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Amherst, Massachusetts

Amherst is a city in Hampshire County, Massachusetts, United States, in the Connecticut River valley. Amherst has a council–manager form of government, and is considered a city under Massachusetts state law. Amherst is one of several Massachusetts municipalities that have city forms of government but retain "The Town of" in their official names. At the 2020 census, the population was 39,263, making it the highest populated municipality in Hampshire County (although the county seat is Northampton). The town is home to Amherst College, Hampshire College, and the University of Massachusetts Amherst, three of the Five Colleges.

Amherst has three census-designated places: Amherst Center, North Amherst, and South Amherst.

Amherst is part of the Springfield, Massachusetts Metropolitan Statistical Area. Lying 22 mi north of the city of Springfield, Amherst is considered the northernmost town in the Hartford–Springfield Metropolitan Region, "The Knowledge Corridor". Amherst is also located in the Pioneer Valley, which encompasses Hampshire, Hampden and Franklin counties.

Name
The name of the town is pronounced without the h ("AM-erst") by natives and long-time residents, giving rise to the local saying, "only the 'h' is silent", in reference both to the pronunciation and to the town's politically active populace.

History
The earliest known document of the lands now comprising Amherst is the deed of purchase dated December 1658 between John Pynchon of Springfield and three native inhabitants, referred to as Umpanchla, Quonquont, and Chickwalopp. According to the deed, "ye Indians of Nolwotogg (Norwottuck) upon ye River of Quinecticott (Connecticut)" sold the entire area in exchange for "two Hundred fatham of Wampam & Twenty fatham, and one large Coate at Eight fatham wch Chickwollop set of, of trusts, besides severall small giftes" [sic].

Amherst was first visited by Europeans no later than 1665, when Nathaniel Dickinson surveyed the lands for its mother town Hadley. The first permanent English settlements arrived in 1727. It remained a part of Hadley, even when it gained precinct status in 1734, before becoming a township in 1759.

When it incorporated, the colonial governor assigned the town the name "Amherst" after Jeffery Amherst, 1st Baron Amherst. Many a colonial governor at the time scattered his name during the influx of new town applications, which is why several towns in the Northeast bear the name. Amherst was Commander-in-Chief of the forces of North America during the French and Indian War who, according to popular legend, singlehandedly won Canada for the British and banished France from North America. Popular belief has it that he supported the American side in the Revolutionary War and resigned his commission rather than fight for the British. Baron Amherst actually remained in the service of the Crown during the war—albeit in Great Britain rather than North America—where he organized the defense against the proposed Franco-Spanish Armada of 1779. Nonetheless, his previous service in the French and Indian War meant he remained popular in New England. Amherst is also infamous for recommending, in a letter to a subordinate, the use of smallpox-covered blankets in warfare against the Native Americans along with any "other method that can serve to Extirpate this Execrable Race". For this reason, there have been occasional ad hoc movements to rename the town.

Amherst celebrated its 250th anniversary in 2009. The Amherst 250th Anniversary Celebration Committee and Amherst Historical Society organized events, including a book published by the Historical Society and written by Elizabeth M. Sharpe, Amherst A to Z.

In 2021 the City Council voted to establish the Amherst African Heritage Reparation Assembly to study reparations for the town's black residents. In 2022, at the Assembly's suggestion, the City Council approved $2,000,000 of initial funding for reparations.

History of town government
The Town converted from an open town meeting to a representative town meeting form in 1938. In 1953, Amherst voters passed the "Town Manager Act", which established the office of a town manager and reduced a number of elected positions. In 1995, a charter commission was approved to study Amherst's government; the charter majority recommended a seven-person Council and a mayor, while also maintaining a reduced size representative Town Meeting (150). This proposal failed in two successive votes.

In 2001, the League of Women Voters Amherst made a number of recommendations that were adopted in 2001 in the form of a revised "Amherst Town Government Act". An effort shortly thereafter to amend the charter to eliminate the town meeting, and establish an elected mayor and a nine-member Town Council, was rejected by voters twice, first in spring 2003 by fourteen votes and again on March 29, 2005 by 252 votes.

In 2016, a charter commission was approved to study Amherst's government. A majority of commissioners proposed a charter that would establish a 13-member council with no mayor. This proposal was voted on the March 27, 2018 local ballot, and was passed by over 1,000 votes, a 58% majority. The new town council was sworn in on December 2, 2018.

Geography
According to the United States Census Bureau, Amherst has a total area of 71.8 sqkm, of which 71.5 sqkm are land and 0.3 sqkm, or 0.48%, are water. The town is bordered by Hadley to the west, Sunderland and Leverett to the north, Shutesbury, Pelham, and Belchertown to the east, and Granby and South Hadley to the south. The highest point in the town is on the northern shoulder of Mount Norwottuck at the southern border of the town; the peak is in Granby but the town's high point is a few yards away and is about 1100 ft. This point is located in the Mount Holyoke Range, which forms the so-called "Tofu Curtain". Amherst is nearly equidistant from Massachusetts' borders with Connecticut and Vermont.

Amherst's ZIP Code of 01002 is the second-lowest number in the continental United States after Agawam (not counting codes used for specific government buildings such as the IRS).

Climate
Amherst has a humid continental climate that under the Köppen system marginally falls into the warm-summer category (Dfb). It is interchangeable with the hot-summer subtype Dfa with July means hovering around 71.7 F. Winters are cold and snowy, albeit daytime temperatures often remain above freezing. Under the 2012 USDA Plant Hardiness Zone system, Amherst (ZIP Code 01002) is in zone 5b; however, Amherst closely borders zone 6a, which penetrates into Massachusetts in the Connecticut River Valley, and climate change may be shifting those zones.

Demographics
As of the 2010 U.S. Census, there were 37,819 people, 9,259 households, and 4,484 families residing in the town. There were 9,711 housing units. The racial makeup of the town was 76.9% White, 5.4% Black or African American, 0.2% Native American, 10.9% Asian, 0.03% Pacific Islander, 2.4% some other race, and 4.1% from two or more races. 7.3% of the population were Hispanic or Latino of any race.

Of the 9,259 households in the town, 23.4% had children under the age of 18 living with them, 35.6% were headed by married couples living together, 16.3% had a female householder with no husband present, and 51.6% were non-families. Of all households, 27.3% were made up of individuals, and 9.7% were someone living alone who was 65 years of age or older. The average household size was 2.44 and the average family size was 2.88.

In the town, 10.0% of the population were under the age of 18, 55.7% were from 18 to 24, 13.3% were from 25 to 44, 13.6% were from 45 to 64, and 7.4% were 65 years of age or older. The median age was 21.6 years. For every 100 females, there were 95.8 males. For every 100 females age 18 and over, there were 94.7 males.

For the period 2011–2015, the estimated median annual income for a household in the town was $48,059, and the median income for a family was $96,005. Male full-time workers had a median income of $64,750 versus $39,278 for females. The per capita income for the town was $18,905. About 8.7% of families and 34.7% of the population were below the poverty line, including 18.2% of those under age 18 and 4.5% of those age 65 or over.

Of residents 25 years old or older, 41.7% have a graduate or professional degree, and only 4.9% did not graduate from high school. The largest industry is education, health, and social services, in which 51.9% of employed persons work.

These statistics given above include some but not all of the large student population, roughly 30,000 in 2010, many of whom only reside in the town part of the year. Amherst is home to thousands of part-time and full-time residents associated with the University of Massachusetts Amherst, Amherst College, and Hampshire College.

Income
Data is from the 2009–2013 American Community Survey 5-Year Estimates.

Economy
Major employers in Amherst include University of Massachusetts Amherst, Amherst College, William D. Mullins Memorial Center, Hampshire College, and Amherst-Pelham Regional School District.

Points of interest

 * Amherst Center Cultural District, formed in 2016.
 * Amherst Area Chamber of Commerce
 * Amherst Cinema Arts Center: a local non-profit theater showing mostly arthouse and independent films
 * Amherst History Museum, which opened in 1916 and is governed by the Amherst Historical Society
 * Beneski Museum of Natural History, including the Hitchcock Ichnological Cabinet
 * Emily Dickinson Museum, birthplace and lifelong residence of poet Emily Dickinson, now a museum.
 * Eric Carle Museum of Picture Book Art
 * Hitchcock Center for the Environment, an environmental education center on the grounds of Hampshire College
 * Jones Library
 * Mead Art Museum at Amherst College: 18,000 items with a particular strength in American art
 * W. E. B. Du Bois Library at the University of Massachusetts Amherst: the tallest academic library in the United States
 * W. E. B. Du Bois Library at the University of Massachusetts Amherst: the tallest academic library in the United States

Sports

 * Games were played in town during the 1996 World Junior Ice Hockey Championships.
 * Amherst Regional High School's 1992–93 girls' basketball team inspired the book In These Girls, Hope is a Muscle by Madeleine Blais.
 * The University of Massachusetts Amherst's Ultimate Frisbee Team was ranked first in the Division 1 Men's Ultimate league for the 2017 season.
 * The Amherst Invitational, founded in 1992, is the oldest high school Ultimate Frisbee tournament in the United States.

Government

Amherst has a town council for its legislative branch and a town manager for its executive branch. The town manager is appointed by the town council.

Amherst's town council consists of ten district councilors and three councilors-at-large. Two district councilors are elected from each of five districts in Amherst. The three councilors-at-large are elected by the whole town. Each councilor serves a two-year term, except for the first council, where each member will serve a three-year term.

