Denali on static display.
 * Gowen Field, Idaho Army National Guard
 * Hardwood Range, an example is on static display at the visitor center at Hardwood Air-to-Ground Weapons Range in Finley, Wisconsin.
 * Ike Skelton Missouri National Guard Training Facility, Jefferson City Missouri. Ike Skelton Training Facility has a M551 in their outside museum.
 * Louisiana National Guard Training Center Pineville in Pineville, LA static display outside of the post museum.
 * Leon Davenport Building in Blairsville, GA has an M551 on display outside.
 * Mott's Military Museum in Groveport, Ohio has an M551 on display outside with other various vehicles.
 * The Museum of American Armor, Old Bethpage, NY on static display.
 * Museum of Missouri Military History, on static display outside the museum.
 * The Ontario Regiment Museum, in Oshawa, has two Sheridan tanks on display. One is in not operating condition and the other has been restored with its original 11th Cavalry markings.
 * Sullenberger Aviation Museum
 * Vietnam Veterans of America, in Baltimore, MD has an M551A1 on display outside of the building at 6401 Beckley St.
 * Watervliet Arsenal
 * Yad La-Shiryon Israel
 * Yuma Proving Ground in Yuma, AZ. On static display outside range control.

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

title: M551 Sheridan


text:
MGM-51 Shillelagh

The Ford MGM-51 Shillelagh was an American anti-tank guided missile designed to be launched from a conventional gun (cannon). It was originally intended to be the medium-range portion of a short, medium, and long-range system for armored fighting vehicles in the 1960s and '70s to defeat future armor without an excessively large gun. Developing a system that could fire both shells and missiles reliably proved complex and largely unworkable for the United States.

It was originally developed for the experimental but never produced MBT-70 tank and served most notably as a primary weapon of the M551 Sheridan light tank, but the missile system was not issued to units serving in South Vietnam and was retired in 1996. It was also used on the M60A2 "Starship", which was phased out by 1981. Ultimately, very few of the 88,000 rounds produced were ever fired in combat, and the system was largely succeeded by the later BGM-71 TOW wire-guided missile, which was first produced in 1970. Western forces largely gave up on the gun-launched missile concept, although it remains in use on former Soviet Union designs.

The name of the system is that of a traditional wooden club from Ireland.

Background
With the rapid increase in armor thickness during World War II, tanks were becoming increasingly able to survive rounds fired from even the largest of World War II-era anti-tank guns. A new generation of guns, notably the British 105 mm Royal Ordnance L7, were able to cope with newer tanks, but it appeared that in another generation the guns needed would be too large to be practical.

To overcome this potential difficulty, the US Army began to favor high-explosive anti-tank (HEAT), or shaped charge rounds in the 1950s. A shaped charge's penetration is not strongly dependent on the speed of the round, allowing rounds to be fired at much lower velocities, and thus from much lighter guns. They also work better at larger diameters, and a large-diameter low-velocity gun makes for an excellent assault gun that can be mounted on light or medium-weight vehicles. However, the low speed of the round makes it hard to aim over longer distances. The US Army sought to overcome this problem by developing guided missiles that had shaped charge warheads and were accurate beyond a few hundred yards.

Development
In 1958, the Army thought that existing knowledge was sufficient to begin work on a guided missile with a HEAT warhead, and in June 1959 Sperry and Ford Aeronutronic were asked for designs to fill the shorter range role. Ford won the contract and started work on the XM13. The first test shots were fired in 1960, and limited production started in 1964. The missile was then known as the MGM-51A.

The basic system was quite advanced for its day. The missile body consisted of a long tube with fold-out fins at the extreme rear, which was propelled from the new M81 gun with a small charge strapped on the rear. Once clear of the gun, the fins popped open and the engine ignited. To keep the missile from spinning while in the gun due to the rifling, a small "key" fitted into a straight groove in the rifled gun. Aiming the missile was simple; the gunner simply kept his gunsight on the target, while electronics in the sighting system tracked the missile optically and sent corrections through an IR link, similarly to a TV remote control. In general the gunners were able to achieve excellent hit rates.

The main problem with the system is firing the main gun with a projectile vs. a missile. The recoil from the gun throws all the missile optics off, limiting the use of the M551 to either anti-tank or bunker buster.

Because the system was so advanced, the development of the Shillelagh was fraught with problems. Ford Aeronutronic underestimated the complexity of the task of designing a missile as advanced as this, and there were major problems with the propellant, igniter, tracker and infrared command link of the missile.

Sheridan
The M81/MGM-51 was first installed on the M551 Sheridan. The Sheridan was a light aluminum-armored AFV designed to be air transportable and provide antitank support for airborne forces. In 1966, the US Army began pressing General Westmoreland to field the tank in South Vietnam, but he declined, stating that with no main gun ammunition, the Sheridan was basically nothing more than a $300,000 machine gun platform. In 1968, 152 mm main gun ammo became available, and the Sheridan was deployed to South Vietnam for combat operations in January 1969. Shillelagh missiles did not prove to be a problem in the Vietnam War: they were not used.

