text:
User:Céçaquiéça/Mont-Laurier

History

 * 1885 -- fondation / colonisation
 * Le train
 * Le pont
 * L'école d'agriculture
 * la polyvalente
 * La fin du train
 * le cégep
 * Le parc linéaire
 * La fusion

Law and government

mayor Michel Adrien

Geography

Canadian shield

Lièvre river Lièvre valley 309 / 117 + parc linéaire

Parc Toussaint Lachapelle

Économie

- Bois (Uniboard / Bellerive) - Transport routier - Tourisme

Demographics

In 2003, Mont-Laurier had a population of 14,186. anglais/français religions?

Sites of interests

- Draveur (Langevin) - Cathédrale

Colleges and universities

- Centre collégial

Sports teams

- Draveurs

Notable natives

les Lemieux

External links

http://www.mrc-antoine-labelle.qc.ca/doc/municipa/23m/m14.html http://www.uqo.ca/futurs-etudiants/mont-laurier/index.asp - le cégep - autres.

title: User:Céçaquiéça/Mont-Laurier


text:
Frovatriptan

Frovatriptan, sold under the brand name Frova, is a triptan drug developed by Vernalis for the treatment of migraine headaches and for short term prevention of menstrual migraine. The product is licensed to Endo Pharmaceuticals in North America and Menarini in Europe.

Medical uses
Frovatriptan is used in the treatment of migraine.

Available forms
It is available as 2.5 mg tablets.

Contraindications
Frovatriptan should not be given to patients with:
 * Ischemic heart disease
 * Cerebrovascular syndrome
 * Peripheral vascular disease
 * Uncontrolled hypertension
 * Hemiplegic or basilar migraine

Side effects
Rare, but serious cardiac events have been reported in patients with risk factors predictive of CAD. These include: coronary artery vasospasm, transient myocardial ischemia, myocardial infarction, ventricular tachycardia and ventricular fibrillation.

Pharmacodynamics
Frovatriptan is a serotonin receptor agonist, with high affinity for the 5-HT1B/1D receptors. It has no significant effects on the GABAA mediated channel activity and benzodiazepine binding sites. Frovatriptan inhibits excessive dilation of arteries that supply blood to the head.

Pharmacokinetics
Frovatriptan has a terminal elimination half-life of approximately 26 hours, making it the longest within its class.

US licensing
Frovatriptan is available only by prescription in the United States and Canada, where a secondary New Drug Approval (sNDA) was filed in July 2006.

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

title: Frovatriptan


text:
User talk:Jarjar

Hello. Who exactly is this Dr. Neil Grant and his philosophy of backwards time? I can't seem to find any mention of him on Google. -- Wikisux 03:17, 31 May 2004 (UTC)

title: User talk:Jarjar


text:
Chinese folklore

Chinese folklore encompasses the folklore of China, and includes songs, poetry, dances, puppetry, and tales. It often tells stories of human nature, historical or legendary events, love, and the supernatural. The stories often explain natural phenomena and distinctive landmarks. Along with Chinese mythology, it forms an important element in Chinese folk religion.

Folktales

The main influences on Chinese folk tales have been Taoism, Confucianism and Buddhism. Some folktales may have arrived from Germany when Grimm brothers had contributed some materials for the folktales regard to the country life of the German dwellers since the 1840s; others have no known western counterparts, but are widespread throughout East Asia. Chinese folktales include a vast variety of forms such as myths, legends, fables, etc. A number of collections of such tales, such as Pu Songling's Strange Stories from a Chinese Studio, now remain popular.

Each Chinese folktale includes the representation of various objects and animals and uses symbolic messages through its characters and usually strives to convey a message that instills the reader with some sort of virtuous insight. These messages are vital to Chinese culture and through these folktales, they will be passed down to future generations to also learn from.

Animals
The Great Race is a folk story that describes the creation of the Chinese zodiac calendar that includes twelves animals each representing a specific year in a twelve-year cycle.

Chinese folklore contains many symbolic folk meanings for the objects and animals within the folktales. One example of this is the symbolic meaning behind frogs and toads. Toads are named Ch'an Chu in Chinese, a folklore about Ch'an Chu illustrates the toad imports the implication of eternal life and perpetual. Chinese folklore unfolds the story of a Ch'an Chu (toad) is saved by Liu Hai, who is a courtier in ancient Chinese period. For recompense the gratitude to Liu Hai, Ch' an Chu divulge the secret of eternal life and being immortal to Liu Hai. And this is the origin of Ch' an Chu as a symbol of eternal in traditional Chinese folklore culture.

In the "Chinese myth of the Moon Goddess, Chang'e", frogs and toads are a symbol of wealth and prosperity as well as symbolize fertility, regeneration, yin, and immortality. It is said that there were ten suns exposing the earth in the ancient times. Hou Yi who was an archer as well as the husband of Chang'e, he shot down nine suns from the sky with his bow and arrow. For expressing gratitude god rewarded him with pill which is an immortal elixir. In some versions of this tale, Chang'e took the pill for in avarice and she transformed into a three-legged Ch'an Chu and eventually flew to the moon. Hou Yi loved his wife so much that God allowed him to reunite annually with Chang'e at moment of the full moon on the 15th of August in Chinese lunar calendar, which is the celebration of Mid-Autumn Festival. From then on, the moon and Chang'e relate to the toad comprise the significance eternal and reunion.

Study
Formal academic study of Chinese folklore began to gain popularity in the 1910s with the New Culture Movement, which advocated Vernacular Chinese as the language of education and literature. Because most folklore was created in the spoken language, this movement brought scholars' attention to the influences of folklore on classical literature. Hu Shi of Peking University, a strong advocate of Vernacular Chinese, concluded that when Chinese writers drew their inspiration from traditional tales and songs, Chinese literature experienced a renaissance. When writers neglected these sources, they lost touch with the people of the nation. An emphasis on the study of folklore, Hu concluded, could usher in a literary renaissance. A rising sense of national identity also spurred the new interest in traditional folklore. The first issue of the Folk-Song Weekly, a publication issued by the Folk-Song Research Society, stated that "Based on the folk songs, on the real feeling of the nation, a kind of new national poetry may be produced."

The Folksong Studies Movement became a key contributor to establishing Chinese folklore as a modern academic discipline. This movement was founded by Hu Shi's students and colleagues at Peking University, such as Gu Jiegang. They were successful in creating a field of study that focused on literature pertaining to Chinese folklore and attempted to bring to light the early traditions and culture of Chinese folklore in order to reestablish China's national spirit.; The May Fourth Movement in 1919 sparked patriotic students and scholars to collect and record historical folklore in both rural and urban areas. Folklore collections in the May Fourth Movement had a broad territorial sweep, including not only the ethnic Han, who form the majority, but also the minority areas. Folksong collection was carried by Peking University one year before the May Fourth Movement, started in 1918.

Some folklore enthusiasts also hoped to improve the condition of the Chinese people and believed it necessary to understand their ideas, beliefs, and customs. Communist activists and scholars collected songs and local lore, often, reinventing and reinterpreting them to emphasize such themes as the virtue of the working commoner and the evil of aristocracy, while they left out stories that expressed praise for the emperor or traditional Confucian values from their collections. Widely circulated stories of today may have been treated in this way. Some claimed that folksongs played a significant part in the integration of folklore culture in the early twentieth century of China, as well as a functional tool to convey the spirit of socialism and communism after the Liberation period. After China emerged from the Maoist period in the late 1970s, the state adopted a more accepting position toward academic research on China's cultural traditions and folklore. Forbidden traditions and practices in early Chinese history became more relevant and accepted.

Poetry and Songs
The Classic of Poetry, the earliest known Chinese collection of poetry, contains 160 folk songs in addition to courtly songs and hymns. One tradition holds that Confucius himself collected these songs, while another says that an emperor compiled them as a means to gauge the mood of the people and the effectiveness of his rule.

It is believed that Confucius did encourage his followers to study the songs contained in the Classic of Poetry, helping to secure the Classic of Poetry's place among the Five Classics. After Confucian ideas became further entrenched in Chinese culture (after about 100 BCE), Confucius's endorsement led many scholars to study the lyrics of the Classic of Poetry and interpret them as political allegories and commentaries.

Folksongs are divided into three major parts which are shan' ge (mountain songs), xiaodiao (little tunes), and chang'ge (long songs). Regarding shan'ge the mountain songs are having a deviation to represent the specific regional level, concentrating on rural rather than urban region. Xiaodiao can be considered as the mainstream folksongs among the genres, which are introduced to the general public with familiarity. Always accompanied by performs and professional stage shows presenting to the public. In terms of the chang'ge, long songs, which is a certain kind of narrative songs utilized mostly by the national minorities in some special events as a narrative form in singing.

Art
Chinese folklore has provided inspiration for visual imagery by Chinese weavers, painters, water colorists, and florists. One of the most striking examples is a silk funerary banner (circa 168 BC) that contains a number of stories from early China.

Film
Modern iterations of traditional Chinese stories can be found internationally as well as in native Chinese literature. Laurence Yep's The Magic Paintbrush, Maxine Hong Kingston's The Woman Warrior, and Walt Disney Pictures' Mulan (based on Hua Mulan) all borrow from Chinese folklore traditions.

Literature
Chinese folklore has provided inspiration for Chinese writers and poets for centuries. Folk songs, which were originally accompanied by dance and other styles of performing arts, provided inspiration for courtly poetry. Classical fiction began in the Han dynasty and was modeled after oral traditions, while Yuan and Ming era dramatic plays were influenced by folk plays.

title: Chinese folklore


text:
Peter Sauber

Peter Paul Sauber (born 13 October 1943) is a retired Swiss motorsport executive. He was the team principal and owner of various motorsports teams, most visibly the eponymous Sauber Formula One team.

Motorsport career
After being trained as an electrician, Sauber became a car salesman in Hinwil, Switzerland. This was Sauber's first real association with automobiles and it proved to be the catalyst for his involvement in motorsports. He competed in hillclimbing events in a Volkswagen Beetle he had purchased, and thus the foundations for his first project as a team owner were laid.

Team Sauber
After opting not to run the family traffic light business, Peter built the Sauber C1 (the C stands for Christiane, the name of his wife) in his parents' basement. It was a car of tubular frame, powered by a 1-litre Ford Cosworth engine. He subsequently drove it to the 1970 Swiss hillclimb championship. It also remained in racing for ten years in the hands of other drivers, notably Friedrich Hürzeler, who took the 1974 crown in the car.

