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Molly Ivins

Mary Tyler "Molly" Ivins (August 30, 1944 – January 31, 2007) was an American newspaper columnist, author, and political commentator, known for her humorous and insightful writing, which often used satire and wit to critique political figures and policies.

Born in California and raised in Texas, Ivins attended Smith College and the Columbia University Graduate School of Journalism. She began her journalism career at the Minneapolis Tribune where she became the first female police reporter at the paper. Ivins joined The Texas Observer in the early 1970s and later moved to The New York Times. She became a columnist for the Dallas Times Herald in the 1980s, and then the Fort Worth Star-Telegram after the Times Herald was sold and shuttered in 1991. Her column was subsequently syndicated by Creators Syndicate and carried by hundreds of newspapers.

A biography of Ivins, Molly Ivins: A Rebel Life, was co-written in 2010 by PEN-USA winning presidential biographer Bill Minutaglio and W. Michael Smith. The Forbes Media Guide Five Hundred, 1994 said: "Ivins's pithy assessments of politics and life at large crackle with broad Texas humor. Combining her talent for culling information with her razor-sharp wit, she throws a powerful knockout punch. ... Whether one agrees with her or not, Ivins's pen pierces both the brain and the funny bone."

Early life
Ivins was born in Monterey, California, and raised in Houston, Texas. Her father, James Ivins, known as "General Jim" because of his rigid authoritarianism (or sometimes "Admiral Jim" for his love of sailing), was an oil and gas executive, and the family lived in Houston's affluent River Oaks neighborhood. Ivins graduated from St. John's School in 1962. In high school, she was active in extracurricular activities, including the yearbook staff. She had her first pieces of journalism published in The Review, the official student newspaper of St. John's School, though she never wrote any of the political columns that would become her specialty later in life. Ivins later became co-editor of the arts and culture section of the student paper. In addition, she frequently participated in theater productions and earned a lifetime membership in Johnnycake, the drama club.

Ivins enrolled in Scripps College in 1962, but was not happy there, and transferred to Smith College in 1963. During that time, she became romantically involved with Henry "Hank" Holland, Jr., a family friend and student at Yale whom she referred to as "the love of my life". After he was killed in a motorcycle accident in 1964, her friends would later say that she never seemed to find anyone else who could replace his memory. Some say that is why she never married. She spent her junior year at the Institute of Political Science in Paris and received a Bachelor of Arts degree in history in 1966. She earned a master's degree from Columbia University's School of Journalism in 1967.

Career
While at Smith, Ivins spent three summers as an intern at the Houston Chronicle. Her jobs there included the complaint department as well as "sewer editor", as she put it, responsible for reporting on the nuts and bolts of local city life. After graduating from Columbia, she took a job in the Twin Cities at the Minneapolis Tribune, where she covered "militant blacks, angry Indians, radical students, uppity women and a motley assortment of other misfits and troublemakers".

In 1970 Ivins left the Tribune for the city of Austin, Texas, hired by Ronnie Dugger, to be the co-editor and political reporter for The Texas Observer. She covered the Texas Legislature and befriended folklorist John Henry Faulk, Secretary of State Bob Bullock and future Governor Ann Richards, among others. She also gained increasing national attention through op-ed and feature stories in The New York Times and The Washington Post along with a busy speaking schedule inside and outside Texas. The Times, concerned that its prevailing writing style was too staid and lifeless, hired her away from the Observer in 1976, and she wrote for the Times until 1982. During her run there, Ivins became Rocky Mountain bureau chief, covering nine western states, although she was known to say she was named chief because there was no one else in the bureau.

Ivins also wrote the obituary for Elvis Presley in The New York Times for the August 17, 1977, edition. Generally, her more colorful writing style clashed with the editors' expectations, and in 1980, after she wrote about a "community chicken-killing festival" in New Mexico and called it a "gang-pluck", she was recalled to New York City as punishment. When Abe Rosenthal, editor of the Times, accused her of trying to inspire readers to think "dirty thoughts" with these words, her response was, "Damn if I could fool you, Mr. Rosenthal." In late 1981, after receiving an offer from the Dallas Times Herald to write a column about anything she liked, Ivins left New York City for Dallas.

Ivins wrote for the Dallas Times Herald for ten years and was nominated for the Pulitzer Prize twice. By 1985 the editors had moved her to the paper's Austin bureau to reduce friction with Dallas city leaders. Her freelance work and speaking engagements continued to grow, and she hired Elizabeth Faulk, John Henry Faulk's widow, as a personal assistant. In 1991, her book Molly Ivins Can't Say That, Can She? was published, and spent 29 weeks on the New York Times bestseller list. Also in 1991, rival newspaper, The Dallas Morning News bought the Times Herald and closed it down. The Fort Worth Star-Telegram immediately made Ivins an offer and said she could stay in Austin. Ivins accepted, and wrote a column for the Fort Worth paper from 1992 until 2001, when she became an independent journalist. Her column, syndicated by Creators Syndicate, eventually appeared in nearly 400 newspapers nationwide. Ivins also remained a board member and contributor to the Texas Democracy Foundation, which publishes the Texas Observer in Austin.

She also wrote for the Progressive, the Nation, Newsweek, Mother Jones, McCall's and Playboy. She has appeared on Nightline, PBS's MacNeil/Lehrer News Hour, National Public Radio’s All Things Considered and Talk of the Nation.

Plagiarism allegations
In 1995, humorist Florence King wrote an article in The American Enterprise claiming that Ivins had plagiarized King's work in a 1988 Mother Jones article. Like Ivins, King—who was referred to as the "Queen of Mean" by National Review, which published her columns—pulled no punches in her writing. David Rubien, writing in Salon, described the incident: "In a 1995 article for Mother Jones on Southern manners and mores, she extensively quoted, with affectionate attribution, statements from Florence King's book Southern Ladies and Gentlemen. But for some careless reason Ivins still fails to comprehend, she left the attribution off a few King statements." Ivins had also included her own words in a quotation she attributed to King. Ivins wrote a letter of apology to King, but characteristically ended it with: "As for the rest of your observations about me and my work ..., boy you really are a mean bitch, aren't you? Sincerely, Molly Ivins, plagiarist." The American Enterprise published Ivins's apology and King's reply in a later issue.

Health issues
For more than three decades, Ivins struggled with alcoholism, described in her The Nation obituary as an "occupational hazard" of journalism. In her notebooks, she wrote of her struggles, "I should like to think the biggest mistake I have made in the first 30 years of my life was to start drinking and keep drinking" and "I have wasted so much time by getting drunk ... I have jeopardized my job from drinking and failed in my responsibilities as a journalist."

Late in her life, she took some steps to treat the condition, spending some time at a "drunk school", then attending Alcoholics Anonymous (AA) meetings for the last year-and-a-half of her life.

In 1999, Ivins was diagnosed with stage III inflammatory breast cancer. The cancer recurred in 2003 and again in late 2005. In January 2006, she reported that she was again undergoing chemotherapy. In December 2006, she took leave from her column to again undergo treatment. She wrote two columns in January 2007 but returned to the hospital on January 26 for further treatment.

Death
Ivins died at her Austin, Texas, home in hospice care on January 31, 2007, at age 62.

After her death, George W. Bush, a frequent target of her barbs, said in a statement, "I respected her convictions, her passionate belief in the power of words. She fought her illness with that same passion. Her quick wit and commitment will be missed."

The Molly Ivins Papers are at the Dolph Briscoe Center for American History, while her personal library was donated to the Witliff Collections at Texas State University.

From August 23 to October 28, 2012, actress Kathleen Turner portrayed Molly Ivins in the play Red Hot Patriot: The Kick-Ass Wit of Molly Ivins by twin sisters and journalists Margaret and Allison Engel at Arena Stage in Washington, D.C.,  and at the Berkeley Repertory Theatre in Berkeley, California. Janice Engel (no relation ) produced and directed a documentary, "Raise Hell: The Life & Times of Molly Ivins," inspired by the play.

Beliefs
Writing from an unabashedly populist perspective, Ivins repeatedly described herself as a populist and, on some occasions, as a left-libertarian. Ivins peppered her columns with colorful phrases to create the "feel" of Texas. Her writings often employ irony and satirical humor to make a very serious point. For example, in her 1993 essay "Taking a Stab at Our Infatuation with Guns", she begins by saying:

When outraged by instances of what she considered malfeasance or stupidity on the part of public officials, she couched her argument in an air of stunned amusement. She enjoyed telling stories about the Texas Legislature, which she simply called "The Lege", calling it one of the most corrupt, incompetent, and funniest governing bodies in the nation. For example:

"Practice, practice, practice, that's what Texas provides when it comes to sleaze and stink. Who can forget such great explanations as 'Well, I'll just make a little bit of money, I won't make a whole lot'? And 'There was never a Bible in the room'?"

In 2003, she coined the term "Great Liberal Backlash of 2003", and was a passionate critic of the 2003 Iraq War. She is also credited with applying the nicknames "Shrub" and "Dubya" to George W. Bush. Ivins supported affirmative action and denounced President Bush for choosing Martin Luther King Jr.'s birthday to announce his opposition to the use of racial quotas at the University of Michigan.

Quotations
Notable quotes attributed to Ivins include:

 * "Politics is not a picture on a wall or a television sitcom that you can decide you don’t much care for… politics is not about those people in Washington, those people in your state capitol… this country is run by us, it is our deal, we run this country, we are the board of directors, we own it, they are just the people we’ve hired to drive the bus for a while."

 * On the subject of Pat Buchanan's combative Culture War Speech at the 1992 Republican Convention, which attracted controversy over Buchanan's aggressive rhetoric against Bill Clinton, liberals, supporters of abortion and gay rights, and for his comparison of American politics to religious warfare, Ivins quipped that the speech had "probably sounded better in the original German".

 * "We are the people who run this country. We are the deciders. And every single day, every single one of us needs to step outside and take some action to help stop this war. ... We need people in the streets, banging pots and pans and demanding, 'Stop it, now!'" (from her last column)

 * "Having breast cancer is massive amounts of no fun. First they mutilate you; then they poison you; then they burn you. I have been on blind dates better than that."

 * "So keep fightin' for freedom and justice, beloveds, but don't you forget to have fun doin' it. Lord, let your laughter ring forth. Be outrageous, ridicule the fraidy-cats, rejoice in all the oddities that freedom can produce. And when you get through kickin' ass and celebratin' the sheer joy of a good fight, be sure to tell those who come after how much fun it was."—quoted by John Nichols for The Nation Original source: "The Fun's in the Fight" column for Mother Jones, 1993. Part of the original quote is currently posted in The Daily Beast offices.