The Sheridans' 152 mm main guns were used in combat operations in Vietnam but proved troublesome. The combustible casings of the 152 mm caseless ammunition rounds did not burn completely, requiring a complicated and slow gas-driven scavenging system. They were also liable to detonate if the vehicle was hit. Firing the gun caused such a large recoil as to result in failures in the delicate missile firing electronics on the tank. These problems, in combination with the lack of suitable targets, resulted in their deployment without the complex missile system.

The Shillelagh was considerably larger than a conventional round, so only a small number could be carried. Typical loads consisted of only nine missiles and twenty M409 HEAT rounds for short-range use. In addition, the missile proved to have a very long minimum range. Due to the layout of the vehicle, the missile did not come into the sight of the gun/tracker system until it was 800 yd from the vehicle, at which point it could start to be guided. Because of its maximum range of about 2200 yd, the system was only effective within a fairly narrow span of combat distances.

While the maximum range of 2200 yd was acceptable, the Army thought that it could and should be improved. Ford received a contract to develop a longer range version in 1963, and returned a slightly larger design the next year. Test firing of the new MGM-51B started the next May, and production began in October 1966. Besides the changes to the missile, the gun was modified. In testing it was found that the key slot in the gun led to cracking after firing only a few shells. After further study, a version with a shallower slot and new barrel was selected, creating the M81E1/MGM-51C.

The new missile was about 45 in long, about 6 in in diameter, and weighed 60 lb. It remained in production until 1971, by which time 88,000 had been produced, probably in anticipation of use by main battle tanks (below). Although it is commonly asserted that some missiles were fired during the Gulf War, the US Army denied this.

M60A2 "Starship"
Even with its problems, the system had shown that it could be used by an airborne tank to destroy a main battle tank. The question of whether or not it could fill its original role as the main armament of all tanks was still open. The Army had originally started development of a low-profile turret with a short barrel for their existing M60 tanks in the 1960s, but did not place an order for delivery until 1971, when the main problems with the system had been resolved. The Shillelagh-equipped M60A2s entered service in 1974, but were hampered by reliability problems, and were phased out in 1980. The final revision of the M60A3 used the same 105 mm gun and turret as the M60A1.

MBT-70
The most ambitious project based on the Shillelagh was the MBT-70, an advanced US–German tank. Design work on the MBT-70 began in 1963. The tank mounted a huge auto-loader turret on top of a very short chassis, so short that there was no room for a driver in the front hull. Instead of being located in the conventional position, the driver was seated in the turret with the other crew members, in a rotating cupola that kept him facing forward. The gun was a new longer-barreled design, the XM-150, which extended range and performance to the point where it was useful for sabot type rounds as well. However, the project dragged on, and in 1969 the estimated unit cost had risen fivefold. Germany pulled out of the project. The Army proposed a "cut-down" version of the system, the XM-803, but Congress cancelled it in November 1971. It initiated and issued funds to the M1 Abrams project the next month. The M1 design incorporated a conventional gun.

title: MGM-51 Shillelagh


text:
Talk:Joachim I Nestor, Elector of Brandenburg

Untitled
David -- when did the Margraves of Brandenburg, Electors of the HRE, become simply electors? Do you know if Kurfürst simply replaced the title? this seems odd to me, since I can't see the King of Bohemia blithely accepting a lesser title (in that case -- or the Duke of Bavaria, for that matter). Just trying to make sense of this before I start on a clean-up campaign. JHK
 * What are you talking about? No one was ever "simply" an elector.


text:
Giovanni Battista Pergolesi

Giovanni Battista Draghi (4 January 1710 – 16 or 17 March 1736), usually referred to as Giovanni Battista Pergolesi, was an Italian Baroque composer, violinist, and organist, leading exponent of the Baroque; he is considered one of the greatest Italian musicians of the first half of the 18th century and one of the most important representatives of the Neapolitan school.

Despite his short life and few years of activity (he died of tuberculosis at the age of 26), he managed to create works of high artistic value and historical importance, among which we remember La serva padrona (The Maid Turned Mistress), of the highest importance for the development and diffusion of the opera buffa in Europe, L'Olimpiade, considered one of the masterpieces of the opera seria of the first half of the eighteenth century, and the Stabat Mater, among the most important works of sacred music of all time.

Biography
Born in Jesi in what is now the Province of Ancona (but was then part of the Papal States), he was commonly given the nickname "Pergolesi", a demonym indicating in Italian the residents of Pergola, Marche, the birthplace of his ancestors. He studied music in Jesi under a local musician, Francesco Santi, before going to Naples in 1725, where he studied under Gaetano Greco and Francesco Feo among others. On leaving the conservatory in 1731, he won some renown by performing the oratorio in two parts  ("The Phoenix on the Pyre, or The Death of Saint Joseph"), and the dramma sacro in three acts, Li prodigi della divina grazia nella conversione e morte di san Guglielmo duca d’Aquitania ("The Miracles of Divine Grace in the Conversion and Death of Saint William, Duke of Aquitaine"). He spent most of his brief life working for aristocratic patrons such as Ferdinando Colonna, Prince of Stigliano, and Domenico Marzio Carafa, Duke of Maddaloni.