In 1971, Sauber handed over the driver's seat to Hans Kunis, who drove the new Sauber C2 model in the same series, as Sauber himself had done so the year before.

Sauber had started to gain a portfolio of customers and in 1973, Sauber built three C3 spec chassis for different customers. Designed by Guy Boisson, the car was used predominantly in the Swiss Sports Car Championship.

The C4 of 1975 heralded the first aluminium chassis developed by the team, and Boisson was joined by Edy Wiss in designing it. Only one C4 was ever produced.

The most successful of the early Sauber cars, the C5 was used to great effect in conjunction with its 2-litre BMW engine—taking the 1976 Interserie Championship in the hands of Herbert Muller.

Being a Group 6 sports car, the car was allowed to take part in the legendary 24 Hours of Le Mans, and Sauber entered the C5 in both 1977 and 1978. In '77 the car led its class before retiring; the same thing happened in '78.

1979 marked the end of Sauber's first foray into sports car building – and the start of preparing chassis for Lola F2 cars. The drivers finished 1–2–4 in the championship that year – one of them was Max Welti, who subsequently joined the team as team manager.

In 1980, and 1981, Sauber and Welti turned their attention to developing BMW M1 sportscars, in the latter year it won the 1000km Nürburgring.

In 1982, with BASF sponsorship, Sauber returned to sports car racing. The C6 was the first car to be tested in a wind tunnel by Sauber. It was during these tests that Sauber built up a strong relationship with Leo Ress, who would later become instrumental in the F1 project.

In 1985, the team's relationship with Mercedes-Benz began. This sports car partnership culminated in November 1991 – having ignited the career of Michael Schumacher and Sauber's own protégé, Karl Wendlinger.

Formula One
Sauber now began to look seriously at launching an F1 team. In the summer of 1991 Harvey Postlethwaite joined the team to design an F1 car and Mercedes funded a vast new factory at Hinwil.

First Sauber team (1991–2005)
In November 1991 Mercedes decided against direct involvement and so Sauber entered F1 by itself in 1993, with drivers JJ Lehto and Karl Wendlinger powered by engines built by Ilmor but rebadged as Saubers. Sauber did convince Mercedes to enter F1 in 1994 but a year later the German company did a deal with McLaren, leaving Sauber to become the Ford F1 works team. This was followed by a deal with the Malaysian oil company Petronas in 1995 and the establishment of an engineering company called Sauber Petronas Engineering to design and build V10 engines. The company began buying old Ferrari engines and rebadging them as Sauber Petronas V10s but the F1 engine program itself was scrapped in 1998. In the later years of this period Sauber saw increased success with the team finishing fourth in the World Championship in 2001 and fifth in 2002 despite having a much smaller budget than many of its rivals. The team however never scored a race win.

The sale to BMW (2005–2009)
In June 2005, BMW acquired the major shareholding stake in the Sauber team from Credit Suisse, which owned more than 60% of the team from a deal Peter Sauber initiated in 1994 selling a majority stake of the team to its major sponsor. It was done with Peter Sauber's blessing, the team was known as BMW Sauber, and Peter took a background advisory role within it, retaining a 20% stake in the team.

Return to Peter Sauber (2009–2016)
In July 2009, BMW announced its withdrawal from Formula One at the end of the season. Peter Sauber worked with BMW to develop a rescue package that would allow the team to continue in the sport without the manufacturer's backing. Qadbak Investments Ltd were thought to have purchased the team, but on 27 November 2009 it was announced that the Qadbak deal had fallen through and BMW had instead reached an agreement to sell the entire F1 operation back to Peter Sauber.

This sale would only go ahead if the team was granted a place on the 2010 grid by the FIA. On 3 December 2009, the FIA announced it had confirmed Sauber's entry for the 2010 season had been granted, and Sauber regained ownership of the team. In May 2012, Sauber transferred a one-third stake in the Sauber Group to Monisha Kaltenborn, the team's CEO and his designated successor. In October, it was announced that Sauber was stepping back from the day-to-day running of his team, promoting Kaltenborn to the team principal's position. He remains President of the Sauber Group's board of directors.

The 2016 Formula One season saw Sauber back on the grid with financial troubles. In July 2016 Longbow Finance, a Swiss investment company, bought Sauber Motorsport gaining complete ownership. With the sale, Peter Sauber announced his retirement from motorsport with Pascal Picci taking his position at the company.

Personal life
Sauber is married to Christiane (for whom all of his cars are designated "C"). They have two sons: Philipp (born 1971) and Alex (born 1973). Alex began working for the Sauber team in 2010.

title: Peter Sauber


text: Category:Argentina

title: Category:Argentina


text:
Ælfwynn

Ælfwynn was the ruler of Mercia as the 'Second Lady of the Mercians' for a few months in 918, following her mother's death on 12 June 918. She was the daughter of Æthelred and Æthelflæd, the rulers of Mercia. Her accession was the only example of rule passing from one woman to another in the early medieval period in the British Isles. Manuscript C of the Anglo-Saxon Chronicle (ASC C) states: "Here also the daughter of Æthelred, Lord of the Mercians, was deprived of all control in Mercia, and was led into Wessex three weeks before Christmas; she was called Ælfwynn." ASC C dates Æthelflæd's death as 12 June 918 and Ælfwynn's deposition to December 919, but most historians revise the deposition to 918. George Molyneux gives the period of Ælfwynn's power as "six or eighteen months". ASC C is the only version of the Chronicle to mention Ælfwynn. Other versions reflect a West Saxon view point and ASC A states that Edward took power in Mercia immediately after Æthelflæd's death, but ASC C includes entries from a lost version called the 'Mercian Chronicle'.

Life
Ælfwynn's parents may have married as early as 882 and not later than 887. According to William of Malmesbury, Ælfwynn was the only child of Æthelflæd and Æthelred. The date of her birth is not recorded, but it is presumed that she was born soon after her parents' marriage, perhaps around 888. William's account states that her birth was a difficult one, and that this led her mother to abstain from further sexual relations.

Ælfwynn's father spent much of the decade after her birth on campaign with his father-in-law King Alfred and brother-in-law Edward Ætheling (later King Edward the Elder). By 902 his health was poor and Æthelflæd was from then onwards the effective ruler of Mercia. William of Malmesbury states that Alfred sent his eldest grandson, Æthelstan son of Edward, to be educated at the court of Æthelflæd. William's panegyric on Æthelstan claims that he received a first-class education in Mercia, and it is thought likely that Ælfwynn would have been equally well educated.

The first contemporary written evidence of Ælfwynn is dated to around 904, a charter (S 1280) recording the lease of land by Æthelred and Æthelflæd for the traditional three lives—those of Æthelred, Æthelflæd and Ælfwynn—in and around Worcester from Bishop Waerferth and the monks and clerics of Worcester Cathedral. Ælfwynn did not witness this charter, but she may have witnessed charter S 225 of circa 915, concerning lands around Farnborough, and she is very probably the Ælfwynn who witnessed S 367 of circa 903 relating to lands in Buckinghamshire.

Reign
Ælfwynn's mother died on 12 June 918. Unlike her mother, Ælfwynn may have lacked broad support. No opposition to Edward's decision to remove her from power and send her to Wessex in December 918 is recorded by the Anglo-Saxon Chronicle or elsewhere. It could be considered that Ælfwynn was the last ruler of Mercia, but that kingdom was not entirely absorbed into the kingdom of the Anglo-Saxons, later the kingdom of England, until much later. Her cousin Æthelstan was ruler of Mercia only before becoming king of the Anglo-Saxons, and so too was King Edgar ruler of the Mercians under his elder brother King Eadwig.

Later life
There is no certain record of Ælfwynn after her removal from power. In Maggie Bailey's view, she probably entered holy orders. It is possible that she is the religious woman named Ælfwynn who is the beneficiary of charter S 535 dated 948 in the reign of King Eadred. Shashi Jayakumar suggests that she may have been the Ælfwynn who was wife of Æthelstan Half-King and foster-mother of the future King Edgar.

Caradoc's History of Wales preserves a tradition that Ælfwynn was deposed on a pretense of secretly planning to marry a Danish king, but this is described by Michael Livingston as "historically unlikely".

title: Ælfwynn


text:
Tannic acid

Tannic acid is a specific form of tannin, a type of polyphenol. Its weak acidity (pKa around 6) is due to the numerous phenol groups in the structure. The chemical formula for commercial tannic acid is often given as C76H52O46, which corresponds with decagalloyl glucose, but in fact it is a mixture of polygalloyl glucoses or polygalloyl quinic acid esters with the number of galloyl moieties per molecule ranging from 2 up to 12 depending on the plant source used to extract the tannic acid. Commercial tannic acid is usually extracted from any of the following plant parts: Tara pods (Caesalpinia spinosa), gallnuts from Rhus semialata or Quercus infectoria or Sicilian sumac leaves (Rhus coriaria).

According to the definitions provided in external references such as international pharmacopoeia, Food Chemicals Codex and FAO-WHO tannic acid monograph only tannins obtained from the above-mentioned plants can be considered as tannic acid. Sometimes extracts from chestnut or oak wood are also described as tannic acid but this is an incorrect use of the term. It is a yellow to light brown amorphous powder.

While tannic acid is a specific type of tannin (plant polyphenol), the two terms are sometimes (incorrectly) used interchangeably. The long-standing misuse of the terms, and its inclusion in scholarly articles has compounded the confusion. This is particularly widespread in relation to green tea and black tea, both of which contain many different types of tannins not just exclusively tannic acid.

Tannic acid is not an appropriate standard for any type of tannin analysis because of its poorly defined composition.

Quercitannic and gallotannic acids
Quercitannic acid is one of the two forms of tannic acid found in oak bark and leaves. The other form is called gallotannic acid and is found in oak galls.

The quercitannic acid molecule is also present in quercitron, a yellow dye obtained from the bark of the Eastern black oak (Quercus velutina), a forest tree indigenous in North America. It is described as a yellowish-brown amorphous powder.

In 1838, Jöns Jacob Berzelius wrote that quercitannate is used to dissolve morphine.

In 1865 in the fifth volume of "A dictionary of chemistry", Henry Watts wrote : It exhibits with ferric salts the same reactions as gallotannic acid. It differs however from the latter in not being convertible into gallic acid, and not yielding pyrogallic acid by dry distillation. It is precipitated by sulfuric acid in red flocks. (Stenhouse, Ann. Ch. Pharm. xlv. 16.) According to Rochleder (ibid lxiii. 202), the tannic acid of black tea is the same as that of oak-bark.

