title: Scotch-Irish Americans

text: Especially in Pennsylvania, whose pacifist Quaker leaders had made no provision for a militia, Scotch-Irish settlements were frequently destroyed and the settlers killed, captured or forced to flee after attacks by Native Americans from tribes of the Delaware (Lenape), Shawnee, Seneca, and others of western Pennsylvania and the Ohio country. Native American attacks took place within 60 miles of Philadelphia, and in July 1763, the Pennsylvania Assembly authorized a 700-strong militia to be raised, to be used only for defensive actions. Formed into two units of rangers, the Cumberland Boys and the Paxton Boys, the militia soon exceeded their defensive mandate and began offensive forays against Lenape villages in western Pennsylvania. After attacking Delaware villages in the upper Susquehanna valley, the militia leaders received information, which they believed credible, that "hostile" tribes were receiving weapons and ammunition from the "friendly" tribe of Conestogas settled in Lancaster County, who were under the protection of the Pennsylvania Assembly. On 14 December 1763, about fifty Paxton Boys rode to Conestogatown, near Millersville, Pennsylvania, and murdered six Conestogas. Governor John Penn placed the remaining fourteen Conestogas in protective custody in the Lancaster workhouse, but the Paxton Boys broke in, killing and mutilating all fourteen on 27 December 1763. Following this, about 400 backcountry settlers, primarily Scotch-Irish, marched on Philadelphia demanding better military protection for their settlements, and pardons for the Paxton Boys. Benjamin Franklin led the politicians who negotiated a settlement with the Paxton leaders, after which they returned home.


title: Scotch-Irish Americans

text: The United States Declaration of Independence contained 56 delegate signatures. Of the signers, eight were of Irish descent. Two signers, George Taylor and James Smith, were born in Ulster. The remaining five Irish-Americans, George Read, Thomas McKean, Thomas Lynch, Jr., Edward Rutledge and Charles Carroll, were the sons or grandsons of Irish immigrants, and at least McKean had Ulster heritage.


title: Scotch-Irish Americans

text: In contrast to the Scottish Highlanders, the Scotch-Irish were generally ardent supporters of American independence from Britain in the 1770s. In Pennsylvania, Virginia, and most of the Carolinas, support for the revolution was "practically unanimous". One Hessian officer said, "Call this war by whatever name you may, only call it not an American rebellion; it is nothing more or less than a Scotch Irish Presbyterian rebellion." A British major general testified to the House of Commons that "half the rebel Continental Army were from Ireland". Mecklenburg County, North Carolina, with its large Scotch-Irish population, was to make the first declaration for independence from Britain in the Mecklenburg Declaration of 1775.


title: Scotch-Irish Americans

text: The Scotch-Irish "Overmountain Men" of Virginia and North Carolina formed a militia which won the Battle of Kings Mountain in 1780, resulting in the British abandonment of a southern campaign, and for some historians "marked the turning point of the American Revolution".


title: Scotch-Irish Americans

text: One exception to the high level of patriotism was the Waxhaw settlement on the lower Catawba River along the North Carolina-South Carolina boundary, where Loyalism was strong. The area experienced two main settlement periods of Scotch-Irish. During the 1750s–1760s, second- and third-generation Scotch-Irish Americans moved from Pennsylvania, Virginia, and North Carolina. This particular group had large families, and as a group they produced goods for themselves and for others. They generally were Patriots.


title: Scotch-Irish Americans

text: Just prior to the Revolution, a second stream of immigrants came directly from Ireland via Charleston. This group was forced to move into an underdeveloped area because they could not afford expensive land. Most of this group remained loyal to the Crown or neutral when the war began. Prior to Charles Cornwallis's march into the backcountry in 1780, two-thirds of the men among the Waxhaw settlement had declined to serve in the army. The British massacre of American prisoners at the Battle of Waxhaws resulted in anti-British sentiment in a bitterly divided region. While many individuals chose to take up arms against the British, the British themselves forced the people to choose sides.


title: Scotch-Irish Americans

text: In the 1790s, the new American government assumed the debts the individual states had amassed during the American Revolutionary War, and the Congress placed a tax on whiskey (among other things) to help repay those debts. Large producers were assessed a tax of six cents a gallon. Smaller producers, many of whom were Scottish (often Scotch-Irish) descent and located in the more remote areas, were taxed at a higher rate of nine cents a gallon. These rural settlers were short of cash to begin with, and lacked any practical means to get their grain to market, other than fermenting and distilling it into relatively potable spirits.


title: Scotch-Irish Americans

text: From Pennsylvania to Georgia, the western counties engaged in a campaign of harassment of the federal tax collectors. "Whiskey Boys" also conducted violent protests in Maryland, Virginia, North Carolina and South Carolina, and Georgia. This civil disobedience eventually culminated in armed conflict in the Whiskey Rebellion. President George Washington accompanied 13,000 soldiers from Carlisle to Bedford, Pennsylvania, where plans were completed to suppress the western Pennsylvania insurrection, and he returned to Philadelphia in his carriage.


title: Scotch-Irish Americans

text: Author and U.S. Senator Jim Webb puts forth a thesis in his book "Born Fighting" (2004) to suggest that the character traits he ascribes to the Scotch-Irish such as loyalty to kin, extreme mistrust of governmental authority and legal strictures, and a propensity to bear arms and to use them, helped shape the American identity. In the same year that Webb's book was released, Barry A. Vann published his second book, entitled "Rediscovering the South's Celtic Heritage". As in his earlier book, "From Whence They Came" (1998), Vann argues that these traits have left their imprint on the Upland South. In 2008, Vann followed up his earlier work with a book entitled "In Search of Ulster Scots Land: The Birth and Geotheological Imagings of a Transatlantic People", which professes how these traits may manifest themselves in conservative voting patterns and religious affiliation that characterizes the Bible Belt.


title: Scotch-Irish Americans

text: The iron and steel industry developed rapidly after 1830 and became one of the dominant factors in industrial America by the 1860s. Ingham (1978) examined the leadership of the industry in its most important center, Pittsburgh, as well as smaller cities. He concludes that the leadership of the iron and steel industry nationwide was "largely Scotch-Irish". Ingham finds that the Scotch-Irish held together cohesively throughout the 19th century and "developed their own sense of uniqueness".


title: Scotch-Irish Americans

text: New immigrants after 1800 made Pittsburgh a major Scotch-Irish stronghold. For example, Thomas Mellon (b. Ulster; 1813–1908) left Ireland in 1823 and became the founder of the famous Mellon clan, which played a central role in banking and industries such as aluminum and oil. As Barnhisel (2005) finds, industrialists such as James H. Laughlin (b. Ulster; 1806–1882) of Jones and Laughlin Steel Company constituted the "Scots-Irish Presbyterian ruling stratum of Pittsburgh society".


title: Scotch-Irish Americans

text: Archeologists and folklorists have examined the folk culture of the Scotch-Irish in terms of material goods, such as housing, as well as speech patterns and folk songs. Much of the research has been done in Appalachia.


title: Scotch-Irish Americans

text: The border origin of the Scotch-Irish is supported by study of the traditional music and folklore of the Appalachian Mountains, settled primarily by the Scotch-Irish in the 18th century. Musicologist Cecil Sharp collected hundreds of folk songs in the region, and observed that the musical tradition of the people "seems to point to the North of England, or to the Lowlands, rather than the Highlands, of Scotland, as the country from which they originally migrated. For the Appalachian tunes...have far more affinity with the normal English folk-tune than with that of the Gaelic-speaking Highlander."


title: Scotch-Irish Americans

text: Similarly, elements of mountain folklore trace back to events in the Lowlands of Scotland. As an example, it was recorded in the early 20th century that Appalachian children were frequently warned, "You must be good or Clavers will get you." To the mountain residents, "Clavers" was simply a bogeyman used to keep children in line, yet unknown to them the phrase derives from the 17th century Scotsman John Graham of Claverhouse, called "Bloody Clavers" by the Presbyterian Scottish Lowlanders whose religion he tried to suppress.


title: Scotch-Irish Americans

text: In terms of the stone houses they built, the "hall-parlor" floor plan (two rooms per floor with chimneys on both ends) was common among the gentry in Ulster. Scotch-Irish immigrants brought it over in the 18th century and it became a common floor plan in Tennessee, Kentucky, and elsewhere. Stone houses were difficult to build, and most pioneers relied on simpler log cabins.


title: Scotch-Irish Americans

text: Scotch-Irish quilters in West Virginia developed a unique interpretation of pieced-block quilt construction. Their quilts embody an aesthetic reflecting Scotch-Irish social history—the perennial condition of living on the periphery of mainstream society both geographically and philosophically. Cultural values espousing individual autonomy and self-reliance within a strong kinship structure are related to Scotch-Irish quilting techniques. Prominent features of these quilts include: 1) blocks pieced in a repeating pattern but varied by changing figure-ground relationships and, at times, obscured by the use of same-value colors and adjacent print fabrics, 2) lack of contrasting borders, and 3) a unified all-over quilting pattern, typically the "fans" design or rows of concentric arcs.


title: Scotch-Irish Americans

text: Montgomery (2006) analyzes the pronunciation, vocabulary, and grammatical distinctions of today's residents of the mountain South and traces patterns back to their Scotch-Irish ancestors. However, Crozier (1984) suggests that only a few lexical characteristics survived Scotch-Irish assimilation into American culture.


title: Scotch-Irish Americans

text: According to "The Source: A Guidebook of American Genealogy", by Kory L. Meyerink and Loretto Dennis Szucs, the following were the countries of origin for new arrivals coming to the United States before 1790. The regions marked * were part of, or ruled by, the Kingdom of Great Britain (the United Kingdom of Great Britain and Ireland after 1801). The ancestry of the 3,929,326 population in 1790 has been estimated by various sources by sampling last names in the 1790 census and assigning them a country of origin.


title: Scotch-Irish Americans

text: According to the Harvard Encyclopedia of American Ethnic Groups (Thernstrom, S 1980, "Irish," p. 528), there were 400,000 Americans of Irish birth or ancestry in 1790; half of these were descended from Ulster, and half were descended from other provinces in Ireland.