 * On Bill Clinton: "If left to my own devices, I'd spend all my time pointing out that he's weaker than bus-station chili. But the man is so constantly subjected to such hideous and unfair abuse that I wind up standing up for him on the general principle that some fairness should be applied. Besides, no one but a fool or a Republican ever took him for a liberal." (Introduction to You Got to Dance With Them What Brung You)

 * On James M. Collins, U.S. Representative, R-Dallas: "If his IQ slips any lower we'll have to water him twice a day." Collins had said that the current energy crisis could be averted if "we didn't use all that gas on school busing." Ivins's quote engendered substantial controversy, with calls and letters pouring into her newspaper, The Dallas Times Herald. The newspaper turned the controversy into a publicity campaign, with billboards all over the city asking, "Molly Ivins Can't Say That, Can She?"—which she later employed as the title for her first book.

 * "Of Bush's credentials as an economic conservative, there is no question at all—he owes his political life to big corporate money; he's a CEO's wet dream. He carries their water, he's stumpbroke—however you put it, George W. Bush is a wholly owned subsidiary of corporate America. ... We can find no evidence that it has ever occurred to him to question whether it is wise to do what big business wants."

Awards

 * William Allen White Award from the University of Kansas (2001)
 * Smith Medal from Smith College (2001)
 * Elected to the American Academy of Arts and Sciences (2001)
 * Ivan Allen Jr. Prize for Progress and Service (2003)
 * Pringle Prize for Washington Journalism from Columbia University (2003)
 * Eugene V. Debs Award in the field of journalism (2003)
 * David Brower Award for journalism from the Sierra Club (2004)
 * David Nyhan Prize for Political Journalism from the Shorenstein Center on Media, Politics and Public Policy at Harvard University (2006)
 * The Molly National Journalism Prize from the Texas Democracy Foundation (2006)
 * Otis Social Justice Award from Wheaton College, MA (2004)

In addition to these formal awards, Ivins said that she was particularly proud of two distinct honors—having the Minneapolis police force's mascot pig named after her, and being banned from the Texas A&M campus.

Newspaper articles

 * Molly Ivins at the Texas Observer, from 1970 through 1976; and syndicated columns
 * Selected Articles by Molly Ivins, The New York Times (1977—1980)
 * "By Molly Ivins" site:washingtonpost.com (1981—2007)
 * https://www.dallasobserver.com/author/molly-ivins (1994—1996)
 * Molly Ivins column archive at Creators Syndicate
 * Molly Ivins tribute, written by her long-time editor Anthony Zurcher.

 * Molly Ivins @ motherjones.com
 * Molly Ivins @ truthdig.com 2006
 * Stories by Molly Ivins at AlterNet

Books
Books by Molly Ivins, in chronological order:

 * The Edge of the West and Other Texas Stories with Bryan Wooley (Texas Western Pr, 1987) ISBN 0-87404-214-3
 * Molly Ivins Can't Say That, Can She? (Random House, 1991) ISBN 0-679-40445-7
 * Nothin' But Good Times Ahead (Random House, 1993) ISBN 0-517-16429-9
 * You Got to Dance With Them What Brung You: Politics in the Clinton Years (Random House, 1998) ISBN 0-679-40446-5
 * Shrub: The Short But Happy Political Life of George W. Bush with Lou Dubose (Random House, 2000) ISBN 0-375-50399-4
 * The Betrayal of America: How the Supreme Court Undermined the Constitution and Chose Our President (2001) with Vincent Bugliosi (Thunder's Mouth Press, 2001) ISBN 1-56025-355-X
 * Sugar's Life in the Hood: The Story of a Former Welfare Mother by Sugar Turner and Tracy Bachrach Ehlers, foreword by Molly Ivins (University of Texas Press, 2002) ISBN 0-292-72102-1
 * Pipe Dreams: Greed, Ego, and the Death of Enron by Robert Bryce, foreword by Molly Ivins (PublicAffairs, 2002) ISBN 1-58648-138-X
 * Bushwhacked: Life in George W. Bush's America with Lou Dubose (Random House, 2003) ISBN 0-375-50752-3
 * Who Let the Dogs In?: Incredible Political Animals I Have Known (Random House, 2004) ISBN 1-4000-6285-3
 * Bill of Wrongs: The Executive Branch's Assault on America's Fundamental Rights (Random House, 2007) ISBN 1-4000-6286-1

Selected C-SPAN interviews
(Source )

Biographical documentary
In 2019 a documentary called Raise Hell: The Life and times of Molly Ivins was released.

Legacy
The MOLLY National Journalism Prize honors Molly Ivins' legacy.

Ivins, is the subject of a one-woman play, Red Hot Patriot: The Kick Ass Wit of Molly Ivins, written by twin-sister journalists, Alison and Margaret Engels.

title: Molly Ivins


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Legatus

A legatus (anglicised as legate) was a high-ranking Roman military officer in the Roman army, equivalent to a high-ranking general officer of modern times. Initially used to delegate power, the term became formalised under Augustus as the officer in command of a legion.

From the times of the Roman Republic, legates received large shares of the military's rewards at the end of a successful campaign. This made the position a lucrative one, so it could often attract even distinguished consuls or other high-ranking political figures within Roman politics (e.g., the consul Lucius Julius Caesar volunteered late in the Gallic Wars as a legate under his first cousin, Gaius Julius Caesar).

Roman Republic
The rank of legatus existed as early as the Samnite Wars, but it was not until 190 BC that it started to be standardized, meant to better manage the higher numbers of soldiers the Second Punic War had forced to recruit. The legatus of a Roman Republican army was essentially a supreme military tribune, drawn from among the senatorial class of Rome (usually a consul or proconsul), who acted as a second-in-command to the magistrate in charge of the force. This role was usually played by either seasoned generals or ambitious young senators; the latter option eventually displaced the military tribune as a path to gain recognition.

The legatus was officially assigned by the Senate, the republic's highest governing body. An appointment was generally only done after consulting with the magistrate in command, hoping to pair a commander and a lieutenant who could work together without trouble. This was established to avoid clashes of leadership like that of the consuls Varro and Paulus in Cannae. The legatus often acted as a military consultant or adviser, like Scipio Africanus did for his brother Lucius during the Roman–Seleucid War, or as a trusted man of action, as in the case of Lucius Quinctius Flamininus and his brother Titus in their campaigns.

After the so-called "Marian reforms", the figure of the legatus as a major second-in-command was eliminated. Multiple legati were assigned to every army, each in command of a legion, which was called legatus legionis. Julius Caesar made wide use of this title throughout the Gallic Wars. Initially, only conflicts on foreign ground had demanded the presence of legati, but the beginning of the Social War in 90 BC saw them being increasingly deployed in Italia.

There were two main positions. The legatus legionis was an ex-praetor given command of one of Rome's legions, while the legatus pro praetore was an ex-consul given the governorship of a Roman province, with the magisterial powers of a praetor, which in some cases included command of four or more legions. A legatus was entitled to twelve lictors, who carried out punishments with fasces (bundled rods). A legatus legionis could order capital punishment.

Roman Empire
From Augustus onwards, the emperor gave the title of legatus legionis to senior commanders (former military tribunes) of a legion, except in Egypt and Mesopotamia where the legions were commanded by a praefectus legionis of an equestrian rank. The legatus legionis was under the supreme command of a legatus Augusti pro praetore of senatorial rank. If the province was defended by a single legion, the legatus Augusti pro praetore was also in direct command of the legion. This post was generally appointed by the emperor. The person chosen for this rank was a former tribune, and although the emperor Augustus set a maximum term of command of two years for a legatus, subsequent emperors extended the tenure to three or four years, although the incumbent could serve for a much longer period. In a province with only one legion, the legatus served as the provincial governor, while in provinces with multiple legions each legion had a legatus and a separate provincial governor who had overall command.

A legatus held full power over his legion. Consul militaris held control of all legions under the Emperor, who held entire control of Rome during the time of the Roman Empire. After the Roman Republic, all of the Senate's controls shifted to the Emperor, making him the most powerful person in Rome. The Legatus legionis would delegate duties to his command staff, who would then carry out his orders. A legatus was one of the most respected military ranks in Rome.

The legatus could be distinguished in the field by his elaborate helmet and body armour, as well as a scarlet paludamentum (cloak) and cincticulus (a waist-band tied around the waist in a bow).

The senatorial legatus legionis was removed from the Roman army by Gallienus, who preferred to entrust the command of a legionary unit to a leader chosen from within the equestrian order who had a long military career.

The title has other uses from the period of Augustus onwards, following the constitutional resettlement of 27 BC "that senatorial governors in the People's provinces bore the republican title of 'proconsul', while those appointed by the Emperor bore a title which explicitly referred to their dependence on him, namely legatus, or deputy".

Diplomatic legatus
Legatus was also a term for an ambassador of the Roman Republic who was appointed by the Senate for a mission (legatio) to a foreign nation, as well as for ambassadors who came to Rome from other countries. The concept remains today as a diplomatic legation.

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

title: Legatus


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Idempotent (ring theory)

In ring theory, a branch of mathematics, an idempotent element or simply idempotent of a ring is an element $a$ such that $a^{2} = a$. That is, the element is idempotent under the ring's multiplication. Inductively then, one can also conclude that $a = a^{2} = a^{3} = a^{4} = ... = a^{n}$ for any positive integer $n$. For example, an idempotent element of a matrix ring is precisely an idempotent matrix.

For general rings, elements idempotent under multiplication are involved in decompositions of modules, and connected to homological properties of the ring. In Boolean algebra, the main objects of study are rings in which all elements are idempotent under both addition and multiplication.

Quotients of Z
One may consider the ring of integers modulo $n$, where $n$ is squarefree. By the Chinese remainder theorem, this ring factors into the product of rings of integers modulo $p$, where $p$ is prime. Now each of these factors is a field, so it is clear that the factors' only idempotents will be $0$ and $1$. That is, each factor has two idempotents. So if there are $m$ factors, there will be $2^{m}$ idempotents.

We can check this for the integers $mod 6$, $R = Z / 6Z$. Since $6$ has two prime factors ($2$ and $3$) it should have $2^{2}$ idempotents.