In 1880, Etti gave for it the molecular formula C17H16O9. He described it as an unstable substance, having a tendency to give off water to form anhydrides (called phlobaphenes), one of which is called oak-red (C34H30O17). For him, it was not a glycoside.

In Allen's "Commercial Organic Analysis", published in 1912, the formula given was C19H16O10.

Other authors gave other molecular formulas like C28H26O15, while another formula found is C28H24O11.

According to Lowe, two forms of the principle exist – "one soluble in water, of the formula C28H28O14, and the other scarcely soluble, C28H24O12. Both are changed by the loss of water into oak red, C28H22O11."

Quercitannic acid was for a time a standard used to assess the phenolic content in spices, given as quercitannic acid equivalent.

In an interesting historical note, the inventor of carborundum, Edward G. Acheson, discovered that gallotannic acid greatly improved the plasticity of clay. In his report of this discovery in 1904 he noted that the only known historical reference to the use of organic material added to clay is the use of straw mixed with clay described in the Bible, Exodus 1:11 and that the Egyptians must have been aware of his (re-)discovery. He stated "This explains why the straw was used and why the children of Israel were successful in substituting stubble for straw, a course that would hardly be possible, were the fibre of the straw depended upon as a bond feasible for the clay, but quite reasonable where the extract of the plant was used."

Uses
Tannins are a basic ingredient in the chemical staining of wood, and are already present in woods like oak, walnut, and mahogany. Tannic acid can be applied to woods low in tannin so chemical stains that require tannin content will react. The presence of tannins in the bark of redwood (Sequoia) is a strong natural defense against wildfire, decomposition and infestation by certain insects such as termites. It is found in the seeds, bark, cones, and heartwood.

Tannic acid is a common mordant used in the dyeing process for cellulose fibers such as cotton, often combined with alum and/or iron. The tannin mordant should be done first as metal mordants combine well with the fiber-tannin complex. However this use has lost considerable interest.

Similarly tannic acid can also be used as an aftertreatment to improve wash fastness properties of acid dyed polyamide. It is also an alternative for fluorocarbon aftertreatments to impart anti-staining properties to polyamide yarn or carpets. However, due to economic considerations currently the only widespread use as textile auxiliary is the use as an agent to improve chlorine fastness, i.e. resistance against dye bleaching due to cleaning with hypochlorite solutions in high-end polyamide 6,6-based carpets and swimwear. It is, however, used in relatively small quantities for the activation of upholstery flock; this serves as an anti-static treatment.

Tannic acid is used in the conservation of ferrous (iron based) metal objects to passivate and inhibit corrosion. Tannic acid reacts with the corrosion products to form a more stable compound, thus preventing further corrosion from taking place. After treatment the tannic acid residue is generally left on the object so that if moisture reaches the surface the tannic acid will be rehydrated and prevent or slow any corrosion. Tannic acid treatment for conservation is very effective and widely used but it does have a significant visual effect on the object, turning the corrosion products black and any exposed metal dark blue. It should also be used with care on objects with copper alloy components as the tannic acid can have a slight etching effect on these metals.

Tannic acid is also found in commercially available iron/steel corrosion treatments, such as Hammerite Kurust.

Use in food
In many parts of the world, its uses in food are permitted. In the United States, tannic acid is generally recognized as safe by the Food and Drug Administration for use in baked goods and baking mixes, alcoholic and non-alcoholic beverages, frozen dairy products, soft and hard candy, meat products, and rendered animal fat.

According to EU directive 89/107/EEC, tannic acid cannot be considered as a food additive and consequently does not hold an E number. Under directive 89/107/EEC, tannic acid can be referred to as a food ingredient. The E-number E181 is sometimes incorrectly used to refer to tannic acid; this in fact refers to the INS number assigned to tannic acid under the FAO-WHO Codex Alimentarius system.

Uses as a medication
In conjunction with magnesium and sometimes activated charcoal, tannic acid was once used as a treatment for many toxic substances, such as strychnine, mushroom, and ptomaine poisonings in the late 19th and early 20th centuries.

The introduction of tannic acid treatment of severe burn injuries in the 1920s significantly reduced mortality rates. During World War I, tannic acid dressings were prescribed to treat "burns, whether caused by incendiary bombs, mustard gas, or lewisite". After the war this use was abandoned due to the development of more modern treatment regimens.

Hazards
Tannic acid could cause potential health hazards such as damage to the eye, skin, respiratory tract, and gastrointestinal tract. It may cause irritation, redness, pain, blurred vision, and possible eye damage. When tannic acid is absorbed through the skin in harmful amounts, it may cause irritation, redness, and pain. Nausea, vomiting and diarrhoea are symptoms of tannic acid ingestion and prolonged exposure may cause liver damage. Upon inhalation, tannic acid may cause respiratory tract irritation.

Crocodilian coloration
Skin color in Crocodilia (crocodiles and alligators) is very dependent on water quality. Algae-laden waters produce greener skin, while tannic acid in the water from decay of leaves from overhanging trees (which produces some types of blackwater rivers) often produce darker skin in these animals.

General references
The Merck Index, 9th edition, Merck & Co., Rahway, New Jersey, 1976.

title: Tannic acid


text: Category:Bolivia

title: Category:Bolivia


text:
Malaysian Chinese

Malaysian Chinese, Chinese Malaysians, or Sino-Malaysians are Malaysian citizens of Han Chinese ethnicity. They form the second-largest ethnic group, after the Malay majority, and are 22.8% of the Malaysian population. Most of them are descendants of Southern Chinese immigrants who arrived in Malaysia between the early 19th and the mid-20th centuries. Malaysian Chinese form the second largest community of Overseas Chinese in the world, after Thai Chinese. Malaysian Chinese are traditionally dominant in the business sector of the Malaysian economy.

The ethnic subgroups of Chinese people in Malaysia include the Hokkien, Teochew, Cantonese, Hakka, Hainan, Fuzhou and Kwongsai. Different Chinese languages are spoken in Malaysian towns and cities. Among them are Hokkien in George Town, Alor Setar, Kangar, Butterworth, Bayan Lepas, Simpang Ampat, Perai, Klang, Taiping, Kota Bharu, Kuala Terengganu, Malacca City, Johor Bahru and Kuching, Teochew in Johor Bahru, Bukit Mertajam, Nibong Tebal, Sungai Petani, Parit Buntar and Miri, Cantonese in Kuala Lumpur, Cheras, Kajang, Ipoh, Kuantan, Seremban, Mersing, Kampar, Petaling Jaya and Sandakan, Hakka in Kota Kinabalu, Balik Pulau, Tawau, Kulai and Kuala Kangsar, Fuzhou in Sibu, Miri and Sitiawan, and Hainanese in Kuala Terengganu and Papar. However, Mandarin is now widely used as a working language or lingua franca among the different Chinese ethnicities, particularly for younger generations.

Most Malaysian Chinese have maintained their Chinese heritage, including their diverse mother tongues. However, the descendants of the earliest Chinese migrants who arrived between the 13th and the 17th centuries have assimilated aspects of the indigenous Malay cultures and formed distinct sub-ethnic groups, such as the Peranakans in Kelantan and Terengganu, Baba-Nyonya in Malacca and Penang, and the Sino-Natives in Sabah. The Malaysian Chinese are usually referred to as simply "Chinese" in Malaysian English, "Orang Cina" in Malay, "Sina" or "Kina" among indigenous groups in Borneo, "Cīṉar" (சீனர்) in Tamil, and "Huaren" (華人/华人, Chinese people), "Huaqiao" (華僑/华侨, Overseas Chinese), or "Huayi" (華裔/华裔, ethnic Chinese) in Mandarin by the local Chinese themselves.

Although the Malaysian Chinese population is increasing in every census, the proportion of ethnic Chinese among the country's total population has been consistently declining because of a lower birth rate and high emigration rate in recent decades. According to a report by the World Bank, the Malaysian diaspora around the world in 2010 included around a million people, most of them ethnic Chinese. The large number of emigrants, many of whom are young with education or skills, constitutes a significant "brain drain" from the country, especially towards the country's immediate neighbour Singapore.

Early history
China and other early kingdoms in the Malay Archipelago, such as the northern area of the Malay Peninsula and Po-Ni in western Borneo, have long been connected. The first recorded movement of people from China into present-day Malaysia was the 1292 arrival of Mongol expeditionary forces under Kublai Khan in Borneo in 1292 in preparation for their invasion of Java the following year. Many of Khan's Chinese followers settled on the island with Chinese traders after the campaign, establishing an enclave along the Kinabatangan River. Their arrival was welcomed by the indigenous people, who benefited from the jars, beads, silk, and pottery brought to the island by the Chinese.

Chinese explorer and sailor Zheng He commanded several expeditions to south-east Asia between 1405 and 1430; during his third voyage, Zheng also visited Malacca. His companion and translator, Ma Huan, described Malacca in his Yingya Shenglan. Formerly part of Thailand, Malacca was founded after convoys from the Ming Dynasty developed a city and the area's chief was crowned king. During his fourth imperial-fleet visit, Ma wrote that the local king had just converted to Islam and dressed like an Arab. The last edition of Mingshi, one of the official Chinese Twenty-Four Histories, mentioned a pre-established Chinese settlement in the area. Mentions in other records exist, especially after trade contacts were established with the Nanyang region. According to Hai Yü (Words about the Sea), written by Huang Zhong and published in 1537, the lifestyle of the Chinese community in Malacca differed from that of the local Malays.

This close relationship was maintained during the Islamisation of the Malacca and Brunei kingdoms, whose thalassocracy once covered much of present-day Malaysia. Both the Muslim sultanates pledged protection to the Chinese dynasties from further conquest by the neighbouring Javanese Majapahit or the Siamese Ayutthaya. This relationship resulted in interethnic marriage between the sultanate's royal family and the Chinese envoy and representatives. Zheng He's arrival encouraged the spread of Islam in the Malay Archipelago and aided the growth of the Chinese Muslim population from the Eastern Chinese coastal towns of Fujian and Canton, with many of their traders arriving in the coastal towns of present-day Malaysia and Indonesia by the early 15th century. In addition to the early settlements in Kinabatangan and Malacca, two more old Chinese settlements are located in Terengganu and the Penang Island as part of trade networks with their respective areas.

