text:
Cyanosis

Cyanosis is the change of body tissue color to a bluish-purple hue, as a result of decrease in the amount of oxygen bound to the hemoglobin in the red blood cells of the capillary bed. Cyanosis is apparent usually in the body tissues covered with thin skin, including the mucous membranes, lips, nail beds, and ear lobes. Some medications may cause discoloration such as medications containing amiodarone or silver. Furthermore, mongolian spots, large birthmarks, and the consumption of food products with blue or purple dyes can also result in the bluish skin tissue discoloration and may be mistaken for cyanosis. Appropriate physical examination and history taking is a crucial part to diagnose cyanosis. Management of cyanosis involves treating the main cause, as cyanosis isn’t a disease, it is a symptom.

Cyanosis is further classified into central cyanosis and peripheral cyanosis.

Pathophysiology
The mechanism behind cyanosis is different depending on whether it is central or peripheral.

Central cyanosis
Central cyanosis occurs due to decrease in arterial oxygen saturation (SaO2), and begins to show once the concentration of deoxyhemoglobin in the blood reaches a concentration of ≥ 5.0 g/dL (≥ 3.1 mmol/L or oxygen saturation of ≤ 85%). This indicates a cardiopulmonary condition.

Causes of central cyanosis are discussed below.

Peripheral cyanosis
Peripheral cyanosis happens when there is increased concentration of deoxyhemoglobin on the venous side of the peripheral circulation. In other words, cyanosis is dependent on the concentration of deoxyhemoglobin. Patients with severe anemia may appear normal despite higher-than-normal concentrations of deoxyhemoglobin. While patients with increased amounts of red blood cells (e.g., polycythemia vera) can appear cyanotic even with lower concentrations of deoxyhemoglobin.

Central cyanosis
Central cyanosis is often due to a circulatory or ventilatory problem that leads to poor blood oxygenation in the lungs. It develops when arterial oxygen saturation drops below 85% or 75%.

Acute cyanosis can be a result of asphyxiation or choking and is one of the definite signs that ventilation is being blocked.

Central cyanosis may be due to the following causes:

 * 1) Central nervous system (impairing normal ventilation):
 * 2) * Intracranial hemorrhage
 * 3) * Drug overdose (e.g., heroin)
 * 4) * Generalized tonic–clonic seizure (GTCS)
 * 5) Respiratory system:
 * 6) * Pneumonia
 * 7) * Bronchiolitis
 * 8) * Bronchospasm (e.g., asthma)
 * 9) * Pulmonary hypertension
 * 10) * Pulmonary embolism
 * 11) * Hypoventilation
 * 12) * Chronic obstructive pulmonary disease, or COPD (emphysema)
 * 13) Cardiovascular system:
 * 14) * Congenital heart disease (e.g., Tetralogy of Fallot, right to left shunts in heart or great vessels)
 * 15) * Heart failure
 * 16) * Valvular heart disease
 * 17) * Myocardial infarction
 * 18) Hemoglobinopathies:
 * 19) * Methemoglobinemia
 * 20) * Sulfhemoglobinemia
 * 21) * Polycythemia
 * 22) * Congenital cyanosis (HbM Boston) arises from a mutation in the α-codon which results in a change of primary sequence, H → Y. Tyrosine stabilizes the Fe(III) form (oxyhaemoglobin) creating a permanent T-state of Hb.Peripheral Cyanosis due to Ischemia.jpg.]]
 * 23) Others:
 * 24) * High altitude, cyanosis may develop in ascents to altitudes >2400 m.
 * 25) * Hypothermia
 * 26) * Frostbite
 * 27) * Obstructive sleep apnea

Peripheral cyanosis
Peripheral cyanosis is the blue tint in fingers or extremities, due to an inadequate or obstructed circulation. The blood reaching the extremities is not oxygen-rich and when viewed through the skin a combination of factors can lead to the appearance of a blue color. All factors contributing to central cyanosis can also cause peripheral symptoms to appear, but peripheral cyanosis can be observed in the absence of heart or lung failures. Small blood vessels may be restricted and can be treated by increasing the normal oxygenation level of the blood. Peripheral cyanosis may be due to the following causes:
 * All common causes of central cyanosis
 * Reduced cardiac output (e.g., heart failure or hypovolemia)
 * Cold exposure
 * Chronic obstructive pulmonary disease (COPD)
 * Arterial obstruction (e.g., peripheral vascular disease, Raynaud phenomenon)
 * Venous obstruction (e.g., deep vein thrombosis)

Differential cyanosis
Differential cyanosis is the bluish coloration of the lower but not the upper extremity and the head. This is seen in patients with a patent ductus arteriosus. Patients with a large ductus develop progressive pulmonary vascular disease, and pressure overload of the right ventricle occurs. As soon as pulmonary pressure exceeds aortic pressure, shunt reversal (right-to-left shunt) occurs. The upper extremity remains pink because deoxygenated blood flows through the patent duct and directly into the descending aorta while sparing the brachiocephalic trunk, left common carotid, and left subclavian arteries.

Evaluation
A detailed history and physical examination (particularly focusing on the cardiopulmonary system) can guide further management and help determine the medical tests to be performed. Tests that can be performed include pulse oximetry, arterial blood gas, complete blood count, methemoglobin level, electrocardiogram, echocardiogram, X-Ray, CT scan, cardiac catheterization, and hemoglobin electrophoresis.

In newborns, peripheral cyanosis typically presents in the distal extremities, circumoral, and periorbital areas. Of note, mucous membranes remain pink in peripheral cyanosis as compared to central cyanosis where the mucous membranes are cyanotic.

It is important to note that skin pigmentation and hemoglobin concentration can affect the evaluation of cyanosis. Cyanosis may be more difficult to detect on people with darker skin pigmentation. However, cyanosis can still be diagnosed with careful examination of the typical body areas such as nail beds, tongue, and mucous membranes where the skin is thinner and more vascular. As mentioned above, patients with severe anemia may appear normal despite higher than normal concentrations of deoxyhemoglobin. Signs of severe anemia may include pale mucosa (lips, eyelids, and gums), fatigue, lightheadedness, and irregular heartbeats.

Management
Cyanosis is a symptom not a disease itself, so management should be focused on treating the underlying cause.

If it is an emergency, management should always begin with securing the airway, breathing, and circulation. In patients with significant respiratory distress, supplemental oxygen (in the form of nasal canula or continuous positive airway pressure depending on severity) should be given immediately.

If the methemoglobin levels are positive for methemoglobinemia, first-line treatment is to administer methylene blue.

History
The name cyanosis literally means the blue disease or the blue condition. It is derived from the color cyan, which comes from cyanós (κυανός), the Greek word for blue.

It is postulated by Dr. Christen Lundsgaard that cyanosis was first described in 1749 by Jean-Baptiste de Sénac, a French physician who served King Louis XV. De Sénac concluded from an autopsy that cyanosis was caused by a heart defect that led to the mixture of arterial and venous blood circulation. But it was not until 1919, when Dr. Lundsgaard was able to derive the concentration of deoxyhemoglobin (8 volumes per cent) that could cause cyanosis.

title: Cyanosis


text:
White Book (CD standard)

The White Book refers to a standard of compact disc that stores not only sound but also still pictures and motion video. It was released in 1993 by Sony, Philips, Matsushita, and JVC. These discs, most commonly found in Asia, are usually called "Video CDs" (VCD). In some ways, VCD can be thought of as the successor to the Laserdisc and the predecessor to DVD. Note that Video CD should not be confused with CD Video which was an earlier and entirely different format.

Several extensions to the White Book were published in later years: VCD 2.0 in 1995, VCD-Internet in 1997, and Super Video CD (SVCD) in 1998. The standard is not freely available and must be licensed from Philips.

The White Book also defines the more general CD-i Bridge format (also called CD-Bridge or simply "bridge discs"), which are CD-ROM XA discs with an additional Green Book CD-i specific application program. The CD-ROM XA information in bridge discs can be obtained through CD-ROM drives, while CD-i players can use the CD-i program to read bridge discs as well (hence the "bridge" status between CD-ROMs and CD-i discs). Bridge discs must conform to both the CD-ROM XA and Green Book CD-i specifications. VCDs and SVCDs fall under the category of bridge discs, as do Photo CDs and Karaoke CDs.

The following is a summary of the specifications for VCDs and SVCDs. For more details, see Video CD and Super Video CD.

 * File system: ISO 9660-compliant
 * Format: Mode 2, Form 2/XA
 * Maximum Length: Usually 74 minutes
 * Audio Format
 * Format: MPEG-1 Audio Layer II
 * Bit rate: 224 kilobits per second
 * Sample rate: 44,100 Hz
 * Number of Channels: 2 (stereo)
 * Video Format
 * Format: MPEG-1 Part 2 (VCD), H.262/MPEG-2 Part 2 (SVCD)
 * Resolution: 352×240 pixel for NTSC video, 352×288 pixel for PAL video (VCD); 480×480 pixel for NTSC video, 480×576 for PAL video (SVCD)
 * Frame rate: 29.97 Hz (NTSC), 25 Hz (PAL)
 * Bit rate: 1150 kbit/s

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

title: White Book (CD standard)


text:
Johnny Sain

John Franklin "Johnny" Sain (September 25, 1917 – November 7, 2006) was an American right-handed pitcher in Major League Baseball who was best known for teaming with left-hander Warren Spahn on the Boston Braves teams from 1946 to 1951. He was the runner-up for the National League's Most Valuable Player Award in the Braves' pennant-winning season of 1948, after leading the National League in wins, complete games and innings pitched. He later became further well known as one of the top pitching coaches in the majors.

Military service
Beginning in late 1942, Sain served in the United States Navy during World War II. As a navy pilot, he spent the next three years stateside, while also playing baseball on the navy bases. He was discharged in November 1945.

Pitching star of post-war Boston Braves
Born in Havana, Arkansas, Sain pitched for 11 years, winning 139 games and losing 116 in his career and compiled an earned run average of 3.49. His best years were those immediately after World War II, when he won 100 games for the Boston Braves, before being traded to the New York Yankees during the 1951 season for Lew Burdette and cash.

Sain had the distinction of being the first pitcher in the Major Leagues to face Jackie Robinson. In 1943, while participating in a benefit game for the Red Cross, Sain became the last man to pitch against Babe Ruth in organized baseball.

In 1948, Sain won 24 games against 15 losses and finished second in the voting for the Most Valuable Player Award behind the St. Louis Cardinals' Stan Musial, who had won two legs of the Triple Crown. Sain and teammate Spahn achieved joint immortality that year when their feats were the subject of sports editor Gerald V. Hern's poem in the Boston Post which was eventually shortened to the epigram "Spahn and Sain; then pray for rain." According to the Baseball Almanac, the original doggerel appeared in Hern's column on September 14, 1948:

 First we'll use Spahn then we'll use Sain Then an off day followed by rain Back will come Spahn followed by Sain And followed we hope by two days of rain. The poem was inspired by the performance of Sain and Spahn during the Braves' 1948 pennant drive. The team swept a Labor Day doubleheader, with Spahn throwing a complete game 14-inning win in the opener, and Sain pitching a shutout in the second game. Following two off days, it did rain. Spahn won the next day, and Sain won the day after that. Three days later, Spahn won again. Sain won the next day. After one more off day, the two pitchers were brought back, and won another doubleheader. The two pitchers had gone 8–0 in twelve days' time.