title: Scotch-Irish Americans

text: The Census Bureau produced official estimates of the colonial American population with roots in the Irish province of Ulster, in collaboration with the American Council of Learned Societies, by scholarly classification of the names of all White heads of families recorded in the 1790 Census. The government required accurate estimates of the origins of the population as basis for computing National Origins Formula immigration quotas in the 1920s (i.e. how much of the annual immigrant quota would be allotted to the Irish Free State, as opposed to Northern Ireland which remained part of the United Kingdom). The final report estimated about 10% of the U.S. population in 1790 had ancestral roots in Ireland, about three fifths of that total from Ulster–broken down by state below:


title: Scotch-Irish Americans

text: Finding the coast already heavily settled, most groups of settlers from the north of Ireland moved into the "western mountains", where they populated the Appalachian regions and the Ohio Valley. Others settled in northern New England, The Carolinas, Georgia and north-central Nova Scotia.


title: Scotch-Irish Americans

text: In the United States Census, 2000, 4.3 million Americans (1.5% of the U.S. population) claimed Scotch-Irish ancestry.


title: Scotch-Irish Americans

text: The author Jim Webb suggests that the true number of people with some Scotch-Irish heritage in the United States is in the region of 27 million.


title: Scotch-Irish Americans

text: As of 2020, the distribution of self-identified Scotch-Irish Americans across the 50 states and DC is as presented in the following table:


title: Scotch-Irish Americans

text: The Scotch-Irish immigrants to North America in the 18th century were initially defined in part by their Presbyterianism. Many of the settlers in the Plantation of Ulster had been from dissenting and non-conformist religious groups which professed Calvinist thought. These included mainly Lowland Scot Presbyterians, but also English Puritans and Quakers, French Huguenots and German Palatines. These Calvinist groups mingled freely in church matters, and religious belief was more important than nationality, as these groups aligned themselves against both their Catholic Irish and Anglican English neighbors.


title: Scotch-Irish Americans

text: After their arrival in the New World, the predominantly Presbyterian Scotch-Irish began to move further into the mountainous back-country of Virginia and the Carolinas. The establishment of many settlements in the remote back-country put a strain on the ability of the Presbyterian Church to meet the new demand for qualified, college-educated clergy. Religious groups such as the Baptists and Methodists had no higher education requirement for their clergy to be ordained, and these groups readily provided ministers to meet the demand of the growing Scotch-Irish settlements. By about 1810, Baptist and Methodist churches were in the majority, and the descendants of the Scotch-Irish today remain predominantly Baptist or Methodist. Vann (2007) shows the Scotch-Irish played a major role in defining the Bible Belt in the Upper South in the 18th century. He emphasizes the high educational standards they sought, their "geotheological thought worlds" brought from the old country, and their political independence that was transferred to frontier religion.


title: Scotch-Irish Americans

text: In 1746, the Scotch-Irish Presbyterians created the College of New Jersey, later renamed Princeton University. The mission was training New Light Presbyterian ministers. The college became the educational as well as religious capital of Scotch-Irish America. By 1808, loss of confidence in the college within the Presbyterian Church led to the establishment of the separate Princeton Theological Seminary, but for many decades Presbyterian control over Princeton College continued. Meanwhile, Princeton Seminary, under the leadership of Charles Hodge, originated a conservative theology that in large part shaped Fundamentalist Protestantism in the 20th century.


title: Scotch-Irish Americans

text: While the larger Presbyterian Church was a mix of Scotch-Irish and Yankees from New England, several smaller Presbyterian groups were composed almost entirely of Scotch-Irish, and they display the process of assimilation into the broader American religious culture. Fisk (1968) traces the history of the Associate Reformed Church in the Old Northwest from its formation by a union of Associate and Reformed Presbyterians in 1782 to the merger of this body with the Seceder Scotch-Irish bodies to form the United Presbyterian Church in 1858. It became the Associate Reformed Synod of the West and remains centered in the Midwest. It withdrew from the parent body in 1820 because of the drift of the eastern churches toward assimilation into the larger Presbyterian Church with its Yankee traits. The Associate Reformed Synod of the West maintained the characteristics of an immigrant church with Scotch-Irish roots, emphasized the Westminster standards, used only the psalms in public worship, was Sabbatarian, and was strongly abolitionist and anti-Catholic. In the 1850s it exhibited many evidences of assimilation. It showed greater ecumenical interest, greater interest in evangelization of the West and of the cities, and a declining interest in maintaining the unique characteristics of its Scotch-Irish past.


title: Scotch-Irish Americans

text: Many presidents of the United States have ancestral links to Ulster, including three whose parents were born in Ulster. Three presidents had at least one parent born in Ulster: Andrew Jackson, James Buchanan and Chester Arthur. The Irish Protestant vote in the U.S. has not been studied as much as that of the Catholic Irish. In the 1820s and 1830s, Jackson supporters emphasized his Irish background, as did supporters of James Knox Polk, but since the 1840s it has been uncommon for a Protestant politician in America to be identified as Irish, but rather as "Scotch-Irish". In Canada, by contrast, Irish Protestants remained a cohesive political force well into the 20th century, identified with the then Conservative Party of Canada and especially with the Orange Institution, although this is less evident in today's politics.


title: Scotch-Irish Americans

text: More than one-third of all U.S. presidents had substantial ancestral origins in the northern province of Ireland (Ulster). President Bill Clinton spoke proudly of that fact, and his own ancestral links with the province, during his two visits to Ulster. Like most US citizens, most US presidents are the result of a "melting pot" of ancestral origins.


title: Scotch-Irish Americans

text: Clinton is one of at least seventeen Chief Executives descended from emigrants to the United States from Ulster. While many of the presidents have typically Ulster-Scots surnames – Jackson, Johnson, McKinley, Wilson – others, such as Roosevelt and Cleveland, have links which are less obvious.


title: Roc (mythology)

text: The roc appears in Arab geographies and natural history, popularized in Arabian fairy tales and sailors' folklore. Ibn Battuta tells of a mountain hovering in the air over the China Seas, which was the roc. The story collection "One Thousand and One Nights" includes tales of Abd al-Rahman and Sinbad the Sailor, both of which include the roc.


title: Roc (mythology)

text: The English form "roc" originates via Antoine Galland's French from Arabic "ruḵḵ" () and that from Persian "ruḵ" (). In both languages, Arabic and Persian, the word is written in the Arabic script as رخ. Common romanizations are "ruḵḵ" for the Arabic form and "ruḵ", "rokh" or "rukh" for the Persian form.


title: Roc (mythology)

text: According to art historian Rudolf Wittkower, the idea of the roc had its origins in the story of the fight between the Indian solar bird Garuda and the chthonic serpent Nāga. The mytheme of Garuda carrying off an elephant that was battling a crocodile appears in two Sanskrit epics, the "Mahabharata" (I.1353) and the "Ramayana" (III.39).


title: Roc (mythology)

text: Rabbi Benjamin of Tudela reported a story reminiscent of the roc in which shipwrecked sailors escaped from a desert island by wrapping themselves in ox-hides and letting griffins carry them off as if they were cattle.


title: Roc (mythology)

text: In the 13th century, Marco Polo (as quoted in Attenborough (1961: 32)) stated It was for all the world like an eagle, but one indeed of enormous size; so big in fact that its quills were twelve paces long and thick in proportion. And it is so strong that it will seize an elephant in its talons and carry him high into the air and drop him so that he is smashed to pieces; having so killed him, the bird swoops down on him and eats him at leisure.


title: Roc (mythology)

text: Polo claimed that the roc flew to Madagascar "from the southern regions", and that the Great Khan sent messengers to the island who returned with a feather (likely a "Raphia" frond). He explicitly distinguishes the bird from a griffin.


title: Roc (mythology)

text: In "The Arabian Nights" the roc appears on a tropical island during Sinbad's second voyage. Because of Polo's account, others identified the island as Madagascar, which became the location for stories about other giant birds. Doubtless, it was Polo's description that inspired Antonio Pigafetta, one of Ferdinand Magellan's companions, who wrote or had ghost-written an embroidered account of the circumglobal voyage: in Pigafetta's account the home grounds of the roc were the seas of China. Such descriptions captured the imaginations of later illustrators, such as Stradanus 1590 or Theodor de Bry in 1594 who showed an elephant being carried off in the roc's talons, or showed the roc destroying entire ships in revenge for destruction of its giant egg, as recounted in the fifth voyage of Sinbad the Sailor. Ulisse Aldrovandi's "Ornithologia" (1599) included a woodcut of a roc with a somewhat pig-like elephant in its talons, but in the rational world of the 17th century, the roc was regarded more critically. In the modern era, the roc, like many other mythological and folkloric creatures, has entered the bestiaries of some fantasy role-playing games such as "Dungeons and Dragons".


title: Roc (mythology)

text: The scientific culture of the 19th century introduced some "scientific" rationalizations for the myth's origins, by suggesting that the origin of the myth of the roc might lie in embellishments of the often-witnessed power of the eagle that could carry away a newborn lamb. In 1863, Bianconi suggested the roc was a raptor (Hawkins and Goodman, 2003: 1031). Recently a giant subfossil eagle, the Malagasy crowned eagle, identified from Madagascar was actually implicated as a top bird predator of the island, whose megafauna once included giant lemurs and pygmy hippopotamuses.


title: Roc (mythology)

text: Another possible origin of the myth is accounts of eggs of another extinct Malagasy bird, the enormous "Aepyornis" elephant bird, hunted to extinction by the 16th century, that was three meters tall and flightless. There were reported elephant bird sightings at least in folklore memory as Étienne de Flacourt wrote in 1658. Its egg, live or subfossilised, was known as early as 1420, when sailors to the Cape of Good Hope found eggs of the roc, according to a caption in the 1456 Fra Mauro map of the world, which says that the roc "carries away an elephant or any other great animal". Between 1830 and 1840 European travelers in Madagascar saw giant eggs and egg shells. English observers were more willing to believe their accounts because they knew of the moa in New Zealand. In 1851 the French Academy of Sciences received three eggs. They and later fossils seemingly confirmed to 19th-century Europeans that "Aepyornis" was the roc, but the real bird does not resemble an eagle as the roc is said to.


title: Roc (mythology)

text: Another rationalizing theory is that the existence of rocs was postulated from the sight of the African ostrich, which, because of its flightlessness and unusual appearance, was mistaken for the chick of a presumably much larger species. There is, however, a claim that ostriches were known to Europeans in Biblical times due to a translation of the Old Testament. On the other hand, a medieval Northern European or Indian traveller, if confronted with tales about ostriches, might very well not have recognized them for what they were (compare History of elephants in Europe).


