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# Ligase
In biochemistry, a **ligase** is an enzyme that can catalyze the joining (ligation) of two molecules by forming a new chemical bond. This is typically via hydrolysis of a small pendant chemical group on one of the molecules, typically resulting in the formation of new C-O, C-S, or C-N bonds. For example, DNA ligase can join two complementary fragments of nucleic acid by forming phosphodiester bonds, and repair single stranded breaks that arise in double stranded DNA during replication.
In general, a ligase catalyzes the following dehydration reaction, thus joining molecules A and B:
A-OH + B-H → A--B + H~2~O
## Nomenclature
The naming of ligases is inconsistent and so these enzymes are commonly known by several different names. Generally, the common names of ligases include the word \"ligase\", such as in DNA ligase, an enzyme commonly used in molecular biology laboratories to join together DNA fragments. However, many common names use the term \"synthetase\" or \"synthase\" instead, because they are used to synthesize new molecules. There are also some ligases that use the name \"carboxylase\" to indicate that the enzyme specifically catalyzes a carboxylation reaction.
To note: biochemical nomenclature has sometimes distinguished synthetases from synthases and sometimes treated the words as synonyms. Commonly, the two terms are used interchangeably and are both used to describe ligases.
## Classification
Ligases are classified as **EC 6** in the EC number classification of enzymes. Ligases can be further classified into six subclasses:
- EC 6.1 includes ligases used to form carbon-oxygen bonds
- EC 6.2 includes ligases used to form carbon-sulfur bonds
- EC 6.3 includes ligases used to form carbon-nitrogen bonds (including argininosuccinate synthetase)
- EC 6.4 includes ligases used to form carbon-carbon bonds, such as acetyl-CoA carboxylase
- EC 6.5 includes ligases used to form phosphoric ester bonds, such as DNA ligase
- EC 6.6 includes ligases used to form nitrogen-metal bonds, as in the chelatases
## Membrane-associated ligases {#membrane_associated_ligases}
Some ligases associate with biological membranes as peripheral membrane proteins or anchored through a single transmembrane helix, for example certain ubiquitin ligase related proteins.
## Etymology and pronunciation {#etymology_and_pronunciation}
The word *ligase* uses combining forms of *lig-* (from the Latin verb *ligāre*, \"to bind\" or \"to tie together\") + *-ase* (denoting an enzyme), yielding \"binding enzyme\"
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# Last rites
The **last rites**, also known as the **Commendation of the Dying**, are the last prayers and ministrations given to an individual of Christian faith, when possible, shortly before death. The Commendation of the Dying is practiced in liturgical Christian denominations, such as the Roman Catholic Church and the Lutheran Church. They may be administered to those mortally injured, terminally ill, or awaiting execution. Last rites cannot be performed on someone who has already died. Last rites, in sacramental Christianity, can refer to multiple sacraments administered concurrently in anticipation of an individual\'s passing (such as Holy Absolution and Holy Communion).
## Catholic Church {#catholic_church}
The Latin Church of the Catholic Church defines Last Rites as Viaticum (Holy Communion administered to someone who is dying), and the ritual prayers of Commendation of the Dying, and Prayers for the Dead.
The sacrament of Anointing of the Sick is usually postponed until someone is near death. Anointing of the Sick has been thought to be exclusively for the dying, though it can be received at any time. Extreme Unction (Final Anointing) is the name given to Anointing of the Sick when received during last rites. If administered to someone who is not just ill but near death, Anointing of the Sick is generally accompanied by celebration of the sacraments of Penance and Viaticum.
The order of the three is important and should be given in the order of Penance (confessing one\'s sins), then Anointing of the Sick, and finally the Viaticum. The principal reason Penance is administered first to the seriously ill and dying is because the forgiveness of one\'s sins, and most especially one\'s mortal sins, is for Catholics necessary for being in a state of grace (in a full relationship with God). Dying while in the state of grace ensures that a Catholic will go to heaven (if they are in a state of grace but still attached to sin, they will eventually make it to heaven but must first go through a spiritual cleansing process called purgatory).
Although these three (Penance, Anointing of the sick, and Viaticum) are not, in the proper sense, the Last Rites, they are sometimes spoken of as such; the Eucharist given as Viaticum is the only sacrament essentially associated with dying. \"The celebration of the Eucharist as Viaticum is the sacrament proper to the dying Christian\".
In the Roman Ritual\'s *Pastoral Care of the Sick: Rites of Anointing and Viaticum*, Viaticum is the only sacrament dealt with in *Part II: Pastoral Care of the Dying*. Within that part, the chapter on Viaticum is followed by two more chapters, one on *Commendation of the Dying*, with short texts, mainly from the Bible, a special form of the litany of the saints, and other prayers, and the other on *Prayers for the Dead*. A final chapter provides *Rites for Exceptional Circumstances*, namely, the *Continuous Rite of Penance, Anointing, and Viaticum*, *Rite for Emergencies*, and *Christian Initiation for the Dying*. The last of these concerns the administration of the sacraments of Baptism and Confirmation to those who have not received them.
In addition, the priest has authority to bestow a blessing in the name of the Pope on the dying person, to which a plenary indulgence is attached.
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# Last rites
## Orthodox and Eastern Catholic Churches {#orthodox_and_eastern_catholic_churches}
In the Eastern Orthodox Church and those Eastern Catholic Churches which follow the Byzantine Rite, the last rites consist of the Sacred Mysteries (sacraments) of Confession and the reception of Holy Communion.
Following these sacraments, when a person dies, there are a series of prayers known as *The Office at the Parting of the Soul From the Body*. This consists of a blessing by the priest, the usual beginning, and after the Lord\'s Prayer, Psalm 50. Then a Canon to the Theotokos is chanted, entitled, \"On behalf of a man whose soul is departing, and who cannot speak\". This is an elongated prayer speaking in the person of the one who is dying, asking for forgiveness of sin, the mercy of God, and the intercession of the saints. The rite is concluded by three prayers said by the priest, the last one being said \"at the departure of the soul.\"
There is an alternative rite known as *The Office at the Parting of the Soul from the Body When a Man has Suffered for a Long Time*. The outline of this rite is the same as above, except that Psalm 70 and Psalm 143 precede Psalm 50, and the words of the canon and the prayers are different.
The rubric in the Book of Needs (priest\'s service book) states, \"With respect to the Services said at the parting of the soul, we note that if time does not permit to read the whole Canon, then customarily just one of the prayers, found at the end of the Canon, is read by the Priest at the moment of the parting of the soul from the body.\"
As soon as the person has died the priest begins *The Office After the Departure of the Soul From the Body* (also known as *The First Pannikhida*).
In the Orthodox Church Holy Unction is not considered to be solely a part of a person\'s preparation for death, but is administered to any Orthodox Christian who is ill, physically or spiritually, to ask for God\'s mercy and forgiveness of sin. There is an abbreviated form of Holy Unction to be performed for a person in imminent danger of death, which does not replace the full rite in other cases.
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# Last rites
## Lutheran Churches {#lutheran_churches}
In the Lutheran Churches, last rites are formally known as the Commendation of the Dying, in which the priest \"opens in the name of the triune God, includes a prayer, a reading from one of the psalms, a litany of prayer for the one who is dying, \[and\] recites the Lord's Prayer\". The dying individual is then anointed with oil and receives the sacraments of Holy Absolution and Holy Communion.
## Anglican Communion {#anglican_communion}
The proposed 1928 revision of the Church of England\'s *Book of Common Prayer* would have permitted reservation of the Blessed Sacrament for use in communing the sick, including during last rites. This revision failed twice in the Parliament of the United Kingdom\'s House of Commons
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# Lamorna
**Lamorna** (*Nansmornow*) is a village, valley and cove in west Cornwall, England, UK. It is on the Penwith peninsula approximately 4 mile south of Penzance. Lamorna became popular with the artists of the Newlyn School, including Alfred Munnings, Laura Knight and Harold Knight, and is also known for former residents Derek and Jean Tangye who farmed land and wrote \"The Minack Chronicles\".
## Toponymy
First recorded as *Nansmorno* (in 1305), than *Nansmurnou* (1309), *Nansmorne* (1319), *Nansmornou* (1339), *Nansmorna* (1387) and *Namorna* (1388). In Cornish *Nans* means valley, and the 2nd element is possibly *mor*, which means sea.
## Geography
Lamorna Cove is at the SE end of a north-west to south-east valley. The cove is delineated by Carn-du (Black Rock) on the eastern side and Lamorna Point on the western side. The valley is privately owned from The Wink (public house) down to the cove, which is reached by a narrow lane to the car park and quay. The small village, half a mile inland, was originally known as Nantewas. The South West Coast Path passes around the cove.
Lamorna lies within the Cornwall Area of Outstanding Natural Beauty (AONB); almost a third of Cornwall has AONB designation, with the same status and protection as a National Park.
## History
The first record of tin streaming is in the 1380s when Alan Hoskyn was killed (murder was not proven) during a dispute with Trewoofe, after the stream was diverted. Mounds along the stream are evidence of past activity. Kemyel Mill was operated by the Hoskyn family from at least the 14th century until the 1920s, but is now a gift shop under different ownership. There were two mills: one milled corn for animal feed, and the other flour. Both mills are grade II listed buildings.
In the 17th century a privateer vessel owned by the Penrose family was regularly moored in the cove and was wrecked during a storm. At one time five cannon were on the sea floor in 15 m of water, and one is now at Stoney Cove, Leicestershire where it is used at an underwater archaeological training area. A number of silver coins found in 1984 and 1985 include one dated 1653. The wreck is a popular diving site.
A school for fifty to sixty infant boys and girls opened for the first time in the village in March 1881. The schoolroom, with a screen at the eastern end, was paid for by Canon Coulson and built on land on which he owned the freehold. The room converted to a mission room for Anglicans by removing a screen to reveal a chancel; the converted chapel had a capacity of 70--80 for services. Previously children had to go to St Buryan, some 4 km away, for schooling.
The valley is now tree-covered, but until around the 1950s the stream- and hillside were grazed by cows, horses and pigs. On the slopes, daffodils and early potatoes were grown; the flowers were sent to markets at Covent Garden (London), Birmingham and Wales.
## Community radio {#community_radio}
The local community radio station is Coast FM (formerly Penwith Radio), which broadcasts on 96.5 and 97.2 FM.
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# Lamorna
## Quarries
Waste tips on the eastern side of the cove are a reminder of the granite quarries first opened by John Freeman, on St Aubyn land, in 1849 and continued working until 1911. Famous buildings and constructions include Admiralty Pier at Dover, London County Council offices, the Thames Embankment and Portland Breakwater. Stone from the cove was also used locally to build the Bishop Rock Lighthouse, Mousehole north pier and the Wolf Rock Lighthouse. Granite was dragged by chains to an iron pier, where the stream enters the sea, and transported by ship. A plinth weighing 20 tons was sent to The Great Exhibition of 1851 by sea but eventually, due to the hazards of loading ships, granite was sent by road via Kemyal and Paul Hill through Newlyn, to the cutting yards in Wherrytown. The present quay was built in the late 19th century, possibly rebuilt on an older quay, and is a grade II listed building. A quarry on the west side of the cove failed due to the high quartz content of the granite. An area of 20 acre and known as the ″Lamorna Harbour Works″ was put up for auction at the Mart, Tokenhouse Yard, City of London on 16 June 1881. The property, on both sides of the valley, included ″the exceedingly valuable″ granite quarry with harbour, wharf and pier, a powder magazine, lime and mill house, carpenter\'s shops, 12 horse-power water-wheel, foreman\'s residence and a \"substantial and superior\" dwelling-house. Despite the 1881 sale claiming the granite quarry was ″exceeding valuable″, Freeman and Sons only employed four men at the quarry two years later and the average-sized blocks were of inferior quality compared with the quarry at nearby Sheffield.
The Lamorna Cove Hotel, built in the 1870s and known as Cliffe House, was originally the quarry manager\'s home, and had a school and chapel (with bell tower) for the quarry workers and their families. It was first used as a hotel in the 1920s. During the Second World War the hotel was occupied by seven French fishing families who fished out of Newlyn.
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# Lamorna
## Newlyn School of Art and the Lamorna Colony {#newlyn_school_of_art_and_the_lamorna_colony}
In the late 19th and early 20th centuries Lamorna became popular with artists of the Newlyn School. It is particularly associated with the artist S J \"Lamorna\" Birch who lived there from 1908. The colony included Birch, Alfred Munnings, Laura Knight and Harold Knight. This period is dramatised in the 1998 novel *Summer in February* by Jonathan Smith, which was adapted for the 2013 movie directed by Christopher Menaul. Lamorna was also the home of the jeweller Ella Naper and her husband, the painter Charles, who built Trewoofe House. The Lamorna Arts Festival was launched in 2009 to celebrate the original Lamorna Colony and today\'s Lamorna art community.
## Lamorna in culture {#lamorna_in_culture}
Lamorna has been immortalised in the song \"Way Down to Lamorna\", about a wayward husband receiving his comeuppance from his wife. The song is beloved of many Cornish singers, including Brenda Wootton.
The actor Robert Newton (1905--1956) was educated in Lamorna and his ashes were scattered in the sea off Lamorna by his son, Nicholas Newton.
The authors Derek Tangye and Jean Tangye lived above Lamorna where he wrote his famous books \"The Minack Chronicles\". A piece of land called \"Oliver Land\" has been preserved as a wildlife sanctuary in memory of the couple. Lamorna was the village used in the novel *The Memory Garden* by Rachel Hore (2007) and was a location used for the shooting of Sam Peckinpah\'s 1971 thriller *Straw Dogs*. *Lamorna Cove* was the title of a poem by W. H. Davies published in 1929.
The name of Lamorna\'s pub, The Wink, alludes to smuggling, \"the wink\" being a signal that contraband could be obtained. The pub is the subject of a novel by Martha Grimes, entitled *The Lamorna Wink*. The interior contains an important collection of maritime artefacts.
The Lamorna Pottery was founded in 1947 by Christopher James Ludlow (known as Jimmy) and Derek Wilshaw. It is currently a working pottery, gift shop and café.
## Gallery
<File:Lamorna> Cove Cornwall.jpg\|Looking out from Lamorna Cove Cornwall <File:Lamorna> Cove Cornwall 2.jpg\|Looking over to Lamorna Cove Cornwall <File:Lamorna> Cove Cornwall 3.jpg\|Lamorna Cove harbour Cornwall <File:Lamorna> Cove Cornwall 4.jpg\|Lamorna Cove Cornwall
<File:Colin> CaffellNaiad greenwave.jpg\|*Naiad* by Lamorna artist Colin Caffell <File:Millennium> Garden at Lamorna
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# Law of averages
The **law of averages** is the commonly held belief that a particular outcome or event will, over certain periods of time, occur at a frequency that is similar to its probability. Depending on context or application it can be considered a valid common-sense observation or a misunderstanding of probability. This notion can lead to the gambler\'s fallacy when one becomes convinced that a particular outcome must come soon simply because it has not occurred recently (e.g. believing that because three consecutive coin flips yielded *heads*, the next coin flip must be virtually guaranteed to be *tails*).
As invoked in everyday life, the \"law\" usually reflects wishful thinking or a poor understanding of statistics rather than any mathematical principle. While there is a real theorem that a random variable will reflect its underlying probability over a very large sample, the law of averages typically assumes that an unnatural short-term \"balance\" must occur. Typical applications also generally assume no bias in the underlying probability distribution, which is frequently at odds with the empirical evidence.
## Examples
### Gambler\'s fallacy {#gamblers_fallacy}
The gambler\'s fallacy is a particular misapplication of the law of averages in which the gambler believes that a particular outcome is more likely because it has not happened recently, or (conversely) that because a particular outcome has recently occurred, it will be less likely in the immediate future.
As an example, consider a roulette wheel that has landed on red in three consecutive spins. An onlooker might apply the law of averages to conclude that on its next spin it is guaranteed (or at least is much more likely) to land on black. Of course, the wheel has no memory and its probabilities do not change according to past results. So even if the wheel has landed on red in ten or a hundred consecutive spins, the probability that the next spin will be black is still no more than 48.6% (assuming a *fair* European wheel with only one green zero; it would be exactly 50% if there were no green zero and the wheel were fair, and 47.4% for a fair American wheel with one green \"0\" and one green \"00\"). Similarly, there is no statistical basis for the belief that lottery numbers which haven\'t appeared recently are due to appear soon. (There is some value in choosing lottery numbers that are, in general, less *popular* than others --- not because they are any more or less likely to come up, but because the largest prizes are usually shared among all of the people who chose the winning numbers. The unpopular numbers are just as likely to come up as the popular numbers are, and in the event of a big win, one would likely have to share it with fewer other people. See parimutuel betting.)
### Expectation values {#expectation_values}
Another application of the law of averages is a belief that a sample\'s behaviour must line up with the expected value based on population statistics. For example, suppose a fair coin is flipped 100 times. Using the law of averages, one might predict that there will be 50 heads and 50 tails. While this is the single most likely outcome, there is only an 8% chance of it occurring according to $P(X = 50 \mid n = 100, p = 0.5)$ of the binomial distribution. Predictions based on the law of averages are even less useful if the sample does not reflect the population.
### Repetition of trials {#repetition_of_trials}
In this example, one tries to increase the probability of a rare event occurring at least once by carrying out more trials. For example, a job seeker might argue, \"If I send my résumé to enough places, the law of averages says that someone will eventually hire me.\" Assuming a non-zero probability, it is true that conducting more trials increases the overall likelihood of the desired outcome. However, there is no particular number of trials that guarantees that outcome; rather, the probability that it will already have occurred approaches but never quite reaches 100%.
### Chicago Cubs {#chicago_cubs}
The Steve Goodman song \"A Dying Cub Fan\'s Last Request\" mentions the law of averages in reference to the Chicago Cubs lack of championship success. At the time Goodman recorded the song in 1981, the Cubs had not won a National League championship since 1945, and had not won a World Series since 1908. This futility would continue until the Cubs would finally win both in 2016
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# Outline of literature
The following outline is provided as an overview of and topical guide to literature:
**Literature** -- prose, written or oral, including fiction and non-fiction, drama, and poetry.
: *See also the Outline of poetry.*
## What type of thing is literature? {#what_type_of_thing_is_literature}
Literature can be described as all of the following:
- Communication -- activity of conveying information. Communication requires a sender, a message, and an intended recipient, although the receiver need not be present or aware of the sender\'s intent to communicate at the time of communication; thus communication can occur across vast distances in time and space.
- Written communication (writing) -- representation of language in a textual medium through the use of a set of signs or symbols (known as a writing system).
- Subdivision of culture -- shared attitudes, values, goals, and practices that characterizes an institution, organization, or group.
- One of the arts -- imaginative, creative, or nonscientific branch of knowledge, especially as studied academically.
## Essence of literature {#essence_of_literature}
- Composition --
- World literature --
## Forms of literature {#forms_of_literature}
### Oral literary genres {#oral_literary_genres}
Oral literature
- Oral poetry --
- Epic poetry --
- Legend --
- Mythology --
- Ballad --
- Folktale --
- Oral Narrative --
- Oral History --
- Urban legend --
### Written literary genres {#written_literary_genres}
- Cordel Literature
- Children\'s literature --
- Constrained writing --
- Erotic literature --
- Electronic literature -- Literary fiction and poetry that uses the capabilities of computers and networks
- Digital poetry --
- Interactive fiction --
- Hypertext fiction -- literary fiction written with hypertextual links
- Fan fiction
- Cell phone novel
- Poetry (see that article for an extensive list of subgenres and types)
- Aubade --
- Clerihew --
- Epic --
- Grook -- form of short aphoristic poem invented by the Danish poet and scientist Piet Hein, who wrote more than 7,000 of them.
- Haiku -- form of short Japanese poetry consisting of three lines.
- Instapoetry
- Tanka -- classical Japanese poetry of five lines.
- Lied --
- Limerick -- a kind of a witty, humorous, or nonsense poem, especially one in five-line `{{tooltip|2=Two short, unstressed syllables followed by one long stressed syllable.|anapestic}}`{=mediawiki} or `{{tooltip|2=One stressed syllable surrounded by two unstressed syllables.|amphibrachic}}`{=mediawiki} meter with a strict rhyme scheme (aabba), which is sometimes obscene with humorous intent
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# Lindow Man
**Lindow Man**, also known as **Lindow II** and (in jest) as **Pete Marsh**, is the preserved bog body of a man discovered in a peat bog at Lindow Moss near Wilmslow in Cheshire, North West England. The remains were found on 1 August 1984 by commercial peat cutters. Lindow Man is not the only bog body to have been found in the moss; Lindow Woman was discovered the year before, and other body parts have also been recovered. The find was described as \"one of the most significant archaeological discoveries of the 1980s\" and caused a media sensation. It helped invigorate the study of British bog bodies, which had previously been neglected.
Dating the body has proven problematic, but it is thought that he was deposited into Lindow Moss, face down, sometime between 2 BC and 119 AD, in either the Iron Age or Romano-British period. At the time of death, Lindow Man was a healthy male in his mid-20s, and may have been of high social status as his body shows little evidence of having done heavy or rough physical labour during his lifetime. There has been debate over the reason for his death; his death was violent and perhaps ritualistic.
The recovered body has been preserved by freeze-drying and is on permanent display at the British Museum, although it occasionally travels to other venues such as the Manchester Museum.
## Background
### Lindow Moss {#lindow_moss}
Lindow Moss is a peat bog in Lindow, an area of Wilmslow, Cheshire, which has been used as common land since the medieval period. It formed after the last ice age, one of many such peat bogs in north-east Cheshire and the Mersey basin that formed in hollows caused by melting ice. Investigations have not yet discovered settlement or agricultural activity around the edge of Lindow Moss that would have been contemporary with Lindow Man, but analysis of pollen in the peat suggests there was some cultivation in the vicinity.
Once covering over 600 ha, the bog has now shrunk to a tenth of its original size. It is a dangerous place and an 18th-century writer recorded people drowning there. For centuries, the peat from the bog was used as fuel, and it continued to be extracted until the 1980s, by which time the process had been mechanised. Lindow Moss is a lowland raised mire, a type of peat bog which often produces the best-preserved bog bodies, allowing more detailed analysis. Lowland raised mires occur mainly in northern England and extend south to the Midlands. Lindow Man is one of 27 bodies to be recovered from such areas.
### Preservation of bog bodies {#preservation_of_bog_bodies}
The preservation of bog bodies is dependent on a set of specific physical conditions, which can occur in peat bogs. A sphagnum moss bog must have a temperature lower than 4 °C at the time of deposition of the body. The subsequent average annual temperature must be lower than 10 °C. Moisture must be stable in the bog year-round: it cannot dry out.
Sphagnum moss affects the chemistry of nearby water, which becomes highly acidic (a pH of roughly 3.3 to 4.5) relative to a more ordinary environment. The concentration of dissolved minerals also tends to be low. Dying moss forms layers of sediment and releases sugars and humic acids which consume oxygen. Since the surface of the water is covered by living moss, water becomes anaerobic. As a result, human tissues buried in the bog tend to tan rather than decay.
### Lindow Woman {#lindow_woman}
On 13 May 1983, two peat workers at Lindow Moss, Andy Mould and Stephen Dooley, noticed an unusual object---about the size of a football---on the elevator taking peat to the shredding machine. They removed the object for closer inspection, joking that it was a dinosaur egg. Once the peat had been removed, their discovery turned out to be a decomposing, incomplete human head with one eye and some hair intact.
Forensics identified the skull as belonging to a European woman, probably aged 30--50. Police initially thought the skull was that of Malika Reyn-Bardt, who had disappeared in 1960 and was the subject of an ongoing investigation. While in prison on another charge, her husband, Peter Reyn-Bardt, had boasted that he had killed his wife and buried her in the back garden of their bungalow, which was on the edge of the area of mossland where peat was being dug. The garden had been examined but no body was found. When Reyn-Bardt was confronted with the discovery of the skull from Lindow Moss, he confessed to the murder of his wife.
The skull was later radiocarbon dated, revealing it to be nearly 2,000 years old. \"Lindow Woman\", as it became known, dated from around 210 AD. This emerged shortly before Reyn-Bardt went to trial, but he was convicted on the evidence of his confession.
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# Lindow Man
## Discovery
A year later, a further discovery was made at Lindow Moss, just 820 ft southwest of the Lindow Woman. On 1 August 1984, Andy Mould, who had been involved in the discovery of Lindow Woman, took what he thought was a piece of wood off the elevator of the peat-shredding machine. He threw the object at Eddie Slack, his workmate. When it hit the ground, peat fell off the object and revealed it to be a human foot. The police were called, and the foot was taken away for examination.
At the same time Rachel Pugh, a trainee journalist for *The Wilmslow World*, was tipped off about the discovery. At the urging of her editor, she cycled out to the site of the discovery and persuaded the two men to show her where the foot had been excavated. Recognising the possible historical significance of the find, she told the diggers to stop work at once, and alerted Rick Turner, the Cheshire County Archaeologist, who subsequently succeeded in finding the rest of the body, which later became known as Lindow Man. Some skin had been exposed and had started to decay, so to prevent further deterioration of the body, it was re-covered with peat. The complete excavation of the block containing the remains was performed on 6 August. Until it could be dated, it was moved to the Macclesfield District General Hospital for storage. As the body of Malika Reyn-Bardt had still not been found, it was initially thought possible the body might be hers, until it was determined to be male, and radiocarbon dated.
The owners of the land where Lindow Man was found donated the body to the British Museum, and on 21 August it was transported to London. At the time, the body was dubbed \"Pete Marsh\" by Middlesex Hospital radiologists, a name subsequently adopted by local journalists, as was the similar \"Pete Bogg\".
The find was announced to the press during the second week of the investigation. As the best-preserved bog body found in Britain, its discovery caused a domestic media sensation and received global coverage. Sparking excitement in the country\'s archaeological community, who had long expected such a find, it was hailed as one of the most important archaeological discoveries of the 1980s. A *Q.E.D.* documentary about Lindow Man broadcast by the BBC in 1985 attracted 10 million viewers.
Lindow Man\'s official name is Lindow II, as there are other finds from the area: Lindow I (Lindow Woman) refers to a human skull, Lindow III to a \"fragmented headless body\", and Lindow IV to the upper thigh of an adult male, possibly that of Lindow Man. After the discovery of Lindow Man, there were no further archaeological excavations at Lindow Moss until 1987. A large piece of skin was found by workmen on the elevator on 6 February 1987. On this occasion, the police left the investigation to the archaeologists. Over 70 pieces were found, constituting Lindow III. Although the bone was not as well preserved as that of Lindow Man, the other tissues survived in better condition. The final discovery was that of Lindow IV on 14 June 1988. Part of a left leg and buttocks were found on the elevator, from a site just 50 ft west of where Lindow Man was found. Nearly three months later, on 12 September, a right thigh was discovered in the peat on the bucket of a digger. The proximity of the discovery sites, coupled with the fact that the remains were shown to come from an adult male, means that Lindow IV is probably part of Lindow Man.
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# Lindow Man
## Remains and investigation {#remains_and_investigation}
Lindow Man marked the first discovery in Britain of a well-preserved bog body; its condition was comparable to that of Grauballe Man and Tollund Man from Denmark. Before Lindow Man was found, it was estimated that 41 bog bodies had been found in England and Wales and 15 in Scotland. Encouraged by the discovery of Lindow Man, a gazetteer was compiled, which revealed a far higher number of bog bodies: over 85 in England and Wales and over 36 in Scotland. Prior to the discovery of the bodies in Lindow Moss, British bog bodies had been a relatively neglected subject compared to European examples. The interest caused by Lindow Man led to more in-depth research of accounts of discoveries in bogs since the 17th century; by 1995, the numbers had changed to 106 in England and Wales and 34 in Scotland. The remains covered a large time frame.
In life, Lindow Man would have been between 5\'6\" and 5\'8\" (168 and 173 cm) tall and weighed about 132 lb. It was possible to ascertain that his age at death was around the mid-20s. The body retains a trimmed beard, moustache, and sideburns of brown hair, as well as healthy teeth with no visible cavities, and manicured fingernails, indicating he did little heavy or rough work.`{{refn|Lindow Man's hair is currently red due to chemical changes caused by the bog in which he was buried; however, his hair was probably originally dark brown.<ref>{{Harvnb|Joy|2009|p=27}}</ref>|group=nb}}`{=mediawiki} Apart from a fox-fur armband, Lindow Man was discovered completely naked. When he died, Lindow Man was suffering from slight osteoarthritis and an infestation of whipworm and maw worm. As a result of the decalcification of the bones and pressure from the peat under which Lindow Man was buried, his skull was distorted. While some preserved human remains may contain DNA, peat bogs such as Lindow Moss are generally poor for such a purpose, and it is unlikely that DNA could be recovered from Lindow Man.
Lindow Man and Lindow III were found to have elevated levels of copper on their skin. The cause for this was uncertain as there could have been natural causes, although a study by Pyatt *et al.* proposed that the bodies may have been painted with a copper-based pigment. To test this, skin samples were taken from places likely to be painted and tested against samples from areas where painting was unlikely. It was found that the copper content of the skin of the torso was higher than the control areas, suggesting that the theory of Pyatt *et al.* may have been correct. However, the conclusion was ambiguous as the overall content was above that expected of a male, and variations across the body may have been due to environmental factors. Similarly, green deposits were found in the hair, originally thought to be a copper-based pigment used for decoration, but it was later found to be the result of a reaction between the keratin in the hair and the acid of the peat bog.
Dating Lindow Man is problematic as samples from the body and surrounding peat have produced dates spanning a 900-year period. Although the peat encasing Lindow Man has been radiocarbon dated to about 300 BC, Lindow Man himself has a different date. Early tests at different laboratories returned conflicting dates for the body; later tests suggested a date between 2 BC and 119 AD. There has been a tendency to ascribe the body to the Iron Age period rather than Roman due to the interpretation that Lindow Man\'s death may have been a ritual sacrifice or execution. Explanations for why the peat in which he was found is much older have been sought. Archaeologist P. C. Buckland suggests that as the stratigraphy of the peat appears undisturbed, Lindow Man may have been deposited into a pool that was already some 300 years old. Geographer K. E. Barber has argued against this hypothesis, saying that pools at Lindow Moss would have been too shallow, and suggests that the peat may have been peeled back to allow the burial and then replaced, leaving the stratigraphy apparently undisturbed.
Lindow Man\'s last meal was preserved in his stomach and intestines and was analysed in some detail. It was hoped that investigations into the contents of the stomach would shed light on the contemporary diet, as was the case with Grauballe Man and Tollund Man in the 1950s. The analysis of the contents of the digestive system of bog bodies had become one of the principal endeavours of investigating such remains. Analysis of the grains present revealed his diet to be mostly of cereals. He probably ate slightly charred bread, although the burning may have had ritual significance rather than being an accident. Some mistletoe pollen was also found in the stomach, indicating that Lindow Man died in March or April.
One of the conclusions of the study was that the people buried in Lindow Moss may have had a less varied diet than their European counterparts. According to Jody Joy, curator of the Iron Age collection at the British Museum, the importance of Lindow Man lies more in how he lived rather than how he died, as the circumstances surrounding his demise may never be fully established.
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# Lindow Man
## Remains and investigation {#remains_and_investigation}
### Cause of death {#cause_of_death}
As the peat was cleaned off the body in the laboratory, it became clear that Lindow Man had suffered a violent death. The injuries included a V-shaped, 3.5 cm cut on top of his head; a possible laceration at the back of the head, ligature marks on the neck where a sinew cord was found, a possible wound on the right side of the neck, a possible stab wound in the upper right chest, a broken neck, and a fractured rib. Xeroradiography revealed that the blow on top of the head (causing the V-shaped cut) was caused by a relatively blunt object; it had fractured the skull and driven fragments into the brain. Swelling along the edges of the wound indicated that Lindow Man had lived after being struck. The blow, possibly from a small axe, would have caused unconsciousness, but the victim could have survived for several hours afterwards. The ligature marks on the neck were caused by tightening the sinew cord found around his neck, possibly a garrotte or necklace.
It is not possible to confirm whether some injuries took place before or after death, due to the body\'s state of decay. This is the case for the wound in the upper right chest and the laceration on the back of the skull. The cut on the right of the neck may have been the result of the body becoming bloated, causing the skin to split, but the straight edges of the wound suggest that it may have been caused by a sharp instrument, such as a knife. The ligature marks on the neck may have occurred after death. In some interpretations of Lindow Man\'s death, the sinew is a garrotte used to break the victim\'s neck. However, Robert Connolly, a lecturer in physical anthropology, suggests that the sinew may have been ornamental and that ligature marks may have been caused by the body swelling when submerged. The rib fracture may also have occurred after death, perhaps during the discovery of the body, but is included in some narratives of the Lindow Man\'s death. The broken neck would have proven the fatal injury, whether caused by the sinew cord tightening around the neck or by blows to the back of the head. After death, Lindow Man was deposited into Lindow Moss face down.
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# Lindow Man
## Hypothesis
Archaeologist Don Brothwell considered that many of the older bodies need re-examining with modern techniques, such as those used in the analysis of Lindow Man. The study of bog bodies, including those found in Lindow Moss, has contributed to a wider understanding of well-preserved human remains, helping to develop new methods of analysis and investigation. The use of sophisticated techniques, such as computed tomography (CT) scans, has marked the investigation of the Lindow bodies as particularly important. Such scans allow the reconstruction of the body and internal examination. Of the 27 bodies recovered from lowland raised mires in England and Wales, only those from Lindow Moss and the remains of Worsley Man have survived, together with a shoe from another body. The remains have a date range from the early 1st to the 4th centuries. Investigation into the other bodies relies on contemporary descriptions of the discovery.
The physical evidence allows a general reconstruction of how Lindow Man was killed, although some details are debated, but it does not explain why he was killed. In North West England, there is little evidence for religious or ritual activity in the Iron Age period. What evidence does survive is usually in the form of artefacts recovered from peat bogs. Late Iron Age burials in the region often took the form of a crouched inhumation, sometimes with personal ornaments. Although dated to the mid-1st century AD, the type of burial of Lindow Man was more common in the pre-historic period. In the latter half of the 20th century, scholars widely believed that bog bodies demonstrating injuries to the neck or head area were examples of ritual sacrifice. Bog bodies were associated with Germanic and Celtic cultures, specifically related to head worship.
According to Brothwell, Lindow Man is one of the most complex examples of \"overkill\" in a bog body, and possibly has ritual meaning as it was \"extravagant\" for a straightforward murder. Archaeologists John Hodgson and Mark Brennand suggest that bog bodies may have been related to religious practice, although there is division in the academic community over this issue. In the case of Lindow Man, scholars debate whether the killing was murder or done as part of ritual. Anne Ross, an expert on Iron Age religion, proposed that the death was an example of human sacrifice and that the \"triple death\" (throat cut, strangled, and hit on the head) was an offering to several different gods. The wide date range for Lindow Man\'s death (2 BC to 119 AD) means he may have met his demise after the Romans conquered northern England in the 60s AD. As the Romans outlawed human sacrifice, such timing would open up other possibilities. This conclusion was emphasised by historian Ronald Hutton, who challenged the interpretation of sacrificial death. Connolly suggests that as Lindow Man was found naked, he could have been the victim of a violent robbery.
Joy said
> The jury really is still out on these bodies, whether they were aristocrats, priests, criminals, outsiders, whether they went willingly to their deaths or whether they were executed -- but Lindow was a very remote place in those days, an unlikely place for an ambush or a murder
According to Anne Ross, a scholar of Celtic history and Don Robins, a chemist at the University of London, Lindow Man was likely a sacrifice victim of extraordinary importance. They identified his stomach contents as including the undigested remains of a partially burned barley griddle cake of a kind used by the ancient Celts to select victims for sacrifice. Such cakes were torn into fragments and placed in a sack, after which all candidates for sacrifice would withdraw a piece, with the one withdrawing the burnt piece being the one who would be sacrificed. They argued that Lindow Man was likely a high-ranking Druid who was sacrificed in a last-ditch effort to call upon the aid of three Celtic gods to stop a Roman offensive against the Celts in AD 60.