Amherst also has the following elected bodies:
 * A five-member School Committee with two-year terms.
 * A six-member library board of trustees with two-year terms.
 * A single Oliver Smith Will Elector with a two-year term.

Amherst also has a five-member housing authority where three of the five members are elected by voters. Each member serves a two-year term.

State and federal representation
In the Massachusetts Senate Amherst is in the "Hampshire, Franklin and Worcester" district, represented by Democratic State Senator Jo Comerford since January 2019. In the Massachusetts House of Representatives Amherst is in the 3rd Hampshire district, represented by Democratic State Representative Mindy Domb since January 2019. Amherst is part of the Eighth Massachusetts Governor's Council district and has been represented by Tara Jacobs since January 2023.

Amherst is represented at the federal level by an all-Democratic delegation, including Senators Elizabeth Warren and Ed Markey, and by Representative Jim McGovern of the Second Congressional District of Massachusetts.

Voter registration

Voter registration data is from the state election enrollment statistics.

Politics
Like many college towns, Amherst leans heavily Democratic. In each of the presidential elections from 2012 to 2020, more than 80% of Amherst's votes went to the Democratic candidate. The last Republican to win Amherst on the Presidential level was Richard Nixon in 1960.

In the 2020 United States Presidential Election, Democrat Joe Biden received 90.3 percent of the vote to incumbent Republican Donald Trump's 7.4 percent. In the 2000 United States Presidential Election, Amherst was one of a small number of places that delivered more votes for Green Party candidate Ralph Nader (who took 24% of the vote) than Republican candidate George W. Bush, who received just 13%.

Education

The town is part of the Amherst Regional School District along with Leverett, Pelham, and Shutesbury. Amherst has three elementary schools: Crocker Farm Elementary School, Fort River Elementary School, and Wildwood Elementary School serving K–6. Students in Amherst then attend Amherst Regional Middle School for grades 7–8. High school students then attend Amherst Regional High School.

There are three tertiary institutions located in the town: the public University of Massachusetts Amherst (the flagship of the UMass system), and two private liberal arts colleges—Amherst College and Hampshire College.

Bus
The Pioneer Valley Transit Authority, funded by local governments and the Five College Consortium, provides public transportation in the area, operated by University of Massachusetts Transportation Services. Service runs well into the early morning hours on weekends when school is in session. Students attending any colleges in the Five Colleges Consortium have a fee included in their tuition bills (service fee for UMass Amherst students and student activity fees for the other colleges) for each semester that prepays their bus fares for the semester. UMass Transit buses operate via a proof-of-payment system, in which there are random inspections of student identification cards and bus passes and transfers.

Peter Pan Bus Lines provides service between Amherst and Springfield, Boston, and other locations in New England. Megabus provides service between New York City, Amherst, and Burlington, Vermont.

Rail
Amtrak rail service is available in nearby Northampton on the Vermonter service between Washington, D.C., and St. Albans, Vermont. More frequent Amtrak service to New York City and Washington, D.C., is available from Union Station in Springfield.

Airports
The closest major domestic and limited international air service is available through Bradley International Airport (BDL) in Windsor Locks, Connecticut. Bradley is located approximately one hour's driving time from Amherst. Major international service is available through Logan International Airport (BOS) in Boston, 90 miles away.

General aviation service is close by, at Northampton Airport, Westover Metropolitan Airport, and Turners Falls Airport.

Police report
Since 1997, the local newspaper, the Amherst Bulletin, has published a weekly log of phone calls received by the Amherst Police Department. This police report, whose tone is deadpan and often unintentionally humorous, has been the subject of at least two books and a 2002 article in Harper's Magazine, "Gone When Police Got There". For example, an entry from the March 27, 2015 police report reads: "2:48 a.m.—An Ann Whalen Apartments resident awoke to find someone on her balcony looking into her bedroom. The woman later told police she thinks she may have been dreaming prior to calling 911."

Historical

 * Chinua Achebe (1930–2013), was a professor at the University of Massachusetts from 1972 to 1976
 * Osmyn Baker (1800–1875), born in Amherst, United States Congressman and lawyer
 * Ray Stannard Baker (1870–1946), newspaperman, biographer of Woodrow Wilson
 * William S. Clark (1825–1886), Academician, politician, businessman; principal founder of the Massachusetts Agricultural College (now the University of Massachusetts Amherst), founder of the Sapporo Agricultural College (now the Hokkaido University)
 * Mason Cook Darling (1801–1866), born in Amherst, United States Congressman from Wisconsin and first mayor of Fond du Lac, Wisconsin
 * Melvil Dewey (1851–1931), devised the Dewey Decimal System while an assistant librarian at Amherst College in 1876
 * Edward Dickinson (1803–1874), born in Amherst, lawyer, United States Congressman, and father of Emily Dickinson
 * Emily Dickinson (1830–1886), born and lived in Amherst, one of the most prominent and celebrated American poets
 * Eugene Field (1850–1895), raised in Amherst by cousin, Mary Field French; poet and humorist who wrote children's poem Wynken, Blynken, and Nod
 * Robert Francis (1901–1987), poet
 * Robert Frost (1874–1963), Pulitzer prize-winning poet who taught at Amherst College and retired there
 * Howard Roger Garis (1873–1962), children's author who wrote the Uncle Wiggily book series
 * Lilian Garis (1873–1954), author of juvenile fiction who under the pseudonym Laura Lee Hope wrote early volumes in the Bobbsey Twins series
 * Edward Hitchcock (1793–1864), educator, early geologist and a founder of the science of ichnology
 * Helen Hunt Jackson (1830–1885), born in Amherst, noted author best known for A Century of Dishonor and her novel Ramona
 * Arthur Lithgow (1915–2004), lived and died in Amherst, noted actor, producer and director of Shakespeare plays, founder of the Great Lakes Shakespeare Festival in Ohio (today known as the Great Lakes Theatre Festival), former director of the McCarter Theatre in Princeton, NJ, father of actor John Lithgow
 * Ebenezer Mattoon (1755–1843), born in North Amherst, Lieutenant in Continental Army during American Revolution, US Congressman (1801–1803).
 * Paul Nitze (1907–2004), born in Amherst, diplomat who helped shape defense policy over numerous presidential administrations
 * Julius Hawley Seelye (1824–1895), Amherst college professor, united States Representative (1875–1877), 5th President of Amherst College
 * Harlan Fiske Stone (1872–1946), attended public schools in Amherst and Amherst College; dean of the Columbia Law School, 52nd Attorney General of the United States, and Chief Justice of the United States
 * Mabel Loomis Todd (1856–1932), world traveler, edited and published the first volume of Emily Dickinson's poetry
 * Noah Webster (1758–1843), Author of An American Dictionary of the English Language

Born or raised in Amherst

 * Annie Baker, playwright
 * Emily Dickinson, poet
 * P. D. Eastman, children's author, illustrator, and screenwriter
 * Helen Palmer Geisel, children's author and first wife of Dr. Seuss
 * Michael Hixon, U.S. Olympic Athlete Rio 2016, men's individual 3 meter springboard; 3 meter springboard synchro
 * James D. Hornfischer, military historian and author
 * James Ihedigbo, Detroit Lions defensive back
 * Martin Johnson, of rock band Boys like Girls
 * John Leonard, ice hockey player
 * Amory Lovins, scientist and environmentalist
 * Michael E. Mann, climatologist
 * J Mascis, singer, guitarist and songwriter for alternative rock band Dinosaur Jr.
 * Eric Mabius, star of ABC show Ugly Betty, attended Amherst schools
 * Makaya McCraven, musician
 * Julie McNiven, actress with recurring roles on Mad Men and Supernatural
 * Ilan Mitchell-Smith, actor starring in 1985 film Weird Science, attended Amherst public schools
 * Ebon Moss-Bachrach, actor with roles on The Bear and Girls, raised in Amherst and attended Amherst public schools
 * Henry Addison Nelson (1820–1906), Presbyterian clergyman
 * Eli Noyes, animator, film producer, director
 * Gil Penchina, Former CEO of Wikia, Inc., attended the University of Massachusetts Amherst
 * John Pettes, US Marshal for Vermont, born in Amherst
 * Steve Porter, music producer
 * Allen St. Pierre, executive director of NORML, attended public schools in Amherst and graduated from the University of Massachusetts Amherst
 * Matt Reid, head baseball coach at Army
 * Timothy Tau, writer and filmmaker
 * Uma Thurman, Oscar-nominated actress, whose father, Robert Thurman, taught at Amherst College
 * Martin M. Wattenberg, artist and computer scientist
 * Zoe Weizenbaum, child actress
 * Jamila Wideman (born 1975), female left-handed point guard basketball player, lawyer and activist
 * Elisha Yaffe, comedian, actor, and producer
 * Kevin Ziomek, American professional baseball pitcher in the Detroit Tigers organization