That year, the Boston Braves won their second, latter National League pennant of the post-1901 era, but fell in six games to the Cleveland Indians in the 1948 World Series. Sain won the first game of the Series, a 1–0 shutout at Braves Field that included a memorable play in which Boston catcher Phil Masi was called safe after an apparent pickoff at second base. Masi went on to score the game's only run.

With the Yankees, Sain became a relief pitcher and enjoyed late-career success, leading the American League in saves with 22 in 1954. He finished his career in 1955 with the Kansas City Athletics.

When Sain was pitching, he thought that merely throwing the ball was not enough to get the ball to vary its course as it travelled to home plate. In order to throw a pitch such as a curveball or a screwball, he had to snap his wrist.

A very good hitting pitcher in his 11 year major league career, Sain posted a .245 batting average with 69 runs, 3 home runs and 101 RBI.

Pitching coach
After retiring as a player, Sain spent many years as a well-regarded and outspoken pitching coach for the Oakland Athletics, New York Yankees, Minnesota Twins, Detroit Tigers, Chicago White Sox and Atlanta Braves. During the 1960s, Sain coached the pitchers of five of the American League's ten pennant-winning teams.

While serving as the Yankees pitching coach, Sain picked up an apple one day and poked a broken car antenna through it. Spinning the apple, Sain came to the idea that he could do the same with a baseball by inserting a wooden rod into it, enabling him to spin the ball differently, imitating the spins used for different pitches. Sain eventually patented the idea and sold his product from his home in Arkansas.

An independent thinker among coaches, Sain tended to be admired by his pitchers, although he battled with at least two of his managers—Sam Mele of the Twins and Mayo Smith of the Tigers—when he disagreed with them. In each case, Sain was fired, but the manager's dismissal soon followed when his pitching staff suffered from Sain's absence. Sain did not make friends among owners and general managers, either, when he would advise pitchers to "climb those golden stairs" to their teams' front offices to demand more money in salary talks. Sain was also well known for ignoring running drills most pitchers despised. He frequently told pitchers and managers "You don't run the damn ball across the plate. If running did it, they'd look for pitchers on track teams."

Jim Bouton, in his book Ball Four, expressed unreserved admiration for Sain, who had been his pitching tutor in New York during his first two Major League seasons, 1962 and 1963. Bouton openly wished to pitch for the 1969 Tigers in order to have yet another opportunity to benefit from Sain's coaching. Sain and Bouton were briefly reunited in the Atlanta Braves system in 1978. Ned Garver said Sain was the best pitching coach he ever encountered. "If he had an idea that he thought could be of value to you, he would tell you about it to try to help you, but by the time he finished visiting with you about it, you would think that you'd thought of it yourself," Garver described Sain's approach.

Tommy John, on the other hand, had trouble working with Sain, who kept trying to get the pitcher to throw a slider, a pitch which always gave John trouble. "Sain could show you how to throw any pitch in the book, but he couldn't look at your motion and tell if your mechanics were off," recalled John. "For a sinkerballer [which John was], that spells trouble."

Pitchers who won 20 or more games under Sain's coaching include Jim Kaat, Whitey Ford, Mudcat Grant, Denny McLain, Jim Bouton, Al Downing, Jim Perry, Wilbur Wood, and Stan Bahnsen.

Personal life
Sain was married twice. His first wife was Doris May McBride of Dallas. They were married on October 1, 1945 and had four children: John Jr., Sharyl, Ronda and Randy. The couple divorced in 1970. Sain's second wife was Mary Ann Zaremba, whom he married on August 24, 1972. They had no children together. Sain was disabled by a stroke in 2002. He died at age 89 in Downers Grove, Illinois. At the time of his death, Sain had 11 grandchildren.

title: Johnny Sain


text:
Sirtaki

Sirtaki or syrtaki (συρτάκι) is a dance of Greek origin, choreographed for the 1964 film Zorba the Greek. It is a recent Greek folkdance, and a mixture of "syrtos" and the slow and fast rhythms of the hasapiko dance. The dance and the accompanying music by Mikis Theodorakis are also called Zorba's dance, the Zorba or "the dance of Zorba". The dance has become popular in Greece and is identified with the Greeks, becoming an invented tradition.

The name sirtaki comes from the Greek word syrtos – from σύρω (τον χορό), which means "drag (the dance)" or "lead (the dance)" – a common name for a group of traditional Greek dances of so-called "dragging" style, as opposed to pidikhtos (πηδηχτός), a hopping or leaping style. Despite its name, sirtaki incorporates both syrtos (in its slower part) and pidikhtós (in its faster part) elements.

Choreography
The dance was created specifically for the film Zorba the Greek rather than a traditional form of dance. The name sirtaki suggests it was created based on a traditional Cretan dance form "syrtos", a type of dance where the dancers drag their feet instead of hopping, however, the dance incorporates both a slower hasapiko dance style, and a faster hasaposerviko style. The dance is therefore an amalgamation of three different dance styles. It also has some characteristics of the zeybek dance. The choreography of the dance for the film has been attributed to Giorgos Provias.

During the filming of Zorba the Greek, Stelios Katsivelakis taught choreography to Anthony Quinn (although another dancer teacher contests this. claiming that several dancers, including himself, were involved in teaching Quinn), including various Greek dances such as the Kalamatianos, Chaniotikos syrtos (syrtos of Chania), pentozali with the psalidia (scissor-like) movements, and hasapiko. The zeibekiko was initially omitted, as the director felt it was not a suitable dance for a non-Greek and that the hasapiko looked better on screen. Quinn claimed that because he had problem doing a hopping motion due to a broken foot, he invented the dragging-sliding dance steps that he said a villager taught him, as well as coming up with its name on the fly when the film was being shot. Quinn could not perform the fast part of choreography planned for the final scene by the choreographer, and the choreography had to be changed on the spot. It is also claimed that this is the reason for having a crane shot moving away from the protagonists at the end of the film.

The dance was named Sirtaki at the first screening of the film.

Performance
Sirtaki can be danced in a line or circle formation with hands held on neighbours' shoulders. When performed alone, the dancer raises his arms horizontally on both sides of the body. Parts of the leg movements may be suggestive of crushing of grapes.

Meter is, tempo increasing, and often the signature is changed to 2/4 in the fastest part. Accordingly, the dance begins with slower, smoother actions, gradually transforming into faster, vivid ones, often including hops and leaps.

Guinness World Records
On August 31, 2012, the previous Sirtaki Dance Guinness World Record (Cyprus, 2010, 1672 persons) was broken by 5,614 people dancing sirtaki for five minutes by the sea, starting from the port of the city of Volos in Greece. The Association for Social Impact and Culture to the Municipality of Magnisia organized the event on the main beach of the town of Volos under the light of the second full moon of the month. Some 5,614 people, aged from 14 to 89, danced to the music of Mikis Theodorakis' Zorba the Greek, filling the town square and making it into the Guinness World Records. Enthusiasts from Volos, Larisa, Athens, Thessaloniki, Trikala, and the Greek islands joined the regional union of blind people, the national synchronized swimming team and many ordinary citizens. The idea came from a Volos resident, Alexia Halvatzakou, who suggested it to the municipal services as an alternative way to promote the area. The President of the Association for Social Impact and Culture, Costas Halevas, liked the idea and set about organizing the event.

title: Sirtaki


text:
Double negation

In propositional logic, the double negation of a statement states that "it is not the case that the statement is not true". In classical logic, every statement is logically equivalent to its double negation, but this is not true in intuitionistic logic; this can be expressed by the formula A ≡ ~(~A) where the sign ≡ expresses logical equivalence and the sign ~ expresses negation.

Like the law of the excluded middle, this principle is considered to be a law of thought in classical logic, but it is disallowed by intuitionistic logic. The principle was stated as a theorem of propositional logic by Russell and Whitehead in Principia Mathematica as:

 * $$\mathbf{*4\cdot13}. \ \ \vdash.\ p \ \equiv \ \thicksim(\thicksim p)$$
 * "This is the principle of double negation, i.e. a proposition is equivalent of the falsehood of its negation."

Elimination and introduction
Double negation elimination and double negation introduction are two valid rules of replacement. They are the inferences that, if not not-A is true, then A is true, and its converse, that, if A is true, then not not-A is true, respectively. The rule allows one to introduce or eliminate a negation from a formal proof. The rule is based on the equivalence of, for example, It is false that it is not raining. and It is raining.

The double negation introduction rule is:
 * P $$\Rightarrow$$ P

and the double negation elimination rule is:
 * P $$\Rightarrow$$ P

Where "$$\Rightarrow$$" is a metalogical symbol representing "can be replaced in a proof with."

In logics that have both rules, negation is an involution.

Formal notation
The double negation introduction rule may be written in sequent notation:
 * $$P \vdash \neg \neg P$$

The double negation elimination rule may be written as:
 * $$\neg \neg P \vdash P$$

In rule form:
 * $$\frac{P}{\neg \neg P}$$

and
 * $$\frac{\neg \neg P}{P}$$

or as a tautology (plain propositional calculus sentence):
 * $$P \to \neg \neg P$$

and
 * $$\neg \neg P \to P$$

These can be combined into a single biconditional formula:

 * $$ \neg \neg P \leftrightarrow P $$.

Since biconditionality is an equivalence relation, any instance of ¬¬A in a well-formed formula can be replaced by A, leaving unchanged the truth-value of the well-formed formula.

Double negative elimination is a theorem of classical logic, but not of weaker logics such as intuitionistic logic and minimal logic. Double negation introduction is a theorem of both intuitionistic logic and minimal logic, as is $$ \neg \neg \neg A \vdash \neg A $$. Because of their constructive character, a statement such as It's not the case that it's not raining is weaker than It's raining. The latter requires a proof of rain, whereas the former merely requires a proof that rain would not be contradictory. This distinction also arises in natural language in the form of litotes.

In classical propositional calculus system
In Hilbert-style deductive systems for propositional logic, double negation is not always taken as an axiom (see list of Hilbert systems), and is rather a theorem. We describe a proof of this theorem in the system of three axioms proposed by Jan Łukasiewicz:
 * A1. $$\phi \to \left( \psi \to \phi \right) $$
 * A2. $$\left( \phi \to \left( \psi \rightarrow \xi \right) \right) \to \left( \left( \phi \to \psi \right) \to \left( \phi \to \xi \right) \right)$$
 * A3. $$\left ( \lnot \phi \to \lnot \psi \right) \to \left( \psi \to \phi \right) $$

We use the lemma $$ p \to p$$ proved here, which we refer to as (L1), and use the following additional lemma, proved here:
 * (L2) $$p \to ((p \to q) \to q) $$

We first prove $$ \neg \neg p \to p$$. For shortness, we denote $$ q \to ( r \to q ) $$ by φ0. We also use repeatedly the method of the hypothetical syllogism metatheorem as a shorthand for several proof steps.
 * (1) $$\varphi_0$$       (instance of (A1))
 * (2) $$(\neg \neg \varphi_0 \to \neg \neg p ) \to (\neg p \to \neg \varphi_0)$$        (instance of (A3))
 * (3) $$ (\neg p \to \neg \varphi_0) \to (\varphi_0 \to p )$$        (instance of (A3))
 * (4) $$ (\neg \neg \varphi_0 \to \neg \neg p ) \to (\varphi_0 \to p )$$       (from (2) and (3) by the hypothetical syllogism metatheorem)
 * (5) $$\neg \neg p \to ( \neg \neg \varphi_0 \to \neg \neg p ) $$       (instance of (A1))
 * (6) $$\neg \neg p \to (\varphi_0 \to p )$$       (from (4) and (5) by the hypothetical syllogism metatheorem)
 * (7) $$\varphi_0 \to ((\varphi_0 \to p) \to p) $$       (instance of (L2))
 * (8) $$(\varphi_0 \to p) \to p $$       (from (1) and (7) by modus ponens)
 * (9) $$\neg \neg p \to p $$       (from (6) and (8) by the hypothetical syllogism metatheorem)

We now prove $$ p \to \neg \neg p $$.

