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# Litre
*Lithraea caustica*}} `{{Use dmy dates|date=March 2021}}`{=mediawiki} `{{Use British English|date=March 2016}}`{=mediawiki} `{{Infobox unit
| name = litre
| image = [[File:CubeLitre.svg|200px]]
| caption = One litre is equal to the volume of a cubic decimetre.
| standard = [[International System of Units#Non-SI units accepted for use with SI|Non-SI unit accepted for use with SI]]
| quantity = [[volume]]
| symbol = L
| symbol2 = l<ref name=SIbrochure>{{SIbrochure8th|page = 124}}.</ref>
| dimension = L<sup>3</sup><ref name="NB_Dimension">The SI standard recommends a sans-serif uppercase letter "L" for the dimension symbol of the length. An uppercase "L" is also one of the official symbols for the litre itself (the other being a lowercase letter "l"). Since unit symbols and dimension symbols are used in different contexts, this does not normally cause confusion.</ref>)
| namedafter = [[Units of measurement in France before the French Revolution#Volume – dry measures|litron]]
| units1 = [[SI base unit]]
| inunits1 = {{val||e=-3|ul=m3}}
| units2 = [[United States customary units|U.S. customary]]
| inunits2 = ≈{{thin space}}{{val|0.264|u=gallon}}
}}`{=mediawiki}
The **litre** (Commonwealth spelling) or **liter** (American spelling) (SI symbols **L** and **l**, other symbol used: **ℓ**) is a metric unit of volume. It is equal to 1 cubic decimetre (dm^3^), 1000 cubic centimetres (cm^3^) or 0.001 cubic metres (m^3^). A cubic decimetre (or litre) occupies a volume of `{{nobr|10 cm × 10 cm × 10 cm}}`{=mediawiki} (see figure) and is thus equal to one-thousandth of a cubic metre.
The original French metric system used the litre as a base unit. The word *litre* is derived from an older French unit, the *litron*, whose name came from Byzantine Greek---where it was a unit of weight, not volume---via Late Medieval Latin, and which equalled approximately 0.831 litres. The litre was also used in several subsequent versions of the metric system and is accepted for use with the SI, despite it not being an SI unit. The SI unit of volume is the cubic metre (m^3^). The spelling used by the International Bureau of Weights and Measures is \"litre\", a spelling which is shared by most English-speaking countries. The spelling \"liter\" is predominantly used in American English.
One litre of liquid water has a mass of almost exactly one kilogram, because the kilogram was originally defined in 1795 as the mass of one cubic decimetre of water at the temperature of melting ice (`{{val|0|u=degC}}`{=mediawiki}). Subsequent redefinitions of the metre and kilogram mean that this relationship is no longer exact.
## Definition
A litre is a cubic decimetre, which is the volume of a cube 10 centimetres × 10 centimetres × 10 centimetres (1 L ≡ 1 dm^3^ ≡ 1000 cm^3^). Hence 1 L ≡ 0.001 m^3^ ≡ 1000 cm^3^; and 1 m^3^ (i.e. a cubic metre, which is the SI unit for volume) is exactly 1000 L.
From 1901 to 1964, the litre was defined as the volume of one kilogram of pure water at maximum density (+3.98 °C) and standard pressure. The kilogram was in turn specified as the mass of the International Prototype of the Kilogram (a specific platinum/iridium cylinder) and was intended to be of the same mass as the 1 litre of water referred to above. It was subsequently discovered that the cylinder was around 28 parts per million too large and thus, during this time, a litre was about `{{val|1.000028|u=dm3}}`{=mediawiki}. Additionally, the mass--volume relationship of water (as with any fluid) depends on temperature, pressure, purity and isotopic uniformity. In 1964, the definition relating the litre to mass was superseded by the current one. Although the litre is not an SI unit, it is accepted by the CGPM (the standards body that defines the SI) for use with the SI. CGPM defines the litre and its acceptable symbols.
A litre is equal in volume to the millistere, an obsolete non-SI metric unit formerly customarily used for dry measure.
## Explanation
Litres are most commonly used for items (such as fluids and solids that can be poured) which are measured by the capacity or size of their container, whereas cubic metres (and derived units) are most commonly used for items measured either by their dimensions or their displacements. The litre is often also used in some calculated measurements, such as density (kg/L), allowing an easy comparison with the density of water.
One litre of water has a mass of almost exactly one kilogram when measured at its maximal density, which occurs at 3.984 °C. It follows, therefore, that `{{sfrac|1000}}`{=mediawiki} of a litre, known as one millilitre (1 mL), of water has a mass of about 1 g, while 1000 litres of water has a mass of about 1000 kg (1 tonne or megagram).
This relationship holds because the gram was originally defined as the mass of 1 mL of water; however, this definition was abandoned in 1799 because the density of water changes with temperature and, very slightly, with pressure.
It is now known that the density of water also depends on the isotopic ratios of the oxygen and hydrogen atoms in a particular sample. Modern measurements of Vienna Standard Mean Ocean Water, which is pure distilled water with an isotopic composition representative of the average of the world\'s oceans, show that it has a density of `{{val|0.999975|0.000001|u=kg/L}}`{=mediawiki} at its point of maximum density (3.984 °C) under one standard atmosphere (101.325 kPa) of pressure.
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# Litre
## SI prefixes applied to the litre {#si_prefixes_applied_to_the_litre}
The litre, though not an official SI unit, may be used with SI prefixes. The most commonly used derived unit is the millilitre, defined as one-thousandth of a litre, and also often referred to by the SI derived unit name \"cubic centimetre\". It is a commonly used measure, especially in medicine, cooking and automotive engineering. Other units may be found in the table below, where the more often used terms are in bold. However, some authorities advise against some of them; for example, in the United States, NIST advocates using the millilitre or litre instead of the centilitre. There are two international standard symbols for the litre: L and l. In the United States the former is preferred because of the risk that (in some fonts) the letter `{{code|l}}`{=mediawiki} and the digit `{{code|1}}`{=mediawiki} may be confused.
Multiple Name Symbols
----------- ---------------- --------- -----
10^−30^ L quectolitre qL ql
10^−27^ L rontolitre rL rl
10^−24^ L yoctolitre yL yl
10^−21^ L zeptolitre zL zl
10^−18^ L attolitre aL al
10^−15^ L femtolitre fL fl
10^−12^ L picolitre pL pl
10^−9^ L nanolitre nL nl
10^−6^ L **microlitre** μL μl
10^−3^ L **millilitre** mL ml
10^−2^ L **centilitre** cL cl
10^−1^ L **decilitre** dL dl
10^0^ L **litre** L l
10^1^ L decalitre daL dal
10^2^ L hectolitre hL hl
10^3^ L **kilolitre** kL kl
10^6^ L **megalitre** ML Ml
10^9^ L **gigalitre** GL Gl
10^12^ L teralitre TL Tl
10^15^ L petalitre PL Pl
10^18^ L exalitre EL El
10^21^ L zettalitre ZL Zl
10^24^ L yottalitre YL Yl
10^27^ L ronnalitre RL Rl
10^30^ L quettalitre QL Ql
## Non-metric conversions {#non_metric_conversions}
Approx. value of 1 litre in non-metric units Non-metric unit
---------------------------------------------- ----------------------- ------------------------ --------------------
≈ 35.19507973 imperial fluid ounces 1 imperial fluid ounce ≡ 28.4130625 mL
≈ 33.8140227 US fluid ounces 1 US fluid ounce ≡ 29.5735295625 mL
≈ 7.03901595 imperial gills 1 imperial gill ≡ 142.0653125 mL
≈ 8.45350568 US gills 1 US gill ≡ 118.29411825 mL
≈ 1.75975399 imperial pints 1 imperial pint ≡ 568.26125 mL
≈ 2.11337642 US pints 1 US pint ≡ 473.176473 mL
≈ 0.87987699 imperial quart 1 imperial quart ≡ 1.1365225 L
≈ 1.05668821 US quarts 1 US quart ≡ 0.946352946 L
≈ 0.21996925 imperial gallon 1 imperial gallon ≡ 4.54609 L
≈ 0.26417205 US gallon 1 US gallon ≡ 3.785411784 L
≈ 0.03531467 cubic foot 1 cubic foot ≡ 28.316846592 L
≈ 61.02374409 cubic inches 1 cubic inch ≡ 16.387064 mL
See also Imperial units and US customary units.
### Rough conversions {#rough_conversions}
One litre is about `{{val|5.7|u=%}}`{=mediawiki} larger than a US liquid quart, and about `{{val|12|u=%}}`{=mediawiki} smaller than an imperial quart.
A mnemonic for its volume relative to an imperial pint is \"a litre of water\'s a pint and three-quarters\"; this is very close, as a litre is about 1.760 imperial pints.
A cubic foot has a volume of exactly `{{val|28.316846592|u=litres}}`{=mediawiki}.
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# Litre
## Symbol
Originally, the only symbol for the litre was **l** (lowercase letter L), following the SI convention that only those unit symbols that abbreviate the name of a person start with a capital letter. In many English-speaking countries, however, the most common shape of a handwritten Arabic digit 1 is just a vertical stroke; that is, it lacks the upstroke added in many other cultures. Therefore, the digit \"1\" may easily be confused with the letter \"l\". In some computer typefaces, the two characters are barely distinguishable. As a result, **L** (uppercase letter L) was adopted by the CGPM as an alternative symbol for litre in 1979. The United States National Institute of Standards and Technology now recommends the use of the uppercase letter L, a practice that is also widely followed in Canada and Australia. In these countries, the symbol L is also used with prefixes, as in mL and μL, instead of the traditional ml and μl used in Europe. In the UK and Ireland, as well as the rest of Europe, lowercase *l* is used with prefixes, though whole litres are often written in full (so, \"750 ml\" on a wine bottle, but often \"1 litre\" on a juice carton). In 1990, the International Committee for Weights and Measures stated that it was too early to choose a single symbol for the litre.