Pergolesi was one of the most important early composers of opera buffa (comic opera). His opera seria, Il prigionier superbo, contained the two-act buffa intermezzo, La serva padrona (The Servant Mistress, 28 August 1733), which became a very popular work in its own right. When it was performed in Paris in 1752, it prompted the so-called Querelle des Bouffons ("quarrel of the comic actors") between supporters of serious French opera by the likes of Jean-Baptiste Lully and Jean-Philippe Rameau and supporters of new Italian comic opera. Pergolesi was held up as a model of the Italian style during this quarrel, which divided Paris's musical community for two years.

Among Pergolesi's other operatic works are his first opera seria La Salustia (1732), Lo frate 'nnamorato (The brother in love, 1732, to a text in the Neapolitan language), L'Olimpiade (January 1735) and Il Flaminio (1735, to a text in the Neapolitan language). All his operas were premiered in Naples, apart from L'Olimpiade, which was first given in Rome.

Pergolesi also wrote sacred music, including a Mass in F and three Salve Regina settings. The Lenten Hymn 'God of Mercy and Compassion' by Redemptorist priest Edmund Vaughan is most commonly set to a tune adapted by Pergolesi. It is his Stabat Mater (1736), however, for soprano, alto, string orchestra and basso continuo, which is his best-known sacred work. It was commissioned by the Confraternita dei Cavalieri di San Luigi di Palazzo, which presented an annual Good Friday meditation in honour of the Virgin Mary. Pergolesi's work replaced the one composed by Alessandro Scarlatti in 1724, but which was already perceived as "old-fashioned," so rapidly had public tastes changed. While classical in scope, the opening section of the setting demonstrates Pergolesi's mastery of the Italian baroque durezze e ligature style, characterized by numerous suspensions over a faster, conjunct bassline. The work remained popular, becoming the most frequently printed musical work of the 18th century, and being arranged by a number of other composers, including Johann Sebastian Bach, who reorchestrated and adapted it for a non-Marian text in his cantata Tilge, Höchster, meine Sünden (Root out my sins, Highest One), BWV 1083.

Pergolesi wrote a number of secular instrumental works, including a violin sonata and a violin concerto. A considerable number of instrumental and sacred works once attributed to Pergolesi have since been shown to be misattributed. Many colourful anecdotes related by Pergolesi's 19th-century biographer Francesco Florimo were later revealed as hoaxes.

Pergolesi died on 16 or 17 March 1736 at the age of 26 in Pozzuoli from tuberculosis and was buried at the Franciscan monastery one day later.

Pergolesi was the subject of a 1932 Italian film biopic Pergolesi. It was directed by Guido Brignone with Elio Steiner playing the role of the composer.

Legend and posthumous fame
If in life, despite numerous awards, Pergolesi's fame was almost exclusively limited to the Neapolitan and Roman musical milieu, so it should come as no surprise that this figure of composer, who died very young with an artistic parable of only five years and yet able to leave a handful of unforgettable compositions, has been able to influence poets and artists who, during the 19th century, reinterpreted the figure in a romantic key.

As the historian and traveler Charles Burney wrote: Indeed, the myth that was born throughout Europe around his life and work after his death represents an exceptional phenomenon in the history of music. Mozart will experience a similar phenomenon after his death. Thus, more than three hundred works have been attributed to him, of which only about thirty have been recognized by modern critics as true Pergolesi's compositions, a phenomenon which testifies the reputation of the composer.

However, already in the middle of the 18th century Pergolesi was immensely better known than he had been in life: as mentioned, the numerous prints of his compositions began to spread throughout Europe. Several years after Pergolesi's death, the performance in Paris, in 1752, of La Serva padrona by an Italian comic opera troupe, triggered the famous Querelle des Bouffons between the defenders of French music and the supporters of the opera buffa. For Jean-Jacques Rousseau, in particular, the freshness and the grace of his music was the dazzling demonstration of the superiority of Italian opera over French lyric tragedy. The French composer André Grétry said: Above all, the scarcity of tangible information about his life and works was fertile ground for the flourishing of imaginative anecdotes of all kinds. The doubt crept in that his tragic end was due not to natural causes but to poisoning by musicians envious of his talent. Apollonian beauty and numerous tragic loves were attributed to him.

Because of this extraordinary posthumous fame, the catalog of his works had an unpredictable destiny: during the 18th century and 19th century spread in Europe the practice of publishing under his name, for the purpose of speculation, any score having the musical style of the Neapolitan school. By the end of the 19th century, this led to over five hundred compositions in the informal catalog of his works. Contemporary studies have reduced Pergolesi's compositions to less than fifty, and of these only twenty-eight are the works whose paternity is considered sure.

There are still serious doubts about the attribution of various works, even among the best known, such as the Salve Regina in F minor. Several music and record editions perpetuate these uncertainties about the authorship of various compositions, publishing in his name compositions certainly produced by other authors, such as the arias Se tu m'ami (certainly composed by the musicologist Alessandro Parisotti in the second half of the 19th century and included in one of his collections of baroque arias under the name of Pergolesi) and Tre giorni son che Nina (attributed to Vincenzo Legrenzio Ciampi) or the Magnificat in D major, composed by his teacher Francesco Durante.