 * (1) $$\neg\neg\neg p \to \neg p $$       (instance of the first part of the theorem we have just proven)
 * (2) $$ (\neg\neg\neg p \to \neg p) \to (p \to \neg\neg p) $$       (instance of (A3))
 * (3) $$ p \to \neg \neg p $$       (from (1) and (2) by modus ponens)

And the proof is complete.

title: Double negation


text: Talk:Ross Perot

title: Talk:Ross Perot


text:
User:Morganmichaels

hi, my name is probably Morgan Michaels.

Thank you for visiting.

title: User:Morganmichaels


text:
One-sided limit

In calculus, a one-sided limit refers to either one of the two limits of a function $$f(x)$$ of a real variable $$x$$ as $$x$$ approaches a specified point either from the left or from the right.

The limit as $$x$$ decreases in value approaching $$a$$ ($$x$$ approaches $$a$$ "from the right" or "from above") can be denoted:

$$\lim_{x \to a^+}f(x) \quad \text{ or } \quad \lim_{x\,\downarrow\,a}\,f(x) \quad \text{ or } \quad \lim_{x \searrow a}\,f(x) \quad \text{ or } \quad f(x+)$$

The limit as $$x$$ increases in value approaching $$a$$ ($$x$$ approaches $$a$$ "from the left" or "from below") can be denoted:

$$\lim_{x \to a^-}f(x) \quad \text{ or } \quad \lim_{x\,\uparrow\,a}\, f(x) \quad \text{ or } \quad \lim_{x \nearrow a}\,f(x) \quad \text{ or } \quad f(x-)$$

If the limit of $$f(x)$$ as $$x$$ approaches $$a$$ exists then the limits from the left and from the right both exist and are equal. In some cases in which the limit $$\lim_{x \to a} f(x)$$ does not exist, the two one-sided limits nonetheless exist. Consequently, the limit as $$x$$ approaches $$a$$ is sometimes called a "two-sided limit".

It is possible for exactly one of the two one-sided limits to exist (while the other does not exist). It is also possible for neither of the two one-sided limits to exist.

Definition
If $$I$$ represents some interval that is contained in the domain of $$f$$ and if $$a$$ is a point in $$I$$ then the right-sided limit as $$x$$ approaches $$a$$ can be rigorously defined as the value $$R$$ that satisfies: $$\text{for all } \varepsilon > 0\;\text{ there exists some } \delta > 0 \;\text{ such that for all } x \in I, \text{ if } \;0 < x - a < \delta \text{ then } |f(x) - R| < \varepsilon,$$ and the left-sided limit as $$x$$ approaches $$a$$ can be rigorously defined as the value $$L$$ that satisfies: $$\text{for all } \varepsilon > 0\;\text{ there exists some } \delta > 0 \;\text{ such that for all } x \in I, \text{ if } \;0 < a - x < \delta \text{ then } |f(x) - L| < \varepsilon.$$

We can represent the same thing more symbolically, as follows.

Let $$I$$ represent an interval, where $$I \subseteq \mathrm{domain}(f)$$, and $$a \in I $$.

\lim_{x \to a^{+}} f(x) = R

\iff

(\forall \varepsilon \in \mathbb{R}_{+}, \exists \delta \in \mathbb{R}_{+}, \forall x \in I,

(0 < x - a < \delta  \longrightarrow   | f(x) - R | < \varepsilon))

$$

\lim_{x \to a^{-}} f(x) = L

\iff

(\forall \varepsilon \in \mathbb{R}_{+}, \exists \delta \in \mathbb{R}_{+}, \forall x \in I,

(0 < a - x < \delta  \longrightarrow   | f(x) - L | < \varepsilon))

$$

Intuition
In comparison to the formal definition for the limit of a function at a point, the one-sided limit (as the name would suggest) only deals with input values to one side of the approached input value.

For reference, the formal definition for the limit of a function at a point is as follows:

\lim_{x \to a} f(x) = L

\iff

\forall \varepsilon \in \mathbb{R}_{+}, \exists \delta \in \mathbb{R}_{+}, \forall x \in I,

0 < |x - a| < \delta  \implies   | f(x) - L | < \varepsilon

.$$

To define a one-sided limit, we must modify this inequality. Note that the absolute distance between $$x$$ and $$a$$ is

$$|x - a| = |(-1)(-x + a)| = |(-1)(a - x)| = |(-1)||a - x| = |a - x|.$$

For the limit from the right, we want $$x$$ to be to the right of $$a$$, which means that $$a < x$$, so $$x - a$$ is positive. From above, $$x - a$$ is the distance between $$x$$ and $$a$$. We want to bound this distance by our value of $$\delta$$, giving the inequality $$x - a < \delta$$. Putting together the inequalities $$0 < x - a$$ and $$x - a < \delta$$ and using the transitivity property of inequalities, we have the compound inequality $$0 < x - a < \delta $$.

Similarly, for the limit from the left, we want $$x$$ to be to the left of $$a$$, which means that $$x < a$$. In this case, it is $$a - x$$ that is positive and represents the distance between $$x$$ and $$a$$. Again, we want to bound this distance by our value of $$\delta$$, leading to the compound inequality $$0 < a - x < \delta $$.

Now, when our value of $$x$$ is in its desired interval, we expect that the value of $$f(x)$$ is also within its desired interval. The distance between $$f(x)$$ and $$L$$, the limiting value of the left sided limit, is $$|f(x) - L|$$. Similarly, the distance between $$f(x)$$ and $$R$$, the limiting value of the right sided limit, is $$|f(x) - R|$$. In both cases, we want to bound this distance by $$\varepsilon$$, so we get the following: $$|f(x) - L| < \varepsilon$$ for the left sided limit, and $$|f(x) - R| < \varepsilon$$ for the right sided limit.

Examples
Example 1: The limits from the left and from the right of $$g(x) := - \frac{1}{x}$$ as $$x$$ approaches $$a := 0$$ are $$\lim_{x \to 0^-} {-1/x} = + \infty \qquad \text{ and } \qquad \lim_{x \to 0^+} {-1/x} = - \infty$$ The reason why $$\lim_{x \to 0^-} {-1/x} = + \infty$$ is because $$x$$ is always negative (since $$x \to 0^-$$ means that $$x \to 0$$ with all values of $$x$$ satisfying $$x < 0$$), which implies that $$- 1/x$$ is always positive so that $$\lim_{x \to 0^-} {-1/x}$$ diverges to $$+ \infty$$ (and not to $$- \infty$$) as $$x$$ approaches $$0$$ from the left. Similarly, $$\lim_{x \to 0^+} {-1/x} = - \infty$$ since all values of $$x$$ satisfy $$x > 0$$ (said differently, $$x$$ is always positive) as $$x$$ approaches $$0$$ from the right, which implies that $$- 1/x$$ is always negative so that $$\lim_{x \to 0^+} {-1/x}$$ diverges to $$- \infty.$$

Example 2: One example of a function with different one-sided limits is $$f(x) = \frac{1}{1 + 2^{-1/x}},$$ (cf. picture) where the limit from the left is $$\lim_{x \to 0^-} f(x) = 0$$ and the limit from the right is $$\lim_{x \to 0^+} f(x) = 1.$$ To calculate these limits, first show that $$\lim_{x \to 0^-} 2^{-1/x} = \infty \qquad \text{ and } \qquad \lim_{x \to 0^+} 2^{-1/x} = 0$$ (which is true because $$\lim_{x \to 0^-} {-1/x} = + \infty \text{ and } \lim_{x \to 0^+} {-1/x} = - \infty$$) so that consequently, $$\lim_{x \to 0^+} \frac{1}{1 + 2^{-1/x}} = \frac{1}{1 + \displaystyle\lim_{x \to 0^+} 2^{-1/x}} = \frac{1}{1 + 0} = 1$$ whereas $$\lim_{x \to 0^-} \frac{1}{1 + 2^{-1/x}} = 0$$ because the denominator diverges to infinity; that is, because $$\lim_{x \to 0^-} 1 + 2^{-1/x} = \infty.$$ Since $$\lim_{x \to 0^-} f(x) \neq \lim_{x \to 0^+} f(x),$$ the limit $$\lim_{x \to 0} f(x)$$ does not exist.

Relation to topological definition of limit
The one-sided limit to a point $$p$$ corresponds to the general definition of limit, with the domain of the function restricted to one side, by either allowing that the function domain is a subset of the topological space, or by considering a one-sided subspace, including $$p.$$ Alternatively, one may consider the domain with a half-open interval topology.

Abel's theorem
A noteworthy theorem treating one-sided limits of certain power series at the boundaries of their intervals of convergence is Abel's theorem.

title: One-sided limit


text:
Gregory Crewdson

Gregory Crewdson (born September 26, 1962) is an American photographer who makes large-scale, cinematic, psychologically charged prints of staged scenes set in suburban landscapes and interiors. He directs a large production and lighting crew to construct his images.

Early life and education
Crewdson was born in the Park Slope neighborhood of Brooklyn, New York. As a child, he attended Brooklyn Friends School, and then John Dewey High School.

As a teenager, he was part of a power pop group called the Speedies. Their song, "Let Me Take Your Foto" was in 2005 used by Hewlett-Packard in advertisements to promote its digital cameras.

Crewdson attended Purchase College, State University of New York, where he initially planned to study psychology. At Purchase, he enrolled in a photography course taught by Laurie Simmons and also studied with Jan Groover. He received an MFA in photography from the Yale School of Art.

Life and work
Crewdson is a professor and the director of graduate studies in photography at Yale School of Art.

Crewdson's photographs are elaborately planned, produced, and lit using crews familiar with motion picture production who light large scenes using cinema production equipment and techniques. He works with a lighting team, art director, make-up and wardrobe department, props and effects to create mood, atmosphere, and open-ended narrative images. He has worked with the same director of photography, Richard Sands, along with other core team members, for some 25 years. He works much like a director with a budget similar to that of a movie production, each image involves dozens of people and weeks to months of planning.

Using shots that resemble film productions, Crewdson deconstructs American suburban life in his work. He has cited the films Vertigo, The Night of the Hunter, Close Encounters of the Third Kind, Blue Velvet, and Safe as having influenced his style, as well as the painter Edward Hopper and photographer Diane Arbus.

Crewdson's most widely-known bodies of work include Twilight (1998–2002), Beneath the Roses (2003–2008), Cathedral of the Pines (2013–2014), An Eclipse of Moths (2018–2019), and Eveningside (2021–2022). Crewdson's only body of work made outside of the U.S. was Sanctuary (2009), set at the abandoned Cinecittá studios outside of Rome. Nearly all of his other work before and since was made in the small towns and cities in Western Massachusetts.

In 2012, he was the subject of the feature documentary film Gregory Crewdson: Brief Encounters. The film series followed the construction of and an explanation by Crewdson of his thought process and vision for pieces of Beneath the Roses.

Personal life
Crewdson lives primarily in western Massachusetts in a former Methodist church. His partner, Juliane Hiam, is a writer and producer and the two work closely together. Hiam has also appeared as a subject in numerous of Crewdson's pictures. He has two children, Lily and Walker, from a previous marriage to Ivy Shapiro. Crewdson is an open-water swimmer and has said that the meditative state he achieves with his daily swimming practice is fundamental to his creative process as an artist.