From these computations, $0^{2} ≡ 0 ≡ 0 (mod 6)$, $1^{2} ≡ 1 ≡ 1 (mod 6)$, $2^{2} ≡ 4 ≡ 4 (mod 6)$, and $3^{2} ≡ 9 ≡ 3 (mod 6)$ are idempotents of this ring, while $4^{2} ≡ 16 ≡ 4 (mod 6)$ and $5^{2} ≡ 25 ≡ 1 (mod 6)$ are not. This also demonstrates the decomposition properties described below: because $0$, there is a ring decomposition $1$. In $3$ the multiplicative identity is $4$ and in $2$ the multiplicative identity is $5$.

Quotient of polynomial ring
Given a ring $3 + 4 ≡ 1 (mod 6)$ and an element $3Z / 6Z ⊕ 4Z / 6Z$ such that $3Z / 6Z$, the quotient ring

has the idempotent $3 + 6Z$. For example, this could be applied to $4Z / 6Z$, or any polynomial $4 + 6Z$.

Idempotents in split-quaternion rings
There is a hyperboloid of idempotents in the split-quaternion ring.

Types of ring idempotents
A partial list of important types of idempotents includes:
 * Two idempotents $R$ and $f ∈ R$ are called orthogonal if $f^{2} ≠ 0$. If $R / (f^{2} − f)$ is idempotent in the ring $f$ (with unity), then so is $x ∈ Z[x]$; moreover, $f ∈ k[x_{1}, ..., x_{n}]$ and $a$ are orthogonal.
 * An idempotent $b$ in $ab = ba = 0$ is called a central idempotent if $a$ for all $R$ in $b = 1 − a$, that is, if $a$ is in the centre of $b$.
 * A trivial idempotent refers to either of the elements $a$ and $R$, which are always idempotent.
 * A primitive idempotent of a ring $ax = xa$ is a nonzero idempotent $x$ such that $R$ is indecomposable as a right $a$-module; that is, such that $R$ is not a direct sum of two nonzero submodules. Equivalently, $0$ is a primitive idempotent if it cannot be written as $1$, where $R$ and $a$ are nonzero orthogonal idempotents in $aR$.
 * A local idempotent is an idempotent $R$ such that $aR$ is a local ring. This implies that $a$ is directly indecomposable, so local idempotents are also primitive.
 * A right irreducible idempotent is an idempotent $a = e + f$ for which $e$ is a simple module. By Schur's lemma, $f$ is a division ring, and hence is a local ring, so right (and left) irreducible idempotents are local.
 * A centrally primitive idempotent is a central idempotent $R$ that cannot be written as the sum of two nonzero orthogonal central idempotents.
 * An idempotent $a$ in the quotient ring $aRa$ is said to lift modulo $aR$ if there is an idempotent $a$ in $aR$ such that $End_{R}(aR) = aRa$.
 * An idempotent $a$ of $a + I$ is called a full idempotent if $R / I$.
 * A separability idempotent; see Separable algebra.

Any non-trivial idempotent $I$ is a zero divisor (because $b$ with neither $R$ nor $b + I = a + I$ being zero, where $a$). This shows that integral domains and division rings do not have such idempotents. Local rings also do not have such idempotents, but for a different reason. The only idempotent contained in the Jacobson radical of a ring is $R$.

Rings characterized by idempotents

 * A ring in which all elements are idempotent is called a Boolean ring. Some authors use the term "idempotent ring" for this type of ring. In such a ring, multiplication is commutative and every element is its own additive inverse.
 * A ring is semisimple if and only if every right (or every left) ideal is generated by an idempotent.
 * A ring is von Neumann regular if and only if every finitely generated right (or every finitely generated left) ideal is generated by an idempotent.
 * A ring for which the annihilator $RaR = R$ every subset $a$ of $ab = 0$ is generated by an idempotent is called a Baer ring. If the condition only holds for all singleton subsets of $a$, then the ring is a right Rickart ring. Both of these types of rings are interesting even when they lack a multiplicative identity.
 * A ring in which all idempotents are central is called an abelian ring. Such rings need not be commutative.
 * A ring is directly irreducible if and only if $b$ and $b = 1 − a$ are the only central idempotents.
 * A ring $0$ can be written as $r.Ann(S)$ with each $S$ a local idempotent if and only if $R$ is a semiperfect ring.
 * A ring is called an SBI ring or Lift/rad ring if all idempotents of $R$ lift modulo the Jacobson radical.
 * A ring satisfies the ascending chain condition on right direct summands if and only if the ring satisfies the descending chain condition on left direct summands if and only if every set of pairwise orthogonal idempotents is finite.
 * If $0$ is idempotent in the ring $1$, then $R$ is again a ring, with multiplicative identity $e_{1}R ⊕ e_{2}R ⊕ ... ⊕ e_{n}R$. The ring $e_{i}$ is often referred to as a corner ring of $R$.  The corner ring arises naturally since the ring of endomorphisms $R$.

Role in decompositions
The idempotents of $a$ have an important connection to decomposition of $R$-modules. If $aRa$ is an $a$-module and $aRa$ is its ring of endomorphisms, then $R$ if and only if there is a unique idempotent $End_{R}(aR) ≅ aRa$ in $R$ such that $R$ and $M$. Clearly then, $R$ is directly indecomposable if and only if $E = End_{R}(M)$ and $A ⊕ B = M$ are the only idempotents in $e$.

In the case when $E$ (assumed unital), the endomorphism ring $A = eM$, where each endomorphism arises as left multiplication by a fixed ring element. With this modification of notation, $B = (1 − e)M$ as right modules if and only if there exists a unique idempotent $M$ such that $0$ and $1$. Thus every direct summand of $E$ is generated by an idempotent.

If $M = R$ is a central idempotent, then the corner ring $End_{R}(R) = R$ is a ring with multiplicative identity $A ⊕ B = R$. Just as idempotents determine the direct decompositions of $e$ as a module, the central idempotents of $eR = A$ determine the decompositions of $(1 − e)R = B$ as a direct sum of rings. If $R$ is the direct sum of the rings $a$, ..., $aRa = Ra$, then the identity elements of the rings $a$ are central idempotents in $R$, pairwise orthogonal, and their sum is $R$. Conversely, given central idempotents $R$, ..., $R$ in $R_{1}$ that are pairwise orthogonal and have sum $R_{n}$, then $R_{i}$ is the direct sum of the rings $R$, ..., $1$. So in particular, every central idempotent $a_{1}$ in $a_{n}$ gives rise to a decomposition of $R$ as a direct sum of the corner rings $1$ and $R$. As a result, a ring $Ra_{1}$ is directly indecomposable as a ring if and only if the identity $Ra_{n}$ is centrally primitive.

Working inductively, one can attempt to decompose $a$ into a sum of centrally primitive elements. If $R$ is centrally primitive, we are done. If not, it is a sum of central orthogonal idempotents, which in turn are primitive or sums of more central idempotents, and so on. The problem that may occur is that this may continue without end, producing an infinite family of central orthogonal idempotents. The condition "$R$ does not contain infinite sets of central orthogonal idempotents" is a type of finiteness condition on the ring. It can be achieved in many ways, such as requiring the ring to be right Noetherian. If a decomposition $aRa$ exists with each $(1 − a)R(1 − a)$ a centrally primitive idempotent, then $R$ is a direct sum of the corner rings $1$, each of which is ring irreducible.

For associative algebras or Jordan algebras over a field, the Peirce decomposition is a decomposition of an algebra as a sum of eigenspaces of commuting idempotent elements.

Relation with involutions
If $1$ is an idempotent of the endomorphism ring $1$, then the endomorphism $R$ is an $R = c_{1}R ⊕ c_{2}R ⊕ ... ⊕ c_{n}R$-module involution of $c_{i}$. That is, $R$ is an $c_{i}Rc_{i}$-module homomorphism such that $a$ is the identity endomorphism of $End_{R}(M)$.

An idempotent element $f = 1 − 2a$ of $R$ and its associated involution $M$ gives rise to two involutions of the module $f$, depending on viewing $R$ as a left or right module. If $f^{2}$ represents an arbitrary element of $M$, $a$ can be viewed as a right $R$-module homomorphism $f$ so that $R$, or $R$ can also be viewed as a left $r$-module homomorphism $R$, where $f$.

This process can be reversed if $R$ is an invertible element of $r ↦ fr$: if $ffr = r$ is an involution, then $f$ and $R$ are orthogonal idempotents, corresponding to $r ↦ rf$ and $rff = r$. Thus for a ring in which $2$ is invertible, the idempotent elements correspond to involutions in a one-to-one manner.

Category of R-modules
Lifting idempotents also has major consequences for the category of $R$-modules. All idempotents lift modulo $2$ if and only if every $2$ direct summand of $2$ has a projective cover as an $2$-module. Idempotents always lift modulo nil ideals and rings for which $b$ is $2^{−1}(1 − b)$-adically complete.

Lifting is most important when $2^{−1}(1 + b)$, the Jacobson radical of $a$. Yet another characterization of semiperfect rings is that they are semilocal rings whose idempotents lift modulo $1 − a$.

Lattice of idempotents
One may define a partial order on the idempotents of a ring as follows: if $2$ and $R$ are idempotents, we write $I$ if and only if $R$. With respect to this order, $R/I$ is the smallest and $R$ the largest idempotent. For orthogonal idempotents $R$ and $I$, $I = J(R)$ is also idempotent, and we have $R$ and $J(R)$. The atoms of this partial order are precisely the primitive idempotents.

When the above partial order is restricted to the central idempotents of $a$, a lattice structure, or even a Boolean algebra structure, can be given. For two central idempotents $b$ and $a ≤ b$, the complement is given by

the meet is given by

and the join is given by

The ordering now becomes simply $ab = ba = a$ if and only if $0$, and the join and meet satisfy $1$ and $a$. It is shown in that if $b$ is von Neumann regular and right self-injective, then the lattice is a complete lattice.

title: Idempotent (ring theory)


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Rongbuk Glacier

The Rongbuk Glacier is located in the Himalaya of southern Tibet. Two large tributary glaciers, the East Rongbuk Glacier and the West Rongbuk Glacier, flow into the main Rongbuk Glacier. It flows north and forms the Rongbuk Valley north of Mount Everest. The famous Rongbuk Monastery is located at the northern end of the Rongbuk valley. Mount Everest is the source of the Rongbuk Glacier and East Rongbuk Glacier.