Colonial era (1500–1900)
Although many Chinese traders avoided Portuguese Malacca after its 1511 conquest, the flow of emigrants from China continued. The Zhengde Emperor retaliated against the Portuguese for their activities in Malacca during the Ming dynasty after the arrival of their fleet in Canton. The Chinese emperor was reluctant to help the deposed Malaccan ruler reclaim his position, however, since the dynasty foreign policy was changing to maintain friendly relations with the Portuguese.

His successor, the Jiajing Emperor, changed the attitude of the Ming court by executing two government officials and reaffirming the importance of Malaccan issues in major policy decisions. Some Chinese, including those from Fujian (defying Ming-Dynasty regulation for the sake of trade), informed the Portuguese of the trade route between Guangdong and Siam. Since the local Malaccan Chinese were not treated favourably by the Portuguese, they and most overseas Chinese refused to cooperate with them. Through the Portuguese administration in Malacca, Chinese Muslims sided with other Islamic traders against the latter by providing ships and human capital. Negotiations were later held in Guangdong between Chinese officials and Portuguese envoys about Malaccan issues, with Malacca remaining under Portuguese control.

After the 1641 Dutch takeover of Malacca, many local Malaccan Chinese were hired to construct Dutch buildings. The Dutch found the Chinese industrious, and encouraged their participation in the colony's economic life; the Dutch also established a settlement in Perak in 1650 through an earlier treaty with Aceh and suggested that Alauddin, the 17th Sultan of Perak, allow the Chinese to develop tin mines. This facilitated Alauddin's plan to request more Chinese workers from Malacca, and the sultan promised to punish any official guilty of mistreating the Chinese.

With the sultan consent, the Chinese played a leading role in the tin-mining industry. The Fourth Anglo-Dutch War in 1780 adversely affected the tin trade, however, and many Chinese miners left. Early Chinese settlements in Malacca and several areas along the archipelago's coasts notwithstanding, most mass Chinese migration to Malaysia occurred after the founding of British settlements in Malaya and Borneo during the early 19th century.

A 1786 British settlement in Penang and another in Singapore in 1819 triggered a mass emigration from China to the Malay Peninsula. After the establishment of British rule in Labuan in 1846, more ethnic Chinese (primarily Hakka, and many from Singapore) arrived in British Borneo. The migration continued through the first few years of the North Borneo Chartered Company. Chinese migration to Labuan and North Borneo was largely confined to the agricultural sector; migration to the Raj of Sarawak was largely restricted to the mining and agricultural sectors. Rajah Charles Brooke of Sarawak promoted the migration of Chinese and Dayak people to interior Sarawak to develop the region. This resulted in the establishment of an administrative center and bazaar by the 19th century, primarily in Sarawak's First, Second, and Third Divisions.

Rajah Charles invited Chinese black-pepper growers from Singapore to settle in Kuching in 1876, and they were later joined by local Chinese miners and others from neighbouring Dutch Borneo. With the introduction of pepper to the kingdom, pepper cultivation in Sarawak's First Division Kuching-Serian region was dominated by the Hakka; Fuzhou and Cantonese people dominated cultivation in the Third Division Sarikei-Binatang region, making Sarawak the world's second-largest pepper producer. After the British gained control of the four states of Perak, Selangor, Negeri Sembilan and Pahang, nearly two million Chinese immigrated to Perak and Selangor.

After the discovery of tin deposits in British Malaya, many Chinese immigrants worked in the tin-mining industry. As tin mines opened in Perak, many Chinese in neighbouring Penang became wealthy. Many Chinese tin-mining communities were established in the Malay Peninsula by the 1870s, particularly in Ipoh (Kinta Valley), Taiping, Seremban and Kuala Lumpur (Klang Valley). Each of the mining communities was governed by a Kapitan Cina, with duties and privileges similar to those in Johor's Kangchu system. Chinese migration sprang from poverty in rural China and employment opportunities in the British colonies or protectorates, and an estimated five million Chinese had immigrated by the 19th century. Despite economic prosperity after immigration, the new Chinese communities split into a number of secret societies. This exacerbated political unrest among the Malay aristocracy, which enlisted help from the secret societies. Contemporary local Malay politics was characterised as anarchy and civil war between people from similar backgrounds, prompting alliances between senior Malay political leaders and officials from China and Europe who were protecting their investments.

Divided nationalism and turbulence (1900–1945)
Civil wars and other conflicts among the indigenous ethnic groups ended when the British gained control of Malaya and the northern island of Borneo by the 1900s. However, none of the Malay kingdoms fell under colonial rule. Their related entities were politically and economically stable. Economic prosperity was fueled by British capital and Chinese and Indian work forces who expanded and supplied tin and rubber production. Before the 1911 Xinhai Revolution which overthrew the Qing dynasty in China, Tongmenghui leader Sun Yat-sen raised funds and organisational support from overseas Chinese communities (primarily in French Indochina, the Dutch East Indies, the Philippines, Siam, British Singapore, Malaya and Borneo) and began Nanyang organising activities in Saigon, Hanoi, Pontianak, Manila, Bangkok, Singapore and George Town. Competition arose among three groups, with each group targeting overseas Chinese (particularly in Malaya and Singapore) for support. One group was a pro-Qing elite who targeted wealthy Chinese; the other two were reformists and revolutionaries who advocated constitutional reforms, the introduction of a parliamentary system, and the overthrow of Qing and Manchu influence on a modern Chinese nation.

After the revolution which established the Republic of China, branches of the Kuomintang emerged in British Malaya. Kuomintang activities in British Borneo were coordinated by the Democratic Party of North Borneo, consisting of Chinese-educated towkays. Patriotism among Chinese immigrant communities focused on China. British colonial authorities initially did not object to Kuomintang membership. A communist movement developed among overseas Chinese by 1925 with the establishment of the South Seas Communist Party in Singapore, followed by the Indochinese Communist Party, Communist Party of Malaya, Communist Party of Burma and Communist Party of Siam; the movement also maintained relations with the earlier, Southeast Asian Communist Party of Indonesia. The Communist Party of Malaya followed the general communist policy of opposing Western democracies before World War II, increasing propaganda against the Malayan government and the colonial government of Singapore in 1940.

At the beginning of the Sino-Japanese conflict and the Japanese occupation of Malaya and British Borneo, Kuomintang activities were ended. When the Chinese Communist Party (under Mao Zedong) reached an agreement with the Kuomintang government (under Chiang Kai-shek) to put aside their differences and rally against Japanese aggression in July 1940, pro-independence sentiment led to bans on the Kuomintang and other Chinese organizations in Malaya. Since the conflict with Japan also involved the British, Chiang Kai-shek urged Kuomintang members to fight alongside them; in return, British colonial authorities lifted their ban of Chinese associations (including the Kuomintang and the Chinese communist movement). This, and British recognition of the Communist Party of Malaya, resulted in the formation of the guerrilla Malayan Peoples' Anti-Japanese Army (MPAJA) in 1941. The MPAJA (primarily consisting of ethnic Chinese in Malaya) waged a guerrilla war against the Imperial Japanese Army (IJA) with 10,000 men in eight battalions, and contacted the British Force 136. Local Kuomintang revolts, such as the Jesselton uprising in British Borneo, were suppressed by the Kenpeitai.

Much Chinese underground anti-Japanese activity in North Borneo was part of the Nanyang Chinese National Salvation Movement, led by Tan Kah Kee; in Sarawak, activities were coordinated by the Sarawak Anti-Fascist League. The MPAJA was disbanded after the 1945 Allied victory in the Pacific, and many of its leaders were commended by the British. It began to massacre perceived collaborators (primarily Malay) after it was disbanded, however, sparking a Malay backlash. The MPAJA also targeted British posts, with several grenade attacks on British troops. In North Borneo, the Chinese co-operated with the British and pledged loyalty to King George VI when the Crown Colony of North Borneo was formed after the war.

Postwar unrest and social integration (1946–1962)

With the MPAJA renamed as the Malayan National Liberation Army (MNLA), communist insurgents used guerrilla tactics in the jungles, sabotaged transportation networks and attacked British plantations (assassinating several European plantation owners). British intelligence estimated MNLA support at about 500,000, out of a total Chinese population of 3.12 million; battling the insurgents was difficult, since most hid in inaccessible jungles. With the 18 June 1948 declaration of the Malayan Emergency, the early government response was chaotic; its primary aim was to guard important economic targets. Most Malayan Chinese opposed the MNLA.

The 1950 Briggs Plan, devised by British general Harold Briggs, intended to isolate the Chinese population from the insurgents. Independence was promised, and supported by the Malays; the Chinese population feared being treated as second-class citizens in an independent Malaya. In addition to new villages, the plan included labour reorganisation, the deployment of troops throughout Malaya, and cooperation between the police, the army, and intelligence. Under the resettlement scheme, more than 700,000 rural Chinese communities were relocated in 582 new government settlements. After British high commissioner Henry Gurney died in a 1951 ambush, Gerald Templer are appointed as the new high commissioner for Malaya by Winston Churchill the following year; Templer preferred winning hearts and minds to military measures against the insurgents. As part of his campaign, Templer incentivised rebel surrender and used strict curfews and tight control of food supplies in involved areas to flush them out. Crops grown by insurgents were sprayed with herbicides and defoliants, and restrictions were lifted in areas free of insurgents by elevating them to "white status". In the Batang Kali massacre, 24 unarmed Malaysian civilians suspected of providing aid to the MNLA were shot by a Scots Guard division in late 1948.

According to Chin Peng, the success of Templer's campaign was primarily due to the Briggs Plan's resettlement programme; Gurney also introduced a quasi-ministerial system, with a bill to increase the number of non-Malays eligible for citizenship after independence. After the 1949 Chinese Communist Revolution, foreign missionaries in China were forced to leave; Templer invited them to Malaya to provide spiritual healing, medical education and welfare measures to residents of the new government villages. By September 1952, every person born in Malaya (includes 1.2 million Chinese) was granted full citizenship.