Publications

 * Hover. Artspace Books, 1995. ISBN 1891273000.
 * Twilight: Photographs by Gregory Crewdson. Harry N. Abrams, 2002. ISBN 0810910039. With an essay by Rick Moody.
 * Gregory Crewdson: 1985–2005. Hatje Cantz, 2005. ISBN 377571622X.
 * Fireflies. Skarstedt Fine Art, 2007. ISBN 0970909055.
 * Beneath the Roses. With Russell Banks. Harry N. Abrams, 2008. ISBN 978-0810993808.
 * Dream House. With text by Tilda Swinton. John Rule, 2009. ISBN 978-8888359410.
 * Sanctuary. With Anthony O. Scott. Hatje Cantz, 2010. ISBN 978-3775727341.
 * In a Lonely Place. Hatje Cantz, 2011. ISBN 978-3775731362.
 * Gregory Crewdson. New York: Rizzoli, 2013. ISBN 978-0847840915.
 * Cathedral of the Pines. New York: Aperture, 2016. ISBN 978-1-597113-50-2. With a text by Alexander Nemerov.
 * An Eclipse of Moths. New York: Aperture, 2020. ISBN 978-1683952213. With an introduction by Jeff Tweedy.
 * Alone Street. New York: Aperture, 2021. ISBN 978-1597115131. With an essay by Joyce Carol Oates and an interview with the artist by Cate Blanchett.
 * Gregory Crewdson: Eveningside, 2012–2022. Milan: Skira Editore, 2022. ISBN 8857248429. Text by Jean-Charles Vergne.
 * Gregory Crewdson. Munich, London, New York: Prestel, 2024. ISBN 9783791391243. Edited by Walter Moser, with texts by David Fincher, Daniela Hammer-Tugendhat, Beate Hofstadler, Astrid Mahler, Watler, Moser, Matthieu Orléan, and Emily St. John Mandel.

Solo exhibitions

 * Gregory Crewdson: Photographs, White Cube Gallery, London, 1995
 * Gregory Crewdson: Hover, Luhring Augustine Gallery, New York, NY, 1997
 * Gregory Crewdson. House Taken Over, Museo Nacional Centro de Arte Reina Sofía, Madrid, Spain, 1998; and traveled to Salamanca, 1999
 * Gregory Crewdson: Twilight, Luhring Augustine, New York, NY, 2002; White Cube, London, 2002; Gagosian Gallery, Beverly Hills, CA, 2002
 * Gregory Crewdson: Beneath the Roses, Luhring-Augustine Gallery, New York, 2005; White Cube, London, 2005; Gagosian Gallery, Beverly Hills, CA, 2005 (all three concurrently)
 * Gregory Crewdson: 1985–2005, Kunstverein Hannover, Hanover, Germany; and traveled to Kunstmuseen Krefeld, Germany, 2006; Fotomuseum Winterthur, Switzerland; and Landsgalerie Linz, Austria, 2006
 * Gregory Crewdson: Fireflies, Skarstedt Fine Art, New York, NY, 2006
 * Gregory Crewdson: Beneath the Roses Gagosian Gallery, Beverly Hills, CA, 2008; Gregory Crewdson, White Cube, London, 2008; Gregory Crewdson, Luhring Augustine, New York, NY, 2008
 * Gregory Crewdson: In a Lonely Place, traveling show, C/O Berlin, Berlin, 2011; Det Kongelige Bibliotek, Kulturhuset, Stockholm, Sweden, 2011; Copenhagen, Denmark, 2011/2012; Centre for Contemporary Photography, Melbourne, Australia, 2012; Institute of Modern Art, Brisbane, Australia, 2013; City Gallery Wellington; and Dunedin Art Gallery, Dunedin, New Zealand, 2013
 * Gregory Crewdson: Fireflies, Wave Hill, Bronx, NY, 2014; SITE Santa Fe, Santa Fe, NM, 2015; Berkshire Botanical Garden, Leonhardt Galleries, Stockbridge, MA, 2021
 * Gregory Crewdson: Sanctuary, Gagosian Gallery, New York, NY. 2010; Gagosian Gallery, Rome, Italy, 2011; TIFF '11 Festival, Toronto, Canada, 2011 La Fábrica Gallery, Madrid, Spain
 * Gregory Crewdson: Dream House, The San Diego Museum of Art, San Diego, CA, 2015
 * Cathedral of the Pines, Gagosian Gallery, New York, 2016; Galerie Templon, Brussels and Paris concurrently, September–October 2016; The Photographers' Gallery, London, 2017; Centre of Contemporary Art, Toruń, Poland, November 2017 – January 2018
 * Gregory Crewdson: Sanctuary, Galerie Wilma Tolksdorf, Frankfurt, Germany, April–July 2017
 * The Becket Pictures, FRAC Auvergne, Clermont-Ferrand, France, 2017
 * Gregory Crewdson: Eveningside (a survey of work from 2012 to 2022), Gallerie d'Italia, Turin, Italy, October 2022 – January 2023, exhibition traveled to the LUMA Foundation at Rencontres d'Arles, Arles, France, July–September 2023, and VB Photography Center, Kuopio, Finland, June 12-Sept. 15 2024
 * Gregory Crewdson: Forest Fables, University of San Diego, San Diego, CA, September–October 2023
 * Gregory Crewdson: Eveningside, Reflex Gallery, Amsterdam, Netherlands, Mar 11-May 6, 2023, Alan Koppel Gallery, Chicago, Apr 7-Aug 11 2023, Templon, Paris, France, Nov. 8-Dec. 23 2023
 * Gregory Crewdson: Retrospektive, The Albertina Museum, Vienna, Austria, May 29-Sept 8 2024

Awards

 * Aaron Siskind Foundation Individual Photographer's Fellowship
 * Skowhegan Medal for Photography, Skowhegan School of Painting and Sculpture, Skowhegan, ME.
 * Skowhegan Medal for Photography
 * National Endowment for the Arts fellowship
 * Honorary Doctorate, Montserrat College of Art, Beverly, MA.
 * Honorary Doctorate, SUNY Purchase, NY.
 * Distinguished Artist Award, St. Botolph Club Foundation, Boston, MA.

Collections
Crewdson's work is held in the permanent collections of major institutions worldwide, including:
 * Albertina Museum, Vienna
 * The Broad, Los Angeles
 * The Getty Museum, Los Angeles
 * Los Angeles County Museum of Art, Los Angeles
 * Metropolitan Museum of Art, New York
 * Museum of Modern Art, New York
 * San Francisco Museum of Modern Art, San Francisco
 * Solomon R. Guggenheim Museum
 * Victoria and Albert Museum, London
 * Whitney Museum, New York
 * Yale University Art Gallery, New Haven

Films about Crewdson

 * Gregory Crewdson: Brief Encounters (2012) – feature documentary directed, produced, and shot by Ben Shapiro
 * There But Not There (2017) – short documentary about Crewdson's casting process, directed by Juliane Hiam
 * Making Eveningside (2022) – short interpretive documentary directed by Harper Glantz, set to original music by Stuart Bogie and James Murphy (electronic musician) about the making of Eveningside

title: Gregory Crewdson


text:
Nizkor Project

The Nizkor Project (נִזְכּוֹר, "we will remember") is an Internet-based project run by B'nai Brith Canada which is dedicated to countering Holocaust denial.

About the project
The website was founded by Ken McVay as a central Web-based archive for the large numbers of documents made publicly available by the users of the newsgroup alt.revisionism and gifted to B'nai Brith Canada in 2010.

The site also archives numerous postings made to the newsgroup since the early 1990s. It does not archive every single posting ever made to the newsgroup; rather, the maintainers of the web site have selected various messages for display that are seen as presenting factual information about the Holocaust; or, in the case of some posters, about the authors of the messages themselves.

In addition to providing an extensive archive of documents regarding the Holocaust, including the transcripts of the 1st Nuremberg Tribunal, the Nizkor Project also seeks to expose the activities of Holocaust deniers themselves. Based on the postings to the newsgroup over the years, it has compiled extensive writings from self-proclaimed revisionists, including David Irving, Ernst Zündel, Michael A. Hoffman II, and others. Among the various pieces of information stored at Nizkor is a sound recording of an answering machine message allegedly made by white supremacist Tom Metzger, encouraging various individuals to "take action" against "Zinkor [sic] on the Internet."

In 2009, the Simon Wiesenthal Center congratulated the Nizkor Project for having initiated an effort which led to the successful prosecution of three Nazi war criminals.

Criticisms
Holocaust denial web sites and spokespersons challenged McVay's neutrality and attacked him personally. The original Nizkor web site was accused by self-proclaimed "Holocaust revisionists" and neo-Nazi Web sites as being funded by Israel and other Zionist sources, though McVay consistently denied these charges. He stated that the Nizkor Project was funded solely by donations from the general public, as well as his own personal finances.

In the late 1990s, the Simon Wiesenthal Center criticized the Nizkor Project for increasing the visibility of hate groups and Holocaust deniers, even as it sought to debunk them. This debate between free speech advocates such as McVay and those who favor the suppression of speech with hate crime laws continued throughout the late 1990s, but has now mostly been resolved with the two sides agreeing on the common goal of confronting Holocaust deniers and keeping their disagreements over specific tactics private. In 1996, McVay spoke out against Internet hate crime laws in Canada in front of a committee of the Canadian parliament, stating that it is better to address the false claims of Holocaust deniers, rather than to censor them.

title: Nizkor Project


text:
Inflection point

In differential calculus and differential geometry, an inflection point, point of inflection, flex, or inflection (rarely inflexion) is a point on a smooth plane curve at which the curvature changes sign. In particular, in the case of the graph of a function, it is a point where the function changes from being concave (concave downward) to convex (concave upward), or vice versa.

For the graph of a function $y = x^{3}$ of differentiability class $f$ (its first derivative $C^{2}$, and its second derivative $f'$, exist and are continuous), the condition $f ''$ can also be used to find an inflection point since a point of $f = ''0$ must be passed to change $f ='' 0$ from a positive value (concave upward) to a negative value (concave downward) or vice versa as $f ''$ is continuous; an inflection point of the curve is where $f ''$ and changes its sign at the point (from positive to negative or from negative to positive). A point where the second derivative vanishes but does not change its sign is sometimes called a point of undulation or undulation point.

In algebraic geometry an inflection point is defined slightly more generally, as a regular point where the tangent meets the curve to order at least 3, and an undulation point or hyperflex is defined as a point where the tangent meets the curve to order at least 4.

Definition
Inflection points in differential geometry are the points of the curve where the curvature changes its sign.

For example, the graph of the differentiable function has an inflection point at $f = ''0$ if and only if its first derivative $f'$ has an isolated extremum at $x$. (this is not the same as saying that $f$ has an extremum). That is, in some neighborhood, $x$ is the one and only point at which $f'$ has a (local) minimum or maximum. If all extrema of $f'$ are isolated, then an inflection point is a point on the graph of $f$ at which the tangent crosses the curve.

A falling point of inflection is an inflection point where the derivative is negative on both sides of the point; in other words, it is an inflection point near which the function is decreasing. A rising point of inflection is a point where the derivative is positive on both sides of the point; in other words, it is an inflection point near which the function is increasing.

For a smooth curve given by parametric equations, a point is an inflection point if its signed curvature changes from plus to minus or from minus to plus, i.e., changes sign.