title: Roc (mythology)

text: In addition to Polo's account of the "rukh" in 1298, Chou Ch'ű-fei (周去非, Zhōu Qùfēi), in his 1178 book "Lingwai Daida", told of a large island off Africa with birds large enough to use their quills as water reservoirs. Fronds of the raffia palm may have been brought to Kublai Khan under the guise of roc's feathers.


title: Roc (mythology)

text: Some recent scholars have compared the legendary roc with the Haast's eagle, of New Zealand. long with a wingspan, it became extinct around the 15th century, but probably inspired the Māori legend of "Te Hokioi" or "Te Hakawai". This was said to be a colorful huge bird which (in some versions of the legend) had occasionally descended to Earth to carry off humans to eat, but generally lived in the clouds unseen. Only its cry, after which it was named, could be heard. Indeed, the "hokioi" seems to be a composite mythical beast inspired by actual animals, just like the roc appears to have been. In the 1980s, it was found that male "Coenocorypha" snipes, tiny nocturnal waders, produce an unexpectedly loud roaring sound with their tails during mating flights. The supposed coloration of the "hokioi" is not matched by any known bird, and generally would be extremely unusual for a bird of prey. Thus, as it seems likely that the "hokioi" was the eerie "drumming" of the snipes, explained with the ancestor's tales about the giant eagles which they still knew from living memory.


title: Roc (mythology)

text: Through the 16th century the existence of the roc could be accepted by Europeans. In 1604, Michael Drayton envisaged the rocs being taken aboard the Ark:


title: Roc (mythology)

text: The rukh is also identified in the Ethiopian holy book "Kebra Negast" as the agent responsible for delivering the blessed piece of wood to Solomon which enabled the great king to complete Solomon's Temple. This piece of wood also is said to have transformed the Queen of Sheba's foot from that of a goat to that of a human. The piece of wood that the rukh brought was therefore given an honored place in the Temple and decorated with silver rings. According to tradition, these silver rings were given to Judas Iscariot as payment for betraying Jesus; the piece of wood became Jesus's cross.


title: The Change-Up

text: The Change-Up is a 2011 American fantasy romantic comedy film produced and directed by David Dobkin and written by Jon Lucas and Scott Moore. The film stars Ryan Reynolds and Jason Bateman as Mitch Planko and Dave Lockwood, two best friends living in Atlanta who switch bodies after urinating into the fountain to wish they had each other's lives. The film was released on August 5, 2011, in North America, by Universal Pictures. It received negative reviews from critics.


title: The Change-Up

text: In Atlanta, Dave Lockwood is married with three children, while his best friend Mitch Planko is single and at his sexual prime. After getting drunk at a bar, Mitch and Dave urinate into a fountain, simultaneously wishing they had each other's lives.


title: The Change-Up

text: The next morning, Mitch and Dave realize they have switched bodies. Returning to the park to wish for their lives back, the fountain has been removed for restoration. Forced to wait until the parks department locates the fountain, Mitch and Dave have to pose as each other.


title: The Change-Up

text: At Dave's law office, Mitch befriends Dave's assistant Sabrina, but his lack of professionalism and legal knowledge sabotage an important merger with a Japanese firm. Dave arrives at Mitch's film shoot, discovering it is a "lorno" – "light" pornography.


title: The Change-Up

text: Dave takes Mitch to tell his wife Jamie the truth, but she does not believe him. Dave advises him on how to behave professionally, and Mitch sets up Dave on a date with Sabrina, as Mitch has a crush.


title: The Change-Up

text: After speaking with his father, Mitch rededicates himself to Dave's life. At her ballet recital, Dave's eldest child Cara takes Mitch's advice and throws her bully to the floor, to which Mitch foul-mouthedly cheers. Cara tells him she loves him and he says the same, but feels guilty.


title: The Change-Up

text: Dave takes the day off to take full advantage of being Mitch, who coaches him how to act like Mitch on the date, and shaves off Dave's pubic hair. Sabrina meets Dave at a classy restaurant and, despite only going because Mitch told her to, genuinely likes him, and they get tattoos. Dave walks her home, and she tells him to call her.


title: The Change-Up

text: Mitch learns Dave told Jamie not to invite Mitch to their anniversary party, afraid he would ruin it. Dave informs Mitch the fountain has been found, but they both want to stay each other a bit longer. Mitch, forgets about the "Dialogue Night" he planned with Jamie, accidentally standing her up.


title: The Change-Up

text: At the new merger meeting, the Japanese representatives offer only $625 million, $75 million short. As Dave's firm is about to agree, Mitch observes that the other representatives have not yet left, and compares the negotiations to sex and porn. He demands $725 million and has the representatives of Dave's firm begin to leave, scaring the other firm into agreement. Mitch and Dave's family go to a gala held by the firm in honor of Dave being made partner, but Jamie is upset by the speech that praises his family values.


title: The Change-Up

text: Dave and Sabrina are at a baseball game when a thunderstorm hits, and wait it out at Mitch's house. She tells him she is going to have sex with him, but when he sees her tattoo of a many-spotted skipperling – his daughter's favorite butterfly – he regretfully leaves.


title: The Change-Up

text: At the gala, Dave's boss delivers a speech about his accomplishments and love for his family, filling Mitch with guilt. Dave rushes in and kisses Jamie, finally convincing her that he is her husband. He and Mitch find the fountain surrounded by people. Proceeding with their plan to urinate in the fountain, Mitch is too embarrassed, especially after the crowd notices Dave doing so. Mitch asks why Dave did not invite him to his anniversary party, and Dave admits he was embarrassed by Mitch, but has grown to respect him while in his body. This relaxes Mitch enough to urinate, but their wish does not work. Security approaches, but on Mitch and Dave's third try the Galleria's lights go out, and they run.


title: The Change-Up

text: In an epilogue, Dave and Mitch are thrilled to have returned to their original bodies. Mitch gets breakfast with Sabrina, not realizing the tattoo Dave got is of his face on Mitch's back, captioned "I ♥ Dave". Mitch speaks at his father's wedding, and attends Dave's anniversary party. In a post-credits scene, Dave and Jamie get high and visit the aquarium, while Mitch and Sabrina have sex for the first time, and Mitch sends Dave the porno he starred in.


title: The Change-Up

text: In addition, Sydney Rouviere and Lauren and Luke Bain portray Dave and Jamie's three children, Cara, Sarah, and Peter, respectively.


title: The Change-Up

text: The film was shot in Atlanta, Georgia from October 2010 to January 2011, which is also its setting. There were open castings at Turner Field and other venues in Atlanta. Several of the bar scenes were shot on location at a bar called Joe's on Juniper, in midtown Atlanta. The exterior and interior scenes of the Lockwood home were shot on location at a Buckhead residence designed by Atlanta residential designer Steve McClanahan. The movie was also shot in Los Angeles. The house used for the Lockwood home is on the 2400 block of Gramercy Park in historic West Adams. Despite being set in the summertime, production continued during a major winter storm that briefly crippled the city in January, leaving Peachtree and other streets covered in snow and ice and nearly preventing the governor's inauguration. Reynolds complimented the city in his interview on "The Tonight Show with Jay Leno", but joked that he thought the city "was trying to kill" him because of several unrelated incidents on the set and in his personal life that happened to occur during production. During her interview on "Jimmy Kimmel Live!", Olivia Wilde stated that she refused to appear naked or take most of her clothes off and used a body double for some shots and wore pasties for close-up and upper shots. Leslie Mann has also followed this technique while other actresses used prosthetics.


title: The Change-Up

text: On Rotten Tomatoes the film has an approval rating of based on reviews and an average rating of . The site's critical consensus reads, "There's a certain amount of fun to be had from watching Bateman and Reynolds play against type, but it isn't enough to carry "The Change-Up" through its crude humor and formulaic plot." On Metacritic, the film has a score of 39 out of 100 based on 35 critics, indicating "generally unfavorable reviews". Audiences polled by CinemaScore gave the film an average grade of "B" on an A+ to F scale.


title: The Change-Up

text: British newspaper "The Telegraph" named "The Change-Up" one of the ten worst films of 2011, saying "Ryan Reynolds and Jason Bateman have skill, charm, timing – everything but the right script."


title: The Change-Up

text: On its opening weekend, "The Change-Up" opened at #4, grossing $13,531,115 in 2,913 theaters with a $4,645 average. The film grossed $37.1 million in North America and $38.4 million in other territories for a worldwide total of $75.5 million against a budget of $52 million.


title: Mother Love Bone

text: Mother Love Bone was an American rock band that formed in Seattle, Washington in 1988. The band was active from 1988 to 1990. Frontman Andrew Wood's personality and lyrics helped to catapult the group to the top of the burgeoning late 1980s/early 1990s Seattle music scene. Wood died only days before the scheduled release of the band's debut album, "Apple", thus ending the group's hopes of success. The album was finally released a few months later.


title: Mother Love Bone

text: As well as being influential to grunge, they are also considered early pioneers in the alternative metal genre.


title: Mother Love Bone

text: Mother Love Bone was established in 1987 by ex-Green River members Jeff Ament, Bruce Fairweather and Stone Gossard, ex-Malfunkshun frontman Andrew Wood and ex-Ten Minute Warning and The Living drummer Greg Gilmore. Initially, the group was formed in 1987 out of the cover band Lords of the Wasteland which featured Wood, Gossard, Ament and Malfunkshun drummer Regan Hagar. By early 1988 the band had added Fairweather, replaced Hagar with drummer Greg Gilmore and changed its name to Mother Love Bone.


title: Mother Love Bone

text: This new line-up quickly set about recording and playing area shows and by late 1988 had become one of Seattle's more promising bands. Wood's exuberant on-stage personality, outlandish clothes and dreamy lyrics helped bring attention to the band. In the 1996 grunge documentary "Hype!", Seattle engineer Jack Endino called Wood "the only stand-up comedian frontman in Seattle", a reference to Wood's playful style of interacting with Mother Love Bone fans.


title: Mother Love Bone

text: In November 1988, the band signed to PolyGram subsidiary Polydor/Stardog and recorded their debut EP. As part of their contract, PolyGram created the Stardog Records imprint exclusively for the band. In March 1989, the group issued its debut EP "Shine", becoming one of the first of the new crop of Seattle bands to have a release on a major label. The record sold well and rapidly increased the profile of the band. John Book of AllMusic said the "record contributed to the buzz about the Seattle music scene."