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# Lindow Man
## Conservation
Environment and situation are the crucial factors that determine how corpses decay. For instance, corpses will decay differently depending on the weather, the way they are buried, and the medium in which they are buried. Peat slows the decay of corpses. It was feared that, once Lindow Man was removed from that environment, which had preserved the body for nearly 2,000 years, the remains would rapidly start to deteriorate, so steps were taken to ensure preservation. After rejecting methods that had been used to maintain the integrity of other bog bodies, such as the \"pit-tanning\" used on Grauballe Man, which took a year and a half, scientists settled on freeze-drying. In preparation, the body was covered in a solution of 15% polyethylene glycol 400 and 85% water to prevent it from becoming distorted. The body was then frozen solid and the ice vaporised to ensure Lindow Man did not shrink. Afterwards, Lindow Man was put in a specially constructed display case to control the environment, maintaining the temperature at 20 °C and the humidity at 55%.
Lindow Man is held in the British Museum. Before the remains were transferred there, people from North West England launched an unsuccessful campaign to keep the body in Manchester. The bog body has been on temporary display in other venues: at the Manchester Museum on three occasions, April to `{{Nowrap|December 1987}}`{=mediawiki}, March to `{{Nowrap|September 1991}}`{=mediawiki}, and `{{Nowrap|April 2008}}`{=mediawiki} to `{{Nowrap|April 2009}}`{=mediawiki}; and at the Great North Museum in Newcastle from August to `{{Nowrap|November 2009}}`{=mediawiki}. The 2008--09 Manchester display, titled *Lindow Man: A Bog Body Mystery Exhibition at the Manchester Museum*, won the category \"Best Archaeological Innovation\" in the 2010 British Archaeological Awards, run by the Council for British Archaeology.
Critics have complained that, by museum display of the remains, the body of Lindow Man has been objectified rather than treated with the respect due to the dead. This is part of a wider discussion about the scientific treatment of human remains and museum researchers and archaeologists using them as information sources
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# Luminance
**Luminance** is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through, is emitted from, or is reflected from a particular area, and falls within a given solid angle.
The procedure for conversion from spectral radiance to luminance is standardized by the CIE and ISO.
Brightness is the term for the *subjective* impression of the *objective* luminance measurement standard (see `{{Section link|Objectivity (science)|Objectivity in measurement}}`{=mediawiki} for the importance of this contrast).
The SI unit for luminance is candela per square metre (cd/m^2^). A non-SI term for the same unit is the nit. The unit in the Centimetre--gram--second system of units (CGS) (which predated the SI system) is the stilb, which is equal to one candela per square centimetre or 10 kcd/m^2^.
## Description
Luminance is often used to characterize emission or reflection from flat, diffuse surfaces. Luminance levels indicate how much luminous power could be detected by the human eye looking at a particular surface from a particular angle of view. Luminance is thus an indicator of how bright the surface will appear. In this case, the solid angle of interest is the solid angle subtended by the eye\'s pupil.
Luminance is used in the video industry to characterize the brightness of displays. A typical computer display emits between `{{val|50|and|300|u=cd/m<sup>2</sup>}}`{=mediawiki}. The sun has a luminance of about `{{val|1.6|e=9|u=cd/m<sup>2</sup>}}`{=mediawiki} at noon.
Luminance is invariant in geometric optics. This means that for an ideal optical system, the luminance at the output is the same as the input luminance.
For real, passive optical systems, the output luminance is `{{em|at most}}`{=mediawiki} equal to the input. As an example, if one uses a lens to form an image that is smaller than the source object, the luminous power is concentrated into a smaller area, meaning that the illuminance is higher at the image. The light at the image plane, however, fills a larger solid angle so the luminance comes out to be the same assuming there is no loss at the lens. The image can never be \"brighter\" than the source.
## Health effects {#health_effects}
Retinal damage can occur when the eye is exposed to high luminance. Damage can occur because of local heating of the retina. Photochemical effects can also cause damage, especially at short wavelengths.
The IEC 60825 series gives guidance on safety relating to exposure of the eye to lasers, which are high luminance sources. The IEC 62471 series gives guidance for evaluating the photobiological safety of lamps and lamp systems including luminaires. Specifically it specifies the exposure limits, reference measurement technique and classification scheme for the evaluation and control of photobiological hazards from all electrically powered incoherent broadband sources of optical radiation, including LEDs but excluding lasers, in the wavelength range from `{{val|200|u=nm}}`{=mediawiki} through `{{val|3000|u=nm}}`{=mediawiki}. This standard was prepared as Standard CIE S 009:2002 by the International Commission on Illumination.
## Luminance meter {#luminance_meter}
A **luminance meter** is a device used in photometry that can measure the luminance in a particular direction and with a particular solid angle. The simplest devices measure the luminance in a single direction while imaging luminance meters measure luminance in a way similar to the way a digital camera records color images.
## Formulation
The luminance of a specified point of a light source, in a specified direction, is defined by the mixed partial derivative $L_\mathrm{v} = \frac{\mathrm{d}^2\Phi_\mathrm{v}}{\mathrm{d}\Sigma\,\mathrm{d}\Omega_\Sigma \cos \theta_\Sigma}$ where
- is the luminance (cd/m^2^);
- is the luminous flux (lm) leaving the area `{{math|dΣ}}`{=mediawiki} in any direction contained inside the solid angle `{{math|dΩ<sub>Σ</sub>}}`{=mediawiki};
- is an infinitesimal area (m^2^) of the source containing the specified point;
- is an infinitesimal solid angle (sr) containing the specified direction; and
- is the angle between the normal `{{math|'''n'''<sub>Σ</sub>}}`{=mediawiki} to the surface `{{math|dΣ}}`{=mediawiki} and the specified direction.
If light travels through a lossless medium, the luminance does not change along a given light ray. As the ray crosses an arbitrary surface `{{mvar|S}}`{=mediawiki}, the luminance is given by $L_\mathrm{v} = \frac{\mathrm{d}^2\Phi_\mathrm{v}}{\mathrm{d}S\,\mathrm{d}\Omega_S \cos \theta_S}$ where
- is the infinitesimal area of `{{mvar|S}}`{=mediawiki} seen from the source inside the solid angle `{{math|dΩ<sub>Σ</sub>}}`{=mediawiki};
- is the infinitesimal solid angle subtended by `{{math|dΣ}}`{=mediawiki} as seen from `{{math|d''S''}}`{=mediawiki}; and
- is the angle between the normal `{{math|'''n'''<sub>''S''</sub>}}`{=mediawiki} to `{{math|d''S''}}`{=mediawiki} and the direction of the light.
More generally, the luminance along a light ray can be defined as $L_\mathrm{v} = n^2\frac{\mathrm{d}\Phi_\mathrm{v}}{\mathrm{d}G}$ where
- is the etendue of an infinitesimally narrow beam containing the specified ray;
- is the luminous flux carried by this beam; and
- is the index of refraction of the medium.
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# Luminance
## Relation to illuminance {#relation_to_illuminance}
thumb\|upright=1.5\|Comparison of photometric and radiometric quantities The luminance of a reflecting surface is related to the illuminance it receives: $\int_{\Omega_\Sigma} L_\text{v} \mathrm{d}\Omega_\Sigma \cos \theta_\Sigma = M_\text{v} = E_\text{v} R,$ where the integral covers all the directions of emission `{{math|Ω<sub>Σ</sub>}}`{=mediawiki},
- is the surface\'s luminous exitance;
- is the received illuminance; and
- is the reflectance.
In the case of a perfectly diffuse reflector (also called a Lambertian reflector), the luminance is isotropic, per Lambert\'s cosine law. Then the relationship is simply $L_\text{v} = \frac{E_\text{v} R}{\pi}.$
## Units
A variety of units have been used for luminance, besides the candela per square metre. Luminance is essentially the same as surface brightness, the term used in astronomy. This is measured with a logarithmic scale, magnitudes per square arcsecond (MPSAS)
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# Lunar calendar
thumb\|upright 1.5\|Lunar calendar year 2025 A **lunar calendar** is a calendar based on the monthly cycles of the Moon\'s phases (synodic months, lunations), in contrast to solar calendars, whose annual cycles are based on the solar year, and lunisolar calendars, whose lunar months are brought into alignment with the solar year through some process of intercalation`{{snd}}`{=mediawiki}such as by insertion of a leap month. The most widely observed lunar calendar is the Islamic calendar. The details of when months begin vary from calendar to calendar, with some using new, full, or crescent moons and others employing detailed calculations.
Since each lunation is approximately `{{frac|29|1|2}}`{=mediawiki} days, it is common for the months of a lunar calendar to alternate between 29 and 30 days. Since the period of 12 such lunations, a **lunar year**, is 354 days, 8 hours, 48 minutes, 34 seconds (354.36707 days), lunar calendars are 11 to 12 days shorter than the solar year. In lunar calendars, which do not make use of lunisolar calendars\' intercalation, the lunar months cycle through all the seasons of a solar year over the course of a 33--34 lunar-year cycle (see, e.g., list of Islamic years).
## History
Scholars have argued that ancient hunters conducted regular astronomical observations of the Moon back in the Upper Palaeolithic. Samuel L. Macey dates the earliest uses of the Moon as a time-measuring device back to 28,000--30,000 years ago.
## Start of the lunar month {#start_of_the_lunar_month}
Lunar and lunisolar calendars differ as to which day is the first day of the month. Some are based on the first sighting of the lunar crescent, such as the Hijri calendar observed by most of Islam. Alternatively, in some lunisolar calendars, such as the Hebrew calendar and Chinese calendar, the first day of a month is the day when an astronomical new moon occurs in a particular time zone. In others, such as some Hindu calendars, each month begins on the day after the full moon.
## Length of the lunar month {#length_of_the_lunar_month}
The length of each lunar cycle varies slightly from the average value. In addition, observations are subject to uncertainty and weather conditions. Thus, to minimise uncertainty, there have been attempts to create fixed arithmetical rules to determine the start of each calendar month. The best known of these is the Tabular Islamic calendar: in brief, it has a 30-year cycle with 11 leap years of 355 days and 19 years of 354 days. In the long term, it is accurate to one day in about 2,500 solar years or 2,570 lunar years. It also deviates from observation by up to about one or two days in the short term. The algorithm was introduced by Muslim astronomers in the 8th century to predict the approximate date of the first crescent moon, which is used to determine the first day of each month in the Islamic lunar calendar.
## List of lunar calendars {#list_of_lunar_calendars}
- Islamic Hijri calendar
- Javanese calendar
## Lunisolar calendars {#lunisolar_calendars}
Most calendars referred to as \"lunar\" calendars are lunisolar calendars. Their months are based on observations of the lunar cycle, with periodic intercalation being used to restore them into general agreement with the solar year. The solar \"civic calendar\" that was used in ancient Egypt showed traces of its origin in the earlier lunar calendar, which continued to be used alongside it for religious and agricultural purposes. Present-day lunisolar calendars include the Chinese, Korean, Vietnamese, Hindu, Hebrew and Thai calendars.
The most common form of intercalation is to add an additional month every second or third year. Some lunisolar calendars are also calibrated by annual natural events which are affected by lunar cycles as well as the solar cycle. An example of this is the lunisolar calendar of the Banks Islands, which includes three months in which the edible palolo worms mass on the beaches. These events occur at the last quarter of the lunar month, as the reproductive cycle of the palolos is synchronized with the moon
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# Lunatic
Looney}} \|A suffragist postcard depicting a lunatic, symbolized by a moon\]\] ***Lunatic*** is a term referring to a person who is seen as mentally ill, dangerous, foolish, or crazy---conditions once attributed to \"lunacy\". The word derives from *lunaticus* meaning \"of the moon\" or \"moonstruck\".
## History
The term \"lunatic\" derives from the Latin word *lunaticus*, which originally referred mainly to epilepsy and madness, as diseases thought to be caused by the moon. The King James Version of the Bible records \"lunatick\" in the Gospel of Matthew, which has been interpreted as a reference to epilepsy. By the fourth and fifth centuries,`{{clarify|date=November 2015}}`{=mediawiki} astrologers were commonly using the term to refer to neurological and psychiatric diseases. Pliny the Elder argued that the full moon induced individuals to lunacy and epilepsy by effects on the brain analogous to the nocturnal dew. Until at least 1700, it was also a common belief that the moon influenced fevers, rheumatism, episodes of epilepsy and other diseases.
## Use of the term \"lunatic\" in legislation {#use_of_the_term_lunatic_in_legislation}
In the jurisdiction of England and Wales, the Madhouses Act 1774 originated what later became Metropolitan Commissioners in Lunacy, under the Madhouses Act 1828. The Lunacy Acts 1890--1922 referred to \"lunatics\", but the Mental Treatment Act 1930 changed the legal term to \"person of unsound mind\", an expression which was replaced under the Mental Health Act 1959 by \"mental illness\". \"Person of unsound mind\" was the term used in 1950 in the English version of the European Convention on Human Rights as one of the types of person who could be deprived of liberty by a judicial process. The 1930 Act also replaced the term \"asylum\" with \"mental hospital\". Criminal lunatics became Broadmoor patients in 1948 under the National Health Service Act 1946.
On December 5, 2012, the US House of Representatives passed legislation approved earlier by the US Senate removing the word \"lunatic\" from all federal laws in the United States. President Barack Obama signed the 21st Century Language Act of 2012 into law on December 28, 2012.
\"Of unsound mind\" or *non compos mentis* are alternatives to \"lunatic\", the most conspicuous term used for insanity in the law in the late 19th century.
## Lunar distance {#lunar_distance}
The term *lunatic* was sometimes used to describe those who sought to discover a reliable method of determining longitude (before John Harrison developed the marine chronometer method of determining longitude, the main theory was the Method of Lunar Distances, advanced by Astronomer Royal Nevil Maskelyne). The artist William Hogarth portrayed a \"longitude lunatic\" in the eight scene of his 1733 work *A Rake\'s Progress*. Twenty years later, though, Hogarth described John Harrison\'s H-1 chronometer as \"one of the most exquisite movements ever made.\"
Later, members of the Lunar Society of Birmingham called themselves *lunaticks*. In an age with little street lighting, the society met on or near the night of the full moon
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# Linear timecode
**Linear (or Longitudinal) Timecode** (**LTC**) is an encoding of SMPTE timecode data in an audio signal, as defined in SMPTE 12M specification. The audio signal is commonly recorded on a VTR track or other storage media. The bits are encoded using the biphase mark code (also known as *FM*): a 0 bit has a single transition at the start of the bit period. A 1 bit has two transitions, at the beginning and middle of the period. This encoding is self-clocking. Each frame is terminated by a \'sync word\' which has a special predefined sync relationship with any video or film content.
A special bit in the linear timecode frame, the *biphase mark correction* bit, ensures that there are an even number of AC transitions in each timecode frame.
The sound of linear timecode is a jarring and distinctive noise and has been used as a sound-effects shorthand to imply *telemetry* or *computers*.
## Generation and Distribution {#generation_and_distribution}
In broadcast video situations, the LTC generator should be tied into house black burst, as should all devices using timecode, **to ensure correct color framing and correct synchronization of all digital clocks.** When synchronizing multiple clock-dependent digital devices together with video, such as digital audio recorders, the devices must be connected to a common word clock signal that is derived from the house black burst signal. This can be accomplished by using a generator that generates both black burst and video-resolved word clock, or by synchronizing the master digital device to video, and synchronizing all subsequent devices to the word clock output of the master digital device (and to LTC).
Made up of 80 bits per frame, where there may be 24, 25 or 30 frames per second, LTC timecode varies from 960 Hz (binary zeros at 24 frames/s) to 2400 Hz (binary ones at 30 frames/s), and thus is comfortably in the audio frequency range. LTC can exist as either a balanced or unbalanced signal, and can be treated as an audio signal in regards to distribution. Like audio, LTC can be distributed by standard audio wiring, connectors, distribution amplifiers, and patchbays, and can be ground-isolated with audio transformers. It can also be distributed via 75 ohm video cable and video distribution amplifiers, although the voltage attenuation caused by using a 75 ohm system may cause the signal to drop to a level that can not be read by some equipment.
Care has to be taken with analog audio to avoid audible \'breakthrough\' (aka \"crosstalk\") from the LTC track to the audio tracks.
**LTC care**:
- Avoid percussive sounds close to LTC
- Never process an LTC with noise reduction, eq or compressor
- Allow pre roll and post roll
- To create negative time code add one hour to time (avoid *midnight effect*)
- Always put slowest device as a master
Longitudinal SMPTE timecode should be played back at a middle-level when recorded on an audio track, as both low and high levels will introduce distortion.
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# Linear timecode
## Longitudinal timecode data format {#longitudinal_timecode_data_format}
thumb\|upright=4\|Linear timecode waveform as displayed in Audacity with 80 bit data frame highlighted
The basic format is an 80-bit code that gives the time of day to the second, and the frame number within the second. Values are stored in binary-coded decimal, least significant bit first. There are thirty-two bits of user data, usually used for a reel number and date.
<table>
<caption>SMPTE linear timecode</caption>
<thead>
<tr class="header">
<th><p>Bit</p></th>
<th><p>Weight</p></th>
<th><p>Meaning</p></th>
<th></th>
<th><p>Bit</p></th>
<th><p>Weight</p></th>
<th><p>Meaning</p></th>
<th></th>
<th><p>Bit</p></th>
<th><p>Weight</p></th>
<th><p>Meaning</p></th>
<th></th>
<th><p>Bit</p></th>
<th><p>Weight</p></th>
<th><p>Meaning</p></th>
<th></th>
<th><p>Bit</p></th>
<th><p>Value</p></th>
<th><p>Meaning</p></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td><p>00</p></td>
<td><p>1</p></td>
<td rowspan="4"><p>Frame number<br />
units<br />
(0–9)</p></td>
<td><p>16</p></td>
<td><p>1</p></td>
<td rowspan="4"><p>Seconds<br />
units<br />
(0–9)</p></td>
<td><p>32</p></td>
<td><p>1</p></td>
<td rowspan="4"><p>Minutes<br />
units<br />
(0–9)</p></td>
<td><p>48</p></td>
<td><p>1</p></td>
<td rowspan="4"><p>Hours<br />
units<br />
(0–9)</p></td>
<td data-bgcolor="#ccffff"><p>64</p></td>
<td data-bgcolor="#ccffff"><p>0</p></td>
<td rowspan="16" data-bgcolor="#ccffff"><p>Sync word,<br />
fixed bit<br />
pattern<br />
0011 1111<br />
1111 1101</p></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td><p>01</p></td>
<td><p>2</p></td>
<td><p>17</p></td>
<td><p>2</p></td>
<td><p>33</p></td>
<td><p>2</p></td>
<td><p>49</p></td>
<td><p>2</p></td>
<td data-bgcolor="#ccffff"><p>65</p></td>
<td data-bgcolor="#ccffff"><p>0</p></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td><p>02</p></td>
<td><p>4</p></td>
<td><p>18</p></td>
<td><p>4</p></td>
<td><p>34</p></td>
<td><p>4</p></td>
<td><p>50</p></td>
<td><p>4</p></td>
<td data-bgcolor="#ccffff"><p>66</p></td>
<td data-bgcolor="#ccffff"><p>1</p></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td><p>03</p></td>
<td><p>8</p></td>
<td><p>19</p></td>
<td><p>8</p></td>
<td><p>35</p></td>
<td><p>8</p></td>
<td><p>51</p></td>
<td><p>8</p></td>
<td data-bgcolor="#ccffff"><p>67</p></td>
<td data-bgcolor="#ccffff"><p>1</p></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td><p>04</p></td>
<td colspan="2" rowspan="4"><p>User bits<br />
field 1</p></td>
<td><p>20</p></td>
<td colspan="2" rowspan="4"><p>User bits<br />
field 3</p></td>
<td><p>36</p></td>
<td colspan="2" rowspan="4"><p>User bits<br />
field 5</p></td>
<td><p>52</p></td>
<td colspan="2" rowspan="4"><p>User bits<br />
field 7</p></td>
<td data-bgcolor="#ccffff"><p>68</p></td>
<td data-bgcolor="#ccffff"><p>1</p></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td><p>05</p></td>
<td><p>21</p></td>
<td><p>37</p></td>
<td><p>53</p></td>
<td data-bgcolor="#ccffff"><p>69</p></td>
<td data-bgcolor="#ccffff"><p>1</p></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td><p>06</p></td>
<td><p>22</p></td>
<td><p>38</p></td>
<td><p>54</p></td>
<td data-bgcolor="#ccffff"><p>70</p></td>
<td data-bgcolor="#ccffff"><p>1</p></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td><p>07</p></td>
<td><p>23</p></td>
<td><p>39</p></td>
<td><p>55</p></td>
<td data-bgcolor="#ccffff"><p>71</p></td>
<td data-bgcolor="#ccffff"><p>1</p></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td><p>08</p></td>
<td><p>10</p></td>
<td rowspan="2"><p>Frame number<br />
tens (0-2)</p></td>
<td><p>24</p></td>
<td><p>10</p></td>
<td rowspan="3"><p>Seconds<br />
tens<br />
(0–5)</p></td>
<td><p>40</p></td>
<td><p>10</p></td>
<td rowspan="3"><p>Minutes<br />
tens<br />
(0–5)</p></td>
<td><p>56</p></td>
<td><p>10</p></td>
<td rowspan="2"><p>Hours<br />
tens (0-2)</p></td>
<td data-bgcolor="#ccffff"><p>72</p></td>
<td data-bgcolor="#ccffff"><p>1</p></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td><p>09</p></td>
<td><p>20</p></td>
<td><p>25</p></td>
<td><p>20</p></td>
<td><p>41</p></td>
<td><p>20</p></td>
<td><p>57</p></td>
<td><p>20</p></td>
<td data-bgcolor="#ccffff"><p>73</p></td>
<td data-bgcolor="#ccffff"><p>1</p></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td data-bgcolor="#ffcccc"><p>10</p></td>
<td data-bgcolor="#ffcccc"><p>D</p></td>
<td data-bgcolor="#ffcccc"><p>Drop frame flag.</p></td>
<td><p>26</p></td>
<td><p>40</p></td>
<td><p>42</p></td>
<td><p>40</p></td>
<td data-bgcolor="ffcccc"><p>58</p></td>
<td data-bgcolor="ffcccc"><p>BGF1</p></td>
<td data-bgcolor="ffcccc"><p>Clock flag</p></td>
<td data-bgcolor="#ccffff"><p>74</p></td>
<td data-bgcolor="#ccffff"><p>1</p></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td><p>11</p></td>
<td><p>C</p></td>
<td><p>"Color frame" flag</p></td>
<td><p>27</p></td>
<td colspan="2"><p>(flag, see below)</p></td>
<td><p>43</p></td>
<td colspan="2"><p>(flag, see below)</p></td>
<td><p>59</p></td>
<td colspan="2"><p>(flag, see below)</p></td>
<td data-bgcolor="#ccffff"><p>75</p></td>
<td data-bgcolor="#ccffff"><p>1</p></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td><p>12</p></td>
<td colspan="2" rowspan="4"><p>User bits<br />
field 2</p></td>
<td><p>28</p></td>
<td colspan="2" rowspan="4"><p>User bits<br />
field 4</p></td>
<td><p>44</p></td>
<td colspan="2" rowspan="4"><p>User bits<br />
field 6</p></td>
<td><p>60</p></td>
<td colspan="2" rowspan="4"><p>User bits<br />
field 8</p></td>
<td data-bgcolor="#ccffff"><p>76</p></td>
<td data-bgcolor="#ccffff"><p>1</p></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td><p>13</p></td>
<td><p>29</p></td>
<td><p>45</p></td>
<td><p>61</p></td>
<td data-bgcolor="#ccffff"><p>77</p></td>
<td data-bgcolor="#ccffff"><p>1</p></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td><p>14</p></td>
<td><p>30</p></td>
<td><p>46</p></td>
<td><p>62</p></td>
<td data-bgcolor="#ccffff"><p>78</p></td>
<td data-bgcolor="#ccffff"><p>0</p></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td><p>15</p></td>
<td><p>31</p></td>
<td><p>47</p></td>
<td><p>63</p></td>
<td data-bgcolor="#ccffff"><p>79</p></td>
<td data-bgcolor="#ccffff"><p>1</p></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
: SMPTE linear timecode`{{r|BR.780-2}}`{=mediawiki}
- Bit 10 is set to 1 if drop frame numbering is in use; frame numbers 0 and 1 are skipped during the first second of every minute, except multiples of 10 minutes. This converts 30 frame/second time code to the 29.97 frame/second NTSC standard.
- Bit 11, the color framing bit, is set to 1 if the time code is synchronized to a color video signal. The frame number modulo 2 (for NTSC and SECAM) or modulo 4 (for PAL) should be preserved across cuts in order to avoid phase jumps in the chrominance subcarrier.
- Bits 27, 43, and 59 differ between 25 frame/s time code, and other frame rates (30, 29.97, or 24).`{{r|BR.780-2|p=9}}`{=mediawiki} The bits are:
- \"Polarity correction bit\" (bit 59 at 25 frame/s, bit 27 at other rates): this bit is chosen to provide an even number of 0 bits in the whole frame, including the sync code. (Since the frame is an even number of bits long, this implies an even number of 1 bits, and is thus an even parity bit. Since the sync code includes an odd number of 1 bits, it is an odd parity bit over the data.) This keeps the phase of each frame consistent, so it always starts with a rising edge at the beginning of bit 0. This allows seamless splicing of different time codes, and lets it be more easily read with an oscilloscope.
- \"Binary group flag\" bits BGF0 and BGF2 (bits 27 and 43 at 25 frame/s, bits 43 and 59 at other rates): these indicate the format of the user bits. Both 0 indicates no (or unspecified) format. Only BGF0 set indicates four 8-bit characters (transmitted little-endian). The combinations with BGF2 set are reserved.`{{r|BR.780-2|p=7–8}}`{=mediawiki}
- Bit 58, unused in earlier versions of the specification, is now defined as \"binary group flag 1\" and indicates that the time code is synchronized to an external clock.`{{r|BR.780-2|p=7}}`{=mediawiki} if zero, the time origin is arbitrary.
- The sync pattern in bits 64 through 79 includes 12 consecutive 1 bits, which cannot appear anywhere else in the time code. Assuming all user bits are set to 1, the longest run of 1 bits that can appear elsewhere in the time code is 10, bits 9 to 18 inclusive.
- The sync pattern is preceded by 00 and followed by 01. This is used to determine whether an audio tape is running forward or backward
| 925 |
Linear timecode
| 1 |
18,382 |
# Lunisolar calendar
A **lunisolar calendar** is a calendar in many cultures, that combines monthly lunar cycles with the solar year. As with all calendars which divide the year into months, there is an additional requirement that the year have a whole number of months (Moon cycles). The majority of years have twelve months but every second or third year is an embolismic year, which adds a thirteenth intercalary, embolismic, or leap month.
Lunisolar calendars are lunar calendars but, in contrast to purely lunar calendars such as the Islamic calendar, have additional intercalation rules that reset them periodically into a rough agreement with the solar year and thus with the seasons.
## Examples
The Chinese, Buddhist, Burmese, Assyrian, Hebrew, Jain, traditional Nepali, Hindu, Japanese, Korean, Mongolian, Tibetan, and Vietnamese calendars (in the East Asian Chinese cultural sphere), plus the ancient Hellenic, Coligny, and Babylonian calendars are all lunisolar. Also, some of the ancient pre-Islamic calendars in south Arabia followed a lunisolar system. The Chinese, Coligny and Hebrew lunisolar calendars track more or less the tropical year whereas the Buddhist and Hindu lunisolar calendars track the sidereal year. Therefore, the first three give an idea of the seasons whereas the last two give an idea of the position among the constellations of the full moon.
### Chinese lunisolar calendar {#chinese_lunisolar_calendar}
The Chinese calendar (華夏曆法) or Chinese lunisolar calendar is also called Agricultural Calendar \[農曆; 农历; Nónglì; \'farming calendar\'\], or Yin Calendar \[陰曆; 阴历; Yīnlì; \'yin calendar\'\]), as movements of the sun (representing Yang) and moon (representing Yin) are the references for the Chinese lunisolar calendar calculations. The Chinese lunisolar calendar is the origin of some variant calendars adopted by other neighboring countries, such as Vietnam and Korea.
Together with astronomical, horological, and phenological observations, definitions, measurements, and predictions of years, months, and days were refined. Astronomical phenomena and calculations emphasized especially the efforts to mathematically correlate the solar and lunar cycles from the perspective of the earth, which however are known to require some degree of numeric approximation or compromise.
The earliest record of the Chinese lunisolar calendar was in the Zhou dynasty (1050 BC -- 771 BC, around 3000 years ago. Throughout history, the Chinese lunisolar calendar had many variations and evolved with different dynasties with increasing accuracy, including the \"six ancient calendars\" in the Warring States period, the Qin calendar in the Qin dynasty, the Han calendar or the Taichu calendar in the Han dynasty and Tang dynasty, the Shoushi calendar in the Yuan dynasty, and the Daming calendar in the Ming dynasty, etc. Starting in 1912, the western solar calendar is used together with the lunisolar calendar in China.
The most celebrated Chinese holidays, such as the Chinese New Year (華夏新年), Lantern Festival (元宵節), Mid-Autumn Festival (中秋節), and Dragon Boat Festival (端午節) are all based upon the Chinese lunisolar calendar. In addition, the popular Chinese zodiac is a classification scheme based on the Chinese calendar that assigns an animal and its reputed attributes to each year in a repeating twelve-year cycle. The traditional calendar used the sexagenary cycle-based *ganzhi* system\'s mathematically repeating cycles of Heavenly Stems and Earthly Branches.
## Movable feasts in the Christian calendars, related to the lunar cycle {#movable_feasts_in_the_christian_calendars_related_to_the_lunar_cycle}
The Gregorian calendar (the world\'s most commonly used) is a solar one but the Western Christian churches use a lunar-based algorithm to determine the date of Easter and consequent movable feasts. Briefly, the date is determined with respect to the ecclesiastical full moon that follows the ecclesiastical equinox in March. (These events are almost, but not quite, the same as the actual astronomical observations.) The Eastern Christian churches have a similar algorithm that is based on the Julian calendar.
| 613 |
Lunisolar calendar
| 0 |
18,382 |
# Lunisolar calendar
## Reconciling lunar and solar cycles {#reconciling_lunar_and_solar_cycles}
### Determining leap months {#determining_leap_months}
A tropical year is approximately 365.2422 days long and a synodic month is approximately 29.5306 days long, so a tropical year is approximately `{{nowrap|365.2422 / 29.5306 ≈ 12.36826}}`{=mediawiki} months long. Because 0.36826 is between `{{1/3}}`{=mediawiki} and `{{1/2}}`{=mediawiki}, a typical year of 12 months needs to be supplemented with one intercalary or leap month every 2 to 3 years. More precisely, 0.36826 is quite close to `{{frac|7|19}}`{=mediawiki} (about 0.3684211): several lunisolar calendars have 7 leap months in every cycle of 19 years (called a \'Metonic cycle\'). The Babylonians applied the 19-year cycle in the late sixth century BCE.
Intercalation of leap months is frequently controlled by the \"epact\", which is the difference between the lunar and solar years (approximately 11 days). The classic Metonic cycle can be reproduced by assigning an initial epact value of 1 to the last year of the cycle and incrementing by 11 each year. Between the last year of one cycle and the first year of the next the increment is 12`{{snd}}`{=mediawiki} the `{{langnf|la|'''saltus lunae'''|leap of the moon}}`{=mediawiki}`{{snd}}`{=mediawiki} which causes the epacts to repeat every 19 years. When the epact reaches 30 or higher, an intercalary month is added and 30 is subtracted. The Metonic cycle states that 7 of 19 years will contain an additional intercalary month and those years are numbered: 3, 6, 8, 11, 14, 17 and 19. Both the Hebrew calendar and the Julian calendar use this sequence.
The Buddhist and Hebrew calendars restrict the leap month to a single month of the year; the number of common months between leap months is, therefore, usually 36, but occasionally only 24 months. Because the Chinese and Hindu lunisolar calendars allow the leap month to occur after or before (respectively) any month but use the true apparent motion of the Sun, their leap months do not usually occur within a couple of months of perihelion, when the apparent speed of the Sun along the ecliptic is fastest (now about 3 January). This increases the usual number of common months between leap months to roughly 34 months when a doublet of common years occurs, while reducing the number to about 29 months when only a common singleton occurs.
### With uncounted time {#with_uncounted_time}
An alternative way of dealing with the fact that a solar year does not contain an integer number of lunar months is by including uncounted time in a period of the year that is not assigned to a named month. Some Coast Salish peoples used a calendar of this kind. For instance, the Chehalis began their count of lunar months from the arrival of spawning chinook salmon (in Gregorian calendar October), and counted 10 months, leaving an uncounted period until the next chinook salmon run.
| 468 |
Lunisolar calendar
| 1 |
18,382 |
# Lunisolar calendar
## List of lunisolar calendars {#list_of_lunisolar_calendars}
The following is a list of lunisolar calendars sorted by family
| 20 |
Lunisolar calendar
| 2 |
18,384 |
# Labarum
The **labarum** (*λάβαρον* or λάβουρον) was a *vexillum* (military standard) that displayed the \"Chi-Rho\" symbol ☧, a christogram formed from the first two Greek letters of the word \"Christ\" (*ΧΡΙΣΤΟΣ*, or Χριστός) -- *Chi* (χ) and *Rho* (ρ). It was first used by the Roman emperor Constantine the Great.
Ancient sources draw an unambiguous distinction between the two terms \"labarum\" and \"Chi-Rho\", even though later usage sometimes regards the two as synonyms. The name labarum was applied both to the original standard used by Constantine the Great and to the many standards produced in imitation of it in the Late Antique world, and subsequently.
## Etymology
Beyond its derivation from Latin *labarum*, the etymology of the word is unclear. The Oxford English Dictionary offers no further derivation from within Latin. Some derive it from Latin *labare* \'to totter, to waver\' (in the sense of the \"waving\" of a flag in the breeze) or *laureum \[vexillum\]* (\"laurel standard\"). An origin as a loan into Latin from a Celtic language or Basque has also been postulated. There is a traditional Basque symbol called the lauburu; though the name is only attested from the 19th century onwards the motif occurs in engravings dating as early as the 2nd century AD.
Harry Thurston Peck, in his *Harpers Dictionary of Classical Antiquities*, wrote: \"The etymology of the term itself has given rise to many conflicting opinions. Some derive the name from labor; others from εὐλάβεια, \'reverence\'; others from λαμβάνειν, \'to take\'; and others, again, from λάφυρα, \'spoils\'. One writer makes Labarum to be like S.P.Q.R., only a notatio, or combination of initials to represent an equal number of terms; and thus, L.A.B.A.R.V.M. will stand for *Legionum aquila Byzantium antiqua Roma urbe mutavit*.\"
| 289 |
Labarum
| 0 |
18,384 |
# Labarum
## Vision of Constantine {#vision_of_constantine}
On the evening of October 27, 312 AD, with his army preparing for the Battle of the Milvian Bridge, the emperor Constantine I claimed to have had a vision which led him to believe he was fighting under the protection of the Christian God.
Lactantius states that in the night before the battle Constantine was commanded in a dream to \"delineate the heavenly sign on the shields of his soldiers\". Obeying this command, \"he marked on their shields the letter X, with a perpendicular line drawn through it and turned round thus at the top, being the cipher of Christ\". Having had their shields marked in this fashion, Constantine\'s troops readied themselves for battle.
From Eusebius, two accounts of a battle survive. The first, shorter one in the *Ecclesiastical History* leaves no doubt that God helped Constantine but does not mention any vision. In his later *Life of Constantine*, Eusebius gives a detailed account of a vision and stresses that he had heard the story from the emperor himself. According to this version, Constantine with his army was marching somewhere (Eusebius does not specify the actual location of the event, but it clearly is not in the camp at Rome) when he looked up to the sun and saw a cross of light above it, and with it the Greek words *Ἐν Τούτῳ Νίκα*. The traditionally employed Latin translation of the Greek is *in hoc signo vinces*--- literally \"In this sign, you will conquer.\" However, a direct translation from the original Greek text of Eusebius into English gives the phrase \"By this, conquer!\"
At first he was unsure of the meaning of the apparition, but the following night he had a dream in which Christ explained to him that he should use the sign against his enemies. Eusebius then continues to describe the labarum, the military standard used by Constantine in his later wars against Licinius, showing the Chi Rho sign.
Those two accounts have been merged in popular notion into Constantine seeing the Chi-Rho sign on the evening before the battle. Both authors agree that the sign was not readily understandable as denoting Christ, which corresponds with the fact that there is no certain evidence of the use of the letters chi and rho as a Christian sign before Constantine. Its first appearance is on a Constantinian silver coin from c. 317, which proves that Constantine did use the sign at that time. He made extensive use of the Chi-Rho and the labarum later in the conflict with Licinius.