### Script l and Unicode `{{anchor|Unicode}}`{=mediawiki} {#script_l_and_unicode}
Prior to 1979, the symbol `{{Litre}}`{=mediawiki} came into common use in some countries; for example, it was recommended by South African Bureau of Standards publication M33 and Canada in the 1970s. This symbol can still be encountered occasionally in some English-speaking and European countries, and its use is ubiquitous in Japan and South Korea.
Fonts covering the CJK characters usually include not only the script small `{{Litre}}`{=mediawiki} but also four precomposed characters: `{{not a typo|㎕, ㎖, ㎗, and ㎘}}`{=mediawiki} for the microlitre, millilitre, decilitre and kilolitre to allow correct rendering for vertically written scripts. These have Unicode equivalents for compatibility, which are not recommended for use with new documents:
-
-
-
-
-
The CJK Compatibility block also includes `{{unichar|3351}}`{=mediawiki} corresponding to *リットル* `{{Transliteration|ja|rittoru}}`{=mediawiki}, Japanese for \'litre\'.
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# Litre
## History
The first name of the litre was \"cadil\"; standards are shown at the Musée des Arts et Métiers in Paris.
The litre was introduced in France in 1795 as one of the new \"republican units of measurement\" and defined as one cubic decimetre. One litre of liquid water has a mass of almost exactly one kilogram, due to the gram being defined in 1795 as one cubic centimetre of water at the temperature of melting ice. The original decimetre length was 44.344 *lignes*, which was revised in 1798 to 44.3296 *lignes*. This made the original litre `{{val|1.000974}}`{=mediawiki} of today\'s cubic decimetre. It was against this litre that the kilogram was constructed.
In 1879, the CIPM adopted the definition of the litre, with the symbol **l** (lowercase letter L).
In 1901, at the 3rd CGPM conference, the litre was redefined as the space occupied by 1 kg of pure water at the temperature of its maximum density (3.98 °C) under a pressure of 1 atm. This made the litre equal to about `{{val|1.000028|u=dm3}}`{=mediawiki} (earlier reference works usually put it at `{{val|1.000027|u=dm3}}`{=mediawiki}).
In 1964, at the 12th CGPM conference, the original definition was reverted to, and thus the litre was once again defined in exact relation to the metre, as another name for the cubic decimetre, that is, exactly 1 dm^3^.
In 1979, at the 16th CGPM conference, the alternative symbol **L** (uppercase letter L) was adopted. It also expressed a preference that in the future only one of these two symbols should be retained, but in 1990 said it was still too early to do so.
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# Litre
## Everyday usage {#everyday_usage}
In spoken English, the symbol \"mL\" (for millilitre) can be pronounced as \"mil\". This can potentially cause confusion with some other measurement words such as:
1. \"mm\" for millimetre, a unit of length equal to one-thousandth of a metre
2. \"mil\" for thousandth of an *inch*
3. \"*mil*\", a Scandinavian unit of length equal to 10 kilometres
4. \"mil\", unit of angular measurement
The abbreviation \"cc\" (for cubic centimetre, equal to a millilitre or mL) is a unit of the cgs system, which preceded the MKS system, which later evolved into the SI system. The abbreviation \"cc\" is still commonly used in many fields, including medical dosage and sizing for combustion engine displacement.
The microlitre (μL) has been known in the past as the lambda (λ), but this usage is now discouraged. In the medical field the microlitre is sometimes abbreviated as **mcL** on test results.
In the SI system, apart from prefixes for powers of 1000, use of the \"centi\" (10^−2^), \"deci\" (10^−1^), \"deca\" (10^+1^) and \"hecto\" (10^+2^) prefixes with litres is common. For example, in many European countries, the hectolitre is the typical unit for production and export volumes of beverages (milk, beer, soft drinks, wine, etc.) and for measuring the size of the catch and quotas for fishing boats; decilitres are common in Croatia, Switzerland and Scandinavia and often found in cookbooks, and restaurant and café menus; centilitres indicate the capacity of drinking glasses and of small bottles. In colloquial Dutch in Belgium, a \"*vijfentwintiger*\" and a \"*drieëndertiger*\" (literally \"twenty-fiver\" and \"thirty-threer\") are the common beer glasses, the corresponding bottles mention 25 cL and 33 cL. Bottles may also be 75 cL or half size at 37.5 cL for \"artisanal\" brews or 70 cL for wines or spirits. Cans come in 25 cL, 33 cL and 50 cL. Similarly, alcohol shots are often marked in cL in restaurant menus, typically 3 cL. In countries where the metric system was adopted as the official measuring system after the SI standard was established, common usage eschews prefixes that are not powers of 1000. For example, in Canada, Australia, and New Zealand, consumer beverages are labelled almost exclusively using litres and millilitres. An exception is in pathology, where for instance blood lead level and blood sugar level may be measured in micrograms/milligrams per decilitre.
For larger volumes, kilolitres, megalitres, and gigalitres, have been used by the Northern Territory Government for measuring water consumption, reservoir capacities and river flows, although cubic metres are also used. Cubic metres are generally used for non-liquid commodities, such as sand and gravel, or storage space
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# Lennon Wall
The **Lennon Wall** (*Lennonova zeď*) or **John Lennon Wall** (Czech: *Zeď Johna Lennona*), located at *Velkopřevorské náměstí* (Grand Priory Square), Malá Strana, is a historic legal graffiti wall in Prague, Czechia. After the 1980 murder of John Lennon a mural of Lennon was painted by an unknown artist onto the wall and as more people expanded upon it, the wall slowly became a place for free expression of then communist Czechoslovakia. It has historically been used for demonstrations and carries a central theme of John Lennon, but it also features designs relating to local and global causes such as global warming. The wall has also inspired other walls across the globe, such as the Hong Kong Lennon wall.
The wall is owned by the Sovereign Military Order of Malta, which until 2019 allowed all graffiti. As of the latest reconstruction, the wall exists as a semi-legal graffiti wall; spray painting has been banned and only some areas of the wall are allowed to be used by the public.
## History
### Under communist Czechoslovakia {#under_communist_czechoslovakia}
Located in a secluded square across from the French Embassy, the wall had love poems and short messages against the communist Czechoslovak government since the 1960s, but the first message connected to John Lennon was painted following the 1980 assassination of Lennon, when an unknown artist painted a single image of the singer-songwriter and some lyrics onto a stone slab foundation of a former public fountain. Following this, a small memorial was created with candles, flowers, photographs and newspaper clippings talking about the murder. Western media was banned in the country at the time, therefore the image and memorial was seen by the authorities as representative of western culture and political resistance, thus in April 1981 it was painted over with green paint and removed by the Czechoslovak secret police who saw it as a protest against the government. The day after the wall was repainted it was filled with political messages, such as \"Palach would cry\", and poems once again. The wall would be repainted and re-graffiti-ed after that, with cameras and over-night guards being stationed at the wall to prevent further attempts, but this was ultimately fruitless as the wall would always end up being marked anyway.
In 1988, the wall was a source of irritation for Gustáv Husák\'s Marxist--Leninist government. Following a short-lived era of democratization and political liberalization known as the Prague Spring, the newly installed communist government dismantled the reforms, inspiring anger and resistance. Young Czechs wrote their grievances on the wall and, according to a report of the time,`{{Which|date=October 2024}}`{=mediawiki} this led to a clash between hundreds of students and security police on the nearby Charles Bridge. The liberalization movement these students followed was described as Lennonism (not to be confused with Leninism), and Czech authorities described participants variously as alcoholic, mentally deranged, sociopathic, and agents of Western free market capitalism.
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# Lennon Wall
## History
### Post velvet revolution and contemporary developments {#post_velvet_revolution_and_contemporary_developments}
After the fall of the iron curtain and replacement of the communist government the wall continuously underwent change and the original portrait of Lennon was long lost under layers of new paint and graffiti.
On 17 November 2014, the 25th anniversary of the Velvet Revolution, a group of art students called Prážská Služba repainted the wall to white leaving a single line of black text, "wall is over"`{{sic}}`{=mediawiki}. The Knights of Malta initially filed a criminal complaint for vandalism against the students, which they later retracted after contacting them.
On 22 April 2019, Earth Day, the environmentalist group Extinction Rebellion repainted the wall as a demand for the Czech government to act on climate change. The wall was almost entirely painted white, with the unpainted parts of the wall reading in large, negative space, block print letters *Klimatická Nouze* (`{{Lit|Climate Emergency}}`{=mediawiki}). Members of the public were encouraged to add their messages, resulting in calls for action painted in several languages. A large image of a skull was also painted. The repaint was carried out in a manner which allowed some of the existing artwork to be included on the new wall.
In July 2019, artists painted a memorial on the wall for Hong Kong democracy activist Marco Leung Ling-kit, who became known as a martyr and a symbol of hope for the 2019 anti-extradition bill protest movement. The image on the wall depicts the yellow raincoat he was wearing during the banner drop that eventually led to a fall from the building, along with some words of solidarity: "Hong Kong, Add oil."
In October 2019, the Sovereign Military Order of Malta and the administrative district of Prague 1 started a reconstruction of the Lennon Wall. A representative of the Order of Malta, Johannes Lobkowicz, in regards to why the wall would be renovated, said \"Our goal was to stop the wall from being a cheap tourist attraction, where anyone could draw nonsense or vulgarisms. It wasn\'t a dignified state \[for the wall\]\". Under the direction of Czech designer Pavel Šťastný over 30 Czech and foreign professional artists painted the wall with new designs. During the renovation a central piece made of reflective metal with a black outline of John Lennon was also installed. The wall opened to the public on the 30th anniversary of the Velvet Revolution, 7 November 2019, as an open-air gallery with new rules - busking and spraying was banned, marking the wall was now only allowed in the designated white zones and in impermanent materials e.g. pencils, markers, or chalk. Police and cameras were stationed at the wall to deter further spray painting and rule breaking.
At the same time as the wall was being renovated the wall was also declared a memorial site, this being the first time the wall was given an officially recognized status as an important landmark.
In July 2021, a new museum about the history of the Lennon Wall, the Lennon Wall Story, was opened on Prokopská Street 8. The museum features varying objects related to the wall, such as photos, historic objects and Beatles memorabilia.