When the Federation of Malaya gained independence from the British in 1957, there was still an insurgency. Chinese communists who surrendered were given a choice of repatriation to China or declaring loyalty to the elected government of Malaya and renouncing communist ideology. The anti-communist campaign continued until 1960, when the Malayan government declared the end of its state of emergency after Chin Peng demobilized his forces and left his hide-out in southern Thailand for Beijing via North Vietnam. At a meeting of Chin and Deng Xiaoping in Beijing, China urged the Communist Party of Malaya to continue their armed struggle. The establishment of a communist government in mainland China affected Chinese youth in Sarawak, who organized the pro-Beijing Sarawak Overseas Chinese Democratic Youth League (later the Sarawak Advanced Youth Association, which sparked the 1960 communist insurgency in Sarawak. Malaysia's economy continued to prosper, dependent on tin and rubber industries dominated by a Chinese and Indian workforce.

Struggle for equality in "Malaysian Malaysia" (1963–1965)
Early in 1961, when Prime Minister Tunku Abdul Rahman outlined a "Grand Malaysian Alliance" of the British protectorate of Brunei and the crown colonies of North Borneo, Sarawak and Singapore, Singapore Prime Minister Lee Kuan Yew supported the proposal. Lee's People's Action Party (PAP) rallied for the equality of all Malaysians, regardless of "class, skin colour or creed", known as "Malaysian Malaysia", in a multi-ethnic society without Malayisation. Although Lee was seen by Malay extremists in the United Malays National Organisation (UMNO) and the Pan-Malaysian Islamic Party (PAS), as opposed to Ketuanan Melayu after the 1963 formation of Malaysia, he had adopted Malay as Singapore's national language and appointed Malay Yusof Ishak as Yang di-Pertuan Negara.

The Malaysian Chinese Association (MCA), led by Tan Cheng Lock and part of the Malaysian Alliance Party, refused to join the struggle for equality. The MCA feared that equality would disrupt an agreement between the United Malays National Organisation (UMNO) and the Malaysian Indian Congress (MIC) in which Malays were politically dominant and the Chinese controlled the country's economy; Malaysian Indians played a smaller economic role, with the Malays promising to share future political power with the other two groups. After two years as part of the federation and the enactment of Article 153 of the Constitution of Malaysia, Lee was joined by the Malay Peninsula's United Democratic Party and People's Progressive Party and Sarawak's United Peoples' Party and Machinda Party in the Malaysian Solidarity Convention to campaign for equality. In a June 1965 speech at the MSC meeting in Singapore, Lee said:

"It took a long time for us all to come to the same conclusions despite our differing experiences in Malaya, Singapore, Sabah and Sarawak. Our friends in Sabah are not here today officially, but I can assure you that we have many friends there. There is no doubt that it took us a long time to reach the inevitable conclusion that these people [referring to the racial politics in Malay Peninsula] were up to no good. You know the line they were taking with growing truculence on a heavy racial accent, the intimidatory postures and the snarling guttural notes on which they sent out their signals to their followers on the basis of the race lead us to only one conclusion -- that if this goes on, Malaysia will not belong to Malaysians. Since there are so many Malaysians, we decided that the time has come for us to speak our minds."

Lee's call for a re-alignment of forces between those who wanted a "true Malaysian nation" and those who preferred a country led by a component of the Alliance Party, and his criticism of Malays advocating Malay dominance, led to bitter PAP–UMNO relations and the 1964 race riots in Singapore; Singapore was later expelled from the federation in August 1965, and became its own sovereign nation.

Communist insurgencies and racial clashes (1965–1990)
The struggle for equality continued with the Democratic Action Party (DAP), which succeeded the PAP in 1965. Many Malaysian Chinese began to view the Malaysian Chinese Association as more concerned with business and economic interests than social factors, although Prime Minister Tunku Abdul Rahman considered the MCA the sole legitimate representative of the federation's Chinese community. In 1968, communists supported by China began a new insurgency from their stronghold in southern Thailand. The following year, the MCA was challenged by the DAP and the Malaysian People's Movement Party (GERAKAN). Of its 33 parliamentary seats contested in the election, the MCA retained 13 and lost control of the Penang state government to GERAKAN; Chinese-Malay tensions culminated in the 13 May incident. Other clashes were also ethnic in nature.

In the aftermath of the riots, Prime Minister Tunku Abdul Rahman blamed the communists rather than racial issues and said that the Vietnam War in their neighbour was "not simply a civil war but communist-ideology expansion". The Malaysian government introduced several policy initiatives in security and development, a neighbourhood-watch program and the People's Volunteer Corps. The Communist Party of Malaya split into two factions during the early 1970s: a revolutionary wing in 1970 and a Marxist–Leninist wing in 1974. Kuala Lumpur and Beijing established diplomatic relations in 1974; China ended its aid to the factions, prompting their 1983 merger into the Malaysian Communist Party before their surrender to Thai authorities four years later and the 1989 peace agreement ending the insurgency. A Chinese communist insurgency in Sarawak, supported by neighboring Indonesia, ended with peace negotiations in 1990.

1990 to present
Issues between the Malaysian Chinese and the Malays remain unresolved. The failure of Malaysia's social contract has led to a strong Chinese identity, in contrast to the Chinese communities in neighbouring Indonesia, the Philippines, Singapore, Thailand and Vietnam. After the 1969 racial clashes, the Malaysian New Economic Policy favouring the Malays from 1971 to 1990 increased Bumiputera economic control by 60 percent. Malaysian Chinese remain the business sector's dominant players; equity ownership doubled from 22.8 percent in 1969 to 45.5 percent in 1990, and nearly all of Malaysia's richest people are Chinese.

Since Malaysian Chinese manage the country's economy, most (75.8 percent in 1991) live in urban areas. They generally do not speak Malay among themselves; this contrasts with earlier Chinese communities such as the Straits-born Chinese of Baba-Nyonya, Kelantanese and Terengganuan Peranakans, Penangite Hokkien and Sabah Sino-natives, who mingled with local Malay and other indigenous peoples. Chinese in East Malaysia in Sabah and Sarawak, particularly in small inland towns, interact more closely with the indigenous communities. Integration issues in present-day Malaysia are largely inherited from Malayan racial politics, in which ethnic communities consolidated into a single political community. Malaysia's contemporary educational and social policies has created a Chinese brain drain to developed countries, especially Singapore. The country has experienced a slight wave of Mandarin-speaking immigrants from northeastern China and a smaller number of Vietnamese immigrants, however, with local men marrying women from China and Vietnam.

Origins and social demographics
Since their early ancient trade connection and subsequent migrations, the majority of ethnic Chinese in Malaysia are ethnic Han from the historical areas of Fujian and Guangdong provinces in southern China. Nearly all ethnic Chinese Malaysians living in the country today are either patrilineal descendants of these early immigrants, or new immigrants born in mainland China. Among the first group from the first migration wave are the Peranakans in Kelantan and Terengganu, Sino-Natives in Sabah and Straits-born Chinese (Baba-Nyonya) in Malacca and Penang. The Taiping Rebellion in the mid-19th century caused much chaos and suffering in southern China, which led many ethnic Chinese civilians to seek refuge overseas, particularly to the Nanyang region (Southeast Asia) in further south. With the expanding British colonial ambitions in the region which led to the establishment of Straits Settlements, more migrants were attracted and the region became an important destination for Chinese emigration.

By the late 19th century with the second wave of migration through the British colonial rule, the Hokkien of southern Fujian led by many of their wealthy and powerful individuals with skills in finance and maritime shipping became the dominant immigrant group as the first group of ethnic Chinese to settle in large numbers with their language become a contact language among Chinese of different linguistics background. The Cantonese from Guangdong follow suit and became well known as mineworkers, land reclamation, mechanics and their familiarity with cash cropping. Another large group, the Hakka are mostly hill farmers originated from northeastern Guangdong and various southern China places who specialise in forest clearance, mining as well on metalworking. Other groups like the Teochew from Chaozhou of eastern Guangdong are mainly on plantation agriculture, the Fuzhou from central Fujian specialise in entrepreneurship, while the Hainanese from Hainan as one of the ethnic Chinese minority saw themselves as sojourners with many of Hainanese chefs and waiters ruled the kitchen of local Chinese kopi tiam and restaurants. The Henghua and Hokchia from eastern Fujian are usually managing family industries while the Kwongsai from Guangxi are employed in labour sectors. Followed by the third wave of ethnic Chinese migration thereafter, this resulted from Malaysia as being one of the countries outside China and Taiwan with largest population of Chinese speakers in the world. Following the establishment of diplomatic relationship between Mainland China and Malaysia in 1974, a joint communiqué was made between the two nations, which stated:

The Chinese government considers anyone of Chinese origin who has taken up his own will or acquired Malaysian nationality as automatically forfeiting Chinese nationality. As for residents who retain Chinese nationality of their own will, the Chinese government, acting in accordance with its consistent policy, will enjoin them to abide by the law of the Government of Malaysia, respect the customs and habits of the people there, and live in unity with them, and their proper rights and interests will be protected by the Government of China and respected by the Government of Malaysia.

Ethnic distributions

The first census conducted in 1970 after Malaysia was formed in 1963 reported that there were 3,555,879 ethnic Chinese Malaysians, with the Hokkien or Min Nan (福建人 or 闽南人) being the majority at 32.4%, followed by Hakka (客家人) at 22.1%, Cantonese (广府人) at 19.8%, Teochew (潮汕人) and Hainanese (海南人) at 12.4% and 4.7% respectively. This increase to 4,554,664 in 1980 and 4,623,900 in 1991. In 2000, the census reported that ethnic Chinese Malaysians numbered at 5,691,908, which was approximately 24.45% of the country's population at the time, with 86% of them living in urban areas. In West Malaysia, Hokkien became the leading group followed by Cantonese, Hakka and Teochew. The pattern differs in East Malaysia where Hakka is the majority in Sabah and Sarawak followed by Hokkien and Cantonese in Sabah and the Fuzhou (福州人), Hokkien and Teochew in Sarawak. In 2010, the population increased further to 6,392,636.

The Hokkien are notably prominent in the states of Johor, Kedah, Kelantan, Malacca, Penang, Perlis, Perak, Sarawak, Labuan and Terengganu while the Hakka is prominent in Sabah and the second largest sub-group in Labuan. The Cantonese (including the smaller population of Kwongsais or Guangxi (广西人) people in states such as Johor, Pahang and Perak) are mostly concentrated in the cities of Kuala Lumpur and Ipoh, and to some extent in Bera, Kuantan, Muallim, Bentong, Kuala Kangsar, Lipis, Mersing, Raub, Cameron Highlands, Jerantut, Temerloh, Bahau, Kampar, Rompin, Gopeng, Maran, Tapah, Pekan, Bidor and Seremban in the peninsular as well as Sandakan and Keningau (Taishanese or 台山人) in Sabah, and to a lesser extent, Miri and Sarikei in Sarawak. The Teochews are mostly found in Johor and Melaka, with a minority of them settling in pockets of Kedah, pockets of Penang and parts of coastal Selangor.