Discovery
The English climber George Mallory first explored the main Rongbuk Valley and its glacier while searching for possible routes to the summit of Mount Everest, during the first British Everest reconnaissance expedition of 1921.

On the same expedition, Oliver Wheeler first explored the East Rongbuk Glacier. His exploration below the Lhakpa La pass led him on 3 August 1921 to realise that the East Rongbuk Valley provided the key to a viable route to the summit of Everest. A few weeks later, a party consisting of George Mallory, Guy Bullock, and Oliver Wheeler explored the head of the valley via the Lhakpa La pass to become the first people to reach the North Col of Everest and set foot on the slopes of that mountain. See 1921 British Reconnaissance Expedition.

Route to Everest
Climbing expeditions attempting the normal route from Tibet use this glacier to reach the Advanced Base Camp of Mount Everest at the upper end of the East Rongbuk Glacier. From there, climbing expeditions try to summit Everest by the North Col and the northeast ridge.

Environmental
Since 2007, American mountaineer and film-maker David Breashears has been chronicling the rapid disappearance of the Rongbuk glacier due to global climate change. Breashears has retraced the steps of Mallory's 1921 expedition, revealing a significant loss of ice mass across the West, Main and East Rongbuk Glaciers. In partnership with Asia Society and MediaStorm, Breashears' GlacierWorks has made the photos available online. In 80 years, the Rongbuk has shrunk by more than 300 vertical feet across the entire glacier, approximately the height of the Statue of Liberty.

title: Rongbuk Glacier


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Colonial Williamsburg

Colonial Williamsburg is a living-history museum and private foundation presenting a part of the historic district in the city of Williamsburg, Virginia. Its 301 acre historic area includes several hundred restored or recreated buildings from the 18th century, when the city was the capital of the Colony of Virginia; 17th-century, 19th-century, and Colonial Revival structures; and more recent reconstructions. The historic area includes three main thoroughfares and their connecting side streets that attempt to suggest the atmosphere and the circumstances of 18th-century Americans. Costumed employees work and dress as people did in the era, sometimes using colonial grammar and diction.

In the late 1920s, the restoration of colonial Williamsburg was championed as a way to celebrate patriots and the early history of the United States. Proponents included the Reverend Dr. W. A. R. Goodwin and other community leaders; the Association for the Preservation of Virginia Antiquities (now called Preservation Virginia), the Colonial Dames of America, the Daughters of the Confederacy, the Chamber of Commerce, and other organizations; and John D. Rockefeller Jr. and his wife Abby Aldrich Rockefeller.

Along with Jamestown and Yorktown, and the Colonial Parkway, Colonial Williamsburg is part of the Historic Triangle in Virginia, The site was once used for conferences by world leaders and heads of state. In 1960, it was designated a National Historic Landmark District.

Overview
The core of Colonial Williamsburg runs along Duke of Gloucester Street and the Palace Green that extends north and south perpendicular to it. This area is largely flat, with ravines and streams branching off on the periphery. Duke of Gloucester Street and other historic area thoroughfares are closed to motorized vehicles during the day, in favor of pedestrians, bicyclists, joggers, dog walkers, and animal-drawn vehicles.

Surviving colonial structures have been restored as close as possible to their 18th-century appearance, with traces removed of later buildings and improvements. Many of the once missing colonial structures were reconstructed on their original sites beginning in the 1930s. Animals, gardens, and dependencies add to the environment, such as kitchens, smokehouses, and privies. Some buildings and most gardens are open to tourists, with the exception of buildings serving as residences for Colonial Williamsburg employees, large donors, the occasional city official, and sometimes College of William & Mary associates.

Prominent buildings include the Raleigh Tavern, the Capitol, the Governor's Palace (all reconstructed), the Courthouse, the Wythe House, the Peyton Randolph House, the Magazine, and the independently owned and functioning Bruton Parish Church (all originals). Colonial Williamsburg's portion of the historic area begins east of the College of William & Mary's College Yard.

Four taverns have been reconstructed for use as restaurants and two for inns. There are craftsmen's workshops for period trades, including a printing shop, a shoemaker, a blacksmith, a cooperage, a cabinetmaker, a gunsmith, a wigmaker, and a silversmith. There are merchants selling tourist souvenirs, books, reproduction toys, pewterware, pottery, scented soap, etc. Some houses are open to tourists, including the Peyton Randolph House, the Geddy House, the Wythe House, and the Everard House, as are such public buildings as the Courthouse, the Capitol, the Magazine, the Public Hospital, and the Public Gaol. Former notorious inmates of the Gaol include pirate Blackbeard's crew who were kept there while they awaited trial.

Colonial Williamsburg operations extend to Merchants Square, a Colonial Revival commercial area designated a historic district in its own right. Nearby are the Abby Aldrich Rockefeller Folk Art Museum and DeWitt Wallace Decorative Arts Museum, operated by Colonial Williamsburg as part of its curatorial efforts.

History of Williamsburg

The Jamestown statehouse housed Virginia's government in the 1600s, but it burned on October 20, 1698. The legislators consequently moved their meetings to the College of William & Mary in Virginia at Middle Plantation, putting an end to Jamestown's 92-year history as Virginia's capital. In 1699, a group of College of William & Mary students delivered addresses during graduation exercises endorsing proposals to move the capital to Middle Plantation, ostensibly to escape the malaria and the mosquitoes at the Jamestown Island site. Interested Middle Plantation landowners donated some of their holdings to advance the plan.

Middle Plantation was renamed Williamsburg by Governor Francis Nicholson in honor of William III of England. Nicholson said that "clear and crystal springs burst from the champagne soil" of Williamsburg. He had the city surveyed and a grid laid out by Theodorick Bland taking into consideration the brick College Building and the then decaying Bruton Parish Church buildings. The grid seems to have obliterated all but the remnants of an earlier plan that laid out the streets in the monogram of William and Mary, a W superimposed on an M. The main street was named Duke of Gloucester after the eldest son of Queen Anne. Nicholson named the street north of it Nicholson Street, for himself, and the one south of it Francis Street.

For 81 years of the 18th century, Williamsburg was the center of government, education, and culture in the Colony of Virginia. George Washington, Thomas Jefferson, Patrick Henry, James Monroe, James Madison, George Wythe, Peyton Randolph, Richard Henry Lee, and others furthered the forms of British government in the Commonwealth of Virginia and later helped adapt its preferred features to the needs of the new United States. The government moved to Richmond on the James River in 1780, under the leadership of Governor Thomas Jefferson, to be more central and accessible from western counties and less susceptible to British attack. There it remains today.

History of Colonial Williamsburg

With the seat of government removed, Williamsburg's businesses floundered or migrated to Richmond, and the city entered a long, slow period of stagnation and decay, although the town maintained much of its 18th-century aspect. It was captured by General George McClellan in 1862 and garrisoned during the Civil War, so the town escaped the devastation experienced by other Southern cities.

Williamsburg relied for jobs on The College of William & Mary, the Courthouse, and the Eastern Lunatic Asylum (now Eastern State Hospital); it was said that the "500 Crazies" of the asylum supported the "500 Lazies" of the college and town. Colonial-era buildings were modified, modernized, neglected, or destroyed. Development that accompanied construction of a World War I gun cotton plant at nearby Penniman and the coming of the automobile blighted the community, but the town kept its appeal to tourists. By the early 20th century, many older structures were in poor condition, no longer in use, or were occupied by squatters.

Dr. Goodwin and the Rockefellers

The Reverend Dr. W. A. R. Goodwin became rector of Williamsburg's Bruton Parish Church in 1903 for the first of two periods. He was born in 1869 at Richmond to a Confederate veteran and his well-to-do wife and reared in rural Nelson County at Norwood. He was educated at Roanoke College, the University of Virginia, the University of Richmond, and the Virginia Theological Seminary. He first visited Williamsburg as a seminarian sent to recruit William & Mary students. He became rector at age 34 of the Bruton Parish Church that was riven by factions. He helped harmonize the congregation and assumed leadership of a flagging campaign to restore the 1711 church building. Goodwin and New York ecclesiastical architect J. Stewart Barney completed the church restoration in time for the 300th anniversary of the founding of America's Anglican Church at nearby Jamestown, Virginia, in 1907. Goodwin traveled the East Coast raising money for the project and establishing philanthropic contacts. Among the 1907 anniversary guests was J. P. Morgan, president of the Episcopal church's General Convention meeting that year in Richmond.

Goodwin accepted a call from wealthy St. Paul's Episcopal Church in Rochester, New York in 1908, and pastored there until his return in 1923 to Williamsburg to become a College of William & Mary fund-raiser and religious studies professor, as well as pastor of Yorktown's Episcopal church and a chapel at Toano. He had maintained his Williamsburg ties, periodically visiting the graves of his first wife and their son, using William & Mary's library for historical research, and vacationing. He saw the ongoing deterioration of colonial-era buildings.

He renewed his connections with the Association for the Preservation of Virginia Antiquities, whose membership included prominent and wealthy Virginians, and he helped to protect and repair the Magazine. He and other William & Mary professors saved the John Blair House from demolition to make way for a gasoline station, and they turned it into a faculty club. In 1924, the college launched a building and fund-raising drive, and Goodwin adopted Barney's proposal for saving other houses in the historic section of the town for use as student and faculty housing. He worked for two years to interest individuals such as Henry Ford and organizations such as the Dames of Colonial America to invest. He eventually obtained the support and financial commitment of John D. Rockefeller Jr., the wealthy son of the founder of Standard Oil. Rockefeller's wife Abby Aldrich Rockefeller also played a role. Goodwin returned to the Bruton Parish pulpit in 1926, keeping his college positions.

Rockefeller's first investment in a Williamsburg house had been a contribution to Goodwin's acquisition of the George Wythe House for next-door Bruton Church's parish house. Rockefeller's second investment was the purchase of the Ludwell–Paradise House in early 1927. Goodwin persuaded him to buy it on behalf of the college for housing in the event that Rockefeller should decide to restore the town. Rockefeller had agreed to pay for college restoration plans and drawings. He later considered limiting his restoration involvement to the college and an exhibition enclave, and he did not commit to the town's large scale restoration until November 22, 1927.

