title: Coca-Cola Vanilla

text: Coca-Cola initially stated that it had no plans to return Coca-Cola Vanilla to the United Kingdom despite high demand. Several enquiries were made throughout 2011 and 2012. Coca-Cola then thought about returning Vanilla Coca-Cola to the United Kingdom sooner or later. It was reintroduced on March as part of Papa Johns promotion campaign before becoming available elsewhere. In April 2017, Vanilla Zero Sugar was made available in the UK. In May 2013, Coca-Cola Vanilla appeared in stores in Romania (imported), expanding to more stores through the year, due to demand, while there is still no official word from Coca-Cola. In July 2013, the drink re-appeared in stores around Belgium and the Netherlands as well. In October 2013, Coca-Cola Vanilla appeared in stores in Czech Republic and Slovakia. In February 2015, it appeared in some Tesco stores in Poland, where it is also available in Carrefour shops. It can also be purchased in many shops in Canada, and is widely available in Sweden, and also in some stores in Finland. In July 2018, Coca-Cola Vanilla re-appeared in Russia as limited edition in Magnit supermarkets, but due to high sales, it became available in all retail chains as a permanent product. In 2018, Coca-Cola confirmed the product's discontinuation in the UK in favour of Vanilla Zero Sugar.


title: Coca-Cola Vanilla

text: Vanilla Coke was packaged in standard bottles in accordance with appropriate Coca-Cola packaging. For a brief period of time in mid-2003, the bottles that Vanilla Coke came in, which had before said "Vanilla Coke", were changed simply to "V" (which matched Cherry Coke's new labeling showing a picture of a cherry).


title: Coca-Cola Vanilla

text: As part of Coca-Cola's ongoing "One Brand" marketing campaign, a new U.S. packaging design for Coca-Cola Vanilla was introduced in January 2019. The new packaging follows the design principles already employed in the United States for Coca-Cola, Coca-Cola Zero Sugar, and Coca-Cola Life. The word "Coca-Cola" is superimposed upon a red disc with a light beige drop (representing a drop of vanilla syrup) below the text. The background color of the can or bottle is light beige in color. The word "Vanilla" is placed above the red disc, similar to the "Original Taste" text currently used on cans and bottles of original Coca-Cola.


title: Coca-Cola Vanilla

text: In late 2002, a sugar-free version, Diet Vanilla Coke, became available. In some countries, including Australia and New Zealand, a similar drink is marketed as "Diet Coke with Vanilla" and in others is known as Coca-Cola light Vanilla (or Vanilla Coke Light) In 2005, the sugar-free product in the United States and Canada became "Diet Coke Vanilla," with more emphasis on the Diet Coke label. All varieties were discontinued in 2005 in the United States, Canada and the United Kingdom. Both varieties are still available in Australia and Hong Kong. Coca-Cola Vanille (translation) is also available in France and Germany. A new Coke Vanilla Zero was introduced in 2007, along with regular Vanilla. Only these two are available in the United States. The company has not announced any plan to resume production of Diet Vanilla Coke. Diet Vanilla Coke is, however, available using a Coca-Cola Freestyle machine. Coca-Cola Zero Sugar Vanilla was made available in the UK in April 2017 in 1.75 L bottles, 330 mL cans, 500 mL bottles and multipack of cans.


title: The Yakuza

text: The Yakuza is a 1974 neo-noir crime drama film directed by Sydney Pollack and starring Robert Mitchum, Ken Takakura and Brian Keith. The screenplay by Paul Schrader and Robert Towne is from a story by Paul's brother, Leonard Schrader.


title: The Yakuza

text: The film is about a retired American detective who returns to Japan after decades away in order to rescue his friend's daughter, kidnapped by the eponymous crime syndicate. Following a lackluster initial release, the film has since gained a cult following.


title: The Yakuza

text: Retired detective Harry Kilmer is called upon by an old friend, George Tanner. Tanner has been doing business with a "yakuza" gangster, Tono, who has kidnapped Tanner's daughter to apply pressure in a business deal involving the sale of guns. Tanner hopes that Kilmer can rescue the girl using his Japanese connections.


title: The Yakuza

text: Kilmer and Tanner had been Marine MPs in Tokyo during the post-war occupation. Kilmer became aware of a woman, Eiko, who was involved in the black market so that she could procure penicillin for her sick daughter. Kilmer intervened on behalf of Eiko during a skirmish, saving her life. After they'd been living together, with Kilmer repeatedly asking Eiko to marry him, her brother Ken returned from an island where he'd been stranded as an Imperial Japanese soldier. Both outraged that she was living with his former enemy and deeply indebted to Kilmer for saving the lives of his (apparently) only remaining family, Ken disappeared into the yakuza criminal underground and refused to see or speak to his sister. Eiko, cautious to do nothing to offend Ken further, broke off contact with Kilmer. Before returning to the US, Kilmer bought Eiko a bar (with money borrowed from George Tanner) which she operates to this day, named "Kilmer House" in his honor. Kilmer has never stopped loving her.


title: The Yakuza

text: Ken's debt to Kilmer, "giri," is a lifelong obligation that traditionally can never be repaid. Tanner believes that Ken would therefore do anything for Kilmer, including rescuing Tanner's daughter. Traveling to Tokyo with Tanner's bodyguard Dusty, they stay at the home of another old military buddy named Oliver Wheat. Kilmer visits Eiko at the bar's closing time, seeking to find Ken. Eiko's feelings for Kilmer are clearly as strong as ever. He also becomes reacquainted with Eiko's daughter, Hanako, who is delighted to see Kilmer again. Eiko tells Kilmer that her brother can be found at his kendo school in Kyoto.


title: The Yakuza

text: Kilmer travels by train to visit Ken at his kendo school. Ken is no longer a yakuza member, but will still help Kilmer. They find and free the girl. In so doing, Ken "takes up the sword" once again, attacking one of Tono's men to save Kilmer. This is an inexcusable intrusion by Ken in yakuza affairs. Contracts on both Ken's and Kilmer's lives are issued. Despite Tanner's protests, Kilmer insists on staying until the danger to Ken can be resolved. Eiko suggests he see Ken's brother, a high-level legal counselor to the yakuza chiefs. Goro is unable to intercede due to his impartial role in yakuza society, but suggests Ken can remove the death threat by killing Tono with a sword. The only alternative is for Kilmer to kill Tono himself, by any means (as an outsider, he is not bound to use a sword). Because Kilmer is known to Goro as an unusual "gaijin" who understands and accepts Japanese values, he proposes that Kilmer now has an obligation to Ken.


title: The Yakuza

text: After an attempt on Kilmer's life at a bathhouse, he learns that his old friend Tanner has taken out the contract on him. Tanner secretly is broke and owes Tono a huge debt. Dusty discloses that Tanner and Tono are business partners. During a violent attack on Ken and Kilmer in Oliver Wheat's house, Dusty is stabbed to death with a sword and Hanako is shot and killed.


title: The Yakuza

text: Seeking advice again from Ken's brother, Goro advises them that they have no choice but to assassinate Tanner and Tono. This will embarrass the partners in the eyes of the yakuza. Goro discloses that he has a "wayward son" who has joined Tono's clan and asks that Ken protect him should he be caught in the battle. In private, Goro then discloses the shocking family secret to Kilmer that Eiko is not Ken's sister but his wife, and Hanako their only child. Kilmer comprehends the true meaning of Eiko and Ken's rift, and Ken's anguish at the death of Hanako, all brought about by his repeated intercessions in their lives.


title: The Yakuza

text: Kilmer storms into Tanner's apartment and kills him, then joins Ken for a near-suicidal attack on Tono's residence. During a prolonged battle, after Ken kills Tono in the traditional way with a "katana," Goro's son attacks them and Ken kills him in self-defense. Bearing the news to his brother, Ken moves to commit "Seppuku," but his brother pleads with him not to bring more anguish to their family. Instead, Ken performs "yubitsume" (the ceremonial yakuza apology by cutting off one's little finger).


title: The Yakuza

text: Before leaving Japan, Kilmer visits with Ken at home and asks to speak to him formally. While Ken prepares tea, Kilmer quietly commits "yubitsume," and when Ken enters the room, waits for him to be seated. Sliding the folded handkerchief that contains his finger to Ken, he says "please accept this token of my apology" for "bringing great pain into your life, both in the past and in the present." Ken accepts, and Kilmer asks that "if you can forgive me, then you can forgive Eiko," adding, "you are greatly loved and respected by "all" your family." Ken professes that "no man has a greater friend than Kilmer-san," and Kilmer, overcome by emotion, says the same of Ken. Their obligations now apparently resolved, Ken takes Kilmer to the airport, and both men bow formally to each other before parting.


title: The Yakuza

text: Paul Schrader says the idea for the film came from a letter sent to him by his brother Leonard, who was then living in Japan; Leonard had left the U.S. when he received his military draft induction card and found work teaching English at a Japanese university, but frequently found himself with nothing to do when radical students shut down the campus and ended up spending a lot of time in yakuza-run bars. He had also been watching yakuza films and been impressed by the presence of Ken Takakura and the rituals involved. He thought there was an interesting film to be made about a Westerner who became involved in the yakuza to such an extent he would "make that ultimate sacrifice that is so foreign to a Westerner. That is the premise we started out on, trying to create a plot that would result in that situation."


title: The Yakuza

text: Schrader told the idea to co-producer Mark Hamilburg, who liked it and paid for the brothers to write it. They spent two months watching films, in particular Toei films at a cinema in Los Angeles. "By the time I started writing, I was thinking like a Toei screenwriter," says Schrader. They wrote the script in an apartment in Venice over a month, between thanksgiving and Christmas. Schrader says Hamilburg saw the script "was going to be a hot item: the intensity with which people became interested was clear. He knew he was incapable of handling a high-level auction, so he went to Robin French" to handle the auction. French sold the script for $300,000.


title: The Yakuza

text: It's hard to see now, looking back at a film which completely flopped, but it was a very commercial idea. It had a lot of commercial hooks plus a strong love story, rich characters, and an "in" theme. It seemed to have all the elements for a rich, commercial action romance.


title: The Yakuza

text: Originally, Robert Aldrich was to direct. Aldrich later called it "one of the few pictures I really wanted to make" although he wanted changes made. "It was a terrible script, I thought, but a sensational idea. I said, 'If I'm going to make this picture, I'm going to turn this script upside down.' I saw it one particular way, and Paul didn't see it that way."