title: Mother Love Bone

text: In late 1989, the group returned to the studio (this time in Sausalito, California) to record its debut album, "Apple". Despite some initial difficulties, the record was on time for its projected March 1990 release. Only days before "Apple" was slated to be released, frontman Andrew Wood, who had a long history with drug problems, overdosed on heroin. Unresponsive and without signs of brain activity, he was in the hospital on life support for two days to allow friends and family to say goodbye. Wood's death effectively brought the group to an end. The album would see release later that year on July 19, 1990. Kim Neely of "Rolling Stone" said that the album "succeeds where countless other hard rock albums have failed, capturing the essence of what made Zep immortal – dynamics, kids! – and giving it a unique Nineties spin."


title: Mother Love Bone

text: In the months following Wood's death, Gossard and Ament were approached by Soundgarden frontman Chris Cornell (who had been Wood's roommate), and asked if they would be interested in recording a single containing two songs he had written in tribute to Wood. The project turned into an entire album and the group took the name Temple of the Dog, a reference to a line in the Mother Love Bone song "Man of Golden Words". Cornell recruited singer Eddie Vedder for the project, which afterward Vedder then joined Mike McCready, Gossard, and Ament to form Pearl Jam, one of the most commercially successful and critically acclaimed rock bands of the 1990s.


title: Mother Love Bone

text: Fairweather initially remained inactive but later joined Seattle based psychedelic rock band Love Battery, replacing Tommy Simpson on bass in 1992. He played on two of the band's albums and many of its tours before leaving that band. In 2006, he resurfaced in The Press Corps, with Garrett Shavlik (The Fluid) and Dan Peters (Mudhoney).


title: Mother Love Bone

text: Gilmore's profile also dropped significantly following Mother Love Bone's demise. Between 1992 and 1994, he drummed with the band Chubby Children, reuniting with former bandmates from 1982–1985, Brian Fox and Garth Brandenburg. Out of the band came a handful of shows and unreleased recordings. He also participated in the reunion of his former band Ten Minute Warning in 1998, and was credited with providing 'inspiration' for the song "Never the Machine Forever" (credited as being written by Kim Thayil) on Soundgarden's studio album, 1996's "Down on the Upside". The song initially came out of a jam session Thayil had with Gilmore.


title: Mother Love Bone

text: In April 2011, Kevin Wood (Andrew Wood's brother) teamed up with hard rock band Lace Weeper to record Mother Love Bone's "Crown of Thorns" in commemoration of 21 years since Andrew's death. The single was released on Kevin's Wammybox Records.


title: Mother Love Bone

text: On April 14, 2010, the four surviving members of Mother Love Bone reunited for the first time in 20 years (with friend and fellow Seattle musician Shawn Smith serving as frontman for the night) as part of a sold-out "Brad and Friends" evening at Seattle's Showbox. The songs featured were part of the band's core repertoire from their early days, including "Stardog Champion", "Holy Roller", "Gentle Groove" and a cover of the Argent song "Hold Your Head Up", a favorite encore from the band's early club days around Seattle.


title: Mother Love Bone

text: On May 5, 2018, they again got together and performed 14 songs (including a cover of Argent’s 1972 hit “Hold Your Head Up”) during the event at Seattle’s Neptune Theatre.


title: Frederick William II of Prussia

text: Frederick William II (; 25 September 1744 – 16 November 1797) was King of Prussia from 1786 until his death in 1797. He was in personal union the Prince-elector of Brandenburg and (via the Orange-Nassau inheritance of his grandfather) sovereign prince of the Canton of Neuchâtel. Pleasure-loving and indolent, he is seen as the antithesis to his predecessor, Frederick the Great. (Frederick II). Under his reign, Prussia was weakened internally and externally, and he failed to deal adequately with the challenges to the existing order posed by the French Revolution. His religious policies were directed against the Enlightenment and aimed at restoring a traditional Protestantism. However, he was a patron of the arts and responsible for the construction of some notable buildings, among them the Brandenburg Gate in Berlin. Haydn, Mozart and Beethoven all dedicated works to him.


title: Frederick William II of Prussia

text: Frederick William was born in Berlin, the son of Prince Augustus William of Prussia (the second son of King Frederick William I of Prussia) and Duchess Luise of Brunswick-Wolfenbüttel. His mother's elder sister, Elisabeth, was the wife of Augustus William's brother King Frederick II ("Frederick the Great"). Frederick William became heir-presumptive to the throne of Prussia on his father's death in 1758, since Frederick II had no children. The boy was of an easy-going and pleasure-loving disposition, averse to sustained effort of any kind, and sensual by nature.


title: Frederick William II of Prussia

text: His marriage with Elisabeth Christine of Brunswick-Wolfenbüttel, Crown Princess of Prussia, daughter of Charles I, Duke of Brunswick-Lüneburg, contracted 14 July 1765 in Charlottenburg, was dissolved in 1769. He then married Frederica Louisa of Hesse-Darmstadt, daughter of Ludwig IX, Landgrave of Hesse-Darmstadt on 14 July 1769 also in Charlottenburg. Although he had seven children by his second wife, he had an ongoing relationship with his mistress, Wilhelmine Enke (created Countess Wilhelmine von Lichtenau in 1796), a woman of strong intellect and much ambition, and had five children by her—the first when she was still in her teens.


title: Frederick William II of Prussia

text: Frederick William, before the corpulence of his middle age, was a man of singularly handsome presence, not without mental qualities of a high order; he was devoted to the arts – Boccherini, Mozart and the young Beethoven enjoyed his patronage, and his private orchestra had a Europe-wide reputation. He also was a talented cellist. But an artistic temperament was hardly what was required of a king of Prussia on the eve of the French Revolution, and Frederick the Great, who had employed him in various services (notably in an abortive confidential mission to the court of Russia in 1780), openly expressed his misgivings as to the character of the prince and his surroundings. For his part, Frederick William, who had never been properly introduced to diplomacy and the business of rulership, resented his uncle for not taking him seriously.


title: Frederick William II of Prussia

text: The misgivings of Frederick II appear justified in retrospect. Frederick William's accession to the throne (17 August 1786) was, indeed, followed by a series of measures for lightening the burdens of the people, reforming the oppressive French system of tax-collecting introduced by Frederick, and encouraging trade by the diminution of customs dues and the making of roads and canals. This gave the new king much popularity with the masses; the educated classes were pleased by Frederick Williams's reversal of his uncle's preference for the French language and the promotion of the German language, with the admission of German writers to the Prussian Academy, and by the active encouragement given to schools and universities. Frederick William also terminated his predecessor's state monopolies for coffee and tobacco and the sugar monopoly. Under his reign the codification known as "Allgemeines Preußisches Landrecht", initiated by Frederick II, continued and was completed in 1794.


title: Frederick William II of Prussia

text: In 1781 Frederick William, then prince of Prussia, inclined to mysticism, had joined the Rosicrucians, and had fallen under the influence of Johann Christoph von Wöllner and Johann Rudolf von Bischoffswerder. On 26 August 1786 Wöllner was appointed privy councillor for finance ("Geheimer Oberfinanzrath"), and on 2 October 1786 was ennobled. Though not in name, he in fact became prime minister; in all internal affairs it was he who decided; and the fiscal and economic reforms of the new reign were the application of his theories. Bischoffswerder, too, still a simple major, was called into the king's counsels; by 1789 he was already an adjutant-general. The opposition to Wöllner was, indeed, at the outset strong enough to prevent his being entrusted with the department of religion; but this too in time was overcome, and on 3 July 1788 he was appointed active privy councillor of state and of justice and head of the spiritual department for Lutheran and Catholic affairs. From this position Wöllner pursued long lasting reforms concerning religion in the Prussian state.


title: Frederick William II of Prussia

text: The king proved eager to aid Wöllner's crusade. On 9 July 1788 a religious edict was issued forbidding Evangelical ministers from teaching anything not contained in the letter of their official books, proclaimed the necessity of protecting the Christian religion against the "enlighteners" ("Aufklärer"), and placed educational establishments under the supervision of the orthodox clergy. On 18 December 1788 a new censorship law was issued to secure the orthodoxy of all published books. This forced major Berlin journals like Christoph Friedrich Nicolai's "Allgemeine Deutsche Bibliothek" and Johann Erich Biester's "Berliner Monatsschrift" to publish only outside the Prussian borders. Moreover, people like Immanuel Kant were forbidden to speak in public on the topic of religion.


title: Frederick William II of Prussia

text: Finally, in 1791, a Protestant commission was established at Berlin ("Immediate-Examinationscommission") to watch over all ecclesiastical and scholastic appointments. Although Wöllner's religious edict had many critics, it was an important measure that, in fact, proved an important stabilizing factor for the Prussian state. Aimed at protecting the multi-confessional rights enshrined in the 1648 Peace of Westphalia, the provisions of Wöllner's edict were intended to safeguard against religious strife by imposing a system of state sponsored limits. The edict was also a notable step forward regarding the rights of Jews, Mennonites, and Herrnhut brethren, who now received full state protection. Given the confessional divides within Prussian society, primarily between Calvinists and Lutherans but increasingly Catholics as well, such a policy was important for maintaining a stable civil society.


title: Frederick William II of Prussia

text: In his zeal for establishing Prussia as a paragon of stable Christian statehood, Frederick William outstripped his minister; he even blamed Wöllner's "idleness and vanity" for the inevitable failure of the attempt to regulate opinion from above, and in 1794 deprived him of one of his secular offices in order that he might have more time "to devote himself to the things of God"; in edict after edict the king continued to the end of his reign to make regulations "in order to maintain in his states a true and active Christianity, as the path to genuine fear of God".


title: Frederick William II of Prussia

text: The attitude of Frederick William II towards the army and foreign policy proved fateful for Prussia. The army was the very foundation of the Prussian state, as both Frederick William I and Frederick the Great had fully realised. The army had been their first care, and its efficiency had been maintained by their constant personal supervision. Frederick William II had no taste for military matters and put his authority as "Warlord" ("Kriegsherr") into commission under a supreme college of war ("Oberkriegs-Collegium") under the Duke of Brunswick and General Wichard Joachim Heinrich von Möllendorf. It was the beginning of the process that ended in 1806 at the disastrous Battle of Jena. Although the Prussian army reached its highest peacetime level of manpower under Frederick William II (189,000 infantry and 48,000 cavalry), under his reign the Prussian state treasury incurred a substantial debt, and the quality of the troops' training deteriorated.