Rockefeller and Goodwin initially kept their acquisition plans secret because they were concerned that prices might rise if their purposes were known, quietly buying houses and lots and taking deeds in blank. Goodwin took Williamsburg attorney Vernon M. Geddy, Sr. into his confidence, without exposing Rockefeller as silent partner. Geddy did much of the title research and legal work related to properties in what became the restored area. He later drafted the Virginia corporate papers for the project, filed them with the Virginia State Corporation Commission, and served briefly as the first president of the Colonial Williamsburg Foundation.

That much property changing hands was noticed by newspaper reporters. After 18 months of increasingly excited rumors, Goodwin and Rockefeller revealed their plans at county and town meetings on June 11 and 12, 1928. The purpose was to obtain the consent of the citizens and enlist them in the project. The restoration project required a new high school and two public greens. The city retained ownership of its streets, an arrangement that forestalled later proposals to raise revenue by charging an admission fee.

Some townsmen had qualms. Major S. D. Freeman, retired Army officer and school board president, said, "We will reap dollars, but will we own our town? Will you not be in the position of a butterfly pinned to a card in a glass cabinet, or like a mummy unearthed in the tomb of Tutankhamun?" To gain the cooperation of people reluctant to sell their homes to the Rockefeller organization, the restoration offered free life tenancies and maintenance in exchange for ownership. Freeman sold his house outright and moved to Virginia's Middle Peninsula.

Restoration and reconstruction

Rockefeller management decided against giving custody of the project to the state-run college, ostensibly to avoid political control by Virginia's Democratic Byrd Machine, but they restored the school's Wren Building, Brafferton House, and President's House. Colonial Williamsburg pursued a program of partial re-creation of some of the rest of the town. It featured shops, taverns, and open-air markets in a colonial style.

The first lead architect in the project was William G. Perry of Perry, Shaw & Hepburn, with Arthur Asahel Shurcliff as the chief landscape architect. An Advisory Board of Architects was selected to provide guidance for the project. Prominent architects who served on the advisory board included Robert P. Bellows, Fiske Kimball, A. Lawrence Kocher, Philip N. Stern, Merril C. Lee, W. Duncan Lee, Marcellus E. Wright Sr., Edmund S. Campbell, Orin M. Bullock Jr., and R. E. Lee Taylor.

During the restoration, the project demolished 720 buildings that postdated 1790, many of which dated from the 19th century. Some decrepit 18th-century homes were demolished, leading to some controversy. The Governor's Palace and the Capitol building were reconstructed on their sites with the aid of period illustrations, written descriptions, early photographs, and informed guesswork. The grounds and gardens were almost all recreated in authentic Colonial Revival style.

The Capitol is a 1930s beaux arts approximation of the 1705 building at the east end of the historic area. It was designed by the architectural firm Perry, Shaw & Hepburn, who had it rebuilt as they thought it should have been, not as it was, despite objections and archaeological evidence to the contrary. The modern reconstruction is off-center, its floorplan is skewed, and its interior is overly elaborate.

The 1705 original was an H-shaped brick statehouse with double-apsed, oarsmen-circular southern facades, but it burned in the 1740s and was replaced by an H-shaped rectangular edifice.

In the second building, Patrick Henry protested against the Stamp Act and first spoke against King George. George Mason introduced the Virginia Bill of Rights there, and from it Virginia's government instructed its delegates to the Second Continental Congress to propose national independence. Its likeness only exists in a period woodcut and in architectural renderings considered but shelved by the Restoration.

The present building was dedicated with a ceremonial meeting of the Virginia General Assembly on February 24, 1934. Virginia's state legislators have reassembled for a day every other year in the Capitol.

Of the approximately 500 buildings reconstructed or restored, 88 are labelled original. They include outbuildings such as smokehouses, privies, and sheds. The foundation reconstructed the Capitol and Governor's Palace on their 18th-century foundations and preserved some below-ground 18th-century brickwork, classifying them as reconstructions. It rebuilt William & Mary's Wren Building on its original foundation, which burned four times in 230 years and was much modified; it saved some above-ground brickwork and classified the result as original.

On the western side of the city, beginning in the 1930s, retail shops were grouped under the name Merchants Square to accommodate and mollify displaced local merchants. Increasing rents and tourist-driven businesses eventually drove out all the old-line community enterprises except a dress shop. One of the last to be forced out was a locally popular drugstore complete with lunch counter.

Outlying landscapes and viewsheds

Beginning in the earliest period of the restoration, Colonial Williamsburg acquired acreage in Williamsburg and the two counties which adjoin it, notably to the north and east of the historic area to preserve natural views and facilitate the experience of as much of the late 18th-century environment as possible. This was described as a "rural, wooded sense of arrival" along corridors to the historic area.

In 2006, announcing a conservation easement on acreage north of the Visitor Center, Colonial Williamsburg President and Chairman Colin G. Campbell said its restrictions protected the view and preserved other features: "This viewshed helps to set the stage for visitors in their journey from modern day life into the 18th-century setting. At the same time, this preserves the natural environment around Queen's Creek and protects a significant archaeological site. It is a tangible and important example of how the Foundation is protecting the vital greenbelt surrounding Colonial Williamsburg's historic area for future generations". The Colonial Parkway, which includes a tunnel running beneath the historic area, was planned and is maintained to reduce modern intrusions.

Near the principal planned roadway approach to Colonial Williamsburg, similar design priorities were employed for the relocated U.S. Route 60 near the intersection of Bypass Road and North Henry Street. Prior to the restoration, U.S. Route 60 ran down Duke of Gloucester Street through town. To shift the traffic away from the historic area, Bypass Road was planned and built through farmland and woods about a mile north of town. Shortly thereafter, when Route 143 was built as the Merrimack Trail (originally designated State Route 168) in the 1930s, the protected vista was extended along Route 132 in York County to the new road, and two new bridges were built across Queen's Creek.

Goodwin, who served as a liaison with the community, as well as with state and local officials, was instrumental in such efforts. Nevertheless, some in the Rockefeller organization, regarding him as meddlesome, gradually pushed Goodwin to the periphery of the Restoration and by the time of his death in 1939 Colonial Williamsburg's administrator, Kenneth Chorley of New York, was indiscreetly at loggerheads with the local reverend. Goodwin's relationship with Rockefeller remained warm, however, and his interest in the project remained keen. Colonial Williamsburg dedicated its headquarters in 1940, naming it The Goodwin Building.

About 30 years later, when Interstate 64 was planned and built in the 1960s and early 1970s, from the designated "Colonial Williamsburg" exit, the additional land along Merrimack Trail to Route 132 was similarly protected from development. Today, visitors encounter no commercial properties before they reach the Visitor's Center.

In addition to considerations regarding highway travel, Williamsburg's brick Chesapeake and Ohio Railway passenger station was less than 20 years old and one of the newer ones along the rail line, it was replaced with a larger station in Colonial style that was located just out of sight and within walking distance of the historic area, on the northern edge of Peacock Hill.

Farther afield was Carter's Grove Plantation. It was begun by a grandson of wealthy planter Robert "King" Carter. For over 200 years, it had gone through a succession of owners and modifications. In the 1960s after the death of its last resident, Ms. Molly McRae, Carter's Grove Plantation came under the control of Winthrop Rockefeller's Sealantic Foundation, which gave it to Colonial Williamsburg as a gift. Archaeologist Ivor Noel Hume discovered in its grounds the remains of 1620s Wolstenholme Towne, a downriver outpost of Jamestown. The Winthrop Rockefeller Archaeology Museum, built just above the site, showcased artifacts from the dig. Colonial Williamsburg operated Carter's Grove until 2003 as a satellite facility of Colonial Williamsburg, with interpretive programs. The property has since been sold.

Kingsmill
Between Carter's Grove and the Historic District was the largely vacant Kingsmill tract, as well as a small military outpost of Fort Eustis known as Camp Wallace (CW). In the mid-1960s, CW owned land that extended from the historic district to Skiffe's Creek, at the edge of Newport News near Lee Hall. Distant from the historic area and not along the protected sight paths, it was developed in the early 1970s, under CW Chairman Winthrop Rockefeller.

Rockefeller, a son of Abby and John D. Rockeller Jr., was a frequent visitor and was particularly fond of Carter's Grove in the late 1960s. He became aware of some expansion plans elsewhere on the Peninsula of his St. Louis-based neighbor, August Anheuser Busch, Jr., head of Anheuser-Busch. By the time Rockefeller and Busch completed their discussions, the biggest changes in the Williamsburg area were underway since the restoration began 40 years before. Among the goals were to complement Colonial Williamsburg attractions and enhance the local economy.

The large tract consisting primarily of the Kingsmill land was sold by the Colonial Williamsburg Foundation to Anheuser-Busch for planned development. The Anheuser-Busch investment included building a large brewery, the Busch Gardens Williamsburg theme park, the Kingsmill planned resort community, and McLaws Circle, an office park. Anheuser-Busch and related entities from that development plan comprise the area's largest employment base, surpassing both Colonial Williamsburg and the local military bases.

Late 20th century
With its historic significance to American democracy, it and the surrounding area was the site of a summit meeting of world leaders, the first World Economic Conference in 1983, and hosted visiting royalty, including King Hussein of Jordan and Emperor Hirohito of Japan. Queen Elizabeth II paid two royal visits to Williamsburg during her reign, once in October 1957 and again, in May 2007, both to celebrate the anniversaries of the founding of nearby Jamestown.

Colonial Williamsburg today

Colonial Williamsburg is an open-air assemblage of buildings populated with historical reenactors (interpreters) who explain and demonstrate aspects of daily life in the past. The reenactors work, dress, and talk as they would have in colonial times.

While there are many living history museums (such as Old Sturbridge Village in Massachusetts, Old Salem in Winston-Salem, or Castell Henllys in the UK), Colonial Williamsburg is unusual for having been constructed from a living town whose inhabitants and post-Colonial-era buildings were removed. Also unlike other living history museums, Colonial Williamsburg allows anyone to walk through the historic district free of charge, at any hour of the day. Charges apply only to those visitors who wish to enter the historic buildings to see arts and crafts demonstrations during daylight hours, or attend scheduled outdoor performances such as the Revolutionary City programs.

The Visitor Center near the Colonial Parkway features a short film, Williamsburg: the Story of a Patriot, which debuted in 1957. Visitors may park at the Visitor's Center, as automobiles are restricted from the restored area. Wheelchair-accessible shuttle bus service is provided to stops around the perimeter of the Historic District of Williamsburg, as well as Jamestown and Yorktown, during the peak summer season.