For a smooth curve which is a graph of a twice differentiable function, an inflection point is a point on the graph at which the second derivative has an isolated zero and changes sign.

In algebraic geometry, a non singular point of an algebraic curve is an inflection point if and only if the intersection number of the tangent line and the curve (at the point of tangency) is greater than 2. The main motivation of this different definition, is that otherwise the set of the inflection points of a curve would not be an algebraic set. In fact, the set of the inflection points of a plane algebraic curve are exactly its non-singular points that are zeros of the Hessian determinant of its projective completion.

A necessary but not sufficient condition
For a function f, if its second derivative $(x, f(x))$ exists at $f(x) = sin(2x)$ and $f(x) = –4sin(2x)$ is an inflection point for $f$, then $f(x)$, but this condition is not sufficient for having a point of inflection, even if derivatives of any order exist. In this case, one also needs the lowest-order (above the second) non-zero derivative to be of odd order (third, fifth, etc.). If the lowest-order non-zero derivative is of even order, the point is not a point of inflection, but an undulation point. However, in algebraic geometry, both inflection points and undulation points are usually called inflection points. An example of an undulation point is $x_{0}$ for the function $f$ given by $x_{0}$.

In the preceding assertions, it is assumed that $f$ has some higher-order non-zero derivative at $f$, which is not necessarily the case. If it is the case, the condition that the first nonzero derivative has an odd order implies that the sign of $f(x_{0}) = 0$ is the same on either side of $x$ in a neighborhood of $x$. If this sign is positive, the point is a rising point of inflection; if it is negative, the point is a falling point of inflection.

Inflection points sufficient conditions:
 * 1) A sufficient existence condition for a point of inflection in the case that $x = 0$ is $x$ times continuously differentiable in a certain neighborhood of a point $k$ with $x_{0}$ odd and $f(x) = x^{4}$, is that  $f'(x)$ for $f(x)$ and $k ≥ 3$. Then $f(x_{0}) = 0$ has a point of inflection at $n = 2, ..., k − 1$.
 * 2) Another more general sufficient existence condition requires $f(x_{0}) ≠ 0$ and $f(x)$ to have opposite signs in the neighborhood of $x_{0}$ (Bronshtein and Semendyayev 2004, p. 231).

Categorization of points of inflection

Points of inflection can also be categorized according to whether $f(x_{0} + ε)$ is zero or nonzero.
 * if $f(x_{0} − ε)$ is zero, the point is a stationary point of inflection
 * if $x_{0}$ is not zero, the point is a non-stationary point of inflection

A stationary point of inflection is not a local extremum. More generally, in the context of functions of several real variables, a stationary point that is not a local extremum is called a saddle point.

An example of a stationary point of inflection is the point $y = x^{4} – x$ on the graph of $f'(x)$. The tangent is the $k$-axis, which cuts the graph at this point.

An example of a non-stationary point of inflection is the point $f'(x)$ on the graph of $f'(x)$, for any nonzero $x$. The tangent at the origin is the line $(0, 0)$, which cuts the graph at this point.

Functions with discontinuities
Some functions change concavity without having points of inflection. Instead, they can change concavity around vertical asymptotes or discontinuities. For example, the function $$x\mapsto \frac1x$$ is concave for negative $a$ and convex for positive $x$, but it has no points of inflection because 0 is not in the domain of the function.

Functions with inflection points whose second derivative does not vanish
Some continuous functions have an inflection point even though the second derivative is never 0. For example, the cube root function is concave upward when x is negative, and concave downward when x is positive, but has no derivatives of any order at the origin.

title: Inflection point


text:
Lynette Woodard

Lynette Woodard (born August 12, 1959) is an American basketball player and former head women's basketball coach at Winthrop University.

Woodward played college basketball for the Kansas Jayhawks. She became the first female member of the Harlem Globetrotters and, at age 38, began playing as one of the oldest members in the newly formed American women's professional basketball league, the WNBA. She is a member of the Basketball Hall of Fame.

Biography
Woodward led Wichita North High School to state basketball championships in 1975 and 1977. She scored 1,678 points and collected 1,030 rebounds in just 62 high school games in three seasons.

Woodard went on to play college basketball with the University of Kansas (KU) in 1978, playing there until 1981 in the AIAW era of college basketball. She was a four-time All-American at KU, and averaged 26 points per game and scored 3,649 points in total during her four years there, and was the first KU woman to be honored by having her jersey retired. Before being passed by Caitlin Clark of Iowa on February 28, 2024, Woodard was the unofficial major college basketball's career women's scoring leader due to the NCAA not recognizing statistics from the AIAW.

In 1981, she was signed by an Italian team, UFO Schio (Vicenza), to participate in their league.

In 1984, she was a member of the United States women's basketball team that won the gold medal at the Los Angeles Olympic Games.

In 1985, Woodard became the first woman ever to play with the Globetrotters. Incidentally, Woodard's cousin, Hubert "Geese" Ausbie, also played for the Globetrotters from 1961 to 1985.

In 1989, she was inducted into the National High School Hall of Fame. In 1990, she was inducted into the Kansas Sports Hall of Fame, and was signed by a Japanese women's team to play in their country. She played there until 1993.

In 1997, she was signed by the Cleveland Rockers of the newly founded Women's National Basketball Association (WNBA). The following year, she was selected in an expansion draft by the Detroit Shock. Woodard's final WNBA game ever was played on August 19, 1998, in a 82–68 win over the New York Liberty where she recorded 18 points, 9 rebounds, 3 assists and 2 steals. She was waived by the Shock on May 7, 1999. During the WNBA's off-season, she began working as a stockbroker in New York City.

She retired from playing in 1999 and returned to KU serving as assistant coach of the women's basketball team. In late January 2004, she was named interim head coach, filling for the regular coach Marian Washington, who had retired for medical reasons. She also served as athletics director for the Kansas City, Missouri School District from 1992 to 1994.

In September 2004, she was inducted into the Naismith Memorial Basketball Hall of Fame in Springfield, Massachusetts. In June 2005, she was inducted into the Women's Basketball Hall of Fame in Knoxville, Tennessee.

Woodard also received the 2015 WBCBL Women's Professional Basketball "Trailblazer" Award on August 2, 2015, along with 9 other female basketball Icons including Cynthia Cooper, Nancy Lieberman, Sarah Campbell, E.C. Hill, Geri Kay Hart, Robelyn Garcia, Kandi Conda, Lisa Leslie and Tamika Catchings. The award recognizes some of the most influential people in professional women's basketball, specifically those who helped blaze the trail, shape the overall landscape and pave the way for women's professional basketball.

Woodard became a financial consultant for A.G. Edwards & Sons Inc., in Wichita.

In 2017, she was named the head coach of the Winthrop Eagles women's basketball team.

USA Basketball
Woodard was named to the team representing the US at the 1979 World University Games, held in Mexico City, Mexico. The USA team won all seven games to take the gold medal. The USA team played and beat Cuba twice, the team that had defeated them at the Pan Am games. Woodard averaged 14.1 points per game.

Woodard was selected to be a member of the team representing the US at the 1980 Olympics, but the team did not go, due to the 1980 Olympic boycott. The team did go 6–1 in Olympic Qualifying games, with Woodard scoring 4.5 points per game.

Woodard was selected to be a member of the team representing the US at the 1983 Pan American Games held in Caracas, Venezuela. The team won all five games to earn the gold medal for the event. Woodard averaged 19.0 points per game and 4.0 rebounds per game, both second best on the team.

Woodard played for the USA National team in the 1983 World Championships, held in Sao Paulo, Brazil. The team won six games, but lost two against the Soviet Union. In an opening round game, the USA team had a nine-point lead at halftime, but the Soviets came back to take the lead, and a final shot by the USA failed to drop, leaving the USSR team with a one-point victory 85–84. The USA team won their next four games, setting up the gold medal game against the USSR. This game was also close, and was tied at 82 points each with six seconds to go in the game. The Soviets' Elena Chausova received the inbounds pass and hit the game winning shot in the final seconds, giving the USSR team the gold medal with a score of 84–82. The USA team earned the silver medal. Woodard averaged 15.8 points per game, second highest on the team, and recorded 33 steals to lead the team.

Woodard was a member of the USA National team at the 1990 World Championships, held in Kuala Lumpur, Malaysia. The team won their opening round games fairly easily, with the closest of the first three games a 27-point victory over Czechoslovakia. Then they faced Cuba, a team that had beaten the US in exhibition matches only a few weeks earlier. The USA team was losing at halftime, but came back to win 87–78. The USA team found itself behind at halftime to Canada in their next game, but came back to win easily 95–70. After an easy match against Bulgaria, the USA team faced Czechoslovakia again, and achieved an almost identical result, winning 87–59. In the title match, the USA team won the gold medal with a score of 88–78. Woodard averaged 6.3 points per game.

In 1984, the USA sent its National team to the 1984 William Jones Cup competition in Taipei, Taiwan, for pre-Olympic practice. The team easily beat each of the eight teams they played, winning by an average of just under 50 points per game. Woodard averaged 11.6 points per game.

Woodard played with the USA team at the 1991 Pan American Games. The team finished with a record of 4–2, but managed to win the bronze medal. The USA team lost a three-point game to Brazil, then responded with wins over Argentina and Cuba, earning a spot in the medal round. The next game was a rematch against Cuba, and this time the team from Cuba won a five-point game. The USA beat Canada to win the bronze. Woodard averaged 2.3 points per game.

Awards and honors

 * 1981: Winner of the Broderick Award (now the Honda Sports Award) for basketball
 * 1981: Wade Trophy
 * 2015: WBCBL Professional Basketball Trailblazer Award
 * 2020: Brookwood Alpacas Elementary Award Kansas Stats

title: Lynette Woodard


text:
Mertens conjecture

In mathematics, the Mertens conjecture is the statement that the Mertens function $$M(n)$$ is bounded by $$\pm\sqrt{n}$$. Although now disproven, it had been shown to imply the Riemann hypothesis. It was conjectured by Thomas Joannes Stieltjes, in an 1885 letter to Charles Hermite (reprinted in ), and again in print by, and disproved by. It is a striking example of a mathematical conjecture proven false despite a large amount of computational evidence in its favor.

Definition
In number theory, the Mertens function is defined as

 * $$M(n) = \sum_{1 \le k \le n} \mu(k),$$

where μ(k) is the Möbius function; the Mertens conjecture is that for all n > 1,

 * $$|M(n)| < \sqrt{n}.$$

Disproof of the conjecture
Stieltjes claimed in 1885 to have proven a weaker result, namely that $$m(n) := M(n)/\sqrt{n}$$ was bounded, but did not publish a proof. (In terms of $$m(n)$$, the Mertens conjecture is that $$ -1 < m(n) < 1 $$.)

In 1985, Andrew Odlyzko and Herman te Riele proved the Mertens conjecture false using the Lenstra–Lenstra–Lovász lattice basis reduction algorithm:
 * $$\liminf m(n) < -1.009 $$ and  $$ \limsup m(n) > 1.06.$$

It was later shown that the first counterexample appears below $$e^{3.21\times10^{64}} \approx 10^{1.39\times10^{64}}$$ but above 1016. The upper bound has since been lowered to $$e^{1.59\times10^{40}}$$ or approximately $$10^{6.91\times10^{39}},$$ and then again to $$e^{1.017\times10^{29}} \approx 10^{4.416\times10^{28}}$$, but no explicit counterexample is known.