On 15 May 2024 the Romani artist Maxim Muchow added a portrait of the late Romani singer Věra Bílá to the wall.
## Lennon Walls in Hong Kong {#lennon_walls_in_hong_kong}
During the 2014 democracy protests in Hong Kong, a similar Lennon Wall appeared along the staircase outside of the Hong Kong Central Government Offices. Inspired by the original in Prague, many thousands of people posted colourful post-it notes expressing democratic wishes for Hong Kong. The wall was one of the major arts of the Umbrella Movement. Throughout several months of occupation and protest, many efforts were made by different groups to ensure physical and digital preservation of the Hong Kong Lennon Wall.
Five years later, during the 2019--20 Hong Kong protests, the same wall was created again, with new post-it notes. Within days, dozens of post-it note Lennon Walls had \"blossomed everywhere\" (遍地開花) throughout Hong Kong, including on Hong Kong Island itself, Kowloon, the New Territories, and on the many outlying islands.`{{Primary source inline|date=May 2020}}`{=mediawiki} There are even some Lennon Walls located inside government offices, including RTHK and the Policy Innovation and Co-ordination Office. According to a crowd-sourced map of Hong Kong, there are over 150 Lennon Walls throughout the region.
On 21 September 2019, police in Hong Kong began tearing down Lennon Walls across the city to remove anti-government statements.
Lennon Walls have also appeared outside of Hong Kong in Toronto, Vancouver, Calgary, Seoul, Tokyo, Berlin, London, Sydney, Manchester, Melbourne, Taipei, and Auckland
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# Leg spin
**Leg spin** is a type of spin bowling in cricket. A bowler who uses this technique is called a **leg spinner**. Leg spinners bowl with their right-arm and a wrist spin action. The leg spinner\'s normal delivery is called a **leg break**, which spins from right to left (from the bowler\'s perspective) when the ball bounces on the pitch. For a right-handed batter, the ball breaks towards them from the leg side, hence the name \'leg break\'.
Leg spinners bowl mostly leg breaks, varying them by adjusting the line and length, and amount of side spin versus topspin of the deliveries. Leg spinners also typically use variations of flight by sometimes looping the ball in the air, allowing any cross-breeze and the aerodynamic effects of the spinning ball to cause the ball to dip and drift before bouncing and spinning or \"turning\", sharply. Leg spinners also bowl other types of delivery, which spin differently, such as the googly.
The terms \'leg spin\', \'leg spinner\', \'leg break\' and \'leggie\' are used in slightly different ways by different sources.
The bowlers with the second- and fourth-highest number of wickets in the history of Test cricket, Shane Warne and Anil Kumble, respectively, were leg spinners. One famous example of leg spin is Warne\'s Ball of the Century.
## History
In the 1970s and 1980s, it was thought that leg spin would disappear from the game due to the success of West Indian, and later Australian teams, exclusively using fast bowlers. During this time Abdul Qadir of Pakistan was the highest-profile leg spinner in the world and is sometimes credited with \"keeping the art alive\". However, leg spin has again become popular with cricket fans and a successful part of cricket teams, driven largely by the success of Shane Warne, beginning with his spectacular Ball of the Century to Mike Gatting in 1993.
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# Leg spin
## Comparison with other types of bowling {#comparison_with_other_types_of_bowling}
A left-handed bowler who bowls with the same (wrist spin) action as a leg spinner is known as a left-arm unorthodox spin bowler. The ball itself spins in the opposite direction.
The same kind of trajectory, which spins from right to left on pitching, when performed by a left-arm bowler is known as left-arm orthodox spin bowling.
As with all spinners, leg spinners bowl the ball far more slowly (70--90 km/h or 45--55 mph) than fast bowlers. The fastest leg spinners will sometimes top 100 km/h (60 mph). While very difficult to bowl accurately, good leg spin is considered one of the most threatening types of bowling to bat against for a right-handed batter, since the flight and sharp turn make the ball\'s movement extremely hard to read, and the turn away from the right-handed batter is more dangerous than the turn into the right-handed batter generated by an off spinner. Any miscalculation can result in an outside edge off the bat and a catch going to the wicket-keeper or slip fielders. Alternatively, for a ball aimed outside the leg stump, the breaking may be so sharp that the ball goes behind a right-handed batter and hits the stumps -- the batter is then said (informally) to be \"bowled around his or her legs\". A left-handed batter has less difficulty facing leg spin bowling, because the ball moves in towards the batter\'s body, meaning the batter\'s legs are usually in the path of the ball if it misses the bat or takes an edge. This makes it difficult for the bowler to get the batter out bowled or caught from a leg break.
**Leg spin:** Some sources make the term \'leg spin\' synonymous with leg break, implying that other deliveries bowled by a leg spinner do not count as \'leg spin\'. However, other sources use the term \'leg spin\' more widely, to include all deliveries bowled by a leg spinner, including non-leg break deliveries. **Leg break:** In the definition of a leg break, some sources actually include the bowler being a leg spinner, which implies that only leg spinners can bowl leg breaks; all leg breaks are bowled by leg spinners. Other sources do not include the bowler being a leg spinner in the definition of a leg break, and say a leg break is simply a delivery that spins from the legside to the offside, and so can also be bowled by other types of bowler. In this case, leg breaks are (only) mostly bowled by leg spinners.
**Leg spinner:** The term leg spinner can be used to mean either the bowler or the leg break delivery.
**Leggie:** The term leggie can also be used to mean either the bowler or the leg break delivery.
## Technique
A leg break is bowled by holding the cricket ball in the palm of the hand with the seam running across under all the fingers. As the ball is released, the wrist is rotated to the left and the ball flicked by the ring finger, giving the ball an anti-clockwise spin as seen from behind.
To grip the ball for a leg-spinning delivery, the ball is placed into the palm with the seam parallel to the palm. The first two fingers then spread and grip the ball, and the third and fourth fingers close together and rest against the side of the ball. The first bend of the third finger should grasp the seam. The thumb resting against the side is up to the bowler but should impart no pressure. When the ball is bowled, the third finger will apply most of the spin. The wrist is cocked as it comes down by the hip, and the wrist moves sharply from right to left as the ball is released, adding more spin. The ball is tossed up to provide flight. The batter will see the hand with the palm facing towards them when the ball is released. `{{clear left}}`{=mediawiki}
## Notable leg spin bowlers {#notable_leg_spin_bowlers}
Players listed below have been included as they meet specific criteria which the general cricketing public would recognise as having achieved significant success in the art of leg spin bowling. For example: leading wicket-takers, and inventors of new deliveries.
- Shane Warne -- 708 Test wickets (second all-time), one of five Wisden Cricketers of the Century
- Bernard Bosanquet -- credited with inventing the googly (also known as the \"Bosie\" in Australia)
- Robin Hobbs -- the last English leg spin bowler to take 1,000 first-class wickets in his career. In all he took 1,099 with a best of 8 for 63 at an average of 27.09.
- B. S. Chandrasekhar -- took 16 five-wicket hauls
- Clarrie Grimmett -- 216 Test wickets
- Anil Kumble -- 619 Test wickets (currently 4th on the list of all-time Test cricket wicket takers), best bowling in an innings of 10/74
- Abdul Qadir -- took 10 wickets in a Test match on five occasions
- Tich Freeman - 3776 first-class wickets, the second of all time and the most of any leg spin bowler. He played his last Test match from August 17-20, 1929, against South Africa at The Oval**.**
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# Leg spin
## Other deliveries bowled by leg spin bowlers {#other_deliveries_bowled_by_leg_spin_bowlers}
Highly skilled leg spin bowlers are also able to bowl deliveries that behave unexpectedly, including the googly, which turns the opposite way to a normal leg break and the top spinner, which does not turn but dips sharply and bounces higher than other deliveries. A few leg spinners such as Abdul Qadir, Anil Kumble, Shane Warne and Mushtaq Ahmed have also mastered the flipper, a delivery that like a top spinner goes straight on landing, but floats through the air before skidding and keeping low, often dismissing batters leg before wicket or bowled. Another variation in the arsenal of some leg spinners is the slider, but travels more straight on
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# Links (web browser)
**Links** is a free software text and graphical web browser with a pull-down menu system. It renders complex pages, has partial HTML 4.0 support (including tables, frames, and support for UTF-8), supports color and monochrome terminals, and allows horizontal scrolling.
It is intended for users who want to retain many typical elements of graphical user interfaces (pop-up windows, menus, etc.) in a text-only environment.
The original version of Links was developed by Mikuláš Patočka in the Czech Republic. His group, *\"Twibright Labs\",* later developed version 2 of the Links browser, which displays graphics, and renders fonts in different sizes (with spatial anti-aliasing), but no longer supports JavaScript (it used to, up to version 2.1pre28). The resulting browser is very fast, but does not display many pages as intended. The graphical mode works even on Unix systems without the X Window System or any other window environment, using either SVGAlib or the framebuffer of the system\'s graphics card.
## Forks
### ELinks
*Experimental/Enhanced Links* (ELinks) is a fork of Links led by Petr Baudis. It is based on Links 0.9. It has a more open development and incorporates patches from other Links versions (such as additional extension scripting in Lua) and from Internet users.
### Hacked Links {#hacked_links}
*Hacked Links* is another version of the Links browser which has merged some of Elinks\' features into Links 2.
Andrey Mirtchovski has ported it to Plan 9 from Bell Labs. It is considered a good browser on that operating system, though some users have complained about its inability to cut and paste with the Plan 9 snarf buffer.
, the last release of Hacked Links is that of July 9, 2003, with some further changes unreleased.
### Other
Links was also ported to run on the Sony PSP platform as PSPRadio by Rafael Cabezas with the last version (2.1pre23_PSP_r1261) released on February 6, 2007.