Live/lived in Amherst

 * Gavin Andresen, Bitcoin Foundation founder and former Bitcoin contributor
 * Christian Appy, author of Patriots and Working-Class War, professor at University of Massachusetts Amherst
 * Christopher Benfey, author of The Great Wave, professor at Mount Holyoke College
 * Holly Black, author of Tithe, Valiant, Ironside, and co-author of the Spiderwick Chronicles
 * Augusten Burroughs, author of Running with Scissors
 * Michelle Chamuel, singer, songwriter, producer
 * Cassandra Clare, author of The Mortal Instruments and The Infernal Devices
 * Arda Collins, poet and winner of the Yale Series of Younger Poets Competition
 * Tony DiTerlizzi, author of The Spider and the Fly and co-author/illustrator for Spiderwick Chronicles
 * Peter Elbow, compositionist and professor emeritus at the University of Massachusetts Amherst
 * Joseph Ellis, historian and author of Founding Brothers
 * Martín Espada, poet, professor at the University of Massachusetts and author of the 2006 The Republic of Poetry, among others
 * Black Francis, singer/guitarist of the alternative rock band the Pixies, attended UMass Amherst
 * Rebecca Guay, artist specializing in watercolor painting and illustration
 * Norton Juster, author of The Phantom Tollbooth
 * John Katzenbach, author of The Madman's Tale
 * Julius Lester, author and professor at the University of Massachusetts Amherst
 * Michael Lesy, author of Wisconsin Death Trip, professor at Hampshire College
 * Cale Makar, professional ice hockey player for the Colorado Avalanche and former University of Massachusetts defenseman.
 * Charles C. Mann (born 1955), journalist and author of 1491: New Revelations of the Americas Before Columbus and 1493: Uncovering the New World Columbus Created
 * Catherine Newman, memoirist and novelist
 * John Olver, politician who served in the US House of Representatives
 * John Elder Robison, author of Look Me in the Eye; older brother of Augusten Burroughs
 * Joey Santiago, lead guitarist of the alternative rock band the Pixies, attended UMass Amherst
 * Archie Shepp, jazz musician and professor emeritus at the University of Massachusetts Amherst
 * Chris Smither, folk/blues singer, guitarist, and songwriter
 * James Tate (born 1943), poet and professor at the University of Massachusetts Amherst
 * Carl Vigeland, author of In Concert and many other books
 * John Edgar Wideman, novelist and writer
 * Dara Wier, poet and professor in the MFA Program for Poets & Writers at the University of Massachusetts Amherst
 * Roman Yakub, composer

Sister cities

 * Nyeri, Kenya
 * La Paz Centro, Nicaragua
 * Kanegasaki, Japan

title: Amherst, Massachusetts


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USS Salt Lake City

Two ships of the United States Navy have borne the name USS Salt Lake City, in honor of the city in Utah which has served successively as the capital of the Provisional State of Deseret, the Utah Territory, and the 45th state. See Salt Lake City, Utah.

 * The first USS Salt Lake City (CA-25) was a heavy cruiser commissioned in 1929, and saw much action in World War II before being used in atomic bomb tests in 1946.
 * The second USS Salt Lake City (SSN-716) was a Los Angeles-class submarine attack submarine, decommissioned in November 2006 at Portsmouth Naval Shipyard.

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

title: USS Salt Lake City


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896

Year 896 (DCCCXCVI) was a leap year starting on Thursday (link will display the full calendar) of the Julian calendar.

Europe

 * February – King Arnulf of Carinthia invades Italy at the head of an East Frankish expeditionary army. He storms Rome (the Leonine City), and has himself crowned Holy Roman Emperor by Pope Formosus at St. Peter's. Arnulf sets out to establish his authority in Spoleto, but suffers a stroke; he is forced to call off the campaign, and returns to Bavaria.
 * March – King Lambert II proceeds to re-conquer Italy. Heading north, he captures western Lombardy, and decapitates count Maginulf of Milan. In the meantime, the deposed king Berengar I recovers Verona (March of Friuli) from Arnulf's candidate, count Walfred of Verona, who dies in office with "great fidelity to the emperor".
 * Battle of Southern Buh: Bulgarian forces under Simeon I ('the Great') defeat the Magyars, near the banks of the Southern Buh river (modern Ukraine). The Magyars withdraw from Bulgaria, and are forced to migrate to new pastures. Led by Árpád, they settle in the Carpathian Basin (modern Hungary).
 * Summer – Battle of Boulgarophygon: Simeon I invades the Theme of Thrace (in the southeastern Balkans). The Byzantines transfer a new army to Europe, to deal with the Bulgarian threat. The armies clash at Boulgarophygon (modern Turkey); the Byzantines are completely destroyed in battle.
 * November – Lambert II and Berengar I agree to sign a treaty at Pavia. Berengar receives the realm between the Adda and the Po, while the rest stays under the control of Lambert (including the March of Tuscany). They share Bergamo, and Lambert pledges to marry Gisela, Berengar's daughter.
 * Prince Klonimir, pretender to the throne of the Serbian Principality, is defeated by his ruling cousin, Petar. He is recognized as sole ruler of Serbia by Simeon I, resulting in a 20-year peace and alliance (approximate date).

Britain

 * Summer – King Alfred the Great orders the building of English warships (almost twice as long as the longships) on the Itchen at Southampton, against the Danish Viking raiders in Wessex.
 * A Viking pirate army under Hastein (a son of Ragnar Lodbrok) ravages the Welsh kingdoms of Brycheiniog and Gwent (approximate date).

Arabian Empire

 * Kharijite Rebellion: The Kharijite uprising against the Abbasid Caliphate in Jazira is ended. Caliph Al-Mu'tadid reunifies the entire province under central government, and installs his son and heir, Al-Muktafi, as governor.

China

 * Emperor Zhao Zong appoints Li Keyong, a Shatuo military governor (jiedushi), as Prince of Jin. He becomes the first ruler of Jin (see 907) following the collapse of the Tang dynasty.

Religion

 * April 4 – Pope Formosus dies at Rome, after a four-year reign. He is succeeded by Boniface VI, as the 112th pope of the Catholic Church.
 * April – Boniface VI dies (probably murdered), after a pontificate of 15 days. He is succeeded by Stephen VI, as the 113th pope of Rome.

Births

 * Al-Masudi, Muslim historian and geographer (approximate date)
 * Liu Hua, Chinese princess and wife of Wang Yanjun (d. 930)

Deaths

 * January 18 – Khumarawayh ibn Ahmad ibn Tulun, ruler of the Tulunid Dynasty (b. 864)
 * April 4 – Formosus, pope of the Catholic Church
 * April – Boniface VI, pope of the Catholic Church
 * May 17 – Liu Jianfeng, Chinese warlord
 * June 1 – Theodosius Romanus, Syriac Orthodox patriarch of Antioch
 * July 3 – Dong Chang, Chinese warlord
 * Abu 'l-Asakir Jaysh ibn Khumarawayh, Muslim emir
 * Abu Hanifa Dinawari, Muslim botanist and geographer (b. 815)
 * Adarnase III, Georgian prince
 * Anselm II, archbishop of Milan
 * Berengar II, Frankish nobleman
 * Cui Zhaowei, chancellor of the Tang Dynasty
 * Flann mac Lonáin, Irish poet
 * Gerolf of Holland, count of Friesland (or 895)
 * Ibn al-Rumi, Muslim poet (b. 836)
 * Klonimir, Serbian prince (approximate date)
 * Miro the Elder, count of Conflent (Spain)
 * Rafi ibn Harthama, ruler of Greater Khorasan
 * Rustam I, ruler of the Bavand Dynasty (Iran)
 * Sahl al-Tustari, Persian scholar (approximate date)
 * Sitriuc mac Ímair, king of Dublin
 * Walfred of Friuli, Lombard nobleman

title: 896


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Gross world product

The gross world product (GWP), also known as gross world income (GWI), is the combined gross national income (previously, the "gross national product") of all the countries in the world. Because imports and exports balance exactly when considering the whole world, this also equals the total global gross domestic product (GDP). According to the World Bank, the 2013 nominal GWP was approximately 75.59 trillion United States dollars. In 2017, according to the CIA's World Factbook, the GWP was around $80.27 trillion in nominal terms and totaled approximately 127.8 trillion international dollars in terms of purchasing power parity (PPP). The per capita PPP GWP in 2017 was approximately 17,500 international dollars according to the World Factbook. According to the World Bank, the 2020 GWP in current dollars was approximately $84.705 trillion.

Recent growth
The table below gives recent percentage values for overall GWP growth from 2006 through 2020, as well as an estimate for 2021, according to the International Monetary Fund (IMF)'s World Economic Outlook database. Data is given in terms of constant year-on-year prices.

Historical and prehistorical estimates
In 1998, economic historian J. Bradford DeLong estimated the total GWP in 1990 U.S. dollars for the main years between one million years BCE and 2000 CE (shown in the table below).

Estimates from 2000 onwards are based on world GDP, PPP estimates in 2021 constant international dollars from the World Bank and subsequently converted to 1990 US$. "Billion" in the table below refers to the short scale usage of the term, where 1 billion = 1,000 million = 109.

title: Gross world product


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904

Year 904 (CMIV) was a leap year starting on Sunday (link will display the full calendar) of the Julian calendar.

Byzantine Empire

 * July 29 – Sack of Thessalonica: A Muslim fleet, led by the Greek renegade Leo of Tripoli, appears outside Thessalonica and begins its attack after a short and silent inspection of the fortification of the city. After attacks from the sea for two days, the Saracens are able to storm the city walls, overcome the Thessalonians' resistance and capture the city. The sacking continues for a full week, before the raiders depart for their base in the Levant. Having freed 4,000 Muslim prisoners and captured 60 ships, gaining a large loot, they carry off 22,000 men and women as slaves.
 * Arab–Byzantine War: The Byzantines under Andronikos Doukas, along with Eustathios Argyros, campaign against the Abbasids and defeat the Muslim garrisons of Mopsuestia and Tarsus, near Marash (modern Turkey).
 * Emperor Leo VI (the Wise) is forced to sign a peace treaty with Simeon I, ruler (knyaz) of the Bulgarian Empire. All Slavic-inhabited lands of Macedonia and southern Albania are ceded to the Bulgarians.