title: The Yakuza

text: Aldrich thought his view might have prevailed if Lee Marvin had been cast in the lead, but Marvin disagreed with Warner Brothers over the size of the actor's fee. Instead they cast Robert Mitchum. Aldrich and Mitchum had worked together on "The Angry Hills" (1959), and the director said "I really considered him my friend, and I admired him. I think he's a brilliant actor - a strange, convoluted guy. I knew I wasn't his favorite director, but I never really knew he disliked me." The two of them met, and Mitchum told Warners afterwards he did not want to do the film with Aldrich. "Too bad," Aldrich said later. "I think it was possible to make a marvelous movie out of "Yakuza"."


title: The Yakuza

text: Sydney Pollack then became attached. Schrader says that Pollack wanted rewrites, notably a "softening" of the Harry character. Schrader says "I was fired, because I was unable to write what Sydney wanted. Sydney and I did not get along well, and he needed someone of his own age, whose work he respected, for feedback." Robert Towne came on to rewrite the film.


title: The Yakuza

text: Pollack remarked in interviews on complications of filming in Japan, using Japanese crews and technicians, and adopting techniques and practices of Japanese filmmaking. Beyond language barriers, there were creative approaches that he synthesized into the film for being appropriate for the subject matter.


title: The Yakuza

text: The musical score for "The Yakuza" was composed by David Grusin. The score applies both Western and Eastern musical influences in what director Sydney Pollack described as a way that "felt and sounded Japanese without being too strange for western ears." A soundtrack album was released by "Film Score Monthly" in July 2005.


title: The Yakuza

text: Schrader says the reception to the film was "disastrous. It cost five million and brought back maybe a million and a half."


title: The Yakuza

text: He felt the casting of Mitchum - which he was "very pleased with" - hurt the movie at the box office and if Redford had played the role "we probably would have made money."


title: The Yakuza

text: Schrader felt Pollack "directed against the grain of the script. I wrote a violent, underworld film about blood, duty, and obligation. He made a sort of rich, romantic, transcultural film. Either of those films would be interesting if fully realized, but the final product fell between those two stools; neither film was made. It didn't satisfy the audience that came to see the hard gangster world, and it didn't satisfy the JEREMIAH JOHNSON audience - Sydney's audience - which came to see some poetic realism."


title: The Yakuza

text: Schrader says his biggest regret from the film is that Takakura did not become an international star.


title: The Yakuza

text: The film received mixed reviews at the time of release. On Rotten Tomatoes the film holds an approval rating of 59% based on 17 reviews.


title: The Yakuza

text: Roger Ebert gave the film a mixed review, awarding it two-and-a-half stars out of four. While praising the characterization and the performances of Robert Mitchum and Ken Takakura, he criticized the plot as being somewhat difficult to follow and expressed concern over the level of violence: "it's for audiences that have grown accustomed over the last few years to buckets of blood, disembowelments and severed hands flying through the air. It's very violent, and the fact that the violence has been choreographed by a skilled director (Sidney Pollack, who made "They Shoot Horses, Don't They?") just makes it all the more extreme." Lawrence Van Gelder of "The New York Times" wrote, "Although admirable for its understated contrast of hoary ritual with modern trappings, 'The Yakuza' ... is also didactic. It is slowed by the need to instruct its audience in the way of the yakuza; it is marred in its early exposition by some impenetrable Japanese-accented English; it is burdened by the attenuation of an unexciting love interest (which Mitchum's character freely admits being too old for); and a couple of formidably important revelations are simply dropped in, as though no one had the time to plot them properly."


title: The Yakuza

text: Arthur D. Murphy of "Variety" called it "a confused and diffused film which bites off more than it can artfully chew." Gene Siskel of the "Chicago Tribune" gave the film three stars out of four and called it "a special kind of gangster picture" with "an extremely complex story" and "stylish sword-fighting sequences. But don't confuse them with the boring karate chops so common in the Oriental sludge that typically fills our downtown theaters. The fighting in 'The Yakuza' is more ritualistic and more meaningful because we know who is attacking whom and why."


title: The Yakuza

text: Kevin Thomas of the "Los Angeles Times" thought that the film "suffers from a self-consciousness so stultifying it never really comes alive, its sense of reality (or lack of it) deriving from other movies instead of life itself."


title: The Yakuza

text: Gary Arnold of "The Washington Post" called the film "such a clumsy combination of violence and inscrutability that the action becomes slightly laughable," further observing, "The right director for this slightly dubious material would have been Sam Peckinpah, who possesses both a taste and a flair for violence ... Sydney Pollack, the director chosen, gets sentimental about violent men, but he isn't on their wavelength."


title: The Yakuza

text: Tony Rayns of "The Monthly Film Bulletin" wrote that Takakura "dominates the screen" with "his masterfully understated performance," concluding, "If "The Yakuza" is ultimately no more than a curious footnote to the Western exploitation of Oriental action movies, then it finds at least some self-justification in bringing a major film personality to a much wider audience."


title: The Yakuza

text: Quentin Tarantino is an admirer of the film saying "for the last time as a lead, Mitchum was vibrantly alive... Takakura Ken’s powerhouse performance, at the height of his fame, in this Hollywood Yakuza flick, seems even more of a triumph... the film’s final coda, “The Finger cutting scene,” is, for me, one of the great endings of any movie of its era. And arguably Mitchum’s single greatest acting moment on film (as long as some fuckwad in the cinema doesn’t laugh during it)."


title: Jesse Birdsall

text: Jesse Birdsall (born 13 February 1963) is an English actor, known for his roles as Marcus Tandy in the BBC1 soap opera "Eldorado", Nick Beckett in the adventure series "Bugs" (1995–1999), football manager Roger Webb in "Footballers' Wives" between 2004 and 2006, and Fraser Black in "Hollyoaks", as well as for villain Ron Gregory in a few episodes of "The Bill".


title: Jesse Birdsall

text: As a child, Birdsall attended the Anna Scher children's theatre school in Islington, and in his teens appeared in Nanette Newman's children's cooking programme "Fun Food Factory" and in several television plays and series, usually with his trademark rockabilly look. He had one line as an extra ("Watch it mate!") in an episode of "Minder" from 1980 entitled "Don't Tell Them Willie Boy was Here". In 1982 he starred alongside singer Hazel O'Connor in the TV drama series set in a nightclub called "Jangles". He first came to wider public attention in the serial "Annika" in 1984, his first notable television role. He then subsequently appeared in the films "Wish You Were Here" (1987), directed by David Leland and co-starring Emily Lloyd, "Getting It Right" (1989), and "Beyond Bedlam" (1994). He appeared in the 1988 music video of Kim Wilde's single "Hey Mister Heartache".


title: Jesse Birdsall

text: Another notable television role was his portrayal of slick playboy Marcus Tandy in the BBC1 soap opera "Eldorado", which ran for just one year from 1992 to 1993 and came to be thought of as a notable flop. Nonetheless, the amount of coverage the programme received for its perceived low quality and lack of success would gain Birdsall much exposure, and from 1995 to 1999 he played one of the lead characters in another BBC1 programme, the successful futuristic action/adventure series "Bugs".


title: Jesse Birdsall

text: Birdsall played the part of John Barron in the last episode of "Morse" in the episode "The Remorseful Day" which aired on 15 November 2000.


title: Jesse Birdsall

text: He guest-starred in "Midsomer Murders", playing two separate characters, in the episodes "Market For Murder" in 2002 as Harry Painter and "Small Mercies" in 2009 as Mike Johnson. He also appeared in several episodes of the ITV police drama "The Bill" in 2003 as a character named Ron Gregory, and for the same network appeared as a regular in series 3–5 of the popular drama "Footballers' Wives".


title: Jesse Birdsall

text: In 2006, Birdsall appeared as patient Dillon Ellis in two episodes of "Holby City" before reappearing in 2018 as Steven Fletcher, the estranged father of Adrian Fletcher.


title: Jesse Birdsall

text: He had a small role in the BBC One soap opera "EastEnders" in August 2012, playing John Hewland, jilted fiancé of Sharon Watts (Letitia Dean), in two episodes.


title: Jesse Birdsall

text: Birdsall played the role of Fraser Black in Channel 4 soap "Hollyoaks" but left the show in spring 2014 following a whodunit storyline in which he was murdered.


title: Jesse Birdsall

text: The son of Penguin Books designer Derek Birdsall, Birdsall attended Hampstead School in north London. He has been married to "Only Fools and Horses" actress Gwyneth Strong, with whom he has two children, since 15 July 2000.


title: Jesse Birdsall

text: Birdsall has twice been in trouble with the police, being convicted of actual bodily harm after an altercation in 1981, and in 1999 being fined £1,000 following an unprovoked attack on a fellow customer at a pub in London.


title: Necco Wafers

text: Necco Wafers are a sugar-based candy, sold in rolls of variously flavored thin disks. First produced in 1847, they became the namesake and core product of the now-defunct New England Confectionery Company (Necco), which operated near Boston, Massachusetts. Production of the candy was suspended in July 2018 when Necco went into bankruptcy, but returned in May 2020 after purchase of the brand and production equipment by the Spangler Candy Company.


title: Necco Wafers

text: Each roll of Necco Wafers contains eight flavors: lemon (yellow), lime (green), orange (orange), clove (purple), cinnamon (white), wintergreen (pink), licorice (black), and chocolate (brown). The ingredients in Necco Wafers are sugar, corn syrup, gelatin, gums, colorings and flavorings.


title: Necco Wafers

text: Necco Wafers date back to 1847. Oliver Chase, an English immigrant, invented a lozenge cutting machine with which he produced the wafers. At the time of the Civil War, these were called "hub wafers" and were carried by Union soldiers. In 1901, Chase and Company merged with two other companies to incorporate the New England Confectionery Company (Necco). By 1912, the wafers were being advertised as "Necco Wafers", a name they have carried since.


title: Necco Wafers

text: During World War II, the United States government ordered Necco to produce its wafers for soldiers overseas. As a result of this action, Necco saw its sales of the wafers peak. Upon returning home, many former soldiers became faithful customers who continued to buy the wafers.


title: Necco Wafers

text: The Necco company was acquired several times, first in 1963, and most recently in 2018. In 2018, the future of Necco Wafers was unclear after the Necco company filed for Chapter 11 bankruptcy. Round Hill Investments purchased the company out of bankruptcy for $17.3 million in May 2018, but then abruptly ended operations at Necco on July 24, 2018, citing "sanitation issues" it claimed it was previously unaware of.


title: Necco Wafers

text: Round Hill sold off various Necco lines to other candy companies. Necco Wafers (which retains the Necco name and logo), Sweethearts, and Canada Mints, as well as the equipment used to manufacture them, were sold to the Spangler Candy Company of Bryan, Ohio. In September 2018, Spangler announced plans to return the Necco Wafer to the market, initially giving a target date of November 2019. In May 2020, Spangler said that Necco Wafers were back in production at a facility in Mexico and ready for release.