The BeOS port was updated by François Revol who also added GUI support. It also runs on Haiku
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# Learning object
A **learning object** is \"a collection of content items, practice items, and assessment items that are combined based on a single learning objective\". The term is credited to Wayne Hodgins, and dates from a working group in 1994 bearing the name. The concept encompassed by \'Learning Objects\' is known by numerous other terms, including: content objects, chunks, educational objects, information objects, intelligent objects, knowledge bits, knowledge objects, learning components, media objects, reusable curriculum components, nuggets, reusable information objects, reusable learning objects, testable reusable units of cognition, training components, and units of learning.
The core idea of the use of learning objects is characterized by the following: discoverability, reusability, and interoperability. To support discoverability, learning objects are described by Learning Object Metadata, formalized as IEEE 1484.12 Learning object metadata. To support reusability, the IMS Consortium proposed a series of specifications such as the IMS Content package. And to support interoperability, the U.S. military\'s Advanced Distributed Learning organization created the Sharable Content Object Reference Model. Learning objects were designed in order to reduce the cost of learning, standardize learning content, and to enable the use and reuse of learning content by learning management systems.
## Definitions
The Institute of Electrical and Electronics Engineers (IEEE) defines a learning object as \"any entity, digital or non-digital, that may be used for learning, education or training\".
Chiappe defined Learning Objects as: \"A digital self-contained and reusable entity, with a clear educational purpose, with at least three internal and editable components: content, learning activities and elements of context. The learning objects must have an external structure of information to facilitate their identification, storage and retrieval: the metadata.\"
The following definitions focus on the relation between learning object and digital media. RLO-CETL, a British inter-university Learning Objects Center, defines \"reusable learning objects\" as \"web-based interactive chunks of e-learning designed to explain a stand-alone learning objective\". Daniel Rehak and Robin Mason define it as \"a digitized entity which can be used, reused or referenced during technology supported learning\".
Adapting a definition from the Wisconsin Online Resource Center, Robert J. Beck suggests that learning objects have the following key characteristics:
- Learning objects are a new way of thinking about learning content. Traditionally, content comes in a several hour chunk. Learning objects are much smaller units of learning, typically ranging from 2 minutes to 15 minutes.
- Are self-contained -- each learning object can be taken independently
- Are reusable -- a single learning object may be used in multiple contexts for multiple purposes
- Can be aggregated -- learning objects can be grouped into larger collections of content, including traditional course structures
- Are tagged with metadata -- every learning object has descriptive information allowing it to be easily found by a search
## Components
The following is a list of some of the types of information that may be included in a learning object and its metadata:
- General Course Descriptive Data, including: course identifiers, language of content (English, Spanish, etc.), subject area (Maths, Reading, etc.), descriptive text, descriptive keywords
- Life Cycle, including: version, status
- Instructional Content, including: text, web pages, images, sound, video
- Glossary of Terms, including: terms, definition, acronyms
- Quizzes and Assessments, including: questions, answers
- Rights, including: cost, copyrights, restrictions on Use
- Relationships to Other Courses, including prerequisite courses
- Educational Level, including: grade level, age range, typical learning time, and difficulty. \[IEEE 1484.12.1:2002\]
- Typology as defined by Churchill (2007): presentation, practice, simulation, conceptual models, information, and contextual representation
## Metadata
One of the key issues in using learning objects is their identification by search engines or content management systems. This is usually facilitated by assigning descriptive learning object metadata. Just as a book in a library has a record in the card catalog, learning objects must also be tagged with metadata. The most important pieces of metadata typically associated with a learning object include:
1. **objective:** The educational objective the learning object is instructing
2. **prerequisites:** The list of skills (typically represented as objectives) which the learner must know before viewing the learning object
3. **topic:** Typically represented in a taxonomy, the topic the learning object is instructing
4. **interactivity:** The Interaction Model of the learning object.
5. **technology requirements:** The required system requirements to view the learning object.
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# Learning object
## Mutability
A mutated learning object is, according to Michael S. Shaw, MSc (2003), a learning object that has been \"re-purposed and/or re-engineered, changed or simply re-used in some way different from its original intended design\". In other words, educational content or learning materials, initially designed for a specific domain, may be intentionally or unintentionally, repurposed or applied, or become relevant in some significant way to the learner or situation, even though it is from a totally different domain. This interpretation aligns with the idea that the inherent properties of the learning objects remain constant, but their application becomes beneficial and adaptable across diverse domains. Shaw\'s speculative interpretation suggests an intrinsic stimulation of cognitive flexibility and creative reuse of learning resources for the learner. Shaw also introduces the term \"contextual learning object\", to describe a learning object with high specificity, that has been \"designed to have specific meaning and purpose to an intended learner\". This may be useful if the intent involves just-in-time learning and the individual needs of individual learners.
## Portability
Before any institution invests a great deal of time and energy into building high-quality e-learning content (which can cost over \$10,000 per classroom hour), it needs to consider how this content can be easily loaded into a Learning Management System. It is possible for example, to package learning objects with SCORM specification and load it in Moodle Learning Management System or Desire2Learn Learning Environment.
If all of the properties of a course can be precisely defined in a common format, the content can be serialized into a standard format such as XML and loaded into other systems. When it is considered that some e-learning courses need to include video, mathematical equations using MathML, chemistry equations using CML and other complex structures, the issues become very complex, especially if the systems needs to understand and validate each structure and then place it correctly in a database.
## Criticism
In 2001, David Wiley criticized learning object theory in his paper, [The Reusability Paradox](https://web.archive.org/web/20041019162710/http://rclt.usu.edu/whitepapers/paradox.html) which is [summarized by D\'Arcy Norman](http://www.darcynorman.net/2003/08/21/addressing-the-reusability-paradox/) `{{Webarchive|url=https://web.archive.org/web/20210502180411/https://darcynorman.net/2003/08/21/addressing-the-reusability-paradox/ |date=2021-05-02 }}`{=mediawiki} as, *If a learning object is useful in a particular context, by definition it is not reusable in a different context. If a learning object is reusable in many contexts, it isn't particularly useful in any.* In [Three Objections to Learning Objects and E-learning Standards](http://www.learningspaces.org/papers/objections.html) `{{Webarchive|url=https://web.archive.org/web/20210415054958/http://www.learningspaces.org/papers/objections.html |date=2021-04-15 }}`{=mediawiki}, Norm Friesen, Canada Research Chair in E-Learning Practices at Thompson Rivers University, points out that the word *neutrality* in itself implies *a state or position that is antithetical \... to pedagogy and teaching
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# List of Labour parties
The name \"Labour Party\" (or \"Labor Party\") is used by political parties around the world, particularly in Commonwealth nations. Historically, these parties are associated with democratic socialism, although not exclusively. Over time, most have evolved into social democratic parties. They are traditionally allied with trade unions and the broader labour movement. Many Labour parties are also members of the Socialist International or participants in the Progressive Alliance.
## Active Labour parties {#active_labour_parties}
+---------------------+-----------------------------------------------------------------+
| Nation or territory | Party |
+=====================+=================================================================+
| | People\'s Movement for the Liberation of Angola -- Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Antigua Labour Party |
+---------------------+-----------------------------------------------------------------+
| | All Armenian Labour Party\ |
| | United Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Australian Labor Party |
+---------------------+-----------------------------------------------------------------+
| | Barbados Labour Party\ |
| | Democratic Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Belarusian Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Progressive Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Bougainville Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Brazilian Labour Renewal Party |
+---------------------+-----------------------------------------------------------------+
| | Democratic Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Independent Labor Party |
+---------------------+-----------------------------------------------------------------+
| | Congolese Party of Labour |
+---------------------+-----------------------------------------------------------------+
| | Croatian Labourists -- Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Labour Party People\'s Crusade |
+---------------------+-----------------------------------------------------------------+
| | Dominica Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Fiji Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Georgian Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Gibraltar Socialist Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Grenada United Labor Party |
+---------------------+-----------------------------------------------------------------+
| | Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Labour House |
+---------------------+-----------------------------------------------------------------+
| | Islamic Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Labour Party of Iran (banned/exiled) |
+---------------------+-----------------------------------------------------------------+
| | Islamic Association of Workers |
+---------------------+-----------------------------------------------------------------+
| | Islamic Labour Welfare Party |
+---------------------+-----------------------------------------------------------------+
| | Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Manx Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Jamaica Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Labor Party of Liberia |
+---------------------+-----------------------------------------------------------------+
| | Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Labor Party |
+---------------------+-----------------------------------------------------------------+
| | Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Labour Party |
+---------------------+-----------------------------------------------------------------+
| | New Zealand Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Social Democratic and Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Labour Party\ |
| | People\'s Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Polish Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Portuguese Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Saint Kitts and Nevis Labour Party |
+---------------------+-----------------------------------------------------------------+
| | People\'s Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Saint Lucia Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Unity Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Scottish Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Solomon Islands Labour Party |
+---------------------+-----------------------------------------------------------------+
| | New Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Labor Party |