The vision has been interpreted in a solar context (e.g., as a sun dog phenomenon), which would have been reshaped to fit with the Christian beliefs of the later Constantine.
An alternate explanation of the intersecting celestial symbol has been advanced by George Latura, which claims that Plato\'s visible god in *Timaeus* is in fact the intersection of the Milky Way and the zodiacal light, a rare apparition important to pagan beliefs that Christian bishops reinvented as a Christian symbol.
## Eusebius\' description of the labarum {#eusebius_description_of_the_labarum}
\"A Description of the Standard of the Cross, which the Romans now call the Labarum.\" \"Now it was made in the following manner. A long spear, overlaid with gold, formed the figure of the cross by means of a transverse bar laid over it. On the top of the whole was fixed a wreath of gold and precious stones; and within this, the symbol of the Saviour's name, two letters indicating the name of Christ by means of its initial characters, the letter P being intersected by X in its centre: and these letters the emperor was in the habit of wearing on his helmet at a later period. From the cross-bar of the spear was suspended a cloth, a royal piece, covered with a profuse embroidery of most brilliant precious stones; and which, being also richly interlaced with gold, presented an indescribable degree of beauty to the beholder. This banner was of a square form, and the upright staff, whose lower section was of great length, of the pious emperor and his children on its upper part, beneath the trophy of the cross, and immediately above the embroidered banner.\"
\"The emperor constantly made use of this sign of salvation as a safeguard against every adverse and hostile power, and commanded that others similar to it should be carried at the head of all his armies.\"
| 740 |
Labarum
| 1 |
18,384 |
# Labarum
## Iconographic career under Constantine {#iconographic_career_under_constantine}
The labarum does not appear on any of several standards depicted on the Arch of Constantine, which was erected just three years after the battle. If Eusebius\' oath-confirmed account of Constantine\'s vision and the role it played in his victory and conversion can be trusted, then a grand opportunity for the kind of political propaganda that the Arch was built to present was missed. Many historians have argued that in the early years after the battle, the Emperor had not yet decided to give clear public support to Christianity, whether from a lack of personal faith or because of fear of religious friction. The arch\'s inscription does say that the Emperor had saved the *res publica* INSTINCTV DIVINITATIS MENTIS MAGNITVDINE (\"by greatness of mind and by instinct \[or impulse\] of divinity\"). Continuing the iconography of his predecessors, Constantine\'s coinage at the time was inscribed with solar symbolism, interpreted as representing *Sol Invictus* (the Unconquered Sun), Helios, Apollo, or Mithras, but in 325 and thereafter the coinage ceases to be explicitly pagan, and Sol Invictus disappears. And although Eusebius\' *Historia Ecclesiae* further reports that Constantine had a statue of himself \"holding the sign of the Savior \[the cross\] in his right hand\" erected after his victorious entry into Rome, there are no other reports to confirm such a monument.
Historians still dispute whether Constantine was the first Christian Emperor to support a peaceful transition to Christianity during his rule, or an undecided pagan believer until middle age, and also how strongly influenced he was in his political-religious decisions by his Christian mother St. Helena.
As for the labarum itself, there is little evidence for its use before 317. In the course of Constantine\'s second war against Licinius in 324, the latter developed a superstitious dread of Constantine\'s standard. During the attack of Constantine\'s troops at the Battle of Adrianople the guard of the labarum standard were directed to move it to any part of the field where his soldiers seemed to be faltering. The appearance of this talismanic object appeared to embolden Constantine\'s troops and dismay those of Licinius. At the final battle of the war, the Battle of Chrysopolis, Licinius, though prominently displaying the images of Rome\'s pagan pantheon on his own battle line, forbade his troops from actively attacking the labarum, or even looking at it directly.
Constantine felt that both Licinius and Arius were agents of Satan, and associated them with the serpent described in the Book of Revelation (12:9). Constantine represented Licinius as a snake on his coins.
Eusebius stated that in addition to the singular labarum of Constantine, other similar standards (labara) were issued to the Roman army. This is confirmed by the two labara depicted being held by a soldier on a coin of Vetranio (illustrated) dating from 350.
| 472 |
Labarum
| 2 |
18,384 |
# Labarum
## Later usage {#later_usage}
A later Byzantine manuscript indicates that a jewelled labarum standard believed to have been that of Constantine was preserved for centuries, as an object of great veneration, in the imperial treasury at Constantinople. The labarum, with minor variations in its form, was widely used by the Christian Roman emperors who followed Constantine.
A miniature version of the labarum became part of the imperial regalia of Byzantine rulers, who were often depicted carrying it in their right hands.
The term \"labarum\" can be generally applied to any ecclesiastical banner, such as those carried in religious processions.
\"The Holy Lavaro\" were a set of early national Greek flags, blessed by the Greek Orthodox Church. Under these banners the Greeks united throughout the Greek Revolution (1821), a war of liberation waged against the Ottoman Empire.
Labarum also gives its name (Labaro) to a suburb of Rome adjacent to Prima Porta, one of the sites where the \'Vision of Constantine\' is placed by tradition
| 166 |
Labarum
| 3 |
18,386 |
# Laconia
**Laconia** or **Lakonia** (*Λακωνία*, *Lakonía*, `{{IPA|el|lakoˈni.a|}}`{=mediawiki}) is a historical and administrative region of Greece located on the southeastern part of the Peloponnese peninsula. Its administrative capital is Sparta. The word *laconic*---to speak in a blunt, concise way---is derived from the name of this region, a reference to the ancient Spartans who were renowned for their verbal austerity and blunt, often pithy remarks.
## Geography
Laconia is bordered by Messenia to the west and Arcadia to the north and is surrounded by the Myrtoan Sea to the east and by the Laconian Gulf and the Mediterranean Sea to the south. It encompasses Cape Malea and Cape Tainaron and a large part of the Mani Peninsula. The Mani Peninsula is in the west region of Laconia. The islands of Kythira and Antikythera lie to the south, but they administratively belong to the Attica regional unit of islands. The island, Elafonisos, situated between the Laconian mainland and Kythira, is part of Laconia.
The Evrotas is the longest river in the prefecture. The Evrotas Valley is predominantly an agricultural region that contains many citrus groves, olive groves, and pasture lands. It is the location of the largest orange production in the Peloponnese and probably in all of Greece. *Lakonia*, a brand of orange juice, is based in Amykles.
The main mountain ranges are the Taygetus 2,407 m in the west and the Parnon 1,961 m in the northeast. Taygetus, known as Pentadaktylos (*five-fingers*) throughout the Middle Ages, is west of Sparta and the Evrotas Valley. It is the highest mountain in Laconia and the Peloponnese and is mostly covered with pine trees. Two roads join the Messenia and Laconia prefectures: one is a tortuous mountain pass through Taygetus and the other bypasses the mountain via the Mani district to the south.
The stalactite cave, Dirou, a major tourist attraction, is located south of Areopolis in the southwest of Laconia.
### Climate
The city of Sparta enjoys a sunny and warm Mediterranean climate (Köppen: *Csa*). January highs are around 14 °C while July and August highs are around 36 °C in the city proper. Sparta records the highest summer average maximum temperatures in Greece. In July 2012 the city registered an average maximum temperature of 38.3 °C, making it Greece\'s second highest monthly average maximum temperature to date after the 38.6 °C recorded in Stylida in July 2023. The highest temperature ever recorded in Sparta is 45.7 °C in August 2021. On average, Sparta records 5 days per year with temperatures of over 40.0 °C. `{{Weather box
|location=Sparta (2009–2024)
|metric first=yes
|single line=yes
|Jan high C=14.4
|Feb high C=16.1
|Mar high C=18.4
|Apr high C=22.8
|May high C=27.8
|Jun high C=32.5
|Jul high C=36.0
|Aug high C=35.9
|Sep high C=31.3
|Oct high C=25.3
|Nov high C=20.2
|Dec high C=16.1
|Jan mean C=8.8
|Feb mean C=10.0
|Mar mean C=12.0
|Apr mean C=15.4
|May mean C=20.0
|Jun mean C=24.6
|Jul mean C=27.7
|Aug mean C=27.7
|Sep mean C=23.8
|Oct mean C=18.5
|Nov mean C=14.1
|Dec mean C=10.2
|Jan low C=3.1
|Feb low C=4.0
|Mar low C=5.6
|Apr low C=8.0
|May low C=12.2
|Jun low C=16.7
|Jul low C=19.5
|Aug low C=19.6
|Sep low C=16.4
|Oct low C=11.8
|Nov low C=7.9
|Dec low C=4.4
|rain colour=green
|Jan rain mm=122.6
|Feb rain mm=82.3
|Mar rain mm=62.4
|Apr rain mm=33.1
|May rain mm=24.8
|Jun rain mm=35.3
|Jul rain mm=11.9
|Aug rain mm=19.0
|Sep rain mm=52.2
|Oct rain mm=61.5
|Nov rain mm=88.1
|Dec rain mm=92.0
| Jan record high C=23.5
| Feb record high C=26.4
| Mar record high C=27.2
| Apr record high C=34.1
| May record high C=40.7
| Jun record high C=44.4
| Jul record high C=44.2
| Aug record high C=45.7
| Sep record high C=40.3
| Oct record high C=36.4
| Nov record high C=30.8
| Dec record high C=23.5
| Jan record low C=-5.3
| Feb record low C=-4.2
| Mar record low C=-4.6
| Apr record low C=-0.7
| May record low C=6.2
| Jun record low C=9.4
| Jul record low C=14.2
| Aug record low C=13.1
| Sep record low C=9.1
| Oct record low C=1.5
| Nov record low C=-1.7
| Dec record low C=-5.2
|source=[[National Observatory of Athens]] (Feb 2009 - Feb 2024),<ref name="auto1">{{cite web |url=https://www.meteo.gr/climate/ |archive-url=https://web.archive.org/web/20220927081043/https://meteo.gr/climate/ |archive-date=27 September 2022 |title=Climate |publisher=National Observatory of Athens |language=el }}</ref><ref>{{cite web |url=https://www.meteo.gr/Monthly_Bulletins.cfm |title=N.O.A Monthly Bulletins |access-date=28 November 2023 |archive-date=2 February 2023 |archive-url=https://web.archive.org/web/20230202121511/https://meteo.gr/Monthly_Bulletins.cfm |url-status=live }}</ref><br/> Sparta N.O.A station,<ref>{{cite web |url=https://penteli.meteo.gr/stations/sparti/ |title=Latest Conditions in Sparta }}</ref> [[World Meteorological Organization]]<ref name="WMO">{{cite web |url=https://oscar.wmo.int/surface/#/search/station/stationReportDetails/0-300-1-sparti |title=World Meteorological Organization |access-date=14 July 2023 |archive-date=12 July 2023 |archive-url=https://web.archive.org/web/20230712151921/https://oscar.wmo.int/surface/#/search/station/stationReportDetails/0-300-1-sparti |url-status=live }}</ref>
}}`{=mediawiki}
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# Laconia
## History
### Ancient
Evidence of Neolithic settlement in southern Laconia has been found during excavations of the Alepotrypa cave site. Significant archaeological recovery exists at the Vaphio-tomb site in Laconia. Found there is advanced Bronze Age art as well as evidence of cultural associations with the contemporaneous Minoan culture on Crete. At the end of the Mycenean period, the population of Laconia sharply declined. In classical Greece, Laconia was Spartan territory but from the 4th century BC onward Sparta lost control of various ports, towns and areas. From the mid-2nd century BC until 395 AD, Laconia was a part of the Roman Empire.
### Medieval
In the medieval period, Laconia formed part of the Byzantine Empire. In the 7th century, Slavic tribes settled in the Peloponnese. Two of them, the Melingoi and the Ezeritai, who settled in parts of Laconia, survived the subsequent Byzantine reconquest and re-Hellenization of the Peloponnese, and are attested until the late Middle Ages.
Following the Fourth Crusade, Laconia was gradually conquered by the Frankish Principality of Achaea. In the 1260s, the Byzantines recovered Mystras and other fortresses in the region and managed to evict the Franks from Laconia, which became the nucleus of a new Byzantine province. By the mid-14th century, this evolved into the Despotate of the Morea, held by the last Greek ruling dynasty, the Palaiologoi. The capital of the Despotate, Mystras, was a major site of the Palaiologan Renaissance, the last flowering of Byzantine culture. With the fall of the Despotate to the Ottomans in 1460, Laconia was conquered as well.
### Modern
With the exception of a 30-year interval of Venetian rule, Laconia remained under Ottoman control until the outbreak of the Greek War of Independence of 1821. Following independence, Sparta was selected as the capital of the modern prefecture, and its economy and agriculture expanded. With the incorporation of the British-ruled Ionian Islands into Greece in 1864, Elafonissos became part of the prefecture. After World War II and the Greek Civil War, its population began to somewhat decline, as people moved from the villages toward the larger cities of Greece and abroad.
In 1992, a devastating fire ruined the finest olive crops in the northern part of the prefecture, and affected the area of Sellasia along with Oinountas and its surrounding areas. Firefighters, helicopters and planes battled for days to put out the horrific fire.
In early 2006, flooding ruined olive and citrus crops as well as properties and villages along the Eurotas river. In the summer 2006, a fire devastated a part of the Mani Peninsula, ruining forests, crops, and numerous villages.
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# Laconia
## Municipalities
The regional unit, Laconia, is subdivided into five municipalities. These are (number as in the map in the infobox):
- East Mani (*Anatoliki Mani*, 2)
- Elafonisos (3)
- Eurotas (4)
- Monemvasia (5)
- Sparta (1)
### Prefecture
As a part of the 2011 Kallikratis government reform, regional unit Laconia was created out of the former prefecture Laconia (*Νομός Λακωνίας*). The prefecture had the same territory as the present regional unit. At the same time, the municipalities were reorganised, according to the table below.
+--------------------+--------------------+------------+
| New municipality | Old municipalities | Seat |
+====================+====================+============+
| East Mani\ | East Mani | Gytheio |
| (*Anatoliki Mani*) | | |
+--------------------+--------------------+------------+
| | Gytheio | |
+--------------------+--------------------+------------+
| | Oitylo | |
+--------------------+--------------------+------------+
| | Sminos | |
+--------------------+--------------------+------------+
| Elafonisos | Elafonisos | Elafonisos |
+--------------------+--------------------+------------+
| Eurotas | Skala | Skala |
+--------------------+--------------------+------------+
| | Geronthres | |
+--------------------+--------------------+------------+
| | Elos | |
+--------------------+--------------------+------------+
| | Krokees | |
+--------------------+--------------------+------------+
| | Niata | |
+--------------------+--------------------+------------+
| Monemvasia | Monemvasia | Molaoi |
+--------------------+--------------------+------------+
| | Asopos | |
+--------------------+--------------------+------------+
| | Voies | |
+--------------------+--------------------+------------+
| | Zarakas | |
+--------------------+--------------------+------------+
| | Molaoi | |
+--------------------+--------------------+------------+
| Sparti | Sparti | Sparti |
+--------------------+--------------------+------------+
| | Therapnes | |
+--------------------+--------------------+------------+
| | Karyes | |
+--------------------+--------------------+------------+
| | Mystras | |
+--------------------+--------------------+------------+
| | Oinountas | |
+--------------------+--------------------+------------+
| | Pellana | |
+--------------------+--------------------+------------+
| | Faris | |
+--------------------+--------------------+------------+
### Provinces
- Epidavros Limira Province -- Molaoi
- Gytheio Province -- Gytheio
- Lacedaemonia Province -- Sparti
- Oitylo Province -- Areopoli
*Note:* Provinces no longer hold any legal status in Greece.
## Population
The main cities and towns of Laconia are (ranked by 2021 census population):
- Sparta 16,782
- Gytheio 4,070
- Molaoi 2,850
- Skala 2,813
- Neapoli 2,715
## Transport
- Greek National Road 39, Tripoli -- Sparti -- Gytheio
- Greek National Road 82, Pylos -- Kalamata -- Sparti
- Greek National Road 86, Gytheio -- Monemvasia
- Molaoi to Leonidi Road, E, NE
## Communications
### Radio
- FLY FM 89,7 (Sparta).
- POLITIA 90,7 -- ΠΟΛΙΤΕΙΑ 90.7 (Sparta)
- Radio Sparti -- 92.7 FM (Sparta)
- Radiofonias Notias Lakonias (Southern Laconia Radio) -- 93.5 (Gytheio)
- Star FM -- 94.7
### Television
- Ellada TV -- UHF 43, Sparta
- TV Notias Lakonias -- Molaoi
### Newspapers
- Λακωνικός Τύπος
- Ελεύθερη Άποψη
- [Νέα Σπάρτη](https://web.archive.org/web/20080318101036/http://www.lakonia.org/gr/gr_nea_sparth
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# Lanista
***Lanista*** is a genus of African bush-crickets (Orthoptera: Tettigoniidae) in the subfamily Conocephalinae
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# Laocoön
**Laocoön** (`{{IPAc-en|l|eɪ|ˈ|ɒ|k|oʊ|ˌ|ɒ|n|,_|-|k|ə|ˌ|w|ɒ|n}}`{=mediawiki}; *Lāokóōn*, `{{IPA|grc|laːokóɔːn|IPA}}`{=mediawiki}, gen.: *Λᾱοκόωντος*) is a figure in Greek and Roman mythology and the Epic Cycle.
Laocoön is a Trojan priest. He and his two young sons are attacked by giant serpents sent by the gods when Laocoön argued against bringing the Trojan horse into the city. The story of Laocoön has been the subject of numerous artists, both in ancient and in more contemporary times.
## Family
Laocoön was variously called as the son of Acoetes, Antenor`{{AI-generated source|date=November 2024}}`{=mediawiki} or Poseidon; or the son of Priam and Hecuba. He had two sons.
## Death
The most detailed description of Laocoön\'s grisly fate was provided by Quintus Smyrnaeus in *Posthomerica*, a later, literary version of events following the *Iliad*. According to Quintus, Laocoön begged the Trojans to set fire to the Trojan horse to ensure it was not a trick.
Athena, angry with him and the Trojans, shook the ground around Laocoön\'s feet and painfully blinded him. The Trojans, watching this unfold, assumed Laocoön was punished for the Trojans\' mutilating and doubting Sinon, the undercover Greek soldier sent to convince the Trojans to let him and the horse inside their city walls. Thus, the Trojans wheeled the great wooden horse in. Laocoön did not give up trying to convince the Trojans to burn the horse.
According to one source, it was Athena who punished Laocoön even further, by sending two giant sea serpents to strangle and kill him and his two sons. Another version of the story says that it was Poseidon who sent the sea serpents to kill them. And according to Apollodorus, it was Apollo who sent the two sea serpents, because Laocoön had insulted Apollo by having sex with his wife in front of his cult statue.
Virgil used the story in the *Aeneid*. According to Virgil, Laocoön advised the Trojans not to receive the horse from the Greeks. They were taken in by the deceitful testimony of Sinon and disregarded Laocoön\'s advice. The enraged Laocoön threw his spear at the Horse in response.
Minerva then sent sea serpents to strangle Laocoön and his two sons, Antiphantes and Thymbraeus, for his actions.
: \"Laocoön, ostensibly sacrificing a bull to Neptune on behalf of the city (lines 201 ff.), becomes himself the tragic victim, as the simile (lines 223--224) makes clear. In some sense, his death must be symbolic of the city as a whole \...\" --- S.V. Tracy (1987)
According to the Hellenistic poet Euphorion of Chalcis, Laocoön was *actually* punished for procreating upon holy ground sacred to Poseidon; it was only unlucky timing that caused the Trojans to misinterpret his death as punishment for striking the horse with a spear, which they bring into the city with disastrous consequences. The episode furnished the subject of Sophocles\' lost tragedy, *Laocoön*.
In *Aeneid*, Virgil describes the circumstances of Laocoön\'s death:
: {\|
\|- \| from the *Aeneid* \| \| English translation \| \| tr. Dryden \|- \| `{{smalldiv|
''Ille simul manibus''
:''tendit divellere nodos''
''perfusus sanie vittas''
:''atroque veneno,''
''clamores simul horrendos''
:''ad sidera tollit:''
''qualis mugitus, fugit''
:''cum saucius aram''
''taurus et incertam''
:''excussit cervice securim.''
}}`{=mediawiki} \| \| `{{smalldiv|
''At the same time he stretched hands''
: ''forth to tear the knots''
''his fillets soaked with saliva''
: ''and black venom''
''at the same time he lifted horrendous''
: ''cries to heaven:''
''like the bellowing when fleeing''
: ''from the altar a wounded''
''bull and has shaken the''
: ''ill-aimed axe from its neck.''
}}`{=mediawiki} \| \| `{{smalldiv|
''With both his hands''
: ''he labors at the knots;''
''His holy fillets''
: ''the blue venom blots;''
''His roaring fills''
: ''the flitting air around.''
''Thus, when an ox''
: ''receives a glancing wound,''
''He breaks his bands,''
: ''the fatal altar flies,''
''And with loud bellowings''
: ''breaks the yielding skies.''
}}`{=mediawiki} \|}
## Classical descriptions {#classical_descriptions}
The story of Laocoön is not mentioned by Homer, but it had been the subject of a tragedy, now lost, by Sophocles and was mentioned by other Greek writers, though the events around the attack by the serpents vary considerably. The most famous account of these is now in Virgil\'s *Aeneid* where Laocoön was a priest of Neptune (Poseidon), who was killed with both his sons after attempting to expose the ruse of the Trojan Horse by striking it with a spear.
Virgil gives Laocoön the famous line
: *\"Equō nē crēdite, Teucrī / Quidquid id est, timeō Danaōs et dōna ferentēs\"*
:
This quote is the source of the saying: *\"Beware of Greeks bearing gifts.\"*
In Sophocles, however, he was a priest of Apollo who should have been celibate, but had married. The serpents killed only the two sons, leaving Laocoön himself alive to suffer. In other versions, he was killed for having committed an impiety by making love with his wife in the presence of a cult image in a sanctuary, or simply making a sacrifice in the temple with his wife present. In this second group of versions, the snakes were sent by Poseidon and in the first by Poseidon and Athena, or Apollo, and the deaths were interpreted by the Trojans as proof that the horse was a sacred object. The two versions have rather different morals: Laocoön was either punished for doing wrong, or for being right.
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# Laocoön
## Later depictions {#later_depictions}
The death of Laocoön was famously depicted in a much-admired marble *Laocoön and His Sons*, attributed by Pliny the Elder to the Rhodian sculptors Agesander, Athenodoros, and Polydorus, which stands in the Vatican Museums, Rome. Copies have been executed by various artists, notably Baccio Bandinelli. These show the complete sculpture (with conjectural reconstructions of the missing pieces) and are located in Rhodes, at the Palace of the Grand Master of the Knights of Rhodes, Rome, the Uffizi Gallery in Florence and in front of the Archaeological Museum, Odesa, Ukraine, amongst others. Alexander Calder also designed a stabile which he called Laocoön in 1947; it\'s in the collection of The Broad museum in Los Angeles.
The marble Laocoön provided the central image for Lessing\'s *Laocoön*, 1766, an aesthetic polemic directed against Winckelmann and the comte de Caylus. Daniel Albright reengages the role of the figure of Laocoön in aesthetic thought in his book *Untwisting the Serpent: Modernism in Literature, Music, and Other Arts*.
In Hector Berlioz\'s 1863 opera *Les Troyens*, the death of Laocoön is a pivotal moment of the first act after Aeneas\' entrance, sung by eight singers and a double choir (\"ottetto et double chœur\"). It begins with the verse \"Châtiment effroyable\" (\"frightful punishment\").
- In addition to other literary references, John Barth employs a bust of Laocoön in his novella, *The End of the Road*.
- The R.E.M. song \"Laughing\", on the band\'s debut album, *Murmur* (1983), references Laocoön, rendering him female (\"Laocoön and her two sons\"); they also reference Laocoön in the song \"Harborcoat\".
- The comic book *Asterix and the Laurel Wreath* parodies statue\'s pose.
- American author Joyce Carol Oates also references Laocoön in her 1989 novel *American Appetites*.
- In Stave V of *A Christmas Carol*, by Charles Dickens (1843), Scrooge awakes on Christmas morning, \"making a perfect Laocoön of himself with his stockings\".
- Barbara Tuchman\'s *The March of Folly* begins with an extensive analysis of the Laocoön story.
- The American feminist poet and author Marge Piercy includes a poem titled \"Laocoön is the name of the figure\", in her collection *Stone, Paper, Knife* (1983), relating love lost and beginning.
- John Steinbeck references Laocoön in his American literary classic *East of Eden*, referring to a picture of "Laocoön completely wrapped in snakes" when describing artwork hanging in classrooms at the Salinas schoolhouse.
- Sinclair Lewis references Laocoön in his novel *Arrowsmith*, remarking of a family argument that \"general composition \[was\] remarkably like the Laocoön.\"
- Postminimalist artist Eva Hesse named her first major freestanding sculpture---a tall wrapped framework with a tangle of cords---Laocoon (1966).
- Russian-American author Vladimir Nabokov makes a passing mention of Laocoön is his novel on totalitarianism, *Bend Sinister*.
- Martin Amis makes a passing mention of Laocoön is his novel The Information
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# Logical positivism
**Logical positivism**, also known as **logical empiricism** or **neo-positivism**, was a philosophical movement, in the empiricist tradition, that sought to formulate a scientific philosophy in which philosophical discourse would be, in the perception of its proponents, as authoritative and meaningful as empirical science.
Logical positivism\'s central thesis was the verification principle, also known as the \"verifiability criterion of meaning\", according to which a statement is *cognitively meaningful* only if it can be verified through empirical observation or if it is a tautology (true by virtue of its own meaning or its own logical form). The verifiability criterion thus rejected statements of metaphysics, theology, ethics and aesthetics as *cognitively meaningless* in terms of truth value or factual content. Despite its ambition to overhaul philosophy by mimicking the structure and process of empirical science, logical positivism became erroneously stereotyped as an agenda to regulate the scientific process and to place strict standards on it.
The movement emerged in the late 1920s among philosophers, scientists and mathematicians congregated within the Vienna Circle and Berlin Circle and flourished in several European centres through the 1930s. By the end of World War II, many of its members had settled in the English-speaking world and the project shifted to less radical goals within the philosophy of science.
By the 1950s, problems identified within logical positivism\'s central tenets became seen as intractable, drawing escalating criticism among leading philosophers, notably from Willard van Orman Quine and Karl Popper, and even from within the movement, from Carl Hempel. These problems would remain unresolved, precipitating the movement\'s eventual decline and abandonment by the 1960s. In 1967, philosopher John Passmore pronounced logical positivism \"dead, or as dead as a philosophical movement ever becomes\".
## Origins
Logical positivism emerged in Germany and Austria amid a cultural background characterised by the dominance of Hegelian metaphysics and the work of Hegelian successors such as F. H. Bradley, whose metaphysics portrayed the world without reference to empirical observation. The late 19th century also saw the emergence of neo-Kantianism as a philosophical movement, in the rationalist tradition.
The logical positivist program established its theoretical foundations in the empiricism of David Hume, Auguste Comte and Ernst Mach, along with the positivism of Comte and Mach, defining its exemplar of science in Einstein\'s general theory of relativity. In accordance with Mach\'s phenomenalism, whereby material objects exist only as sensory stimuli rather than as observable entities in the real world, logical positivists took all scientific knowledge to be only sensory experience. Further influence came from Percy Bridgman\'s operationalism---whereby a concept is not knowable unless it can be measured experimentally---as well as Immanuel Kant\'s perspectives on aprioricity.
Ludwig Wittgenstein\'s *Tractatus Logico-Philosophicus* established the theoretical foundations for the verifiability principle. His work introduced the view of philosophy as \"critique of language\", discussing theoretical distinctions between intelligible and nonsensical discourse. *Tractatus* adhered to a correspondence theory of truth, as opposed to a coherence theory of truth. Logical positivists were also influenced by Wittgenstein\'s interpretation of probability though, according to Neurath, some objected to the metaphysics in *Tractatus*.
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# Logical positivism
## History
### Vienna and Berlin Circles {#vienna_and_berlin_circles}
The Vienna Circle was led principally by Moritz Schlick, congregating around the University of Vienna and at the Café Central. A manifesto written by Otto Neurath, Hans Hahn and Rudolf Carnap in 1929 summarised the Vienna Circle\'s positions. Schlick had originally held a neo-Kantian position, but later converted, via Carnap\'s 1928 book *Der logische Aufbau der Welt* (*The Logical Structure of the World*). The Viennese maintained closely cooperative ties with the Berlin Circle, among whom Hans Reichenbach was pre-eminent. Carl Hempel, who studied under Reichenbach in Germany, was also to prove influential in the movement\'s later history. A friendly but tenacious critic of the movement was Karl Popper, whom Neurath nicknamed the \"Official Opposition\".
Early in the movement, Carnap, Hahn, Neurath and others recognised that the verifiability criterion was too stringent in that it rejected universal statements, which are vital to scientific hypothesis. A radical *left wing* emerged from the Vienna Circle, led by Neurath and Carnap, who proposed revisions to weaken the criterion, a program they referred to as the \"liberalisation of empiricism\". A conservative *right wing*, led by Schlick and Waismann, instead sought to classify universal statements as analytic truths, thereby to reconcile them with the existing criterion. Within the liberal wing Carnap emphasised fallibilism, as well as pragmatics, which he considered integral to empiricism. Neurath prescribed a move from Mach\'s phenomenalism to physicalism, though this would be opposed by Schlick. As Neurath and Carnap sought to pose science toward social reform, the split in the Vienna Circle also reflected political differences.
Both Schlick and Carnap had been influenced by and sought to define logical positivism versus the neo-Kantianism of Ernst Cassirer, the contemporary leading figure of the Marburg school, and against Edmund Husserl\'s phenomenology. Logical positivists especially opposed Martin Heidegger\'s obscure metaphysics, the epitome of what they had rejected through their epistemological doctrines. In the early 1930s, Carnap debated Heidegger over \"metaphysical pseudosentences\".
### Anglosphere
As the movement\'s first emissary to the New World, Moritz Schlick visited Stanford University in 1929, yet otherwise remained in Vienna and was murdered in 1936 at the University by a former student, Johann Nelböck, who was reportedly deranged. That year, A. J. Ayer, a British attendee at various Vienna Circle meetings since 1933, published *Language, Truth and Logic*, which imported logical positivism to the English-speaking world. In 1933, the Nazi Party\'s rise to power in Germany had triggered flight of intellectuals, which accelerated upon Germany\'s annexation of Austria in 1938. The logical positivists, many of whom were Jewish, were targeted and continued flight throughout the pre-war period. Their philosophy thus became dominant in the English-speaking world.
By the late 1930s, many in the movement had replaced phenomenalism with Neurath\'s physicalism, whereby material objects are not reducible to sensory stimuli but exist as publicly observable entities in the real world. Neurath settled in England, where he died in 1945. Carnap, Reichenbach and Hempel settled permanently in America.
### Post-war period {#post_war_period}
Following the Second World War, logical positivism---now referred to by some as *logical empiricism*---turned to less radical objectives in the philosophy of science. Led by Carl Hempel, who expounded the covering law model of scientific explanation, the movement became a major underpinning of analytic philosophy in the English-speaking world and its influence extended beyond philosophy into the social sciences. At the same time, the movement drew intensifying scrutiny over its central problems and its doctrines were increasingly criticised, most trenchantly by Willard Van Orman Quine, Norwood Hanson, Karl Popper, Thomas Kuhn and Carl Hempel.
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# Logical positivism
## Principles
### Verification and Confirmation {#verification_and_confirmation}
#### Verifiability Criterion of Meaning {#verifiability_criterion_of_meaning}
According to the verifiability criterion of meaning, a statement is *cognitively meaningful* only if it is either verifiable by empirical observation or is an analytic truth (i.e. true by virtue of its own meaning or its own logical form). *Cognitive meaningfulness* was defined variably: possessing truth value; or corresponding to a possible state of affairs; or intelligible or understandable as are scientific statements. Other types of meaning---for instance, emotive, expressive or figurative---were dismissed from further review.
Metaphysics, theology, as well as much of ethics and aesthetics failed this criterion, and so were found cognitively meaningless and only *emotively meaningful* (though, notably, Schlick considered ethical and aesthetic statements cognitively meaningful). Ethics and aesthetics were considered subjective preferences, while theology and metaphysics contained \"pseudostatements\" that were neither true nor false. Thus, logical positivism indirectly asserted Hume\'s law, the principle that factual statements cannot justify evaluative statements, and that the two are separated by an unbridgeable gap. A. J. Ayer\'s *Language, Truth and Logic* (1936) presented an extreme version of this principle---the boo/hooray doctrine---whereby all evaluative judgments are merely emotional reactions.
#### Revisions to the criterion {#revisions_to_the_criterion}
Logical positivists in the Vienna Circle recognised quickly that the verifiability criterion was too restrictive. Specifically, universal statements were noted to be empirically unverifiable, rendering vital domains of science and reason, such as scientific hypothesis, *cognitively meaningless* under verificationism. This would pose significant problems for the logical positivist program, absent revisions to its criterion of meaning.
In his 1936 and 1937 papers, *Testability and Meaning*, Carnap proposed *confirmation* in place of verification, determining that, though universal laws cannot be verified, they can be confirmed. Carnap employed abundant logical and mathematical tools to research an inductive logic that would account for probability according to *degrees of confirmation*. However, he was never able to formulate a model. In Carnap\'s inductive logic, a universal law\'s degree of confirmation was always zero. The formulation of what eventually came to be called the \"criterion of cognitive significance\", stemming from this research, took three decades (Hempel 1950, Carnap 1956, Carnap 1961). Carl Hempel, who became a prominent critic of the logical positivist movement, elucidated the paradox of confirmation.
In his 1936 book, *Language, Truth and Logic*, A. J. Ayer distinguished *strong* and *weak* verification. He stipulated that, \"A proposition is said to be verifiable, in the strong sense of the term, if, and only if, its truth could be conclusively established by experience\", but is verifiable in the weak sense \"if it is possible for experience to render it probable\". He would add that, \"no proposition, other than a tautology, can possibly be anything more than a probable hypothesis\". Thus, he would conclude that all are open to weak verification.
### Analytic-synthetic distinction {#analytic_synthetic_distinction}
In theories of justification, *a priori* statements are those that can be known independently of observation, contrasting with *a posteriori* statements, which are dependent on observation. Statements may also be categorised into *analytic* and *synthetic*: Analytic statements are true by virtue of their own meaning or their own logical form, therefore are tautologies that are true by necessity but uninformative about the world. Synthetic statements, in comparison, are contingent propositions that refer to a state of facts concerning the world.
David Hume proposed an unambiguous distinction between analytic and synthetic, categorising knowledge exclusively as either \"relations of ideas\" (which are *a priori*, analytic and abstract) or \"matters of fact and real existence\" (*a posteriori*, synthetic and concrete), a classification referred to as Hume\'s fork. Immanuel Kant identified a further category of knowledge: Synthetic *a priori* statements, which are informative about the world, but known without observation. This principle is encapsulated in Kant\'s transcendental idealism, which attributes the mind a constructive role in phenomena whereby intuitive truths---including synthetic *a priori* conceptions of space and time---function as an interpretative filter for an observer\'s experience of the world. His thesis would serve to rescue Newton\'s law of universal gravitation from Hume\'s problem of induction by determining uniformity of nature to be in the category of *a priori* knowledge.
The Vienna Circle rejected Kant\'s conception of synthetic *a priori* knowledge given its incompatibility with the verifiability criterion. Yet, they adopted the Kantian position of defining mathematics and logic---ordinarily considered synthetic truths---as *a priori*. Carnap\'s solution to this discrepancy would be to reinterpret logical truths as tautologies, redefining logic as analytic, building upon theoretical foundations established in Wittgenstein\'s *Tractatus*. Mathematics, in turn, would be reduced to logic through the logicist approach proposed by Gottlob Frege. In effect, Carnap\'s reconstruction of analyticity expounded Hume\'s fork, affirming its analytic-synthetic distinction. This would be critically important in rendering the verification principle compatible with mathematics and logic.
### Observation-theory distinction {#observation_theory_distinction}
Carnap devoted much of his career to the cornerstone doctrine of *rational reconstruction*, whereby scientific theories can be formalised into predicate logic and the components of a theory categorised into *observation terms* and *theoretical terms*. Observation terms are specified by direct observation and thus assumed to have fixed empirical definitions, whereas theoretical terms refer to the unobservables of a theory, including abstract conceptions such as mathematical formulas. The two categories of primitive terms would be interconnected in meaning via a deductive interpretative framework, referred to as *correspondence rules*.