The situation of extreme uncertainty that distinguishes the catalog of Pergolesi's works can be easily described with the case of Pulcinella by Igor Stravinsky: composed in 1920 as a tribute to the style of the composer from Jesi, the most recent music critics have established that of the 21 pieces used for this composition, as many as 11 are to be attributed to other authors (mainly Domenico Gallo), two are of dubious attribution and only eight (mostly taken from his operas) can be attributed to Pergolesi.

Pergolesi's works on screen
Pergolesi's Salve Regina is a highlighted performance in the movie Farinelli (1994), in which Farinelli also performs Stabat Mater Dolorosa in the only duet. The first and last parts of Pergolesi's Stabat Mater were used in the soundtrack of the movie Jesus of Montreal (Jésus de Montréal) (1989); the fifth part ("Quis est homo") was used in the soundtrack of the movie Smilla's Sense of Snow (1997); the last part was also used in the movie Amadeus (1984) and in the movie The Mirror (1975) by Andrei Tarkovsky. The film Cactus (1986) by the Australian director Paul Cox also features Pergolesi's Stabat Mater on the soundtrack. Nothing Left Unsaid, a 2016 documentary on Gloria Vanderbilt and Anderson Cooper, used the last movement ("Quando Corpus / Amen") of Pergolesi's Stabat Mater.

Works
The standard catalogue of Pergolesi's works was produced by Marvin Paymer in 1977, ascribing a unique P number to each item so that – for example – the well-known Stabat Mater is P.77.

Sacred music

 * Antifona "In caelestibus regnis" (1731)
 * Confitebor tibi Domine (Psalm 111) in C for Soprano, Alto, Choir, Strings and Continuo (1732)
 * Dixit Dominus (Psalm 110) for Soprano, Bass, 2 Choirs and 2 Orchestras (1732)
 * Laudate pueri Dominum (Psalm 113) in D for Soprano, Mezzo, Choir and Orchestra (1734)
 * Mass in D (1732)
 * Mass in F "San Emidio" (Missa romana) for Soprano, Alto, 2 Choirs, 2 Orchestras and Continuo (1732)
 * Oratorio  (1731, atrium of the Chiesa dei Girolamini, Naples)
 * Dramma sacro Li prodigi della divina grazia nella conversione e morte di san Guglielmo duca d'Aquitania (1731, Monastery of Sant'Agnello Maggiore, Naples)
 * Salve regina in a for Soprano, Strings and Continuo (1731)
 * Salve regina in c for Soprano, Strings and Continuo (1735)
 * Salve regina in f for Alto, Strings and Continuo (1736, adapted from the Salve regina in c)
 * Stabat Mater in f (wr. 1735, pr. 1736, Naples)

Operas

 * La Salustia, January 1732, Teatro San Bartolomeo, Naples; text possibly by Sebastiano Morelli after Alessandro Severo by Apostolo Zeno
 * Lo frate 'nnamorato, 27 September 1732, Teatro dei Fiorentini, Naples
 * Il prigionier superbo, containing the intermezzo La serva padrona, 28 August 1733, Teatro San Bartolomeo, Naples
 * Adriano in Siria, containing the intermezzo Livietta e Tracollo, 25 October 1734, Teatro San Bartolomeo, Naples
 * L'Olimpiade, January 1735, Teatro Tordinona, Rome
 * Il Flaminio, autumn 1735, Teatro Nuovo, Naples

Orchestral music

 * Sinfonia in B-flat major
 * Sinfonia in D major
 * Sinfonia in F major
 * Sinfonia in G major, P.35
 * Sinfonia in G minor, P.24c
 * Flute Concerto in G major, P.33 (very doubtful)
 * Concerto for Flute and 2 Violins in D major
 * Concerto for Flute and 2 Violins in G major
 * Concerto for 2 Harpsichords and Orchestra
 * Violin Concerto in B flat major

Spurious

 * 6 Concerti armonici for 4 violins, viola and continuo, long attributed to Pergolesi but in fact by Wassenaer

Keyboard works

 * Harpsichord Sonata in A major, P.1
 * Harpsichord Sonata in D major
 * Organ Sonata in F major
 * Organ Sonata in G major

Chamber works

 * Trio Sonata in G major, P.12
 * Trio Sonata in G minor
 * Unspecified Andantino, for violin and piano
 * Violin Sonata in G major
 * Sonata No.1 in G major, for 2 violins
 * Sinfonia in F major, for cello and continuo

title: Giovanni Battista Pergolesi


text:
Talk:Early music

Statutory perpetual copyright
Early Music says:
 * (except that protected by a statutory perpetual copyright in one or more Berne Convention signatories

I've never ever heard of such a thing as a 'statutory perpetual copyright'... -- SJK

 * Some countries' laws (but not the US; see US Const. 1.8.8) provide for a perpetual copyright on specific works.
 * For instance, the UK has one on Peter Pan works by Barrie.
 * See also the following:
 * Wikipedia article public domain
 * Bono Act on E2
 * Google search for |"peter pan" "perpetual copyright"|
 * --Damian Yerrick

 * Early music is in the public domain, but OTOH, early music notation is very different from modern music notation. (Heck, just putting it that way is a little deceptive; there is no single early music notation.) Early music notation doesn't indicate dynamics or articulation, and even omits some accidentals (the so-called "musica ficta") much like vowels in Semitic languages. (The notion is that "everybody knows" that if you don't apply the accidental, a dissonance results, so why write it in?) Early music notation time signatures, where they even exist, are quite different--the same note shape is used for the subdivision of the beat ("prolation") whether it's duple or triple, which will certainly throw off modern notation readers. A modern edition of an early music piece thus requires significant knowledge and editorial judgment, and such editions typically are copyrighted. (That's not to say that someone working from the original manuscripts or fascimiles thereof can't make a public domain or copylefted edition in modern notation, just that just because the original is PD, derived works aren't necessarily PD.)