+---------------------+-----------------------------------------------------------------+
| | Surinamese Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Swedish Social Democratic Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Swiss Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Tanzania Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Labor Party |
+---------------------+-----------------------------------------------------------------+
| | Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Labour Party\ |
| | Socialist Labour Party\ |
| | Labour and Co-operative Party |
+---------------------+-----------------------------------------------------------------+
| | Minnesota Democratic--Farmer--Labor Party |
+---------------------+-----------------------------------------------------------------+
| | Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Welsh Labour Party |
+---------------------+-----------------------------------------------------------------+
| | Zimbabwe Labour Party |
+---------------------+-----------------------------------------------------------------+
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# List of Labour parties
## Historical Labour parties {#historical_labour_parties}
+--------+---------------------------------------------------------------------------------+
| Nation | Party |
+========+=================================================================================+
| | Party of Labour of Albania |
+--------+---------------------------------------------------------------------------------+
| | Socialist Labor Party\ |
| | Industrial Socialist Labor Party\ |
| | United Labour Party (S.A., 1891--1917) see ALP history |
+--------+---------------------------------------------------------------------------------+
| | Agrarian Socialist and Labour Renewal Party 1985--1990\ |
| | Brazilian Labour Party 1945--1964\ |
| | Brazilian Labour Party 1981--2023\ |
| | Brazilian Renewal Labour Party 1993--1995\ |
| | Christian Labour Party (former name of Agir)\ |
| | Comunitary Labour Party 1992\ |
| | Labour Party of Brazil (former name of Avante)\ |
| | National Labour Party 1945--1965\ |
| | Orienting Labour Party 1945--1961\ |
| | Reformer Labour Party 1985--1986\ |
| | Renewal Labour Movement 1959--1965\ |
| | Renewal Labour Party 1985--1993\ |
| | Republican Labour Party 1948--1965\ |
| | Social Labour Party 1946--1965\ |
| | Social Labour Party 1996--2003 |
+--------+---------------------------------------------------------------------------------+
| | Belgian Labour Party |
+--------+---------------------------------------------------------------------------------+
| | Party of Labour of Burkina\ |
| | Voltaic Labour Party 1970 |
+--------+---------------------------------------------------------------------------------+
| | Canadian Labour Party 1917-1929\ |
| | Labour Party of Canada 1870s-1960s\ |
| | Co-operative Commonwealth Federation - (Farmer-Labour-Socialist) 1932-1961\ |
| | Labor-Progressive Party\ |
| | North American Labour Party |
+--------+---------------------------------------------------------------------------------+
| | Croatian Labour Party, 1906-1918 |
+--------+---------------------------------------------------------------------------------+
| | Gibraltar Labour Party |
+--------+---------------------------------------------------------------------------------+
| | Socialist Labour Party of Greece |
+--------+---------------------------------------------------------------------------------+
| | Labour Party |
+--------+---------------------------------------------------------------------------------+
| | Guatemalan Party of Labour -- Alamos |
+--------+---------------------------------------------------------------------------------+
| | Independent Labour Party\ |
| | Labour Kisan Party of Hindustan |
+--------+---------------------------------------------------------------------------------+
| | Labour Party (1949)\ |
| | Labour Party of Indonesia\ |
| | Labour Party (1998) |
+--------+---------------------------------------------------------------------------------+
| | Israeli Labor Party |
+--------+---------------------------------------------------------------------------------+
| | Labour Federation |
+--------+---------------------------------------------------------------------------------+
| | National Labour Party |
+--------+---------------------------------------------------------------------------------+
| | Democratic Labour Party of Lithuania |
+--------+---------------------------------------------------------------------------------+
| | Labour Party |
+--------+---------------------------------------------------------------------------------+
| | Labour Party |
+--------+---------------------------------------------------------------------------------+
| | Central Democratic Labour Party |
+--------+---------------------------------------------------------------------------------+
| | Labour Party (original)\ |
| | United Labour Party\ |
| | Democratic Labour Party\ |
| | NewLabour Party |
+--------+---------------------------------------------------------------------------------+
| | Cape Breton Labour Party 1970-1984 |
+--------+---------------------------------------------------------------------------------+
| | Labour Party |
+--------+---------------------------------------------------------------------------------+
| | Labor Party |
+--------+---------------------------------------------------------------------------------+
| | Western Samoa Labour Party |
+--------+---------------------------------------------------------------------------------+
| | Labour Party of Sine Saloum |
+--------+---------------------------------------------------------------------------------+
| | Labour Party |
+--------+---------------------------------------------------------------------------------+
| | Labour Party |
+--------+---------------------------------------------------------------------------------+
| | Labour Party\ |
| | Labour Party (Coloured) |
+--------+---------------------------------------------------------------------------------+
| | Democratic Labor Party |
+--------+---------------------------------------------------------------------------------+
| | Trinidad Labour Party\ |
| | Democratic Labour Party\ |
| | United Labour Front\ |
| | Social Democratic Labour Party of Trinidad and Tobago\ |
| | Caribbean National Labour Party |
+--------+---------------------------------------------------------------------------------+
| | Communist Labour Party (Scotland)\ |
| | Independent Labour Party\ |
| | National Labour\ |
| | Belfast Labour Party\ |
| | Labour Party of Northern Ireland\ |
| | Labour Party of Scotland (former name of Scottish branch of Labour Party (UK))\ |
| | Northern Ireland Labour Party\ |
| | Republican Labour Party (In Northern Ireland)\ |
| | Scottish Labour Party (1888-1895)\ |
| | Scottish Labour Party (1976-1981) |
+--------+---------------------------------------------------------------------------------+
| | Labor Party (United States, 19th century)\ |
| | Union Labor Party (California)\ |
| | Socialist Labor Party of America\ |
| | Farmer--Labor Party (United States)\ |
| | Minnesota Farmer-Labor Party\ |
| | Labor Party of the United States\ |
| | American Labor Party\ |
| | American Labor Party (1932)\ |
| | U.S
| 623 |
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# Lorenz curve
upright=1.2\|thumb\|A typical Lorenz curve In economics, the **Lorenz curve** is a graphical representation of the distribution of income or of wealth. It was developed by Max O. Lorenz in 1905 for representing inequality of the wealth distribution.
The curve is a graph showing the proportion of overall income or wealth assumed by the bottom `{{nowrap|{{mvar|x}}%}}`{=mediawiki} of the people, although this is not rigorously true for a finite population (see below). It is often used to represent income distribution, where it shows for the bottom `{{nowrap|{{mvar|x}}%}}`{=mediawiki} of households, what percentage `{{nowrap|({{mvar|y}}%)}}`{=mediawiki} of the total income they have. The percentage of households is plotted on the `{{mvar|x}}`{=mediawiki}-axis, the percentage of income on the `{{mvar|y}}`{=mediawiki}-axis. It can also be used to show distribution of assets. In such use, many economists consider it to be a measure of social inequality.
The concept is useful in describing inequality among the size of individuals in ecology and in studies of biodiversity, where the cumulative proportion of species is plotted against the cumulative proportion of individuals. It is also useful in business modeling: e.g., in consumer finance, to measure the actual percentage `{{nowrap|{{mvar|y}}%}}`{=mediawiki} of delinquencies attributable to the `{{nowrap|{{mvar|x}}%}}`{=mediawiki} of people with worst risk scores. Lorenz curves were also applied to epidemiology and public health, e.g., to measure pandemic inequality as the distribution of national cumulative incidence (y%) generated by the population residing in areas (x%) ranked with respect to their local epidemic attack rate.
## Explanation
Data from 2005. Points on the Lorenz curve represent statements such as, \"the bottom 20% of all households have 10% of the total income.\"
A perfectly equal income distribution would be one in which every person has the same income. In this case, the bottom `{{nowrap|{{mvar|N}}%}}`{=mediawiki} of society would always have `{{nowrap|{{mvar|N}}%}}`{=mediawiki} of the income. This can be depicted by the straight line `{{math|1=''y'' = ''x''}}`{=mediawiki}; called the \"line of perfect equality.\"
By contrast, a perfectly unequal distribution would be one in which one person has all the income and everyone else has none. In that case, the curve would be at `{{math|1=''y'' = 0%}}`{=mediawiki} for all `{{math|''x'' < 100%}}`{=mediawiki}, and `{{math|1=''y'' = 100%}}`{=mediawiki} when `{{math|1=''x'' = 100%}}`{=mediawiki}. This curve is called the \"line of perfect inequality.\"
The Gini coefficient is the ratio of the area between the line of perfect equality and the observed Lorenz curve to the area between the line of perfect equality and the line of perfect inequality. The higher the coefficient, the more unequal the distribution is. In the diagram on the right, this is given by the ratio `{{math|''A'' / (''A''+''B'')}}`{=mediawiki}, where `{{mvar|A}}`{=mediawiki} and `{{mvar|B}}`{=mediawiki} are the areas of regions as marked in the diagram.
| 444 |
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| 0 |
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# Lorenz curve
## Definition and calculation {#definition_and_calculation}
upright=1.2\|thumb\|Lorenz curve for US wealth distribution in 2016 showing negative wealth and oligarchy The Lorenz curve is a probability plot (a P--P plot) comparing the distribution of a variable against a hypothetical uniform distribution of that variable. It can usually be represented by a function `{{math|''L''(''F'')}}`{=mediawiki}, where `{{mvar|F}}`{=mediawiki}, the cumulative portion of the population, is represented by the horizontal axis, and `{{mvar|L}}`{=mediawiki}, the cumulative portion of the total wealth or income, is represented by the vertical axis.
The curve `{{mvar|L}}`{=mediawiki} need not be a smoothly increasing function of `{{mvar|F}}`{=mediawiki}, For wealth distributions there may be oligarchies or people with negative wealth for instance.
For a discrete distribution of Y given by values `{{math|''y''{{sub|1}}}}`{=mediawiki}, \..., `{{math|''y''{{sub|''n''}}}}`{=mediawiki} in non-decreasing order `{{math|(''y''{{sub|''i''}} ≤ ''y''{{sub|''i''+1}})}}`{=mediawiki} and their probabilities $f(y_j) := \Pr(Y=y_j)$ the Lorenz curve is the continuous piecewise linear function connecting the points `{{math|(''F''{{sub|''i''}}, ''L''{{sub|''i''}})}}`{=mediawiki}, `{{math|1=''i'' = 0 to ''n''}}`{=mediawiki}, where `{{math|1=''F''{{sub|0}} = 0}}`{=mediawiki}, `{{math|1=''L''{{sub|0}} = 0}}`{=mediawiki}, and for `{{math|1=''i'' = 1 to ''n''}}`{=mediawiki}: $\begin{align}
F_i &:= \sum_{j=1}^i f(y_j) \\
S_i &:= \sum_{j=1}^i f(y_j) \, y_j \\
L_i &:= \frac{S_i}{S_n}
\end{align}$
When all `{{math|''y''{{sub|''i''}}}}`{=mediawiki} are equally probable with probabilities `{{math|1 / ''n''}}`{=mediawiki} this simplifies to $\begin{align}
F_i &= \frac i n \\
S_i &= \frac 1 n \sum_{j=1}^i \; y_j \\
L_i &= \frac{S_i}{S_n}
\end{align}$
For a continuous distribution with the probability density function `{{mvar|f}}`{=mediawiki} and the cumulative distribution function `{{mvar|F}}`{=mediawiki}, the Lorenz curve `{{mvar|L}}`{=mediawiki} is given by: $L(F(x)) = \frac{\int_{-\infty}^x t\,f(t)\,dt}{\int_{-\infty}^\infty t\,f(t)\,dt} = \frac{\int_{-\infty}^x t\,f(t)\,dt}{\mu}$ where $\mu$ denotes the average. The Lorenz curve `{{math|''L''(''F'')}}`{=mediawiki} may then be plotted as a function parametric in `{{mvar|x}}`{=mediawiki}: `{{math|''L''(''x'')}}`{=mediawiki} vs. `{{math|''F''(''x'')}}`{=mediawiki}. In other contexts, the quantity computed here is known as the length biased (or size biased) distribution; it also has an important role in renewal theory.