Early in his research, Carnap postulated that correspondence rules could be used to define theoretical terms from observation terms, contending that scientific knowledge could be unified by reducing theoretical laws to \"protocol sentences\" grounded in observable facts. He would soon abandon this model of reconstruction, suggesting instead that theoretical terms could be defined implicitly by the axioms of a theory. Furthermore, that observation terms could, in some cases, garner meaning from theoretical terms via correspondence rules. Here, definition is said to be \'implicit\' in that the axioms serve to exclude those interpretations that falsify the theory. Thus, axioms define theoretical terms indirectly by restricting the set of possible interpretations to those that are true interpretations.
By reconstructing the semantics of scientific language, Carnap\'s thesis builds upon earlier research in the reconstruction of syntax, referring to Bertrand Russell\'s logical atomism---the view that statements in natural language can be converted to standardised subunits of meaning assembled via a logical syntax. Rational reconstruction is sometimes referred to as the *received view* or *syntactic view of theories* in the context of subsequent work by Carl Hempel, Ernest Nagel and Herbert Feigl.
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# Logical positivism
## Principles
### Logicism
By reducing mathematics to logic, Bertrand Russell sought to convert the mathematical formulas of physics to symbolic logic. Gottlob Frege began this program of logicism, continuing it with Russell, but eventually lost interest. Russell then continued it with Alfred North Whitehead in their *Principia Mathematica*, inspiring some of the more mathematical logical positivists, such as Hans Hahn and Rudolf Carnap.
Carnap\'s early anti-metaphysical works employed Russell\'s theory of types. Like Russell, Carnap envisioned a universal language that could reconstruct mathematics and thereby encode physics. Yet Kurt Gödel\'s incompleteness theorem showed this to be impossible, except in trivial cases, and Alfred Tarski\'s undefinability theorem finally undermined all hopes of reducing mathematics to logic. Thus, a universal language failed to stem from Carnap\'s 1934 work *Logische Syntax der Sprache* (*Logical Syntax of Language*). Still, some logical positivists, including Carl Hempel, continued support of logicism.
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# Logical positivism
## Philosophy of science {#philosophy_of_science}
The logical positivist movement shed much of its revolutionary zeal following the defeat of Nazism and the decline of rival philosophies that sought radical reform, notably Marburg neo-Kantianism, Husserlian phenomenology and Heidegger\'s existential hermeneutics. Hosted in the climate of American pragmatism and common sense empiricism, its proponents no longer crusaded to revise traditional philosophy into a radical *scientific philosophy*, but became respectable members of a new philosophical subdiscipline, *philosophy of science*. Receiving support from Ernest Nagel, they were especially influential in the social sciences.
### Scientific explanation {#scientific_explanation}
Carl Hempel was prominent in the development of the deductive-nomological (DN) model, then the foremost model of scientific explanation defended even among critics of neo-positivism such as Popper. According to the DN model, a scientific explanation is valid only if it takes the form of a deductive inference from a set of explanatory premises (*explanans*) to the observation or theory to be explained (*explanandum*). The model stipulates that the premises must refer to at least one law, which it defines as an unrestricted generalization of the conditional form: \"If *A*, then *B*\". Laws therefore differ from mere *regularities* (\"George always carries only \$1 bills in his wallet\") which do not necessarily support counterfactual claims. Furthermore, laws must be empirically verifiable in compliance with the verification principle.
The DN model ignores causal mechanisms beyond the principle of constant conjunction (\"first event *A* and then always event *B*\") in accordance with the Humean empiricist postulate that, though sequences of events are observable, the underpinning causal principles are not. Hempel stated that well-formulated natural laws (empirically confirmed regularities) are satisfactory in approximating causal explanation.
Hempel later proposed a probabilistic model of scientific explanation: The inductive-statistical (IS) model. Derivation of statistical laws from other statistical laws would further be designated as the deductive-statistical (DS) model. The DN and IS models are collectively referred to as the \"covering law model\" or \"subsumption theory\", the latter referring to the movement\'s stated goals of \"theory reduction\".
### Unity of science {#unity_of_science}
Logical positivists were committed to the vision of a unified science encompassing all scientific fields (including the special sciences, such as biology, anthropology, sociology and economics, and *the fundamental science*, or fundamental physics) which would be synthesised into a singular epistemic entity. Key to this concept was the doctrine of *theory reduction*, according to which the covering law model would be used to interconnect the special sciences and, thereupon, to reduce all laws in the special sciences to fundamental physics.
The movement envisioned a universal scientific language that could express statements with common meaning intelligible to all scientific fields. Carnap sought to realise this goal through the systematic reduction of the linguistic terms of more specialised fields to those of more fundamental fields. Various methods of reduction were proposed, referring to the use of set theory to manipulate logically primitive concepts (as in Carnap\'s *Logical Structure of the World*, 1928) or via analytic and *a priori* deductive operations (as described in *Testability and Meaning*, 1936, 1937). A number of publications over a period of thirty years would attempt to elucidate this concept.
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# Logical positivism
## Criticism
In the post-war period, key tenets of logical positivism, including the verifiability criterion, analytic-synthetic distinction and observation-theory distinction, drew escalated criticism. This would become sustained from various directions by the 1950s, so that, even among fractious philosophers who disagreed on the general objectives of epistemology, most would concur that the logical positivist program had become untenable. Notable critics included Karl Popper, W. V. O. Quine, Norwood Hanson, Thomas Kuhn, Hilary Putnam, as well as J. L. Austin, Peter Strawson, Nelson Goodman and Richard Rorty. Hempel himself became a major critic from within the movement, denouncing the positivist thesis that empirical knowledge is restricted to *basic statements*, *observation statements* or *protocol statements*.
### Karl Popper {#karl_popper}
Karl Popper, a graduate of the University of Vienna, was an outspoken critic of the logical positivist movement from its inception. In *Logik der Forschung* (1934, published in English in 1959 as *The Logic of Scientific Discovery*) he attacked verificationism directly, contending that the problem of induction renders it impossible for scientific hypotheses and other universal statements to be verified conclusively. Any attempt to do so, he argued, would commit the fallacy of affirming the consequent, given that verification cannot---in itself---exclude alternative valid explanations for a specific phenomenon or instance of observation. He would later affirm that the content of the verifiability criterion cannot be empirically verified, thus is meaningless by its own proposition and ultimately self-defeating as a principle.
In the same book, Popper proposed *falsifiability*, which he presented, not as a criterion of *cognitive meaning* like verificationism (as commonly misunderstood), but as a criterion to distinguish scientific from non-scientific statements, thereby to demarcate the boundaries of science. Popper observed that, though universal statements cannot be verified, they can be falsified, and that the most productive scientific theories were apparently those that carried the greatest \'predictive risks\' of being falsified by observation. He would conclude that the scientific method should be a hypothetico-deductive model, wherein scientific hypotheses must be falsifiable (per his criterion), held as provisionally true until proven false by observation, and are *corroborated* by supporting evidence rather than verified or confirmed.
In rejecting neo-positivist views of cognitive meaningfulness, Popper considered metaphysics to be rich in meaning and important in the origination of scientific theories and value systems to be integral to science\'s quest for truth. At the same time, he disparaged pseudoscience, referring to the confirmation biases that embolden support for unfalsifiable conjectures (notably those in psychology and psychoanalysis) and *ad hoc* arguments used to entrench predictive theories that have been proven conclusively false.
### Willard V. O. Quine {#willard_v._o._quine}
In his influential 1951 paper *Two Dogmas of Empiricism*, American philosopher and logicist Willard Van Orman Quine challenged the analytic-synthetic distinction. Specifically, Quine examined the concept of analyticity, determining that all attempts to explain the idea reduce ultimately to circular reasoning. He would conclude that, if analyticity is untenable, so too is the neo-positivist proposition to redefine its boundaries. Yet Carnap\'s reconstruction of analyticity was necessary for logic and mathematics to be deemed meaningful under verificationism. Quine\'s arguments encompassed numerous criticisms on this topic he had articulated to Carnap since 1933. His work effectively pronounced the verifiability criterion untenable, threatening to uproot the broader logical positivist project.
### Norwood Hanson {#norwood_hanson}
In 1958, Norwood Hanson\'s *Patterns of Discovery* characterised the concept of theory-ladenness. Hanson and Thomas Kuhn held that even direct observations are never truly neutral in that they are *laden with theory*, i.e. influenced by a system of theoretical presuppositions that function as an interpretative framework for the senses. Accordingly, individuals subscribed to different theories might report radically different observations even as they investigate the same phenomena. Hanson\'s thesis attacked the observation-theory distinction, which draws a dividing line between observational and non-observational (theoretical) language. More broadly, its findings challenged the central-most tenets of empiricism in questioning the infallibility and objectivity of empirical observation.
### Thomas Kuhn {#thomas_kuhn}
Thomas Kuhn\'s landmark book of 1962, *The Structure of Scientific Revolutions*---which discussed paradigm shifts in fundamental physics---critically undermined confidence in scientific foundationalism. Kuhn proposed in its place a coherentist model of science, whereby scientific progress revolves around cores of established, coherent ideas which periodically undergo abrupt revolutionary changes.
Though foundationalism was often considered a constituent doctrine of logical positivism (and Kuhn\'s thesis an epistemological criticism of the movement) such views were simplistic: In the 1930s, Neurath had argued for the adoption of coherentism, famously comparing the progress of science to reconstruction of a boat at sea. Carnap had entertained foundationalism from 1929 to 1930, but he, Hans Hahn and others would later join Neurath in converting to a coherentist philosophy. The conservative wing of the Vienna Circle under Moritz Schlick subscribed to a form of foundationalism, but its principles were defined unconventionally or ambiguously.
In some sense, Kuhn\'s book unified science, but through historical and social assessment rather than by networking the scientific specialties using epistemological or linguistic models. His ideas were adopted quickly by scholars in non-scientific disciplines, such as the social sciences in which neo-positivists were dominant, ushering academia into postpositivism or postempiricism.
### Hilary Putnam {#hilary_putnam}
In his critique of the received view in 1962, Hilary Putnam attacked the observation-theory distinction. Putnam proposed that the division between \"observation terms\" and \"theoretical terms\" was untenable, determining that both categories have the potential to be theory-laden. Accordingly, he remarked that observational reports frequently refer to theoretical terms in practice. He illustrated cases in which observation terms can be applied to entities that Carnap would classify as unobservables. For example, in Newton\'s corpuscular theory of light, observation concepts can be applied to the consideration of both sub-microscopic and macroscopic objects.
Putnam advocated scientific realism, whereby scientific theory describes a real world existing independently of the senses. He rejected positivism, which he dismissed as a form of metaphysical idealism, in that it precluded any possibility to acquire knowledge of the unobservable aspects of nature. He also spurned instrumentalism, according to which a scientific theory is judged, not by whether it corresponds to reality, but by the extent to which it allows empirical predictions or resolves conceptual problems.
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# Logical positivism
## Decline and legacy {#decline_and_legacy}
In 1967, John Passmore wrote, \"Logical positivism is dead, or as dead as a philosophical movement ever becomes\". His opinions concurred with widespread sentiment in academic circles that the movement had run its course by the late 1960s. Logical positivism\'s fall heralded postpositivism, distinguished by Popper\'s critical rationalism---which characterised human knowledge as continuously evolving via conjectures and refutations---and Kuhn\'s historical and social perspectives on the saltatory course of scientific progress.
In a 1976 interview, A. J. Ayer, who had introduced logical positivism to the English-speaking world in the 1930s, was asked what he saw as its main defects and answered that, \"nearly all of it was false\". Yet, he maintained that it was \"true in spirit\", referring to the principles of empiricism and reductionism whereby mental phenomena resolve to the material or physical and philosophical questions largely resolve to ones of language and meaning. Despite its problems, logical positivism helped to anchor analytic philosophy in the English-speaking world and its influence extended beyond philosophy in shaping the course of psychology and the social sciences. In the post-war period, Carl Hempel\'s contributions were vitally important in establishing the subdiscipline of the philosophy of science.
Logical positivism\'s fall reopened the debate over the metaphysical merit of scientific theory, whether it can offer knowledge of the world beyond human experience (scientific realism) or whether it is simply an instrument to predict human experience (instrumentalism). Philosophers increasingly critiqued the movement\'s doctrine and history, often misrepresenting it without thorough examination, sometimes reducing it to oversimplifications and stereotypes, such as its association with foundationalism
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# LAME
**LAME** is a software encoder that converts digital audio into the MP3 audio coding format. LAME is a free software project that was first released in 1998 and has incorporated many improvements since then, including an improved psychoacoustic model. The LAME encoder outperforms early encoders like L3enc and possibly the \"gold standard encoder\" MP3enc, both marketed by Fraunhofer.
LAME was required by some programs released as free software in which LAME was linked for MP3 support. This avoided including LAME itself, which used patented techniques, and so required patent licenses in some countries. All relevant patents have since expired, and LAME is now bundled with Audacity.
## History
The name **LAME** is a recursive acronym for \"LAME Ain\'t an MP3 Encoder\".
Around mid-1998, Mike Cheng created LAME 1.0 as a set of modifications against the 8Hz-MP3 encoder source code. After some quality concerns were raised by others, he decided to start again from scratch based on the dist10 MPEG reference software sources. His goal was only to speed up the dist10 sources, and leave its quality untouched. That branch (a patch against the reference sources) became Lame 2.0. The project quickly became a team project. Mike Cheng eventually left leadership and started working on tooLAME (an MP2 encoder).
Mark Taylor then started pursuing increased quality in addition to better speed, and released version 3.0 featuring gpsycho, a new psychoacoustic model he developed. A few key improvements since LAME 3.x, in chronological order:
- May 1999 (LAME 3.0): a new psychoacoustic model (GPSYCHO) is released.
- June 1999 (LAME 3.11): The first variable bitrate (VBR) implementation is released. Soon after this, LAME also became able to target lower sampling frequencies from MPEG-2. (LAME 3.99 also supports the technologically simpler average bitrate (ABR), but it is unclear whether it was added before or with VBR.)
- November 1999 (LAME 3.52): LAME switches from a GPL license to an LGPL license, which allows using it with closed-source applications.
- May 2000 (LAME 3.81): the last pieces of the original ISO demonstration code are removed. LAME is not a patch anymore, but a full encoder.
- December 2003 (LAME 3.94): substantial improvement to default settings, along with improved speed. LAME no longer requires users to enter complicated parameters to produce good results.
- May 2007 (LAME 3.98): default variable bitrate encoding speed is vastly improved.
## Patents and legal issues {#patents_and_legal_issues}
Like all MP3 encoders, LAME implemented techniques covered by patents owned by the Fraunhofer Society and others. The developers of LAME did not license the technology described by these patents. Distributing compiled binaries of LAME, its libraries, or programs that derive from LAME in countries where those patents have been granted may have constituted infringement, but since 23 April 2017, all of these patents have expired.
The LAME developers stated that, since their code was only released in source code form, it should only be considered as an educational description of an MP3 encoder, and thus did not infringe any patent in itself. They also advised users to obtain relevant patent licenses before including a compiled version of the encoder in a product. Some software was released using this strategy: companies used the LAME library, but obtained patent licenses.
In the course of the 2005 Sony BMG copy protection rootkit scandal, there were reports that the Extended Copy Protection rootkit included on some Sony compact discs had portions of the LAME library without complying with the terms of the LGPL
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# Basis (linear algebra)
Basis}}
In mathematics, a set `{{mvar|B}}`{=mediawiki} of elements of a vector space `{{math|''V''}}`{=mediawiki} is called a **basis** (`{{plural form}}`{=mediawiki}: **bases**) if every element of `{{math|''V''}}`{=mediawiki} can be written in a unique way as a finite linear combination of elements of `{{mvar|B}}`{=mediawiki}. The coefficients of this linear combination are referred to as **components** or **coordinates** of the vector with respect to `{{mvar|B}}`{=mediawiki}. The elements of a basis are called **`{{visible anchor|basis vectors}}`{=mediawiki}**.
Equivalently, a set `{{mvar|B}}`{=mediawiki} is a basis if its elements are linearly independent and every element of `{{mvar|V}}`{=mediawiki} is a linear combination of elements of `{{mvar|B}}`{=mediawiki}. In other words, a basis is a linearly independent spanning set.
A vector space can have several bases; however all the bases have the same number of elements, called the dimension of the vector space.
This article deals mainly with finite-dimensional vector spaces. However, many of the principles are also valid for infinite-dimensional vector spaces.
Basis vectors find applications in the study of crystal structures and frames of reference.
## Definition
A **basis** `{{math|''B''}}`{=mediawiki} of a vector space `{{math|''V''}}`{=mediawiki} over a field `{{math|''F''}}`{=mediawiki} (such as the real numbers `{{math|'''R'''}}`{=mediawiki} or the complex numbers `{{math|'''C'''}}`{=mediawiki}) is a linearly independent subset of `{{math|''V''}}`{=mediawiki} that spans `{{math|''V''}}`{=mediawiki}. This means that a subset `{{mvar|B}}`{=mediawiki} of `{{math|''V''}}`{=mediawiki} is a basis if it satisfies the two following conditions:
*linear independence*
: for every finite subset $\{\mathbf v_1, \dotsc, \mathbf v_m\}$ of `{{mvar|B}}`{=mediawiki}, if $c_1 \mathbf v_1 + \cdots + c_m \mathbf v_m = \mathbf 0$ for some $c_1,\dotsc,c_m$ in `{{math|''F''}}`{=mediawiki}, then `{{nowrap|<math>c_1 = \cdots = c_m = 0</math>;}}`{=mediawiki}
*spanning property*
: for every vector `{{math|'''v'''}}`{=mediawiki} in `{{math|''V''}}`{=mediawiki}, one can choose $a_1,\dotsc,a_n$ in `{{math|''F''}}`{=mediawiki} and $\mathbf v_1, \dotsc, \mathbf v_n$ in `{{mvar|B}}`{=mediawiki} such that `{{nowrap|<math>\mathbf v = a_1 \mathbf v_1 + \cdots + a_n \mathbf v_n</math>.}}`{=mediawiki}
The scalars $a_i$ are called the coordinates of the vector `{{math|'''v'''}}`{=mediawiki} with respect to the basis `{{math|''B''}}`{=mediawiki}, and by the first property they are uniquely determined.
A vector space that has a finite basis is called finite-dimensional. In this case, the finite subset can be taken as `{{math|''B''}}`{=mediawiki} itself to check for linear independence in the above definition.
It is often convenient or even necessary to have an ordering on the basis vectors, for example, when discussing orientation, or when one considers the scalar coefficients of a vector with respect to a basis without referring explicitly to the basis elements. In this case, the ordering is necessary for associating each coefficient to the corresponding basis element. This ordering can be done by numbering the basis elements. In order to emphasize that an order has been chosen, one speaks of an **ordered basis**, which is therefore not simply an unstructured set, but a sequence, an indexed family, or similar; see `{{slink||Ordered bases and coordinates}}`{=mediawiki} below.
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# Basis (linear algebra)
## Examples
The set `{{math|'''R'''<sup>2</sup>}}`{=mediawiki} of the ordered pairs of real numbers is a vector space under the operations of component-wise addition $(a, b) + (c, d) = (a + c, b+d)$ and scalar multiplication $\lambda (a,b) = (\lambda a, \lambda b),$ where $\lambda$ is any real number. A simple basis of this vector space consists of the two vectors `{{math|1='''e'''<sub>1</sub> = (1, 0)}}`{=mediawiki} and `{{math|1='''e'''<sub>2</sub> = (0, 1)}}`{=mediawiki}. These vectors form a basis (called the standard basis) because any vector `{{math|1='''v''' = (''a'', ''b'')}}`{=mediawiki} of `{{math|'''R'''<sup>2</sup>}}`{=mediawiki} may be uniquely written as $\mathbf v = a \mathbf e_1 + b \mathbf e_2.$ Any other pair of linearly independent vectors of `{{math|'''R'''<sup>2</sup>}}`{=mediawiki}, such as `{{math|(1, 1)}}`{=mediawiki} and `{{math|(−1, 2)}}`{=mediawiki}, forms also a basis of `{{math|'''R'''<sup>2</sup>}}`{=mediawiki}.
More generally, if `{{mvar|F}}`{=mediawiki} is a field, the set $F^n$ of `{{mvar|n}}`{=mediawiki}-tuples of elements of `{{mvar|F}}`{=mediawiki} is a vector space for similarly defined addition and scalar multiplication. Let $\mathbf e_i = (0, \ldots, 0,1,0,\ldots, 0)$ be the `{{mvar|n}}`{=mediawiki}-tuple with all components equal to 0, except the `{{mvar|i}}`{=mediawiki}th, which is 1. Then $\mathbf e_1, \ldots, \mathbf e_n$ is a basis of $F^n,$ which is called the *standard basis* of $F^n.$
A different flavor of example is given by polynomial rings. If `{{mvar|F}}`{=mediawiki} is a field, the collection `{{math|''F''[''X'']}}`{=mediawiki} of all polynomials in one indeterminate `{{mvar|X}}`{=mediawiki} with coefficients in `{{mvar|F}}`{=mediawiki} is an `{{mvar|F}}`{=mediawiki}-vector space. One basis for this space is the monomial basis `{{mvar|B}}`{=mediawiki}, consisting of all monomials: $B=\{1, X, X^2, \ldots\}.$ Any set of polynomials such that there is exactly one polynomial of each degree (such as the Bernstein basis polynomials or Chebyshev polynomials) is also a basis. (Such a set of polynomials is called a polynomial sequence.) But there are also many bases for `{{math|''F''[''X'']}}`{=mediawiki} that are not of this form.
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# Basis (linear algebra)
## Properties
Many properties of finite bases result from the Steinitz exchange lemma, which states that, for any vector space `{{mvar|V}}`{=mediawiki}, given a finite spanning set `{{mvar|S}}`{=mediawiki} and a linearly independent set `{{mvar|L}}`{=mediawiki} of `{{mvar|n}}`{=mediawiki} elements of `{{mvar|V}}`{=mediawiki}, one may replace `{{mvar|n}}`{=mediawiki} well-chosen elements of `{{mvar|S}}`{=mediawiki} by the elements of `{{mvar|L}}`{=mediawiki} to get a spanning set containing `{{mvar|L}}`{=mediawiki}, having its other elements in `{{mvar|S}}`{=mediawiki}, and having the same number of elements as `{{mvar|S}}`{=mediawiki}.
Most properties resulting from the Steinitz exchange lemma remain true when there is no finite spanning set, but their proofs in the infinite case generally require the axiom of choice or a weaker form of it, such as the ultrafilter lemma.
If `{{mvar|V}}`{=mediawiki} is a vector space over a field `{{mvar|F}}`{=mediawiki}, then:
- If `{{mvar|L}}`{=mediawiki} is a linearly independent subset of a spanning set `{{math|''S'' ⊆ ''V''}}`{=mediawiki}, then there is a basis `{{mvar|B}}`{=mediawiki} such that $L\subseteq B\subseteq S.$
- has a basis (this is the preceding property with `{{mvar|L}}`{=mediawiki} being the empty set, and `{{math|1=''S'' = ''V''}}`{=mediawiki}).
- All bases of `{{mvar|V}}`{=mediawiki} have the same cardinality, which is called the dimension of `{{mvar|V}}`{=mediawiki}. This is the dimension theorem.
- A generating set `{{mvar|S}}`{=mediawiki} is a basis of `{{mvar|V}}`{=mediawiki} if and only if it is minimal, that is, no proper subset of `{{mvar|S}}`{=mediawiki} is also a generating set of `{{mvar|V}}`{=mediawiki}.
- A linearly independent set `{{mvar|L}}`{=mediawiki} is a basis if and only if it is maximal, that is, it is not a proper subset of any linearly independent set.
If `{{mvar|V}}`{=mediawiki} is a vector space of dimension `{{mvar|n}}`{=mediawiki}, then:
- A subset of `{{mvar|V}}`{=mediawiki} with `{{mvar|n}}`{=mediawiki} elements is a basis if and only if it is linearly independent.
- A subset of `{{mvar|V}}`{=mediawiki} with `{{mvar|n}}`{=mediawiki} elements is a basis if and only if it is a spanning set of `{{mvar|V}}`{=mediawiki}.
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# Basis (linear algebra)
## Coordinates `{{anchor|Ordered bases and coordinates}}`{=mediawiki}
Let `{{mvar|V}}`{=mediawiki} be a vector space of finite dimension `{{mvar|n}}`{=mediawiki} over a field `{{mvar|F}}`{=mediawiki}, and $B = \{\mathbf b_1, \ldots, \mathbf b_n\}$ be a basis of `{{mvar|V}}`{=mediawiki}. By definition of a basis, every `{{math|'''v'''}}`{=mediawiki} in `{{mvar|V}}`{=mediawiki} may be written, in a unique way, as $\mathbf v = \lambda_1 \mathbf b_1 + \cdots + \lambda_n \mathbf b_n,$ where the coefficients $\lambda_1, \ldots, \lambda_n$ are scalars (that is, elements of `{{mvar|F}}`{=mediawiki}), which are called the *coordinates* of `{{math|'''v'''}}`{=mediawiki} over `{{mvar|B}}`{=mediawiki}. However, if one talks of the *set* of the coefficients, one loses the correspondence between coefficients and basis elements, and several vectors may have the same *set* of coefficients. For example, $3 \mathbf b_1 + 2 \mathbf b_2$ and $2 \mathbf b_1 + 3 \mathbf b_2$ have the same set of coefficients `{{math|{2, 3}<nowiki/>}}`{=mediawiki}, and are different. It is therefore often convenient to work with an **ordered basis**; this is typically done by indexing the basis elements by the first natural numbers. Then, the coordinates of a vector form a sequence similarly indexed, and a vector is completely characterized by the sequence of coordinates. An ordered basis, especially when used in conjunction with an origin, is also called a ***coordinate frame*** or simply a *frame* (for example, a Cartesian frame or an affine frame).
Let, as usual, $F^n$ be the set of the `{{mvar|n}}`{=mediawiki}-tuples of elements of `{{mvar|F}}`{=mediawiki}. This set is an `{{mvar|F}}`{=mediawiki}-vector space, with addition and scalar multiplication defined component-wise. The map $\varphi: (\lambda_1, \ldots, \lambda_n) \mapsto \lambda_1 \mathbf b_1 + \cdots + \lambda_n \mathbf b_n$ is a linear isomorphism from the vector space $F^n$ onto `{{mvar|V}}`{=mediawiki}. In other words, $F^n$ is the coordinate space of `{{mvar|V}}`{=mediawiki}, and the `{{mvar|n}}`{=mediawiki}-tuple $\varphi^{-1}(\mathbf v)$ is the coordinate vector of `{{math|'''v'''}}`{=mediawiki}.
The inverse image by $\varphi$ of $\mathbf b_i$ is the `{{mvar|n}}`{=mediawiki}-tuple $\mathbf e_i$ all of whose components are 0, except the `{{mvar|i}}`{=mediawiki}th that is 1. The $\mathbf e_i$ form an ordered basis of $F^n$, which is called its standard basis or canonical basis. The ordered basis `{{mvar|B}}`{=mediawiki} is the image by $\varphi$ of the canonical basis of `{{nowrap|<math>F^n</math>.}}`{=mediawiki}
It follows from what precedes that every ordered basis is the image by a linear isomorphism of the canonical basis of `{{nowrap|<math>F^n</math>,}}`{=mediawiki} and that every linear isomorphism from $F^n$ onto `{{mvar|V}}`{=mediawiki} may be defined as the isomorphism that maps the canonical basis of $F^n$ onto a given ordered basis of `{{mvar|V}}`{=mediawiki}. In other words, it is equivalent to define an ordered basis of `{{mvar|V}}`{=mediawiki}, or a linear isomorphism from $F^n$ onto `{{mvar|V}}`{=mediawiki}.
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# Basis (linear algebra)
## Change of basis {#change_of_basis}
Let `{{math|''V''}}`{=mediawiki} be a vector space of dimension `{{mvar|n}}`{=mediawiki} over a field `{{math|''F''}}`{=mediawiki}. Given two (ordered) bases $B_\text{old} = (\mathbf v_1, \ldots, \mathbf v_n)$ and $B_\text{new} = (\mathbf w_1, \ldots, \mathbf w_n)$ of `{{math|''V''}}`{=mediawiki}, it is often useful to express the coordinates of a vector `{{mvar|x}}`{=mediawiki} with respect to $B_\mathrm{old}$ in terms of the coordinates with respect to $B_\mathrm{new}.$ This can be done by the *change-of-basis formula*, that is described below. The subscripts \"old\" and \"new\" have been chosen because it is customary to refer to $B_\mathrm{old}$ and $B_\mathrm{new}$ as the *old basis* and the *new basis*, respectively. It is useful to describe the old coordinates in terms of the new ones, because, in general, one has expressions involving the old coordinates, and if one wants to obtain equivalent expressions in terms of the new coordinates; this is obtained by replacing the old coordinates by their expressions in terms of the new coordinates.
Typically, the new basis vectors are given by their coordinates over the old basis, that is, $\mathbf w_j = \sum_{i=1}^n a_{i,j} \mathbf v_i.$ If $(x_1, \ldots, x_n)$ and $(y_1, \ldots, y_n)$ are the coordinates of a vector `{{math|'''x'''}}`{=mediawiki} over the old and the new basis respectively, the change-of-basis formula is $x_i = \sum_{j=1}^n a_{i,j}y_j,$ for `{{math|1=''i'' = 1, ..., ''n''}}`{=mediawiki}.
This formula may be concisely written in matrix notation. Let `{{mvar|A}}`{=mediawiki} be the matrix of the `{{nowrap|<math>a_{i,j}</math>,}}`{=mediawiki} and $X= \begin{bmatrix} x_1 \\ \vdots \\ x_n \end{bmatrix} \quad \text{and} \quad Y = \begin{bmatrix} y_1 \\ \vdots \\ y_n \end{bmatrix}$ be the column vectors of the coordinates of `{{math|'''v'''}}`{=mediawiki} in the old and the new basis respectively, then the formula for changing coordinates is $X = A Y.$
The formula can be proven by considering the decomposition of the vector `{{math|'''x'''}}`{=mediawiki} on the two bases: one has $\mathbf x = \sum_{i=1}^n x_i \mathbf v_i,$ and $\mathbf x =\sum_{j=1}^n y_j \mathbf w_j
= \sum_{j=1}^n y_j\sum_{i=1}^n a_{i,j}\mathbf v_i
= \sum_{i=1}^n \biggl(\sum_{j=1}^n a_{i,j}y_j\biggr)\mathbf v_i.$
The change-of-basis formula results then from the uniqueness of the decomposition of a vector over a basis, here `{{nowrap|<math>B_\text{old}</math>;}}`{=mediawiki} that is $x_i = \sum_{j=1}^n a_{i,j} y_j,$ for `{{math|1=''i'' = 1, ..., ''n''}}`{=mediawiki}.
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# Basis (linear algebra)
## Related notions {#related_notions}
### Free module {#free_module}
If one replaces the field occurring in the definition of a vector space by a ring, one gets the definition of a module. For modules, linear independence and spanning sets are defined exactly as for vector spaces, although \"generating set\" is more commonly used than that of \"spanning set\".
Like for vector spaces, a *basis* of a module is a linearly independent subset that is also a generating set. A major difference with the theory of vector spaces is that not every module has a basis. A module that has a basis is called a *free module*. Free modules play a fundamental role in module theory, as they may be used for describing the structure of non-free modules through free resolutions.
A module over the integers is exactly the same thing as an abelian group. Thus a free module over the integers is also a free abelian group. Free abelian groups have specific properties that are not shared by modules over other rings. Specifically, every subgroup of a free abelian group is a free abelian group, and, if `{{mvar|G}}`{=mediawiki} is a subgroup of a finitely generated free abelian group `{{mvar|H}}`{=mediawiki} (that is an abelian group that has a finite basis), then there is a basis $\mathbf e_1, \ldots, \mathbf e_n$ of `{{mvar|H}}`{=mediawiki} and an integer `{{math|0 ≤ ''k'' ≤ ''n''}}`{=mediawiki} such that $a_1 \mathbf e_1, \ldots, a_k \mathbf e_k$ is a basis of `{{mvar|G}}`{=mediawiki}, for some nonzero integers `{{nowrap|<math>a_1, \ldots, a_k</math>.}}`{=mediawiki} For details, see `{{slink|Free abelian group|Subgroups}}`{=mediawiki}.
### Analysis
In the context of infinite-dimensional vector spaces over the real or complex numbers, the term **`{{visible anchor|Hamel basis}}`{=mediawiki}** (named after Georg Hamel) or **algebraic basis** can be used to refer to a basis as defined in this article. This is to make a distinction with other notions of \"basis\" that exist when infinite-dimensional vector spaces are endowed with extra structure. The most important alternatives are orthogonal bases on Hilbert spaces, Schauder bases, and Markushevich bases on normed linear spaces. In the case of the real numbers **R** viewed as a vector space over the field **Q** of rational numbers, Hamel bases are uncountable, and have specifically the cardinality of the continuum, which is the cardinal number `{{nowrap|<math>2^{\aleph_0}</math>,}}`{=mediawiki} where $\aleph_0$ (aleph-nought) is the smallest infinite cardinal, the cardinal of the integers.
The common feature of the other notions is that they permit the taking of infinite linear combinations of the basis vectors in order to generate the space. This, of course, requires that infinite sums are meaningfully defined on these spaces, as is the case for topological vector spaces -- a large class of vector spaces including e.g. Hilbert spaces, Banach spaces, or Fréchet spaces.
The preference of other types of bases for infinite-dimensional spaces is justified by the fact that the Hamel basis becomes \"too big\" in Banach spaces: If *X* is an infinite-dimensional normed vector space that is complete (i.e. *X* is a Banach space), then any Hamel basis of *X* is necessarily uncountable. This is a consequence of the Baire category theorem. The completeness as well as infinite dimension are crucial assumptions in the previous claim. Indeed, finite-dimensional spaces have by definition finite bases and there are infinite-dimensional (*non-complete*) normed spaces that have countable Hamel bases. Consider `{{nowrap|<math>c_{00}</math>,}}`{=mediawiki} the space of the sequences $x=(x_n)$ of real numbers that have only finitely many non-zero elements, with the norm `{{nowrap|<math display="inline">\|x\|=\sup_n |x_n|</math>.}}`{=mediawiki} Its standard basis, consisting of the sequences having only one non-zero element, which is equal to 1, is a countable Hamel basis.
#### Example
In the study of Fourier series, one learns that the functions `{{math|1={1} ∪ { sin(''nx''), cos(''nx'') : ''n'' = 1, 2, 3, ... }<nowiki/>}}`{=mediawiki} are an \"orthogonal basis\" of the (real or complex) vector space of all (real or complex valued) functions on the interval \[0, 2π\] that are square-integrable on this interval, i.e., functions *f* satisfying $\int_0^{2\pi} \left|f(x)\right|^2\,dx < \infty.$
The functions `{{math|1={1} ∪ { sin(''nx''), cos(''nx'') : ''n'' = 1, 2, 3, ... }<nowiki/>}}`{=mediawiki} are linearly independent, and every function *f* that is square-integrable on \[0, 2π\] is an \"infinite linear combination\" of them, in the sense that $\lim_{n\to\infty} \int_0^{2\pi} \biggl|a_0 + \sum_{k=1}^n \left(a_k\cos\left(kx\right)+b_k\sin\left(kx\right)\right)-f(x)\biggr|^2 dx = 0$
for suitable (real or complex) coefficients *a*~*k*~, *b*~*k*~. But many square-integrable functions cannot be represented as *finite* linear combinations of these basis functions, which therefore *do not* comprise a Hamel basis. Every Hamel basis of this space is much bigger than this merely countably infinite set of functions. Hamel bases of spaces of this kind are typically not useful, whereas orthonormal bases of these spaces are essential in Fourier analysis.
### Geometry
The geometric notions of an affine space, projective space, convex set, and cone have related notions of `{{anchor|affine basis}}`{=mediawiki} *basis*. An **affine basis** for an *n*-dimensional affine space is $n+1$ points in general linear position. A **`{{visible anchor|projective basis}}`{=mediawiki}** is $n+2$ points in general position, in a projective space of dimension *n*. A **`{{visible anchor|convex basis}}`{=mediawiki}** of a polytope is the set of the vertices of its convex hull. A **`{{visible anchor|cone basis}}`{=mediawiki}** consists of one point by edge of a polygonal cone. See also a Hilbert basis (linear programming).