title: Necco Wafers

text: In 2009, Necco changed the formula for its Necco Wafers. Artificial colors and flavors were eliminated. The candy was made softer through the addition of glycerine. The lime flavor was removed due to difficulties in creating an all-natural green coloring, resulting in a 7-flavor Necco Wafer roll.


title: Necco Wafers

text: According to Jackie Hague, Necco's vice president of marketing, switching to all-natural flavors and colors "would draw young mothers concerned about their children's diet." According to Corby Kummer of "The Atlantic" the new cinnamon flavor was "less like Red Hots" and the new lemon, "less like paper candy dots and more like lemon meringue pie filling." The chocolate flavor—previously a vanilla flavor "with a hint of chocolate flavoring"—switches to a more intense all-cocoa flavor. In addition, the Necco Chocolate assortment changed from 100% of the standard Necco chocolate wafers into a four-flavor chocolate assortment.


title: Necco Wafers

text: However, the change was not as popular with long-time customers as anticipated. The company received “some complaints about the new formulations.” In response to these concerns, Necco Wafer production switched back to the original formula in the summer of 2011.


title: Necco Wafers

text: In 2020, Spangler posted a statement on their website regarding a slight change in the formula. Seven of the eight flavored wafers retained the original formula except for the chocolate wafer which they stated: "True Necco Wafers connoisseurs may detect a richer cocoa flavor in the chocolate wafers due to a minor improvement made in the cooking process."


title: Necco Wafers

text: Tropical Necco Wafers launched in 2012, offering a new assortment of tropical fruity flavors: mango, passion fruit, coconut, banana, lime, and strawberry.


title: Necco Wafers

text: Necco Sour Wafers are in a roll of six tart flavors: Watermelon, Wildberry Grape, Sour Apple, Lemon, Extreme Tangerine, and Blue Raspberry. As of June 2018, they were not shown on Necco's varieties website, but could still be found in some stores.


title: Chlorophyllum molybdites

text: Chlorophyllum molybdites, which has the common names of false parasol, green-spored Lepiota and vomiter, is a widespread mushroom. Poisonous and producing severe gastrointestinal symptoms of vomiting and diarrhea, it is commonly conflated with the shaggy parasol or shaggy mane, and is the most commonly misidentified poisonous mushroom in North America. Its large size and similarity to the edible parasol mushroom, as well as its habit of growing in areas near human habitation, are reasons cited for this. The nature of the poisoning is predominantly gastrointestinal.


title: Chlorophyllum molybdites

text: It is an imposing mushroom with a pileus (cap) ranging from 8 to 30 cm in diameter, hemispherical and with a flattened top. The cap is whitish in colour with coarse brownish scales. The gills are free and white, usually turning dark and green with maturity. It has a rare green spore print. The stipe ranges from 5 to 30 cm tall and bears a double-edged ring. This mushroom lacks the snakeskin pattern that is generally present on the parasol mushroom.


title: Chlorophyllum molybdites

text: "Chlorophyllum molybdites" grows in lawns and parks across eastern North America and California, as well as temperate and subtropical regions around the world. Fruiting bodies generally appear after summer and autumn rains. It appears to have spread to other countries, with reports from Scotland, Australia, and Cyprus.


title: Chlorophyllum molybdites

text: "Chlorophyllum molybdites" is the most frequently eaten poisonous mushroom in North America. The symptoms are predominantly gastrointestinal in nature, with vomiting, diarrhea and colic, often severe, occurring 1–3 hours after consumption. Although these poisonings can be severe, particularly in children, none have yet resulted in death.


title: Chlorophyllum molybdites

text: Professor James Kimbrough writes:"Chlorophyllum molybdites", the green-spored Morgan's Lepiota, is responsible for the greatest number of cases of mushroom poisonings in North America, and in Florida. This is probably due to the fact that it is easily confused with choice edible species such as "Lepiota procera" and "L. rhacodes", and it is one of the most common mushrooms found on lawns and pastures throughout the country, with the exception of the Pacific Northwest. When eaten raw "C. molybdites" produce severe symptoms, including bloody stools, within a couple of hours. When cooked well, or parboiled and decanting the liquid before cooking, others eat and enjoy it. Eilers and Nelso (1974) found a heat-labile, high molecular weight protein which showed an adverse effect when given by intraperitoneal injection into laboratory animals.


title: Serzh Sargsyan

text: Serzh Azati Sargsyan (, ; born 30 June 1954) is an Armenian politician who served as the third President of Armenia from 2008 to 2018, and twice as the Prime Minister of Armenia from 2007 to 2008 and again from 17 to 23 April 2018, when he was forced to resign in the 2018 Armenian revolution.


title: Serzh Sargsyan

text: He won the February 2008 presidential election with the backing of the ruling Republican Party of Armenia, a party in which he serves as chairman, and took office in April 2008. On 18 February 2013, he was re-elected as president and served the entire term.


title: Serzh Sargsyan

text: Despite pledging in 2014 not to become Prime Minister again while supporting an amendment of the constitution in 2015 that would allow it, Sargsyan was again elected Prime Minister of Armenia in April 2018, in what opposition figures described as a "power grab". Six days after taking office, Sargsyan resigned after large-scale protests. Sargsyan is currently the leader of the Republican Party, which was the ruling party of Armenia from 1999 to 2018 and is currently represented in parliament as a part of the opposition I Have Honor Alliance.


title: Serzh Sargsyan

text: Serzh Sargsyan (born Serzhik Azati Sargysan) was born on 30 June 1954 in Stepanakert in the Nagorno-Karabakh Autonomous Oblast. He is the son of Azat Avetisi Sargsyan (1929–2013) and Nora Sargsyan․ His father's family hailed from the village of Tegh in the Armenian SSR, and moved to Stepanakert after the arrest of Serzh Sargsyan's grandfather during the 1937 Great Purge. He entered Yerevan State University in 1971 and served in the Soviet Armed Forces in the Ural region from 1971 to 1972. He began his career in 1975 at the Electrical Devices Factory in Yerevan. He graduated from the Philological Department of Yerevan State University in 1979. In 1983, he married his wife, Rita (née Dadayan). In addition to his native Armenian, he is fluent in Russian and also knows Azerbaijani. He is not related to the former Prime Minister of Armenia, Tigran Sargsyan, or current President of Armenia Armen Sarkissian.


title: Serzh Sargsyan

text: Starting in 1979, Sargsyan held several positions in the Stepanakert Komsomol Committee: first as division head, then second secretary and first secretary (his long-time political ally Robert Kocharyan served as his deputy). He then became the Stepanakert City Committee Propaganda Division Head, the Nagorno-Karabakh Regional Committee Communist Organizations' Unit Instructor, and finally became assistant to Genrikh Poghosyan, the First Secretary of the Nagorno-Karabakh Regional Committee.


title: Serzh Sargsyan

text: In November 1989, Sargsyan was a delegate from Nagorno-Karabakh to the first congress of the Pan-Armenian National Movement. He was elected to the Supreme Council of Armenia in 1990. During the First Nagorno-Karabakh War, Sargsyan was involved in organizing the defense of Nagorno-Karabakh and the formation of the NKR Defense Army in various capacities. In January 1992, when the first government of the Nagorno-Karabakh Republic (NKR) was formed with Oleg Yesayan as prime minister, Sargsyan was appointed head of the Defense Committee, a position he held until the dissolution of the government in August 1992. Sargsyan then became a member of the seven-man State Defense Committee of the NKR (effectively the government of the NKR) which was formed in August 1992. Sargsyan held the position of minister of the army within the State Defense Committee.


title: Serzh Sargsyan

text: From 1993 to 1995 he served his first term as Armenia's Minister of Defense under President Levon Ter-Petrosyan. In 1995 he became Minister of National Security of Armenia (initially called the State Security Department) and from 1996 to 1999 he concurrently served as Minister of Interior. In February 1998, Sargsyan, along with then-Prime Minister Robert Kocharyan and Defense Minister Vazgen Sargsyan, forced President Ter-Petrosyan to resign in order to prevent him from accepting a peace plan for the Nagorno-Karabakh conflict put forward by international mediators in September 1997. The proposal envisioned the return of most of the Armenian-occupied territories surrounding Nagorno-Karabakh to Azerbaijan in exchange for security guarantees, but left the final resolution of the status of Nagorno-Karabakh for future negotiations. From 1999 to 2000 he served as the Chief of Staff for President Robert Kocharyan, and then served once again as the Defense Minister of Armenia from 2000 to 2007. He was also the Secretary of the National Security Council led by President Kocharyan from 1999 to 2007. On 4 April 2007 Sargsyan was appointed as the Prime Minister of Armenia, following the sudden death of Andranik Margaryan.


title: Serzh Sargsyan

text: Sargsyan, with President Kocharyan's backing, was viewed as the strongest contender for the post of the President of Armenia in the February 2008 presidential election. Full provisional results showed him winning about 53% of the vote, a first round majority, well ahead of second place candidate Levon Ter-Petrosyan. The 2008 Presidential election was hailed as largely democratic by OSCE, the European Union (EU) and Western monitors.


title: Serzh Sargsyan

text: Ter-Petrosyan's supporters, disputing the official results, held large protests in Yerevan for over a week following the election, until they were violently broken up on 1 March; ten people (eight protestors and two police officers) were killed, and a state of emergency was imposed for 20 days, ending on 20 March 2008.


title: Serzh Sargsyan

text: Serzh Sargsyan was sworn in as President at the Yerevan Opera House on 9 April 2008. Referring to the "painful events" that followed the election, he " everybody to look forward, together, to seek and find the way for reconciliation, development, and future of Armenia." He appointed Tigran Sargsyan, who had been the Chairman of the Central Bank and is not a member of a political party, as Prime Minister. According to the Freedom House report "In 2011, the government took concrete steps to fulfill longstanding and often repeated promises to confront corruption. E-government services reduced opportunities for bribery, while new regulations and stricter enforcement led to higher numbers of corruption lawsuits and fines against senior officials and large companies. Owing to a more consolidated government effort to eradicate corruption, Armenia's corruption rating from 5.50 to 5.25."


title: Serzh Sargsyan

text: During Sargsyan's presidency the record of the freedom of speech and the freedom of press in general also improved in Armenia. Internet penetration rose sharply


title: Serzh Sargsyan

text: – from 6.2 percent in 2008 to 37 percent in 2011, providing greater access to online media, which rapidly grew in number, including blogosphere – with over 10,000 bloggers in 2011.


title: Serzh Sargsyan

text: After the elections Sargsyan also authorized opposition rallies to take place in Yerevan and pledged to comply with the Council of Europe's demands for an end to the government's crackdown on the opposition.


title: Serzh Sargsyan

text: Civil society also grew considerably during Sargsyan's presidency, with the number of non-governmental organizations growing at a higher rate and with civic activists succeeding in raising public awareness and holding important campaigns in the sphere of human rights, environmental protection and social justice. However, according to Freedom House, public advocacy still had limited impact on public policy.