Alternatively, for a cumulative distribution function `{{math|''F''(''x'')}}`{=mediawiki} with inverse `{{math|''x''(''F'')}}`{=mediawiki}, the Lorenz curve `{{math|''L''(''F'')}}`{=mediawiki} is directly given by: $L(F) = \frac{\int_0^F x(F_1)\,dF_1}{\int_0^1 x(F_1)\,dF_1}$
The inverse `{{math|''x''(''F'')}}`{=mediawiki} may not exist because the cumulative distribution function has intervals of constant values. However, the previous formula can still apply by generalizing the definition of `{{math|''x''(''F'')}}`{=mediawiki}: $x(F_1) = \inf \{y : F(y) \geq F_1\}$ where `{{math|inf}}`{=mediawiki} is the infimum.
For an example of a Lorenz curve, see Pareto distribution.
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# Lorenz curve
## Properties
A Lorenz curve always starts at (0,0) and ends at (1,1).
The Lorenz curve is not defined if the mean of the probability distribution is zero or infinite.
The Lorenz curve for a probability distribution is a continuous function. However, Lorenz curves representing discontinuous functions can be constructed as the limit of Lorenz curves of probability distributions, the line of perfect inequality being an example.
The information in a Lorenz curve may be summarized by the Gini coefficient and the Lorenz asymmetry coefficient.
The Lorenz curve cannot rise above the line of perfect equality.
A Lorenz curve that never falls beneath a second Lorenz curve and at least once runs above it, has Lorenz dominance over the second one.
If the variable being measured cannot take negative values, the Lorenz curve:
- cannot sink below the line of perfect inequality,
- is increasing.
Note however that a Lorenz curve for net worth would start out by going negative due to the fact that some people have a negative net worth because of debt.
The Lorenz curve is invariant under positive scaling. If `{{math|'''''X'''''}}`{=mediawiki} is a random variable, for any positive number `{{mvar|c}}`{=mediawiki} the random variable `{{mvar|c'''X'''}}`{=mediawiki} has the same Lorenz curve as `{{math|'''''X'''''}}`{=mediawiki}.
The Lorenz curve is flipped twice, once about `{{math|1=''F'' = 0.5}}`{=mediawiki} and once about `{{math|1=''L'' = 0.5}}`{=mediawiki}, by negation. If `{{math|'''''X'''''}}`{=mediawiki} is a random variable with Lorenz curve `{{math|''L''{{sub|'''''X'''''}}(''F'')}}`{=mediawiki}, then `{{math|−'''''X'''''}}`{=mediawiki} has the Lorenz curve:
:
The Lorenz curve is changed by translations so that the equality gap `{{math|''F'' − ''L''(''F'')}}`{=mediawiki} changes in proportion to the ratio of the original and translated means. If `{{math|'''''X'''''}}`{=mediawiki} is a random variable with a Lorenz curve `{{math|1=''L''{{sub|'''''X'''''}}(''F'')}}`{=mediawiki} and mean `{{math|''μ''{{sub|'''''X'''''}}}}`{=mediawiki}, then for any constant `{{math|''c'' ≠ −''μ''{{sub|'''''X'''''}}}}`{=mediawiki}, `{{math|'''''X''''' + ''c''}}`{=mediawiki} has a Lorenz curve defined by: $F - L_{X+c}(F) = \frac{\mu_X}{\mu_X + c} ( F - L_X(F))$
For a cumulative distribution function `{{math|''F''(''x'')}}`{=mediawiki} with mean `{{mvar|μ}}`{=mediawiki} and (generalized) inverse `{{math|''x''(''F'')}}`{=mediawiki}, then for any `{{mvar|F}}`{=mediawiki} with 0 \< `{{math|''F'' < 1}}`{=mediawiki} :
- If the Lorenz curve is differentiable$$\frac{d L(F)}{d F} = \frac{x(F)}{\mu}$$
- If the Lorenz curve is twice differentiable, then the probability density function `{{math|''f''(''x'')}}`{=mediawiki} exists at that point and: $\frac{d^2 L(F)}{d F^2} = \frac{1}{\mu\,f(x(F))}\,$
- If `{{math|''L''(''F'')}}`{=mediawiki} is continuously differentiable, then the tangent of `{{math|''L''(''F'')}}`{=mediawiki} is parallel to the line of perfect equality at the point `{{math|''F''(''μ'')}}`{=mediawiki}. This is also the point at which the equality gap `{{math|''F'' − ''L''(''F'')}}`{=mediawiki}, the vertical distance between the Lorenz curve and the line of perfect equality, is greatest. The size of the gap is equal to half of the relative mean absolute deviation: $F(\mu) - L(F(\mu)) = \frac{\text{mean absolute deviation}}{2\,\mu}$
## Examples
Both `{{math|1=''L''(''F'') = ''F''{{isup|''P''}}}}`{=mediawiki} and `{{math|1=''L''(''F'') = 1 − (1 − ''F''){{isup|1/''P''}}}}`{=mediawiki}, for `{{math|''P'' ≥ 1}}`{=mediawiki}, are well-known functional forms for the Lorenz curve
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# League of Nations mandate
A **League of Nations mandate** represented a legal status under international law for specific territories following World War I, involving the transfer of control from one nation to another. These mandates served as legal documents establishing the internationally agreed terms for administering the territory on behalf of the League of Nations. Combining elements of both a treaty and a constitution, these mandates contained minority rights clauses that provided for the rights of petition and adjudication by the Permanent Court of International Justice.
The mandate system was established under Article 22 of the Covenant of the League of Nations, entered into force on 28 June 1919. With the dissolution of the League of Nations after World War II, it was stipulated at the Yalta Conference that the remaining mandates should be placed under the trusteeship of the United Nations, subject to future discussions and formal agreements. Most of the remaining mandates of the League of Nations (with the exception of South West Africa) thus eventually became United Nations trust territories.
Two governing principles formed the core of the Mandate System, being non-annexation of the territory and its administration as a \"sacred trust of civilisation\" to develop the territory for the benefit of its native people.
According to historian Susan Pedersen, colonial administration in the mandates did not differ substantially from colonial administration elsewhere. Even though the Covenant of the League committed the great powers to govern the mandates differently, the main difference appeared to be that the colonial powers spoke differently about the mandates than their other colonial possessions.
## Basis
The mandate system was established by Article 22 of the Covenant of the League of Nations, drafted by the victors of World War I. The article referred to territories which after the war were no longer ruled by their previous sovereign, but their peoples were not considered \"able to stand by themselves under the strenuous conditions of the modern world\". The article called for such people\'s tutelage to be \"entrusted to advanced nations who by reason of their resources, their experience or their geographical position can best undertake this responsibility\".
U.S. President Woodrow Wilson and South African General Jan Smuts played influential roles in pushing for the establishment of a mandates system. The mandates system reflected a compromise between Smuts (who wanted colonial powers to annex the territories) and Wilson (who wanted trusteeship over the territories).
## Generalities
All of the territories subject to League of Nations mandates were previously controlled by states defeated in World War I, principally Imperial Germany and the Ottoman Empire. The mandates were fundamentally different from the protectorates in that the mandatory power undertook obligations to the inhabitants of the territory and to the League of Nations.
The process of establishing the mandates consisted of two phases:
1. The formal removal of sovereignty of the state previously controlling the territory.
2. The transfer of mandatory powers to individual states among the Allied Powers.
### Treaties
The divestiture of Germany\'s overseas colonies, along with three territories disentangled from its European homeland area (the Free City of Danzig, the Memel Territory, and the Saar), was accomplished in the Treaty of Versailles (1919), with the territories being allotted among the Allies on 7 May of that year. Ottoman territorial claims were first addressed in the Treaty of Sèvres (1920) and finalised in the Treaty of Lausanne (1923). The Ottoman territories were allotted among the Allied Powers at the San Remo conference in 1920.
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# League of Nations mandate
## Types of mandates {#types_of_mandates}
The League of Nations decided the exact level of control by the mandatory power over each mandate on an individual basis. However, in every case the mandatory power was forbidden to construct fortifications or raise an army within the territory of the mandate, and was required to present an annual report on the territory to the Permanent Mandates Commission of the League of Nations.
The mandates were divided into three distinct groups based upon the level of development each population had achieved at that time.
### Class A mandates {#class_a_mandates}
The first group, or *Class A mandates*, were territories formerly controlled by the Ottoman Empire that were deemed to \"\... have reached a stage of development where their existence as independent nations can be provisionally recognised subject to the rendering of administrative advice and assistance by a Mandatory until such time as they are able to stand alone. The wishes of these communities must be a principal consideration in the selection of the Mandatory.\"
### Class B mandates {#class_b_mandates}
The second group of mandates, or *Class B mandates*, were all former German colonies in West and Central Africa, referred to by Germany as *Schutzgebiete* (protectorates or territories), which were deemed to require a greater level of control by the mandatory power: \"\...the Mandatory must be responsible for the administration of the territory under conditions which will guarantee freedom of conscience and religion.\" The mandatory power was forbidden to construct military or naval bases within the mandates.