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# Basis (linear algebra)
## Related notions {#related_notions}
### Random basis {#random_basis}
For a probability distribution in `{{math|'''R'''<sup>''n''</sup>}}`{=mediawiki} with a probability density function, such as the equidistribution in an *n*-dimensional ball with respect to Lebesgue measure, it can be shown that `{{mvar|n}}`{=mediawiki} randomly and independently chosen vectors will form a basis with probability one, which is due to the fact that `{{mvar|n}}`{=mediawiki} linearly dependent vectors `{{math|'''x'''<sub>1</sub>}}`{=mediawiki}, \..., `{{math|'''x'''<sub>''n''</sub>}}`{=mediawiki} in `{{math|'''R'''<sup>''n''</sup>}}`{=mediawiki} should satisfy the equation `{{math|1=det['''x'''<sub>1</sub> ⋯ '''x'''<sub>''n''</sub>] = 0}}`{=mediawiki} (zero determinant of the matrix with columns `{{math|'''x'''<sub>''i''</sub>}}`{=mediawiki}), and the set of zeros of a non-trivial polynomial has zero measure. This observation has led to techniques for approximating random bases.
It is difficult to check numerically the linear dependence or exact orthogonality. Therefore, the notion of ε-orthogonality is used. For spaces with inner product, *x* is ε-orthogonal to *y* if $\left|\left\langle x,y \right\rangle\right| / \left(\left\|x\right\|\left\|y\right\|\right) < \varepsilon$ (that is, cosine of the angle between `{{mvar|x}}`{=mediawiki} and `{{mvar|y}}`{=mediawiki} is less than `{{mvar|ε}}`{=mediawiki}).
In high dimensions, two independent random vectors are with high probability almost orthogonal, and the number of independent random vectors, which all are with given high probability pairwise almost orthogonal, grows exponentially with dimension. More precisely, consider equidistribution in *n*-dimensional ball. Choose *N* independent random vectors from a ball (they are independent and identically distributed). Let *θ* be a small positive number. Then for `{{NumBlk||<math display="block">N\leq {\exp}\bigl(\tfrac14\varepsilon^2n\bigr)\sqrt{-\ln(1-\theta)}</math>|Eq. 1}}`{=mediawiki}
random vectors are all pairwise ε-orthogonal with probability `{{math|1 − ''θ''}}`{=mediawiki}. This `{{mvar|N}}`{=mediawiki} growth exponentially with dimension `{{mvar|n}}`{=mediawiki} and $N\gg n$ for sufficiently big `{{mvar|n}}`{=mediawiki}. This property of random bases is a manifestation of the so-called `{{em|measure concentration phenomenon}}`{=mediawiki}.
The figure (right) illustrates distribution of lengths N of pairwise almost orthogonal chains of vectors that are independently randomly sampled from the *n*-dimensional cube `{{math|[−1, 1]<sup>''n''</sup>}}`{=mediawiki} as a function of dimension, *n*. A point is first randomly selected in the cube. The second point is randomly chosen in the same cube. If the angle between the vectors was within `{{math|π/2 ± 0.037π/2}}`{=mediawiki} then the vector was retained. At the next step a new vector is generated in the same hypercube, and its angles with the previously generated vectors are evaluated. If these angles are within `{{math|π/2 ± 0.037π/2}}`{=mediawiki} then the vector is retained. The process is repeated until the chain of almost orthogonality breaks, and the number of such pairwise almost orthogonal vectors (length of the chain) is recorded. For each *n*, 20 pairwise almost orthogonal chains were constructed numerically for each dimension. Distribution of the length of these chains is presented.
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# Basis (linear algebra)
## Proof that every vector space has a basis {#proof_that_every_vector_space_has_a_basis}
Let `{{math|'''V'''}}`{=mediawiki} be any vector space over some field `{{math|'''F'''}}`{=mediawiki}. Let `{{math|'''X'''}}`{=mediawiki} be the set of all linearly independent subsets of `{{math|'''V'''}}`{=mediawiki}.
The set `{{math|'''X'''}}`{=mediawiki} is nonempty since the empty set is an independent subset of `{{math|'''V'''}}`{=mediawiki}, and it is partially ordered by inclusion, which is denoted, as usual, by `{{math|⊆}}`{=mediawiki}.
Let `{{math|'''Y'''}}`{=mediawiki} be a subset of `{{math|'''X'''}}`{=mediawiki} that is totally ordered by `{{math|⊆}}`{=mediawiki}, and let `{{math|L<sub>'''Y'''</sub>}}`{=mediawiki} be the union of all the elements of `{{math|'''Y'''}}`{=mediawiki} (which are themselves certain subsets of `{{math|'''V'''}}`{=mediawiki}).
Since `{{math|('''Y''', ⊆)}}`{=mediawiki} is totally ordered, every finite subset of `{{math|L<sub>'''Y'''</sub>}}`{=mediawiki} is a subset of an element of `{{math|'''Y'''}}`{=mediawiki}, which is a linearly independent subset of `{{math|'''V'''}}`{=mediawiki}, and hence `{{math|L<sub>'''Y'''</sub>}}`{=mediawiki} is linearly independent. Thus `{{math|L<sub>'''Y'''</sub>}}`{=mediawiki} is an element of `{{math|'''X'''}}`{=mediawiki}. Therefore, `{{math|L<sub>'''Y'''</sub>}}`{=mediawiki} is an upper bound for `{{math|'''Y'''}}`{=mediawiki} in `{{math|('''X''', ⊆)}}`{=mediawiki}: it is an element of `{{math|'''X'''}}`{=mediawiki}, that contains every element of `{{math|'''Y'''}}`{=mediawiki}.
As `{{math|'''X'''}}`{=mediawiki} is nonempty, and every totally ordered subset of `{{math|('''X''', ⊆)}}`{=mediawiki} has an upper bound in `{{math|'''X'''}}`{=mediawiki}, Zorn\'s lemma asserts that `{{math|'''X'''}}`{=mediawiki} has a maximal element. In other words, there exists some element `{{math|L<sub>'''max'''</sub>}}`{=mediawiki} of `{{math|'''X'''}}`{=mediawiki} satisfying the condition that whenever `{{math|L<sub>'''max'''</sub> ⊆ L}}`{=mediawiki} for some element `{{math|L}}`{=mediawiki} of `{{math|'''X'''}}`{=mediawiki}, then `{{math|1=L = L<sub>'''max'''</sub>}}`{=mediawiki}.
It remains to prove that `{{math|L<sub>'''max'''</sub>}}`{=mediawiki} is a basis of `{{math|'''V'''}}`{=mediawiki}. Since `{{math|L<sub>'''max'''</sub>}}`{=mediawiki} belongs to `{{math|'''X'''}}`{=mediawiki}, we already know that `{{math|L<sub>'''max'''</sub>}}`{=mediawiki} is a linearly independent subset of `{{math|'''V'''}}`{=mediawiki}.
If there were some vector `{{math|'''w'''}}`{=mediawiki} of `{{math|'''V'''}}`{=mediawiki} that is not in the span of `{{math|L<sub>'''max'''</sub>}}`{=mediawiki}, then `{{math|'''w'''}}`{=mediawiki} would not be an element of `{{math|L<sub>'''max'''</sub>}}`{=mediawiki} either. Let `{{math|1=L<sub>'''w'''</sub> = L<sub>'''max'''</sub> ∪ {'''w'''}<nowiki/>}}`{=mediawiki}. This set is an element of `{{math|'''X'''}}`{=mediawiki}, that is, it is a linearly independent subset of `{{math|'''V'''}}`{=mediawiki} (because **w** is not in the span of `{{math|L<sub>'''max'''</sub>}}`{=mediawiki}, and `{{math|L<sub>'''max'''</sub>}}`{=mediawiki} is independent). As `{{math|L<sub>'''max'''</sub> ⊆ L<sub>'''w'''</sub>}}`{=mediawiki}, and `{{math|L<sub>'''max'''</sub> ≠ L<sub>'''w'''</sub>}}`{=mediawiki} (because `{{math|L<sub>'''w'''</sub>}}`{=mediawiki} contains the vector `{{math|'''w'''}}`{=mediawiki} that is not contained in `{{math|L<sub>'''max'''</sub>}}`{=mediawiki}), this contradicts the maximality of `{{math|L<sub>'''max'''</sub>}}`{=mediawiki}. Thus this shows that `{{math|L<sub>'''max'''</sub>}}`{=mediawiki} spans `{{math|'''V'''}}`{=mediawiki}.
Hence `{{math|L<sub>'''max'''</sub>}}`{=mediawiki} is linearly independent and spans `{{math|'''V'''}}`{=mediawiki}. It is thus a basis of `{{math|'''V'''}}`{=mediawiki}, and this proves that every vector space has a basis.
This proof relies on Zorn\'s lemma, which is equivalent to the axiom of choice. Conversely, it has been proved that if every vector space has a basis, then the axiom of choice is true. Thus the two assertions are equivalent
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# Loch
***Loch*** (`{{IPAc-en|l|ɒ|x}}`{=mediawiki} `{{respell|LOKH}}`{=mediawiki}) is a word meaning \"lake\" or \"sea inlet\" in Scottish and Irish Gaelic, subsequently borrowed into English. In Irish contexts, it often appears in the anglicized form \"**lough**\". A small loch is sometimes called a **lochan**. Lochs which connect to the sea may be called \"sea lochs\" or \"sea loughs\".
## Background
This name for a body of water is Insular Celtic in origin and is applied to most lakes in Scotland and to many sea inlets in the west and north of Scotland.
Many of the loughs in Northern England have also previously been called \"meres\" (a Northern English dialect word for \"lake\", and an archaic Standard English word meaning \"a lake that is broad in relation to its depth\"), similar to the Dutch *meer*, such as the *Black Lough* in Northumberland.
Some lochs in Southern Scotland have a Brythonic, rather than Goidelic, etymology, such as Loch Ryan, where the Gaelic *loch* has replaced a Cumbric equivalent of Welsh *llwch*. The same is, perhaps, the case for bodies of water in Northern England named with \'Low\' or \'Lough\', or else represents a borrowing of the Brythonic word into the Northumbrian dialect of Old English.
## Scottish lakes {#scottish_lakes}
Scotland has very few bodies of water called lakes. The Lake of Menteith, an Anglicisation of the Scots *Laich o Menteith* meaning a \"low-lying bit of land in Menteith\", is applied to the loch there because of the similarity of the sounds of the words *laich* and *lake*. Until the 19th century the body of water was known as the *Loch of Menteith*. The Lake of the Hirsel, Pressmennan Lake, Lake Louise and Raith Lake are man-made bodies of water in Scotland, referred to as lakes.
## Lochs outside Scotland and Ireland {#lochs_outside_scotland_and_ireland}
As \"loch\" is a common Gaelic word, it is found as the root of several Manx place names.
The United States naval port of Pearl Harbor, on the south coast of the main Hawaiian island of Oʻahu, is one of a complex of sea inlets. It contains three subareas called \'lochs\' named East, Middle, and West or Kaihuopala'ai, Wai'awa, and Komoawa.
Loch Raven Reservoir is a reservoir in Baltimore County, Maryland.
Brenton Loch in the Falkland Islands is a sea loch, near Lafonia, East Falkland.
In the Scottish settlement of Glengarry County in present-day Eastern Ontario, there is a lake called Loch Garry. Loch Garry was named by those who settled in the area, Clan MacDonell of Glengarry, after the well-known loch their clan is from, Loch Garry in Scotland. Similarly, lakes named Loch Broom, Big Loch, Greendale Loch, and Loch Lomond can be found in Nova Scotia, along with Loch Leven in Newfoundland, and Loch Leven in Saskatchewan.
Loch Fyne is a fjord in Greenland named by Douglas Clavering in 1823
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# Livonia
**Livonia**, known in earlier records as **Livland**, is a historical region on the eastern shores of the Baltic Sea. It is named after the Livonians, who lived on the shores of present-day Latvia.
By the end of the 13th century, the name was extended to most of present-day Estonia and Latvia, which the Livonian Brothers of the Sword had conquered during the Livonian Crusade (1193--1290). Medieval Livonia, or *Terra Mariana*, reached its greatest extent after the Saint George\'s Night Uprising (1343--1345), which forced Denmark to sell the Duchy of Estonia (northern Estonia conquered by Denmark in the 13th century) to the State of the Teutonic Order in 1346. Livonia, as understood after the retreat of Denmark in 1346, bordered on the Gulf of Finland in the north, Lake Peipus and Russia to the east, and Lithuania to the south.
As a consequence of the Livonian War (1558--1583), the territory of Livonia was reduced to the southern half of Estonia and the northern half of Latvia.
The indigenous inhabitants of Livonia were various Finnic tribes in the north and Baltic tribes in the south. The descendants of the crusaders formed the nucleus of the new ruling class of Livonia after the Livonian Crusade, and they eventually became known as Baltic Germans.
## History
Beginning in the 12th century, Livonia became a target for economic and political expansion by Danes and Germans, particularly for the Hanseatic League and the Cistercian Order. Around 1160, Hanseatic traders from Lübeck established a trading post on the site of the future city of Riga, which Bishop Albrecht von Buxthoeven founded in 1201.
### Livonian Crusade and the Livonian Brothers of the Sword (1198--1229) {#livonian_crusade_and_the_livonian_brothers_of_the_sword_11981229}
The *Livonian Chronicle of Henry* from the 1220s gives a firsthand account of the Christianization of Livonia, granted as a fief by the Hohenstaufen (*de facto* but not known as) the King of Germany, Philip of Swabia (`{{reign|1198|1208}}`{=mediawiki}), to Bishop Albert of Riga (Albert of Buxhoeveden), nephew of Hartwig II, the Archbishop of Bremen, who sailed (1200) with a convoy of ships filled with armed crusaders to carve out a Catholic territory in the east as part of the Livonian Crusade. Bishop Albert founded the military order of the Livonian Brothers of the Sword (*Fratres militiæ Christi Livoniae*, *Schwertbrüderorden*) in 1202; Pope Innocent III sanctioned the establishment in 1204. Albert did so in order to aid the Bishopric of Riga in the conversion of the pagan Curonians, Livonians, Semigallians, and Latgalians living on the shores of the Gulf of Riga. The membership of the order comprised German \"warrior monks\". Alternative names of the order include the Christ Knights, Sword Brethren, and the Militia of Christ of Livonia. From its foundation, the undisciplined Order tended to ignore its supposed vassalage to the bishops. In 1215, Albert ordered the construction of a cathedral in Riga. In 1218, he asked King Valdemar II of Denmark for assistance, but Valdemar instead arranged a deal with the Brotherhood and conquered the north of Estonia for Denmark. The Brotherhood had its headquarters at Fellin (Viljandi) in present-day Estonia, where the walls of the Master\'s castle `{{As of|2008|alt= still}}`{=mediawiki} stand. Other strongholds included Wenden (Cēsis), Segewold (Sigulda) and Ascheraden (Aizkraukle). The commanders of Fellin, Goldingen (Kuldīga), Marienburg (Alūksne), Reval (Tallinn), and the bailiff of Weißenstein (Paide) belonged to the five-member entourage of the Order\'s Master.
Pope Gregory IX asked the Brothers to defend Finland from Novgorodian attacks in his letter of 24 November 1232; however, no known information regarding the knights\' possible activities in Finland has survived. (Sweden eventually took over Finland after the Second Swedish Crusade in 1249.) In the Battle of Saule in 1236 the Lithuanians and Semigallians decimated the Order. This disaster led the surviving Brothers to become incorporated into the Order of Teutonic Knights in the following year, and from that point on they became known as the Livonian Order. They continued, however, to function in all respects (rule, clothing and policy) as an autonomous branch of the Teutonic Order, headed by their own Master (himself *de jure* subject to the Teutonic Order\'s Grand Master).
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# Livonia
## History
### Internal conflicts in Livonia (1229--1236) {#internal_conflicts_in_livonia_12291236}
The January 1229 death of Albert of Riga caused a diocesan feud in the Archbishopric of Riga, as two rival candidates were elected. Pope Gregory IX, through cardinal Otto of Tonengo, tasked Baldwin of Alna as papal legate to resolve the dispute. After securing the submission of Courland, Baldwin soon found himself in conflict with various factions in Livonia, fleeing to Dünamünde and temporarily leaving Livonia in early 1232. The pope made him bishop of Semigallia and gave him papal legation throughout much of Livonia, and Baldwin returned by 1233. He tried to take the castle of Reval (modern Tallinn) from the Sword Brothers, but in c. August--September 1233 they defeated Baldwin, who excommunicated many Sword Brothers in retaliation.
At that point, Livonia was divided into two camps: Baldwin\'s Bishopric of Semigallia, the Bishopric of Dorpat and the late Albert of Riga\'s Buxhöveden family plus several monasteries, most Estonians and Curonians, versus the Livonian Sword Brothers, Nicholas\' Bishopric of Riga, and the city of Riga. Previous generations of historians have argued that Baldwin attempted to make the whole Baltic region an ecclesiastical state, but Manfred Hellmann (historian) (1993) refuted this idea as \"fanciful speculation\". Similarly, the traditional assertion that Baldwin had extensive plans to conquer and convert eastwards into parts of Pskov and Novgorod do not stand up under scrutiny, showing that papal correspondence with Baldwin was primarily concerned with ending the internal conflict in Livonia on terms favourable to Rome. Therefore, no Livonian faction was allowed to form an alliance with an external power, be they pagan or Novgorodian, to prevent the internal conflict from spilling over and threaten Livonia\'s external security.
In 1234, the pope recalled Baldwin, and replaced him with William of Modena. The pope did not give a verdict until April 1236, when the Sword Brothers were tasked to return Reval to the Danish king. The terms of the agreement were not finalised until the Treaty of Stensby (7 June 1238), when the Livonian Sword Brothers, crushed at Saule and now submitted to the Teutonic Order, relinquished their claims to Reval and much of northern Estonia to Denmark, and to share future territorial gains with two-thirds for the Danish king and one third for the Livonian Order.
### Livonian Order, the Bishoprics and Riga from 1237 until 1418 {#livonian_order_the_bishoprics_and_riga_from_1237_until_1418}
The Livonian Order was a largely autonomous branch of the Teutonic Knights (or Teutonic Order) and a member of the Livonian Confederation from 1418 to 1561. After being defeated by Lithuanian forces in the 1236 Battle of Saule, the remnants of the Livonian Brothers of the Sword were incorporated into the Teutonic Knights as the Livonian Order in 1237. Between 1237 and 1290, the Livonian Order conquered all of Courland, Livonia, and Semigallia, but their attack on northern Russia was repelled in the Battle of Rakvere (1268). In 1346, after the St. George\'s Night Uprising the Order purchased the rest of Estonia from King Valdemar IV of Denmark. The *Chronicle of Henry of Livonia* and the *Livonian Rhymed Chronicle* describe conditions within the Order\'s territory. The Teutonic Order fell into decline following its defeat in the Battle of Grunwald in 1410 and the secularization of its Prussian territories by Albert of Brandenburg in 1525, but the Livonian Order managed to maintain an independent existence.
### Livonian Confederation (1418--1561) {#livonian_confederation_14181561}
In 1418, the Archbishop of Riga, Johannes Ambundii, organised the five ecclesiastical states of the Holy Roman Empire in Medieval Livonia (Livonian Order, Courland, Ösel--Wiek, Dorpat and Riga) into the Livonian Confederation. A diet or *Landtag* was formed in 1419. The city of Walk was chosen as the site of the diet.
From the 14th to the 16th centuries, Middle Low German -- as spoken in the towns of the Hanseatic League --- functioned as the established language of the Livonian lands, but High German subsequently succeeded it as the official language in the course of the 16th and 17th centuries.
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# Livonia
## History
### Livonian War (1558--1583) {#livonian_war_15581583}
Ferdinand I, Holy Roman Emperor once again asked for help of Gustav I of Sweden, and the Kingdom of Poland also began direct negotiations with Gustav, but nothing resulted because on 29 September 1560, Gustav I Vasa died. The chances for success of Magnus, (who had become Bishop of Courland and of Ösel-Wiek) in 1560 and his supporters looked particularly good in 1560 (and in 1570). In 1560 he had been recognised as their sovereign by the Bishopric of Ösel-Wiek and by the Bishopric of Courland, and as their prospective ruler by the authorities of the Bishopric of Dorpat; the Bishopric of Reval with the Harrien-Wierland gentry were on his side; the Livonian Order conditionally recognised his right of ownership of the (future) Duchy of Estonia. Then along with Archbishop Wilhelm von Brandenburg of the Archbishopric of Riga and his Coadjutor Christoph von Mecklenburg, Kettler, the last Master of the Teutonic Order, gave to Magnus the portions of the Kingdom of Livonia which he had taken possession of, but they refused to give him any more land.
Once Eric XIV of Sweden became king in September 1560 he took quick actions to get involved in the war. He negotiated a continued peace with Muscovy and spoke to the burghers of Reval city. He offered them goods to submit to him as well as threatening them. By 6 June 1561,they submitted to him contrary to the persuasions of Kettler to the burghers. King Eric\'s brother and future King Johan married the Polish-Lithuanian princess Catherine Jagiellon in 1562. Wanting to obtain his own land in Livonia, he loaned Poland money and then claimed the castles that they had pawned as his own instead of using them to pressure Poland. After Johan returned to Finland, Erik XIV forbade him to deal with any foreign countries without his consent.
Shortly after that, Erik XIV quickly lost any allies that he was about to obtain, either in the form of Magnus or of the Archbishop of Riga. Magnus was upset that he had been tricked out of his inheritance of Holstein. After Sweden occupied Reval, Frederick II of Denmark made a treaty with Erik XIV of Sweden in August 1561. Magnus and his brother Frederick II were in great disagreement, and Frederick II negotiated a treaty with Ivan IV on 7 August 1562 to help his brother obtain more land and to stall further Swedish advances. Erik XIV did not like this, and the Northern Seven Years\' War (1563--1570) broke out, with Sweden pitted against the Free City of Lübeck, Denmark, and Poland-Lithuania. While only losing land and trade, Frederick II and Magnus were not faring well. But in 1568 Erik XIV became insane and his brother Johan took his place as King John III of Sweden.
Johan III, due to his friendship with Poland-Lithuania, began a policy against Muscovy. He would try to obtain more land in Livonia and to dominate Denmark. After all parties had been financially drained, Frederick II let his ally, King Sigismund II Augustus of Polish--Lithuanian Commonwealth, know that he was ready for peace. On 15 December 1570, the Treaty of Stettin concluded the Northern Seven Years\' War.
It is, however, more difficult to estimate the scope and magnitude of the support Magnus received in Livonian cities. Compared to the Harrien-Wierland gentry, the Reval city council, and hence probably the majority of citizens, demonstrated a much more reserved attitude towards Denmark and towards King Magnus of Livonia. Nevertheless, there is no reason to speak about any strong pro-Swedish sentiments among the residents of Reval. The citizens who had fled to the Bishopric of Dorpat or had been deported to Muscovy hailed Magnus as their saviour until 1571. Analysis indicates that during the Livonian War a pro-independence wing emerged among the Livonian gentry and townspeople, forming the so-called \"Peace Party\". Dismissing hostilities, these forces perceived an agreement with Muscovy as a chance to escape the atrocities of war and to avoid the division of Livonia. Thus Magnus, who represented Denmark and later struck a deal with Ivan IV, proved a suitable figurehead for this faction.
The Peace Party, however, had its own armed forces -- scattered bands of household troops (*Hofleute*) under diverse command, which only united in action in 1565 (Battle of Pärnu and Siege of Reval), in 1570--1571 (Siege of Reval; 30 weeks), and in 1574--1576 (first on Sweden\'s side, then came the sale of Ösel--Wiek to the Danish Crown, and the loss of territory to Tsardom of Russia). In 1575, after Muscovy attacked Danish claims in Livonia, Frederick II dropped out of the competition, as did the Holy Roman Emperor. After this Johan III held off on his pursuit for more land due to Muscovy obtaining lands that Sweden controlled. He used the next two years of truce to get in a better position. In 1578, he resumed the fight, not only for Livonia, but also for everywhere due to an understanding that he made with the Polish--Lithuanian Commonwealth. In 1578, Magnus retired to the Commonwealth and his brother all but gave up the land in Livonia.
During the many years of the Livonian War (1558--1582), the Livonian Order suffered a decisive defeat at the hands of troops of Muscovite Russia in the Battle of Ergeme in 1560 and continued living under great threat. Letters to the Holy Roman Emperor arrived from many European countries, warning *that Moscow has its eyes on much more than only a few harbors or the province of Liefland* \... the East Sea (Ostsee-Baltic Sea) and the West Sea (Atlantic) are equally in danger. Duke Barnim the Elder, 50 years duke of Pomerania, warned, *that never before did he experience the fear than now, where even in his land, where people send by Moscow are everywhere*. At stake was the Narva-trade-route and practically all trade in the North, and with that all of Europe. Due to the religious upheavals of the Reformation the distant Holy Roman Empire could not send troops, which it could not afford anyway. The Duchy of Prussia was not able to help for much of the same reason, and Duke Albrecht (`{{reign | 1525 | 1568}}`{=mediawiki}) was under continuous ban by the Empire. The Hanseatic League was greatly weakened by this`{{clarify|date=June 2020}}`{=mediawiki} and the city state of Luebeck fought its last great war. The emperor Maximilian II (`{{reign | 1564 | 1576}}`{=mediawiki}) diffused the greatest threat by remaining on friendly terms with Tsar Ivan IV of Russia (`{{reign | 1533 | 1584}}`{=mediawiki}), but not sending Ivan IV troops as requested in his struggles with the Polish--Lithuanian Commonwealth.
In 1570, Tsar Ivan IV of Russia installed Duke Magnus as King of Livonia. The other forces opposed this appointment. The Livonian Order saw no other way than to seek protection from Sigismund II Augustus (King of Poland and Grand Duke of Lithuania), who had intervened in a war between Bishop William of Riga and the Brothers in 1557. After coming to an agreement with Sigismund II Augustus and his representatives (especially Mikołaj \"the Black\" Radziwiłł), the last Livonian Master, Gotthard Kettler, secularized the Order and converted to Lutheranism. In the southern part of the Brothers\' lands, he set up the Duchy of Courland and Semigallia for his family. Most of the remaining lands were seized by the Grand Duchy of Lithuania. Denmark and Sweden re-occupied the north of Estonia.
### Duchy of Livonia (1561--1621) {#duchy_of_livonia_15611621}
In 1561, during the Livonian War, Livonia fell to the Grand Duchy of Lithuania and became a dependent vassal of Lithuania. Eight years later, in 1569, when the Grand Duchy of Lithuania and the Kingdom of Poland formed the Polish--Lithuanian Commonwealth, Livonia became a joint domain administered directly by the king and grand duke. Having rejected peace proposals from its enemies, Ivan the Terrible found himself in a difficult position by 1579, when Crimean Khanate devastated Muscovian territories and burnt down Moscow (see Russo-Crimean Wars), the drought and epidemics have fatally affected the economy, Oprichnina had thoroughly disrupted the government, while The Grand Principality of Lithuania had united with The Kingdom of Poland (1385--1569) and acquired an energetic leader, Stefan Batory, supported by Ottoman Empire (1576). Stefan Batory replied with a series of three offensives against Muscovy, trying to cut The Kingdom of Livonia from Muscovian territories. During his first offensive in 1579, with 22,000 men, he retook Polotsk; during the second, in 1580, with 29,000-strong army, he took Velikie Luki, and in 1581 with a 100,000-strong army he started the Siege of Pskov. Frederick II of Denmark and Norway had trouble continuing the fight against Muscovy unlike Sweden and Poland. He came to an agreement with John III in 1580, giving him the titles in Livonia. That war would last from 1577 to 1582. Muscovy recognized Polish--Lithuanian control of Ducatus Ultradunensis only in 1582. After Magnus von Lyffland died in 1583, Poland invaded his territories in The Duchy of Courland, and Frederick II decided to sell his rights of inheritance. Except for the island of Œsel, Denmark was out of the Baltic by 1585. As of 1598 Inflanty Voivodeship was divided onto:
- Wenden Voivodeship (*województwo wendeńskie*, Kieś)
- Dorpat Voivodeship (*województwo dorpackie*, Dorpat)
- Parnawa Voivodeship (*województwo parnawskie*, Parnawa)
Based on a guarantee by Sigismund II Augustus from the 1560s, the German language retained its official status.
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# Livonia
## History
### Kingdom of Livonia (1570--1578) {#kingdom_of_livonia_15701578}
The armies of Ivan the Terrible were initially successful, taking Polotsk (1563) and Parnawa (1575) and overrunning much of Grand Duchy of Lithuania up to some 250 km proximity of Vilnius. Eventually, the Grand Duchy of Lithuania and Kingdom of Poland formed the Polish--Lithuanian Commonwealth in 1569 under the Union of Lublin. Eric XIV of Sweden did not like this, and the Northern Seven Years\' War between the Free City of Lübeck, Denmark, Poland, and Sweden broke out. While only losing land and trade, Frederick II of Denmark and Magnus von Lyffland of the Œsel-Wiek did not fare well. But, in 1569, Erik XIV became insane and his brother John III of Sweden took his place. After all parties had been financially drained, Frederick II let his ally, King Zygmunt II August, know that he was ready for peace. On 15 December 1570, the Treaty of Stettin was concluded.
In the next phase of the conflict, in 1577, Ivan IV took advantage of the Commonwealth\'s internal strife (called the war against Gdańsk in Polish historiography), and during the reign of Stefan Batory in Poland, invaded Livonia, quickly taking almost the entire territory, with the exception of Riga and Reval. In 1578, Magnus of Livonia recognized the sovereignty of the Polish--Lithuanian Commonwealth (not ratified by the Sejm of Poland-Lithuania, nor recognized by Denmark). The Kingdom of Livonia was beaten back by Muscovy on all fronts. In 1578, Magnus of Livonia retired to The Bishopric of Courland, and his brother all but gave up the land in Livonia.
### Swedish Livonia (1629--1721) {#swedish_livonia_16291721}
Sweden was given roughly the same area as the former Duchy of Livonia after the 1626--1629 Polish--Swedish War. The area, usually known as Swedish Livonia, became a very important Swedish dominion, with Riga being the second largest Swedish city and Livonia paying for one third of the Swedish war costs. Sweden lost Swedish Livonia, Duchy of Estonia and Swedish Ingria to the Russian Empire almost 100 years later, by the Capitulation of Estonia and Livonia in 1710 and the Treaty of Nystad in 1721.
### Livonian Voivodeship (1620s--1772) {#livonian_voivodeship_1620s1772}
The Livonian Voivodeship (*Livonijos vaivadija*; *Województwo inflanckie*) was a unit of administrative division and local government in the Duchy of Livonia, part of the Polish--Lithuanian Commonwealth, since it was formed in the 1620s out of the Wenden Voivodeship till the First Partition of Poland in 1772.
### Riga Governorate (1721--1796) {#riga_governorate_17211796}
The Russian Empire conquered Swedish Livonia during the course of the Great Northern War and acquired the province in the Capitulation of Estonia and Livonia in 1710, confirmed by the Treaty of Nystad in 1721. Peter the Great confirmed German as the exclusive official language. Russia then added Polish Livonia in 1772 during the Partitions of Poland.
### Governorate of Livonia (1796--1918) {#governorate_of_livonia_17961918}
*Main article: Governorate of Livonia* `{{See also|Governor-General of Baltic provinces}}`{=mediawiki} In 1796, the Riga Governorate was renamed as the Governorate of Livonia (*Лифляндская губе́рния* / *Liflyandskaya guberniya*, *Vidzemes guberņa*, *Liivimaa kubermang*). From 1845 to 1876, the Baltic governorates of Estonia, Livonia, and Courland --- an area roughly corresponding to the historical medieval Livonia --- were administratively subordinated to a common Governor-General. Amongst the holders of this post were Count Alexander Arkadyevich Suvorov and Count Pyotr Andreyevich Shuvalov.
Livonia remained within the Russian Empire until the end of World War I, when it was split between the newly independent states of Latvia and Estonia. The United Baltic Duchy, alternately known as the \"Grand Duchy of Livonia\", proclaimed by the Baltic German nobility on 12 April 1918, was never recognised by any state, and dissolved at the German surrender in November 1918. Livonia had ceased to exist. From 1918 to 1920, both Soviet troops and German Freikorps fought against Latvian and Estonian troops for control over former Livonia, but their attempts were defeated.
## Legacy
The historical land of Livonia has been split between Latvia and Estonia ever since 1918. The Livonian language is spoken by fewer than 100 individuals as a second language, and is understood to be fast approaching extinction. The last native Livonian speaker died in June 2013.
The unofficial anthem of the Livonians, \"Min izāmō\", shares the melody of the Finnish and Estonian national anthems.
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# Livonia
## Gallery
Europe mediterranean 1190.jpg\|Livonia in Europe, 1190. Europe 1550.jpg\|Europe, 1550. Litvania map 1570.png\|Livonia on a 1570 map Europe 1740.jpg\|Europe, 1740. Europe1815 1905.jpg\|Europe, 1815. Meyerbaltikum.jpg\|Livonia, 1898
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# Lysithea (moon)
**Lysithea** `{{IPAc-en|l|aɪ|ˈ|s|ɪ|θ|i|ə}}`{=mediawiki} is a prograde irregular satellite of Jupiter. It was discovered by Seth Barnes Nicholson in 1938 at Mount Wilson Observatory and is named after the mythological Lysithea, daughter of Oceanus and one of Zeus\' lovers.
Lysithea did not receive its present name until 1975; before then, it was simply known as **`{{nowrap|Jupiter X}}`{=mediawiki}**. It was sometimes called \"Demeter\" from 1955 to 1975.
It belongs to the Himalia group, moons orbiting between 11 and 13 Gm from Jupiter at an inclination of about 28.3°. Its orbital elements are as of January 2000. They are continuously changing due to solar and planetary perturbations. It is gray`{{Failed verification|date=January 2025}}`{=mediawiki} in color (B−V=0.72, V−R=0.36, V−I=0.74) and intermediate between C-type and P-type asteroids
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# Leda and the Swan
**Leda and the Swan** is a story and subject in art from Greek mythology in which the god Zeus, in the form of a swan, seduces Leda, a Spartan queen. According to later Greek mythology, Leda bore Helen and Polydeuces, children of Zeus, while at the same time bearing Castor and Clytemnestra, children of her husband Tyndareus, the King of Sparta. According to many versions of the story, Zeus took the form of a swan and slept with Leda on the same night she slept with her husband King Tyndareus. In some versions, she laid two eggs from which the children hatched. In other versions, Helen is a daughter of Nemesis, the goddess who personified the disaster that awaited those suffering from the pride of Hubris.
Especially in art, the degree of consent by Leda to the relationship seems to vary considerably; there are numerous depictions, for example by Leonardo da Vinci, that show Leda affectionately embracing the swan, as their children play.
The subject was rarely seen in the large-scale sculpture of antiquity, although a representation of Leda in sculpture has been attributed in modern times to Timotheus (*compare illustration, below left*); small-scale sculptures survive showing both reclining and standing poses, in cameos and engraved gems, rings, and terracotta oil lamps. Thanks to the literary renditions of Ovid and Fulgentius it was a well-known myth through the Middle Ages, but emerged more prominently as a classicizing theme, with erotic overtones, in the Italian Renaissance.
## Eroticism
The historian Procopius claims, in his Secret History, that the Roman Empress Theodora acted in a reproduction of this particular myth at some point in her youth in the early sixth century CE prior to her becoming the empress. This account is heavily disputed for the biases Roman aristocrats including Procopius had towards the role of women and the reputation of actresses and sex workers at the time.
The subject undoubtedly owed its 16th-century popularity to the paradox that it was considered more acceptable to depict a woman in the act of copulation with a swan than with a man. The earliest depictions show the pair love-making with some explicitness---more so than in any depictions of a human pair made by artists of high quality in the same period.
The fate of the erotic album *I Modi* some years later shows why this was so. The theme remained a dangerous one in the Renaissance, as the fates of the three best known paintings on the subject demonstrate. The earliest depictions were all in the more private medium of the old master print, and mostly from Venice. They were often based on the extremely brief account in the *Metamorphoses* of Ovid (who does not imply a rape), though Lorenzo de\' Medici had both a Roman sarcophagus and an antique carved gem of the subject, both with reclining Ledas.