The law of the iterated logarithm states that if $μ$ is replaced by a random sequence of +1s and −1s then the order of growth of the partial sum of the first $n$ terms is (with probability 1) about $√n log log n$, which suggests that the order of growth of $m(n)$ might be somewhere around $√log log n$. The actual order of growth may be somewhat smaller; in the early 1990s Steve Gonek conjectured that the order of growth of $m(n)$ was $$(\log\log\log n)^{5/4},$$ which was affirmed by Ng (2004), based on a heuristic argument, that assumed the Riemann hypothesis and certain conjectures about the averaged behavior of zeros of the Riemann zeta function.

In 1979, Cohen and Dress found the largest known value of $$m(n) \approx 0.570591$$ for $M(7766842813) = 50286,$ and in 2011, Kuznetsov found the largest known negative value (in the sense of absolute value) $$m(n) \approx -0.585768$$ for $M(11609864264058592345) = −1995900927.$ In 2016, Hurst computed $M(n)$ for every $n ≤ 10^{16}$ but did not find larger values of $m(n)$.

In 2006, Kotnik and te Riele improved the upper bound and showed that there are infinitely many values of $n$ for which $m(n) > 1.2184$, but without giving any specific value for such an $n$. In 2016, Hurst made further improvements by showing
 * $$\liminf m(n) < -1.837625 $$ and  $$ \limsup m(n) > 1.826054.$$

Connection to the Riemann hypothesis
The connection to the Riemann hypothesis is based on the Dirichlet series for the reciprocal of the Riemann zeta function,

 * $$\frac{1}{\zeta(s)} = \sum_{n=1}^\infty \frac{\mu(n)}{n^s},$$

valid in the region $$\mathcal{Re}(s) > 1$$. We can rewrite this as a Stieltjes integral

 * $$\frac{1}{\zeta(s)} = \int_0^\infty x^{-s} dM(x)$$

and after integrating by parts, obtain the reciprocal of the zeta function as a Mellin transform

 * $$\frac{1}{s \zeta(s)} = \left\{ \mathcal{M} M \right\}(-s)

= \int_0^\infty x^{-s} M(x)\, \frac{dx}{x}.$$

Using the Mellin inversion theorem we now can express $M$ in terms of $1/ζ$ as

 * $$M(x) = \frac{1}{2 \pi i} \int_{\sigma-i\infty}^{\sigma+i\infty} \frac{x^s}{s \zeta(s)}\,ds$$

which is valid for $1 < σ < 2$, and valid for $1/2 < σ < 2$ on the Riemann hypothesis. From this, the Mellin transform integral must be convergent, and hence $M(x)$ must be $O(x^{e})$ for every exponent e greater than $1⁄2$. From this it follows that
 * $$M(x) = O\Big(x^{\tfrac{1}{2} + \epsilon}\Big)$$

for all positive $ε$ is equivalent to the Riemann hypothesis, which therefore would have followed from the stronger Mertens hypothesis, and follows from the hypothesis of Stieltjes that
 * $$M(x) = O\Big(x^\tfrac{1}{2}\Big).$$

title: Mertens conjecture


text:
The Dish

The Dish is a 2000 Australian historical comedy-drama film that tells the story of the Parkes Observatory's role in relaying live television of humanity's first steps on the Moon during the Apollo 11 mission in 1969. It was the top-grossing Australian film in 2000.

Plot
An old man drives up to the Parkes Radio Telescope to admire the dish. A technician gently cautions him that he has driven in through "the old entrance" and is therefore trespassing. Requesting that the man leave immediately, the technician encourages him to visit the observatory's nearby visitor centre and take the tour, as the dish has seen some amazing times. The old man thoughtfully agrees.

The movie flashes back to July, 1969, days before the launch of Apollo 11. NASA anticipates using the dish as a primary receiving antenna for the video transmission of Neil Armstrong's historic first steps on the Moon. The dish’s staff, Mitch, Glenn, and their boss, Cliff (the old man from the prologue) have been assigned a liaison by NASA, Al Burnett. Mitch resents Al, as he feels that Al is condescending; and that his presence likewise reflects a wider perception among NASA that the Australians are incompetent and unreliable. Cliff chastises Mitch for his hostility, explaining that Al's presence is justified, and that he and NASA merely want to ensure that the Moon landing proceeds as smoothly as possible. The major role that the dish is set to play in the Moon landing draws great interest upon the sleepy town of Parkes from major dignitaries, including the U.S. Ambassador and the Prime Minister. Parkes mayor, Bob, is delighted, as he played a key role in securing the dish's construction at Parkes, and thus the dish's prominent role in the Moon landing will be a boon to his political career.

A power cut strikes Parkes. The dish’s backup generator fails, as Mitch had previously conducted a maintenance procedure on it incorrectly. When the mains power returns, the station's tracking computers have been wiped of all their programming, and the dish can no longer locate Command Module Columbia's signal in space. Houston notices that they are no longer receiving any information from the Parkes station and queries them about the problem. Fearing that NASA may demote the team’s role in the Moon landing if it learns of the mistake, Cliff falsely responds that the dish is receiving a clear signal from the spacecraft. Al reluctantly corroborates the lie. Mitch confesses his own culpability to Al, who immediately forgives him, mending their strained relationship. The four men work together to try to relocate Apollo 11’s signal. After several hours and mishaps, they are able to lock on to the spacecraft's signal with minutes to spare before their scheduled shift as Apollo 11's main receiver begins, thus ensuring their mistake has gone undiscovered.

After the Lunar Module Eagle makes a successful landing upon the Moon, Cliff notes with concern that the wind seems unusually strong. Regulations state that if the wind reaches 30 knots, the dish must be "stowed", meaning it can not be pointed at the Moon, and thus will not be able to receive Eagle's video broadcasts. Events conspire such that the Parkes dish becomes the only antenna on Earth capable of receiving the historic video footage of Armstrong's first steps upon the Moon.

The wind reaches and exceeds 30 knots. Despite risking the total collapse of the dish, and therefore, their own lives, all four members of the dish team opt to keep the dish pointed at the Moon, adamant that allowing the world to witness and record the first moonwalk is worth the risk.

The world watches in silent awe as man sets foot upon the Moon. As the Prime Minister, the ambassador, and Parkes dignitaries watch the moonwalk together, Bob is informed that the video feed is coming from the dish. Everybody is delighted, and the Prime Minister toasts Parkes. As the moonwalk concludes, the dish staff congratulate one another.

Back in the present day, the technician once again insists that Cliff must leave. Cliff solemnly takes one last look at the dish before returning to his car. Before he leaves, the technician remarks that Cliff seems familiar, suggesting that Cliff's legacy is immortalized within the observatory's visitor centre.

A title card explains that the dish withstood winds of over 60 mph to deliver the video footage of man walking on the Moon.

Production

Much of the film was shot on location; the "cricket match" and "hayride" scenes were shot on the real dish and researchers often postponed experiments to position the dish for photography. The set reconstructing the 1969 control room was extremely accurate, down to some details as small as ashtrays. Some of the "props" were in fact original NASA equipment used during the Apollo 11 landing, left behind in Australia as they were too heavy (i.e. too expensive) to ship back to the U.S. Staff from that era expressed amazement at seeing the set; they said it was like stepping through a time warp.

The Dish was written by Santo Cilauro, Tom Gleisner, Jane Kennedy and Rob Sitch, and directed by Sitch.

Apart from the radio telescope scenes, the majority of the movie was actually filmed in the small town of Forbes, 33 km south of Parkes because of its old historic buildings, and also in Old Parliament House in Canberra, and Crawford Studios in Melbourne.

Historical accuracy
Although the film is based on actual events, it uses fictional characters and alters historical details for dramatic effect. NASA's Honeysuckle Creek near Canberra and the Goldstone station in California both had the signal first, but Parkes's signal was used eight and a half minutes after the beginning of the moonwalk. Armstrong's first step on the Moon and his words, "That's one small step for man, one giant leap for mankind", were received on Earth by the Honeysuckle Creek antenna. No power failure occurred, there was no friction with the NASA representatives (of whom there were not just one but several), and Prime Minister John Gorton visited Honeysuckle Creek, not Parkes. They did, however, operate in very high winds gusting to 110 km/h at 60 degrees inclination, risking damage to the dish and even injury to themselves to keep the antenna pointed at the Moon during the moonwalk. Also the Moon was not full in the preceding two weeks prior the Moon landing, while in the movie they used a full moon to retrieve the signal.

Box office
The Dish had three days of paid previews prior to its official opening in Australia on 19 October 2000. During its official opening (four-day) weekend, it had a record opening weekend for an Australian film with gross of $2.98 million from 281 screens. Including the previews, its gross was $4.3 million (US$2.25 million). It went on to gross $17,999,473 at the box office in Australia, and was the top grossing Australian film in Australia in 2000.

Reception
On the review aggregator Rotten Tomatoes, the film holds a 96% approval rating based on 99 reviews, with an average rating of 7.4/10. The website's critics consensus reads: "A feel good movie without an abundance of mush."

title: The Dish


text:
Bishop Asbury Cottage

Bishop Asbury Cottage is a 17th-century cottage on Newton Road, Great Barr, England, known for being the boyhood home of Francis Asbury (1745 – 1816), one of the first two bishops of the Methodist Episcopal Church (now The United Methodist Church) in the United States. It is now a museum in his memory.

Architecture
The single-storey cottage, then in Staffordshire, was built c. 1700 from brick. It has an attic with dormer windows, tiled roof and rendered plinth.

The Asburys
Asbury was born in nearby Hamstead in 1745 and the family moved to the cottage the next year. Asbury worshipped as a Methodist at nearby Wednesbury. He had an apprenticeship as a blacksmith before becoming a full-time preacher, at the age of 21.

He left for America in 1771, never to return. His family remained at the cottage until the death of his mother Eliza in 1802. During that time, the cottage was used for religious worship. These services continued after the death of Asbury's parents and eventually the cause moved to "The Institute" across the road, which eventually became the Newton Road United Reformed Church which continued until 2017.

Later history
By the 1950s, the cottage was owned by a brewery, but had no running water and only a cesspit toilet. It was occupied by a Mrs Randles and her daughter Mrs Searle, who often showed visiting American Methodists around the building. The brewery applied for permission to demolish it, but this was refused at the behest of local councillor Mrs Parfitt, a Methodist, once its history became apparent. In around 1955, the cottage was purchased by the local council, who then rehoused the occupants.

The building was part of a terraced pair, but in 1964 the adjacent, southern, cottage was demolished when Newton Road (designated the A4041) was widened. Local legend has it that it was the demolished cottage which was the Asburys', but documentary evidence in Sandwell Museum disproves this.

A Grade II listed building since September 1955, the cottage is now operated as a museum, furnished in period style, with memorabilia and information relating to Asbury's life in West Bromwich and Great Barr in England and later in the United States. It also has displays about the rise of Methodism in the surrounding Black Country, and John Wesley's life and times, and visits to the local area.

title: Bishop Asbury Cottage


text:
Talk:National Liberal Party (UK)

Relevant
Is it relevant to mention this group with only 25 members in 2007?

Lloyd George
Lloyd George is described on the Prime Minister of the United Kingdom page as being a "National Liberal" during his tenure 1916-22; is this just a previous use of the name, or was there any relationship between the two? Psmith 09:42, 26 Nov 2003 (UTC)

They were a different group altogether, though annoyingly the same term is frequently used for both. The Liberals split during the First World War but reunified in 1923. Another split occurred in 1931 and just to confuse things even further a tiny group of Liberals followed Lloyd George (most were members of his family) in complete opposition to the National Government whilst the two main groups remained in government during the general election.