title: Serzh Sargsyan

text: The start of Sargsyan's presidency coincided with the Great Recession. In 2009, Armenia's GDP contracted over 14%, which according to the World Bank was the fifth worst in the world that year after the three Baltic states and Ukraine. GDP growth subsequently stabilized at around 3% by 2013. As of 2014, Armenia's GDP is below the pre-crisis levels. During his first term of presidency, the official poverty rate doubled and reached 32.4% in 2012. According to official data, some 213,000 people have left Armenia from 2008 to 2013. In 2012, Armenia was ranked 39th out of 179 economies according to the Index of Economic Freedom and ranked 19th freest among the 43 countries in the Europe region.


title: Serzh Sargsyan

text: In September 2013 and under Sargsyan's direction, Armenia announced its intentions of joining the Eurasian Economic Union with Belarus, Kazakhstan and Russia. The Eurasian Economic Union (EAEU or EEU) is an economic union of Belarus, Kazakhstan and Russia, and came into force on 1 January 2015. Treaties aiming for Armenia's accession to the Eurasian Economic Union was signed on 9 October 2014. Armenia's accession treaty came into force on 2 January 2015. The Eurasian Economic Union has an integrated single market of 176 million people and a gross domestic product of over 4 trillion U.S. dollars (PPP). The EEU introduces the free movement of goods, capital, services and people and provides for common transport, agriculture and energy policies, with provisions for a single currency and greater integration in the future.


title: Serzh Sargsyan

text: Sargsyan made his first address in front of the 63rd session of the United Nations General Assembly in New York on 25 September 2008. In his speech he referenced the 2008 South Ossetia conflict and emphasized the need for the United Nations to help bring peaceful resolution to armed conflicts around the world, including the one in Nagorno-Karabakh. He also mentioned how Azerbaijan's military buildup along with increasing war rhetoric and threats risked causing renewed problems in the South Caucasus.


title: Serzh Sargsyan

text: Sargsyan continued the policy towards the peaceful resolution of the Nagorno-Karabakh conflict pursued by his predecessors, which constitutes one of the main goals of the Armenian foreign policy. Sargsyan repeatedly stated that the Armenian side is interested in finding a just and exclusively peaceful solution to the conflict and that the OSCE Minsk Group is the viable format within which the peace talks should continue. He continued negotiations with Azerbaijan and had a number of meetings with the president of Azerbaijan within the framework of OSCE Minsk Group. On 2 November 2008, Ilham Aliyev and Serzh Sargsyan traveled to Moscow for talks with Dmitry Medvedev. The talks ended in the three Presidents signing a declaration confirming their commitment to continue talks. The two presidents met again in 2009 in Saint Petersburg and on 22 November 2009, together with several world leaders, in Munich where President Aliyev once more threatened to resort to military force to reestablish control over the region if the two sides did not reach an agreeable settlement.


title: Serzh Sargsyan

text: Sargsyan blames the Azerbaijani side for hampering the peace process and for pursuing an openly anti-Armenian stance. According to him, the anti-Armenian policies of Azerbaijan, such as "state-supported falsifications of history", "hostile propaganda against Armenia and Armenians" and "military build-up" prove that Azerbaijan does not want peace.


title: Serzh Sargsyan

text: The most vivid expression of anti-Armenian policies of Azerbaijan was the hero's welcome given to the convicted ax murderer Ramil Safarov who had brutally killed Armenian officer Gurgen Margaryan during the NATO's Partnership for Peace program in Budapest in 2004. The fact that after his extradition to Azerbaijan in 2012 Safarov was pardoned by president Aliyev, promoted to the rank of major, given an apartment with over eight years of back pay and was made a national hero, hampers the negotiation process and proves, in Sargsyan's words, that "the Azeri propaganda brings up an entire generation in the atmosphere of xenophobia and intolerance."


title: Serzh Sargsyan

text: Sargsyan has also clearly stated:The Armenophobic and aggressive stance of Azerbaijan reinforces our conviction that Nagorno-Karabakh has no future within Azerbaijan. Moreover, Azerbaijan has neither legal nor political or moral grounds to claim over Nagorno-Karabakh.


title: Serzh Sargsyan

text: Our belief is that the settlement of the Karabakh conflict should be based on human rights and the will of the Karabakh people… It is the only way to achieve lasting, feasible, and peaceful settlement. The alternative to this settlement is the forcing of the Karabakh people back into Azerbaijan, which will inevitably lead to attempts of new ethnic cleansing of Armenians in Karabakh. There is no alternative here.”


title: Serzh Sargsyan

text: Responding to the persistent war rhetoric of Azerbaijan, Sargsyan has condemned it as a violation of the norms of the international law, as the parties had signed a truce which Azerbaijan, the "defeated aggressor", had asked for.


title: Serzh Sargsyan

text: He repeatedly said that his country is categorically against the resumption of military hostilities, but at the same time is ready to counter any military aggression. In 2014, Sargsyan stated "We don't want war and never wanted, but at that time [i.e. during Nagorno-Karabakh war] we had to defend our Motherland. If the time comes again, this time our blow will be final and deadly."


title: Serzh Sargsyan

text: In this regard, Sargsyan declared that in the case of military aggression from Azerbaijan "Armenia will have no other choice but to recognize the Nagorno-Karabakh Republic "de jure" and to employ all its capabilities to ensure the security of the people of Artsakh."


title: Serzh Sargsyan

text: Sargsyan met with Ilham Aliyev again in Russian-mediated talks in Kazan in June 2011, where the two sides reportedly came close to an agreement. The basic principles discussed at Kazan envisioned the return of five of the seven districts of Azerbaijan occupied by Armenia in exchange for "interim status" for Nagorno-Karabakh and the deployment of international peacekeepers, with the final status of the region to be decided by a legally-binding referendum. The proposals made at Kazan were ultimately rejected by the Azerbaijani side.


title: Serzh Sargsyan

text: In his electoral program of 2013, Sargsyan promised to increase the security guarantees of Nagorno-Karabakh and its people given Azerbaijan's policy of Armenophobia. He also highlighted the importance of strengthening the defensive system of Armenia "as a factor restraining the Azerbaijani aggression and ensuring stability in the South Caucasus". He also promised to take all the necessary efforts to ensure that Karabakh becomes a negotiating side in the peace talks as well as to foster the ties between Karabakh and the international community.


title: Serzh Sargsyan

text: As for the position of Armenia concerning the independence of Kosovo, Sargsyan stated that "Armenia's possible recognition of Kosovo's independence will not strain the Armenian-Russian relations" but also noted that the "Kosovo recognition issue needs serious discussion... Armenia has always been an adherent to the right of nations to self-determination and in this aspect we welcome Kosovo's independence."


title: Serzh Sargsyan

text: In April 2016, Sargsyan led Armenia through the 2016 Nagorno-Karabakh conflict (also known as the Four-Day War or the April War), the most significant outbreak of violence on the Nagorno-Karabakh line of contact after the 1994 ceasefire and before the 2020 Nagorno-Karabakh war. The four days of fighting resulted in at least dozens of deaths and the loss of approximately 800 hectares of land. Sargsyan described the outcome of the four-day clashes as a victory for Armenia, although he faced criticism for shortcomings during the clashes as well as accusations that he had agreed to cede territory to Azerbaijan in the wake of the fighting. In order to stop this purported cession of territory, a group of armed men calling themselves "Daredevils of Sasun" seized a police headquarters in Yerevan in July 2016 and took hostages, demanding Sargsyan's resignation. The crisis, which coincided with mass protests in support of the attackers, ended with the surrender of the gunmen on 31 July 2016.


title: Serzh Sargsyan

text: Reflecting on his presidency and the negotiation process after the 2020 Nagorno-Karabakh war, during which the Armenian side lost much of the territory it controlled in and around Nagorno-Karabakh, Sargsyan stated that he intended to achieve a final negotiated solution to the Nagorno-Karabakh conflict and that this was the reason for his decision to remain as prime minister in 2018, which led to protests that forced his resignation. He denied that he had deliberately delayed the negotiation process in order to maintain the status quo or that he had ever held the view that "not one inch of land" could be handed over to Azerbaijan in order to resolve the conflict. He added that he was "ready to bear the label of traitor, but resolve the [Nagorno-Karabakh] question."


title: Serzh Sargsyan

text: Having been elected as a president for his first term in 2008, Sargsyan pledged to continue Armenia's policy towards Turkey, to normalize relations without any preconditions while continuing to strive for international recognition of the 1915 Armenian genocide.


title: Serzh Sargsyan

text: Coming to power, Sargsyan took steps towards the normalization of ties with Turkey, a policy termed as "football diplomacy". In 2008, Sargsyan took a historical initiative to invite Turkish President Abdullah Gül to Armenia to watch a 2010 FIFA World Cup qualifier match between Armenia and Turkey. Abdullah Gül attended the game in Armenia while Serzh Sargsyan made a reciprocal visit to Turkey to watch the second match.


title: Serzh Sargsyan

text: On 10 October 2009 the foreign ministers of Armenia and Turkey signed protocols on establishing diplomatic relations between the two countries without any preconditions. The accord also presupposed the opening of the border between Armenia and Turkey which had been closed by Turkey in 1993. The protocols were signed in Geneva, Switzerland under the international mediation, chiefly that of the United States.


title: Serzh Sargsyan

text: Sargsyan's policy of rapprochement with Turkey received controversial reaction among the Armenian people. While one part was for the opening of the border and fostering trade with Turkey the other part was concerned that by this move Armenia would be forced to make concessions to Turkey in the most vital and strategic matters. Armenian influential opposition parties, most notably the Armenian Revolutionary Federation were categorically against the signing of the protocols, given the recognition of the existing Turkish-Armenian border and the setting up of a joint commission of historians researching the Armenian Genocide, as envisioned by the protocols. They considered these steps as a sellout and staged mass protests against the signing of the protocols.


title: Serzh Sargsyan

text: The Armenian Diaspora was also largely opposed to this type of reconciliation with Turkey, arguing (despite Sargsyan's assurances to the contrary) that this would jeopardize the international recognition of the Armenian genocide as well as the prospects of legitimate territorial claims of Armenians from Turkey.