Europe

 * Summer – King Louis IV (the Child) invites Kurszán, a Hungarian leader (gyula) of the Magyar tribal confederation, and his entourage to negotiate at the Fischa River, but they are killed in an ambush.
 * In Portugal, for the third time in less than 30 years, the Christians take control of Coimbra, this time for almost a century.
 * Beginning of the Saeculum obscurum ('Dark Age'), a period of 60 years in which the papacy was heavily influenced by the powerful Theophylacti family, the counts of Tusculum.

Britain

 * Prince Hywel ap Cadell of Seisyllwg (Wales) marries Princess Elen of Dyfed. The latter's father, King Llywarch ap Hyfaidd, dies. The throne of Dyfed is claimed by Llywarch's brother, Rhodri ap Hyfaidd, but he is probably forced to flee from Hywel's armies.

Arabian Empire

 * Winter – Shayban ibn Ahmad ibn Tulun succeeds his nephew Harun ibn Khumarawayh as emir of the Tulunid dynasty, who is killed in a mutiny during the invasion of Egypt by the Abbasid Caliphate.

China

 * September 22 – The warlord Zhu Quanzhong kills Emperor Zhao Zong, along with his family and many ministers, after seizing control of the imperial government. Zhu places Zhao Zong's 13-year-old son Ai (Li Zhou) on the imperial throne as a puppet ruler of the Tang dynasty.
 * Zhu Quanzhong has Chang'an, the capital of the Tang dynasty and the largest city in the ancient world, destroyed, and moves the materials to Luoyang, which becomes the new capital.

Religion

 * January 29 – Pope Sergius III succeeds Leo V and the deposed Antipope Christopher (both of whom are murdered or exiled) as the 119th pope of the Catholic Church. The ascension of Sergius marks the beginning of the Pornocracy ('rule of the whores'), which will last for 150 years. During this time, the clergy will be sidelined and rule over Rome is dominated by the Roman nobility.
 * Sergius III allies himself with Theophylact I, count of Tusculum, who becomes ruler of Rome and the papal administration. Sergius rewards him (for his support and rise of power) with the position of sacri palatii vestararius and essentially becomes his puppet.

Births

 * September 10 – Guo Wei, emperor of Later Zhou (d. 954)
 * Æthelwold, bishop of Winchester (or 909)
 * Egill Skallagrímsson, Viking warrior and poet (approximate date)
 * Yongming Yanshou, Chinese Zen master (d. 975)

Deaths

 * September 22 – Zhao Zong, emperor of the Tang dynasty (b. 867)
 * Abu'l-Abbas Ahmad ibn al-Furat, Abbasid official
 * Al-Husayn ibn Zikrawayh, Qarmatian leader
 * Al-Qasim ibn Ubayd Allah, Abbasid vizier
 * Christopher, antipope of the Catholic Church
 * Cui Yin, chancellor of the Tang dynasty (b. 854)
 * Du Xunhe, Chinese poet (b. 846)
 * Erenfried I, Frankish nobleman
 * Harun ibn Khumarawayh, Tulunid emir
 * Ímar ua Ímair, Norse king of Dublin
 * John the Old Saxon, abbot of Athelney
 * Ki no Tomonori, Japanese poet (approximate date)
 * Kurszán, ruler (gyula) of the Magyars
 * Lady Zhang, wife of Zhu Quanzhong
 * Leo V, pope of the Catholic Church
 * Li Shenfu, general of the Tang dynasty
 * Llywarch ap Hyfaidd, king of Dyfed (Wales)
 * Tannet of Pagan, king of Burma (b. 859)
 * Wigmund, bishop of Dorchester (approximate date)
 * Zhang Jun, chancellor of the Tang dynasty

title: 904


text:
Multivariate random variable

In probability, and statistics, a multivariate random variable or random vector is a list or vector of mathematical variables each of whose value is unknown, either because the value has not yet occurred or because there is imperfect knowledge of its value. The individual variables in a random vector are grouped together because they are all part of a single mathematical system — often they represent different properties of an individual statistical unit. For example, while a given person has a specific age, height and weight, the representation of these features of an unspecified person from within a group would be a random vector. Normally each element of a random vector is a real number.

Random vectors are often used as the underlying implementation of various types of aggregate random variables, e.g. a random matrix, random tree, random sequence, stochastic process, etc.

More formally, a multivariate random variable is a column vector $$ \mathbf{X} = (X_1,\dots,X_n)^\mathsf{T} $$ (or its transpose, which is a row vector) whose components are scalar-valued random variables on the same probability space as each other, $$(\Omega, \mathcal{F}, P)$$, where $$\Omega$$ is the sample space, $$\mathcal{F}$$ is the sigma-algebra (the collection of all events), and $$P$$ is the probability measure (a function returning each event's probability).

Probability distribution
Every random vector gives rise to a probability measure on $$\mathbb{R}^n$$ with the Borel algebra as the underlying sigma-algebra. This measure is also known as the joint probability distribution, the joint distribution, or the multivariate distribution of the random vector.

The distributions of each of the component random variables $$X_i$$ are called marginal distributions. The conditional probability distribution of $$X_i$$ given $$X_j$$ is the probability distribution of $$X_i$$ when $$X_j$$ is known to be a particular value.

The cumulative distribution function $$F_{\mathbf{X}} : \R^n \mapsto [0,1]$$ of a random vector $$\mathbf{X}=(X_1,\dots,X_n)^\mathsf{T} $$ is defined as

where $$\mathbf{x} = (x_1, \dots, x_n)^\mathsf{T}$$.

Operations on random vectors
Random vectors can be subjected to the same kinds of algebraic operations as can non-random vectors: addition, subtraction, multiplication by a scalar, and the taking of inner products.

Affine transformations
Similarly, a new random vector $$\mathbf{Y}$$ can be defined by applying an affine transformation $$g\colon \mathbb{R}^n \to \mathbb{R}^n$$ to a random vector $$\mathbf{X}$$:

 * $$\mathbf{Y}=\mathbf{A}\mathbf{X}+b$$, where $$\mathbf{A}$$ is an $$n \times n$$ matrix and $$b$$ is an $$n \times  1$$ column vector.

If $$\mathbf{A}$$ is an invertible matrix and $$\textstyle\mathbf{X}$$ has a probability density function $$f_{\mathbf{X}}$$, then the probability density of $$\mathbf{Y}$$ is

 * $$f_{\mathbf{Y}}(y)=\frac{f_{\mathbf{X}}(\mathbf{A}^{-1}(y-b))}{|\det\mathbf{A}|}$$.

Invertible mappings
More generally we can study invertible mappings of random vectors.

Let $$g$$ be a one-to-one mapping from an open subset $$\mathcal{D}$$ of $$\mathbb{R}^n$$ onto a subset $$\mathcal{R}$$ of $$\mathbb{R}^n$$, let $$g$$ have continuous partial derivatives in $$\mathcal{D}$$ and let the Jacobian determinant of $$g$$ be zero at no point of $$\mathcal{D}$$. Assume that the real random vector $$\mathbf{X}$$ has a probability density function $$f_{\mathbf{X}}(\mathbf{x})$$ and satisfies $$ P(\mathbf{X} \in \mathcal{D}) = 1$$. Then the random vector $$\mathbf{Y}=g(\mathbf{X})$$ is of probability density

 * $$\left. f_{\mathbf{Y}}(\mathbf{y})=\frac{f_{\mathbf{X}}(\mathbf{x})}{\left |\det\frac{\partial \mathbf{x}}{\partial \mathbf{y}}\right |} \right |_{\mathbf{x}=g^{-1}(\mathbf{y})} \mathbf{1}(\mathbf{y} \in R_\mathbf{Y})$$

where $$\mathbf{1}$$ denotes the indicator function and set $$R_\mathbf{Y} = \{ \mathbf{y} = g(\mathbf{x}): f_{\mathbf{X}}(\mathbf{x}) > 0 \} \subseteq \mathcal{R} $$ denotes support of $$\mathbf{Y}$$.

Expected value
The expected value or mean of a random vector $$\mathbf{X}$$ is a fixed vector $$\operatorname{E}[\mathbf{X}]$$ whose elements are the expected values of the respective random variables.

Definitions
The covariance matrix (also called second central moment or variance-covariance matrix) of an $$n \times 1$$ random vector is an $$n \times n$$ matrix whose (i,j)th element is the covariance between the ith and the jth random variables. The covariance matrix is the expected value, element by element, of the $$n \times n$$ matrix computed as $$[\mathbf{X}-\operatorname{E}[\mathbf{X}]] [\mathbf{X}-\operatorname{E}[\mathbf{X}]]^T$$, where the superscript T refers to the transpose of the indicated vector:

By extension, the cross-covariance matrix between two random vectors $$\mathbf{X}$$ and $$\mathbf{Y}$$ ($$\mathbf{X}$$ having $$n$$ elements and $$\mathbf{Y}$$ having $$p$$ elements) is the $$n \times p$$ matrix

where again the matrix expectation is taken element-by-element in the matrix. Here the (i,j)th element is the covariance between the ith element of $$\mathbf{X}$$ and the jth element of $$\mathbf{Y}$$.