title: Frederick William II of Prussia

text: Under the circumstances, Frederick William's interventions in European affairs were of little benefit to Prussia. The Dutch campaign of 1787, entered into for purely family reasons, was indeed successful, but Prussia received not even the cost of her intervention. An attempt to intervene in the war of Russia and Austria against the Ottoman Empire failed to achieve its objective; Prussia did not succeed in obtaining any concessions of territory, and the dismissal of minister Hertzberg (5 July 1791) marked the final abandonment of the anti-Austrian tradition of Frederick the Great.


title: Frederick William II of Prussia

text: Meanwhile, the French Revolution alarmed the ruling monarchs of Europe, and in August 1791 Frederick William, at the meeting at Pillnitz Castle, agreed with Emperor Leopold II to join in supporting the cause of King Louis XVI of France. However the king's character and the confusion of the Prussian finances could not sustain effective action in this regard. A formal alliance was indeed signed on 7 February 1792, and Frederick William took part personally in the campaigns of 1792 and 1793, but the king was hampered by want of funds, and his counsels were distracted by the affairs of a deteriorating Poland, which promised a richer booty than was likely to be gained by the anti-revolutionary crusade into France. A subsidy treaty with the sea powers (Great Britain and the Netherlands, signed at The Hague, 19 April 1794) filled Prussia's coffers, but at the cost of a promise to supply 64,000 land troops to the coalition. The insurrection in Poland that followed the partition of 1793, and the threat of unilateral intervention by Russia, drove Frederick William into the separate Treaty of Basel with the French Republic (5 April 1795), which was regarded by the other great monarchies as a betrayal, and left Prussia morally isolated in the struggle between the monarchical principle and the new republican creed of the Revolution. Although the land area of the Prussian state reached a new peak under his rule after the third partition of Poland in 1795, the new territories included parts of Poland such as Warsaw that had virtually no German population, severely straining administrative resources due to various pro-Polish revolts; it also removed the last remaining buffer state between Prussia and Russia.


title: Frederick William II of Prussia

text: Frederick William's first marriage, to Elisabeth Christine of Brunswick (his first cousin) had ended after four years during which both spouses had been unfaithful. Their uncle, Frederick II, granted a divorce reluctantly, as he was more fond of Elisabeth than of Frederick William. His second marriage lasted until his death, but he continued his relationship with Wilhelmine Enke. In 1794–1797 he had a castle built for her on the Pfaueninsel. Moreover, he was involved in two more (bigamist) morganatic marriages: with Elisabeth Amalie, Gräfin von Voß, Gräfin von Ingenheim in 1787 and (after her death in 1789) with Sophie Juliane Gräfin von Dönhoff. He had another seven children with those two women, which explains why his people also called him "der Vielgeliebte" ("the much loved") and "der dicke Lüderjahn" ("the fat scallywag"). His favourite son—with Wilhelmine Enke—was Graf Alexander von der Mark. His daughter from Sophie Juliane, Countess Julie of Brandenburg (4 January 1793, Neuchâtel – 29 January 1848, Vienna), married to Frederick Ferdinand, Duke of Anhalt-Köthen.


title: Frederick William II of Prussia

text: Other buildings constructed under his reign were the Marmorpalais in Potsdam and the world-famous Brandenburger Tor in Berlin.


title: Frederick William II of Prussia

text: On 16 November 1797, Frederick William II died in Potsdam. He was succeeded by his son, Frederick William III, who had resented his father's lifestyle and acted swiftly to deal with what he considered the immoral state of the court. Frederick William II is buried in the Berliner Dom.


title: Hamiltonian mechanics

text: Hamiltonian mechanics emerged in 1833 as a reformulation of Lagrangian mechanics. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities formula_1 used in Lagrangian mechanics with (generalized) "momenta". Both theories provide interpretations of classical mechanics and describe the same physical phenomena.


title: Hamiltonian mechanics

text: Hamiltonian mechanics has a close relationship with geometry (notably, symplectic geometry and Poisson structures) and serves as a link between classical and quantum mechanics.


title: Hamiltonian mechanics

text: Let formula_2 be a mechanical system with the configuration space formula_3 and the smooth Lagrangian formula_4 Select a standard coordinate system formula_5 on formula_6 The quantities formula_7 are called "momenta". (Also "generalized momenta", "conjugate momenta", and "canonical momenta"). For a time instant formula_8 the Legendre transformation of formula_9 is defined as the map formula_10 which is assumed to have a smooth inverse formula_11 For a system with formula_12 degrees of freedom, the Lagrangian mechanics defines the "energy function"


title: Hamiltonian mechanics

text: The inverse of the Legendre transform of formula_9 turns formula_15 into a function formula_16 known as the . The Hamiltonian satisfies


title: Hamiltonian mechanics

text: where the velocities formula_19 are found from the (formula_12-dimensional) equation formula_21 which, by assumption, is uniquely solvable for formula_22 The (formula_23-dimensional) pair formula_24 is called "phase space coordinates". (Also "canonical coordinates").


title: Hamiltonian mechanics

text: Let formula_29 be the set of smooth paths formula_30 for which formula_31 and formula_32 The action functional formula_33 is defined via


title: Hamiltonian mechanics

text: where formula_35 and formula_36 (see above). A path formula_37 is a stationary point of formula_38 (and hence is an equation of motion) if and only if the path formula_39 in phase space coordinates obeys the Hamilton's equations.


title: Hamiltonian mechanics

text: A simple interpretation of Hamiltonian mechanics comes from its application on a one-dimensional system consisting of one particle of mass . The value formula_40 of the Hamiltonian is the total energy of the system, i.e. the sum of kinetic and potential energy, traditionally denoted and , respectively. Here is the momentum and is the space coordinate. Then


title: Hamiltonian mechanics

text: In this example, the time derivative of is the velocity, and so the first Hamilton equation means that the particle's velocity equals the derivative of its kinetic energy with respect to its momentum. The time derivative of the momentum equals the "Newtonian force", and so the second Hamilton equation means that the force equals the negative gradient of potential energy.


title: Hamiltonian mechanics

text: A spherical pendulum consists of a mass "m" moving without friction on the surface of a sphere. The only forces acting on the mass are the reaction from the sphere and gravity. Spherical coordinates are used to describe the position of the mass in terms of ("r", "θ", "φ"), where is fixed, .


title: Hamiltonian mechanics

text: Hamilton's equations give the time evolution of coordinates and conjugate momenta in four first-order differential equations,


title: Hamiltonian mechanics

text: Momentum formula_48, which corresponds to the vertical component of angular momentum formula_49, is a constant of motion. That is a consequence of the rotational symmetry of the system around the vertical axis. Being absent from the Hamiltonian, azimuth formula_50 is a cyclic coordinate, which implies conservation of its conjugate momentum.


title: Hamiltonian mechanics

text: Hamilton's equations can be derived by a calculation with the Lagrangian formula_51, generalized positions , and generalized velocities , where formula_52. Here we work off-shell, meaning formula_53 are independent coordinates in phase space, not constrained to follow any equations of motion (in particular, formula_54 is not a derivative of formula_55). The total differential of the Lagrangian is: formula_56 The generalized momentum coordinates were defined as formula_57, so we may rewrite the equation as:


title: Hamiltonian mechanics

text: The term in parentheses on the left-hand side is just the Hamiltonian formula_60 defined previously, therefore:


title: Hamiltonian mechanics

text: One may also calculate the total differential of the Hamiltonian formula_62 with respect to coordinates formula_63 instead of formula_53, yielding:


title: Hamiltonian mechanics

text: One may now equate these two expressions for formula_66, one in terms of formula_51, the other in terms of formula_62:


title: Hamiltonian mechanics

text: Since these calculations are off-shell, one can equate the respective coefficients of formula_70 on the two sides:


title: Hamiltonian mechanics

text: On-shell, one substitutes parametric functions formula_72 which define a trajectory in phase space with velocities formula_73, obeying Lagrange's equations:


title: Hamiltonian mechanics

text: In the case of time-independent formula_62 and formula_51, i.e. formula_80, Hamilton's equations consist of first-order differential equations, while Lagrange's equations consist of second-order equations. Hamilton's equations usually do not reduce the difficulty of finding explicit solutions, but important theoretical results can be derived from them, because coordinates and momenta are independent variables with nearly symmetric roles.


title: Hamiltonian mechanics

text: Hamilton's equations have another advantage over Lagrange's equations: if a system has a symmetry, so that some coordinate formula_81 does not occur in the Hamiltonian (i.e. a "cyclic coordinate"), the corresponding momentum coordinate formula_82 is conserved along each trajectory, and that coordinate can be reduced to a constant in the other equations of the set. This effectively reduces the problem from coordinates to coordinates: this is the basis of symplectic reduction in geometry. In the Lagrangian framework, the conservation of momentum also follows immediately, however all the generalized velocities formula_83 still occur in the Lagrangian, and a system of equations in coordinates still has to be solved.


title: Hamiltonian mechanics

text: The Lagrangian and Hamiltonian approaches provide the groundwork for deeper results in classical mechanics, and suggest analogous formulations in quantum mechanics: the path integral formulation and the Schrödinger equation.


title: Hamiltonian mechanics

text: A sufficient illustration of Hamiltonian mechanics is given by the Hamiltonian of a charged particle in an electromagnetic field. In Cartesian coordinates the Lagrangian of a non-relativistic classical particle in an electromagnetic field is (in SI Units):


title: Hamiltonian mechanics

text: where is the electric charge of the particle, is the electric scalar potential, and the are the components of the magnetic vector potential that may all explicitly depend on formula_102 and formula_103.


title: Hamiltonian mechanics

text: Note that the values of scalar potential and vector potential would change during a gauge transformation, and the Lagrangian itself will pick up extra terms as well; But the extra terms in Lagrangian add up to a total time derivative of a scalar function, and therefore won't change the Euler–Lagrange equation.


title: Hamiltonian mechanics

text: Note that canonical momenta are not gauge invariant, and are not physically measurable. However, the kinetic momentum:


title: Hamiltonian mechanics

text: where is any scalar function of space and time, the aforementioned Lagrangian, canonical momenta, and Hamiltonian transform like:


title: Hamiltonian mechanics

text: In quantum mechanics, the wave function will also undergo a local U(1) group transformation during the Gauge Transformation, which implies that all physical results must be invariant under local U(1) transformations.