title: Serzh Sargsyan

text: The process of reconciliation, however, was suspended after a year. In Armenia, before sending the protocols to the parliament, it was sent to the Constitutional Court to have their approval. The Constitutional Court made references to the preamble of the protocols underlying three main issues. One of them stated that the implementation of the protocols did not imply Armenia’s official recognition of the existing Turkish-Armenian border established by the Treaty of Kars. By doing so, the Constitutional Court rejected one of the main premises of the protocols, i.e. "the mutual recognition of the existing border between the two countries as defined by relevant treaties of international law". This was regarded by the Turkish Government as effectively revising the protocols and thus the reason to back down from the process. As a consequence, the Turkish Parliament did not ratify the protocols. The Armenian side accused Turkey to tie the reconciliation process with the resolution of the Nagorno-Karabakh conflict, expecting concessions on the Armenian side, which was unacceptable for the latter. Sargsyan explained the suspension of the reconciliation process by the Armenian side in the following way: For a whole year, Turkey's senior officials have not spared public statements in the language of preconditions. For a whole year, Turkey has done everything to protract time and fail the process... We consider unacceptable the pointless efforts of making the dialogue between Armenia and Turkey an end in itself; from this moment on, we consider the current phase of normalization exhausted."


title: Serzh Sargsyan

text: Sargsyan however has also stated that unlike Ankara, Yerevan remains committed to its initiative to normalizing relations with Turkey.


title: Serzh Sargsyan

text: President Sargsyan supported Armenia's efforts to ink an Association Agreement with the EU, which contains a Deep and Comprehensive Free Trade Area, for several years. Under his Presidency, the negotiations for the agreement were completed and Armenia was set to sign the agreement at an upcoming EU Summit. However, President Sargsyan made a drastic policy reversal when in September 2013, after a meeting with President Vladimir Putin in Moscow, he opted to join the Russian-led Eurasian Economic Union. It was widely believed that Russian pressure and threats killed Armenia's deal with the EU. Even though such a reversal was made, President Sargsyan's administration was determined to further EU inspired reforms in law and governance, and this led to Armenia signing the Comprehensive and Enhanced Partnership Agreement with the European Union on 24 November 2017. Behind the scenes, Russia granted approval to Armenia to sign the deal after any economic provisions were removed from the deal.


title: Serzh Sargsyan

text: Major protests against Sargsyan's regime began in 2011, with the president's 2008 rival Levon Ter-Petrosyan at their helm. In a concession to protesters, Sargsyan said on 20 April 2011 that the government would recommit to a thorough investigation of the post-election violence of three years prior.


title: Serzh Sargsyan

text: In July 2016, thousands of Armenians protested in the capital Yerevan in support of the "Daredevils of Sasun," an armed group that stormed police headquarters in Yerevan and took hostages while calling for the release of all political prisoners and the resignation of president Serzh Sargsyan. The National Security Service of Armenia called the takeover (which resulted in the deaths of three policemen) a terrorist attack, but a growing number of Armenians disagreed with that assessment.


title: Serzh Sargsyan

text: Shortly after the end of his presidency on 9 April 2018, Sargsyan was elected Prime Minister of Armenia on 17 April. Opposition figures described this as a "power grab" and there were large-scale protests against him. On 22 April, Sargsyan held a three-minute televised meeting with opposition MP and leader of the protests Nikol Pashinyan. Sargsyan accused the opposition of delivering an ultimatum for his resignation instead of engaging in dialogue, and left the meeting early; Pashinyan was detained by police hours after the meeting. The continuing protests were eventually successful in pressuring Sargsyan. On 23 April, Pashinyan was released from detention and Sargsyan announced his resignation. Former Prime Minister Karen Karapetyan succeeded Sargsyan as acting Prime Minister. Armenia's National Assembly, still controlled by Sargsyan's Republican Party, elected Nikol Pashinyan Prime Minister on 8 May 2018.


title: Serzh Sargsyan

text: Sargsyan has been under criminal prosecution within the scope of a criminal case on embezzlement. The Special Investigative Service of Armenia on 4 December 2019, has brought embezzlement charges against Sargsyan, particularly for the organization of the embezzlement of half a billion AMD within the scope of the state program on assisting farmers to obtain diesel fuel on affordable price in 2013. In January 2020, based on sufficient evidence collected, the Special Investigative Service has indicted Sargsyan for embezzlement on especially large scale (AMD ֏489,160,310) and the criminal case with the indictment has been handed to the prosecutor supervising the case for approval and sending it to court.


title: Serzh Sargsyan

text: In 1983, he married his wife, Rita Sargsyan née Dadayan, with whom he has two daughters, Anush and Satenik. They have two granddaughters, Mariam and Rita, and two grandsons, Ara and Serzh. Sargsyan is also the chairman of the Armenian Chess Federation. His wife Rita died on 20 November 2020, from COVID-19 at the age of 58.


title: Serzh Sargsyan

text: Sargsyan has two younger brothers: Alexander (Sashik), a businessman and former member of Armenia's parliament, and Levon, a diplomat and professor at Yerevan State University.


title: Serzh Sargsyan

text: Other transcriptions of his given name are "Serge" and "Serj", of the surname "Sarkissian, Sarkisyan, Sargsyan, Sarkissyan", the transliteration is "Serž Azati Sargsyan" (see Romanization of Armenian). His name during the Soviet era was Russified as "Serzh Azatovich Sargsyan" (Серж Аза́тович Саргся́н).


title: Kerry Wood

text: Kerry Lee Wood (born June 16, 1977) is an American former baseball pitcher who played 14 seasons in Major League Baseball (MLB) for the Chicago Cubs, Cleveland Indians, and New York Yankees.


title: Kerry Wood

text: Wood first came to prominence as a 20-year-old rookie when he recorded 20 strikeouts in a one-hit shutout against the Houston Astros, which some have argued may be the greatest single-game pitching performance in MLB history. The game also made Wood the co-holder of the MLB record for strikeouts in a single game (20) and earned Wood the nickname Kid K. He was later named the 1998 National League Rookie of the Year.


title: Kerry Wood

text: Wood would go on to record over 200 strikeouts in four out of his first five seasons, with a high of 266 in 2003. He holds several MLB strikeout records. Though he struggled with injuries throughout his career, Wood was twice named an All-Star. Wood transitioned to a relief pitcher in 2007 due to continued struggles with injuries, ultimately reviving his career as a closer. During his career Wood was placed on the disabled list 14 times in 14 major league seasons, which included missing the entire 1999 season due to Tommy John surgery. After a slow start to the 2012 season, Wood retired on May 18, 2012.


title: Kerry Wood

text: Wood attended MacArthur High School in Irving, Texas, for his first three seasons of high school baseball. He continued his education at Grand Prairie High School for his final season as a high school player. Wood was high school teammates with Kevin Walker. He initially committed to play college baseball at McLennan Community College in Waco.


title: Kerry Wood

text: The Chicago Cubs drafted Wood as the fourth overall selection in the 1995 Major League Baseball draft. He spent three years playing in the minor leagues. His best season in the minors came in 1996, when he posted a 10–2 record for the Daytona Cubs. He also played for the Triple-A Iowa Cubs. In 1997, he led all minor league pitchers in walks, with 131.


title: Kerry Wood

text: Wood made his first appearance in the major leagues on April 12, 1998. In his fifth career start, on May 6, he threw a one-hit, no-walk, 20-strikeout shutout against the Houston Astros in Wrigley Field, tying Roger Clemens' record for strikeouts in a nine-inning game and breaking Bill Gullickson's single-game rookie record of 18 strikeouts in 1980. Wood allowed only two baserunners: Ricky Gutiérrez on an infield single and Craig Biggio, who was hit by a pitch with a count of one ball and two strikes. (Biggio had led the league in that category each of the previous three years and is second all-time in hit-by-pitches with 285.) Only seven balls reached fair territory. The Astros went on to lead the league in on-base percentage, and all of the regulars were in the lineup, including the four who finished the season batting over .300. The performance garnered a game score of 105 – the highest number ever calculated for a pitcher in a nine-inning game.


title: Kerry Wood

text: Wood finished the 1998 season with a 13–6 record; despite missing the last month of the season with elbow soreness, he easily won the National League Rookie of the Year award. He pitched one game in the playoffs, losing against the Atlanta Braves.


title: Kerry Wood

text: During spring training of 1999, he tore his ulnar collateral ligament (UCL). Wood underwent successful Tommy John surgery to repair damage to the UCL in his right elbow, and missed the entire 1999 season.


title: Kerry Wood

text: Wood returned in 2000 and had an 8–7 record, but the following season, he returned to form. In 2001, Wood went 12–6 with a 3.36 ERA. He recorded a one-hit, 14-strikeout complete-game shutout on May 25, 2001. On August 3, 2001, he struck out nine batters and gave up only one run over eight innings to defeat Chan Ho Park and the Los Angeles Dodgers 2-1 to extend the Cubs' lead in National League Central to 3.5 games. The following season, Wood finished 12–11 with a 3.67 ERA, and did not miss a start all year long, setting career highs with 213.6 innings pitched and 33 starts. He had 217 strikeouts in both seasons.


title: Kerry Wood

text: In 2003, Wood set career highs with 266 strikeouts, 14 wins (as part of a 14–11 record), a 3.20 ERA, and two shutouts. He threw the fastest fastball in the majors among starters, averaging 95.4 miles per hour. He also walked 100 batters and surrendered 24 home runs, also career highs, but was selected as a National League All-Star and helped lead the Cubs to the playoffs as one half of ""Chicago Heat"" along with fellow pitcher Mark Prior.


title: Kerry Wood

text: Wood earned two wins in the Divisional Series against the Atlanta Braves and was the starter in Game 3 of the 2003 National League Championship Series, which the Cubs won in extra innings. However, the Cubs lost in seven games to the eventual World Series champion Florida Marlins. In the decisive Game 7, Wood hit the first home run by a pitcher in an NLCS game since another Cub, Rick Sutcliffe, did so in Game 1 in 1984. However, the Marlins won the game 9-6. Wood was the losing pitcher and the Cubs were eliminated.


title: Kerry Wood

text: Wood went 8-9 during the 2004 season and was sidelined for nearly two months with a strained triceps.


title: Kerry Wood

text: In 2005, Wood continued to struggle. On August 31, 2005, Wood underwent surgery and missed the remainder of the season. During Spring training in 2006, Wood suffered several injuries which required an additional surgery (on his knee). On May 18, 2006, Wood returned to the Cubs' pitching rotation when he started and lost a home game against the Washington Nationals. In June, Wood returned to the DL with a sore shoulder. The following month, the Cubs announced that Wood had sustained a partially torn rotator cuff which was likely to keep him from pitching again for the rest of the year. At the end of the 2006 season, the Cubs exercised their option on Wood's contract and bought out the remaining $13M.