Properties
The covariance matrix is a symmetric matrix, i.e.
 * $$\operatorname{K}_{\mathbf{X}\mathbf{X}}^T = \operatorname{K}_{\mathbf{X}\mathbf{X}}$$.

The covariance matrix is a positive semidefinite matrix, i.e.
 * $$\mathbf{a}^T \operatorname{K}_{\mathbf{X}\mathbf{X}} \mathbf{a} \ge 0 \quad \text{for all } \mathbf{a} \in \mathbb{R}^n$$.

The cross-covariance matrix $$\operatorname{Cov}[\mathbf{Y},\mathbf{X}]$$ is simply the transpose of the matrix $$\operatorname{Cov}[\mathbf{X},\mathbf{Y}]$$, i.e.
 * $$\operatorname{K}_{\mathbf{Y}\mathbf{X}} = \operatorname{K}_{\mathbf{X}\mathbf{Y}}^T$$.

Uncorrelatedness
Two random vectors $$\mathbf{X}=(X_1,...,X_m)^T $$ and $$\mathbf{Y}=(Y_1,...,Y_n)^T $$ are called uncorrelated if
 * $$\operatorname{E}[\mathbf{X} \mathbf{Y}^T] = \operatorname{E}[\mathbf{X}]\operatorname{E}[\mathbf{Y}]^T$$.

They are uncorrelated if and only if their cross-covariance matrix $$\operatorname{K}_{\mathbf{X}\mathbf{Y}}$$ is zero.

Definitions
The correlation matrix (also called second moment) of an $$n \times 1$$ random vector is an $$n \times n$$ matrix whose (i,j)th element is the correlation between the ith and the jth random variables. The correlation matrix is the expected value, element by element, of the $$n \times n$$ matrix computed as $$\mathbf{X} \mathbf{X}^T$$, where the superscript T refers to the transpose of the indicated vector:

By extension, the cross-correlation matrix between two random vectors $$\mathbf{X}$$ and $$\mathbf{Y}$$ ($$\mathbf{X}$$ having $$n$$ elements and $$\mathbf{Y}$$ having $$p$$ elements) is the $$n \times p$$ matrix

Properties
The correlation matrix is related to the covariance matrix by
 * $$\operatorname{R}_{\mathbf{X}\mathbf{X}} = \operatorname{K}_{\mathbf{X}\mathbf{X}} + \operatorname{E}[\mathbf{X}]\operatorname{E}[\mathbf{X}]^T$$.

Similarly for the cross-correlation matrix and the cross-covariance matrix:
 * $$\operatorname{R}_{\mathbf{X}\mathbf{Y}} = \operatorname{K}_{\mathbf{X}\mathbf{Y}} + \operatorname{E}[\mathbf{X}]\operatorname{E}[\mathbf{Y}]^T$$

Orthogonality
Two random vectors of the same size $$\mathbf{X}=(X_1,...,X_n)^T $$ and $$\mathbf{Y}=(Y_1,...,Y_n)^T $$ are called orthogonal if
 * $$\operatorname{E}[\mathbf{X}^T \mathbf{Y}] = 0$$.

Independence
Two random vectors $$\mathbf{X}$$ and $$\mathbf{Y}$$ are called independent if for all $$\mathbf{x}$$ and $$\mathbf{y}$$
 * $$F_{\mathbf{X,Y}}(\mathbf{x,y}) = F_{\mathbf{X}}(\mathbf{x}) \cdot F_{\mathbf{Y}}(\mathbf{y})$$

where $$F_{\mathbf{X}}(\mathbf{x})$$ and $$F_{\mathbf{Y}}(\mathbf{y})$$ denote the cumulative distribution functions of $$\mathbf{X}$$ and $$\mathbf{Y}$$ and$$F_{\mathbf{X,Y}}(\mathbf{x,y})$$ denotes their joint cumulative distribution function. Independence of $$\mathbf{X}$$ and $$\mathbf{Y}$$ is often denoted by $$\mathbf{X} \perp\!\!\!\perp \mathbf{Y}$$. Written component-wise, $$\mathbf{X}$$ and $$\mathbf{Y}$$ are called independent if for all $$x_1,\ldots,x_m,y_1,\ldots,y_n$$
 * $$F_{X_1,\ldots,X_m,Y_1,\ldots,Y_n}(x_1,\ldots,x_m,y_1,\ldots,y_n) = F_{X_1,\ldots,X_m}(x_1,\ldots,x_m) \cdot F_{Y_1,\ldots,Y_n}(y_1,\ldots,y_n)$$.

Characteristic function
The characteristic function of a random vector $$ \mathbf{X} $$ with $$ n $$ components is a function $$\mathbb{R}^n \to \mathbb{C}$$ that maps every vector $$\mathbf{\omega} = (\omega_1,\ldots,\omega_n)^T$$ to a complex number. It is defined by

 * $$ \varphi_{\mathbf{X}}(\mathbf{\omega}) = \operatorname{E} \left [ e^{i(\mathbf{\omega}^T \mathbf{X})} \right ] = \operatorname{E} \left [ e^{i( \omega_1 X_1 + \ldots + \omega_n X_n)} \right ]$$.

Expectation of a quadratic form
One can take the expectation of a quadratic form in the random vector $$\mathbf{X}$$ as follows:

 * $$\operatorname{E}[\mathbf{X}^{T}A\mathbf{X}] = \operatorname{E}[\mathbf{X}]^{T}A\operatorname{E}[\mathbf{X}] + \operatorname{tr}(A K_{\mathbf{X}\mathbf{X}}),$$

where $$K_{\mathbf{X}\mathbf{X}}$$ is the covariance matrix of $$\mathbf{X}$$ and $$\operatorname{tr}$$ refers to the trace of a matrix — that is, to the sum of the elements on its main diagonal (from upper left to lower right). Since the quadratic form is a scalar, so is its expectation.

Proof: Let $$\mathbf{z}$$ be an $$m \times 1$$ random vector with $$\operatorname{E}[\mathbf{z}] = \mu$$ and $$\operatorname{Cov}[\mathbf{z}]= V$$ and let $$A$$ be an $$m \times m$$ non-stochastic matrix.

Then based on the formula for the covariance, if we denote $$\mathbf{z}^T = \mathbf{X}$$ and $$\mathbf{z}^T A^T = \mathbf{Y}$$, we see that:

 * $$\operatorname{Cov}[\mathbf{X},\mathbf{Y}] = \operatorname{E}[\mathbf{X}\mathbf{Y}^T]-\operatorname{E}[\mathbf{X}]\operatorname{E}[\mathbf{Y}]^T $$

Hence

 * $$\begin{align}

\operatorname{E}[XY^T]  &= \operatorname{Cov}[X,Y]+\operatorname{E}[X]\operatorname{E}[Y]^T \\ \operatorname{E}[z^T Az] &= \operatorname{Cov}[z^T,z^T A^T] + \operatorname{E}[z^T]\operatorname{E}[z^T A^T ]^T \\ &=\operatorname{Cov}[z^T, z^T A^T] + \mu^T (\mu^T A^T)^T \\ &=\operatorname{Cov}[z^T, z^T A^T] + \mu^T A \mu , \end{align}$$

which leaves us to show that

 * $$\operatorname{Cov}[z^T, z^T A^T ]=\operatorname{tr}(AV).$$

This is true based on the fact that one can cyclically permute matrices when taking a trace without changing the end result (e.g.: $$\operatorname{tr}(AB) = \operatorname{tr}(BA)$$).

We see that

 * $$\begin{align}

\operatorname{Cov}[z^T,z^T A^T] &= \operatorname{E} \left[\left(z^T - E(z^T) \right)\left(z^T A^T - E\left(z^T A^T \right) \right)^T \right] \\ &= \operatorname{E} \left[ (z^T - \mu^T) (z^T A^T - \mu^T A^T )^T \right]\\ &= \operatorname{E} \left[ (z - \mu)^T (Az - A\mu) \right]. \end{align}$$

And since

 * $$\left( {z - \mu } \right)^T \left( {Az - A\mu } \right)$$

is a scalar, then

 * $$(z - \mu)^T ( Az - A\mu)= \operatorname{tr}\left( {(z - \mu )^T (Az - A\mu )} \right) = \operatorname{tr} \left((z - \mu )^T A(z - \mu ) \right)$$

trivially. Using the permutation we get:

 * $$\operatorname{tr}\left( {(z - \mu )^T A(z - \mu )} \right) = \operatorname{tr}\left( {A(z - \mu )(z - \mu )^T} \right),$$

and by plugging this into the original formula we get:

 * $$\begin{align}

\operatorname{Cov} \left[ {z^T,z^T A^T} \right] &= E\left[ {\left( {z - \mu } \right)^T (Az - A\mu)} \right] \\ &= E \left[ \operatorname{tr}\left( A(z - \mu )(z - \mu )^T \right) \right] \\ &= \operatorname{tr} \left( {A \cdot \operatorname{E} \left((z - \mu )(z - \mu )^T \right) } \right) \\ &= \operatorname{tr} (A V). \end{align}$$

Expectation of the product of two different quadratic forms
One can take the expectation of the product of two different quadratic forms in a zero-mean Gaussian random vector $$\mathbf{X}$$ as follows:

 * $$\operatorname{E}\left[(\mathbf{X}^{T}A\mathbf{X})(\mathbf{X}^{T}B\mathbf{X})\right] = 2\operatorname{tr}(A K_{\mathbf{X}\mathbf{X}} B K_{\mathbf{X}\mathbf{X}}) + \operatorname{tr}(A K_{\mathbf{X}\mathbf{X}})\operatorname{tr}(B K_{\mathbf{X}\mathbf{X}})$$

where again $$K_{\mathbf{X}\mathbf{X}}$$ is the covariance matrix of $$\mathbf{X}$$. Again, since both quadratic forms are scalars and hence their product is a scalar, the expectation of their product is also a scalar.