title: Hamiltonian mechanics

text: The relativistic Lagrangian for a particle (rest mass formula_111 and charge formula_112) is given by:


title: Hamiltonian mechanics

text: An equivalent expression for the Hamiltonian as function of the relativistic (kinetic) momentum, formula_120, is


title: Hamiltonian mechanics

text: This has the advantage that kinetic momentum formula_122 can be measured experimentally whereas canonical momentum formula_123 cannot. Notice that the Hamiltonian (total energy) can be viewed as the sum of the relativistic energy (kinetic+rest), formula_124, plus the potential energy, formula_125.


title: Hamiltonian mechanics

text: The Hamiltonian can induce a symplectic structure on a smooth even-dimensional manifold in several equivalent ways, the best known being the following:


title: Hamiltonian mechanics

text: As a closed nondegenerate symplectic 2-form ω. According to the Darboux's theorem, in a small neighbourhood around any point on there exist suitable local coordinates formula_126 ("canonical" or "symplectic" coordinates) in which the symplectic form becomes:


title: Hamiltonian mechanics

text: The form formula_128 induces a natural isomorphism of the tangent space with the cotangent space: formula_129 This is done by mapping a vector formula_130 to the 1-form formula_131 where formula_132 for all formula_133 Due to the bilinearity and non-degeneracy of formula_134 and the fact that formula_135 the mapping formula_136 is indeed a linear isomorphism. This isomorphism is "natural" in that it does not change with change of coordinates on formula_6 Repeating over all formula_138 we end up with an isomorphism formula_139 between the infinite-dimensional space of smooth vector fields and that of smooth 1-forms. For every formula_140 and formula_141


title: Hamiltonian mechanics

text: (In algebraic terms, one would say that the formula_143-modules formula_144 and formula_145 are isomorphic). If formula_146 then, for every fixed formula_147 formula_148 and formula_149 formula_150 is known as a Hamiltonian vector field. The respective differential equation on formula_3


title: Hamiltonian mechanics

text: is called . Here formula_153 and formula_154 is the (time-dependent) value of the vector field formula_150 at formula_156


title: Hamiltonian mechanics

text: A Hamiltonian system may be understood as a fiber bundle over time , with the fiber being the position space at time . The Lagrangian is thus a function on the jet bundle over ; taking the fiberwise Legendre transform of the Lagrangian produces a function on the dual bundle over time whose fiber at is the cotangent space , which comes equipped with a natural symplectic form, and this latter function is the Hamiltonian. The correspondence between Lagrangian and Hamiltonian mechanics is achieved with the tautological one-form.


title: Hamiltonian mechanics

text: Any smooth real-valued function on a symplectic manifold can be used to define a Hamiltonian system. The function is known as "the Hamiltonian" or "the energy function." The symplectic manifold is then called the phase space. The Hamiltonian induces a special vector field on the symplectic manifold, known as the Hamiltonian vector field.


title: Hamiltonian mechanics

text: The Hamiltonian vector field induces a Hamiltonian flow on the manifold. This is a one-parameter family of transformations of the manifold (the parameter of the curves is commonly called "the time"); in other words, an isotopy of symplectomorphisms, starting with the identity. By Liouville's theorem, each symplectomorphism preserves the volume form on the phase space. The collection of symplectomorphisms induced by the Hamiltonian flow is commonly called "the Hamiltonian mechanics" of the Hamiltonian system.


title: Hamiltonian mechanics

text: The symplectic structure induces a Poisson bracket. The Poisson bracket gives the space of functions on the manifold the structure of a Lie algebra.


title: Hamiltonian mechanics

text: If and are smooth functions on then the smooth function is properly defined; it is called a "Poisson bracket" of functions and and is denoted . The Poisson bracket has the following properties:


title: Hamiltonian mechanics

text: if there is a probability distribution , then (since the phase space velocity formula_161 has zero divergence and probability is conserved) its convective derivative can be shown to be zero and so


title: Hamiltonian mechanics

text: This is called Liouville's theorem. Every smooth function over the symplectic manifold generates a one-parameter family of symplectomorphisms and if , then is conserved and the symplectomorphisms are symmetry transformations.


title: Hamiltonian mechanics

text: A Hamiltonian may have multiple conserved quantities . If the symplectic manifold has dimension and there are functionally independent conserved quantities which are in involution (i.e., ), then the Hamiltonian is Liouville integrable. The Liouville–Arnold theorem says that, locally, any Liouville integrable Hamiltonian can be transformed via a symplectomorphism into a new Hamiltonian with the conserved quantities as coordinates; the new coordinates are called "action-angle coordinates". The transformed Hamiltonian depends only on the , and hence the equations of motion have the simple form


title: Hamiltonian mechanics

text: for some function . There is an entire field focusing on small deviations from integrable systems governed by the KAM theorem.


title: Hamiltonian mechanics

text: The integrability of Hamiltonian vector fields is an open question. In general, Hamiltonian systems are chaotic; concepts of measure, completeness, integrability and stability are poorly defined.


title: Hamiltonian mechanics

text: An important special case consists of those Hamiltonians that are quadratic forms, that is, Hamiltonians that can be written as


title: Hamiltonian mechanics

text: where is a smoothly varying inner product on the fibers , the cotangent space to the point in the configuration space, sometimes called a cometric. This Hamiltonian consists entirely of the kinetic term.


title: Hamiltonian mechanics

text: If one considers a Riemannian manifold or a pseudo-Riemannian manifold, the Riemannian metric induces a linear isomorphism between the tangent and cotangent bundles. (See Musical isomorphism). Using this isomorphism, one can define a cometric. (In coordinates, the matrix defining the cometric is the inverse of the matrix defining the metric.) The solutions to the Hamilton–Jacobi equations for this Hamiltonian are then the same as the geodesics on the manifold. In particular, the Hamiltonian flow in this case is the same thing as the geodesic flow. The existence of such solutions, and the completeness of the set of solutions, are discussed in detail in the article on geodesics. See also Geodesics as Hamiltonian flows.


title: Hamiltonian mechanics

text: When the cometric is degenerate, then it is not invertible. In this case, one does not have a Riemannian manifold, as one does not have a metric. However, the Hamiltonian still exists. In the case where the cometric is degenerate at every point of the configuration space manifold , so that the rank of the cometric is less than the dimension of the manifold , one has a sub-Riemannian manifold.


title: Hamiltonian mechanics

text: The Hamiltonian in this case is known as a sub-Riemannian Hamiltonian. Every such Hamiltonian uniquely determines the cometric, and vice versa. This implies that every sub-Riemannian manifold is uniquely determined by its sub-Riemannian Hamiltonian, and that the converse is true: every sub-Riemannian manifold has a unique sub-Riemannian Hamiltonian. The existence of sub-Riemannian geodesics is given by the Chow–Rashevskii theorem.


title: Hamiltonian mechanics

text: The continuous, real-valued Heisenberg group provides a simple example of a sub-Riemannian manifold. For the Heisenberg group, the Hamiltonian is given by


title: Hamiltonian mechanics

text: Hamiltonian systems can be generalized in various ways. Instead of simply looking at the algebra of smooth functions over a symplectic manifold, Hamiltonian mechanics can be formulated on general commutative unital real Poisson algebras. A state is a continuous linear functional on the Poisson algebra (equipped with some suitable topology) such that for any element of the algebra, maps to a nonnegative real number.


title: Hamiltonian mechanics

text: Hamilton's equations above work well for classical mechanics, but not for quantum mechanics, since the differential equations discussed assume that one can specify the exact position and momentum of the particle simultaneously at any point in time. However, the equations can be further generalized to then be extended to apply to quantum mechanics as well as to classical mechanics, through the deformation of the Poisson algebra over and to the algebra of Moyal brackets.


title: Hamiltonian mechanics

text: where is some function of and , and is the Hamiltonian. To find out the rules for evaluating a Poisson bracket without resorting to differential equations, see Lie algebra; a Poisson bracket is the name for the Lie bracket in a Poisson algebra. These Poisson brackets can then be extended to Moyal brackets comporting to an inequivalent Lie algebra, as proven by Hilbrand J. Groenewold, and thereby describe quantum mechanical diffusion in phase space (See the phase space formulation and the Wigner–Weyl transform). This more algebraic approach not only permits ultimately extending probability distributions in phase space to Wigner quasi-probability distributions, but, at the mere Poisson bracket classical setting, also provides more power in helping analyze the relevant conserved quantities in a system.


title: Executive order

text: In the United States, an executive order is a directive by the president of the United States that manages operations of the federal government. The legal or constitutional basis for executive orders has multiple sources. Article Two of the United States Constitution gives presidents broad executive and enforcement authority to use their discretion to determine how to enforce the law or to otherwise manage the resources and staff of the executive branch. The ability to make such orders is also based on expressed or implied Acts of Congress that delegate to the president some degree of discretionary power (delegated legislation). The vast majority of executive orders are proposed by federal agencies before being issued by the president.


title: Executive order

text: Like both legislative statutes and the regulations promulgated by government agencies, executive orders are subject to judicial review and may be overturned if the orders lack support by statute or the Constitution. Some policy initiatives require approval by the legislative branch, but executive orders have significant influence over the internal affairs of government, deciding how and to what degree legislation will be enforced, dealing with emergencies, waging wars, and in general fine-tuning policy choices in the implementation of broad statutes. As the head of state and head of government of the United States, as well as commander-in-chief of the United States Armed Forces, only the President of the United States can issue an executive order.


title: Executive order

text: Presidential executive orders, once issued, remain in force until they are canceled, revoked, adjudicated unlawful, or expire on their terms. At any time, the president may revoke, modify or make exceptions from any executive order, whether the order was made by the current president or a predecessor. Typically, a new president reviews in-force executive orders in the first few weeks in office.


title: Executive order

text: The United States Constitution does not have a provision that explicitly permits the use of executive orders. ArticleII, Section1, of the Constitution simply states: "The executive Power shall be vested in a President of the United States of America." Sections2 and3 describe the various powers and duties of the president, including "He shall take care that the Laws be faithfully executed".


title: Executive order

text: The U.S. Supreme Court has held that all executive orders from the president of the United States must be supported by the Constitution, whether from a clause granting specific power, or by Congress delegating such to the executive branch. Specifically, such orders must be rooted in Article II of the US Constitution or enacted by the Congress in statutes. Attempts to block such orders have been successful at times, when such orders either exceeded the authority of the President or could be better handled through legislation.