 * Does Lilypond support the more common of the old notations? In that case, would it be possible to write a program that uses heuristic methods to convert the old notations to the less-ambiguous modern notation? --Damian Yerrick

Notation and performance
This sentence seems untrue or at least inaccurate: As the article explains: Early music musicians, composers, and transcribers had a "contract" just as we do today, with contemporary musicians being trained with the knowledge necessary to interpret contemporary notation. Hyacinth 07:16, 2 Jul 2004 (UTC)
 * "Early music notation is, by current standards, very sketchy."
 * "Renaissance musicians would have been highly trained in dyadic counterpoint and thus possessed this and other information necessary to read a score."

 * Furthermore, the term "dyadic counterpoint" is a strange term and doesn't really relate to the rest of the paragraph. How about a reference to Musica ficta and notes inegales instead? Wahoofive 00:43, 8 Mar 2005 (UTC)

 * Does a redirect to an explination (polyphony) help? Hyacinth 21:49, 10 Mar 2005 (UTC)

Eras in music history
The sidebar on "eras in music history" shows the "early music" era as 1500-1750. Surely that's not what you mean. Early music starts more like 1100.

 * That is Template:European art music eras. Hyacinth 01:12, 8 Mar 2005 (UTC)

Now it claims that Early Music ends in 1600, when I've never seen a practitioner exclude the Baroque from Early Music. Where do they make this stuff up? Greg 07:56, 23 January 2007 (UTC)

True! I'll change it! Lfjslohll (talk) 18:10, 11 March 2009 (UTC)

Classical music?
Why is early music said to be classical music? Early musicians generally take the attitude that they are doing pre-classical music, i.e. music up to and including the Baroque. It's classical musicians who think that early music is a kind of classical music. Greg 05:13, 26 April 2006 (UTC)

 * Perhaps you are confusing European classical music and the Classical music era. Hyacinth 17:09, 26 April 2006 (UTC)

I assure you that *I* am not the one confused. Greg 07:57, 23 January 2007 (UTC)
 * It's also interesting to note that early music performers often perform what might be considered "popular music" from earlier times. The distinction between pop music and serious music, while perhaps less important in former times, is virtually ignored in most early-music contexts. —Wahoofive (talk) 18:06, 24 January 2007 (UTC)

Early Music Dates Citation Needed
I just noticed that this page and others defining music 'eras' need a ref. for the dates. This prompted me to look on Grove Music Online and in the Oxford Concise Dictionary of Music (to find suitable refs.) - but both state that the term 'Early Music' is frequently considered to incorporates the Baroque Era(as I'm sure you all know). Grove says the following in fact: "A term once applied to music of the Baroque and earlier periods... now commonly used to denote any music for which a historically appropriate style of performance must be reconstructed". So we need to change the date, of course there will be overlap between the common practice period, but that's how things work... This may also shed some light on the above query...? Matt.kaner 03:28, 19 February 2007 (UTC)
 * It really IS a pain to define, especially as when different people discuss it, as they often mean different things. For example, I was acutally surprised when I discovered that the definition included baroque, as I had generally interpreted from fans talking about it, that it referred mainly to the renaissance era and before, when instrumental forms were either highly under-developed, or just nowhere near dominant as they became in the baorque. If it does turn out to be difficult to get a single definition pinned down, we'll have to make a section explaining the subtleties of the definition... Le  the  15:42, 9 August 2007 (UTC)

The page used to read : Early music is a term used to describe pre-Classical Western music, from the earliest written music (ca. 1000 A.D.) to 1500 at the earliest (Judd, 1998, p.4) and the end of the Baroque era in about 1750 at the latest. For information on early music, see the following articles:

Hyacinth (talk) 08:33, 29 April 2010 (UTC)
 * Medieval music (roughly 1000-1450)
 * Renaissance music (roughly 1450-1600)
 * Baroque music (roughly 1600-1750)

Citation style
as opposed to. Hyacinth (talk) 08:30, 29 April 2010 (UTC)
 * You are quite right, the citation style was long in place before I added the requests for page numbers. I stand corrected.—Jerome Kohl (talk) 16:15, 29 April 2010 (UTC)

Citation "needed"
There is NO possible way to give a citation on somethings. For example, on the fact that until a certain period music did NOT follow certain rules in writing, as is portrayed in this article. In order to properly provide a citation for that the author would have to show all works of music referred to which DID NOT follow those rules, which is quite impossible and useless... therefore I think the "citation needed" thing should be removed... I wanted to myself but I'd rather bring the subject up for discussion here first. —Preceding unsigned comment added by 109.253.35.112 (talk) 23:53, 25 December 2010 (UTC)