Both groups
Perhaps this article should mention both groups of National Liberals, perhaps with a horizontal border (like above) between them G-Man 00:41, 3 Jan 2004 (UTC)

First half
The first half of this article is hopeless. It doesn't actually say anywhere which group of Liberals was which, or who led which one. Someone needs to improve it. Thedreamdied 13:16, 28 October 2006 (UTC)

Simonites - one to watch out for
There's a major book on the Liberal Nationals due out in a couple of months called "Liberals in Schism: A History of the National Liberal Party" by David Dutton. It will be the first significant work on the party, including its origins, exactly when it became a clear separate party (something that in places at the local level wasn't clear for the entire decade) and its nature in the post war period (when it's traditionally written off as being just being a name used by a few post merger). When it comes out I'll aim to expand the article a bit, but we may want to split the Simonite party into an article in its own right. Timrollpickering (talk) 21:17, 24 February 2008 (UTC)
 * Any word on this? Also, who were the leaders of the party after 1945, if any?  john k (talk) 02:48, 14 June 2009 (UTC)

Splitting
This article needs splitting, we shouldn't have three separate entities discussed in the same article. Fences &  Windows  01:04, 18 February 2010 (UTC)

Separate pages please
While I think some of the criticism above is over the top, I do agree that it would make more sense to have separate pages, one dealing with the Lloyd George National Liberals of 1922 and another for the later group formed at the time of the National Government in 1931 which eventually merged with the Conservative Party. This makes more sense as the two groups are not connected either in terms of continuity of history or significant overlap of personnel. If we do have two separate pages, the section about the Third Way grouping which has no true connection with the historic Liberal Party, could disappear or the name National Liberal Party - the Third Way, could simply redirect to the main Third Way (UK) page.

Also, the page List of National Liberal Party (UK) MPs deals exclusively with the 1931-1947 entity, which is quite right but some may think it odd not to find the Lloyd George MPs included. If we separate the pages, a new page listing all the MPs elected in 1922 as LG National Liberals might be a good idea.

Hope this helps--Graham Lippiatt (talk) 15:15, 24 June 2010 (UTC)

I shall go ahead and split the pages.

--Thehelpinghand (talk) 06:03, 3 July 2010 (UTC)

 * I agree with the split - but when this happens, remember that the meta data will have to be updated as well for differentiation in the Election box templates. At the moment there is:
 * Template:National Liberal Party (UK)/meta/color Content:
 * Template:National Liberal Party (UK)/meta/shortname Content: National Liberal Party (UK, 1931)/meta/shortname
 * Template:National Liberal Party/meta/color Content:
 * Template:National Liberal Party/meta/shortname Content: National Liberal Party (Denmark)/meta/shortname

 * I'd suggest if we're moving the 1922 party info to National Liberal Party (UK, 1922) then we should move the "National Liberal Party" meta data to "National Liberal Party (UK, 1922)" meta data. Cheers Zangar (talk) 23:51, 23 October 2010 (UTC)

 * Not only should Lloyd George's group be split off, it is wrong to refer to the group from 1931 to 1948 as 'National Liberals'. They were Liberal Nationals, so referred in all contemporary sources. Their sponsorship was structurally different to the years after the Woolton-Teviot agreement. Sam Blacketer (talk) 23:05, 8 March 2011 (UTC)

title: Talk:National Liberal Party (UK)


text:
Gerrard Winstanley

Gerrard Winstanley (baptised 19 October 1609 – 10 September 1676) was an English Protestant religious reformer, political philosopher, and activist during the period of the Commonwealth of England. Winstanley was the leader and one of the founders of the English group known as the True Levellers or Diggers. The group occupied formerly common land that had been privatised by enclosures and dug them over, pulling down hedges and filling in ditches, to plant crops. "True Levellers" was the name they used to describe themselves, whereas the term "Diggers" was coined by contemporaries.

Early life
Gerrard Winstanley was baptised on 19 October 1609, the son of Edward Winstanley, mercer, and was baptised in the parish of Wigan, then part of the West Derby hundred of Lancashire. His mother's identity remains unknown and he could have been born anywhere in the parish of Wigan. The parish of Wigan contained the townships of Abram, Aspull, Billinge-and-Winstanley, Dalton, Haigh, Hindley, Ince-in-Makerfield, Orrell, Pemberton, and Upholland, as well as Wigan itself.

In 1630, Winstanley migrated to the City of London, where he became an apprentice to a Merchant Tailor. In 1638, he was admitted as a freeman of the Merchant Tailors' Company, a trade guild. In 1639, he married Susan King, the daughter of William King, a London surgeon.

The First English Civil War disrupted Winstanley’s business, and in 1643 he was made bankrupt. His father-in-law helped him to move to Cobham, Surrey, where he initially worked as a cowherd.

The New Law of Righteousness
Winstanley published a pamphlet called The New Law of Righteousness. The basis of this work came from the Book of Acts, chapter two, verses 44 and 45: "And all that believed were together, and had all things common; And sold their possessions and goods, and parted them to all men, as every man had need." Winstanley argued that "In the beginning of Time, the great Creator Reason, made the Earth to be a Common Treasury, to preserve Beasts, Birds, Fishes, and Man, the lord that was to govern this Creation; for Man had Domination given to him, over the Beasts, Birds, and Fishes; but not one word was spoken in the beginning, That one branch of mankind should rule over another. And the Reason is this, Every single man, Male and Female, is a perfect Creature of himself; and the same Spirit that made the Globe, dwels in man to govern the Globe; so that the flesh of man being subject to Reason, his Maker, hath him to be his Teacher and Ruler within himself, therefore needs not run abroad after any Teacher and Ruler without him, for he needs not that any man should teach him, for the same Anoynting that ruled in the Son of man, teacheth him all things... And so selfish imaginations taking possession of the Five Sences, and ruling as King in the room of Reason therein, and working with Covetousnesse, did set up one man to teach and rule over another; and thereby the Spirit was killed, and man was brought into bondage, and became a greater Slave to such of his own kind, then the Beasts of the field were to him."

Winstanley took as his basic texts the Biblical sacred history, with its affirmation that all men were descended from a common stock, and with its scepticism about the rulership of kings, voiced in the Books of Samuel; and the New Testament's affirmations that God was no respecter of persons, that there were no masters or slaves under the New Covenant. From these and similar texts, he interpreted Christian teaching as calling for the abolition of property [in land] and aristocracy. For him, nature "is in effect God, and this pantheistic materialism proclaimed the equality of all people through nature as well as the usefulness of popular sciences -alchemy, astrology, herbal medicine and the magical arts."

Winstanley wrote: "Seeing the common people of England by joynt consent of person and purse have caste out Charles our Norman oppressour, wee have by this victory recovered ourselves from under his Norman yoake."

His theme was rooted in ancient English radical thought. It went back at least to the days of the Peasants' Revolt (1381) led by Wat Tyler, because that is when a verse of the Lollard priest John Ball was circulated:
 * When Adam delved and Eve span,
 * Who was then the gentleman?

The Diggers
On 1 April 1649, Winstanley and his followers took over vacant or common lands on St George's Hill in Surrey. Other Digger colonies followed in Buckinghamshire, Kent, and Northamptonshire. Their action was to cultivate the land and distribute food without charge to any who would join them in the work. Local landowners took fright from the Diggers' activities and in 1650 sent hired armed men to beat the Diggers and destroy their colony. Winstanley protested to the government, but to no avail, and eventually the colony was abandoned.

After the failure of the Digger experiment in Surrey in 1650 Winstanley temporarily fled to Pirton, Hertfordshire, where he took up employment as an estate steward for the aristocratic mystic Lady Eleanor Davies. This employment lasted less than a year. It ended when Davies accused Winstanley of mismanaging her property, and he then returned to Cobham.

Winstanley continued to advocate the redistribution of land. In 1652 he published another pamphlet called The Law of Freedom in a Platform, in which he argued that the Christian basis for society is where property and wages are abolished. In keeping with Winstanley's adherence to biblical models, the tract envisages a communistic society structured on non-hierarchical lines, though one likely to have voluntary patriarchs.

Quakers
By 1654 Winstanley was possibly assisting Edward Burrough, an early leader of the Quakers, later called the Society of Friends. It seems that Winstanley remained a Quaker for the rest of his life, since his death was noted in Quaker records. However, his Quakerism may not have been very strong as he was involved in the government of his local parish church from 1659 onwards though it is not unknown for committed Quakers to retain strong ties to other religious traditions, even including priesthood. He may have been buried in a Quaker cemetery.

Winstanley believed in Christian Universalism, the doctrine that everyone, however sinful, will eventually be reconciled to God; he wrote that "in the end every man shall be saved, though some at the last hour." His book The Mysterie of God is apparently the first theological work in the English language to state this universalism.

Later life
In 1657 Winstanley and his wife Susan received a gift of property in Ham Manor in Cobham, from his father-in-law William King. This marked Winstanley's renovation in social status locally and he became waywarden of the parish in 1659, overseer of the poor in 1660 and churchwarden of the Church of England parish church in 1667–68. He was elected Chief Constable of Elmbridge, Surrey, in October 1671. These offices on the face of it conflicted with Winstanley's apparent Quakerism, a religion which later became more quietist.

When Susan died in about 1664, Winstanley sold the land in Cobham to King for £50. Winstanley returned to London to trade, whilst retaining some connections in Surrey. In about 1665 he married his second wife, Elizabeth Stanley, and re-entered commerce as a corn chandler. Winstanley died in 1676, aged 66, vexed by legal disputes concerning a small legacy owed to him in a will.

Legacy
The Soviet-era Alexander Garden Obelisk in Moscow, Russia, in 1918 included his name among a list of outstanding thinkers and personalities of the struggle for the liberation of workers.

In 1999, the British activist group The Land is Ours celebrated the Digger movement's 350th anniversary with a march and reoccupation of St George's Hill, the site of the first Digger colony. Like the original colony, this settlement was quickly disbanded. Since 2010 a Wigan Diggers’ Festival has been held annually in Winstanley's birth town of Wigan attracting support across the North of England.

Collected works
The Complete Works of Gerrard Winstanley, edited jointly by Thomas N. Corns, Ann Hughes and David Loewenstein, were published by the Oxford University Press in December 2009 at £229 (ISBN 978-0-19-957606-7).

A shorter and less comprehensive volume containing all the major works, Gerrard Winstanley: A Common Treasury edited by Andrew Hopton, was published in 1989 by Aporia (ISBN 978-0-948518-45-4) and reprinted several times since, most recently in 2011 (paperback) by Verso Books (UK) with an introduction by Tony Benn (ISBN 978-1-84467-595-1).

Related works
1975 saw the release of Kevin Brownlow and Andrew Mollo's film Winstanley. As with the duo's previous film, It Happened Here, it had taken several years to produce with a very low budget. Winstanley was loosely based on a 1961 novel by David Caute entitled Comrade Jacob and was produced in a quasi-documentary style, with great attention to period detail – even to the point of only using breeds of animals which were known to exist at the time, and actual Civil War armour and weapons borrowed from the Tower of London museum.

In 2009 UKA Press released Winstanley: Warts and all (ISBN 978-1-905796-22-9), the story of the making of the film Winstanley, written by film director and film historian Kevin Brownlow.