Portfolio theory
In portfolio theory in finance, an objective often is to choose a portfolio of risky assets such that the distribution of the random portfolio return has desirable properties. For example, one might want to choose the portfolio return having the lowest variance for a given expected value. Here the random vector is the vector $$\mathbf{r}$$ of random returns on the individual assets, and the portfolio return p (a random scalar) is the inner product of the vector of random returns with a vector w of portfolio weights — the fractions of the portfolio placed in the respective assets. Since p = wT$$\mathbf{r}$$, the expected value of the portfolio return is wTE($$\mathbf{r}$$) and the variance of the portfolio return can be shown to be wTCw, where C is the covariance matrix of $$\mathbf{r}$$.

Regression theory
In linear regression theory, we have data on n observations on a dependent variable y and n observations on each of k independent variables xj. The observations on the dependent variable are stacked into a column vector y; the observations on each independent variable are also stacked into column vectors, and these latter column vectors are combined into a design matrix X (not denoting a random vector in this context) of observations on the independent variables. Then the following regression equation is postulated as a description of the process that generated the data:

 * $$y = X \beta + e,$$

where β is a postulated fixed but unknown vector of k response coefficients, and e is an unknown random vector reflecting random influences on the dependent variable. By some chosen technique such as ordinary least squares, a vector $$\hat \beta$$ is chosen as an estimate of β, and the estimate of the vector e, denoted $$\hat e$$, is computed as

 * $$\hat e = y - X \hat \beta.$$

Then the statistician must analyze the properties of $$\hat \beta$$ and $$\hat e$$, which are viewed as random vectors since a randomly different selection of n cases to observe would have resulted in different values for them.

Vector time series
The evolution of a k×1 random vector $$\mathbf{X}$$ through time can be modelled as a vector autoregression (VAR) as follows:

 * $$\mathbf{X}_t = c + A_1 \mathbf{X}_{t-1} + A_2 \mathbf{X}_{t-2} + \cdots + A_p \mathbf{X}_{t-p} + \mathbf{e}_t, \, $$

where the i-periods-back vector observation $$\mathbf{X}_{t-i}$$ is called the i-th lag of $$\mathbf{X}$$, c is a k × 1 vector of constants (intercepts), Ai is a time-invariant k × k matrix and $$\mathbf{e}_t$$ is a k × 1 random vector of error terms.

title: Multivariate random variable


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Creole language

A creole language,  or simply creole, is a stable natural language that develops from the process of different languages simplifying and mixing into a new form (often a pidgin), and then that form expanding and elaborating into a full-fledged language with native speakers, all within a fairly brief period. While the concept is similar to that of a mixed or hybrid language, creoles are often characterized by a tendency to systematize their inherited grammar (e.g., by eliminating irregularities or regularizing the conjugation of otherwise irregular verbs). Like any language, creoles are characterized by a consistent system of grammar, possess large stable vocabularies, and are acquired by children as their native language. These three features distinguish a creole language from a pidgin. Creolistics, or creology, is the study of creole languages and, as such, is a subfield of linguistics. Someone who engages in this study is called a creolist.

The precise number of creole languages is not known, particularly as many are poorly attested or documented. About one hundred creole languages have arisen since 1500. These are predominantly based on European languages such as English and French due to the European Age of Discovery and the Atlantic slave trade that arose at that time. With the improvements in ship-building and navigation, traders had to learn to communicate with people around the world, and the quickest way to do this was to develop a pidgin; in turn, full creole languages developed from these pidgins. In addition to creoles that have European languages as their base, there are, for example, creoles based on Arabic, Chinese, and Malay. The Middle English creole hypothesis posits that English is descended from a creole, of some combination of Old English, Norman French, Old Norse, and Common Brittonic.

The lexicon of a creole language is largely supplied by the parent languages, particularly that of the most dominant group in the social context of the creole's construction. However, there are often clear phonetic and semantic shifts. On the other hand, the grammar that has evolved often has new or unique features that differ substantially from those of the parent languages.

Overview
A creole is believed to arise when a pidgin, developed by adults for use as a second language, becomes the native and primary language of their children – a process known as nativization. The pidgin-creole life cycle was studied by American linguist Robert Hall in the 1960s.

Some linguists, such as Derek Bickerton, posit that creoles share more grammatical similarities with each other than with the languages from which they are phylogenetically derived. However, there is no widely accepted theory that would account for those perceived similarities. Moreover, no grammatical feature has been shown to be specific to creoles.

Many of the creoles known today arose in the last 500 years, as a result of the worldwide expansion of European maritime power and trade in the Age of Discovery, which led to extensive European colonial empires. Like most non-official and minority languages, creoles have generally been regarded in popular opinion as degenerate variants or dialects of their parent languages. Because of that prejudice, many of the creoles that arose in the European colonies, having been stigmatized, have become extinct. However, political and academic changes in recent decades have improved the status of creoles, both as living languages and as object of linguistic study. Some creoles have even been granted the status of official or semi-official languages of particular political territories.

Linguists now recognize that creole formation is a universal phenomenon, not limited to the European colonial period, and an important aspect of language evolution.

Other scholars, such as Salikoko Mufwene, argue that pidgins and creoles arise independently under different circumstances, and that a pidgin need not always precede a creole nor a creole evolve from a pidgin. Pidgins, according to Mufwene, emerged in trade colonies among "users who preserved their native vernaculars for their day-to-day interactions". Creoles, meanwhile, developed in settlement colonies in which speakers of a European language, often indentured servants whose language would be far from the standard in the first place, interacted extensively with non-European slaves, absorbing certain words and features from the slaves' non-European native languages, resulting in a heavily basilectalized version of the original language. These servants and slaves would come to use the creole as an everyday vernacular, rather than merely in situations in which contact with a speaker of the superstrate was necessary.

Etymology
The English term creole comes from French créole, which is cognate with the Spanish term criollo and Portuguese crioulo, all descending from the verb criar ('to breed' or 'to raise'), all coming from Latin creare to produce, create. The specific sense of the term was coined in the 16th and 17th century, during the great expansion in European maritime power and trade that led to the establishment of European colonies in other continents.

The terms criollo and crioulo were originally qualifiers used throughout the Spanish and Portuguese colonies to distinguish the members of an ethnic group who were born and raised locally from those who immigrated as adults. They were most commonly applied to nationals of the colonial power, e.g. to distinguish españoles criollos (people born in the colonies from Spanish ancestors) from españoles peninsulares (those born in the Iberian Peninsula, i.e. Spain). However, in Brazil the term was also used to distinguish between negros crioulos (blacks born in Brazil from African slave ancestors) and negros africanos (born in Africa). Over time, the term and its derivatives (Creole, Kréol, Kreyol, Kreyòl, Kriol, Krio, etc.) lost the generic meaning and became the proper name of many distinct ethnic groups that developed locally from immigrant communities. Originally, therefore, the term "creole language" meant the speech of any of those creole peoples.

Geographic distribution
As a consequence of colonial European trade patterns, most of the known European-based creole languages arose in coastal areas in the equatorial belt around the world, including the Americas, western Africa, Goa along the west of India, and along Southeast Asia up to Indonesia, Singapore, Macau, Hong Kong, the Philippines, Malaysia, Mauritius, Réunion, Seychelles and Oceania.

Many of those creoles are now extinct, but others still survive in the Caribbean, the north and east coasts of South America (The Guyanas), western Africa, Australia (see Australian Kriol language), the Philippines (see Chavacano), Island Countries such as Mauritius and Seychelles and in the Indian Ocean.

Atlantic Creole languages are based on European languages with elements from African and possibly Amerindian languages. Indian Ocean Creole languages are based on European languages with elements from Malagasy and possibly other Asian languages. There are, however, creoles like Nubi and Sango that are derived solely from non-European languages.

Social and political status
Because of the generally low status of the Creole peoples in the eyes of prior European colonial powers, creole languages have generally been regarded as "degenerate" languages, or at best as rudimentary "dialects" of the politically dominant parent languages. Because of this, the word "creole" was generally used by linguists in opposition to "language", rather than as a qualifier for it.

Another factor that may have contributed to the relative neglect of creole languages in linguistics is that they do not fit the 19th-century neogrammarian "tree model" for the evolution of languages, and its postulated regularity of sound changes (these critics including the earliest advocates of the wave model, Johannes Schmidt and Hugo Schuchardt, the forerunners of modern sociolinguistics). This controversy of the late 19th century profoundly shaped modern approaches to the comparative method in historical linguistics and in creolistics.

Because of social, political, and academic changes brought on by decolonization in the second half of the 20th century, creole languages have experienced revivals in the past few decades. They are increasingly being used in print and film, and in many cases, their community prestige has improved dramatically. In fact, some have been standardized, and are used in local schools and universities around the world. At the same time, linguists have begun to come to the realization that creole languages are in no way inferior to other languages. They now use the term "creole" or "creole language" for any language suspected to have undergone creolization, terms that now imply no geographic restrictions nor ethnic prejudices.