title: Executive order

text: The Office of the Federal Register is responsible for assigning the executive order a sequential number, after receipt of the signed original from the White House and printing the text of the executive order in the daily "Federal Register" and eventually in Title3 of the "Code of Federal Regulations".


title: Executive order

text: With the exception of William Henry Harrison, all presidents since George Washington in 1789 have issued orders that in general terms can be described as executive orders. Initially, they took no set form and so they varied as to form and substance.


title: Executive order

text: The first executive order was issued by Washington on June 8, 1789; addressed to the heads of the federal departments, it instructed them "to impress me with a full, precise, and distinct general idea of the affairs of the United States" in their fields.


title: Executive order

text: According to political scientist Brian R. Dirck, the most famous executive order was by President Abraham Lincoln, when he issued the Emancipation Proclamation on September 22, 1862:


title: Executive order

text: Until the early 1900s, executive orders were mostly unannounced and undocumented, and seen only by the agencies to which they were directed.


title: Executive order

text: That changed when the US Department of State instituted a numbering scheme in 1907, starting retroactively with United States Executive Order 1, issued on October 20, 1862, by President Lincoln. The documents that later came to be known as "executive orders" apparently gained their name from that order issued by Lincoln, which was captioned "Executive Order Establishing a Provisional Court in Louisiana". That court functioned during the military occupation of Louisiana during the American Civil War, and Lincoln also used Executive Order1 to appoint Charles A. Peabody as judge and designate the salaries of the court's officers.


title: Executive order

text: President Harry Truman's Executive Order 10340 placed all the country's steel mills under federal control, which was found invalid in "Youngstown Sheet & Tube Co. v. Sawyer", 343 US 579 (1952), because it attempted to make law, rather than to clarify or to further a law put forth by the Congress or the Constitution. Presidents since that decision have generally been careful to cite the specific laws under which they act when they issue new executive orders; likewise, when presidents believe that their authority for issuing an executive order stems from within the powers outlined in the Constitution, the order instead simply proclaims "under the authority vested in me by the Constitution".


title: Executive order

text: Wars have been fought upon executive order, including the 1999 Kosovo War during President Bill Clinton's second term in office; however, all such wars have also had authorizing resolutions from Congress. The extent to which the president may exercise military power independently of Congress and the scope of the War Powers Resolution remain unresolved constitutional issues, but all presidents since the passage of the resolution have complied with its terms, while maintaining that they are not constitutionally required to do so.


title: Executive order

text: Harry S. Truman issued 907 executive orders, with 1,081 orders made by Theodore Roosevelt, 1,203 orders made by Calvin Coolidge, and 1,803 orders made by Woodrow Wilson. Franklin D. Roosevelt has the distinction of making a record 3,522 executive orders.


title: Executive order

text: In 2021, President Joseph Biden issued 42 executive orders in the first 100 days of his presidency, more than any other president since Harry Truman.


title: Executive order

text: Before 1932, uncontested executive orders had determined such issues as national mourning on the death of a president and the lowering of flags to half-staff.


title: Executive order

text: President Franklin Roosevelt issued the first of his 3,522 executive orders on March 6, 1933, declaring a bank holiday, and forbidding banks to release gold coin or bullion. Executive Order 6102 forbade the hoarding of gold coin, bullion and gold certificates. A further executive order required all newly mined domestic gold be delivered to the Treasury.


title: Executive order

text: By Executive Order 6581, the president created the Export-Import Bank of the United States. On March 7, 1934, he established the National Recovery Review Board (Executive Order 6632). On June 29, the president issued Executive Order 6763 "under the authority vested in me by the Constitution", thereby creating the National Labor Relations Board.


title: Executive order

text: In 1934, while Charles Evans Hughes was Chief Justice of the United States (the period being known as the Hughes Court), the Court found that the National Industrial Recovery Act (NIRA) was unconstitutional. The president then issued Executive Order 7073 "by virtue of the authority vested in me under the said Emergency Relief Appropriation Act of 1935", re-establishing the National Emergency Council to administer the functions of the NIRA in carrying out the provisions of the Emergency Relief Appropriations Act. On June 15, he issued Executive Order 7075, which terminated the NIRA and replaced it with the Office of Administration of the National Recovery Administration.


title: Executive order

text: In the years that followed, Roosevelt replaced outgoing justices of the Supreme Court with people more in line with his views: Hugo Black, Stanley Reed, Felix Frankfurter, William O. Douglas, Frank Murphy, Robert H. Jackson and James F. Byrnes. Historically, only George Washington has had equal or greater influence over Supreme Court appointments (as he chose all its original members).


title: Executive order

text: Justices Frankfurter, Douglas, Black, and Jackson dramatically checked presidential power by invalidating the executive order at issue in "Youngstown Sheet & Tube Co. v. Sawyer": in that case Roosevelt's successor, Harry S. Truman, had ordered private steel production facilities seized in Executive Order 10340 to support the Korean War effort: the Court held that the executive order was not within the power granted to the President by the Constitution.


title: Executive order

text: Large policy changes with wide-ranging effects have been implemented by executive order, including the racial integration of the armed forces under President Truman.


title: Executive order

text: Two extreme examples of an executive order are Franklin Roosevelt's Executive Order 6102 "forbidding the hoarding of gold coin, gold bullion, and gold certificates within the continental United States", and Executive Order 9066, which delegated military authority to remove any or all people in a military zone (used to target Japanese Americans, non-citizen Germans, and non-citizen Italians in certain regions). The order was then delegated to General John L. DeWitt, and it subsequently paved the way for all Japanese-Americans on the West Coast to be sent to internment camps for the duration of World War II.


title: Executive order

text: President George W. Bush issued Executive Order 13233 in 2001, which restricted public access to the papers of former presidents. The order was criticized by the Society of American Archivists and other groups, who say it "violates both the spirit and letter of existing U.S. law on access to presidential papers as clearly laid down in 44 USC 2201–07", and adding that the order "potentially threatens to undermine one of the very foundations of our nation". President Barack Obama subsequently revoked Executive Order 13233 in January 2009.


title: Executive order

text: The Heritage Foundation has accused presidents of abusing executive orders by using them to make laws without Congressional approval and moving existing laws away from their original mandates.


title: Executive order

text: In 1935, the Supreme Court overturned five of Franklin Roosevelt's executive orders (6199, 6204, 6256, 6284 and 6855).


title: Executive order

text: , issued by President Bill Clinton in 1995, attempted to prevent the federal government from contracting with organizations that had strike-breakers on the payroll: a federal appeals court ruled that the order conflicted with the National Labor Relations Act and overturned the order.


title: Executive order

text: Congress has the power to overturn an executive order by passing legislation that invalidates it, and can also refuse to provide funding necessary to carry out certain policy measures contained with the order or legitimize policy mechanisms.


title: Executive order

text: In the case of the former, the president retains the power to veto such a decision; however, Congress may override a veto with a two-thirds majority to end an executive order. It has been argued that a Congressional override of an executive order is a nearly impossible event, because of the supermajority vote required, and the fact that such a vote leaves individual lawmakers vulnerable to political criticism.


title: Executive order

text: On July 30, 2014, the US House of Representatives approved a resolution authorizing Speaker of the House John Boehner to sue President Obama over claims that he exceeded his executive authority in changing a key provision of the Affordable Care Act ("Obamacare") on his own and over what Republicans claimed had been "inadequate enforcement of the health care law", which Republican lawmakers opposed. In particular, Republicans "objected that the Obama administration delayed some parts of the law, particularly the mandate on employers who do not provide health care coverage". The suit was filed in the US District Court for the District of Columbia on November 21, 2014.


title: Executive order

text: Part of President Donald Trump's executive order Protecting the Nation from Foreign Terrorist Entry into the United States, which temporarily banned entry to the US of citizens of seven Muslim-majority countries, including for permanent residents, was stayed by a federal court on January 28, 2017. However, on June 26, 2018, the US Supreme Court overturned the lower court order in "Trump v. Hawaii" and affirmed that the executive order was within the president's constitutional authority.


title: Executive order

text: The degree to which the President has the power to use executive orders to set policy for independent federal agencies is disputed. Many orders specifically exempt independent agencies, but some do not. Executive Order 12866 has been a particular matter of controversy; it requires cost-benefit analysis for certain regulatory actions.


title: Executive order

text: Executive orders issued by state governors are not the same as statutes passed by state legislatures. State executive orders are usually based on existing constitutional or statutory powers of the governor and do not require any action by the state legislature to take effect.<ref name= "https://www.colorado.governor/executive-orders"></ref><ref name= "https://gov.georgia.gov/executive-orders"></ref><ref name= "https://www.governor.wa.gov/office-governor/official-actions/executive-orders"></ref><ref name= "https://www.flgov.com/all-executive-orders"></ref><ref name= "https://rules.utah.gov/executive-documents"></ref>


title: Executive order

text: Executive orders may, for example, demand budget cuts from state government when the state legislature is not in session, and economic conditions take a downturn, thereby decreasing tax revenue below what was forecast when the budget was approved. Depending on the state constitution, a governor may specify by what percentage each government agency must reduce and may exempt those that are already particularly underfunded or cannot put long-term expenses (such as capital expenditures) off until a later fiscal year. The governor may also call the legislature into special session.


title: Executive order

text: There are also other uses for gubernatorial executive orders. In 2007, for example, Sonny Perdue, the governor of Georgia, issued an executive order for all its state agencies to reduce water use during a major drought. The same was demanded of its counties' water systems as well, but it was unclear whether the order would have the force of law.


title: Executive order

text: According to political expert Phillip J. Cooper, a presidential proclamation "states a condition, declares a law and requires obedience, recognizes an event or triggers the implementation of a law (by recognizing that the circumstances in law have been realized)". Presidents define situations or conditions on situations that become legal or economic truth. Such orders carry the same force of law as executive orders, the difference between being that executive orders are aimed at those inside government, but proclamations are aimed at those outside government.


title: Executive order

text: The administrative weight of those proclamations is upheld because they are often specifically authorized by congressional statute, making them "delegated unilateral powers". Presidential proclamations are often dismissed as a practical presidential tool for policy making because of the perception that proclamations are largely ceremonial or symbolic in nature. However, the legal weight of presidential proclamations suggests their importance to presidential governance.