### Class C mandates {#class_c_mandates}
*Class C mandates*, including South West Africa and the South Pacific Islands, were considered to be \"best administered under the laws of the Mandatory as integral portions of its territory.\"
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# League of Nations mandate
## List of mandates {#list_of_mandates}
+-------+-------------------------------------------------------------------------------------------------------------------------+-------------------------+----------------+---------------------------------------------------------------------------+-------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------------+-----------------------------------------------------------------------------------------+
| Class | Mandate | Territory | Mandate Power | Prior name | Prior sovereignty | Comments | Current state | Document |
+=======+=========================================================================================================================+=========================+================+===========================================================================+===================+============================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================+=================================+=========================================================================================+
| **A** | Mandate for Syria and the Lebanon | Greater Lebanon | France | Ottoman sanjaks of Beirut, Tripoli, and Mount Lebanon | Ottoman Empire | 29 September 1923 -- 24 October 1945. Joined the United Nations on 24 October 1945 as an independent state and Founding Member | Lebanon | |
+-------+-------------------------------------------------------------------------------------------------------------------------+-------------------------+----------------+---------------------------------------------------------------------------+-------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------------+-----------------------------------------------------------------------------------------+
| | | Syria | | Ottoman sanjaks of Damascus, Hauran, Latakia, Homs, Hama, Aleppo, and Zor | | 29 September 1923 -- 24 October 1945: This mandate included Hatay Province (a former Ottoman Alexandretta sanjak), which broke away from the mandate on 2 September 1938 to become a separate French protectorate, which lasted until Hatay Province was ceded to the new Republic of Turkey on 29 June 1939. Joined the United Nations on 24 October 1945 as an independent state | Syria | |
+-------+-------------------------------------------------------------------------------------------------------------------------+-------------------------+----------------+---------------------------------------------------------------------------+-------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------------+-----------------------------------------------------------------------------------------+
| | Mandate for Palestine | Mandatory Palestine | United Kingdom | Ottoman sanjaks of Jerusalem, Nablus, and Acre | | 29 September 1923 -- 15 May 1948. A United Nations Partition Plan for Palestine for peacefully dividing the remainder of the Mandate failed. The Mandate terminated at midnight between 14 May and 15 May 1948. On the evening of 14 May, the Chairman of the Jewish Agency for Palestine had declared the establishment of the State of Israel. Following the war, 75% of the area was controlled by the new State of Israel. Other parts, until 1967, formed the West Bank of the Hashemite Kingdom of Jordan and the All-Palestine Government under the Egyptian-controlled Gaza Strip. | Israel\ | |
| | | | | | | | Palestine | |
+-------+-------------------------------------------------------------------------------------------------------------------------+-------------------------+----------------+---------------------------------------------------------------------------+-------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------------+-----------------------------------------------------------------------------------------+
| | | Emirate of Transjordan | | Ottoman sanjaks of Hauran and Ma\'an | | In April 1921, the Emirate of Transjordan was provisionally added as an autonomous area under the United Kingdom, and it became the independent Hashemite Kingdom of Transjordan (later Jordan) on 17 June 1946 upon joint ratification of the Treaty of London of 1946. | Jordan | |
+-------+-------------------------------------------------------------------------------------------------------------------------+-------------------------+----------------+---------------------------------------------------------------------------+-------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------------+-----------------------------------------------------------------------------------------+
| | *Indirect* | Mandatory Iraq | | Various Ottoman sanjaks | | The draft British Mandate for Mesopotamia was not enacted and was replaced by the Anglo-Iraqi Treaty of October 1922. Britain committed to act the responsibilities of a Mandatory Power in 1924. Iraq attained independence from the United Kingdom on 3 October 1932. | Iraq | |
+-------+-------------------------------------------------------------------------------------------------------------------------+-------------------------+----------------+---------------------------------------------------------------------------+-------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------------+-----------------------------------------------------------------------------------------+
| **B** | Belgian Mandate for East Africa | Ruanda-Urundi | Belgium | German East Africa | German Empire | From 20 July 1922 to 13 December 1946. Formerly two separate German protectorates, they were joined as a single mandate on 20 July 1922. From 1 March 1926 to 30 June 1960, Ruanda-Urundi was in administrative union with the neighbouring colony of the Belgian Congo. After 13 December 1946, it became a United Nations trust territory, remaining under Belgian administration until the separate nations of Rwanda and Burundi gained independence on 1 July 1962. | Rwanda\ | |
| | | | | | | | Burundi | |
+-------+-------------------------------------------------------------------------------------------------------------------------+-------------------------+----------------+---------------------------------------------------------------------------+-------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------------+-----------------------------------------------------------------------------------------+
| | British Mandate for East Africa | Tanganyika Territory | United Kingdom | | | From 20 July 1922 to 11 December 1946. It became a United Nations trust territory on 11 December 1946, and was granted internal self-rule on 1 May 1961. On 9 December 1961, it became independent while retaining the British monarch as nominal head of state, transforming into a republic on the same day the next year. On 26 April 1964, Tanganyika merged with the neighbouring island of Zanzibar to become the modern nation of Tanzania. | Tanzania | *Equivalent document as for Ruanda-Urundi, with all articles substantially the same* |
+-------+-------------------------------------------------------------------------------------------------------------------------+-------------------------+----------------+---------------------------------------------------------------------------+-------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------------+-----------------------------------------------------------------------------------------+
| | British Mandate for the Cameroons | British Cameroon | United Kingdom | German Kamerun | | Became part of the United Nations trust territories after World War II on 13 December 1946 | Part of Cameroon and Nigeria | *Equivalent document as for French Cameroons, with all articles substantially the same* |
+-------+-------------------------------------------------------------------------------------------------------------------------+-------------------------+----------------+---------------------------------------------------------------------------+-------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------------+-----------------------------------------------------------------------------------------+
| | French Mandate for the Cameroons | French Cameroon | France | | | Under a Resident and a Commissioner until 27 August 1940, then under a governor. Became part of the United Nations trust territories after World War II on 13 December 1946 | Cameroon | |
+-------+-------------------------------------------------------------------------------------------------------------------------+-------------------------+----------------+---------------------------------------------------------------------------+-------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------------+-----------------------------------------------------------------------------------------+
| | British Mandate for Togoland | British Togoland | United Kingdom | German Togoland | | British Administrator post filled by the colonial Governor of the British Gold Coast (present day Ghana) except 30 September 1920 -- 11 October 1923 Francis Walter Fillon Jackson). Transformed on 13 December 1946 into a United Nations trust territory; on 13 December 1956 it ceased to exist as it became part of Ghana. | Volta Region, Ghana | *Equivalent document as for French Togoland, with all articles substantially the same* |
+-------+-------------------------------------------------------------------------------------------------------------------------+-------------------------+----------------+---------------------------------------------------------------------------+-------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------------+-----------------------------------------------------------------------------------------+
| | French Mandate for Togoland | French Togoland | France | | | French Togoland under a Commissioner till 30 August 1956, then under a High Commissioner as the Autonomous Republic of Togo | Togo | |
+-------+-------------------------------------------------------------------------------------------------------------------------+-------------------------+----------------+---------------------------------------------------------------------------+-------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------------+-----------------------------------------------------------------------------------------+
| **C** | Mandate for the German Possessions in the Pacific Ocean situated South of the Equator other than German Samoa and Nauru | Territory of New Guinea | Australia | German New Guinea | German Empire | Included German New Guinea and \"the group of islands in the Pacific Ocean lying south of the equator other than German Samoa and Nauru\". From 17 December 1920 under an (at first Military) Administrator; after (wartime) Japanese/U.S. military commands from 8 December 1946 under UN mandate as North East New Guinea (under Australia, as administrative unit), until it became part of present Papua New Guinea at independence in 1975 | Part of Papua New Guinea | *Equivalent document as for Nauru, with all articles substantially the same* |
+-------+-------------------------------------------------------------------------------------------------------------------------+-------------------------+----------------+---------------------------------------------------------------------------+-------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------------+-----------------------------------------------------------------------------------------+
| | Mandate for Nauru | Nauru | United Kingdom | | | British mandate, administered by Australia, New Zealand, and the United Kingdom. Became part of the United Nations trust territories after liberation from Japanese occupation in World War II | Nauru | |
+-------+-------------------------------------------------------------------------------------------------------------------------+-------------------------+----------------+---------------------------------------------------------------------------+-------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------------+-----------------------------------------------------------------------------------------+
| | Mandate for the German Possessions in the Pacific Ocean lying North of the Equator | South Seas Mandate | Japan | | | Known as the South Seas Mandate. Became part of the United Nations trust territories and administered by the United States after World War II | Palau\ | *Equivalent document as for Nauru, with all articles substantially the same* |
| | | | | | | | Marshall Islands\ | |
| | | | | | | | Federated States of Micronesia\ | |
| | | | | | | | Northern Mariana Islands | |
+-------+-------------------------------------------------------------------------------------------------------------------------+-------------------------+----------------+---------------------------------------------------------------------------+-------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------------+-----------------------------------------------------------------------------------------+
| | Mandate for German Samoa | Western Samoa | New Zealand | German Samoa | | From 17 December 1920 a League of Nations mandate, renamed Western Samoa (as opposed to American Samoa), from 25 January 1947 a United Nations trust territory until its independence on 1 January 1962 | Samoa | *Equivalent document as for Nauru, with all articles substantially the same* |
+-------+-------------------------------------------------------------------------------------------------------------------------+-------------------------+----------------+---------------------------------------------------------------------------+-------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------------+-----------------------------------------------------------------------------------------+
| | Mandate for German South West Africa | South West Africa | South Africa | German South West Africa | | From 1 October 1922, Walvis Bay\'s administration (still merely having a Magistrate until its 16 March 1931 Municipal status, hence a Mayor) was also assigned to the mandate. | Namibia | *Equivalent document as for Nauru, with all articles substantially the same* |
+-------+-------------------------------------------------------------------------------------------------------------------------+-------------------------+----------------+---------------------------------------------------------------------------+-------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------------+-----------------------------------------------------------------------------------------+
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# League of Nations mandate
## Rules of establishment {#rules_of_establishment}
According to the Council of the League of Nations, meeting of August 1920: \"draft mandates adopted by the Allied and Associated Powers would not be definitive until they had been considered and approved by the League\... the legal title held by the mandatory Power must be a double one: one conferred by the Principal Powers and the other conferred by the League of Nations.\"
Three steps were required to establish a Mandate under international law: (1) The Principal Allied and Associated Powers confer a mandate on one of their number or on a third power; (2) the principal powers officially notify the council of the League of Nations that a certain power has been appointed mandatory for such a certain defined territory; and (3) the council of the League of Nations takes official cognisance of the appointment of the mandatory power and informs the latter that it \[the council\] considers it as invested with the mandate, and at the same time notifies it of the terms of the mandate, after ascertaining whether they are in conformance with the provisions of the covenant.\"
The U.S. State Department\'s *Digest of International Law* says that the terms of the Treaty of Lausanne provided for the application of the principles of state succession to the \"A\" Mandates. The Treaty of Versailles provisionally recognised the former Ottoman communities as independent nations. It also required Germany to recognise the disposition of the former Ottoman territories and to recognise the new states laid down within their boundaries. The terms of the Treaty of Lausanne required the newly created states that acquired the territory detached from the Ottoman Empire to pay annuities on the Ottoman public debt and to assume responsibility for the administration of concessions that had been granted by the Ottomans. The treaty also let the States acquire, without payment, all the property and possessions of the Ottoman Empire situated within their territory. The treaty provided that the League of Nations was responsible for establishing an arbitral court to resolve disputes that might arise and stipulated that its decisions were final.