There is controversy about the extent to which creolization influenced the evolution of African-American Vernacular English (AAVE). In the American education system, as well as in the past, the use of the word ebonics to refer to AAVE mirrors the historical negative connotation of the word creole.

Historic classification
According to their external history, four types of creoles have been distinguished: plantation creoles, fort creoles, maroon creoles, and creolized pidgins. By the very nature of a creole language, the phylogenetic classification of a particular creole usually is a matter of dispute; especially when the pidgin precursor and its parent tongues (which may have been other creoles or pidgins) have disappeared before they could be documented.

Phylogenetic classification traditionally relies on inheritance of the lexicon, especially of "core" terms, and of the grammar structure. However, in creoles, the core lexicon often has mixed origin, and the grammar is largely original. For these reasons, the issue of which language is the parent of a creole – that is, whether a language should be classified as a "French creole", "Portuguese creole" or "English creole", etc. – often has no definitive answer, and can become the topic of long-lasting controversies, where social prejudices and political considerations may interfere with scientific discussion.

Substrate and superstrate
The terms substrate and superstrate are often used when two languages interact. However, the meaning of these terms is reasonably well-defined only in second language acquisition or language replacement events, when the native speakers of a certain source language (the substrate) are somehow compelled to abandon it for another target language (the superstrate). The outcome of such an event is that erstwhile speakers of the substrate will use some version of the superstrate, at least in more formal contexts. The substrate may survive as a second language for informal conversation. As demonstrated by the fate of many replaced European languages (such as Etruscan, Breton, and Venetian), the influence of the substrate on the official speech is often limited to pronunciation and a modest number of loanwords. The substrate might even disappear altogether without leaving any trace.

However, there is dispute over the extent to which the terms "substrate" and "superstrate" are applicable to the genesis or the description of creole languages. The language replacement model may not be appropriate in creole formation contexts, where the emerging language is derived from multiple languages without any one of them being imposed as a replacement for any other. The substratum–superstratum distinction becomes awkward when multiple superstrata must be assumed (such as in Papiamento), when the substratum cannot be identified, or when the presence or the survival of substratal evidence is inferred from mere typological analogies. On the other hand, the distinction may be meaningful when the contributions of each parent language to the resulting creole can be shown to be very unequal, in a scientifically meaningful way. In the literature on Atlantic Creoles, "superstrate" usually means European and "substrate" non-European or African.

Decreolization
Since creole languages rarely attain official status, the speakers of a fully formed creole may eventually feel compelled to conform their speech to one of the parent languages. This decreolization process typically brings about a post-creole speech continuum characterized by large-scale variation and hypercorrection in the language.

It is generally acknowledged that creoles have a simpler grammar and more internal variability than older, more established languages. However, these notions are occasionally challenged. (See also language complexity.)

Phylogenetic or typological comparisons of creole languages have led to divergent conclusions. Similarities are usually higher among creoles derived from related languages, such as the languages of Europe, than among broader groups that include also creoles based on non-Indo-European languages (like Nubi or Sango). French-based creole languages in turn are more similar to each other (and to varieties of French) than to other European-based creoles. It was observed, in particular, that definite articles are mostly prenominal in English-based creole languages and English whereas they are generally postnominal in French creoles and in the variety of French that was exported to what is now Quebec in the 17th and 18th century. Moreover, the European languages which gave rise to the creole languages of European colonies all belong to the same subgroup of Western Indo-European and have highly convergent grammars; to the point that Whorf joined them into a single Standard Average European language group. French and English are particularly close, since English, through extensive borrowing, is typologically closer to French than to other Germanic languages. Thus the claimed similarities between creoles may be mere consequences of similar parentage, rather than characteristic features of all creoles.

Creole genesis
There are a variety of theories on the origin of creole languages, all of which attempt to explain the similarities among them. outline a fourfold classification of explanations regarding creole genesis:
 * 1) Theories focusing on European input
 * 2) Theories focusing on non-European input
 * 3) Gradualist and developmental hypotheses
 * 4) Universalist approaches

In addition to the precise mechanism of creole genesis, a more general debate has developed whether creole languages are characterized by different mechanisms than traditional languages (which is McWhorter's 2018 main point) or whether in that regard creole languages develop by the same mechanisms as any other languages (e.g. DeGraff 2001).

Monogenetic theory of pidgins and creoles
The monogenetic theory of pidgins and creoles hypothesizes that all Atlantic creoles derived from a single Mediterranean Lingua Franca, via a West African Pidgin Portuguese of the seventeenth century, relexified in the so-called "slave factories" of Western Africa that were the source of the Atlantic slave trade. This theory was originally formulated by Hugo Schuchardt in the late nineteenth century and popularized in the late 1950s and early 1960s by Taylor, Whinnom, Thompson, and Stewart. However, this hypothesis is now not widely accepted, since it relies on all creole-speaking slave populations being based on the same Portuguese-based creole, despite no to very little historical exposure to Portuguese for many of these populations, no strong direct evidence for this claim, and with Portuguese leaving almost no trace on the lexicon of most of them, with the similarities in grammar explainable by analogous processes of loss of inflection and grammatical forms not common to European and West African languages. For example, points out that relexification postulates too many improbabilities and that it is unlikely that a language "could be disseminated round the entire tropical zone, to peoples of widely differing language background, and still preserve a virtually complete identity in its grammatical structure wherever it took root, despite considerable changes in its phonology and virtually complete changes in its lexicon".

Domestic origin hypothesis
Proposed by for the origin of English-based creoles of the West Indies, the Domestic Origin Hypothesis argues that, towards the end of the 16th century, English-speaking traders began to settle in the Gambia and Sierra Leone rivers as well as in neighboring areas such as the Bullom and Sherbro coasts. These settlers intermarried with the local population leading to mixed populations, and, as a result of this intermarriage, an English pidgin was created. This pidgin was learned by slaves in slave depots, who later on took it to the West Indies and formed one component of the emerging English creoles.

European dialect origin hypothesis
The French creoles are the foremost candidates to being the outcome of "normal" linguistic change and their creoleness to be sociohistoric in nature and relative to their colonial origin. Within this theoretical framework, a French creole is a language phylogenetically based on French, more specifically on a 17th-century koiné French extant in Paris, the French Atlantic harbours, and the nascent French colonies. Supporters of this hypothesis suggest that the non-Creole French dialects still spoken in many parts of the Americas share mutual descent from this single koiné. These dialects are found in Canada (mostly in Québec and in Acadian communities), Louisiana, Saint-Barthélemy and as isolates in other parts of the Americas. Approaches under this hypothesis are compatible with gradualism in change and models of imperfect language transmission in koiné genesis.

Foreigner talk and baby talk
The Foreigner Talk (FT) hypothesis argues that a pidgin or creole language forms when native speakers attempt to simplify their language in order to address speakers who do not know their language at all. Because of the similarities found in this type of speech and speech directed to a small child, it is also sometimes called baby talk.

suggest that four different processes are involved in creating Foreigner Talk:
 * Accommodation
 * Imitation
 * Telegraphic condensation
 * Conventions

This could explain why creole languages have much in common, while avoiding a monogenetic model. However,, in analyzing German Foreigner Talk, claims that it is too inconsistent and unpredictable to provide any model for language learning.

While the simplification of input was supposed to account for creoles' simple grammar, commentators have raised a number of criticisms of this explanation:
 * 1) There are a great many grammatical similarities amongst pidgins and creoles despite having very different lexifier languages.
 * 2) Grammatical simplification can be explained by other processes, i.e. the innate grammar of Bickerton's language bioprogram theory.
 * 3) Speakers of a creole's lexifier language often fail to understand, without learning the language, the grammar of a pidgin or creole.
 * 4) Pidgins are more often used amongst speakers of different substrate languages than between such speakers and those of the lexifier language.

Another problem with the FT explanation is its potential circularity. points out that FT is often based on the imitation of the incorrect speech of the non-natives, that is the pidgin. Therefore, one may be mistaken in assuming that the former gave rise to the latter.

Imperfect L2 learning
The imperfect L2 (second language) learning hypothesis claims that pidgins are primarily the result of the imperfect L2 learning of the dominant lexifier language by the slaves. Research on naturalistic L2 processes has revealed a number of features of "interlanguage systems" that are also seen in pidgins and creoles:
 * invariant verb forms derived from the infinitive or the least marked finite verb form;
 * loss of determiners or use of demonstrative pronouns, adjectives or adverbs as determiners;
 * placement of a negative particle in preverbal position;
 * use of adverbs to express modality;
 * fixed single word order with no inversion in questions;
 * reduced or absent nominal plural marking.

Imperfect L2 learning is compatible with other approaches, notably the European dialect origin hypothesis and the universalist models of language transmission.

Theories focusing on non-European input
Theories focusing on the substrate, or non-European, languages attribute similarities amongst creoles to the similarities of African substrate languages. These features are often assumed to be transferred from the substrate language to the creole or to be preserved invariant from the substrate language in the creole through a process of relexification: the substrate language replaces the native lexical items with lexical material from the superstrate language while retaining the native grammatical categories. The problem with this explanation is that the postulated substrate languages differ amongst themselves and with creoles in meaningful ways. argues that the number and diversity of African languages and the paucity of a historical record on creole genesis makes determining lexical correspondences a matter of chance. coined the term "cafeteria principle" to refer to the practice of arbitrarily attributing features of creoles to the influence of substrate African languages or assorted substandard dialects of European languages.