title: Kerry Wood

text: With his long history of injuries and inability to stay in the starting rotation, Wood accepted the Cubs' offer to return as a relief pitcher in 2007. Wood attempted to sustain a regular throwing schedule and appearances during Spring training games. However, Wood was placed on the 15-day DL with soreness in his elbow and was then moved to the 60-day DL. Wood considered retiring if he continued to have pain in his throwing arm. He began playing catch on May 21. In his first rehab assignment in Cubs Rookie Ball, he struck out all three batters he faced. On July 24, he pitched 1 inning with the Single-A Peoria Chiefs, throwing 9 pitches. He made back-to-back appearances on July 26 and July 27, throwing his fastball between 92–94 mph with no discomfort.


title: Kerry Wood

text: The Cubs activated Wood from the 60-Day disabled list on August 3, causing many to believe that he would make his actual return on that day. In the seventh inning, however, Lou Piniella opted to send Bob Howry to the mound, and most fans, eager to see Kerry back on the hill, mistakenly gave Howry a standing ovation, only to realize moments later it was actually not Wood. Piniella later stated he wanted Wood to receive a "softer landing", or in other words, make his return in a game where the Cubs have a comfortable lead over their opponents. Wood made his return on August 5, with the Cubs trailing the New York Mets by four runs. He pitched a single inning, during which he allowed one hit, and struck out another batter. Piniella praised Wood's performance, stating "He threw the ball real good", and "His breaking ball had some bite to it, and he threw it up there about 93–94, about what we expected". He remained healthy appearing in 22 games and posting a 1–1 record with a solid 3.33 ERA.


title: Kerry Wood

text: He was generally limited to one inning per outing, not appearing in games on back-to-back days, though he did pitch in both halves of a doubleheader on September 15. Wood was a major contributor to the Cubs' NL Central Division Championship down the stretch in late September, earning a win and 8 holds. Wood filed for free-agency on November 11, 2007, though he suggested that he wanted to remain in pinstripes for the 2008 season. Despite multi-year offers from other teams, Wood agreed to a one-year, $4.2 million deal with the Cubs.


title: Kerry Wood

text: Wood, along with Bob Howry and Carlos Mármol, competed for the role as the Cubs' closer after Ryan Dempster was moved to the starting rotation. After posting a 2.84 ERA in the spring, Wood won the job. He recorded his first career save April 3, 2008 with a win over the Brewers. Wood recorded 34 saves in 39 opportunities, 82 strike-outs and a 1.12 WHIP. He was selected to the 2008 MLB All-Star Game as a relief pitcher on July 6, 2008, along with six other teammates.


title: Kerry Wood

text: On November 13, 2008, after acquiring closer Kevin Gregg from the Florida Marlins, Cubs general manager Jim Hendry announced that the organization did not plan to re-sign Wood. He had previously requested a multi-year contract with the team, but was deferred due to financial reasons. Wood stated he wished to remain with the Cubs, but also wanted to continue playing baseball.


title: Kerry Wood

text: Cubs fans showed their appreciation for him by giving him a standing ovation when the Cleveland Indians played at Wrigley Field on June 19, 2009. During the 2010 season, Wood was placed on the disabled list until May 8 due to an upper back muscle strain. On July 17, 2010, Wood was placed on the disabled list for the 14th time in his major league career, this time due to a blister on his right index finger.


title: Kerry Wood

text: Wood was traded from the Cleveland Indians to the New York Yankees on July 31, 2010, for Andrew Shive, Matt Cusick, and cash. With the Yankees, he went 2–0 with a 0.69 ERA in 24 games, including 21 straight scoreless appearances, and served as the bridge to Mariano Rivera in the 2010 postseason. During the 2010 postseason, Wood had a 2.25 ERA appearing in 7 games overall. The Yankees won the 2010 ALDS against the Minnesota Twins in 3 games but lost to the Texas Rangers in 6 games of the 2010 ALCS.


title: Kerry Wood

text: The Yankees announced on October 27 that the club had declined to exercise their option for Wood for 2011.


title: Kerry Wood

text: On December 16, 2010, Wood agreed to a one-year deal worth $1.5 million with the Cubs. Wood reportedly turned down offers for long-term deals from several other teams worth more money due to his desire to keep his family in Chicago. Wood re-signed with the Cubs on January 13, 2012, for a 1-year, $3 million deal with a team option for 2013.


title: Kerry Wood

text: On May 18, 2012, Wood retired, striking out the only (and therefore final) batter he faced, Dayán Viciedo of the Chicago White Sox. The fans at Wrigley Field gave Wood a long standing ovation as his son, Justin, ran out to greet him as he exited the field. On his baseball career: "I had fun, I had a blast", Wood said. "I wouldn't trade anything in."


title: Kerry Wood

text: On February 13, 1999, Wood and former high school teammate Kevin Walker were ticketed for urinating in a parking lot at 1:10 a.m. in Scottsdale, Arizona. Wood missed his initial court appearance and an arrest warrant was issued. He later pleaded guilty and paid a fine of $90.


title: Kerry Wood

text: Wood is married to Sarah Pates of Waukegan, Illinois. The couple has one son, Justin, and two daughters, Katie and Charlotte. Until 2008, the family resided in the Old Town neighborhood of Chicago.


title: Kerry Wood

text: While playing for the Cubs, the Woods hosted a celebrity bowling tournament called "Kerry Wood's Strike Zone", which also featured a silent auction that raised over $2 million.


title: Kerry Wood

text: On June 24, 2013, while paddleboarding in waters in Chicago, Wood happened upon a corpse floating in Belmont Harbor. He immediately reported the grisly discovery to local authorities, who determined the deceased to be a 40-year-old man who had been reported missing by a North Side nursing home days earlier.


title: Betty Botter

text: Betty Botter is a tongue-twister written by Carolyn Wells. It was originally titled "The Butter Betty Bought." By the middle of the 20th century, it had become part of the Mother Goose collection of nursery rhymes.


title: Betty Botter

text: The construction is based on alliteration, using the repeated two-syllable pattern /'b__tə 'b__tə 'b__tə/ with a range of vowels in the first, stressed syllable.


title: Betty Botter

text: Betty Botter bought some butter but, she said, this butters bitter; if I put it in my batter, it will make my batter bitter. But, a bit of better butter will make my batter better. So, Betty Botter bought a bit of better butter and made her batter a bit better.


title: Betty Botter

text: Betty Batta bought some butter, but she said "this butter's bitter if I put it in my batter it will make my batter bitter". So she bought some better butter, better than the bitter butter put it in her batter and the batter tasted better.


title: Betty Botter

text: There was an animated version featured on PBS Kids Television Channel, animated by Lynn Tomlinson. In this variation the rhyme is as follows:


title: Matrix mechanics

text: Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually autonomous and logically consistent formulation of quantum mechanics. Its account of quantum jumps supplanted the Bohr model's electron orbits. It did so by interpreting the physical properties of particles as matrices that evolve in time. It is equivalent to the Schrödinger wave formulation of quantum mechanics, as manifest in Dirac's bra–ket notation.


title: Matrix mechanics

text: In some contrast to the wave formulation, it produces spectra of (mostly energy) operators by purely algebraic, ladder operator methods. Relying on these methods, Wolfgang Pauli derived the hydrogen atom spectrum in 1926, before the development of wave mechanics.


title: Matrix mechanics

text: In 1925, Werner Heisenberg, Max Born, and Pascual Jordan formulated the matrix mechanics representation of quantum mechanics.


title: Matrix mechanics

text: In 1925 Werner Heisenberg was working in Göttingen on the problem of calculating the spectral lines of hydrogen. By May 1925 he began trying to describe atomic systems by observables only. On June 7, after weeks of failing to alleviate his hay fever with aspirin and cocaine, Heisenberg left for the pollen-free North Sea island of Helgoland. While there, in between climbing and memorizing poems from Goethe's "West-östlicher Diwan", he continued to ponder the spectral issue and eventually realised that adopting "non-commuting" observables might solve the problem. He later wrote:


title: Matrix mechanics

text: It was about three o' clock at night when the final result of the calculation lay before me. At first I was deeply shaken. I was so excited that I could not think of sleep. So I left the house and awaited the sunrise on the top of a rock.


title: Matrix mechanics

text: After Heisenberg returned to Göttingen, he showed Wolfgang Pauli his calculations, commenting at one point:


title: Matrix mechanics

text: Everything is still vague and unclear to me, but it seems as if the electrons will no more move on orbits.


title: Matrix mechanics

text: On July 9 Heisenberg gave the same paper of his calculations to Max Born, saying that "he had written a crazy paper and did not dare to send it in for publication, and that Born should read it and advise him" prior to publication. Heisenberg then departed for a while, leaving Born to analyse the paper.


title: Matrix mechanics

text: In the paper, Heisenberg formulated quantum theory without sharp electron orbits. Hendrik Kramers had earlier calculated the relative intensities of spectral lines in the Sommerfeld model by interpreting the Fourier coefficients of the orbits as intensities. But his answer, like all other calculations in the old quantum theory, was only correct for large orbits.


title: Matrix mechanics

text: Heisenberg, after a collaboration with Kramers, began to understand that the transition probabilities were not quite classical quantities, because the only frequencies that appear in the Fourier series should be the ones that are observed in quantum jumps, not the fictional ones that come from Fourier-analyzing sharp classical orbits. He replaced the classical Fourier series with a matrix of coefficients, a fuzzed-out quantum analog of the Fourier series. Classically, the Fourier coefficients give the intensity of the emitted radiation, so in quantum mechanics the magnitude of the matrix elements of the position operator were the intensity of radiation in the bright-line spectrum. The quantities in Heisenberg's formulation were the classical position and momentum, but now they were no longer sharply defined. Each quantity was represented by a collection of Fourier coefficients with two indices, corresponding to the initial and final states.


title: Matrix mechanics

text: When Born read the paper, he recognized the formulation as one which could be transcribed and extended to the systematic language of matrices, which he had learned from his study under Jakob Rosanes at Breslau University. Born, with the help of his assistant and former student Pascual Jordan, began immediately to make the transcription and extension, and they submitted their results for publication; the paper was received for publication just 60 days after Heisenberg's paper.


title: Matrix mechanics

text: A follow-on paper was submitted for publication before the end of the year by all three authors. (A brief review of Born's role in the development of the matrix mechanics formulation of quantum mechanics along with a discussion of the key formula involving the non-commutivity of the probability amplitudes can be found in an article by Jeremy Bernstein. A detailed historical and technical account can be found in Mehra and Rechenberg's book "The Historical Development of Quantum Theory. Volume 3. The Formulation of Matrix Mechanics and Its Modifications 1925–1926.")


title: Matrix mechanics

text: Up until this time, matrices were seldom used by physicists; they were considered to belong to the realm of pure mathematics. Gustav Mie had used them in a paper on electrodynamics in 1912 and Born had used them in his work on the lattices theory of crystals in 1921. While matrices were used in these cases, the algebra of matrices with their multiplication did not enter the picture as they did in the matrix formulation of quantum mechanics.