title: Lost Girls (film)

text: Lost Girls is a 2020 American mystery drama film. "Lost Girls" was directed by Liz Garbus, from a screenplay by Michael Werwie, and based on the book "Lost Girls: An Unsolved American Mystery" by Robert Kolker. The film revolves around the murders of young female sex workers on the South Shore barrier islands of Long Island, committed by the Long Island serial killer, who remains unidentified.


title: Lost Girls (film)

text: "Lost Girls" stars Amy Ryan as the real life activist Mari Gilbert, along with Thomasin McKenzie, Lola Kirke, Oona Laurence, Dean Winters, Miriam Shor, Reed Birney, Kevin Corrigan, and Gabriel Byrne. The film premiered at the Sundance Film Festival on January 28, 2020, and was later released on March 13, 2020, by Netflix.


title: Lost Girls (film)

text: Mari Gilbert relentlessly drives law enforcement agents to search for her missing daughter, Shannan, and, in the process, sheds light on a wave of unsolved murders of young female sex workers on the South Shore barrier islands of Long Island, committed by the Long Island serial killer.


title: Lost Girls (film)

text: In March 2016, it was announced that Liz Garbus would direct the film, from a screenplay by Michael Werwie, based on the book of the same name by Robert Kolker. Kevin McCormack, David Kennedy, Rory Koslow, Amy Nauiokas, and Anne Carey served as producers on the film, while Pamela Hirsch executive produced. Amazon Studios was initially set to distribute. In February 2017, Sarah Paulson was set to star in the film as real-life activist Mari Gilbert. In May 2018, Amy Ryan replaced Paulson, and Netflix was set as the distributor. In October 2018, Thomasin McKenzie (who dropped out of "" to work on the film), Gabriel Byrne, Oona Laurence, Lola Kirke, Miriam Shor, Reed Birney, Kevin Corrigan, and Rosal Colon joined the cast.


title: Lost Girls (film)

text: The film had its world premiere at the Sundance Film Festival on January 28, 2020, and was released on March 13, 2020, by Netflix.


title: Lost Girls (film)

text: "Lost Girls" holds approval rating on the review aggregator website Rotten Tomatoes, based on reviews, with an average of . The website's critical consensus reads, "Raw yet rewarding, "Lost Girls" overcomes uneven storytelling with powerful performances and a willingness to resist easy catharsis." On Metacritic, the film holds a rating of 69 out of 100, based on 13 critics, indicating "generally favorable reviews."


title: The Incredible Dr. Pol

text: The Incredible Dr. Pol is an American reality television show on Nat Geo Wild that follows Dutch-American veterinarian Jan Pol and his family and employees at his practice in rural Weidman, Michigan. The series premiered October 29, 2011 and has two seasons every year, for a total of 20 through February 2022.


title: The Incredible Dr. Pol

text: Pol is surprised that the show became a hit "watched by everybody—all kinds of life, all ages, big family show, and I think this is what is so fantastic." He credits his son Charles, who is the series producer, and who successfully pitched the series to National Geographic. According to Pol, Charles counseled him, "Dad, do your work. That is interesting enough. Don't look at the camera, don't do anything for the camera." Pol continues. "... it's not scripted; it is real."


title: The Incredible Dr. Pol

text: Pol's style has received a mixed reception by veterinarians, and in 2014, Pol was fined $500 and had his license put on probation by the Michigan Board of Veterinary Medicine for not wearing proper surgical attire during treatment of a Boston terrier. However, a year later, the sentencing was overturned by the Michigan Court of Appeals, which reversed and remanded, holding "inter alia" that there was no competent evidence that there was a breach of the standard of care and citing the fact that "the owners of the dog were happy with the care it has been given."


title: The Library of Babel

text: "The Library of Babel" () is a short story by Argentine author and librarian Jorge Luis Borges (1899–1986), conceiving of a universe in the form of a vast library containing all possible 410-page books of a certain format and character set.


title: The Library of Babel

text: The story was originally published in Spanish in Borges' 1941 collection of stories "El jardín de senderos que se bifurcan" ("The Garden of Forking Paths"). That entire book was, in turn, included within his much-reprinted "Ficciones" (1944). Two English-language translations appeared approximately simultaneously in 1962, one by James E. Irby in a diverse collection of Borges's works titled "Labyrinths" and the other by Anthony Kerrigan as part of a collaborative translation of the entirety of "Ficciones".


title: The Library of Babel

text: Borges' narrator describes how his universe consists of an enormous expanse of adjacent hexagonal rooms. In each room, there is an entrance on one wall, the bare necessities for human survival on another wall, and four walls of bookshelves. Though the order and content of the books are random and apparently completely meaningless, the inhabitants believe that the books contain every possible ordering of just 25 basic characters (22 letters, the period, the comma, and space). Though the vast majority of the books in this universe are pure gibberish, the library also must contain, somewhere, every coherent book ever written, or that might ever be written, and every possible permutation or slightly erroneous version of every one of those books. The narrator notes that the library must contain all useful information, including predictions of the future, biographies of any person, and translations of every book in all languages. Conversely, for many of the texts, some language could be devised that would make it readable with any of a vast number of different contents.


title: The Library of Babel

text: Despite—indeed, because of—this glut of information, all books are totally useless to the reader, leaving the librarians in a state of suicidal despair. This leads some librarians to superstitious and cult-like behaviors, such as the "Purifiers", who arbitrarily destroy books they deem nonsense as they scour through the library seeking the "Crimson Hexagon" and its illustrated, magical books. Others believe that since all books exist in the library, somewhere one of the books must be a perfect index of the library's contents; some even believe that a messianic figure known as the "Man of the Book" has read it, and they travel through the library seeking him.


title: The Library of Babel

text: The story repeats the theme of Borges' 1939 essay "The Total Library" ("La Biblioteca Total"), which in turn acknowledges the earlier development of this theme by Kurd Lasswitz in his 1901 story "The Universal Library" ("Die Universalbibliothek"):


title: The Library of Babel

text: Certain examples that Aristotle attributes to Democritus and Leucippus clearly prefigure it, but its belated inventor is Gustav Theodor Fechner, and its first exponent, Kurd Lasswitz. [...] In his book "The Race with the Tortoise" (Berlin, 1919), Dr Theodor Wolff suggests that it is a derivation from, or a parody of, Ramón Llull's thinking machine [...] The elements of his game are the universal orthographic symbols, not the words of a language [...] Lasswitz arrives at twenty-five symbols (twenty-two letters, the space, the period, the comma), whose recombinations and repetitions encompass everything possible to express in all languages. The totality of such variations would form a Total Library of astronomical size. Lasswitz urges mankind to construct that inhuman library, which chance would organize and which would eliminate intelligence. (Wolff's "The Race with the Tortoise" expounds the execution and the dimensions of that impossible enterprise.)


title: The Library of Babel

text: Many of Borges' signature motifs are featured in the story, including infinity, reality, cabalistic reasoning, and labyrinths. The concept of the library is often compared to Borel's dactylographic monkey theorem. There is no reference to monkeys or typewriters in "The Library of Babel", although Borges had mentioned that analogy in "The Total Library": "[A] half-dozen monkeys provided with typewriters would, in a few eternities, produce all the books in the British Museum." In this story, the closest equivalent is the line, "A blasphemous sect suggested [...] that all men should juggle letters and symbols until they constructed, by an improbable gift of chance, these canonical books." Borges makes an oblique reference to reproducing Shakespeare, as the only decipherable sentence in the library "O time thy pyramids" is surely taken from Shakespeare's Sonnet 123 which opens with the lines "No Time, thou shalt not boast that I do change, Thy pyramids...".


title: The Library of Babel

text: Borges would examine a similar idea in his 1976 story, "The Book of Sand", in which there is an infinite book (or book with an indefinite number of pages) rather than an infinite library. Moreover, the story's "Book of Sand" is said to be written in an unknown alphabet and its content is not obviously random. In The Library of Babel, Borges interpolates Italian mathematician Bonaventura Cavalieri's suggestion that any solid body could be conceptualized as the superimposition of an infinite number of planes.


title: The Library of Babel

text: The concept of the library is also overtly analogous to the view of the universe as a sphere having its center everywhere and its circumference nowhere. The mathematician and philosopher Blaise Pascal employed this metaphor, and in an earlier essay Borges noted that Pascal's manuscript called the sphere "effroyable," or "frightful".


title: The Library of Babel

text: In any case, a library containing "all" possible books, arranged at random, might as well be a library containing "zero" books, as any true information would be buried in, and rendered indistinguishable from, all possible forms of false information; the experience of opening to any page of any of the library's books has been simulated by websites which create screenfuls of random letters.


title: The Library of Babel

text: The quote at the beginning of the story, "By this you may contemplate the variation of the twenty-four letters," is from Robert Burton's 1621 "The Anatomy of Melancholy".


title: The Library of Babel

text: In mainstream theories of natural language syntax, every syntactically-valid utterance can be extended to produce a new, longer one, because of recursion. However, the books in the Library of Babel are of bounded length ("each book is of four hundred and ten pages; each page, of forty lines, each line, of some eighty letters"), so the Library can only contain a finite number of distinct strings. Borges' narrator notes this fact, but believes that the Library is nevertheless infinite; he speculates that it repeats itself periodically, giving an eventual "order" to the "disorder" of the seemingly random arrangement of books. Mathematics professor William Goldbloom Bloch confirms the narrator's intuition, deducing in his popular mathematics book "The Unimaginable Mathematics of Borges' Library of Babel" that the library's structure necessarily has at least one room whose shelves are not full (because the number of books per room does not divide the total number of books evenly), and the rooms on each floor of the library must either be connected into a single Hamiltonian cycle, or possibly be disconnected into subsets that cannot reach each other.


title: The Library of Babel

text: W. V. O. Quine notes that the Library of Babel is finite, and that any text that does not fit in a single book can be reconstructed by finding a second book with the continuation. The size of the alphabet can be reduced by using Morse code even though it makes the books more verbose; the size of the books can also be reduced by splitting each into multiple volumes and discarding the duplicates. Writes Quine, "The ultimate absurdity is now staring us in the face: a universal library of two volumes, one containing a single dot and the other a dash. Persistent repetition and alternation of the two are sufficient, we well know, for spelling out any and every truth. The miracle of the finite but universal library is a mere inflation of the miracle of binary notation: everything worth saying, and everything else as well, can be said with two characters."