The earliest known explicit Renaissance depiction is one of the many woodcut illustrations to *Hypnerotomachia Poliphili*, a book published in Venice in 1499. This shows Leda and the Swan making love with gusto, despite being on top of a triumphal car, being pulled along and surrounded by a considerable crowd. An engraving dating to 1503 at the latest, by Giovanni Battista Palumba, also shows the couple in coitus, but in deserted countryside. Another engraving, certainly from Venice and attributed by many to Giulio Campagnola, shows a love-making scene, but there Leda\'s attitude is highly ambiguous. Palumba made another engraving, perhaps in about 1512, presumably influenced by Leonardo\'s sketches for his earlier composition, showing Leda seated on the ground and playing with her children.
There were also significant depictions in the smaller decorative arts, also private media. Benvenuto Cellini made a medallion, now in Vienna, early in his career, and Antonio Abondio one on the obverse of a medal celebrating a Roman courtesan.
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# Leda and the Swan
## In painting {#in_painting}
A fresco depicting the Greek myth of Leda and the Swan was unearthed at the Pompeii archeological site.
Leonardo da Vinci began making studies in 1504 for a painting, apparently never executed, of Leda seated on the ground with her children. In 1508, he painted a different composition of the subject, with a nude standing Leda cuddling the Swan, with the two sets of infant twins (also nude), and their huge broken egg-shells. The original of this is lost, possibly deliberately destroyed, and was last recorded in the French royal Château de Fontainebleau in 1625 by Cassiano dal Pozzo. However it is known from many copies, of which the earliest are probably the *Spiridon Leda*, perhaps by a studio assistant and now in the Uffizi, and the one at Wilton House in the United Kingdom (illustrated).
Also lost, and probably deliberately destroyed, is Michelangelo\'s tempera painting of the pair making love, commissioned in 1529 by Alfonso d\'Este for his palazzo in Ferrara, and taken to France for the royal collection in 1532; it was at Fontainebleau in 1536. Michelangelo\'s cartoon for the work---given to his assistant Antonio Mini, who used it for several copies for French patrons before his death in 1533---survived for over a century. This composition is known from many copies, including an ambitious engraving by Cornelis Bos, c. 1563; the marble sculpture by Bartolomeo Ammanati in the Bargello, Florence; two copies by the young Rubens on his Italian voyage, and the painting after Michelangelo, ca. 1530, in the National Gallery, London. The Michelangelo composition, of about 1530, shows Mannerist tendencies of elongation and twisted pose (the *figura serpentinata*) that were popular at the time. In addition, a sculptural group, similar to the Prado Roman group illustrated, was believed until at least the 19th century to be by Michelangelo.
The last very famous Renaissance painting of the subject is Correggio\'s elaborate composition of c. 1530 (Berlin); this too was damaged whilst in the collection of Philippe II, Duke of Orléans, the Regent of France in the minority of Louis XV. His son Louis, though a great lover of painting, had periodic crises of conscience about his way of life, in one of which he attacked the figure of Leda with a knife. The damage has been repaired, though full restoration to the original condition was not possible. Both the Leonardo and Michelangelo paintings also disappeared when in the collection of the French Royal Family, and are believed to have been destroyed by more moralistic widows or successors of their owners.
There were many other depictions in the Renaissance, including cycles of book illustrations to Ovid, but most were derivative of the compositions mentioned above. The subject remained largely confined to Italy, and sometimes France---Northern versions are rare. After something of a hiatus in the 18th and early 19th centuries (apart from a very sensuous Boucher), Leda and the Swan became again a popular motif in the later 19th and 20th centuries, with many Symbolist and Expressionist treatments.
Also from that era were sculptures of the theme by Antonin Mercié and Max Klinger.
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# Leda and the Swan
## In modern and contemporary art {#in_modern_and_contemporary_art}
Cy Twombly executed an abstract version of *Leda and the Swan* in 1962. It was purchased by Larry Gagosian for \$52.9 million at Christie\'s May 2017 Post-War and Contemporary Art Evening Sale.
Avant-garde filmmaker Kurt Kren along with other members of the Viennese Actionist movement, including Otto Muehl and Hermann Nitsch, made a film-performance called *7/64 Leda und der Schwan* in 1964. The film retains the classical motif, portraying, for most of its duration, a young woman embracing a swan.
There is a life-sized marble statue of *Leda and the Swan* at the Jai Vilas Palace Museum in Gwalior, Northern Madhya Pradesh, India.
American artist and photographer Carole Harmel created the \"Bird\" series (1983), a Jean Cocteau-influenced collection of photographs that explored the \"Leda and the Swan\" myth in tightly cropped, voyeuristic images of a nude female and an undefinable birdlike creature hinting at intimacy.
Bristol Museum and Art Gallery currently exhibits Karl Weschke\'s *Leda and the Swan*, painted in 1986. The Winnipeg Art Gallery in Canada has, in its permanent collection, a ceramic \"Leda and the Swan\" by Japanese-born American artist Akio Takamori. Genieve Figgis painted her version of Leda and the Swan in 2018 after an earlier work by François Boucher. Figgis' contemporary version reinvents the idyllic romantic scene of lavish playfulness with a dark humor creating a scene of profanity and horror. There is a sculpture in neon lights depicting Leda and the Swan in Berlin, near Sonnenallee metro station and the Estrel hotel, designed by AES+F. Photographer Charlie White included a portrait of Leda in his \"And Jeopardize the Integrity of the Hull\" series. Zeus, as the swan, only appears metaphorically.
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# Leda and the Swan
## In poetry {#in_poetry}
Ronsard wrote a poem on *La Défloration de Lède*, perhaps inspired by the Michelangelo, which he may well have known. He imagines the beak going into Leda\'s mouth.
\"Leda and the Swan\" is a sonnet by William Butler Yeats composed in 1923 and first published in the *Dial* in June, 1924, and later published in the collection \'The Cat the Moon and Certain Poems\' in 1924. Combining psychological realism with a mystic vision, it describes the swan\'s rape of Leda. It also alludes to the Trojan War, which will be provoked by the abduction of Helen, who will be begotten by Zeus on Leda (along with Castor and Pollux, in some versions of the myth). Clytaemnestra, who killed her husband, Agamemnon, leader of the Greeks at Troy, was also supposed to have hatched from one of Leda\'s eggs. The poem is regularly praised as one of Yeats\'s masterpieces. Camille Paglia, who called the poem \"the greatest poem of the twentieth century,\" and said \"all human beings, like Leda, are caught up moment by moment in the \'white rush\' of experience. For Yeats, the only salvation is the shapeliness and stillness of art.\" See external links for a bas relief arranged in the position as described by Yeats.
Nicaraguan poet Rubén Darío\'s 1892 poem \"Leda\" contains an oblique description of the rape, watched over by the god Pan.
H.D. (Hilda Doolittle) also wrote a poem called \"Leda\" in 1919, suggested to be from the perspective of Leda. The description of the sexual action going on makes it seem almost beautiful, as if Leda had given her consent.
In the song \"Power and Glory\" from Lou Reed\'s 1992 album *Magic and Loss*, Reed recalls the experience of seeing his friend dying of cancer and makes reference to the myth: `{{Poemquote|
I saw [[isotope]]s introduced into his lungs
trying to stop the cancerous spread
And it made me think of Leda and The Swan
and gold being made from lead<ref>{{Cite news |url=https://www.newspapers.com/article/winston-salem-journal-lou-reeds-magic/149553421/ |title=Lou Reed's 'Magic and Loss' a requiem that leads to hope |first=Ed |last=Bumgardner |newspaper=[[Winston-Salem Journal]] |pages=50, [https://www.newspapers.com/article/winston-salem-journal-lou-reeds-magic/149553442/ 51] |date=1992-01-25 |access-date=2024-06-17 |via=Newspapers.com}}</ref>}}`{=mediawiki}
Sylvia Plath alludes to the myth in her radio play *Three Women* written for the BBC in 1962. The play features the voices of three women. The first is a married woman who keeps her baby. The second is a secretary who suffers a miscarriage. The third voice, a student who is pregnant and gives her baby up for adoption, mentions \"the great swan, with its terrible look,/ Coming at me,/ There is a snake in swans./ He glided by; his eye had a black meaning.\" and repeats a refrain of \"I wasn\'t ready\" stating \"the face/ Went on shaping itself with love, as if I was ready.\" describing the unwanted pregnancy.
## In literature {#in_literature}
Several references to the myth are presented in novels by Angela Carter, including *Nights at the Circus* and *The Magic Toyshop*. In the latter novel, the myth is brought to life in the form of a performance in which a frightened young girl is forced to act as Leda in accompaniment with a large mechanical swan.
The myth is also mentioned in Richard Yates\' 1962 novel *Revolutionary Road*. The character Frank Wheeler, married to April Wheeler, after having had sex with an office secretary ponders what to say as he is leaving: \"Did the swan apologize to Leda? Did an eagle apologize? Did a lion apologize? Hell no!\"
In Robert Galbraith\'s 2020 novel, *Troubled Blood*, one of the main characters, Robin Ellacott, visits a painting gallery where she sees a painting of Leda and the swan done by one character who is an artist in the novel. Furthermore, the other protagonist of the Strike series, the eponymous detective Cormoran Strike, was born to a mother named Leda and swans appear in several of the novels.
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# Leda and the Swan
## In fashion {#in_fashion}
In 1935, German-born movie star Marlene Dietrich wore a dramatically designed Leda costume to a Hollywood costume party. Designed by the acclaimed costume designer Travis Banton, a longtime Dietrich collaborator, the white tulle and feather dress featured a thigh-slit, a mid-length train and, most characteristically, a fabric and feather \"swan\" neck which coiled around Dietrich\'s own neck, as well a pair of large feathered wings, one stretching downwards across her chest and the other one upwards across her left shoulder.
Sixty-six years later, at the 2001 Academy Awards, Icelandic singer Björk wore a dress by Marjan Pejoski in nude mesh and a white tulle skirt. The skirt gradually narrowed upwards over the torso to turn into a swan-neck made out of fabric which coiled around the wearer\'s neck in exactly the same way as Dietrich\'s dress from 1935. Although Dietrich\'s costume remains largely unknown to the general public, Björk\'s dress \"attained cult status instantly\" and became an icon of red carpet culture. Yet, the reference to Marlene Dietrich\'s costume was rarely (if ever) mentioned at the time.
In June 2021, Maria Grazia Chiuri as creative director for the French fashion house Dior, designed a collection strongly inspired by Hellenistic culture, the Olympic Games, and Ancient Greek Mythology, and showed it at the Panathenaic Stadium in Athens as an homage to the Olympic tradition (the collection was shown a month before the beginning of the 2020 Summer Olympics). The collection\'s closing pièce de résistance was a Leda-inspired swan dress. The immediate visual similarity between Chiuri\'s swan Dress and Björk\'s swan dress sparked excitement on social media as most people inevitably thought the Dior dress was directly inspired by Pejoski\'s iconic 2001 creation. However, only a few days later, Dior openly defended the inspiration of the dress referring to it on its Twitter account as a recreation of a costume worn by Marlene Dietrich, who was, famously, an important and loyal client of the French brand during the 40s and 50s. Notably, Chiuri\'s 2021 Dior dress featured feathered swan-wings spanning over the chest and shoulder. This dramatic detail, taken directly from Dietrich\'s costume from 1935, sets Chiuri\'s dress for Dior entirely apart from Björk\'s red-carpet dress, and makes it, irrefutably, a reference to Dietrich\'s costume, and by extension, to the myth of Leda and the Swan.
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# Leda and the Swan
## In modern media {#in_modern_media}
A version of the Leda and the Swan story is the foundation myth in the Canadian futuristic thriller television series *Orphan Black* which aired over 5 seasons from 2013 to 2017. A corporation uses genetic engineering to create a series of female clones (Leda) and a series of male clones (Castor) who are also brothers and sisters clones as they derive from one mother who is a chimera with male and female genomes.
Musical artist Hozier released the single Swan Upon Leda in 2022, referencing the myth as a tool to advocate for reproductive rights.
The 2021 wordless, 3D feature film Leda transports the myth to dark forests and deep lakes that surround a mid-19th-century mansion. Directed by Samuel Tressler IV and starring Adeline Thery, the story focuses on a pregnant Leda, nightmarishly haunted by the image of a swan and lost between dream and reality in a state of trauma.
The Philadelphia cigar maker Bobrow Brothers made a brand of cigars with the name \"Leda\" which was sold at least into the 1940s. The cigar label depicted Leda and the Swan in a river.
## Modern censorship {#modern_censorship}
In April 2012 an art gallery in London, England, was instructed by the police to remove a modern exhibit of Leda and the Swan. The law concerned was Section 63 of the Criminal Justice and Immigration Act 2008, condemning \"violent pornography\", brought in by the Labour Party government of 2005--2010.
## Gallery
<File:0> Léda et Zeus métamorphosé en cygne - Musei Capitolini (1).JPG\|*Leda and Zeus transformed into a swan*. A 2nd century BCE Roman version of an earlier Greek statue attributed to Timotheos from the 300s BCE. More than two dozen examples of this statue survive. Palazzo Nuovo (Capitoline Museums), Rome. <File:Leda> and the Swan, Pompeian fresco.jpg\|*Leda and the Swan*, ancient fresco from Pompeii Image:Leda Melzi Uffizi.jpg\|*Leda and the Swan* copy by Giovanni Francesco Melzi after the lost painting by Leonardo, 1508--1515, oil on canvas, Galleria degli Uffizi, Florence, Italy. <File:Cornelis> Bos - Leda and the Swan - WGA2486.jpg\|Drawing by Cornelis Bos after the lost original by Michelangelo. Between 1530 and 1550 <File:Leda> y el cisne (Pencz).jpg\|*Leda and the Swan*. Georg Pencz <File:Benvenuto> cellini, leda e il cigno.JPG\|*Leda and the Swan* by Benvenuto Cellini <File:Leda> and the Swan, by Massimiliano Soldani, 11364501.jpg\|*Leda and the Swan*, by Massimiliano Soldani, 1725 <File:Attribué> à François Boucher, Léda et le Cygne (vers 1740).jpg\|Attributed to François Boucher, 1740, oil on canvas. <File:Leda> y el cisne.jpg\|*Leda and the Swan*, charcoal, gouache on paper. (Ulpiano Checa) <File:Leda> and the Swan by Fernando Botero.jpg\|alt=Leda and the Swan by Fernando Botero\|*Leda and the Swan* by Fernando Botero, 1996 <File:Genieve> Figgis Leda and the Swan (after Boucher) 2018 23x31 inches Acrylic in canvas 37kB.JPEG\|Genieve Figgis, *Leda and the Swan (after Boucher)*, 2018, Acrylic on canvas, 23 x 31 inches <File:Egg> on Pefnos island.jpg\|Egg sculpture on Pefnos, 2020, by Yiannis Gouzos and Petros Themelis
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# Laches (equity)
In common-law legal systems, **laches** (`{{IPAc-en|ˈ|l|æ|tʃ|ɪ|z}}`{=mediawiki} `{{respell | LAT | chiz}}`{=mediawiki}, `{{IPAc-en|ˈ|l|eɪ|-}}`{=mediawiki}; Law French: *remissness*, *dilatoriness*, from *laschesse*) is a lack of diligence and activity in making a legal claim, or moving forward with legal enforcement of a right, particularly in regard to equity. It is an unreasonable delay that can be viewed as prejudicing the opposing party. When asserted in litigation, it is an equity defense, that is, a defense to a claim for an equitable remedy. It is often understood in comparison to a statute of limitations, a statutory defense, which traditionally is a defense to a claim \"at law\".
The person invoking laches is asserting that an opposing party has \"slept on its rights\", and that, as a result of this delay, circumstances have changed (witnesses or evidence may have been lost or no longer available, etc.), such that it is no longer a just resolution to grant the plaintiff\'s claim. Laches is associated with the maxim of equity: \"Equity aids the vigilant\"`{{snd}}`{=mediawiki}not those who sleep on their rights. Put another way, failure to assert one\'s rights in a timely manner can result in a claim being barred by laches.
## Origin, definition, overview {#origin_definition_overview}
Laches is a legal term derived from the Old French *laschesse,* meaning \"remissness\" or \"dilatoriness\", and is viewed as the opposite of \"vigilance\". The United States Supreme Court case *Costello v. United States* 365 US 265, 282 (1961) is often cited for a definition of laches. *Costello* defined Laches as \"Lack of diligence by the party against whom the defense is asserted combined with prejudice to the party asserting the defense\".
Invoking laches is a reference to a lack of diligence and activity in making a legal claim, or moving forward with legal enforcement of a right, in particular with regard to equity, and so is an \"unreasonable delay pursuing a right or claim, in a way that prejudices the \[opposing\] party\". When asserted in litigation, it is an equitable defense, that is, a defense to a claim for an equitable remedy. The essential element of *laches* is an unreasonable delay by the plaintiff in bringing the claim; because laches is an equitable defense, it is ordinarily applied only to claims for equitable relief (such as injunctions), and not to claims for legal relief (such as damages). The person invoking laches is asserting that an opposing party has \"slept on its rights\", and that, as a result of this delay, witnesses or evidence may have been lost or no longer available, and circumstances have changed such that it is no longer just to grant the plaintiff\'s original claim; hence, laches is associated with the maxim of equity: *\[\[Vigilantibus non dormientibus æquitas subvenit\]\]* (\"Equity aids the vigilant, not the sleeping ones \[that is, those who sleep on their rights\]\"). Put another way, failure to assert one\'s rights in a timely manner can result in a claim being barred by laches. Sometimes courts will also require that the party invoking the doctrine has changed its position as a result of the delay, but that requirement is more typical of the related (but more stringent) defense and equally cause of action of estoppel.
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# Laches (equity)
## Components
A claim of laches requires the following components:
1. a delay in bringing the action,
2. a delay that is unreasonable and
3. that prejudices the defendant.
### Delay
The period of delay begins when the plaintiff knew, or reasonably ought to have known, that the cause of action existed; the period of delay ends only when the legal action is formally filed. Informing or warning the defendant of the cause of action (for example by sending a cease-and-desist letter or merely *threatening* a lawsuit) does *not*, by itself, end the period of delay.
### Unreasonableness
In order to invoke laches, the delay by the opposing party in initiating the lawsuit must be unreasonable. The courts have recognized the following causes of delay as reasonable:
- the exhaustion of remedies through the administrative process
- the evaluation and preparation of a complicated claim
- to determine whether the scope of proposed infringement will justify the cost of litigation
By contrast, it is *not* reasonable to delay a lawsuit to \"capitalize on the value of the infringer\'s labor\". In *Danjaq v. Sony*, the Ninth Circuit decided that a screenwriter who waited for a film studio to publicize and distribute a film based on a script he allegedly owned had delayed his lawsuit unreasonably.
### Prejudice
Unreasonable delay must prejudice the defendant. Examples of such prejudice include:
- evidence favorable to the defendant becoming lost or degraded
- witnesses favorable to the defendant dying or losing their memories
- the defendant making economic decisions (e.g. investing in a movie or a manufacturing process) that it would not have done, had the lawsuit been filed earlier.
Unreasonable delay may also prejudice the rights of third-parties who were unknown in the case earlier but whose rights got created in the intervening period of the delay (e.g.: the defendant inducts new persons on a disputed property by sale, or by lease).
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# Laches (equity)
## Procedure
A defense lawyer raising the defense of *laches* against a motion for injunctive relief (a form of equitable relief) might argue that the plaintiff comes \"waltzing in at the eleventh hour\" when it is now too late to grant the relief sought, at least not without causing great harm that the plaintiff could have avoided. In certain types of cases (for example, cases involving time-sensitive matters, such as elections), a delay of even a few days is likely to be met with a defense of *laches*, even where the applicable statute of limitations might allow the type of action to be commenced within a much longer time period. In courts in the United States, laches has often been applied even where a statute of limitations exists, although there is a division of authority on this point.
If a court does accept the laches defense, it can decide either to deny the request for equitable relief or to narrow the equitable relief that it would otherwise give. Even if the court denies equitable relief to a plaintiff because of laches, the plaintiff may still have a claim for legal relief if the statute of limitations has not run out.
Under the United States Federal Rules of Civil Procedure, *laches* is an affirmative defense, which means that the burden of asserting *laches* is on the party responding to the claim to which it applies.
The *laches* defense does not apply if the claimant was a minor during the time that the claim was not brought, so a party can bring a claim against an historical injustice when they reach their majority.`{{primary source inline|date=January 2016}}`{=mediawiki}
## Compared to statute of limitations {#compared_to_statute_of_limitations}
The defense of *laches* resembles a statute of limitations since both are concerned with ensuring that plaintiffs bring their claims in a timely fashion.
However, a statute of limitations is concerned only with the time that has passed. Laches is concerned with the reasonableness of the delay in a particular situation and so is more case-specific and more focused on the equitable conduct of the plaintiff. Those considerations are not unique to the laches defense because they are characteristic of equitable reasoning and equitable remedies, whereas limitation is a statutory remedy.
In the US, the proper disposal of claims in light of those two areas of law has required attention through to the Supreme Court. In *Petrella v. Metro-Goldwyn-Mayer* (2014), the US Supreme Court rebuffed a defendant\'s claim that laches barred a copyright infringement suit because Congress had established a detailed statutory scheme, including a statute of limitations. `{{primary source inline|date=January 2016}}`{=mediawiki}
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# Laches (equity)
## Examples
In the Virginia Republican primary for the 2012 US presidential election, several candidates did not appear on the ballot because they failed to obtain sufficient petition signatures. Four of the unsuccessful candidates---Rick Perry, Jon Huntsman, Newt Gingrich, and Rick Santorum---sued, claiming that restrictions on the persons allowed to gather signatures were unconstitutional. Their claim was dismissed by the district court on the grounds of laches, because, in the words of the appellate court: `{{blockquote|...plaintiffs could have brought their constitutional challenge to Virginia's residency requirement for petition circulators as soon they were able to circulate petitions in the summer of 2011, but instead chose to wait until after the December 22, 2011 deadline before seeking relief. The district court concluded this delay 'displayed an unreasonable and inexcusable lack of diligence' on plaintiffs' part that 'has significantly harmed the defendants.' Specifically, it determined that the delayed nature of this suit had already transformed the Board's orderly schedule for printing and mailing absentee ballots 'into a chaotic attempt to get absentee ballots out on time.' The district court consequently held that laches barred their request for relief.<ref name="perry">{{cite web|url=http://www.ca4.uscourts.gov/Opinions/Unpublished/121067R1.U.pdf | title= United States Court of Appeals for the Fourth Circuit, The Honorable Rick Perry, Plaintiff-Appellant-Movant, The Honorable Newt Gingrich, The Honorable Jon Huntsman, Jr., and the Honorable Rick Santorum, Intervenor-Plaintiffs, v. Charles Judd, Kimberly Bowers, and Don Palmer, members of the Virginia Board of Elections, in their official capacities, Defendants-Appellees-Respondents, Proceeding No. 12-1067 |date= January 17, 2012 | work=ca4.uscourts.gov | access-date=5 January 2016}}</ref>{{primary source inline|date=January 2016}}}}`{=mediawiki} The appeals court upheld the dismissal on grounds of laches, but it added that the challenge would likely have succeeded if it had been brought in a timely fashion.
In Grand Haven, Michigan, the Northwest Ottawa Community Health System sued Grand Haven Township and Health Pointe, which was in the process of building a competing medical facility in the township, arguing that the township ignored its own zoning ordinance in approving the project. On March 24, 2017, as part of a ruling dismissing the lawsuit, Circuit Court Judge Jon A. Van Allsburg noted that the Northwest Ottawa Community Health System waited more than eight months from the date the project was approved before filing the lawsuit and that during that time, defendant Health Pointe had purchased construction materials.
The defense of laches is often used as an affirmative defense in patent infringement lawsuits in the USA. In 2021, the Court of Appeals for the Federal Circuit allowed the USPTO to use laches as a reason for denying patents to an applicant, who filed hundreds of applications, that were \"atypically long and complex\", and who filed amendments, which increased the total number of claims to roughly 115,000. This applicant alone forced the USPTO to create an art unit of twelve experienced examiners solely to examine its patents
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# Lyman Abbott
**Lyman J. Abbott** (December 18, 1835 -- October 22, 1922) was an American Congregationalist theologian, editor, and author.
## Biography
### Early years {#early_years}
Abbott was born at Roxbury, Massachusetts, on December 18, 1835, the son of the prolific author, educator and historian Jacob Abbott, and his mother being Harriet Vaughan. Abbott grew up in Farmington, Maine, and later in New York City. Abbott\'s ancestors were from England, and came to America roughly twenty years after Plymouth Rock.
He graduated from the New York University in 1853, where he was a member of the Eucleian Society, studied law, and was admitted to the bar in 1856. Abbott soon abandoned the legal profession, however, and after studying theology with his uncle, John Stevens Cabot Abbott, was ordained a minister of the Congregational Church in 1860. He was married October 14, 1857, to Abby F. Hamlin, whose father Hannibal Hamlin (1809-1863) was the cousin of the politician Hannibal Hamlin of Boston, Mass.
### Career
He was pastor of the Congregational Church in Terre Haute, Indiana, from 1860 to 1865 and of the New England Church in New York City in 1865--1869. From 1865 to 1868 he was secretary of the American Union Commission (later called the American Freedmen\'s and Union Commission). In 1869 he resigned his pastorate to devote himself to literature.
Abbott worked variously in the publishing profession as an associate editor of *Harper\'s Magazine*, and was the founder of a publication called the *Illustrated Christian Weekly,* which he edited for six years. He was also the co-editor of *The Christian Union* with Henry Ward Beecher from 1876 to 1881. Abbott later succeeded Beecher in 1888 as pastor of Plymouth Church, Brooklyn. He also wrote the official biography of Beecher and edited his papers.
From 1881 Abbott was editor-in-chief of *The Christian Union*, renamed *The Outlook* in 1891; this periodical reflected his efforts toward social reform, and, in theology, a liberality, humanitarianism and nearly unitarian. The latter characteristics marked his published works also.
Abbott\'s opinions differed from those of Beecher. Abbott was a constant advocate of Industrial Democracy, and was an advocate of Theodore Roosevelt\'s progressivism for almost 20 years. He later adopted a pronouncedly liberal theology.
He was a pronounced Christian Evolutionist. In two of his books, *The Evolution of Christianity* and *The Theology of an Evolutionist* (1897), Abbott applied the concept of evolution in a Christian theological perspective. Although he objected to being called an advocate of Darwinism, he was an optimistic advocate of evolution, once saying \"what Jesus saw, humanity is becoming.\"
Abbott was a religious figure of some public note and was called upon on October 30, 1897, to deliver an address in New York at the funeral of economist, Henry George. He ultimately resigned his pastorate in November 1898.
His son, Lawrence Fraser Abbott, accompanied President Roosevelt on a tour of Europe and Africa (1909--10). In 1913 Lyman Abbott was expelled from the American Peace Society because military preparedness was vigorously advocated in *The Outlook*, which he edited, and because he was a member of the Army and Navy League. During World War I, he supported the government\'s war policies.
He received the degree D.D. from the University of the City of New York in 1879; from Harvard in 1891, from Yale in 1903, and LL.D. from Western Reserve in 1900.
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# Lyman Abbott
## Biography
### Death and legacy {#death_and_legacy}
Lyman Abbott died on October 22, 1922, and was buried in Woodlawn Cemetery at New Windsor, New York.
The editors of *The Outlook* kept their normal routine, publishing without \"departure from the normal course of publication\" since that was what their departed colleague would have wanted. The issue asked readers for understanding as the paper \"wait\[ed\] until \[the\] next week to give to his friends, known and unknown, a record of his life and of the tributes which marked his passing.\" A brief tribute appeared in that issue, but the November 8th edition contained the official remembrance and tributes. Fifteen pages in that issue dealt with Abbott, and the publishers included \"several long essays in Abbott\'s honor from close relatives, shorter tributes from friends and past associates, and blurbs from many American press companies.\"
The many diverse and prominent author who contributed tributes \"demonstrated the scope and magnitude of Lyman Abbott\'s influence within American religious and intellectual culture during his long career.\" Prominent examples include a re-published 1915 tribute from former United States president Theodore Roosevelt and articles from prestigious newspapers such as *The New York Times* and the *New York Herald*. Roosevelt praised Abbott for being \"one of those men whose work and life give strength to all who believe in this country,\" and the New York Herald recalled Abbott\'s ability to \"convey his valuable opinions to the entire intellectual public.\" Dr. Henry Sloane Coffin noted at a later memorial service, \"Measured by the number of people he reached, Dr. Abbott was unquestionably the greatest teacher of religion of this generation.\"
Abbott\'s lasting influence and widespread appeal is readily apparent in later evaluations of his life. Abbott\'s one biographer, Ira V. Brown, confirmed Abbott\'s importance via \"testimonials by the dozen,\" and added that Abbott \"directly reached several hundred thousands of people\" through his work as a \"minister, lecturer, author, and editor.\" Abbott was \"something of a national patriarch\" by the time of his death, and according to Brown, he was \"no less than a modern oracle\" to thousands of followers. Abbott influenced hundreds every week through his sermons at the prestigious Plymouth Avenue Congregationalist Church. He also gave speeches at many American colleges, published several books that sold between five and ten thousand copies, and edited the Outlook that, at its peak, sold \"about 125,000 copies a week.\" The magazine \"was a prominent news source for Protestant ministers and laypeople all over the United States, demonstrating Abbott\'s lasting influence.\"
## Works
- *Sermons of Henry Ward Beecher* (Editor). (2 vols., 1868)
- *Jesus of Nazareth* (1869)
- *Illustrated Commentary on the New Testament* (4 vols., 1875)
- *A Study in Human Nature* (1885)
- [*What is Christianity?*](https://archive.org/stream/ArenaMagazine-Volume03/9012-arena-volume03#page/n43/mode/2up) in: *The Arena* (1891)
- *Life of Christ* (1894)
- *The Evolution of Christianity* (1896) (Lowell Lectures, reissued by Cambridge University Press, 2009, `{{ISBN|978-1-108-00019-2}}`{=mediawiki})
- *The Theology of an Evolutionist* (1897)
- *Christianity and Social Problems* (1897)
- *Life and Letters of Paul* (1898)
- *The Life that Really is* (1899)
- *Why Go To Church?* (1900) (Published in \"The Day\'s Work Series\" by L. C
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# Lucius Afranius (poet)
**Lucius Afranius** was an ancient Roman comic poet who lived at the beginning of the 1st century BC.
## Life
Afranius\' comedies described Roman scenes and manners (the genre called *comoediae togatae*) and the subjects were mostly taken from the life of the lower classes (*comoediae tabernariae*). They were considered by some ancients to be frequently polluted with disgraceful amours, which, according to Quintilian, were only a representation of the conduct of Afranius. He depicted, however, Roman life with such accuracy that he is classed with Menander, from whom indeed he borrowed largely. He imitated the style of Gaius Titius, and his language is praised by Cicero. His comedies are spoken of in the highest terms by the ancient writers, and under the Empire they not only continued to be read, but were even acted, of which an example occurs in the time of Nero. They seem to have been well known even at the latter end of the 4th century AD.
## Quintilian\'s judgement {#quintilians_judgement}
The Spanish-Roman teacher of rhetoric Quintilian wrote of Afranius\'s plays:
: *Togātīs excellit Afrānius: utinam non inquināsset argūmenta puerōrum foedīs amōribus, mōrēs suōs fassus.*
: (\"Afranius excelled in Roman-style comedies: if only he hadn\'t polluted his plots with unseemly sexual affairs with boys, confessing his own habits.\")
Such is the generally accepted interpretation of this sentence. An alternative view is proposed by Welsh (2010), who, noting that there is no trace of pederasty or any lewdness in any of the quoted fragments of Afranius, proposed to translate the sentence \"if only he hadn\'t polluted his plots with disreputable love affairs (conducted) by boys\", something which Quintilian perhaps thought unsuited to the moralising tone of Roman comedies. A problem with this interpretation, as Welsh himself admits, is that in Roman literature the word *pueri* is usually used for the boys who are object of love affairs, not the young men who conduct them.
## Surviving titles and fragments {#surviving_titles_and_fragments}
Afranius wrote many comedies
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# London Post Office Railway
The **Post Office Railway**, known since 1987 as **Mail Rail**, is a `{{RailGauge|2ft|lk=on}}`{=mediawiki} narrow-gauge, driverless underground railway in London that was built by the Post Office with assistance from the Underground Electric Railways Company of London, to transport mail between sorting offices. Inspired by the Chicago Tunnel Company, it opened in 1927 and operated for 76 years until it closed in 2003. A museum within the former railway was opened in September 2017.
## Geography
The line ran from Paddington Head District Sorting Office in the west to the Eastern Head District Sorting Office at Whitechapel in the east, a distance of 6.5 mi. It had eight stations, the largest of which was underneath Mount Pleasant, but by 2003 only three stations remained in use because the sorting offices above the other stations had been relocated.
## History
### Use as post office railway {#use_as_post_office_railway}
In 1911, a plan evolved to build an underground railway 6+1/2 mi long from Paddington to Whitechapel serving the main sorting offices along the route; road traffic congestion was causing unacceptable delays. The plan was approved by the **`{{visible anchor|Post Office (London) Railway Act 1913}}`{=mediawiki}** (3 & 4 Geo. 5. c. cxvi). The contract to build the tunnels was won by John Mowlem and Co. Construction of the tunnels started in February 1915 from a series of shafts. Most of the line was constructed using the Greathead shield system, with limited amounts of hand-mining for connecting tunnels at stations.
The main line has a single 9 ft diameter tube with two tracks. Just before stations, tunnels diverge into two single-track 7 ft diameter tunnels leading to two parallel 25 ft diameter station tunnels. The main tube is at a depth of around 70 ft. Stations are at a much shallower depth, with a 1-in-20 gradient into the stations. The gradients assist in slowing the trains when approaching stations, and accelerating them away. There is also less distance to lift mail from the stations to the surface. At Oxford Circus the tunnel runs close to the Bakerloo line tunnel of the London Underground. The tunnel also runs under Selfridges as the recent 2018 refurbishment of the building revealed.
During 1917, work was suspended due to the shortage of labour and materials. By June 1924, track laying had started, and additional time was granted by the **`{{visible anchor|Post Office (London) Railway Act 1924}}`{=mediawiki}** (14 & 15 Geo. 5. c. lxxx). In February 1927, the first section, between Paddington and the West Central District Office, was made available for training. The line became available for the Christmas parcel post in 1927 and letters were carried from February 1928.
In 1954, plans were developed for a new Western District Office at Rathbone Place, which required a diversion, opening in 1958. It was not until 3 August 1965 that the new station and office were opened by the Postmaster General, Tony Benn. The disused section was used as a store tunnel; some parts of it still have the track in place.
In 1987, the railway changed its name to Mail Rail in celebration of its 60th anniversary, and some trains were rebuilt with more aerodynamic casings.
### Closure
A Royal Mail press release in April 2003 said that the railway would be closed and mothballed at the end of May that year. Royal Mail had earlier stated that using the railway was five times more expensive than using road transport for the same task. The Communication Workers Union claimed the actual figure was closer to three times more expensive but argued that this was the result of a deliberate policy of running the railway down and using it at only one-third of its capacity. A local governmental report by the Greater London Authority stated that the \"line carries an average of four million letters and parcels per day\" and was in support of continued use and criticized the increase of lorries on local roads, estimated to be 80 more truck loads per week. The railway was closed on 31 May 2003.
In April 2011, an urban exploration group called the \"Consolidation Crew\" published accounts of illicit access to the tunnels. Detailed photography and text revealed that the railway is still largely in good condition, despite some natural decay. More recently, media have been admitted to the tunnels as part of the pre-launch publicity for the Postal Museum. Photographs show much of the infrastructure in place.
A team from the University of Cambridge has taken over a short, double track section of unused Post Office tunnel near Liverpool Street Station, where a newly built tunnel for Crossrail is situated some two metres beneath. The study is to establish how the original cast-iron lining sections, which are similar to those used for many miles of railway under London, resist possible deformation and soil movement caused by the new works. Digital cameras, fibre optic deformation sensors, laser scanners and other low-cost instruments, reporting in real time, have been installed in the vacated tunnel. As well as providing information about the behaviour of the old construction materials, the scheme can also provide an early warning if the new tunnel bores are creating dangerous soil movement.