The Fuzhounese are numerous in Yong Peng, Sitiawan, Sungai Pelek, Miri, Bintangor, Sarikei, Bintulu, Kapit, and Sibu. The population of Hainanese can be found in all cities and towns in Malaysia, numerously in Malacca and Terengganu and Henghuas or Putian (兴化人 or 莆田人) and Hockchia or Fuqing (福清人) in various other areas.

There is also a small community of Huáběi-ren (Northern Chinese or 华北人) in Sabah whose ancestors coming from various parts of Hebei (河北) and Shandong (山东) provinces in China with most of them calling themselves as Tiānjīn-ren (天津人 or 津侨). Besides that, Sanjiang-ren is a collective term used to categorise the group of people whose ancestors hailed from Shanghai (上海), Zhejiang (浙江), Jiangsu (江苏), Hubei (湖北) and Jiangxi (江西). It is a subgroup of mixed spoken dialects and has the fewest people as compared to other Chinese subgroups. The first San Jiang Clansmen Association or San Kiang Association was formed in Penang back in 1897.

Although the ethnic Chinese population had been increasing since the 1970s, their proportion within the total population had been decreasing gradually, particularly caused by the lower birth rate among the Chinese community.

Economic and political representation
Ethnic Chinese Malaysians have been traditionally dominant in the business sector of the Malaysian economy with large local Chinese enterprises involved in natural resources and food ingredients industries such as sugar and palm oil. Almost every biscuits manufacturer in the country is dominated by ethnic Chinese Malaysians. Up to the 1970s, their economic structure was intertwined with very much family and kinship ties. By the 21st century with the rising of China's economic influence, their economy network are jointly connected with other Overseas Chinese through the bamboo network. The local Chinese played a key role in facilitating China's capital to invest in Malaysia while in the process both benefited from expanded markets, lower labour costs and the introduction of different kind of technologies and managerial systems which resulted from Malaysia becoming the largest trading partner to China in Association of Southeast Asian Nations (ASEAN) region. Nevertheless, unlike the more transboundary business influence by neighbouring Chinese Singaporeans, a majority of Chinese Malaysian businesses are still seen as less concentrating on developing business ties with other Southeast Asian Chinese businessmen despite there have been few businesses made by several local Malaysian Chinese companies.

Since the country's foundation in 1963, the Malaysian Chinese Association (MCA) was the sole legitimate political representation for ethnic Chinese in Malaysia under the multi-racial political coalition of the Alliance Party (later expanded into National Front coalition). However, the growing restriction of non-Malay interests in Malaysian society and politics since the 1970s caused deep dissension among Chinese Malaysians. The perception that their ethnic party representatives were unable to stand for their people's rights grew, and that decision-making was influenced by the Malay supremacists dominated party of United Malays National Organisation (UMNO). The UMNO was the most influential part of the existing political coalition, and also championed Islamic values. Despite the coalition's multi-racial appearance, UMNO founding president Onn Jaafar has once said that their movement did not adhere to any ideology other than "Malayism", defined by Malay scholar Ariffin Omar as the belief that the interests of the Malay race must be upheld over anything else. From 1968, the inability of MCA to preserve ethnic Chinese Malaysian interests, particularly with regards to their culture, education, and language, resulted in the formation of another ethnic Chinese representative party, the Malaysian People's Movement Party (GERAKAN) led by Chinese overseas-educated elite, although this party also joined the Alliance Party coalition in 1972.

The growing Islamisation with "Islamic version of non-tolerant and open", increasing racism within the Malay party members throughout the coalition imposing further into the country social demographics as well as the government discriminative policies on their education and employment, caused further disenchantment among non-Malays, especially ethnic Chinese. This subsequently caused dwindling support from ethnic Chinese Malaysians when many original strongholds of MCA constituents and even Gerakan turned to the Democratic Action Party (DAP) as the latter were seen as more vocal on their rights. The recent country general election in 2018 saw the fall of National Front coalition following additional aid from Bornean parliamentary seats particularly in Sabah that were won by Pakatan Harapan coalition ally of regionalist Sabah Heritage Party (WARISAN) as well from another indigenous party of United Pasokmomogun Kadazandusun Murut Organisation (UPKO) as a result of similar growing frustration over long-time manipulation of the state demographics and resources with lack of development through the administration of the Malay-led supremacists government of UMNO with frequent labelling as "fixed deposit state". During the election, the DAP won a large amount of seats due to the support of many Chinese constituents and subsequently diminished MCA influence among ethnic Chinese Malaysians.

Contributions towards local medical practice

Aside from their economic dominance, ethnic Chinese Malaysians are known for their contribution in the country healthcare sectors with their traditional health practice. Around 3,000 medicine shops in the country sell traditional Chinese medicine with development support also given by the country Health Ministry. Chinese traditional health practice services in the country generally encompass the zhong yi 中医 (Chinese medicine), qigong (气功), chiropractic care (整骨), acupuncture (针灸) and several others. In 2012, the Traditional and Complementary Medicine Bill (T&CM) was passed by the Parliament of Malaysia for the establishment of "Traditional and Complementary Medicine Council or Majlis Perubatan Tradisional dan Komplementari" to register and regulate traditional and complementary medicine practitioners, including traditional Chinese medicine practitioners as well Malay, indigenous and Indians traditional medicine which followed by the enforcement of T&CM Act in the following year. Since most of the traditional medicine pharmacies are family-apprentice trade, most of the traditional medicine practitioners are not registered as a doctor under the health department despite the support given by the Health Ministry with most can practice the career without needed to be registered under government law.

Education
In educational aspects, Malaysia is the only country outside China and Taiwan with a comprehensive and complete Chinese education system and the only Southeast Asian country that has perpetuated the Chinese education system established since the colonial era as a result of heavy brokerage and lobbying efforts by ethnic Chinese Malaysians political leaders with continual funding from local Chinese communities. The first Chinese schools had been established in the country in the 19th century during the British colonial administration. At the same time, Christian missions from China also founded schools for Chinese students to nurture Church workers, this are most notable among many Chinese Christians of Hakka origin in Sabah and the Fuzhou in Sarawak. Following the country's independence, some of the Chinese independent schools who were influenced by the new national agenda and desperately needed government financial support were willingly converted into English medium-schools. However, these schools were later scrupulously converted into Malay medium-schools following the massive elimination of English medium-schools by the Malay-dominated regime in the 1970s in an effort to impose the Malay language as the only medium of instructions in all schools in the aftermath of ethnic riots in 1969. The following period was considered a dark time for local Chinese education and witnessed a growing belief in the idea that the ethnic Chinese in Malaysia had to proceed on a basis of self-reliance and vigilance in order to preserve their language rights as the national education policy was seen as exclusionary and discriminatory for non-Malays, summed up in the aphorism "non-Malays belong to Malaysia but Malaysia only belongs to the Malays".

Although other remaining Chinese independent schools or 独中 were also included in the national school system in 1996, these independent schools still did not receive any financial assistance from the federal government and its United Examinations Certificate (UEC) or 统考 is not recognised by the government, making students who finish their studies from the local Chinese independent schools unable to enrol in government-funded public tertiary institutions. Since late 1970, ethnic Chinese Malaysians had expanded their own Mandarin-language primary schools where around 90% of their children were enrolled based on the figures from 2006. These schools gained a reputation for not only maintaining good discipline but also providing the high-quality education that the Malay schools were seen by some to lack. This perceived superiority attracted significant interest among Bumiputera parents with various analyses placing the number of Bumiputera students enrollment in Chinese schools between 60,000 and 100,000 in 2000. The federal government's failure to impose Malay as the sole unifying language throughout the country's educational systems unlike in China with Standard Chinese or Indonesia with Indonesian language are mainly attributed to the racial-based policy enforcement of ethnic inclusion and exclusion. Some argue that the educational policies imposed by the federal government over the years in regard to minority language education have created negative consequences for Malaysian youth: a mounting brain drain in particular. A study from 2000 found that the country had lost an ample amount of talented and skilled youth to other more favourable countries as the result of students from the large non-Malay minority language communities being forced to go to university abroad because they did not attend Malay language schools.

Culture

Chinese cultural influences made their mark when ancient trade relations were established with the Nanyang (南洋) region. The massive ethnic Chinese migration during the British colonial period causing a subsequent strong influence on the country's culture, including in cuisine and the language. Aside from the Chinese cultural influence on local culture, ethnic Chinese from the first wave migration before English arrival had mainly adopted a localised culture. The Baba-Nyonya in Malacca had a very strong Malay influence in their clothing and food although still maintaining their Chinese heritage of religion, name, and identity. Their food are made with Malay ingredients and recipes but produced using the Chinese method while their houses are constructed with the infusion of Victorian, Chinese and Malay elements. Together with the Peranakans in Penang, both sides use a mixture of Hokkien and Malay despite the Penang Peranakans speak mainly Hokkien with some borrowed words from Malay words while in Malacca, the Peranakans have adopted Malay patois with some Hokkien words. The food prepared by Penang Peranakans also infuses both Chinese and Malay elements, albeit with an additional Thai influence. The Peranakans in the east coast of Malaysia in Kelantan and Terengganu have much closer ties with the Malay and Siamese community there since most of them has adopted the Malay and Siamese lifestyle.

Further, close blood relations between ethnic Chinese and local indigenous in northern Borneo since the early kingdoms period produced the "Sino-Natives" persons in Sabah as a result of inter-marriage between ethnic Chinese there and natives of Sabah. Instead of speaking Chinese languages, these communities spoke the localized Sabah Malay dialect as their main lingua franca since the 14th century. The close relations are marked with earliest records of the "Kina" term which is widely used by the indigenous Dusun to refer to the Chinese ethnicity including for the Dusun homeland mountain of "Mount Kinabalu" (Chinese widow mountain), "Kinabatangan River" (Chinese river) and several other places such as the Kinabalu mountain stream of "Kinataki", a small river in the northeastern coast of "Kinabañgun" and a Chinese land in Labuan Island, the "Kinabenua". The Na Tuk Kong shrine for example shown another sign of assimilation with local culture, where it refers to local Malay guardian spirits worshipped by some ethnic Chinese in West Malaysia and neighbouring Singapore and Indonesia. The term Na Tuk originated from the Malay word of Datuk (grandfather) which then merged with Kong (公, sometimes addressed as 'Kung' meaning elderly male), similar with Tu Ti Kung, an earth deity worshipped in East Asia.