The song, "The World Turned Upside Down", by English folksinger Leon Rosselson, weaves many of Winstanley's own words into the lyrics. An older song, the "Diggers' Song", said to have been written by Winstanley, was recorded by the English group Chumbawamba on their English Rebel Songs 1381–1914 in 1988.

Quotations
From A Declaration from the Poor Oppressed People of England: "The power of enclosing land and owning property was brought into the creation by your ancestors by the sword; which first did murder their fellow creatures, men, and after plunder or steal away their land, and left this land successively to you, their children. And therefore, though you did not kill or thieve, yet you hold that cursed thing in your hand by the power of the sword; and so you justify the wicked deeds of your fathers, and that sin of your fathers shall be visited upon the head of you and your children to the third and fourth generation, and longer too, till your bloody and thieving power be rooted out of the land." From A Watch-word to the City of London, and Army: "Alas! you poor blind earth-moles, you strive to take away my livelihood and the liberty of this poor weak frame my body of flesh, which is my house I dwell in for a time; but I strive to cast down your kingdom of darkness, and to open hell gates, and to break the devil's bonds asunder wherewith you are tied, and that you my enemies may live in peace; and that is all the harm I would have you to have." From A New-year's Gift for the Parliament and Army: "The life of this dark kingly power, which you have made an act of Parliament and oath to cast out, if you search it to the bottom, you shall see it lies within the iron chest of cursed covetousness, who gives the earth to some part of mankind and denies it to another part of mankind: and that part that hath the earth, hath no right from the law of creation to take it to himself and shut out others; but he took it away violently by theft and murder in conquest." From The Law of Freedom in a Platform: "If they prove desperate, wanton or idle, and will not quietly submit to the law, the task-master is to feed them with short diet, and to whip them, for a rod is prepared for the fool's back, till such time as their proud hearts do bend to the law ... If any have so highly broke the laws as they come within the compass of whipping, imprisoning and death, the executioner shall cut off the head, hang or shoot to death, or whip the offender according to the sentence of law. Thus you may see what the work of every officer in a town or city is.'"

title: Gerrard Winstanley


text:
Kent Conrad

Gaylord Kent Conrad (born March 12, 1948) is a former American politician who was a United States Senator from North Dakota. He is a member of the Democratic Party. First elected to the Senate in 1986, he served as chairman or Ranking Member of the Senate Budget Committee for 12 years.

On January 18, 2011, Conrad announced that he was retiring from politics and would not run for reelection in 2012. He said in a statement that it was more important that "I spend my time and energy trying to focus on solving the nation's budget woes than be distracted by another campaign." Fellow Democrat Heidi Heitkamp was elected to replace him.

Conrad currently co-chairs the Bipartisan Policy Center's Commission on Retirement Security and Personal Savings. He is also a member of the ReFormers Caucus of Issue One. In addition, he serves on the board of directors of the Committee for a Responsible Federal Budget.

Early life
Conrad was born in Bismarck, North Dakota, the son of Abigail and Gaylord E. Conrad. He was orphaned at a young age and subsequently raised by his grandparents in Bismarck. He attended Roosevelt Elementary, Hughes Junior High, and Wheelus Air Base high school in Tripoli, Libya, before eventually graduating from Phillips Exeter Academy. He then went to college at Stanford, and received an M.B.A. from The George Washington University.

Personal life
Conrad has been married twice. His first wife, Pam, is the sister of former U.S. Secretary of Agriculture and former North Dakota Governor Ed Schafer; they have a daughter, Jessamyn. Jessamyn Conrad is the author of What You Should Know About Politics ... But Don't, subtitled a Nonpartisan Guide, which was praised by Barack Obama and Bob Dole.

On February 14, 1987, Conrad married Lucy Calautti, his 1986 Senate campaign manager, who is now a lobbyist for Major League Baseball.

Early political career
After graduating from college, Conrad became a civil servant, working as an assistant to the North Dakota State Tax Commissioner, Byron Dorgan, who later became his colleague in the Senate. Conrad made his first entry into politics when he ran unsuccessfully for the North Dakota Auditor's office in 1976. In 1980 Conrad succeeded Dorgan as Tax Commissioner. Conrad was state tax commissioner until 1986, when he ran for the Senate.

Committee assignments

 * Committee on Agriculture, Nutrition, and Forestry
 * Subcommittee on Energy, Science and Technology
 * Subcommittee on Domestic and Foreign Marketing, Inspection, and Plant and Animal Health
 * Subcommittee on Production, Income Protection and Price Support
 * Committee on the Budget (chairman)
 * Committee on Finance
 * Subcommittee on Energy, Natural Resources, and Infrastructure
 * Subcommittee on Taxation, IRS Oversight, and Long-Term Growth (chairman)
 * Subcommittee on Fiscal Responsibility and Economic Growth
 * Committee on Indian Affairs
 * Joint Committee on Taxation

Political positions
In April 2006 Time named Conrad one of "America's 10 Best Senators". That same year The American commended him for his knowledge of economic issues. Conrad endorsed Barack Obama in the 2008 Democratic presidential primary.

Conrad was a leading member of the "Gang of 10", a conservative group that pushed for much greater offshore drilling in sensitive environmental areas. He was well known for using charts as visual aids when speaking in the Senate, which earned him the nickname "Godfather of Charts."

Health care
In the 2009 negotiations over reforming America's healthcare system, Conrad strongly opposed a "public option." The AFL-CIO announced it would fund a primary challenge to Conrad in 2012 if he continued to oppose a public option.

On September 29, 2009, Conrad voted with Senate Finance Committee Republicans against an amendment to a health care bill that would have provided for a public option. He was supportive of the Stupak-Pitts Amendment, which places limits on taxpayer-funded abortions in the context of the November 2009 Affordable Health Care for America Act.

Social policies
Conrad is more politically conservative than most Democrats. He voted consistently in favor of banning the partial-birth abortion medical procedure. He also opposes public funding of abortion, but voted in favor of lifting the ban on abortions on military bases. Conrad has a mixed record on gay rights. While he personally opposes gay marriage, he voted against a proposed constitutional ban on it and has supported bills that prevent discrimination based on sexual orientation. On January 31, 2006, Conrad was one of four Democrats to vote in favor of confirming Judge Samuel Alito to the Supreme Court.

Fiscal policies
On April 17, 2012, Conrad, a strong supporter of the Simpson-Bowles plan, announced his plan to offer a version of it that he, as a member of the National Commission on Fiscal Responsibility and Reform, helped to develop. Lawmakers on the Senate Budget Committee could be forced to vote or modify the plan.

Conrad was known for his deep understanding of monetary policies and budget issues. He identifies as a "deficit hawk", supporting a balanced federal budget, but continues to support farm subsidies. He voted against Republican proposals to repeal the estate and alternative minimum taxes. He supported lower middle-class taxes, but increased taxes for people making more than $1 million per year. In 2010 he supported extending the expiring Bush tax cuts "at least until the economy is clearly recovering."

Conrad was very vocal in his opposition to the spending policies of the George W. Bush administration. He contended that Bush worsened the national debt. Conrad also opposed most free-trade measures and strongly supported subsidies to family farmers.

Foreign policy and national security
In 1991 Conrad voted against approving the use of military force in Iraq. He was one of only 23 senators to vote against the war resolution of 2002. While he initially voted in favor of the USA PATRIOT Act, he has opposed warrantless wiretapping and government's continued use of the Guantanamo Bay detention facility.

Countrywide Financial loan scandal
In June 2008 it was reported that Conrad had received mortgages on favorable terms for a second home and an apartment building due to his association with Countrywide Financial CEO Angelo R. Mozilo. Conrad acknowledged that he had spoken with Mozilo by phone. In an April 23, 2004, email about one of Conrad's loans, Mozilo encouraged an employee to "make an exception due to the fact that the borrower is a senator." Conrad denied any prior knowledge of such treatment and gave the mortgage discount to charity. Citizens for Responsibility and Ethics in Washington (CREW) called on the Senate Ethics Committee to investigate Conrad. In August 2009, after a yearlong inquiry, the Ethics Committee exonerated Conrad of any unethical behavior in his dealings with Countrywide.

Overview
In the 1986 election, Conrad defeated the Republican incumbent, Mark Andrews, by 2,120 votes. Andrews had represented North Dakota at the federal level since 1963 (he had previously served in the House before moving to the Senate in 1981).

During the campaign, Conrad pledged that he would not run for reelection if the federal budget deficit had not fallen substantially by the end of his term. By 1992 it became obvious that this would not be the case, and although polls showed that the electorate would have welcomed his reneging on that pledge, Conrad considered his promise binding and did not run for reelection. Byron Dorgan won the Democratic primary election.

Conrad received an opportunity to remain in the Senate when North Dakota's other senator, long-serving Dem-NPLer Quentin Burdick, died on September 8, 1992. Burdick's widow, Jocelyn Birch Burdick, was appointed to the seat temporarily, but a special election was needed to fill the rest of the term. Viewing this opportunity as different from running for reelection, Conrad ran for and won the Democratic-NPL's nomination. He went on to win the special election, and was sworn in on December 14, 1992, resigning his original Senate seat the same day. (Conrad's original Senate seat was then filled by Dorgan, via appointment by the governor on December 15, 1992, to fill the seat for the brief period until he would have been sworn in under normal circumstances.)

Despite North Dakota's Republican leanings, Conrad was comfortably reelected in 1994—a year when Republicans won most of the Congressional seats that were not in heavily Democratic-leaning states.

1986

 * Kent Conrad (D) 50%
 * Mark Andrews (R) (inc.) 49%

1992

 * Kent Conrad (D) 63%
 * Jack Dalrymple (R) 34%

1994

 * Kent Conrad (D) (inc.) 58%
 * Ben Clayburgh (R) 42%

2000

 * Kent Conrad (D) (inc.) 61%
 * Duane Sand (R) 39%

2006

 * Kent Conrad (D) (inc.) 69%
 * Dwight Grotburg (R) 30%
 * Roland Riemers (I) 1%
 * James Germalic (I) 0.6%

title: Kent Conrad


text:
Ô Canada! mon pays, mes amours

The lyrics to "Ô Canada! mon pays, mes amours", meaning "O Canada! my country, my love" is a French-Canadian patriotic song. It was written by George-Étienne Cartier and first sung in 1834, during a patriotic banquet of the Saint-Jean-Baptiste Society held in Montreal. The words were first published in the June 29, 1835 edition of La Minerve. It was later published in Le Chansonnier des collèges (Quebec 1850), this time with music, but with only four of the original six verses. It was reproduced in Le Passe-Temps on June 21, 1913. The song was recorded on 78 rpm discs by both Victor Occellier and Joseph Saucier around the turn of the century and in 1925 or 1926 by Rodolphe Plamondon Roger Doucet included it in his LP Chants glorieux (Songs of Glory) in 1976.

The music currently used was composed by Jean-Baptiste Labelle. It is uncertain when the lyrics and music were put together, probably by Ernest Gagnon sometime between 1850 and 1868.

Excerpt
Comme le dit un vieil adage : Rien n'est si beau que son pays; Et de le chanter, c'est l'usage; Le mien je chante à mes amis L'étranger voit avec un œil d'envie Du Saint-Laurent le majestueux cours; À son aspect le Canadien s'écrie : Ô Canada! mon pays! mes amours!

English translation
As the old proverb says: Nothing is more beautiful than one's country; And to sing it is the tradition; And mine I sing to my friends The stranger looks with an envious eye Of the St. Lawrence the majestic course; At its aspect the Canadian sings: O Canada! my country! my love!

title: Ô Canada! mon pays, mes amours