 * All that is needed is a reliable source that states the same.--''' SabreBD  (talk ) 00:01, 26 December 2010 (UTC)
 * Absolutely correct. The really difficult thing is not finding one author who will stick his neck out and state that (for example) suspensions were never resolved upward before 11:53 AM on 13 April 1477, and whether or not this is true does not matter, since "The threshold for inclusion in Wikipedia is verifiability, not truth". What is nearly impossible to establish is weasel language such as saying "most authorities agree" on such a thing—that really would require an impossible amount of documentation, unless you got very, very lucky! If absolutely no authority can be found to support claims like this, they should be removed, or modified to conform to a source that can be found.—Jerome Kohl (talk) 00:39, 26 December 2010 (UTC)

title: Talk:Early music


text:
BMX

BMX, an abbreviation for bicycle motocross or bike motocross, is a cycle sport performed on BMX bikes, either in competitive BMX racing or freestyle BMX, or else in general street or off-road recreation.

History
BMX began during the early 1970s in the United States when children began racing their bicycles on dirt tracks in southern California, inspired by the motocross stars of the time. The size and availability of the Schwinn Sting-Ray and other wheelie bikes made them the natural bike of choice for these races, since they were easily customized for better handling and performance. BMX racing was a phenomenon by the mid-1970s. Children were racing standard road bikes off-road around purpose-built tracks in California.

The motorcycle racing documentary On Any Sunday (1971) is generally credited with inspiring the movement nationally in the United States; its opening scene shows kids riding their Sting-Rays off-road. By the middle of that decade, the sport achieved critical mass, and manufacturers began creating bicycles designed especially for the sport.

US timeline
In 1974, George E. Esser founded the National Bicycle League as a non-profit bicycle motocross sanctioning organization. Before they set up the NBL, Esser and his wife, Mary, sanctioned motorcycle races with the American Motocross Association (AMA). Their two sons, Greg and Brian, raced motorcycles, but also enjoyed riding and racing BMX with their friends. It was their sons' interest, and the lack of BMX organizations in the East, which prompted Esser to start the NBL in Florida.

By 1977, the American Bicycle Association (ABA) was organized as a national sanctioning body for the growing sport.

Freestyle BMX is now one of the staple events at the annual Summer X Games Extreme Sports competition and the Etnies Backyard Jam, held primarily on the East and West coasts of the United States. The popularity of the sport has increased due to its relative ease and availability of places to ride and do tricks.

UK BMX explosion
In the UK, BMX was a craze which took off in the early 1980s, specifically 1982 and 1983, when the BMX bike became the must-have bicycle for children and teenagers. Previously a small niche area, BMX exploded at this time into the dominant bicycle for the younger rider, with older teenagers and even adults becoming known names through publications like BMX Bi-Weekly, featuring big names like Tim March and Andy Ruffell. The shift to freestyle from racing came in 1985 with popular styling moving from chrome frames and contrasting components in black blue or red being the norm, to brightly coloured bikes in one colour only, including their magnesium alloy wheels and even matching tyres. Because BMX exploded into Britain's streets so suddenly, it was perhaps inevitable that it would implode with similar speed, when the children who rode the bikes left school and went to work. By 1986–1987 sales in the UK had dropped off dramatically, with the new all-terrain bike or mountain bike (another trend from mid-1970s California) taking off, soon to become the most popular adult bicycle.

In 1980, the first BMX track in the UK was founded in Landseer Park, Ipswich, by the Ipswich BMX Club, which still provides coaching and races on a regular basis.

International development
In April 1981, the International BMX Federation was founded, and the first world championships were held in 1982. Since January 1993, BMX has been integrated into the Union Cycliste Internationale.

In 2003, the International Olympic Committee made BMX a full medal Olympic sport for the 2008 Summer Olympic Games in Beijing, China, and Māris Štrombergs (male, for Latvia) and Anne-Caroline Chausson (female, for France) became the first Olympic champions.

Many talented BMX riders go on to other cycling sports like downhill, including Australian Olympian Jared Graves, Eric Carter and youth BMX racer Aaron Gwin. Multiple world and Olympic champion track sprinter Chris Hoy also began as a BMX rider.

title: BMX


text:
Actual infinity

In the philosophy of mathematics, the abstraction of actual infinity, also called completed infinity, involves the acceptance (if the axiom of infinity is included) of infinite entities as given, actual and completed objects. These might include the set of natural numbers, extended real numbers, transfinite numbers, or even an infinite sequence of rational numbers. Actual infinity is to be contrasted with potential infinity, in which a non-terminating process (such as "add 1 to the previous number") produces a sequence with no last element, and where each individual result is finite and is achieved in a finite number of steps. This type of process occurs in mathematics, for instance, in standard formalizations of the notions of an infinite series, infinite product, or limit.