Cuisine
The ethnic Chinese cuisine in Malaysia is derived from the culinary traditions of their early immigrants and descendants, who have adopted or modified their culinary traditions under the influence of Malaysian culture. Additionally due to the immigration of Chinese to the country, Chinese cuisine has now become an inseparable part in the country’s cultural mixture. When Chinese merchants sailed their junks across the South China Sea, they visited ports in Borneo and Malacca, which had a profound influence on the region. Since the local king at that time enjoyed Chinese cuisine, the traders would bring along cooks with them to the island. They introduced ingredients in Chinese cooking such as noodles, bean sprouts, tofu and soy sauce which are by now widely used by every ethnic group in the country. Apart from introducing new ingredients, these earlier traders also discovered ingredients among the local population along the coast, such as the expensive edible bird's nest with the best quality nests claiming to come from Borneo. Since a vast majority of Chinese Malaysians today are descendants of immigrants from southern China, local Chinese cuisine is predominantly based from Fujian, Cantonese, Hakka and Teochew cuisines. Their technique of stir frying ingredients and adding a small portion of cooking oil over high heat in a wok (锅) is widely adopted among the nation.

Chinese Malaysian cuisine had developed a strong penchant for spices and chillies where any local Chinese kopi tiam or restaurant will offer pickled green or red chillies sambal for noodles and rice-based meals. They borrowed curry leaves from the Indians and have since adapted English Worcestershire sauce and tomato sauce along with Indian and Malay spices to the cooking pot. Among the notable Chinese dishes in the country including the bak kut teh (肉骨茶) (pork rib soup with Chinese herbs), char kway teow (炒粿条) (stir fried rice noodle), dim sum (点心) (ready-to-serve dishes), hae mee (虾面) (spicy prawn noodle soup served in savoury broth), Hainanese chicken rice (海南鸡饭), kai si hor fun (鸡丝河粉) (flat rice noodle soup with chicken slices, shrimps and bean sprouts), kolok or kolo mee (干捞面) (Sarawakian egg noodle served in dark sauce, tomato sauce or chilli sauce), lor mee (卤面) (thick yellow noodle served in dark sauce and thick broth), ngiu chap mee (牛杂面) (special Sabah mixed beef noodle), pan mee (板面) (handmade noodle soup served with pork balls, minced pork, dried anchovies, black fungus and vegetable), sang nyuk mee (生肉面) (special Sabah dry pork noodle or pork noodle soup), wonton mee (云吞面) (dry noodle or noodle soup served with BBQ pork, minced pork and pork or shrimp dumplings) and yong tau foo (酿豆腐) (tofu and mixed vegetables filled with ground pork mixture or fish paste). Many Chinese Malaysians also can cook Malay-style chicken or fish with most versions of laksa (叻唦) are prepared by them. Some examples of basic Chinese Malaysians drinks that are commercially produced in the country include the black tea, chrysanthemum tea, grass jelly, green tea, jasmine tea, soy milk and white coffee while popular snacks including the cakoi (油炸鬼) (long deep-fried dough), egg tart, hum ji peng (咸煎饼) (circle shaped fried dough with or without fillings), ngoi sing tart (外星塔) (UFO shaped tart), ngo hiang (炸五香) (various spiced, minced meat rolls prepared in deep fried style and served with vegetables), pau (包) (steamed buns), popiah (薄饼) (fried or plain spring rolls filled with mixed vegetables), and tau sar piah (豆沙饼) (pastry biscuits filled with a sweet or savoury filling). The legacy from the first wave migration created the Peranakan (土生华人) (including the Baba-Nyonya (峇峇娘惹)) ethnicity through a blend between Chinese and Malay which subsequently produced the Peranakan cuisine where they served Indian-style curries with eating etiquette different from mainstream ethnic Chinese society by following the Malay usage of fingers than chopsticks. The Baba-Nyonya also specialized in making a variety of local snacks called kuih which require plenty of patience and skills.

Dialects and languages
The 1970 Malaysian Census reported the Southern Min dialects being the largest which accounting for 34.2% of the country Chinese population, followed by Hakka with 22.1%, Cantonese by 19.8%, Chaozhou (Teochew) by 12.4% and Hainanese by 4.7%. In 2003, a more detailed statistics for each dialects reported the Hokkien with 2,020,914, Hakka with 1,092,835, Cantonese with 1,068,008, Teochew with 497,280, Fuzhou with 251,553, Hainanese with 141,045, Kwongsai with 51,674, Henghua with 24,654, Hockchia with 14,935 and different other ethnic Chinese with 202,977, for a total of 5,365,875. The Malaysian Hokkien are divided into two localised dialects; the Penang Hokkien (northern) comprising Penang, Kedah, Perlis and Perak, and Southern Peninsular Hokkien in Johor, Malacca and neighbouring Singapore. The northern Hokkien contains more Malay loanwords than the southern with the latter maintaining more of their original Hokkien words. Many Hokkien living in Sarawak have been influenced heavily by indigenous language similarly with Hokkien in Kelantan where their language was heavily localised following close interaction with local Malays and Siamese. Localised Hokkien also spoken primarily by the Peranakan community (Baba-Nyonya) in both Malacca and Penang. Generally, Hokkien became a contact language among ethnic Chinese of different linguistic background in most parts of Malaysia.

The Malaysian Cantonese became the contact language in the Malaysia's capital of Kuala Lumpur albeit with a distinct phonology and grammar from standard Cantonese spoken in Pearl River Delta region of China including in Hong Kong and Macau. Hakka dialect assumes the role of contact language in Sabah but in the rest of the country the language are more commonly used as an intra-group language than a lingua franca within the Chinese community with about 66.2% of Hakka in Johor prefer localised Mandarin. Similar studies on Eastern Min speakers of Fuzhou community in Sarawak also found a general shift of language choice from their own dialect to Mandarin Chinese and English. The Chaozhou dialect despite being not a largest dialect group has become a bridge language for trade between Teochew exporters in China and wholesalers in Malaysia. Hainan dialect is another minority and the sub-dialect of the Min Chinese dialect family although it is treated in the country as an independent dialect. Several others like Henghua are also generally termed as "dialects", which in fact together with the rest are variety of Chinese languages from different Chinese ethnicity. Mandarin, which is generally spoken by northern Chinese minority in Sabah become the main working language among all Chinese in the country with Standard Mandarin is used as the medium of instruction in local Chinese medium school and independent high school although the language still not necessarily spoken in their daily life practice. Based on early Malaysian Census in 1970, around 41% of ethnic Chinese Malaysians are able to converse in Mandarin.

Holidays and festivities
With the large presence of ethnic Chinese in the country nationwide, Chinese New Year is celebrated as a national public holiday. 11 states and three federal territories in the country celebrate with two days holidays while two remaining states of Kelantan and Terengganu only celebrate a one-day holiday. During the New Year, many Chinese living with their family in the urban areas will celebrate together, while some who may have family in rural areas will return for family reunions. Traditional dinner with the entire family is the most important aspect of the celebration and may include a traditional food tossing of yee sang, especially among the Cantonese. Elders will usually give the young a red envelope (ang pow or angpau). A variety of festival sweets are presented in the house for visitors. Most Chinese settlements and Chinatown streets will be decorated before the New Year with colorful lanterns. Dragon and lion dances will be performed with firecracker and fireworks shows also featured as part of the celebrations.

Chingay processions are also being held as part of the New Year festivities especially in Johor Bahru and Penang. Several other festivals are celebrated through the seasons in a year including the Dongzhi Festival, Dragon Boat Festival, Hungry Ghost Festival, Lantern Festival (Chap Goh Mei), Mid-Autumn Festival, Nine Emperor Gods Festival and Qingming Festival which originated from much of Chinese folk beliefs and traditional agricultural society. Throughout the festivals, especially for major Chinese festivals such as the New Year, Hungry Ghost, and Mid-Autumn, Chinese temples will organize cultural and religious activities. The Hungry Ghost Festival is generally not observed by most Dejiao (Zi) group in Malaysia which descended directly from Dejiao association in China, it is only mainly observed by three Zi associations in Kuala Lumpur (Zi Fang Ge), Pulau Ketam (Zi Bang Ge) and Butterworth (Zi Wei Gi) with the three calling the festival as Wanyuan Shenghui than Yulan Shanghui. The Mooncake Festival is celebrated through the Mid-Autumn Festival where there people will exchange and eat mooncake. Traditional Chinese weddings remain popular to some ethnic Chinese Malaysian couples even though most have preferred the Western-influenced wearing of white wedding dresses and black jackets.

Religion
Based on the 2000 Malaysian Census, 86.6% of ethnic Chinese Malaysians adhere to Buddhism and Chinese folk religion with numerous Chinese temples and shrines visible nationwide. More detailed statistics in 2010 found a total of 5,341,687 ethnic Chinese Malaysians adhere to Buddhism, 706,479 are Christians, 218,261 practising Confucianism, Taoism and other Chinese folk religious sects, 49,320 were irreligious, 42,048 are Muslims, 14,878 are Hindus, 11,387 with unknown religion while 8,576 practising other different religion. Among the common deities worshipped by ethnic Chinese Malaysians in temples are Lord Guan (Guansheng Dijun 关圣帝君), Guan Yin (Goddess of Mercy 观世音菩萨), Dabo Gong 大伯公 (Earth Deity) and Mazu (Goddess of Sea 妈祖).

Commonly found in ethnic Chinese homes and shops are altars installed for deities of their affinities together with ancestral worship. Most of the deities are of Chinese origin but it is still common to see a few local deities. Most, if not all cities in Malaysia include the presence of Chinese Buddhist temples and societies. However, there exists towns with only Buddhist statues, although some may have one or two other Chinese deities. Other Buddhist branches of Theravāda and various Tibetan traditions (Vajrayāna) also have Chinese members and some of the buildings of these branches were built with the funds and philanthropic efforts from local Chinese Buddhists, examples being the establishment of Buddhist Maha Vihara in Kuala Lumpur and Wat Chayamangkalaram in Penang. Unlike the institutional religion of Buddhism, Christianity and Islam, ethnic Chinese who follow traditional folk religion do not have separate names for their belief and practices, as similar to the indigenous Malaysians such as Iban and the Orang Asli. They describe their religious beliefs as either bai shen or bai fo (worshipping deities) which does usually include the worshipping of Buddha since Mahayana Buddhist deities are also commonly worshipped by the followers of Chinese traditional religion.