For a representative debate on this issue, see the contributions to ; for a more recent view,.

Because of the sociohistoric similarities amongst many (but by no means all) of the creoles, the Atlantic slave trade and the plantation system of the European colonies have been emphasized as factors by linguists such as.

Gradualist and developmental hypotheses
One class of creoles might start as pidgins, rudimentary second languages improvised for use between speakers of two or more non-intelligible native languages. Keith Whinnom (in ) suggests that pidgins need three languages to form, with one (the superstrate) being clearly dominant over the others. The lexicon of a pidgin is usually small and drawn from the vocabularies of its speakers, in varying proportions. Morphological details like word inflections, which usually take years to learn, are omitted; the syntax is kept very simple, usually based on strict word order. In this initial stage, all aspects of the speech – syntax, lexicon, and pronunciation – tend to be quite variable, especially with regard to the speaker's background.

If a pidgin manages to be learned by the children of a community as a native language, it may become fixed and acquire a more complex grammar, with fixed phonology, syntax, morphology, and syntactic embedding. Pidgins can become full languages in only a single generation. "Creolization" is this second stage where the pidgin language develops into a fully developed native language. The vocabulary, too, will develop to contain more and more items according to a rationale of lexical enrichment.

Universalist approaches
Universalist models stress the intervention of specific general processes during the transmission of language from generation to generation and from speaker to speaker. The process invoked varies: a general tendency towards semantic transparency, first-language learning driven by universal process, or a general process of discourse organization. Bickerton's language bioprogram theory, proposed in the 1980s, remains the main universalist theory. Bickerton claims that creoles are inventions of the children growing up on newly founded plantations. Around them, they only heard pidgins spoken, without enough structure to function as natural languages; and the children used their own innate linguistic capacities to transform the pidgin input into a full-fledged language. The alleged common features of all creoles would then stem from those innate abilities being universal.

Recent studies
The last decades have seen the emergence of some new questions about the nature of creoles: in particular, the question of how complex creoles are and the question of whether creoles are indeed "exceptional" languages.

Creole prototype
Some features that distinguish creole languages from noncreoles have been proposed (by Bickerton, for example).

John McWhorter has proposed the following list of features as defining the creole prototype, that is, any language born recently of a pidgin:
 * a lack of contextual inflection, that is, a lack of inflection that marks only agreement in case or gender (as opposed to inherent inflection that marks tense, mood or number);
 * a lack of functional tone marking, that is, a lack of tone that serves to distinguish lexical items (e.g. Mandarin Chinese mā mother vs. mǎ horse) or to encode grammatical features; and
 * a lack of semantically opaque word formation, that is, a lack of words like “understand” or “make up”, the meaning of which is not analyzable in terms of the meanings of their components.

McWhorter argues that the absence of these three features is predictable in languages that were born recently of a pidgin, since learning them would constitute a distinct challenge to the non-native speaker. Over the course of generations, however, such features would be expected to gradually (re-)appear, and therefore “many creoles would harbor departures from the Prototype identifiable as having happened after the creole was born” (McWhorter 2018). As one example, McWhorter (2013) notes that the creole Sranan, which has existed for centuries in a diglossic relationship with Dutch, has borrowed some Dutch verbs containing the ver- prefix (fer- in Sranan) and whose meaning is not analyzable; for instance the pair morsu to soil, fermorsu to squander.

McWhorter claims that these three properties characterize any language that was born recently as a pidgin, and states “At this writing, in twenty years I have encountered not a single counterexample“ (McWhorter 2018). Nevertheless, the existence of a creole prototype has been disputed by others:
 * Henri Wittmann (1999) and David argue that languages such as Manding, Soninke, Magoua French and Riau Indonesian have all these three features but show none of the sociohistoric traits of creole languages. McWhorter (2011, 2018) disagrees: for instance, he points out that Soninke has “a goodly amount” of inherent (i.e. non-contextual) inflection, that Magoua “retains ample marking of gender, person and number distinctions on verbs as well as conjugational classes” and therefore that these languages should not be considered creoles.
 * Others (see overview in ) have claimed the existence of creoles that serve as counterexamples to McWhorter's hypothesis – the existence of inflectional morphology in Berbice Dutch Creole, for example, or tone in Papiamentu. Again, McWhorter (2018) disagrees. For instance, he points out that the use of tone in Papiamentu to distinguish participial verb forms from base ones appeared only after extensive contact with native Spanish speakers.

Exceptionalism
Building up on this discussion, McWhorter proposed that "the world's simplest grammars are Creole grammars", claiming that every noncreole language's grammar is at least as complex as any creole language's grammar. Gil has replied that Riau Indonesian has a simpler grammar than Saramaccan, the language McWhorter uses as a showcase for his theory. The same objections were raised by Wittmann in his 1999 debate with McWhorter.

The lack of progress made in defining creoles in terms of their morphology and syntax has led scholars such as Robert Chaudenson, Salikoko Mufwene, Michel DeGraff, and Henri Wittmann to question the value of creole as a typological class; they argue that creoles are structurally no different from any other language, and that creole is a sociohistoric concept – not a linguistic one – encompassing displaced populations and slavery.

spell out the idea of creole exceptionalism, claiming that creole languages are an instance of nongenetic language change due to language shift with abnormal transmission. Gradualists question the abnormal transmission of languages in a creole setting and argue that the processes which created today's creole languages are no different from universal patterns of language change.

Given these objections to creole as a concept, DeGraff and others question the idea that creoles are exceptional in any meaningful way. Additionally, argues that some Romance languages are potential creoles but that they are not considered as such by linguists because of a historical bias against such a view.

Controversy
Creolistics investigates the relative creoleness of languages suspected to be creoles, what calls "the cline of creoleness." No consensus exists among creolists as to whether the nature of creoleness is prototypical or merely evidence indicative of a set of recognizable phenomena seen in association with little inherent unity and no underlying single cause.

"Creole", a sociohistoric concept
Creoleness is at the heart of the controversy with John McWhorter and Mikael Parkvall opposing Henri Wittmann (1999) and Michel DeGraff. In McWhorter's definition, creoleness is a matter of degree, in that prototypical creoles exhibit all of the three traits he proposes to diagnose creoleness: little or no inflection, little or no tone, and transparent derivation. In McWhorter's view, less prototypical creoles depart somewhat from this prototype. Along these lines, McWhorter defines Haitian Creole, exhibiting all three traits, as "the most creole of creoles." A creole like Palenquero, on the other hand, would be less prototypical, given the presence of inflection to mark plural, past, gerund, and participle forms. Objections to the McWhorter-Parkvall hypotheses point out that these typological parameters of creoleness can be found in languages such as Manding, Sooninke, and Magoua French which are not considered creoles. Wittmann and DeGraff come to the conclusion that efforts to conceive a yardstick for measuring creoleness in any scientifically meaningful way have failed so far. comes to the same conclusion for Riau Indonesian. have adduced evidence as to creole languages which respond unexpectedly to one of McWhorter's three features (for example, inflectional morphology in Berbice Creole Dutch, tone in Papiamentu). and have argued further that Creole languages are structurally no different from any other language, and that Creole is in fact a sociohistoric concept (and not a linguistic one), encompassing displaced population and slavery. discuss creolistics in relation to colonialist ideologies, rejecting the notion that Creoles can be responsibly defined in terms of specific grammatical characteristics. They discuss the history of linguistics and nineteenth-century work that argues for the consideration of the sociohistorical contexts in which Creole languages emerged.

"Creole", a genuine linguistic concept
On the other hand, McWhorter points out that in languages such as Bambara, essentially a dialect of Manding, there is ample non-transparent derivation, and that there is no reason to suppose that this would be absent in close relatives such as Mandinka itself. Moreover, he also observes that Soninke has what all linguists would analyze as inflections, and that current lexicography of Soninke is too elementary for it to be stated with authority that it does not have non-transparent derivation. Meanwhile, Magoua French, as described by Henri Wittmann, retains some indication of grammatical gender, which qualifies as inflection, and it also retains non-transparent derivation. Michel DeGraff's argument has been that Haitian Creole retains non-transparent derivation from French.

Additional resources
critically assesses the proposal that creole languages exist as a homogeneous structural type with shared and/ or peculiar origins.

groups creole genesis theories into four categories:

 * Theories focusing on the European input
 * Theories focusing on the non-European input
 * Gradualist and developmental hypotheses
 * Universalist approaches

The authors also confine Pidgins and mixed languages into separate chapters outside this scheme whether or not relexification come into the picture.

Creoles by parent language

 * Arabic-based creole languages
 * Assamese-based: Nagamese
 * Bengali-Meitei creole: Bishnupriya Manipuri
 * Chinese-based creole languages
 * Dutch-based creole languages
 * English-based creole languages
 * French-based creole languages
 * German-based creole languages
 * Hindi-based: Andaman Creole Hindi
 * Japanese-based creole languages
 * Kongo-based: Kituba
 * Malay-based creole languages
 * Ngbandi-based: Sango
 * Portuguese-based creole languages
 * Spanish-based creole languages
 * Sinhala-based: Vedda
 * Swahili-based: Kutchi-Swahili

In French

 * Groupe Européen de Recherches en Langues Créoles
 * Associação Brasileira de Estudos Crioulos e Similares
 * Society for Caribbean Linguistics
 * Society for Caribbean Linguistics

title: Creole language