Anaximander
The ancient Greek term for the potential or improper infinite was apeiron (unlimited or indefinite), in contrast to the actual or proper infinite aphorismenon. Apeiron stands opposed to that which has a peras (limit). These notions are today denoted by potentially infinite and actually infinite, respectively.

Anaximander (610–546 BC) held that the apeiron was the principle or main element composing all things. Clearly, the 'apeiron' was some sort of basic substance. Plato's notion of the apeiron is more abstract, having to do with indefinite variability. The main dialogues where Plato discusses the 'apeiron' are the late dialogues Parmenides and the Philebus.

Aristotle
Aristotle sums up the views of his predecessors on infinity as follows: "'Only the Pythagoreans place the infinite among the objects of sense (they do not regard number as separable from these), and assert that what is outside the heaven is infinite. Plato, on the other hand, holds that there is no body outside (the Forms are not outside because they are nowhere), yet that the infinite is present not only in the objects of sense but in the Forms also.' (Aristotle)"

The theme was brought forward by Aristotle's consideration of the apeiron—in the context of mathematics and physics (the study of nature):

"'Infinity turns out to be the opposite of what people say it is. It is not 'that which has nothing beyond itself' that is infinite, but 'that which always has something beyond itself'.' (Aristotle)"Belief in the existence of the infinite comes mainly from five considerations:
 * 1) From the nature of time – for it is infinite.
 * 2) From the division of magnitudes – for the mathematicians also use the notion of the infinite.
 * 3) If coming to be and passing away do not give out, it is only because that from which things come to be is infinite.
 * 4) Because the limited always finds its limit in something, so that there must be no limit, if everything is always limited by something different from itself.
 * 5) Most of all, a reason which is peculiarly appropriate and presents the difficulty that is felt by everybody – not only number but also mathematical magnitudes and what is outside the heaven are supposed to be infinite because they never give out in our thought. (Aristotle)

Aristotle postulated that an actual infinity was impossible, because if it were possible, then something would have attained infinite magnitude, and would be "bigger than the heavens." However, he said, mathematics relating to infinity was not deprived of its applicability by this impossibility, because mathematicians did not need the infinite for their theorems, just a finite, arbitrarily large magnitude.

Aristotle's potential–actual distinction
Aristotle handled the topic of infinity in Physics and in Metaphysics. He distinguished between actual and potential infinity. Actual infinity is completed and definite, and consists of infinitely many elements. Potential infinity is never complete: elements can be always added, but never infinitely many.

"'For generally the infinite has this mode of existence: one thing is always being taken after another, and each thing that is taken is always finite, but always different.'"

Aristotle distinguished between infinity with respect to addition and division.

"But Plato has two infinities, the Great and the Small.""'As an example of a potentially infinite series in respect to increase, one number can always be added after another in the series that starts 1,2,3,... but the process of adding more and more numbers cannot be exhausted or completed.'"With respect to division, a potentially infinite sequence of divisions might start, for example, 1, 1/2, 1/4, 1/8, 1/16, but the process of division cannot be exhausted or completed.

"'For the fact that the process of dividing never comes to an end ensures that this activity exists potentially, but not that the infinite exists separately.'"

Aristotle also argued that Greek mathematicians knew the difference among the actual infinite and a potential one, but they "do not need the [actual] infinite and do not use it" (Phys. III 2079 29).

Scholastic, Renaissance and Enlightenment thinkers
The overwhelming majority of scholastic philosophers adhered to the motto Infinitum actu non datur. This means there is only a (developing, improper, "syncategorematic") potential infinity but not a (fixed, proper, "categorematic") actual infinity. There were exceptions, however, for example in England.

"It is well known that in the Middle Ages all scholastic philosophers advocate Aristotle's 'infinitum actu non datur' as an irrefutable principle. (G. Cantor)"

"Actual infinity exists in number, time and quantity. (J. Baconthorpe [9, p. 96])"

During the Renaissance and by early modern times the voices in favor of actual infinity were rather rare.

"The continuum actually consists of infinitely many indivisibles (G. Galilei [9, p. 97])"

"I am so in favour of actual infinity. (G.W. Leibniz [9, p. 97])"

However, the majority of pre-modern thinkers agreed with the well-known quote of Gauss:

"I protest against the use of infinite magnitude as something completed, which is never permissible in mathematics. Infinity is merely a way of speaking, the true meaning being a limit which certain ratios approach indefinitely close, while others are permitted to increase without restriction. (C.F. Gauss [in a letter to Schumacher, 12 July 1831])"

Modern era
Actual infinity is now commonly accepted in mathematics, although the term is no longer in use, being replaced by the concept of infinite sets. This drastic change was initialized by Bolzano and Cantor in the 19th century, and was one of the origins of the foundational crisis of mathematics.

Bernard Bolzano, who introduced the notion of set (in German: Menge), and Georg Cantor, who introduced set theory, opposed the general attitude. Cantor distinguished three realms of infinity: (1) the infinity of God (which he called the "absolutum"), (2) the infinity of reality (which he called "nature") and (3) the transfinite numbers and sets of mathematics.