The costumed interpreters have not always worn Colonial dress. As an experiment in anticipation of the Bicentennial, in summer 1973 the hostesses were dressed in special red, white, and blue polyester knit pantsuits. This confused and disappointed visitors, so the experiment was dropped at the end of summer, and for the Bicentennial, docents wore historical costumes.

Many reenactments by Colonial Williamsburg's historical interpreters wearing period costumes are posted online. In addition to simple period reenactments, Colonial Williamsburg, at various times, features themes, including the founding of Williamsburg, occupation by British forces, or visits from Colonial leaders of the day, including General George Washington.

Some of the costumed interpreters work with animals. The Colonial Williamsburg Rare Breed Program helps to preserve and showcase animals that would have been present during the colonial period. John P. Hunter's book on the topic, Link to the Past, Bridge to the Future: Colonial Williamsburg's Animals, explains the importance of, as well as details how interpreters are a part, of this program.

Colonial Williamsburg is a partly pet-friendly destination. Leashed pets are permitted in specific outdoor areas and may be taken on shuttle buses, but are not permitted in buildings except the visitor center.

Grand Illumination

The Grand Illumination is an outdoor ceremony and mass celebration involving the simultaneous activation of thousands of Christmas lights each year on the first Sunday of December. The ceremony, Goodwin's idea, began in 1935, loosely based on a colonial (and English) tradition of placing lighted candles in the windows of homes and public buildings to celebrate a special event, such as the winning of a war or the birthday of the reigning monarch. The Grand Illumination also has incorporated extravagant fireworks displays, loosely based on the 18th-century practice of using fireworks to celebrate significant occasions.

Educational outreach

In the 1990s, Colonial Williamsburg implemented the Teaching Institute in Early American History, and Electronic Field Trips. Designed for elementary and middle/high school teachers, the institute offers workshops for educators to meet with historians, character interpreters, and to prepare instructional materials for use in the classroom. Electronic Field Trips are a series of multimedia classroom presentations available to schools. Each program is designed around a particular topic in history and includes a lesson plan as well as classroom and online activities. Monthly live broadcasts on local PBS television stations allow participating classes to interact with historical interpreters via telephone or internet.

In 2007, Colonial Williamsburg launched iCitizenForum.com. A mix of historical documents and user-generated content such as blogs, videos, and message boards, the site aims to prompt discussion about the roles, rights, and responsibilities of citizens in a democracy. Preservation of the Founding Fathers' ideals in light of recent world events is a focus of the site.

Colonial Williamsburg hired former NBC journalist Lloyd Dobyns to produce the early podcasts for the museum usually interviewing staff about their specialties. Podcast interviews continued by others after his retirement.

John D. Rockefeller Jr. Library
The John D. Rockefeller Jr. Library is considered the "intellectual center of the Colonial Williamsburg Foundation." The library houses special collections including:
 * Rare books from the 15th to 20th centuries
 * Original manuscripts from the 17th to 20th centuries
 * 18th-century British and American newspapers
 * Reproduction maps of the Williamsburg region
 * Reproductions of manuscripts from the 17th to 19th centuries in a variety of formats.

The library also has a visual resources collection, Colonial Williamsburg Foundation corporate archives, media collections, and photo reproduction and licensing services. The library publishes a quarterly newsletter in digital format, as well as a podcast.

Merchandising
Colonial American craft items, some manufactured abroad, are sold in historic area stores. Many shops sell such items as floral and herbal soaps, knitted hats, and handcrafted toys made from wood and clay.

Management

Colonial Williamsburg is owned and operated as a living museum by the Colonial Williamsburg Foundation, the non-profit entity endowed initially by the Rockefeller family and over the years by others, notably Reader's Digest founders Lila and DeWitt Wallace, and Philadelphia publisher Walter Annenberg.

The major goal of the restoration was to re-create the physical colonial environment and to facilitate education about the origins of the idea of America, which was conceived during the decades before the American Revolution. In this environment, Colonial Williamsburg strives to tell the story of how diverse peoples, having different and sometimes conflicting ambitions, evolved into a society that valued liberty and equality.

Cliff Fleet, former President of the Jamestown-Yorktown Foundation, was appointed president and CEO of The Colonial Williamsburg Foundation in 2019. Mitchell Reiss, former President of Washington College, was the Foundation's president and CEO from 2014 to 2019. Reiss succeeded Colin G. Campbell, who held the position for 14 years. Thomas F. Farrell II was Chair of the Colonial Williamsburg Foundation's Board of Trustees from 2011 to 2016 and served on the Board from 2006 to 2018.

Attendance
Attendance at Colonial Williamsburg peaked in 1985 at 1.1 million visitors. After years of lower attendance, it began to rebound somewhat with the Jamestown 2007 celebration and the Revolutionary City programs of live, interactive street theater between reenactors and audience members, which began in 2006.

Since its lowest point in 2004, total attendance has climbed about 10 percent total over the following years, according to a report in July 2008. During 2008, CW's hospitality revenue increase of 15 percent was much stronger than the ticket sale gain of 5 percent, reflecting how the hospitality revenue is not always coming from CW historic area tourists, according to an official.

The foundation's attendance figures are best read in context. Until the 1990s they reflected only general admission tickets sold, and that number was sometimes artificially bolstered by internal year-end sales and new year repurchases between the non-profit foundation and its for-profit wholly owned subsidiary hotels. Afterward, the foundation estimated the number of tourists who walked the streets without purchasing a ticket, and added them to attendance figures. In the 2000s, head counts were adjusted to reflect tourists who rode the foundation's buses, who visited its museums, who bought carriage rides, who went to night programs, etc. These numbers were reported as "turnstile" counts.

Financial challenges
Persistent operating deficits challenge the Colonial Williamsburg Foundation. Income comes from attendance and merchandising, but is lost at hospitality properties. Other funds come from investments of the endowments and a fundraising operation that occupies half of the foundation's four-story headquarters. Financially focused efforts in recent years have primarily concentrated on cost containment and stimulating attendance and hospitality revenues. The foundation has also sold some property assets that were no longer essential to its core mission, including most of its formerly owned properties on nearby Peacock Hill, which has the local distinction of having formerly been home to Georgia O'Keeffe, Mayor Polly Stryker, and Dr. Donald W. Davis, founder of the Virginia Institute of Marine Science.

In 2017, due to losses, Colonial Williamsburg former President Mitchell Reis outsourced management of commercial operations of their hotels, 19 retail stores, and three golf courses.

Land divestment
In 2003, as CW attendance and operating revenues continued to drop, Carter's Grove was closed to the public while its mission and role in CW's programs were redefined. After the sale, officials belatedly determined Carters Grove was paying for itself, one of the bright spots in its troubled balance sheet. Later in 2003, Hurricane Isabel seriously damaged Carter's Grove Country Road, which had linked the estate to the historic area, a distance of 8 mi, bypassing commercial and public roadways. Colonial Williamsburg shifted some of the interpretive programs to locations contiguous to the historic area in Williamsburg, including the ersatz farm Great Hopes Plantation next to its Visitor Center.

The foundation announced in late 2006 that Carter's Grove would be sold under restrictive conditions. In a front-page article December 31, The New York Times reported that the foundation, struggling because of dwindling attendance and insufficient endowment for upkeep, would be offering the Carter's Grove mansion and grounds for sale to a private purchaser, possibly as soon as January 2007. The foundation justified the sale, in part, by saying it wanted to concentrate on its 18th-century core—as opposed to such attractions as the reconstruction of a 17th-century village on the site—a position at odds with its later, and subsequently undone, decision to assume management of 17th-century historic Jamestowne. The Times said that the dilemma of historic museums and houses is that there are too many of them, upkeep is too expensive, and fewer people are visiting them.

In December 2007, the Georgian-style mansion and 476 acre were acquired for $15.3 million by CNET founder Halsey Minor, whose announced plans to use the property as a private residence and a center for a Thoroughbred horse breeding program. The conservation easement on the mansion and 400 of the 476 acre is co-held by the Virginia Outdoors Foundation and the Virginia Department of Historic Resources. Some local residents lamented CW's decision to sell Carter's Grove; others stated relief that it would remain largely intact, no small matter in one of the fastest developing counties in Virginia. There was general agreement, however, that the transaction was a disaster for the foundation's management and reputation. In 2011, Halsey Minor stopped making payments, and was foreclosed on by CW after a lengthy legal battle and some deterioration of the house and grounds. In 2014, CW repurchased Carter's Grove from the bankruptcy court, and sold it to a new private investor.

In addition to the large sale of surplus land of the old Kingsmill plantation to Anheuser Busch in the 1970s and the more recent sale of Carter's Grove, the foundation has also sold outlying tracts of land not considered fundamental to its mission, as well as multiple now-privately owned homes in Peacock Hill.

One of these is a 360 acre tract along historic Quarterpath Road north of State Route 199 and south of U.S. Route 60 east of the historic area. In 2005, it was the City of Williamsburg's largest undeveloped tract under single ownership". Observers have noted that, while most of the Quarterpath land will be developed, the previously vacant land will include park and recreational facilities, and Redoubt Park, dedicated to preserving some of the battlegrounds from the Battle of Williamsburg that occurred on May 5, 1862, during the Peninsula Campaign of the American Civil War.

A portion of the 437 acre Carr's Hill Tract in York County, north and west of Bypass Road and State Route 132, was also sold. Developments thereon were restricted under the terms of sale so as to not negatively impact the vista available to motorists approaching Colonial Williamsburg. In February, 2007, a developer announced that 313 homes were planned to be built on 65 acre of the historic tract's 437 acre, but these plans were scrapped due to the Great Recession's impact on the greater town economy. CW had earlier announced that it had donated three conservation easements to the Williamsburg Land Conservancy on 230 acre of the Carr's Hill tract land west of Route 132 in York County.

Transportation

The closest commercial airport is Newport News/Williamsburg International Airport 25–30 minutes driving distance away. Williamsburg is midway between two larger commercial airports, Richmond International Airport and Norfolk International Airport, each about an hour's distance away.

Amtrak offers a passenger rail service stop at Williamsburg, as does Greyhound and Carolina Trailways with intercity buses.