title: Matrix mechanics

text: Born, however, had learned matrix algebra from Rosanes, as already noted, but Born had also learned Hilbert's theory of integral equations and quadratic forms for an infinite number of variables as was apparent from a citation by Born of Hilbert's work "Grundzüge einer allgemeinen Theorie der Linearen Integralgleichungen" published in 1912.


title: Matrix mechanics

text: Jordan, too, was well equipped for the task. For a number of years, he had been an assistant to Richard Courant at Göttingen in the preparation of Courant and David Hilbert's book "Methoden der mathematischen Physik I", which was published in 1924. This book, fortuitously, contained a great many of the mathematical tools necessary for the continued development of quantum mechanics.


title: Matrix mechanics

text: In 1926, John von Neumann became assistant to David Hilbert, and he would coin the term Hilbert space to describe the algebra and analysis which were used in the development of quantum mechanics.


title: Matrix mechanics

text: A linchpin contribution to this formulation was achieved in Dirac's reinterpretation/synthesis paper of 1925, which invented the language and framework usually employed today, in full display of the noncommutative structure of the entire construction.


title: Matrix mechanics

text: Before matrix mechanics, the old quantum theory described the motion of a particle by a classical orbit, with well defined position and momentum "X"("t"), "P"("t"), with the restriction that the time integral over one period "T" of the momentum times the velocity must be a positive integer multiple of Planck's constant


title: Matrix mechanics

text: right energy values "E", the old quantum mechanical formalism did not describe time dependent processes, such as the emission or absorption of radiation.


title: Matrix mechanics

text: When a classical particle is weakly coupled to a radiation field, so that the radiative damping can be neglected, it will emit radiation in a pattern that repeats itself every orbital period. The frequencies that make up the outgoing wave are then integer multiples of the orbital frequency, and this is a reflection of the fact that "X"("t") is periodic, so that its Fourier representation has frequencies 2π"n"/"T" only.


title: Matrix mechanics

text: The coefficients "X" are complex numbers. The ones with negative frequencies must be the complex conjugates of the ones with positive frequencies, so that "X"("t") will always be real,


title: Matrix mechanics

text: A quantum mechanical particle, on the other hand, can not emit radiation continuously, it can only emit photons. Assuming that the quantum particle started in orbit number "n", emitted a photon, then ended up in orbit number "m", the energy of the photon is , which means that its frequency is .


title: Matrix mechanics

text: For large "n" and "m", but with "n"−"m" relatively small, these are the classical frequencies by Bohr's correspondence principle


title: Matrix mechanics

text: In the formula above, "T" is the classical period of either orbit "n" or orbit "m", since the difference between them is higher order in "h". But for "n" and "m" small, or if "n" − "m" is large, the frequencies are not integer multiples of any single frequency.


title: Matrix mechanics

text: Since the frequencies that the particle emits are the same as the frequencies in the Fourier description of its motion, this suggests that "something" in the time-dependent description of the particle is oscillating with frequency . Heisenberg called this quantity "X",


title: Matrix mechanics

text: and demanded that it should reduce to the classical Fourier coefficients in the classical limit. For large values of "n", "m" but with "n" − "m" relatively small,


title: Matrix mechanics

text: "X" is the th Fourier coefficient of the classical motion at orbit "n". Since "X" has opposite frequency to "X", the condition that "X" is real becomes


title: Matrix mechanics

text: Given two arrays "X" and "P" describing two physical quantities, Heisenberg could form a new array of the same type by combining the terms "XP", which also oscillate with the right frequency. Since the Fourier coefficients of the product of two quantities is the convolution of the Fourier coefficients of each one separately, the correspondence with Fourier series allowed Heisenberg to deduce the rule by which


title: Matrix mechanics

text: Born pointed out that "this is the law of matrix multiplication", so that the position, the momentum, the energy, all the observable quantities in the theory, are interpreted as matrices. Under this multiplication rule, the product depends on the order: "XP" is different from "PX".


title: Matrix mechanics

text: The "X" matrix is a complete description of the motion of a quantum mechanical particle. Because the frequencies in the quantum motion are not multiples of a common frequency, the matrix elements "cannot be interpreted as the Fourier coefficients of a sharp classical trajectory". Nevertheless, as matrices, "X"("t") and "P"("t") satisfy the classical equations of motion; also see Ehrenfest's theorem, below.


title: Matrix mechanics

text: When it was introduced by Werner Heisenberg, Max Born and Pascual Jordan in 1925, matrix mechanics was not immediately accepted and was a source of controversy, at first. Schrödinger's later introduction of wave mechanics was greatly favored.


title: Matrix mechanics

text: Part of the reason was that Heisenberg's formulation was in an odd mathematical language, for the time, while Schrödinger's formulation was based on familiar wave equations. But there was also a deeper sociological reason. Quantum mechanics had been developing by two paths, one led by Einstein, who emphasized the wave–particle duality he proposed for photons, and the other led by Bohr, that emphasized the discrete energy states and quantum jumps that Bohr discovered. De Broglie had reproduced the discrete energy states within Einstein's framework—the quantum condition is the standing wave condition, and this gave hope to those in the Einstein school that all the discrete aspects of quantum mechanics would be subsumed into a continuous wave mechanics.


title: Matrix mechanics

text: Matrix mechanics, on the other hand, came from the Bohr school, which was concerned with discrete energy states and quantum jumps. Bohr's followers did not appreciate physical models that pictured electrons as waves, or as anything at all. They preferred to focus on the quantities that were directly connected to experiments.


title: Matrix mechanics

text: In atomic physics, spectroscopy gave observational data on atomic transitions arising from the interactions of atoms with light quanta. The Bohr school required that only those quantities that were in principle measurable by spectroscopy should appear in the theory. These quantities include the energy levels and their intensities but they do not include the exact location of a particle in its Bohr orbit. It is very hard to imagine an experiment that could determine whether an electron in the ground state of a hydrogen atom is to the right or to the left of the nucleus. It was a deep conviction that such questions did not have an answer.


title: Matrix mechanics

text: The matrix formulation was built on the premise that all physical observables are represented by matrices, whose elements are indexed by two different energy levels. The set of eigenvalues of the matrix were eventually understood to be the set of all possible values that the observable can have. Since Heisenberg's matrices are Hermitian, the eigenvalues are real.


title: Matrix mechanics

text: If an observable is measured and the result is a certain eigenvalue, the corresponding eigenvector is the state of the system immediately after the measurement. The act of measurement in matrix mechanics 'collapses' the state of the system. If one measures two observables simultaneously, the state of the system collapses to a common eigenvector of the two observables. Since most matrices don't have any eigenvectors in common, most observables can never be measured precisely at the same time. This is the uncertainty principle.


title: Matrix mechanics

text: If two matrices share their eigenvectors, they can be simultaneously diagonalized. In the basis where they are both diagonal, it is clear that their product does not depend on their order because multiplication of diagonal matrices is just multiplication of numbers. The uncertainty principle, by contrast, is an expression of the fact that often two matrices "A" and "B" do not always commute, i.e., that "AB − BA" does not necessarily equal 0. The fundamental commutation relation of matrix mechanics,


title: Matrix mechanics

text: This principle of uncertainty holds for many other pairs of observables as well. For example, the energy does not commute with the position either, so it is impossible to precisely determine the position and energy of an electron in an atom.


title: Matrix mechanics

text: In 1928, Albert Einstein nominated Heisenberg, Born, and Jordan for the Nobel Prize in Physics. The announcement of the Nobel Prize in Physics for 1932 was delayed until November 1933. It was at that time that it was announced Heisenberg had won the Prize for 1932 "for the creation of quantum mechanics, the application of which has, inter alia, led to the discovery of the allotropic forms of hydrogen" and Erwin Schrödinger and Paul Adrien Maurice Dirac shared the 1933 Prize "for the discovery of new productive forms of atomic theory".


title: Matrix mechanics

text: It might well be asked why Born was not awarded the Prize in 1932, along with Heisenberg, and Bernstein proffers speculations on this matter. One of them relates to Jordan joining the Nazi Party on May 1, 1933, and becoming a stormtrooper. Jordan's Party affiliations and Jordan's links to Born may well have affected Born's chance at the Prize at that time. Bernstein further notes that when Born finally won the Prize in 1954, Jordan was still alive, while the Prize was awarded for the statistical interpretation of quantum mechanics, attributable to Born alone.


title: Matrix mechanics

text: Heisenberg's reactions to Born for Heisenberg receiving the Prize for 1932 and for Born receiving the Prize in 1954 are also instructive in evaluating whether Born should have shared the Prize with Heisenberg. On November 25, 1933, Born received a letter from Heisenberg in which he said he had been delayed in writing due to a "bad conscience" that he alone had received the Prize "for work done in Göttingen in collaboration – you, Jordan and I." Heisenberg went on to say that Born and Jordan's contribution to quantum mechanics cannot be changed by "a wrong decision from the outside."


title: Matrix mechanics

text: In 1954, Heisenberg wrote an article honoring Max Planck for his insight in 1900. In the article, Heisenberg credited Born and Jordan for the final mathematical formulation of matrix mechanics and Heisenberg went on to stress how great their contributions were to quantum mechanics, which were not "adequately acknowledged in the public eye."


title: Matrix mechanics

text: Once Heisenberg introduced the matrices for "X" and "P", he could find their matrix elements in special cases by guesswork, guided by the correspondence principle. Since the matrix elements are the quantum mechanical analogs of Fourier coefficients of the classical orbits, the simplest case is the harmonic oscillator, where the classical position and momentum, "X"("t") and "P"("t"), are sinusoidal.


title: Matrix mechanics

text: In units where the mass and frequency of the oscillator are equal to one (see nondimensionalization), the energy of the oscillator is


title: Matrix mechanics

text: The level sets of are the clockwise orbits, and they are nested circles in phase space. The classical orbit with energy is


title: Matrix mechanics

text: The old quantum condition dictates that the integral of over an orbit, which is the area of the circle in phase space, must be an integer multiple of Planck's constant. The area of the circle of radius is . So


title: Matrix mechanics

text: Both and have only a single frequency, and "X" and "P" can be recovered from their sum and difference.


title: Matrix mechanics

text: Since has a classical Fourier series with only the lowest frequency, and the matrix element is the -th Fourier coefficient of the classical orbit, the matrix for is nonzero only on the line just above the diagonal, where it is equal to . The matrix for is likewise only nonzero on the line below the diagonal, with the same elements. Thus, from and, reconstruction yields


title: Matrix mechanics

text: which, up to the choice of units, are the Heisenberg matrices for the harmonic oscillator. Both matrices are hermitian, since they are constructed from the Fourier coefficients of real quantities.