"A multitude which is larger than any finite multitude, i.e., a multitude with the property that every finite set [of members of the kind in question] is only a part of it, I will call an infinite multitude. (B. Bolzano [2, p. 6])"

"Accordingly I distinguish an eternal uncreated infinity or absolutum, which is due to God and his attributes, and a created infinity or transfinitum, which has to be used wherever in the created nature an actual infinity has to be noticed, for example, with respect to, according to my firm conviction, the actually infinite number of created individuals, in the universe as well as on our earth and, most probably, even in every arbitrarily small extended piece of space. (Georg Cantor) (G. Cantor [8, p. 252])"

"The numbers are a free creation of human mind. (R. Dedekind [3a, p. III])"

"One proof is based on the notion of God. First, from the highest perfection of God, we infer the possibility of the creation of the transfinite, then, from his all-grace and splendor, we infer the necessity that the creation of the transfinite in fact has happened. (G. Cantor [3, p. 400])"

Cantor distinguished two types of actual infinity, the transfinite and the absolute, about which he affirmed: "These concepts are to be strictly differentiated, insofar the former is, to be sure, infinite, yet capable of increase, whereas the latter is incapable of increase and is therefore indeterminable as a mathematical concept. This mistake we find, for example, in Pantheism. (G. Cantor, Über verschiedene Standpunkte in bezug auf das aktuelle Unendliche, in Gesammelte Abhandlungen mathematischen und philosophischen Inhalts, pp. 375, 378)"

Current mathematical practice
Actual infinity is now commonly accepted in mathematics under the name "infinite set". Indeed, set theory has been formalized as the Zermelo–Fraenkel set theory (ZF). One of the axioms of ZF is the axiom of infinity, that essentially says that the natural numbers form a set.

All mathematics has been rewritten in terms of ZF. In particular, line, curves, all sort of spaces are defined as the set of their points. Infinite sets are so common, that when one considers finite sets, this is generally explicitly stated; for example finite geometry, finite field, etc.

Fermat's Last Theorem is a theorem that was stated in terms of elementary arithmetic, which has been proved only more than 350 years later. The original Wiles's proof of Fermat's Last Theorem, used not only the full power of ZF with the axiom of choice, but used implicitly a further axiom that implies the existence of very large sets. The requirement of this further axiom has been later dismissed, but infinite sets remains used in a fundamental way. This was not an obstacle for the recognition of the correctness of the proof by the community of mathematicians.

Opposition from the Intuitionist school
The mathematical meaning of the term "actual" in actual infinity is synonymous with definite, completed, extended or existential, but not to be mistaken for physically existing. The question of whether natural or real numbers form definite sets is therefore independent of the question of whether infinite things exist physically in nature.

Proponents of intuitionism, from Kronecker onwards, reject the claim that there are actually infinite mathematical objects or sets. Consequently, they reconstruct the foundations of mathematics in a way that does not assume the existence of actual infinities. On the other hand, constructive analysis does accept the existence of the completed infinity of the integers.

For intuitionists, infinity is described as potential; terms synonymous with this notion are becoming or constructive. For example, Stephen Kleene describes the notion of a Turing machine tape as "a linear 'tape', (potentially) infinite in both directions." To access memory on the tape, a Turing machine moves a read head along it in finitely many steps: the tape is therefore only "potentially" infinite, since — while there is always the ability to take another step — infinity itself is never actually reached.

Mathematicians generally accept actual infinities. Georg Cantor is the most significant mathematician who defended actual infinities. He decided that it is possible for natural and real numbers to be definite sets, and that if one rejects the axiom of Euclidean finiteness (that states that actualities, singly and in aggregates, are necessarily finite), then one is not involved in any contradiction.

The present-day conventional finitist interpretation of ordinal and cardinal numbers is that they consist of a collection of special symbols, and an associated formal language, within which statements may be made. All such statements are necessarily finite in length. The soundness of the manipulations is founded only on the basic principles of a formal language: term algebras, term rewriting, and so on. More abstractly, both (finite) model theory and proof theory offer the needed tools to work with infinities. One does not have to "believe" in infinity in order to write down algebraically valid expressions employing symbols for infinity.

Modern set theory
The philosophical problem of actual infinity concerns whether the notion is coherent and epistemically sound.

Zermelo–Fraenkel set theory is presently the standard foundation of mathematics. One of its axioms is the axiom of infinity that states that there exist infinite sets, and in particular that the natural numbers form an infinite set. However, some finitist philosophers of mathematics and constructivists still object to the notion.

title: Actual infinity


text:
User:QIM

"QIM" is the internet handle for Tom Smith. It derives from a spiritual project Tom did with autistics using Facilitated Communication FC in the early 1990s which produced a book they named "QIM/QIM Tunes". It's an acronym for "The Source I aM", with "Q" coming from the German word "quelle" meaning "Source". It's frequently used to describe the suspected source document, Q document, for the books of the New Testament.

My work on the net can be found linked below. The first two links are well established discussion groups that I own and the other two are writings on men and autism:

Autismlist

American Union of Men

Masculist Trinity

QIM Tunes

Bio:

Born in Tonawanda New York, attended State University of New York at Oneonta from '65-'69. My career for the next 35 years was in nursing, mental health, social work and with developmental disabilities. I'm divorced with two grown children and live in Santa Barbara Ca.

title: User:QIM