Williamsburg is adjacent to east–west Interstate 64 and the parallel U.S. Route 60 passes through the city. A third road, State Route 143, also extends east to Newport News and Hampton, ending at Fort Monroe. From Richmond, Interstate 295, and other points west, many visitors approach via State Route 5, a scenic byway which passes many of the James River Plantations, or from the south via State Route 10, State Route 31 and the Jamestown Ferry. The Virginia Capital Trail is available for bicycles and pedestrians along the Colonial Parkway and Virginia Route5.

Williamsburg is served by non-automobile driving alternatives. The area has a central intermodal transportation center and Williamsburg Area Transit Authority (WATA), a public transit bus system which operates a network of local routes. The community's public bus system has its central hub at the transportation center. Color-coded routes, with buses accessible to disabled persons, serve hotels and motels, restaurants, stores, and non-Colonial Williamsburg attractions.

Buses stop close to attractions in the historic area, although no motor vehicles operate during the day on Duke of Gloucester Street (to maintain the colonial-era atmosphere). At night, the historic area streets are open to automobiles.

The 1920s and 1930s
Some residents of Williamsburg, including Major S. D. Freeman and Cara Armistead, questioned the 1928 transfer of public lands (as compared to private properties). In January 1932, the large marble Confederate Civil War monument was removed from Palace Green, where it had stood since 1908, and placed in the Cedar Grove Cemetery, on the outskirts of town. This was disagreeable to some citizens who supported the colonial reconstruction. The case went to court, and eventually the monument was moved to a new site east of the then-new courthouse. For many years, the memorial rested in Bicentennial Park, just outside the Historic Area. In July 2020 the city council voted unanimously to remove it, and it was returned to the United Daughters of the Confederacy in August 2020.

Issues of "accuracy" and "authenticity"
The approach to restoration and preservation taken by the Colonial Williamsburg Foundation has long been subject to criticism.

Goodwin was troubled by what he perceived as encroaching commercialization. Among his parting words of advice to Colonial Williamsburg's management were: "If there is one firm guiding and restraining word which should be passed on to those who will be responsible for the restoration in the future, that one word is integrity. A departure from truth here and there will inevitably produce a cumulative deterioration of authenticity and consequent loss of public confidence. Loyalty demands that this principle of integrity be adhered to".

One of the foundation's in-house publications concedes that "Colonial Williamsburg bears the burden of criticism that the restored town appears too neat and clean, too 'spick-and-span', and too manicured to be believable". Ada Louise Huxtable, an architecture critic, wrote in 1965: "Williamsburg is an extraordinary, conscientious and expensive exercise in historical playacting in which real and imitation treasures and modern copies are carelessly confused in everyone's mind. Partly because it is so well done, the end effect has been to devalue authenticity and denigrate the genuine heritage of less picturesque periods to which an era and a people gave life".

All of the restored houses were improved with electricity, plumbing, and heating by 19th- and 20th-century residents and later by Colonial Williamsburg. They have also been furnished with stoves, air conditioners, refrigerators, and bathrooms by today's residents or the foundation. Plaster, woodwork, flooring, siding and roofs were replaced.

In 1997, anthropologists Eric Gable and Richard Handler discussed Colonial Williamsburg as an attraction which catered to America's upper/middle to high-level affluent socioeconomic classes. Their report mentions instances where some of Colonial Williamsburg's employees often straddle expectations of maintaining authenticity of the museum's programs while still in-authentically creating products to sell in the museum's gift shops. A more harsh interpretation is that of University of Virginia Professor of Architectural History Richard Guy Wilson, author of Buildings of Virginia: Tidewater and Piedmont, who described Colonial Williamsburg as "a superb example of an American suburb of the 1930s, with its in-authentically tree-lined streets of Colonial Revival houses and segregated commerce". All of these reproaches have led many critics to label Colonial Williamsburg and its Foundation a "Republican Disneyland".

Among the answers to these criticisms is that "Colonial Williamsburg's Historic Area is a compromise between historical authenticity and common sense, between brutal realism and gentle ambiance, between being a moment in time in the eighteenth century and being nearly three hundred years old". Critics assert that setting "historical authenticity" against "common sense" is a false dichotomy and that commercial and proprietary factors are what are really at issue. Of course archaeological and historical research is an ongoing process at Colonial Williamsburg, and as new information surfaces, reconsideration is often prompted and changes made accordingly.

In March 2016, the foundation's new president and chief executive officer, Mitchell Reiss, told the Richmond Times-Dispatch that Colonial Williamsburg aimed to be "accurate-ish."

At Appalachian State University a graduate level class focuses on the preservation and restoration of Colonial Williamsburg as part of its Public History program.

African Americans
Colonial Williamsburg has been criticized for neglecting the role of free African Americans in colonial life, in addition to those who were slaves. When it first opened in the 1930s, Colonial Williamsburg had segregated dormitories for its reenactors. African Americans filled historical roles as servants, rather than free people as in the present day. In a segregated state, Colonial Williamsburg allowed the entry of Blacks, but Williamsburg-area hotels denied them accommodation, and state law forbade Black people from eating with white people in such public facilities as the restored taverns and from shopping in nearby stores.

Colonial Williamsburg offered some of the earlier public accommodations on an integrated basis. In the 1970s, in reaction to increasing scorn of its one-sided portrayal of colonial life, Colonial Williamsburg increased its number of African American interpreters who played slaves. This was parodied by a sketch that aired on Saturday Night Live, which showed a reenactor abusing his accuracy by being racist to employees. In 1994, it added slave auctions and slave marriages; the NAACP and the Southern Christian Leadership Conference later protested. One controversial example was the “Publick Times” program, a reenactment of a slave auction staged in October 1994. The event was widely publicized by news outlets such as The Baltimore Sun, Chicago Tribune, and The New York Times. While some members of the public applauded the reenactment as a reflection of the reality of slavery in the American colonies, others criticized the program for using a slave auction as a source of entertainment.

In 1981, Colonial Williamsburg added a program to explain slavery and its role in Colonial America, but this "Other Half Tour," which is composed by the Foundation's African American and Interpretation Programs Department (AAIP), provides a different form of historical interpretation than does its counterpart tour, "The Patriots' Tour," thus creating a marked dichotomy between how visitors are expected to interpret history at the museum.

In recent years, Colonial Williamsburg has expanded its portrayal of 18th-century African Americans to include free Blacks as well as slaves. Examples of these expanded portrayals in the Revolutionary City program include Gowan Pamphlet, a former slave who became a free landowner and Baptist minister, Edith Cumbo, a free Black woman, Matthew Ashby, a free Black man who eventually purchased the freedom of his family, and a number of other enslaved men and women who were part of the Williamsburg community during the Revolutionary period. A re-created Great Hopes Plantation represents a middling plantation, not one owned by the wealthy, in which working-class farmers worked alongside their slaves. Their lives were more typical of colonial Virginians in general than the lives of the wealthier planters, their families, and slaves.

Depictions

 * A short film called "The Bill of Rights" in 1939 depicting the 1st Virginia Convention. Created by Warner Bros. It is currently available on the 2007 DVD Release of Allegheny Uprising (1939).
 * The Howards of Virginia filmed on location.
 * Williamsburg: The Story of a Patriot, an orientation film created for the Visitor Center.
 * Felicity: An American Girl Adventure; not filmed in Colonial Williamsburg, but takes places in-story. A special feature on the DVD contains Felicity actress, Shailene Woodley and her co-star visiting Colonial Williamsburg.
 * Episode 1 of season 3 of Mister T takes place in Colonial Williamsburg.
 * KaBlam! season 4 episode 3, "Holdeth the Pickle, Holdeth the Lettuce" takes place in Colonial Williamsburg.
 * Several locations were used throughout the George Washington (miniseries).
 * Certain locations such as the Public Gaol are used in John Adams to represent 18th century locations in Massachusetts.
 * Episode 17 of season 4 of The Goldbergs "Deadheads" the b-plot is about the family having a swear jar contest. If the kids fill it up then they'll go to Colonial Williamsburg again. If the parents fill it up then they'll take a trip to the Bahamas. The end scenes takes place on a tour in a colonial house (obviously not filmed on location) where Adam Goldberg disrupts the tour by dressing as a robot from the future.
 * Season 13 episode 8 of Lassie as part of a multi-episode story arc (Lassier the Voyager) of Lassie getting lost and finding her way back to the Rangers that she currently lives/works with at this point in the series. In part 3 she finds herself in Colonial Williamsburg, takes in some of the sights before winding up at a nearby turkey farm before being chased back to the Governor's Palace. Luckily for Lassie a local lawyer takes up her case to defend her from the farmer pressing charges.
 * In episode 1675 of Mister Rogers' Neighborhood, Fred Rogers goes to the millinery shop in Colonial Williamsburg to talk with some of the tradeswomen working there.
 * In 1978, there was a special called "Perry Como's Early American Christmas" aired on TV. Hosted by Perry Como and featuring one of the final appearances of John Wayne.
 * Some scenes were filmed in the Historic Area of Colonial Williamsburg for the feature film, "Sergeant Cheerleader" in 2009. Filmed by film students at William and Mary.

title: Colonial Williamsburg


text:
I Love the '70s

I Love the '70s may refer to:

 * I Love the '70s (British TV series), a BBC series examining the pop culture of the decade
 * I Love the '70s (American TV series), a VH1 series based on the British series
 * I Love the '70s: Volume 2, a follow-up to the VH1 series

title: I Love the '70s


text:
Network Control Protocol (ARPANET)

The Network Control Protocol (NCP) was a communication protocol for a computer network in the 1970s and early 1980s. It provided the transport layer of the protocol stack running on host computers of the ARPANET, the predecessor to the modern Internet.

NCP preceded the Transmission Control Protocol (TCP) as a transport layer protocol used during the early ARPANET. NCP was a simplex protocol that utilized two port numbers, establishing two connections, for two-way communications. An odd and an even port were reserved for each application layer application or protocol. The standardization of TCP and UDP reduced the need for the use of two simplex ports for each application down to one duplex port.

There is some confusion over the name, even among the engineers who worked with the ARPANET. Originally, there was no need for a name for the protocol stack as a whole, so none existed. When the development of TCP started, a name was required for its predecessor, and the pre-existing acronym 'NCP' (which originally referred to Network Control Program, the software which implemented this stack) was organically adopted for that use. Eventually, it was realized that the original expansion of that acronym was inappropriate for its new meaning, so a new quasi-backronym was created, 'Network Control Protocol' - again, organically, not via a formal decision.