### Redevelopment and preservation {#redevelopment_and_preservation}
In October 2013, the British Postal Museum & Archive announced that it intended opening part of the network to the public. After approval was granted by Islington Council, work on the new museum and the railway began in 2014. Special tourist trains were installed in late 2016. It was planned to open a circular route, running beneath the depot at Mount Pleasant with a journey time of around 15 minutes, by mid-2017. The museum opened on 5 September.
In its first year of operation (2017--2018), the trains performed 9,000 trips totalling 6213 mi, with the railway and museum hosting over 198,000 visitors.
## Rolling stock {#rolling_stock}
The first stock was delivered in 1926 with the opening of the system. All stock used was electrically powered.
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# London Post Office Railway
## Rolling stock {#rolling_stock}
### Electric locomotives {#electric_locomotives}
- Original 1926 electric locomotives
### Electric units {#electric_units}
- 1927 Stock --- Original stock
- 1930 & 1936 Stock --- Replacement stock for 1927 Stock
- 1962 Stock --- Prototype stock
- 1980 Stock --- Replacement stock
Some trains have been preserved at the Launceston Steam Railway.
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# London Post Office Railway
## In fiction {#in_fiction}
- The railway features in the novel *The Horn of Mortal Danger* by Lawrence Leonard in which there is a connecting tunnel to a secret railway to the North London network. The only other known connection is in the disused tunnel between Highgate and the disused Cranley Gardens.
- A version of the railway is featured in the novel *The Great Game* by Lavie Tidhar. It takes mail to Buckingham Palace, and is run by the book\'s featured Simulacra.
- The railway appears in the film *Hudson Hawk* as \'Poste Vaticane\' in the Vatican City. Bruce Willis (as Hawk) stows away in one of the mail containers.
- A mail train system closely based on the railway is in Charlie Higson\'s third *Young Bond* book, *Double or Die*.
- The railway is prominent in Oliver Harris\'s 2014 book *Deep Shelter*.
- The railway features in Mark Leggatt\'s 2016 novel *The London Cage,* as a means for Connor Montrose to move about London. The International Thriller, a follow-up to *Names of the Dead*,*was* published by Scottish-based publisher Fledgling Press in June 2016.
- The railways make an appearance in Adrian Tchaikovsky\'s 2020 novel *The Doors of Eden* as Khan and Lee are being led by Stig towards a door to escape from pursuit by Rove\'s henchmen.
## Similar railways {#similar_railways}
A pneumatic underground railway was used by the Post Office in London between 1863 and 1874 using individual wheeled capsules, operated by the London Pneumatic Despatch Company.
In 1910, a 450 m tunnel railway opened in Munich, Germany between München Hauptbahnhof and the nearby Post office. The tunnels were damaged in World War II, restored in 1948 and partially rebuilt in 1966 to allow for the first Munich S-Bahn tunnel. Operations ceased in 1988.
Postal Telegraph and Telephone (Switzerland) opened the 340 m Post-U-Bahn (underground railway) in Zürich in 1938. It ran between Zürich Hauptbahnhof and the Sihlpost, Zürich\'s main post office. The track gauge was 60 cm, and the small electric railcar, which could carry 250 kg of mail, collected power from wires between the tracks. Operations ceased on 11 October 1980 when a rubber-tired system replaced the train.
The Chicago Tunnel Company, in operation between 1906 and 1959, delivered freight, parcels, and coal, and disposed of ash and excavation debris. It operated an elaborate network of `{{RailGauge|2ft}}`{=mediawiki} narrow-gauge track in 2.29 x tunnels running under the streets throughout the central business district including and surrounding the \"Loop\"
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# Lead and follow
In some types of partner dance, **lead** and **follow** are designations for the two dancers\' roles in a dance pairing. The leader is responsible for guiding the couple and initiating transitions to different dance steps and, in improvised dances, for choosing the dance steps to perform. The leader communicates choices to the follower, and directs the follower by means of subtle physical and visual signals, thereby allowing the pair to be smoothly coordinated.
The amount of direction given by the leader depends on several factors, including dance style, social context of the dance, and experience and personalities of the dancers. Traditionally, the male dance partner was the leader and the female dance partner was the follower. In the 21st century, it has become increasingly common to see partnerships that buck this dynamic, particularly in more socially progressive dance styles.
## Gender roles {#gender_roles}
Traditionally, the male dance partner is the leader and the female dance partner is the follower, though this is not always the case, such as in Schottische danced in the Madrid style where women lead and men follow (although this is not totally true: during the dance there is an exchange of roles, the leader becomes the follower and vice versa). Many social dance forms have a long history of same-sex (e.g. tango) and role-crossing partnerships, and there have been some changes to the strict gendering of partner dances in some competition or performance contexts. An example is a \"Jack and Jack\" dance contest.
## Communication
Partner dancing requires awareness and clear communication; this is essential both for safety and for the overall success of the dance. If following in the dance, it helps to maintain a centered readiness to the leader. This helps the follower be ready for cues both visually and physically. The leader in the dance will best support the follower by giving clear directions.
For the leader and follower to interact with each other, communication needs to occur between the dance couple. Dancers take cues through physical connection, with the follower using it to communicate feedback to the leader just as the leader uses it to suggest moves to the follower. The most accomplished dancers use connection as a line of communication which allows the leader to incorporate the follower\'s ideas, abilities, and creative suggestions into their own styling and selection of moves.
In many partner dances, the leader\'s steps differ from the follower\'s. In face-to-face positions, the follower generally \"mirrors\" the leader\'s footwork. For example, if the leader begins on their left foot, the follower will begin on their right foot. In choreographed pieces and other situations where the follower is in a tandem position or shadow position, the leader and follower will use the same footwork. Usually both partners move together as a unit, but in some dances the partners move in opposite directions - together and apart again.
In partner dancing, dancers seek to work together to create synchronized or complementary movements. The leader is largely responsible for *initiating* movement, whereas the follower\'s role is to *maintain* this movement (though they may choose not to). This process can be described as involving the initiation of momentum or \'energy\' (by the leader) and then the subsequent maintenance, exaggeration, decreasing or dissolving of this momentum by both partners. This momentum or energy may be manifested as movement (in its most obvious form), or in a range of more complex interactions between partners:
- Compression (where each partner \'compress\' the energy by bending joints and moving towards or \'into\' their partner, to varying degrees);
- Leverage (where one partner -- usually the leader -- exploits the development of compression or connection to shift their follower\'s weight or to \'ground\' (develop \'compression\' downwards, with the contact their feet make with the floor) themselves more thoroughly before initiating movement);
- Tension (is the opposite of compression - partners moving away from each other but still in contact)
It is also helpful for dancers to regard their partners in terms of their *points of balance* to help the leader initiate movements for their follower. These points of balance include the front-facing side of the shoulders, the front facing side of the hips, and the follower\'s center (the abdomen). If the leader wants to bring the follower close, the leader is to apply tension and draw the hand in and down toward the leader\'s own hip; to send the follower away, the leader would guide the hand toward the follower and add compression, signaling the move away.
### Obstruction avoidance {#obstruction_avoidance}
A general rule is that both leader and follower watch each other\'s back in a dance hall situation. Collision avoidance is one of the cases when the follower is required to \"backlead\" or at least to communicate about the danger to the leader. In travelling dances, such as waltz, common follower signals of danger are an unusual resistance to the leader, or a slight tap by the shoulder. In open-position dances, such as swing or Latin dances, maintaining eye contact with the partner is an important safety communication link.
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# Lead and follow
## Communication
### Weight transfer {#weight_transfer}
For partner dancers, using weight transfers is a way for a leader to communicate a \'lead\' for a dance step to a follower.
In another example, for a leader to have their follower walk forwards while connected, the leader begins by taking his or her center back, indicating a backward walking move. As the partners\' arms/points of contact move away from each other, they develop tension, which the follower may either break by dropping their arms or breaking the hold, or \'follow\' by moving.
A more experienced leader may realize (if only on an unconscious level) that the most effective execution of even this \"simple\" step is achieved by preparing for movement before the step begins.
The leader-follower connection facilitates this. The principles of leading and following are explored in contact improvisation of modern dance.
### Recovery from miscommunication {#recovery_from_miscommunication}
Sometimes a miscommunication will occur between the leader and follower. Techniques of the recovery of connection and synchronization vary from dance to dance, but below are a few common examples.
- In dances without obligatory body contact (Latin, swing, hustle, American Smooth), free spin recovers from anything.
- In dances danced in body contact (waltz, tango, quickstep, foxtrot) it is very important to recover the feet match. To recover, leaders may initiate a well-known (i.e. basic) step with slightly exaggerated sideways shift of weight to force the follower to free the required foot. For example, in waltz or foxtrot one might end a measure in the open promenade position, as there would then be no doubt as to the direction of the movement and which foot to use at the beginning of the next measure.
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# Lead and follow
## Lead
### Methods to lead {#methods_to_lead}
- Body lead
- Arm lead
#### Body lead vs. arm lead {#body_lead_vs._arm_lead}
A body lead occurs where the leader initiates a lead by moving their body, which moves their arm(s), and thus transmits a lead to the follower. \'Body lead\' means much the same as \'weight transfer\'. An arm lead occurs where the leader moves their arm(s) without moving their body, or moves their body in a different direction to their arm. While an \'arm lead\' without the transfer of weight (or movement of the body) on the part of the leader is often a marker of an inexperienced or poorly taught dancer, the process of leading and following, particularly at an advanced level, often involves the contrasting uses of weight transfers and \'arm moves\'. As an example, a leader may lead a follower back onto their right foot through the leader\'s own weight transfer forwards onto their left foot; yet at the same time turn the follower\'s torso to the left from above the hips.
### Techniques of leading {#techniques_of_leading}
The leader has to communicate the direction of the movement to the follower. Traditionally, the leader\'s right hand is on the follower\'s back, near the lowest part of the shoulder-blade. This is the strongest part of the back and the leader can easily pull the follower\'s body inwards. To enable the leader to communicate a step forward (backward for the follower) the follower has to constantly put a little weight against the leader\'s right hand. When the leader goes forward, the follower will naturally go backwards.
An important leading mechanism is the leader\'s left hand, which usually holds the follower\'s right hand. At no point should it be necessary for any partner to firmly grab the other\'s hand. It is sufficient to press the hand or even only finger tips slightly against each other, the follower\'s hand following the leader\'s hand.
Another important leading mechanism is hip contact. Though not possible in traditional Latin dances like Rumba, Cha-cha, Tango Argentino because of partner separation, hip contact is a harmonious and sensual way of communicating movement to the partner, used primarily in Standard or Ballroom dances (English / slow waltz, European tango, quickstep etc.) and Caribbean dances.
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# Lead and follow
## Follow
### Types of follow {#types_of_follow}
- Active follow
- Passive follow
### Techniques of following {#techniques_of_following}
### Backleading
Backleading is when a follower is executing steps without waiting for, or contrary to the lead\'s lead. Both are considered bad dancing habits because it makes the follower difficult to lead and dance with.
Backleading can be a teaching tool that is often used intentionally by an instructor when dancing with a student lead, in order to help them learn the desired technique.
Backleading sounds similar to \"hijacking\", and indeed it is often used in place of \"hijacking\". However the two terms have significant differences, stemming from intentions. The first difference is superficial; hijacking is usually an occasional \"outburst\" from the follower, who otherwise diligently follows the lead, while a \"backlead\" may refer to a consistent habit. The second difference is more significant; hijacking is an actual reversal of roles, meaning that the hijacker leads the leader and takes control of the dance, while backleading only takes care of the follower.
### Hijacking
Sometimes the follower steals the lead and the couple reverses roles for some time. This is called *hijacking* (also known as *lead stealing*). Hijacking requires experience and good connection, since without proper timing it may look like sloppy dancing. A signal for hijacking is typically an unusually changed (mostly, increased) stress in the connection from the follower\'s side. \"Unusually\" meaning more than typically required for the execution of the current step (by these partners). For a follower to hijack, they must be sure that the lead will understand or at least guess the follower\'s intentions
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# Lightworks
**Lightworks** is a freemium non-linear editing system (NLE) for editing and mastering digital video. It was an early developer of computer-based non-linear editing systems, and has been in development since 1998. The development of an open-source version was announced on April 11, 2010. However, no source code of the program has been released. In July 2020, a Lightworks product manager confirmed that they \"still hope to announce something in the future\" about Lightworks\' open source development.
## Features
The free version comes with a limited number of features:
- Multicam editing
- Second monitor output
- Ability to import a range of file types
- Export to Vimeo (H.264/MPEG-4) up to 720p
- Export to YouTube (H.264/MPEG-4) up to 720p
The free version cannot export to DVD or Blu-ray, but can export to a hard drive (since Lightworks 14).
## History
OLE Limited was founded in 1994 by Paul Bamborough, Nick Pollock and Neil Harris. In 1995 it was sold to Tektronix. In 1999 it was sold on to the newly formed Lightworks Inc., then owned by Fairlight Japan, and then purchased by Gee Broadcast in May 2004.
### Gee Broadcast ownership, 2004--2009 {#gee_broadcast_ownership_20042009}
Under Gee Broadcast ownership, new product releases resumed with the release of the Lightworks *Touch* range, and the *Alacrity* and *Softworks* ranges for SD & HD editing. Softworks offered the Lightworks User Interface and toolset in a software only package for laptops or office workstations. Alacrity supported dual outputs while the same facility was available for Softworks users as an option.
### EditShare ownership, 2009--2020 {#editshare_ownership_20092020}
In August 2009, the UK and US based company *EditShare* acquired Gee Broadcast and the Lightworks editing platform from, along with their video server system *GeeVS*.
At the annual convention of the National Association of Broadcasters, NAB Show, on 11 April 2010, EditShare announced that they plan to transform Lightworks into Lightworks Open Source. It was presented at IBC in Amsterdam September 2010.
On 9 November 2010, EditShare announced that Lightworks would be downloadable on 29 November of the same year, at first exclusively for the users who had registered during the initial announcement, but subsequently publishing the software as \"public beta\".
EditShare planned the release of the open source version in Q4 of 2011, after they finished code review. They plan to make money from proprietary plugins offered in their associated online shop, including plugins needed to access professional video formats. Shortly before the scheduled release date of 29 November 2011, EditShare announced that an open source release of the software would be temporarily delayed, but did not announce a new release date. The announcement noted that they were not yet satisfied with the stability of the new version.
#### Windows version released at NAB 2012 {#windows_version_released_at_nab_2012}
After an 18-month beta program, EditShare released Lightworks 11, for Windows only, on 28 May 2012. The non beta release of Lightworks includes a host of new features for editors, and runs on wide range of PC hardware. The software was re-designed and re-written for portability (versions for Linux and Mac OS X have also been released) and now supports many more codecs including AVCHD, H.264, AVC-Intra, DNxHD, ProRes, Red R3D, DPX, XDCAM HD 50, XDCAM EX, DVD, Blu-ray, and 4K, but only for the paid Pro version. The free version supports DV, MPEG, Uncompressed and other codecs for both import and export.
#### Windows version 11.1 released 29 May 2013 {#windows_version_11.1_released_29_may_2013}
On 29 May 2013, v11.1 stable release was made available for download. A major development in the Pro version is improved performance of the H.264/AVC codec in MP4 and MOV containers. This makes it possible to edit this format natively, even with less powerful CPUs. This should interest HDSLR and GoPro camera users.`{{Why?|reason=Systems with discrete GPUs which anyone doing any sort of video editing or raw developing from DSLRs back then had were capable of hardware decoding H.264, which wasn't new at all. The larger issue with video editing was and still is the computing power required to apply any filters, transitions, etc to video quickly enough to make editing them painless|date=November 2024}}`{=mediawiki} Native editing of H.264 MTS files has been possible since version 11.0.3.
This version of Lightworks has also replaced HASP with the new EditShare Licensing System (ELS), which eliminates some installation problems.`{{Which?|reason=Probably the ones that revolved around hardware locks for software being absolute garbage, Lightworks Free users can now download the 64 bit version, which was previously limited to Pro users.|date=April 2025}}`{=mediawiki} The Free version now also comes with a 30-day Pro Trial period.
#### Linux version announced at IBC 2012 {#linux_version_announced_at_ibc_2012}
EditShare demonstrated the Linux version at the NAB in Las Vegas in April 2012, and posted a video of it running on Ubuntu on their YouTube channel. At IBC in Amsterdam in September, an updated Linux demo was presented, and EditShare announced that the initial Linux alpha version would become available on 30 October . Lightworks 11 alpha for Linux was released on 30 April 2012, but only to a limited audience. The Linux version of Lightworks was made available as a Public Beta on 30 April 2013.
#### Lightworks 12 beta released for Windows, Linux and Mac {#lightworks_12_beta_released_for_windows_linux_and_mac}
On 8 August 2014, the first beta of Lightworks version 12 working on Windows, Linux and Mac was released.
#### Lightworks 12.6 released for Windows, Linux and Mac {#lightworks_12.6_released_for_windows_linux_and_mac}
On 29 August 2015, Lightworks version 12.5 for Windows, Linux and Mac was released.
#### Lightworks 12.7 released for Windows, Linux and Mac {#lightworks_12.7_released_for_windows_linux_and_mac}
On 4 February 2016, Lightworks version 12.6 for Windows, Linux and Mac was released.
#### Lightworks 14.5 released for Windows, Linux and Mac {#lightworks_14.5_released_for_windows_linux_and_mac}
In October 2018, Lightworks released version 14.5 for Windows, Linux and Mac platforms. 14.5 added a vast array of new features including variable frame rate support, a huge amount of codec support including Red Cinema R3D, Cineform and Blackmagic Q1 codecs.
### LWKS Software Ltd ownership, 2020-present {#lwks_software_ltd_ownership_2020_present}
In September 2020, a new company, LWKS Software Ltd, founded in August of the same year by two members of the development team, took ownership of Lightworks, as well as QScan AQC software. the agreement also mentions Key member of the development teams of both software joining the new company.
## Users
Over the years, Lightworks has confirmed that over 4-million downloads and registrations had taken place. There are several films that used the editing software and the most example were the series of films directed by Martin Scorsese with the film editor Thelma Schoonmaker being the only known user.
Film title Year Director Editor
------------------------------ ------ ------------------- --------------------
*Pulp Fiction* 1994 Quentin Tarantino Sally Menke
*The Cure* 1995 Peter Horton Anthony Sherin
*Congo* 1995 Frank Marshall Anne V. Coates
*Heat* 1995 Michael Mann Dov Hoenig
*Braveheart* 1995 Mel Gibson Steven Rosenblum
*Romeo + Juliet* 1996 Baz Luhrmann Jill Bilcock
*Broken Arrow* 1996 John Woo John Wright
*L.A
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# Lost Generation
The **Lost Generation** was the demographic cohort that reached early adulthood during World War I, and preceded the Greatest Generation. The social generation is generally defined as people born from 1883 to 1900, coming of age in either the 1900s or the 1910s, and were the first generation to mature in the 20th century. The term is also particularly used to refer to a group of American expatriate writers living in Paris during the 1920s. Gertrude Stein is credited with coining the term, and it was subsequently popularized by Ernest Hemingway, who used it in the epigraph for his 1926 novel *The Sun Also Rises*: \"You are all a lost generation.\" \"Lost\" in this context refers to the \"disoriented, wandering, directionless\" spirit of many of the war\'s survivors in the early interwar period.
In the wake of the Industrial Revolution, Western members of the Lost Generation grew up in societies that were more literate, consumerist, and media-saturated than ever before, but which also tended to maintain strictly conservative social values. Young men of the cohort were mobilized on a mass scale for World War I, a conflict that was often seen as the defining moment of their age group\'s lifespan. Young women also contributed to and were affected by the war, and in its aftermath gained greater freedoms politically and in other areas of life. The Lost Generation was also heavily vulnerable to the Spanish flu pandemic and became the driving force behind many cultural changes, particularly in major cities during what became known as the Roaring Twenties.
Later in their midlife, they experienced the economic effects of the Great Depression and often saw their own sons leave for the battlefields of World War II. In the developed world, they tended to reach retirement and average life expectancy during the decades after the conflict, but some significantly outlived the norm. The Lost Generation became completely ancestral when the last surviving person who was known to have been born in the Lost Generation or during the 19th century, Nabi Tajima, died in 2018 at age 117.
## Terminology
The first named generation, the term \"Lost Generation\" is used for the young people who came of age around the time of World War I. In Europe, they are mostly known as the \"Generation of 1914\", for the year World War I began. In France, they were sometimes called the *Génération du feu*, the \"(gun)fire generation\". In the United Kingdom, the term was originally used for those who died in the war,`{{r|aftermath}}`{=mediawiki} and often implicitly referred to upper-class casualties who were perceived to have died disproportionately, robbing the country of a future elite.`{{r|winter}}`{=mediawiki} Many felt that \"the flower of youth and the best manhood of the peoples \[had\] been mowed down\", for example, such notable casualties as the poets Isaac Rosenberg, Rupert Brooke, Edward Thomas, and Wilfred Owen,`{{r|bbc}}`{=mediawiki} composer George Butterworth, and physicist Henry Moseley.
## Date and age range definitions {#date_and_age_range_definitions}
Authors William Strauss and Neil Howe define the Lost Generation as the cohort born from 1883 to 1900, who came of age during World War I and the Roaring Twenties.`{{r|strauss}}`{=mediawiki}
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# Lost Generation
## Characteristics
### As children and adolescents {#as_children_and_adolescents}
#### Family life and upbringing {#family_life_and_upbringing}
When the Lost Generation was growing up, the ideal family arrangement was generally seen as the man of the house being the breadwinner and primary authority figure while his wife dedicated herself to caring for the home and children. Most, even less well-off, married couples attempted to conform to this ideal. It was common for family members of three different generations to share a home. Wealthier households also tended to include domestic servants, though their numbers would have varied from a single maid to a large team depending on how well-off the family was.
Public concern for the welfare of children was intensifying by the later 19th century with laws being passed and societies formed to prevent their abuse. The state increasingly gained the legal right to intervene in private homes and family life to protect minors from harm. However, beating children for misbehaviour was not only common but viewed as the duty of a responsible caregiver.
#### Health and living conditions {#health_and_living_conditions}
thumb\|left\|upright=0.85\|*The Child\'s Bath* by Mary Cassatt from 1893 of a woman giving a child a wash. The link between hygiene and good health was becoming better understood in Western society by the end of the 19th century and frequent bathing had become common.
Sewer systems designed to remove human waste from urban areas had become widespread in industrial cities by the late 19th century, helping to reduce the spread of diseases such as cholera. Legal standards for the quality of drinking water also began to be introduced. However, the introduction of electricity was slower, and during the formative years of the Lost Generation gas lights and candles were still the most common form of lighting.
Though statistics on child mortality dating back to the beginning of the Lost Generation\'s lifespan are limited, the Centers for Disease Control and Prevention report that in 1900 one in ten American infants died before their first birthday. Figures for the United Kingdom state that during the final years of the 19th century, mortality in the first five years of childhood was plateauing at a little under one in every four births. At around one in three in 1800, the early childhood mortality rate had declined overall throughout the next hundred years but would fall most sharply during the first half of the 20th century, reaching less than one in twenty by 1950. This meant that members of the Lost Generation were somewhat less likely to die at a very early age than their parents and grandparents, but were significantly more likely to do so than children born even a few decades later.
#### Literacy and education {#literacy_and_education}
Laws restricting child labour in factories had begun to appear from around 1840 onwards and by the end of the 19th century, compulsory education had been introduced throughout much of the Western world for at least a few years of childhood. By 1900, levels of illiteracy had fallen to less than 11% in the United States, around 3% in Great Britain, and only 1% in Germany. However, the problems of illiteracy and lack of school provision or attendance were felt more acutely in parts of Eastern and Southern Europe.
Schools of this time period tended to emphasise strict discipline, expecting pupils to memorize information by rote. To help deal with teacher shortages, older students were often used to help supervise and educate their younger peers. Dividing children into classes based on age became more common as schools grew.
However, while elementary schooling was becoming increasingly accessible for Western children at the turn of the century, secondary education was still much more of a luxury. Only 11% of American fourteen to seventeen-year-olds were enrolled at High School in 1900, a figure which had only marginally increased by 1910. Though the school leaving age was officially meant to be 14 by 1900, until the First World War, most British children could leave school through rules put in place by local authorities at 12 or 13 years old. It was not uncommon at the end of the 19th century for Canadian children to leave school at nine or ten years old.
#### Leisure and play {#leisure_and_play}
By the 1890s, children\'s toys entered into mass production. In 1893, the British toy company William Britain revolutionized the production of toy soldiers by devising the method of hollow casting, making soldiers that were cheaper and lighter than their competitors. This led to metal toy soldiers, which had previously been the preserve of boys from wealthier families, gaining mass appeal during the late Victorian and Edwardian period. Dolls often sold by street vendors at a low price were popular with girls. Teddy bears appeared for the first time in the early 1900s. Tin plated penny toys were also sold by street sellers for a single penny.
The turn of the 20th century saw a surge in public park building in parts of the west to provide public space in rapidly growing industrial towns. They provided a means for children from different backgrounds to play and interact together, sometimes in specially designed facilities. They held frequent concerts and performances.
#### Popular culture and mass media {#popular_culture_and_mass_media}
Beginning around the middle of the 19th century, magazines of various types which had previously mainly targeted the few that could afford them found rising popularity among the general public. The latter part of the century not only saw rising popularity for magazines targeted specifically at young boys but the development of a relatively new genre aimed at girls.
A significant milestone was reached in the development of cinema when, in 1895, projected moving images were first shown to a paying audience in Paris. Early films were very short (generally taking the form of newsreels, comedic sketches, and short documentaries). They lacked sound but were accompanied by music, lectures, and a lot of audience participation. A notable film industry had developed by the start of the First World War.
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# Lost Generation
## Characteristics
### As young adults {#as_young_adults}
#### Military service in the First World War {#military_service_in_the_first_world_war}
The Lost Generation is best known as being the cohort that primarily fought in World War I. More than 70 million people were mobilized during the First World War, around 8.5 million of whom were killed and 21 million wounded in the conflict. About 2 million soldiers are believed to have been killed by disease, while individual battles sometimes caused hundreds of thousands of deaths.
Around 60 million of the enlisted originated from the European continent, which saw its younger men mobilized on a mass scale. Most of Europe\'s great powers operated peacetime conscription systems where men were expected to do a brief period of military training in their youth before spending the rest of their lives in the army reserve. Nations with this system saw a huge portion of their manpower directly invested in the conflict: 55% of male Italians and Bulgarians aged 18 to 50 were called to military service. Elsewhere the proportions were even higher: 63% of military-aged men in Serbia, 78% in Austro-Hungary, and 81% of military-aged men in France and Germany served. Britain, which traditionally relied primarily on the Royal Navy for its security, was a notable exception to this rule and did not introduce conscription until 1916. Around 5 million British men fought in the First World War out of a total United Kingdom population of 46 million including women, children, and men too old to bear arms.
Additionally, nations recruited heavily from their colonial empires. Three million men from around the British Empire outside the United Kingdom served in the British Army as soldiers and laborers, while France recruited 475,000 soldiers from its colonies. Other nations involved include the United States which enlisted 4 million men during the conflict and the Ottoman Empire which mobilized 2,850,000 soldiers.
Beyond the extent of the deaths, the war had a profound effect on many of its survivors, giving many young men severe mental health problems and crippling physical disabilities. The war also unsettled many soldiers\' sense of reality, who had gone into the conflict with a belief that battle and hardship was a path to redemption and greatness. When years of pain, suffering, and loss seemed to bring about little in the way of a better future, many were left with a profound sense of disillusionment.
#### Young women in the 1910s and 1920s {#young_women_in_the_1910s_and_1920s}
Though soldiers on the frontlines of the First World War were exclusively men, women contributed to the war effort in other ways. Many took the jobs men had left in previously male-dominated sectors such as heavy industry, while some even took on non-combat military roles. Many, particularly wealthier women, took part in voluntary work to contribute to the war effort or to help those suffering due to it, such as the wounded or refugees. Often they were experiencing manual labor for the first time. However, this reshaping of the female role led to fears that the sexes having the same responsibilities would disrupt the fabric of society and that more competition for work would leave men unemployed and erode their pay. Most women had to exit the employment they had taken during the war as soon as it concluded.
The war also had a personal impact on the lives of female members of the Lost Generation. Many women lost their husbands in the conflict, which frequently meant losing the main breadwinner of the household. However, war widows often received a pension and financial assistance to support their children. Even with some economic support, raising a family alone was often financially difficult and emotionally draining, and women faced losing their pensions if they remarried or were accused of engaging in frowned-upon behavior. In some cases, grief and the other pressures on them drove widows to alcoholism, depression, or suicide. Additionally, the large number of men killed in the First World War made it harder for many young women who were still single at the start of conflict to get married; this accelerated a trend towards them gaining greater independence and embarking on careers.
Women\'s gaining of political rights sped up in the Western world after the First World War, while employment opportunities for unmarried women widened. This time period saw the development of a new type of young woman in popular culture known as a flapper, who was known for their rebellion against previous social norms. They had a physically distinctive appearance compared to their predecessors only a few years earlier, cutting their hair into bobs, wearing shorter dresses and more makeup, while taking on a new code of behaviour filled with more recklessness, party-going, and overt sexuality.
#### Aftermath of the First World War {#aftermath_of_the_first_world_war}
The aftermath of the First World War saw substantive changes in the political situation, including a trend towards republicanism, the founding of many new relatively small nation-states which had previously been part of larger empires, and greater suffrage for groups such as the working class and women. France and the United Kingdom both gained territory from their enemies, while the war and the damage it did to the European empires are generally considered major stepping stones in the United States\' path to becoming the world\'s dominant superpower. The German and Italian populations\' resentment against what they generally saw as a peace settlement that took too much away from the former or did not give enough to the latter fed into the fascist movements, which would eventually turn those countries into totalitarian dictatorships. For Russia, the years after its revolution in 1917 were plagued by disease, famine, terror, and civil war eventually concluded in the establishment of the Soviet Union. The immediate post-World War One period was characterized by continued political violence and economic instability. The late 1910s saw the Spanish flu pandemic, which was unusual in the sense that it killed many younger adults of the same Lost Generation age group that had mainly died in the war. Later, especially in major cities, much of the 1920s is considered to have been a more prosperous period when the Lost Generation, in particular, escaped the suffering and turmoil they had lived through by rebelling against the social and cultural norms of their elders.
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# Lost Generation
## Characteristics
### In midlife {#in_midlife}
#### 1930s
##### Politics and economics {#politics_and_economics}
This more optimistic period was short-lived, however, as 1929 saw the beginning of the Great Depression, which would continue throughout the 1930s and become the longest and most severe financial downturn ever experienced in Western industrialized history. Though it had begun in the United States, the crises led to sharp increases in worldwide unemployment, reductions in economic output and deflation. The depression was also a major catalyst for the rise of Nazism in Germany and the beginnings of its quest to establish dominance over the European continent, which would eventually lead to World War II in Europe. Additionally, the 1930s saw the less badly damaged Imperial Japan engage in its own empire-building, contributing to conflict in the Far East, where some scholars have argued the Second World War began as early as 1931.
##### Popular media {#popular_media}
The 1930s saw rising popularity for radio, with the vast majority of Western households having access to the medium by the end of the decade. Programming included soap operas, music, and sport. Educational broadcasts were frequently available. The airwaves also provided a source of news and, particularly for the era\'s autocratic regimes, an outlet for political propaganda.
#### Second World War {#second_world_war}
When World War II broke out in 1939, the Lost Generation faced a major global conflict for the second time in their lifetime, and now often had to watch their sons go to the battlefield. The place of the older generation who had been young adults during World War I in the new conflict was a theme in popular media of the time period, with examples including *Waterloo Bridge* and *Old Bill and Son.* Civil defense organizations designed to provide a final line of resistance against invasion and assist in home defense more broadly recruited heavily from the older male population. Like in the First World War, women helped to make up for labour shortages caused by mass military recruitment by entering more traditionally masculine employment and entering the conflict more directly in female military branches and underground resistance movements. However, those in middle age were generally less likely to become involved in this kind of work than the young. This was particularly true of any kind of military involvement.
### In later life {#in_later_life}
In the West, the Lost Generation tended to reach the end of their working lives around the 1950s and 1960s. For those members of the cohort who had fought in World War I, their military service frequently was viewed as a defining moment in their lives even many years later. Retirement notices of this era often included information on a man\'s service in the First World War.
Though there were slight differences between individual countries and from one year to the next, the average life expectancy in the developed world during the 1950s, 1960s and early 1970s was typically around seventy years old. However, some members of the Lost Generation outlived the norm by several decades. Nabi Tajima, the last surviving person known to have been born in the 19th century, died in 2018. The final remaining veteran to have served in World War I in any capacity was Florence Green, who died in 2012, while Claude Choules, the last veteran to have been involved in combat, had died the previous year. However, these individuals were born in 1902 and 1901 respectively, putting them outside the usual birth years for the Lost Generation.
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# Lost Generation
## In literature {#in_literature}
thumb\|right\|upright=0.9\|Gertrude Stein with Ernest Hemingway\'s son Jack in 1924. Stein is credited with bringing the term \"Lost Generation\" into use.
In his memoir *A Moveable Feast* (1964), published after Hemingway\'s and Stein\'s deaths, Ernest Hemingway writes that Gertrude Stein heard the phrase from a French garage owner who serviced Stein\'s car. When a young mechanic failed to repair the car quickly enough, the garage owner shouted at the young man, \"You are all a {{\'-}}*génération perdue*{{\'}}.\"`{{r|hemingway|page=29}}`{=mediawiki} While telling Hemingway the story, Stein added: \"That is what you are. That\'s what you all are \... all of you young people who served in the war. You are a lost generation.\"`{{r|hemingway|page=29}}`{=mediawiki} Hemingway thus credits the phrase to Stein, who was then his mentor and patron.
The 1926 publication of Hemingway\'s *The Sun Also Rises* popularized the term; that novel serves to epitomize the post-war expatriate generation.`{{r|mellow1992|page=302}}`{=mediawiki} However, Hemingway later wrote to his editor Max Perkins that the \"point of the book\" was not so much about a generation being lost, but that \"the earth abideth forever\".`{{r|baker|page=82}}`{=mediawiki} Hemingway believed the characters in *The Sun Also Rises* may have been \"battered\" but were not lost.`{{r|baker|page=82}}`{=mediawiki}
Consistent with this ambivalence, Hemingway employs \"Lost Generation\" as one of two contrasting epigraphs for his novel. In *A Moveable Feast*, Hemingway writes, \"I tried to balance Miss Stein\'s quotation from the garage owner with one from Ecclesiastes.\" A few lines later, recalling the risks and losses of the war, he adds: \"I thought of Miss Stein and Sherwood Anderson and egotism and mental laziness versus discipline and I thought \'who is calling who a lost generation?{{\'\"}}`{{r|hemingway|pages=29–30}}`{=mediawiki}
### Themes
The writings of the Lost Generation literary figures often pertained to the writers\' experiences in World War I and the years following it. It is said that the work of these writers was autobiographical based on their use of mythologized versions of their lives. One of the themes that commonly appear in the authors\' works is decadence and the frivolous lifestyle of the wealthy. Both Hemingway and F. Scott Fitzgerald touched on this theme throughout the novels *The Sun Also Rises* and *The Great Gatsby*. Another theme commonly found in the works of these authors was the death of the American Dream, which is exhibited throughout many of their novels. It is particularly prominent in *The Great Gatsby*, in which the character Nick Carraway comes to realize the corruption that surrounds him.
### Notable figures {#notable_figures}
Notable figures of the Lost Generation include F. Scott Fitzgerald, Thomas Wolfe, Gertrude Stein, Ernest Hemingway, Dorothy Parker, T. S. Eliot, Ezra Pound, Jean Rhys, Henry Strater, and Sylvia Beach
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# Lynx (web browser)
**Lynx** is a customizable text-based web browser for use on cursor-addressable character cell terminals. `{{As of|2025}}`{=mediawiki}, it is the oldest web browser still being maintained, having started in 1992.
## History
Lynx was a product of the Distributed Computing Group within Academic Computing Services of the University of Kansas. It was initially developed in 1992 by a team of students and staff at the university (Lou Montulli, Michael Grobe and Charles Rezac) as a hypertext browser used solely to distribute campus information as part of a *Campus-Wide Information System* and for browsing the Gopher space. Beta availability was announced to Usenet on 22 July 1992. In 1993, Montulli added an Internet interface and released a new version (2.0) of the browser.