title: Matrix mechanics

text: The matrix product of and is not hermitian, but has a real and imaginary part. The real part is one half the symmetric expression , while the imaginary part is proportional to the commutator formula_16 It is simple to verify explicitly that in the case of the harmonic oscillator, is , multiplied by the identity.


title: Matrix mechanics

text: The harmonic oscillator is an important case. Finding the matrices is easier than determining the general conditions from these special forms. For this reason, Heisenberg investigated the anharmonic oscillator, with Hamiltonian


title: Matrix mechanics

text: In this case, the and matrices are no longer simple off diagonal matrices, since the corresponding classical orbits are slightly squashed and displaced, so that they have Fourier coefficients at every classical frequency. To determine the matrix elements, Heisenberg required that the classical equations of motion be obeyed as matrix equations,


title: Matrix mechanics

text: He noticed that if this could be done, then , considered as a matrix function of and , will have zero time derivative.


title: Matrix mechanics

text: Given that all the off diagonal elements have a nonzero frequency; being constant implies that is diagonal.


title: Matrix mechanics

text: It was clear to Heisenberg that in this system, the energy could be exactly conserved in an arbitrary quantum system, a very encouraging sign.


title: Matrix mechanics

text: The process of emission and absorption of photons seemed to demand that the conservation of energy will hold at best on average. If a wave containing exactly one photon passes over some atoms, and one of them absorbs it, that atom needs to tell the others that they can't absorb the photon anymore. But if the atoms are far apart, any signal cannot reach the other atoms in time, and they might end up absorbing the same photon anyway and dissipating the energy to the environment. When the signal reached them, the other atoms would have to somehow recall that energy. This paradox led Bohr, Kramers and Slater to abandon exact conservation of energy. Heisenberg's formalism, when extended to include the electromagnetic field, was obviously going to sidestep this problem, a hint that the interpretation of the theory will involve wavefunction collapse.


title: Matrix mechanics

text: Demanding that the classical equations of motion are preserved is not a strong enough condition to determine the matrix elements. Planck's constant does not appear in the classical equations, so that the matrices could be constructed for many different values of and still satisfy the equations of motion, but with different energy levels.


title: Matrix mechanics

text: So, in order to implement his program, Heisenberg needed to use the old quantum condition to fix the energy levels, then fill in the matrices with Fourier coefficients of the classical equations, then alter the matrix coefficients and the energy levels slightly to make sure the classical equations are satisfied. This is clearly not satisfactory. The old quantum conditions refer to the area enclosed by the sharp classical orbits, which do not exist in the new formalism.


title: Matrix mechanics

text: The most important thing that Heisenberg discovered is how to translate the old quantum condition into a simple statement in matrix mechanics.


title: Matrix mechanics

text: There are several problems with this integral, all stemming from the incompatibility of the matrix formalism with the old picture of orbits. Which period "T" should be used? "Semiclassically", it should be either "m" or "n", but the difference is order , and an answer to order is sought. The "quantum" condition tells us that "J" is 2π"n" on the diagonal, so the fact that "J" is classically constant tells us that the off-diagonal elements are zero.


title: Matrix mechanics

text: His crucial insight was to differentiate the quantum condition with respect to "n". This idea only makes complete sense in the classical limit, where "n" is not an integer but the continuous action variable "J", but Heisenberg performed analogous manipulations with matrices, where the intermediate expressions are sometimes discrete differences and sometimes derivatives.


title: Matrix mechanics

text: In the following discussion, for the sake of clarity, the differentiation will be performed on the classical variables, and the transition to matrix mechanics will be done afterwards, guided by the correspondence principle.


title: Matrix mechanics

text: In the classical setting, the derivative is the derivative with respect to "J" of the integral which defines "J", so it is tautologically equal to 1.


title: Matrix mechanics

text: where the derivatives "dP"/"dJ" and "dX"/"dJ" should be interpreted as differences with respect to "J" at corresponding times on nearby orbits, exactly what would be obtained if the Fourier coefficients of the orbital motion were differentiated. (These derivatives are symplectically orthogonal in phase space to the time derivatives "dP"/"dt" and "dX"/"dt").


title: Matrix mechanics

text: The final expression is clarified by introducing the variable canonically conjugate to "J", which is called the angle variable "θ": The derivative with respect to time is a derivative with respect to "θ", up to a factor of 2π"T",


title: Matrix mechanics

text: So the quantum condition integral is the average value over one cycle of the Poisson bracket of "X" and "P".


title: Matrix mechanics

text: An analogous differentiation of the Fourier series of "P dX" demonstrates that the off-diagonal elements of the Poisson bracket are all zero. The Poisson bracket of two canonically conjugate variables, such as "X" and "P", is the constant value 1, so this integral really is the average value of 1; so it is 1, as we knew all along, because it is "dJ/dJ" after all. But Heisenberg, Born and Jordan, unlike Dirac, were not familiar with the theory of Poisson brackets, so, for them, the differentiation effectively evaluated {"X, P"} in "J, θ" coordinates.


title: Matrix mechanics

text: The Poisson Bracket, unlike the action integral, does have a simple translation to matrix mechanics−−it normally corresponds to the imaginary part of the product of two variables, the commutator.


title: Matrix mechanics

text: To see this, examine the (antisymmetrized) product of two matrices "A" and "B" in the correspondence limit, where the matrix elements are slowly varying functions of the index, keeping in mind that the answer is zero classically.


title: Matrix mechanics

text: In the correspondence limit, when indices "m", "n" are large and nearby, while "k","r" are small, the rate of change of the matrix elements in the diagonal direction is the matrix element of the "J" derivative of the corresponding classical quantity. So its possible to shift any matrix element diagonally through the correspondence,


title: Matrix mechanics

text: where the right hand side is really only the ("m" − "n")'th Fourier component of "dA"/"dJ" at the orbit near "m" to this semiclassical order, not a full well-defined matrix.


title: Matrix mechanics

text: The semiclassical time derivative of a matrix element is obtained up to a factor of "i" by multiplying by the distance from the diagonal,


title: Matrix mechanics

text: since the coefficient "A" is semiclassically the "k"'th Fourier coefficient of the "m"-th classical orbit.


title: Matrix mechanics

text: The imaginary part of the product of "A" and "B" can be evaluated by shifting the matrix elements around so as to reproduce the classical answer, which is zero.


title: Matrix mechanics

text: The leading nonzero residual is then given entirely by the shifting. Since all the matrix elements are at indices which have a small distance from the large index position ("m","m"), it helps to introduce two temporary notations:


title: Matrix mechanics

text: Flipping the summation variable in the first sum from to "r"' = "k" − "r", the matrix element becomes,


title: Matrix mechanics

text: The leading quantum part, neglecting the higher order product of derivatives in the residual expression, is then equal to


title: Matrix mechanics

text: Heisenberg's original differentiation trick was eventually extended to a full semiclassical derivation of the quantum condition, in collaboration with Born and Jordan.


title: Matrix mechanics

text: this condition replaced and extended the old quantization rule, allowing the matrix elements of "P" and "X" for an arbitrary system to be determined simply from the form of the Hamiltonian.


title: Matrix mechanics

text: The new quantization rule was "assumed to be universally true", even though the derivation from the old quantum theory required semiclassical reasoning.


title: Matrix mechanics

text: To make the transition to standard quantum mechanics, the most important further addition was the quantum state vector, now written |"ψ"⟩,


title: Matrix mechanics

text: which is the vector that the matrices act on. Without the state vector, it is not clear which particular motion the Heisenberg matrices are describing, since they include all the motions somewhere.


title: Matrix mechanics

text: The interpretation of the state vector, whose components are written , was furnished by Born. This interpretation is statistical: the result of a measurement of the physical quantity corresponding to the matrix is random, with an average value equal to


title: Matrix mechanics

text: Alternatively, and equivalently, the state vector gives the probability amplitude for the quantum system to be in the energy state .


title: Matrix mechanics

text: Once the state vector was introduced, matrix mechanics could be rotated to "any basis", where the matrix need no longer be diagonal. The Heisenberg equation of motion in its original form states that evolves in time like a Fourier component,


title: Matrix mechanics

text: and it can be restated so that it is true in an arbitrary basis, by noting that the matrix is diagonal with diagonal values ,


title: Matrix mechanics

text: This is now a matrix equation, so it holds in any basis. This is the modern form of the Heisenberg equation of motion.


title: Matrix mechanics

text: All these forms of the equation of motion above say the same thing, that is equivalent to , through a basis rotation by the unitary matrix , a systematic picture elucidated by Dirac in his bra–ket notation.


title: Matrix mechanics

text: Conversely, by rotating the basis for the state vector at each time by , the time dependence in the matrices can be undone. The matrices are now time independent, but the state vector rotates,


title: Matrix mechanics

text: This is the Schrödinger equation for the state vector, and this time-dependent change of basis amounts to transformation to the Schrödinger picture, with ⟨"x"|"ψ"⟩ = "ψ"("x").


title: Matrix mechanics

text: In quantum mechanics in the Heisenberg picture the state vector, |"ψ"⟩ does not change with time, while an observable "A" satisfies the "Heisenberg equation of motion",


title: Matrix mechanics

text: The extra term is for operators such as formula_38which have an "explicit time dependence", in addition to the time dependence from the unitary evolution discussed.


title: Matrix mechanics

text: The Heisenberg picture does not distinguish time from space, so it is better suited to relativistic theories than the Schrödinger equation. Moreover, the similarity to classical physics is more manifest: the Hamiltonian equations of motion for classical mechanics are recovered by replacing the commutator above by the Poisson bracket (see also below). By the Stone–von Neumann theorem, the Heisenberg picture and the Schrödinger picture must be unitarily equivalent, as detailed below.


title: Matrix mechanics

text: Matrix mechanics rapidly developed into modern quantum mechanics, and gave interesting physical results on the spectra of atoms.


title: Matrix mechanics

text: which, together with linearity, implies that a "P"-commutator effectively differentiates any analytic matrix function of "X".


title: Matrix mechanics

text: Assuming limits are defined sensibly, this extends to arbitrary functions−−but the extension need not be made explicit until a certain degree of mathematical rigor is required,


title: Matrix mechanics

text: Since "X" is a Hermitian matrix, it should be diagonalizable, and it will be clear from the eventual form of "P" that every real number can be an eigenvalue. This makes some of the mathematics subtle, since there is a separate eigenvector for every point in space.


title: Matrix mechanics

text: In the basis where "X" is diagonal, an arbitrary state can be written as a superposition of states with eigenvalues "x",


title: Matrix mechanics

text: so that the operator −"iD" obeys the same commutation relation as "P". Thus, the difference between "P" and −"iD" must commute with "X",


title: Matrix mechanics

text: so it may be simultaneously diagonalized with "X": its value acting on any eigenstate of "X" is some function "f" of the eigenvalue "x".