History
NCP was first specified and described in the ARPANETs earliest RFC documents in 1969 after a series of meetings on the topic with engineers from UCLA, University of Utah, and SRI. It was finalized in in early 1970, and deployed to all nodes on the ARPANET in December 1970. It remained in use until the end of 1982; see Flag Day below.

NCP provided connections and flow control between processes running on different ARPANET host computers. Application services, such as remote login and the file transfer, would be built on top of NCP, using it to handle connections to other host computers.

On the ARPANET, the protocols in the physical layer, the data link layer, and the network layer used within the network were implemented on separate Interface Message Processors (IMPs). The host usually connected to an IMP using another kind of interface, with different physical, data link and network layer specifications. The IMP's capabilities were specified by the Host/IMP Protocol in BBN Report 1822.

Since lower protocol layers were provided by the IMP-host interface, NCP essentially provided a transport layer consisting of the ARPANET Host-to-Host Protocol (AHHP) and the Initial Connection Protocol (ICP). AHHP defined procedures to transmit a unidirectional, flow-controlled data stream between two hosts. The ICP defined the procedure for establishing a bidirectional pair of such streams between a pair of host processes. Application protocols (e.g., FTP) accessed network services through an interface to the top layer of the NCP, a forerunner to the Berkeley sockets interface.

Stephen D. Crocker, then a graduate student at UCLA, formed and led the Network Working Group (NWG) and specifically led the development of NCP. Other participants in the NWG developed application level protocols such as TELNET, FTP, and, in the 1980s, SMTP, among others.

Network Control Program
Network Control Program (usually given as NCP) was the name for the software on hosts which implemented the Network Control Protocol of the ARPANET.

It was almost universally referred to by the acronym, NCP. This was later taken over to refer to the protocol suite itself.

NCP's were written for many operating systems, including Multics, TENEX, UNIX and TOPS-10, and many of those NCP's survive (although of course they are now only used by vintage computer enthusiasts).

Transition to TCP/IP
On January 1, 1983, in what is known as a flag day, NCP was officially rendered obsolete when the ARPANET changed its core networking protocols from NCP to the more flexible and powerful TCP/IP protocol suite, marking the start of the modern Internet.

title: Network Control Protocol (ARPANET)


text:
User talk:MathMartin

 * Archive: - 2004
 * Archive: 2005
 * Archive: 2006

Closeness relations
I love your definition of continuity in terms of closeness relations! However, as has been pointed out on the talk page, "closeness relation" is not standard terminology. In the textbook Introduction to General Topology, K. D. Joshi uses the term "nearness relation" for the concept you describe.

More importantly, the axioms you list for a closeness relation are not equivalent to the ones given by Joshi, which are equivalent to the Kuratowski_closure_axioms. For example, your axioms do not guarantee that $$p \in A$$ implies $$p$$ close to $$A$$. This breaks the important connection between closeness and closure.

Also, your closeness relation between two sets is typically known as a "proximity" (again, see Joshi), and I think one of your axioms would have to be strengthened slightly to make your axioms equivalent to Joshi's.

With your permission, I would like to request that Closeness_(mathematics) be moved to Nearness relation (I can't move it myself, because my account isn't autoconfirmed yet), and make a major edit that changes the axioms and terminology to match Joshi's.

Vectornaut (talk) 00:57, 26 June 2009 (UTC)

Edit at Periodic point
You said:
 * Given a periodic point x with prime period t, then $$\Phi(t, x) = \Phi(t + s, x)$$ for all s in R

Are you sure? I don't really know anything about dynamical systems, but that doesn't sound right to me. This would make $$\Phi(a,x) = \Phi(b,x)$$ for all a and b, which means that $$\Phi(s,x) = x$$ for any s, which sounds far too restrictive. Staecker 19:36, 25 February 2007 (UTC)

 * Thanks, you are correct. I fixed my mistake. MathMartin 19:41, 25 February 2007 (UTC)

Hyperbolic fixed points
Hi, MathMartin!

I've been reading the new articles (Hartman-Grobman theorem, stable manifold theorem) that you've been writing lately, and doing my best to add references. You might want to take a look, to be sure you approve. If you have any reference information yourself, I'd be heppy to hear from you. The Hartman-Grobman name was fairly simple to track down, but the stable manifold theorem is giving me more trouble. It seems there are several of these, and the one you've written about is (I think) a result attributed to Ya. B. Pesin and D. Ruelle. Is that right? Thanks! DavidCBryant 00:11, 11 March 2007 (UTC)

 * Thanks for putting references in the article. I was unable to check the paper by Pesin. The paper by Ruelle seems to talk about a generalization of the basic stable manifold theorem.

 * I am currently working on articles connected with dynamical systems and I created Hartman-Grobman theorem, stable manifold theorem as stubs, because those articles are basic (important) theorems in the field needed for reference in other articles. The main problem with those articles is that their content is quite well known but there still do not exist canonical statements of those theorems. Especially the stable manifold theorem is giving me a headache because every author seems to proof a slightly different version of it. So basically I cannot provide solid reference for the theorems and I think in these cases it is neither possible nor useful. Dynamical systems is a very confusing topic because the terminology in the field is not yet standarized and before you can state any sort of interesting theorem, you first have to fix a notation.

 * On the other hand adding a reference to the first paper, the theorem was published in, is a very good idea and I would very much like to see wikipedia add original (historical) statements of important theorems to math articles.

 * I have been following your discussion at Wikipedia talk:WikiProject Mathematics about this topic and I understand that in order to increase the quality of the articles and fend of cranks we need references. But I think in this case it is not possible and at least I did not find any canonical and easy to understand version of the theorems on the net or in books. I must admit though that I am currently studying these topics so perhaps the wikipedia dynamical system expert(s) might disagree. MathMartin 14:59, 11 March 2007 (UTC)

Clenshaw algorithm
Hi there! I just came across Clenshaw algorithm which you wrote a while back. I wonder if you know of a good algorithm for finding Chebyshev coefficients for a given polynomial? I'd be interested to expand the Clenshaw algorithm page...could you point me to a good resource for finding materials about the algorithm? --HappyCamper 17:04, 10 May 2007 (UTC)

 * I have written the article quite some time ago (2 1/2 years) and I am not very deep into numerical analysis at the moment. Feel free to expand the article but I cannot provide any help. All the information I have on the Clenshaw algorithm is in the article :). You could ask User:Jitse Niesen for help, as he works in numerical analysis, or post a request at Wikipedia_talk:WikiProject_Mathematics, where the mathematicians hang out. Greetings. MathMartin 17:30, 10 May 2007 (UTC)
 * OK, I just might do that. Thanks for getting back to me! --HappyCamper 19:09, 10 May 2007 (UTC)

Mathematics CotW
Hey Martin, I am writing you to let you know that the Mathematics Collaboration of the week(soon to "of the month") is getting an overhaul of sorts and I would encourage you to participate in whatever way you can, i.e. nominate an article, contribute to an article, or sign up to be part of the project. Any help would be greatly appreciated, thanks--Cronholm144 23:18, 13 May 2007 (UTC)

Knot span
Another editor has added the "prod" template to the article Knot span, suggesting that it be deleted according to the proposed deletion process. All contributions are appreciated, but the editor doesn't believe it satisfies Wikipedia's criteria for inclusion, and has explained why in the article (see also What Wikipedia is not and Notability). Please either work to improve the article if the topic is worthy of inclusion in Wikipedia or discuss the relevant issues at its talk page. If you remove the prod template, the article will not be deleted, but note that it may still be sent to Articles for deletion, where it may be deleted if consensus to delete is reached. BJBot (talk) 05:16, 25 January 2008 (UTC)

WP Computing
Greetings. You are receiving this note as you are a member of this WikiProject. Currently there is not much of activity in the project and I am hoping to revive the project with your help. I have made a few changes to the project page Diff. You are welcome to make suggestions of improvement / changes in the design. I have also make a proposal to AutoTagg articles with WikiProject Computing for the descendant wikiprojects articles also. Please express your opinion here --  TinuCherian  (Wanna Talk?) - 12:55, 23 June 2008 (UTC)

Unreferenced BLPs
Hello MathMartin! Thank you for your contributions. I am a bot alerting you that 1 of the articles that you created  is an  Unreferenced Biography of a Living Person. Please note that all biographies of living persons must be sourced. If you were to add reliable, secondary sources to this article, it would greatly help us with the current Category:All_unreferenced_BLPs article backlog. Once the article is adequately referenced, please remove the unreferencedBLP tag. Here is the article:

Thanks!--DASHBot (talk) 19:35, 2 January 2010 (UTC)
 * 1) Reinhold Remmert -

Proposed deletion of Knot span

The article Knot span has been proposed for deletion  because of the following concern:
 * Wikipedia is not a dictionary, no reasonable claim of notability, article has been unsourced for six years.

While all contributions to Wikipedia are appreciated, content or articles may be deleted for any of several reasons.

You may prevent the proposed deletion by removing the  notice, but please explain why in your edit summary or on the article's talk page.

Please consider improving the article to address the issues raised. Removing  will stop the proposed deletion process, but other deletion processes exist. The speedy deletion process can result in deletion without discussion, and articles for deletion allows discussion to reach consensus for deletion. Beeblebrox (talk) 23:44, 19 September 2010 (UTC)

Nomination of Adjacent for deletion
A discussion is taking place as to whether the article Adjacent is suitable for inclusion in Wikipedia according to Wikipedia's policies and guidelines or whether it should be deleted.

The article will be discussed at Articles for deletion/Adjacent until a consensus is reached, and anyone is welcome to contribute to the discussion. The nomination will explain the policies and guidelines which are of concern. The discussion focuses on high-quality evidence and our policies and guidelines.

Users may edit the article during the discussion, including to improve the article to address concerns raised in the discussion. However, do not remove the article-for-deletion notice from the top of the article. Bg9989 (talk) 12:03, 9 March 2013 (UTC)

Class numbber (group theory) listed at Redirects for discussion
An editor has asked for a discussion to address the redirect Class numbber (group theory). Since you had some involvement with the Class numbber (group theory) redirect, you might want to participate in the redirect discussion if you have not already done so. Ten Pound Hammer • (What did I screw up now?) 22:51, 9 April 2014 (UTC)

ArbCom elections are now open!
MediaWiki message delivery (talk) 08:54, 23 November 2015 (UTC)

"Continuous linear form" listed at Redirects for discussion
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"Trivial extension" listed at Redirects for discussion
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title: User talk:MathMartin