, the support of communication protocols in Lynx is implemented using a version of libwww, forked from the library\'s code base in 1996. The supported protocols include Gopher, HTTP, HTTPS, FTP, NNTP and WAIS. Support for NNTP was added to libwww from ongoing Lynx development in 1994. Support for HTTPS was added to Lynx\'s fork of libwww later, initially as patches due to concerns about encryption.`{{Dead link|date=September 2022}}`{=mediawiki}
Garrett Blythe created DosLynx in April 1994 and later joined the Lynx effort as well. Foteos Macrides ported much of Lynx to VMS and maintained it for a time. In 1995, Lynx was released under the GNU General Public License, and is now maintained by a group of volunteers led by Thomas Dickey.
## Features
Browsing in Lynx consists of highlighting the chosen link using cursor keys, or having all links on a page numbered and entering the chosen link\'s number. Current versions support SSL and many HTML features. Tables are formatted using spaces, while frames are identified by name and can be explored as if they were separate pages. Lynx is not inherently able to display various types of non-text content on the web, such as images and video, but it can launch external programs to handle it, such as an image viewer or a video player.
Unlike most web browsers, Lynx does not support JavaScript, which many websites require to work correctly.
The speed benefits of text-only browsing are most apparent when using low bandwidth internet connections, or older computer hardware that may be slow to render image-heavy content.
### Privacy
Because Lynx does not support graphics, web bugs that track user information are not fetched, meaning that web pages can be read without the privacy concerns of graphic web browsers. However, Lynx does support HTTP cookies, which can also be used to track user information. Lynx therefore supports cookie whitelisting and blacklisting, or alternatively cookie support can be disabled permanently.
As with conventional browsers, Lynx also supports browsing histories and page caching, both of which can raise privacy concerns.
### Configurability
Lynx supports both command-line options and configuration files. There are 142 command-line options according to its help message. The template configuration file `lynx.cfg` lists 233 configurable features. There is some overlap between the two approaches to configuration, although there are command-line options such as `-restrict` which are not matched in `lynx.cfg`. In addition to pre-set options by command-line and configuration file, Lynx\'s behavior can be adjusted at runtime using its options menu. Again, there is some overlap between the settings. Lynx implements many of these runtime optional features, optionally (controlled through a setting in the configuration file) allowing the choices to be saved to a separate writable configuration file. The reason for restricting the options which can be saved originated in a usage of Lynx which was more common in the mid-1990s, i.e., using Lynx itself as a front-end application to the Internet accessed by dial-in connections.
### Accessibility
Because Lynx is a text-based browser, it can be used for internet access by visually impaired users on a refreshable braille display and is easily compatible with text-to-speech software. As Lynx substitutes images, frames and other non-textual content with the text from `alt`, `name` and `title` HTML attributes and allows hiding the user interface elements, the browser becomes specifically suitable for use with cost-effective general purpose screen reading software. A version of Lynx specifically enhanced for use with screen readers on Windows was developed at Indian Institute of Technology Madras.
### Remote access {#remote_access}
Lynx is also useful for accessing websites from a remotely connected system in which no graphical display is available. Despite its text-only nature and age, it can still be used to effectively browse much of the modern web, including performing interactive tasks such as editing Wikipedia.
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# Lynx (web browser)
## Features
### Web design and robots {#web_design_and_robots}
Since Lynx will take keystrokes from a text file, it is still very useful for automated data entry, web page navigation, and web scraping. Consequently, Lynx is used in some web crawlers. Web designers may use Lynx to determine the way in which search engines and web crawlers see the sites that they develop. Online services that provide Lynx\'s view of a given web page are available.
Lynx is also used to test websites\' performance. As one can run the browser from different locations over remote access technologies like Telnet and SSH, one can use Lynx to test the website\'s connection performance from different geographical locations simultaneously. Another possible web design application of the browser is quick checking of the site\'s links.
## Supported platforms {#supported_platforms}
Lynx was originally designed for Unix-like operating systems. It was ported to VMS soon after its public release and to other systems, including DOS, Microsoft Windows, Classic Mac OS and OS/2. It was included in the default OpenBSD installation from OpenBSD 2.3 (May 1998) to 5.5 (May 2014), being in the main tree prior to July 2014, subsequently being made available through the ports tree. Lynx can also be found in the repositories of most Linux distributions, as well as in the Homebrew, Fink, and MacPorts repositories for macOS. Ports to BeOS, MINIX, QNX, AmigaOS and OS/2 are also available.
The sources can be built on many platforms, such as Google\'s Android operating system
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# Lynx (programming language)
**Lynx** is a programming language for large distributed networks, using remote procedure calls. It was developed by the University of Wisconsin--Madison in 1984 for the Charlotte multicomputer operating system.
In 1986 at the University of Rochester Lynx was ported to the Chrysalis operating system running on a BBN Butterfly multiprocessor
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# Lake Abitibi
**Lake Abitibi** (*Lac Abitibi*, *Aabitibiiwi-zaaga'igan*) is a shallow lake in northeastern Ontario and western Quebec, Canada. The lake, which lies within the vast Clay Belt, is separated in two distinct portions by a short narrows, making it actually two lakes. Its total area is 931 km2, and net area 903 km2. The lake is shallow and studded with islands. Its shores and vicinity are covered with small timber.
Its outlet is the Abitibi River, a tributary of the Moose River, which empties into James Bay. The lake takes its name from the river. \"Abitibi\" comes from the Algonquin words *abitah*, meaning middle and *nipi* meaning water, possibly a reference to its geographic location between the Harricana (from the Algonquin word *Nanikana*, meaning \"the main way\") to the east and the Kapuskasing--Mattagami river system to the west.
Water levels on the lake are influenced by the Twin Falls Dam on the Abitibi River.
Portions of Lake Abitibi\'s southern shores and a section of the Abitibi River are part of the Abitibi-de-Troyes Provincial Park. The islands in Ontario\'s portion of the lake are protected in the Lake Abitibi Islands Provincial Park. The entire McDougall Point Peninsula, that separates the lake in two, is part of the 6036 ha Mcdougal Point Peninsula Conservation Reserve.
Pointe Abitibi at the mouth of the Duparquet River is a National Historic Site of Canada. This 272 ha site, known as Apitipik National Historic Site of Canada, was a summer gathering place for the Abitibiwinnik until 1956 and the location of several trading posts between 1686 and 1922.
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# Lake Abitibi
## History
Artifacts dating to the Late Archaic period have been found at Lake Abitibi.
Application of *Abitibi* to describe the lake and the people living in the area around it was first noted in The Jesuit Relations in 1640. One of the first Europeans in this area was Pierre de Troyes, who built a post on Lake Abitibi when he was on his way to capture English HBC posts on James Bay in 1686. The Abitibi Post lay halfway between trading posts on James Bay and those on the Ottawa River and was in continuous existence throughout the French period.
The lake was part of the canoe route from James Bay to Montreal, via the Moose and Abitibi Rivers, then a series of intermediate streams and portages to Lake Temiskaming and the Ottawa River.
After the British conquered Canada in 1763, free traders either took over the French fort or built another post on the lake, providing strong trading competition to the main Hudson\'s Bay Company (HBC) fort at Moose Factory and the HBC outpost at Frederick House. This moved the HBC to set up a post, called Abitibi House, on Lake Abitibi in 1794, located on the peninsula at the mouth of the Duparquet River. In subsequent decades this post, as well as competing posts of the North West Company, were rebuilt or moved to various locations around the lake and its islands. Being unproductive due to competition, the HBC abandoned Abitibi House in 1811. When two companies merged in 1821, the HBC took over the trading post of the North West Company on Lake Abitibi.
The construction of the Grand Trunk Pacific Railway (now Canadian National Railway) through this district made it of some importance at the start of the 20th century.
## Lake Abitibi Islands {#lake_abitibi_islands}
The Lake Abitibi Islands Provincial Park protects nearly all the islands on the Ontario side of Lake Abitibi. It includes 786 islands, from tiny shoals to large islands of up to 550 ha. Some of the larger islands are Deer, Dominion, and St. Patrick, as well as the Mistaken Islands (the largest island in the lake, Nepawa Island, is not part of the park since it is in Clerval, Quebec). The park was created in 2005 when the Abitibi-De-Troyes Provincial Park was reconfigured.
The park is an important nesting habitat for many bird species, including great blue heron, bald eagle, osprey, and double-crested cormorant. The vegetation is characterized by intolerant hardwood and mixedwood forests, with black spruce, white spruce, and white birch as the common tree species.
It is a non-operating park, meaning that there are no facilities or services, and only accessible via air or water
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# Length
**Length** is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the International System of Units (SI) system, the base unit for length is the metre.
Length is commonly understood to mean the most extended dimension of a fixed object. However, this is not always the case and may depend on the position the object is in.
Various terms for the length of a fixed object are used, and these include height, which is vertical length or vertical extent, width, breadth, and depth. *Height* is used when there is a base from which vertical measurements can be taken. *Width* and *breadth* usually refer to a shorter dimension than *length*. *Depth* is used for the measure of a third dimension.
Length is the measure of one spatial dimension, whereas area is a measure of two dimensions (length squared) and volume is a measure of three dimensions (length cubed).
## History
Measurement has been important ever since humans settled from nomadic lifestyles and started using building materials, occupying land and trading with neighbours. As trade between different places increased, the need for standard units of length increased. And later, as society has become more technologically oriented, much higher accuracy of measurement is required in an increasingly diverse set of fields, from micro-electronics to interplanetary ranging.
Under Einstein\'s special relativity, length can no longer be thought of as being constant in all reference frames. Thus a ruler that is one metre long in one frame of reference will not be one metre long in a reference frame that is moving relative to the first frame. This means the length of an object varies depending on the speed of the observer.
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# Length
## Use in mathematics {#use_in_mathematics}
### Euclidean geometry {#euclidean_geometry}
In Euclidean geometry, length is measured along straight lines unless otherwise specified and refers to segments on them. Pythagoras\'s theorem relating the length of the sides of a right triangle is one of many applications in Euclidean geometry. Length may also be measured along other types of curves and is referred to as arclength.
In a triangle, the length of an altitude, a line segment drawn from a vertex perpendicular to the side not passing through the vertex (referred to as a base of the triangle), is called the height of the triangle.
The area of a rectangle is defined to be length × width of the rectangle. If a long thin rectangle is stood up on its short side then its area could also be described as its height × width.
The volume of a solid rectangular box (such as a plank of wood) is often described as length × height × depth.
The perimeter of a polygon is the sum of the lengths of its sides.
The circumference of a circular disk is the length of the boundary (a circle) of that disk.
### Other geometries {#other_geometries}
In other geometries, length may be measured along possibly curved paths, called geodesics. The Riemannian geometry used in general relativity is an example of such a geometry. In spherical geometry, length is measured along the great circles on the sphere and the distance between two points on the sphere is the shorter of the two lengths on the great circle, which is determined by the plane through the two points and the center of the sphere.
### Graph theory {#graph_theory}
In an unweighted graph, the length of a cycle, path, or walk is the number of edges it uses. In a weighted graph, it may instead be the sum of the weights of the edges that it uses.
Length is used to define the shortest path, girth (shortest cycle length), and longest path between two vertices in a graph.
### Measure theory {#measure_theory}
In measure theory, length is most often generalized to general sets of $\mathbb{R}^n$ via the Lebesgue measure. In the one-dimensional case, the Lebesgue outer measure of a set is defined in terms of the lengths of open intervals. Concretely, the length of an open interval is first defined as
: $\ell(\{x\in\mathbb R\mid a<x<b\})=b-a.$
so that the Lebesgue outer measure $\mu^*(E)$ of a general set $E$ may then be defined as
: $\mu^*(E)=\inf\left\{\sum_k \ell(I_k):I_k\text{ is a sequence of open intervals such that }E\subseteq\bigcup_k I_k\right\}.$
## Units
In the physical sciences and engineering, when one speaks of `{{em|[[unit of length|units of length]]}}`{=mediawiki}, the word `{{em|length}}`{=mediawiki} is synonymous with distance. There are several units that are used to measure length. Historically, units of length may have been derived from the lengths of human body parts, the distance travelled in a number of paces, the distance between landmarks or places on the Earth, or arbitrarily on the length of some common object.
In the International System of Units (SI), the base unit of length is the metre (symbol, m), now defined in terms of the speed of light (about 300 million metres per second). The millimetre (mm), centimetre (cm) and the kilometre (km), derived from the metre, are also commonly used units. In U.S. customary units, English or imperial system of units, commonly used units of length are the inch (in), the foot (ft), the yard (yd), and the mile (mi). A unit of length used in navigation is the nautical mile (nmi).
km = `{{calculator|id=miles|type=number|size=16|default=1|formula=km/1.609344}}`{=mediawiki} miles
Units used to denote distances in the vastness of space, as in astronomy, are much longer than those typically used on Earth (metre or kilometre) and include the astronomical unit (au), the light-year, and the parsec (pc).
Units used to denote sub-atomic distances, as in nuclear physics, are much smaller than the millimetre. Examples include the fermi (fm)
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# Left-arm unorthodox spin
**Left-arm unorthodox spin**, also known as **slow left-arm wrist spin**, is a type of spin bowling in the sport of cricket. Left-arm unorthodox spin bowlers use wrist spin to spin the ball, and make it deviate, or \'turn\' from left to right after pitching. The direction of turn is the same as that of a traditional right-handed off spin bowler, although the ball will usually turn more sharply due to the spin being imparted predominantly by the wrist.
Some left-arm unorthodox bowlers also bowl what has historically been referred to as a **chinaman**, the equivalent of a googly, or \'wrong\'un\', which turns from right to left on the pitch. The ball turns away from the right-handed batsman, as if the bowler were an orthodox left-arm spinner.
## Notable left-arm unorthodox spin bowlers {#notable_left_arm_unorthodox_spin_bowlers}
The first cricketer known to bowl the style of delivery was 19th-century South African bowler Charlie Llewellyn. Llewellyn toured North America with Bernard Bosanquet, the originator of the googly delivery, and it is likely that Llewellyn learned the googly-style of delivery from him, bowling it with his left-arm.
Among noted players who have bowled the delivery are Denis Compton, who originally bowled orthodox slow-left arm deliveries but developed left-arm wrist spin, taking most of his 622 first-class wickets using the delivery. Chuck Fleetwood-Smith used the delivery in the 1930s, including in his 10 Test matches. Although better known for fast bowling and orthodox slow left-arm, Garfield Sobers could also use it to good effect. In cricket\'s modern era, Australian Brad Hogg brought the delivery to wider notice and had one of the most well-disguised wrong\'uns. Kuldeep Yadav, who debuted for India in March 2017, bowls left-arm wrist spin, and Paul Adams played 45 Test matches and 24 One-day internationals for South Africa between 1995 and 2004 using the delivery. Michael Bevan and Dave Mohammed are also considered to be \"among the better known\" bowlers to use the style.
In 2021 *The Guardian* claimed that Kuldeep, Tabraiz Shamsi of South Africa and the Afghan bowler Noor Ahmad were \"probably the foremost left-arm wrist-spinners in world cricket\", while in 2022 Michael Rippon was reported as \"the first specialist left-arm wristspinner\" to play for New Zealand. In the women\'s game, Kary Chan of Hong Kong uses left-arm wrist spin deliveries.
Instances of left-arm unorthodox spinners taking a ten-wicket haul in a Test match are rare. Examples include Chuck Fleetwood-Smith against England in 1936--37, Michael Bevan against the West Indies in 1996--97, and Paul Adams against Bangladesh in 2002--03.
In 2007 CricInfo suggested that left-arm wrist-spin bowlers are uncommon because it is \"difficult to control left-arm wrist spin. And \[\...\] the ball coming in to a right-hander is considered less dangerous than the one leaving him\". A left-arm wrist spin bowler\'s standard delivery will turn towards a right-handed batsman, as opposed to a right-arm leg spin bowler who will turn the ball away from them. In 2024 Cameron Ponsonby reiterated this view on The Final Word podcast, stating in jest of the success of Kuldeep Yadav,
> \"The hardest thing in the world, in this sport, is to bowl wrist spin. The reason why right arm leg spin works and is effective is because it spins the ball away from the bat. That\'s the positive. The negative side of that is you have less control. \[\...\] What\'s bad about off spin? You spin the ball into the right-hander. What\'s good about off spin? You have control. Left arm wrist spin: what\'s good about it? Nothing, because you spin the ball into the right-hander without control.\"
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# Left-arm unorthodox spin
## Historical use of the term \'chinaman\' {#historical_use_of_the_term_chinaman}
Historically the term \"chinaman\" was sometimes used to describe the googly delivery or other unusual deliveries, whether bowled by right or left-arm bowlers. The left-arm wrist spinner\'s delivery that is the equivalent of the googly eventually became known as the \"chinaman\".
The origin of the term is unclear, although it is known to have been in use in Yorkshire during the 1920s and may have been first used in reference to Roy Kilner. It is possible that it is a guarded reference to Charlie Llewellyn, the first left-arm bowler to bowl the equivalent of the googly. It is first known to have been used in print in *The Guardian* in 1926 in reference to the possibility of Yorkshire bowler George Macaulay bowling a googly, but the term became more widely used after a Test match between England and West Indies at Old Trafford in 1933. Ellis Achong, a player of Chinese origin who bowled slow left-arm orthodox spin, had Walter Robins stumped off a surprise delivery that spun into the right-hander from outside the off stump. As he walked back to the pavilion, Robins reportedly said to the umpire, \"fancy being done by a bloody Chinaman!\", leading to the more widespread use of the term.
In 2017, Australian journalist Andrew Wu, who is of Chinese descent, raised concerns about the use of the term as \"racially offensive\", arguing the term itself \"has historically been used in a contemptuous manner to describe the Chinese\". *Wisden* formally changed their wording of the term to slow left-arm wrist-spin in the 2018 edition of the Almanack, describing chinaman as \"no longer appropriate\". CricInfo followed suit in 2021, noting that although some argued that its use in cricket \"was not meant to be derogatory\", that its continued use was inappropriate. Some writers continue to use the term
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# Lists of newspapers
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# Larousse Gastronomique
****Larousse Gastronomique**** (`{{IPA|fr|laʁus ɡastʁɔnɔmik}}`{=mediawiki}) is an encyclopedia of gastronomy first published by Éditions Larousse in Paris in 1938. The majority of the book is about French cuisine, and contains recipes for French dishes and cooking techniques. The first edition included few non-French dishes and ingredients; later editions include many more.
## Background
The first edition (1938) was edited by Prosper Montagné, with the collaboration of Dr Alfred Gottschalk, with prefaces by each of the author-chefs Georges Auguste Escoffier and Philéas Gilbert (1857--1942). Gilbert was a collaborator in the creation of this book as well as *Le Guide Culinaire* (1903) with Escoffier, leading to some cross-over with the two books. It caused Escoffier to note when he was asked to write the preface that he could \"see with my own eyes\", and \"Montagné cannot hide from me the fact that he has used *Le Guide* as a basis for his new book, and certainly used numerous recipes.\"
The third English edition (2001), which runs to approximately 1,350 pages, has been modernized and includes additional material on other cuisines. It is also available in a concise edition (2003). A new, updated and revised edition was released in October 2009, published by Hamlyn in the UK
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# Laurence of Canterbury
**Laurence** (died 2 February 619) was the second Archbishop of Canterbury, serving from about 604 to 619. He was a member of the Gregorian mission sent from Italy to England to Christianise the Anglo-Saxons from their native Anglo-Saxon paganism, although the date of his arrival is disputed. He was consecrated archbishop by his predecessor, Augustine of Canterbury, during Augustine\'s lifetime, to ensure continuity in the office. While archbishop, he attempted unsuccessfully to resolve differences with the native British bishops by corresponding with them about points of dispute. Laurence faced a crisis following the death of King Æthelberht of Kent, when the king\'s successor abandoned Christianity; he eventually reconverted. Laurence was revered as a saint after his death in 619.
## Early life {#early_life}
Laurence was part of the Gregorian mission originally dispatched from Rome in 595 to convert the Anglo-Saxons from their native paganism to Christianity; he landed at Thanet, Kent, with Augustine in 597, or, as some sources state, first arrived in 601 and was not a part of the first group of missionaries. He had been a monk in Rome before his travels to England, but nothing else is known of his history or background. The medieval chronicler Bede says that Augustine sent Laurence back to Pope Gregory I to report on the success of converting King Æthelberht of Kent and to carry a letter with questions for the pope. Accompanied by Peter of Canterbury, another missionary, he set off sometime after July 598, and returned by June 601. He brought back with him Gregory\'s replies to Augustine\'s questions, a document commonly known as the *Libellus responsionum*, that Bede incorporated in his *Historia ecclesiastica gentis Anglorum*. Laurence is probably the Laurence referred to in the letter from Gregory to Bertha, queen of Kent. In that letter, Gregory praises Bertha for her part in the conversion of her husband, details of which Gregory says he received from Laurence the priest. It is known that Laurence returned to England with Mellitus and others of the second group of missionaries in the summer of 601, but there is no record of Peter being with them.
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# Laurence of Canterbury
## Archbishop
Laurence succeeded Augustine to the see of Canterbury in about 604, and ruled until his death on 2 February 619. To secure the succession, Augustine had consecrated Laurence before he died, even though that was prohibited by canon law. Augustine was afraid though that if someone did not step into the office immediately, it would damage the missionary efforts in Britain. However, Laurence never received a pallium from Rome, so he may have been considered uncanonical by the papacy. Bede makes a point of comparing Augustine\'s action in consecrating Laurence to Saint Peter\'s action of consecrating Clement as Bishop of Rome during Peter\'s lifetime, which the theologian J. Robert Wright believes may be Bede\'s way of criticising the practices of the church in his day.
In 610 Laurence received letters from Pope Boniface IV, addressed to him as archbishop and Augustine\'s successor. The correspondence was in response to Laurence having sent Mellitus to Rome earlier in 610, to solicit advice from the papacy on matters concerning the English Church. While in Rome Mellitus attended a synod and brought the synodical decrees back with him to Laurence.
In 613 Laurence consecrated the monastery church built by Augustine in Canterbury, and dedicated it to saints Peter and Paul; it was later re-consecrated as St Augustine\'s Abbey, Canterbury. Laurence also wrote to the bishops in the lands held by the Scots and by the Britons, urging them to hold Easter on the day that the Roman church celebrated it, instead of their traditional date, as part of the Easter controversy. The letter is also preserved in Bede\'s history. Laurence in 609 stated that Dagan, a native bishop, would not eat with Laurence or share a roof with the archbishop, due to the differences between the two Churches.
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# Laurence of Canterbury
## Pagan reaction {#pagan_reaction}
Æthelberht died in 616, during Laurence\'s tenure; his son Eadbald abandoned Christianity in favour of Anglo-Saxon paganism, forcing many of the Gregorian missionaries to flee the pagan backlash that followed Æthelberht\'s death. Among them in Gaul were Mellitus, who was Bishop of London, and Justus, who was Bishop of Rochester. Remaining in Britain, Laurence succeeded in reconverting Eadbald to Christianity. Bede relates the story that Laurence had been prepared to give up when he was visited by St Peter in a dream or vision. St Peter chastised Laurence and whipped him, and the marks of the whipping remained after the vision or dream ended. Laurence then displayed them to Eadbald, and the king was converted on the spot. Bede, however, hints that it was the death of some of the leaders of the pagan party in battle that really persuaded Laurence to stay. According to Benedicta Ward, a historian of Christianity, Bede uses the story of the whipping as an example of how suffering was a reminder of Christ\'s suffering for humans, and how that example could lead to conversion. Wright argues that another point Bede is making is that it is because of the intercession of St Peter himself that the mission continued. David Farmer, in the *Oxford Dictionary of Saints*, suggests that the whipping story may have been a blending of the *Quo vadis* story with some information given by Jerome in a letter.
Modern historians have seen political overtones in the pagan reaction. The historian D. P. Kirby sees Eadbald\'s actions as a repudiation of his father\'s pro-Frankish policies. Alcuin, a later medieval writer, wrote that Laurence was \"censured by apostolic authority\". This may have been a letter from Pope Adeodatus I, commanding Laurence to stay in Kent. Kirby goes on to argue that it was Justus, not Laurence, who converted Eadbald, and this while Justus was archbishop, sometime around 624. Not all historians agree with this argument, however. Nicholas Brooks states that the king was converted during Laurence\'s archiepiscopate, within a year of him succeeding his father. The historian Barbara Yorke argues that there were two co-rulers of Kent after Æthelberht\'s death, Eadbald and a Æthelwald, and that Eadbald was converted by Laurence while Æthelwald was converted by Justus after his return to Rochester. Another factor in the pagan reaction was Laurence\'s objection to Eadbald\'s marriage to his father\'s widow, something that Christians considered to be unlawful.
All efforts to extend the church beyond Kent encountered difficulties due to the attitude of King Rædwald of East Anglia, who had become the leading king in the south after Æthelberht\'s death. Rædwald was converted before the death of Æthelberht, perhaps at the urging of Æthelberht, but his kingdom was not, and Rædwald seems to have converted only to the extent of placing a Christian altar in his pagan temple. It proved impossible for Mellitus to return to London as bishop, although Justus did resume his duties at Rochester.
## Death and legacy {#death_and_legacy}
Laurence died on 2 February 619, and was buried in the abbey of St Peter and Paul in Canterbury, later renamed St Augustine\'s; his relics, or remains, were moved, or translated, to the new church of St Augustine\'s in 1091. His shrine was in the axial chapel of the abbey church, flanking the shrine of Augustine, his predecessor. Laurence came to be regarded as a saint, and was given the feast day of 3 February. The ninth century Stowe Missal commemorates his feast day, along with Mellitus and Justus. A *Vita* (or *Life*) was written about the time of his translation, by Goscelin, but it is mainly based on information in Bede. His tomb was opened in 1915. Besides his feast day, the date of his translation, 13 September, was also celebrated after his death. Laurence\'s tenure as archbishop is mainly remembered for his failure to secure a settlement with the Celtic church and for his reconversion of Eadbald following Æthelbert\'s death. He was succeeded as archbishop by Mellitus, the Bishop of London
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# Leaf by Niggle
\"**Leaf by Niggle**\" is a short story written by J. R. R. Tolkien in 1938--39 and first published in the *Dublin Review* in January 1945. It was reprinted in Tolkien\'s book *Tree and Leaf*, and in several later collections. Contrary to Tolkien\'s claim that he despised allegory in any form, the story is an allegory of Tolkien\'s own creative process, and, to an extent, of his own life, following the structure of Dante\'s *Purgatorio*. It also expresses his philosophy of divine creation and human sub-creation. The story came to him in a dream.
## Context
J. R. R. Tolkien was a scholar of English literature, a philologist and medievalist interested in language and poetry from the Middle Ages, especially that of Anglo-Saxon England and Northern Europe. His professional knowledge of works such as *Beowulf* shaped his fictional world of Middle-earth, including his high fantasy novel *The Lord of the Rings*.
## Plot summary {#plot_summary}
In this story, an artist named Niggle lives in a society that does not value art. Working only to please himself, he paints a canvas of a great tree with a forest in the distance. He invests each and every leaf of his tree with obsessive attention to detail, making every leaf uniquely beautiful. Niggle ends up discarding all his other artworks, or tacks them onto the main canvas, which becomes a single vast embodiment of his vision.
However, mundane duties constantly prevent Niggle from giving his work the attention it deserves, so it remains incomplete and is not fully realised. At the back of his head, Niggle knows that he has a great trip looming, and he must prepare for it, but Niggle\'s next door neighbour, a gardener named Parish, frequently drops by asking for assistance. Parish is lame, has a sick wife, and genuinely needs help. Niggle, having a good heart, takes time out to help---but he is also reluctant because he would rather work on his painting. Niggle has other pressing work duties as well that require his attention. Then Niggle himself catches a chill doing errands for Parish in the rain.
Eventually, Niggle is forced to take his trip, and cannot get out of it. He has not prepared, and as a result the trip goes wrong, and he ends up in a kind of institution, in which he must perform menial labour each day. Back at the home to which he cannot return, Niggle\'s painting is abandoned, used to patch a damaged roof, and all but destroyed (except for the one perfect leaf of the story\'s title, which is placed in the local museum).
In time, Niggle is paroled from the institution, and he is sent to a place \"for a little gentle treatment\". He discovers that this new place is the country of the tree and forest of his great painting. This place is the true realisation of his vision, not the flawed and incomplete version in his painting.
Niggle is reunited with his old neighbour, Parish, who now proves his worth as a gardener, and together they make the tree and forest even more beautiful. Finally, Niggle journeys farther and deeper into the Forest, and beyond into the great mountains that he only faintly glimpsed in his painting.
Long after both Niggle and Parish have taken their journeys, the place that they created together becomes a destination for many travellers to visit before their final voyage into the mountains, and it earns the name \"Niggle\'s Parish\".
## Publication history {#publication_history}
\"Leaf by Niggle\" was first published in the *Dublin Review* in 1945. It first appeared in a book in 1964 alongside \"On Fairy-Stories\" in *Tree and Leaf*. It has been republished in the collections *The Tolkien Reader* (1966), *Poems & Stories* (1980), *A Tolkien Miscellany* (2002), and *Tales from the Perilous Realm* (2021).
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# Leaf by Niggle
## Analysis
### Allegory
Tolkien made the general statement \"I dislike allegory\" in one of his letters, but in specific references to \"Leaf by Niggle\", he wrote that \"It is not really or properly an \'allegory\' so much as \'mythical\'\", and \"I tried to show allegorically how `{{bracket|[[sub-creation]]}}`{=mediawiki} might come to be taken up into Creation in some plane in my \'purgatorial\' story *Leaf by Niggle*.\"
#### Of the journey of death {#of_the_journey_of_death}
The Tolkien scholar and fellow-philologist Tom Shippey states categorically that the story is \"quite certainly\" an allegory, and that its first words recall \"to any Anglo-Saxonist\" the opening lines of the Old Northumbrian poem *Bede\'s Death Song*. Those lines, he states, equate death to a journey, hinting to the reader to continue making such \"equations\" of things in the world to elements of the story; and further, that the reader of the story is meant to interpret the story in this way, every tiny detail exactly and entertainingly fitting the pattern.
thumb\|upright=1.2\|\"Leaf by Niggle\" matches the structure of Dante\'s *Purgatorio*, and fits Dante\'s romantic theology. Here, Dante looks longingly at Beatrice (centre) as she strolls by the River Arno. *Dante and Beatrice*, by Henry Holiday, 1883
A religious reading could lead to the conclusion that the allegory of \"Leaf by Niggle\" is life, death, purgatory and paradise. Niggle is not prepared for his unavoidable trip, as humans often are not prepared for death. His time in the institution and subsequent discovery of his Tree represent purgatory and heaven; Sebastian Knowles writes that the story \"follows Dante\'s \'Purgatorio\' in its general structure and in its smallest detail.\"
Michael Milburn argues that Charles Williams\'s view of Dante as romantic theology -- which Milburn glosses as the serious theology of romantic experiences, including romantic love -- can be applied to Tolkien\'s story. Dante, he writes, has a \"glorious vision\" of Beatrice that is \"as real\" as the actual Beatrice. She dies, leaving Dante with the inspiration to \"*be* love\", to stay faithful to his vision of her. This can be applied to art with \"a source text that not only takes art for its subject but locates the vision of great art in the afterlife with Beatrice, includes an experience analogous to the death of Beatrice, and explores the relationship between artistic beauty and *caritas*. Milburn states that Tolkien\'s \"Leaf by Niggle\" is just such a text, because Niggle\'s allegorical \"journey\" signifies death, the \"Workhouse\" signifies purgatory, and the place Niggle reaches after that is the Earthly Paradise, the place for Tolkien as for Dante of final purification before heaven, Niggle\'s \"mountains\". Tolkien had met Williams, as they were both members of the Inklings literary group. Further, Milburn notes, Tolkien, despite denying that Williams had been an influence, wrote a poem about him, in which he praises William\'s understanding of Dante, his romantic theology: \"But heavenly footsteps, too, can Williams trace, / and after Dante, plunging, soaring, race / up to the threshold of Eternal Grace\".
#### Of Tolkien\'s life {#of_tolkiens_life}
An autobiographical interpretation places Tolkien himself as Niggle---in mundane matters as well as spiritual ones. Tolkien was compulsive in his writing, his endless revisions, his desire for perfection in form and in the \"reality\" of his invented world, its languages, its chronologies, its existence. Like Niggle, Tolkien came to abandon other projects or graft them onto his \"Tree\", Middle-earth. Like Niggle, Tolkien faced many chores and duties that kept him from the work he loved; and like Niggle, Tolkien was a confirmed procrastinator. Shippey comments that whereas Tolkien had once felt that one could return to Faërie in some way, later in his life he came to doubt that he would \"\[rejoin\] his own creations after death, like Niggle; he felt they were lost, like the Silmarils.\" He adds that when Tolkien presents images of himself in his writings, as with Niggle and Smith, there is \"a persistent streak of alienation\". Shippey lists several elements of the allegory in \"Leaf by Niggle\".
Story element Aspect of Tolkien\'s life
------------------------------------------------------------------------- ----------------------------------------------------------------------------
Niggle the painter Tolkien the writer
Niggle\'s \"leaf\" *The Hobbit*, published 1937
Niggle\'s \"Tree\" *The Lord of the Rings*, still in work when \"Leaf by Niggle\" was written
The \"country\" that opens from it Middle-earth
The \"other pictures \... tacked on to the edges of his great picture\" Tolkien\'s poems and other works which he fitted into his novel
\"Potatoes\" sacrificed to \"paint\" Medievalist research articles sacrificed to *The Lord of the Rings*
: Tom Shippey\'s analysis of \"Leaf by Niggle\" as an allegory of Tolkien\'s life
#### Of creation and sub-creation {#of_creation_and_sub_creation}
\"Leaf by Niggle\" can be interpreted, too, as an illustration of Tolkien\'s religious philosophy of creation and sub-creation. In this philosophy, true creation is the exclusive province of God, and those who aspire to creation can only make echoes (good) or mockeries (evil) of truth. The sub-creation of works that echo the true creations of God is one way that mortals honour God. This philosophy is evident in Tolkien\'s other works, especially *The Silmarillion*---one Vala, Morgoth, creates the Orc race as a foul mockery of the Elves. Another Vala, Aulë, creates the Dwarf race as an act of subcreation that honoured Eru Ilúvatar (the analogue of God in Tolkien\'s writings), and which Eru accepted and made real, just as Niggle\'s Tree was made real. Niggle\'s yearnings after truth and beauty (God\'s creations) are echoed in his great painting. After death, Niggle is rewarded with the realisation (the making-real) of his yearning; or, alternatively, Niggle\'s Tree always existed and he simply echoed it in his art. From a metanarrative viewpoint, Tolkien\'s Arda is itself a subcreation designed to honour the true stories of the real world. Thus, *The Lord of the Rings*, despite its lack of overt religious elements, can be interpreted as a profoundly religious work.
### Surrealistic dream memory {#surrealistic_dream_memory}
Michael Organ, writing in the *Journal of Tolkien Research*, notes that Tolkien stated in a letter that the story came to him one morning in 1939, shortly before the start of the Second World War, when he woke up with the story, which he called \"that odd thing\", in his mind \"virtually\" complete. Tolkien stated in another letter that he then wrote it out \"almost in a sitting and very nearly in the form in which it now appears\", commenting that looking back at the story , he thought it \"arose\" from a combination of his love of trees and his concern that *The Lord of the Rings* would never be finished. Organ describes the birth of \"Leaf by Niggle\" as \"a frenzy of activity\" resembling the automatic writing \"popularised by proponents of Dada and Surrealism\" in the early 20th century. He notes, too, that Tolkien knew that dreams had an irrational side, and had commented that it was \"exceptional\" for fantasy to appear in dreams, as \"Fantasy is a rational, not an irrational, activity\". Organ comments that Tolkien may have resisted \"what he saw as the morbidity of surrealism\" in connection with his story, precisely because \"Leaf by Niggle\"\'s message is so positive.
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# Leaf by Niggle
## Analysis
### Visual imagery {#visual_imagery}
Jeffrey MacLeod and Anna Smol write in *Mythlore* that while Tolkien defines sub-creation \"in linguistic terms\", he often links such verbal creation to visual images. For instance, in his poem \"Mythopoeia\", he mentions \"script and limning packed of various hue\", which they gloss as \"writing and drawing, alphabet and image, the linguistic and the visual \... side by side.\" Similarly, they comment, in \"Leaf by Niggle\", the allegory uses the image of a painter . In his own life, Tolkien combined the writing of fiction with his artwork, while he defined imagination visually as the \"mental power of image-making\"
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