Chinese Christians, including both Catholic and Protestants presence, are mainly visible with their active missionary activities especially among ethnic Chinese in East Malaysia, having a large proportion compared to other regions. The majority of Christians in West Malaysia also are of Chinese origin. Most early Chinese churches including Baptists, Methodists and Presbyterians have their origins from missionary migrants that introduced the missions established in China to Malaysia. The number of Chinese Muslims is very small compared to Chinese Christians since the latter religion is seen as more tolerant, mainly due to the general perception that embracing Islam in Malaysia is to become Malayised, in addition to the ethnic rivalry between Malay and Chinese that makes Islam as less desirable to ethnic Chinese Malaysians. A majority of Chinese Malaysians, especially those who have received Chinese education, follow Confucian values and to a lesser extent, Taoism. Some that are more traditional may hold more conservative views on filial piety and social relations, while also consulting Chinese horoscopes as well on Chinese geomancy of feng shui. Taoist activities gain increasing interests and significance among Chinese Malaysians although it is not deeply practiced.

title: Malaysian Chinese


text:
Löb's theorem

In mathematical logic, Löb's theorem states that in Peano arithmetic (PA) (or any formal system including PA), for any formula P, if it is provable in PA that "if P is provable in PA then P is true", then P is provable in PA. If Prov(P) means that the formula P is provable, we may express this more formally as

 * If
 * $$\mathit{PA} \vdash {\mathrm{Prov}(P) \rightarrow P}$$
 * then
 * $$\mathit{PA} \vdash P$$.

An immediate corollary (the contrapositive) of Löb's theorem is that, if P is not provable in PA, then "if P is provable in PA, then P is true" is not provable in PA. For example, "If $$1+1=3$$ is provable in PA, then $$1+1=3$$" is not provable in PA.

Löb's theorem is named for Martin Hugo Löb, who formulated it in 1955. It is related to Curry's paradox.

Löb's theorem in provability logic
Provability logic abstracts away from the details of encodings used in Gödel's incompleteness theorems by expressing the provability of $$\phi$$ in the given system in the language of modal logic, by means of the modality $\Box \phi$. That is, when $$\phi$$ is a logical formula, another formula can be formed by placing a box in front of $$\phi$$, and is intended to mean that $$\phi$$ is provable.

Then we can formalize Löb's theorem by the axiom

 * $$\Box(\Box P\rightarrow P)\rightarrow \Box P,$$

known as axiom GL, for Gödel–Löb. This is sometimes formalized by means of the inference rule:

 * If
 * $$\vdash \Box P \rightarrow P$$
 * then
 * $$\vdash P$$.

The provability logic GL that results from taking the modal logic K4 (or K, since the axiom schema 4, $$\Box A\rightarrow\Box\Box A$$, then becomes redundant) and adding the above axiom GL is the most intensely investigated system in provability logic.

Modal proof of Löb's theorem
Löb's theorem can be proved within modal logic using only some basic rules about the provability operator (the K4 system) plus the existence of modal fixed points.

Modal formulas
We will assume the following grammar for formulas:
 * 1) If $$X$$ is a propositional variable, then $$X$$ is a formula.
 * 2) If $$K$$ is a propositional constant, then $$K$$ is a formula.
 * 3) If $$A$$ is a formula, then $$\Box A$$ is a formula.
 * 4) If $$A$$ and $$B$$ are formulas, then so are $$\neg A$$, $$A \rightarrow B$$, $$A \wedge B$$, $$A \vee B$$, and $$A \leftrightarrow B$$

A modal sentence is a formula in this syntax that contains no propositional variables. The notation $$\vdash A$$ is used to mean that $$A$$ is a theorem.

Modal fixed points
If $$F(X)$$ is a modal formula with only one propositional variable $$X$$, then a modal fixed point of $$F(X)$$ is a sentence $$\Psi$$ such that
 * $$\vdash \Psi \leftrightarrow F(\Box \Psi)$$

We will assume the existence of such fixed points for every modal formula with one free variable. This is of course not an obvious thing to assume, but if we interpret $$\Box$$ as provability in Peano Arithmetic, then the existence of modal fixed points follows from the diagonal lemma.

Modal rules of inference
In addition to the existence of modal fixed points, we assume the following rules of inference for the provability operator $$\Box$$, known as Hilbert–Bernays provability conditions:

 * 1) (necessitation) From $$\vdash A$$ conclude $$\vdash \Box A$$: Informally, this says that if A is a theorem, then it is provable.
 * 2) (internal necessitation) $$\vdash \Box A \rightarrow \Box \Box A$$: If A is provable, then it is provable that it is provable.
 * 3) (box distributivity) $$\vdash \Box (A \rightarrow B) \rightarrow (\Box A \rightarrow \Box B)$$:  This rule allows you to do modus ponens inside the provability operator. If it is provable that A implies B, and A is provable, then B is provable.

Proof of Löb's theorem
Much of the proof does not make use of the assumption $$\Box P \to P$$, so for ease of understanding, the proof below is subdivided to leave the parts depending on $$\Box P \to P$$ until the end.

Let $$P$$ be any modal sentence.

More informally, we can sketch out the proof as follows.
 * 1) Apply the existence of modal fixed points to the formula $$F(X) = X \rightarrow P$$. It then follows that there exists a sentence $$\Psi$$ such that $$\vdash \Psi \leftrightarrow (\Box \Psi \rightarrow P)$$.
 * 2) $$\vdash \Psi \rightarrow (\Box \Psi \rightarrow P)$$, from 1.
 * 3) $$\vdash \Box(\Psi \rightarrow (\Box \Psi \rightarrow P))$$, from 2 by the necessitation rule.
 * 4) $$\vdash \Box\Psi \rightarrow \Box(\Box \Psi \rightarrow P)$$, from 3 and the box distributivity rule.
 * 5) $$\vdash \Box(\Box \Psi \rightarrow P) \rightarrow (\Box\Box\Psi \rightarrow \Box P)$$, by applying the box distributivity rule with $$ A = \Box \Psi $$ and $$ B= P$$.
 * 6) $$\vdash \Box \Psi \rightarrow (\Box\Box\Psi \rightarrow \Box P)$$, from 4 and 5.
 * 7) $$\vdash \Box \Psi \rightarrow \Box \Box \Psi$$, from 6 by the internal necessitation rule.
 * 8) $$\vdash \Box \Psi \rightarrow \Box P$$, from 6 and 7.  Now comes the part of the proof where the hypothesis is used.
 * 9) Assume that $$\vdash \Box P \rightarrow P$$.  Roughly speaking, it is a theorem that if $$P$$ is provable, then it is, in fact true.  This is a claim of soundness.
 * 10) $$\vdash \Box \Psi \rightarrow P$$, from 8 and 9.
 * 11) $$\vdash (\Box \Psi \rightarrow P) \rightarrow \Psi$$, from 1.
 * 12) $$\vdash \Psi$$, from 10 and 11.
 * 13) $$\vdash \Box \Psi$$, from 12 by the necessitation rule.
 * 14) $$\vdash P$$, from 13 and 10.

 * 1) Since $$\mathit{PA} \vdash {\mathrm{Prov}_{PA}(P) \rightarrow P}$$ by assumption, we also have $$\mathit{PA} \vdash {\neg P \rightarrow \neg \mathrm{Prov}_{PA}(P)} $$, which implies $$\{ \mathit{PA},  \neg P\} \vdash { \neg \mathrm{Prov}_{PA} (P)}   $$.
 * 2) Now, the hybrid theory $$\{ \mathit{PA},  \neg P\}  $$ can reason as follows:
 * 3) Suppose $$\{ \mathit{PA},  \neg P\}  $$ is inconsistent, then PA proves $$\neg P \to \bot{} $$, which is the same as $$P $$.
 * 4) However, $$\{ \mathit{PA},  \neg P\}  $$ already knows that $$\neg \mathrm{Prov}_{PA} (P)  $$, a contradiction.
 * 5) Therefore, $$\{ \mathit{PA},  \neg P\}  $$ is consistent.
 * 6) By Godel's second incompleteness theorem, this implies $$\{ \mathit{PA},  \neg P\}  $$ is inconsistent.
 * 7) Thus, PA proves $$\neg P \to \bot{} $$, which is the same as $$P $$.

Examples
An immediate corollary of Löb's theorem is that, if P is not provable in PA, then "if P is provable in PA, then P is true" is not provable in PA. Given we know PA is consistent (but PA does not know PA is consistent), here are some simple examples:
 * "If $$1+1=3$$ is provable in PA, then $$1+1=3$$" is not provable in PA, as $$1+1=3$$ is not provable in PA (as it is false).
 * "If $$1+1=2$$ is provable in PA, then $$1+1=2$$" is provable in PA, as is any statement of the form "If X, then $$1+1=2$$".
 * "If the strengthened finite Ramsey theorem is provable in PA, then the strengthened finite Ramsey theorem is true" is not provable in PA, as "The strengthened finite Ramsey theorem is true" is not provable in PA (despite being true).

In Doxastic logic, Löb's theorem shows that any system classified as a reflexive "type 4" reasoner must also be "modest": such a reasoner can never believe "my belief in P would imply that P is true", without also believing that P is true.

Gödel's second incompleteness theorem follows from Löb's theorem by substituting the false statement $$\bot$$ for P.

Converse: Löb's theorem implies the existence of modal fixed points
Not only does the existence of modal fixed points imply Löb's theorem, but the converse is valid, too. When Löb's theorem is given as an axiom (schema), the existence of a fixed point (up to provable equivalence) $$p\leftrightarrow A(p)$$ for any formula A(p) modalized in p can be derived. Thus in normal modal logic, Löb's axiom is equivalent to the conjunction of the axiom schema 4, $$(\Box A\rightarrow \Box\Box A)$$, and the existence of modal fixed points.

title: Löb's theorem


text: Category:Brazil

title: Category:Brazil


text:
Category:Thermodynamics

Thermodynamics concerns the physics of heat, work, temperature, energy, and entropy.

title: Category:Thermodynamics


text: Category:Chile

title: Category:Chile