A disagreement regarding the legal status and the portion of the annuities to be paid by the \"A\" mandates was settled when an Arbitrator ruled that some of the mandates contained more than one State:
> The difficulty arises here how one is to regard the Asiatic countries under the British and French mandates. Iraq is a Kingdom in regard to which Great Britain has undertaken responsibilities equivalent to those of a Mandatory Power. Under the British mandate, Palestine and Transjordan have each an entirely separate organisation. We are, therefore, in the presence of three States sufficiently separate to be considered as distinct Parties. France has received a single mandate from the Council of the League of Nations, but in the countries subject to that mandate, one can distinguish two distinct States: Syria and the Lebanon, each State possessing its own constitution and a nationality clearly different from the other.
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# League of Nations mandate
## Later history {#later_history}
After the United Nations was founded in 1945 and the League of Nations was disbanded, all but one of the mandated territories became United Nations trust territories, a roughly equivalent status. In each case, the colonial power that held the mandate on each territory became the administering power of the trusteeship, except that of the Empire of Japan, which had been defeated in World War II, lost its mandate over the South Pacific islands, which became a \"strategic trust territory\" known as the Trust Territory of the Pacific Islands under U.S. administration.
The sole exception to the transformation of the League of Nations mandates into UN trusteeships was that of South Africa and its mandated territory South West Africa. Rather than placing South West Africa under trusteeship like other former mandates, South Africa proposed annexation, a proposition rejected by the UN General Assembly. Despite South Africa\'s resistance, the International Court of Justice affirmed that South Africa continued to have international obligations regarding the South West Africa mandate. Eventually, in 1990, the mandated territory, now Namibia, gained independence, culminating from the Tripartite Accords and the resolution of the South African Border War --- a prolonged guerrilla conflict against the apartheid regime that lasted from 1966 until 1990.
Nearly all the former League of Nations mandates had become sovereign states by 1990, including all of the former UN trust territories with the exception of a few successor entities of the gradually dismembered Trust Territory of the Pacific Islands (formerly Japan\'s South Pacific Trust Mandate). These exceptions include the Northern Mariana Islands which is a commonwealth in political union with the U.S. with the status of unincorporated organised territory. The Northern Mariana Islands does elect its own governor to serve as territorial head of government, but it remains a U.S. territory with its head of state being the President of the United States and federal funds to the commonwealth administered by the Office of Insular Affairs of the U.S. Department of the Interior.
Remnant Micronesia and the Marshall Islands, the heirs of the last territories of the Trust, attained final independence on 22 December 1990. (The UN Security Council ratified termination of trusteeship, effectively dissolving trusteeship status, on 10 July 1987.) The Republic of Palau, split off from the Federated States of Micronesia, became the last to effectively gain its independence, on 1 October 1994
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# List of laser applications
Many scientific, military, medical and commercial **laser applications** have been developed since the invention of the laser in 1958. The coherency, high monochromaticity, and ability to reach extremely high powers are all properties which allow for these specialized applications.
## Scientific
In science, lasers are used in many ways, including:
- A wide variety of interferometric techniques
- Raman spectroscopy
- Laser induced breakdown spectroscopy
- Atmospheric *remote sensing*
- Investigating nonlinear optics phenomena
- Holographic techniques employing lasers also contribute to a number of measurement techniques.
- Laser based lidar (LIght raDAR) technology applications in geology, seismology, remote sensing and atmospheric physics.
- Three-dimensional structural modifications and writing inside technological materials.
- Lasers have been used aboard spacecraft such as in the Cassini-Huygens mission.
- In astronomy, lasers have been used to create artificial *laser guide stars*, used as reference objects for adaptive optics telescopes.
Lasers may also be indirectly used in spectroscopy as a micro-sampling system, a technique termed Laser ablation (LA), which is typically applied to ICP-MS apparatus resulting in the powerful LA-ICP-MS.
The principles of laser spectroscopy are discussed by Demtröder.
### Spectroscopy
Most types of laser are an inherently pure source of light; they emit near-monochromatic light with a very well defined range of wavelengths. By careful design of the laser components, the purity of the laser light (measured as the \"linewidth\") can be improved more than the purity of any other light source. This makes the laser a very useful source for spectroscopy. The high intensity of light that can be achieved in a small, well collimated beam can also be used to induce a nonlinear optical effect in a sample, which makes techniques such as Raman spectroscopy possible. Other spectroscopic techniques based on lasers can be used to make extremely sensitive detectors of various molecules, able to measure molecular concentrations in the parts-per-10^12^ (ppt) level. Due to the high power densities achievable by lasers, beam-induced atomic emission is possible: this technique is termed Laser induced breakdown spectroscopy (LIBS).
### Heat treatment {#heat_treatment}
Heat treating with the lasers allows selective surface hardening against wear with little or no distortion of the component. Because this eliminates much part reworking that is currently done, the laser system\'s capital cost is recovered in a short time. An inert, absorbent coating for laser heat treatment has also been developed that eliminates the fumes generated by conventional paint coatings during the heat-treating process with `{{CO2}}`{=mediawiki} laser beams.
One consideration crucial to the success of a heat treatment operation is control of the laser beam irradiance on the part surface. The optimal irradiance distribution is driven by the thermodynamics of the laser-material interaction and by the part geometry.
Typically, irradiances between 500 and 5000 W/cm\^2 satisfy the thermodynamic constraints and allow the rapid surface heating and minimal total heat input required. For general heat treatment, a uniform square or rectangular beam is one of the best options. For some special applications or applications where the heat treatment is done on an edge or corner of the part, it may be better to have the irradiance decrease near the edge to prevent melting.
### Weather
Research shows that scientists may one day be able to induce rain and lightning storms (as well as micro-manipulating some other weather phenomena) using high energy lasers. Such a breakthrough could potentially eradicate droughts, help alleviate weather related catastrophes, and allocate weather resources to areas in need.
### Lunar laser ranging {#lunar_laser_ranging}
When the Apollo astronauts visited the Moon, they planted retroreflector arrays to make possible the Lunar Laser Ranging Experiment. Laser beams are focused through large telescopes on Earth aimed toward the arrays, and the time taken for the beam to be reflected back to Earth measured to determine the distance between the Earth and Moon with high accuracy.
### Photochemistry
Some laser systems, through the process of mode locking, can produce extremely brief pulses of light - as short as picoseconds or femtoseconds (10^−12^ - 10^−15^ seconds). Such pulses can be used to initiate and analyze chemical reactions, a technique known as *photochemistry*. The short pulses can be used to probe the process of the reaction at a very high temporal resolution, allowing the detection of short-lived intermediate molecules. This method is particularly useful in biochemistry, where it is used to analyse details of protein folding and function.
### Laser scanner {#laser_scanner}
Laser barcode scanners are ideal for applications that require high speed reading of linear codes or stacked symbols.
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# List of laser applications
## Scientific
### Laser cooling {#laser_cooling}
A technique that has recent success is *laser cooling*. This involves atom trapping, a method where a number of atoms are confined in a specially shaped arrangement of electric and magnetic fields. Shining particular wavelengths of light at the ions or atoms slows them down, thus *cooling* them. As this process is continued, they all are slowed and have the same energy level, forming an unusual arrangement of matter known as a Bose--Einstein condensate.
### Nuclear fusion {#nuclear_fusion}
Some of the world\'s most powerful and complex arrangements of multiple lasers and optical amplifiers are used to produce extremely high intensity pulses of light of extremely short duration, e.g. laboratory for laser energetics, National Ignition Facility, GEKKO XII, Nike laser, Laser Mégajoule, HiPER. These pulses are arranged such that they impact pellets of tritium--deuterium simultaneously from all directions, hoping that the squeezing effect of the impacts will induce atomic fusion in the pellets. This technique, known as \"inertial confinement fusion\", so far has not been able to achieve \"breakeven\", that is, so far the fusion reaction generates less power than is used to power the lasers, however; experiments at the National Ignition Facility were able to demonstrate fusion reactions that generate more energy than was contained within the lasers driving the reaction.
### Particle acceleration {#particle_acceleration}
Powerful lasers producing ultra-short (in the tens of femtoseconds) and ultra-intense (up to 10^23^ W/cm^2^) laser pulses offer much greater acceleration gradients than that of conventional accelerators. This fact is exploited in several plasma acceleration techniques used for accelerating both electrons and charged ions to high energies.
### Microscopy
Confocal laser scanning microscopy and Two-photon excitation microscopy make use of lasers to obtain blur-free images of thick specimens at various depths. Laser capture microdissection use lasers to procure specific cell populations from a tissue section under microscopic visualization.
Additional laser microscopy techniques include harmonic microscopy, four-wave mixing microscopy and interferometric microscopy.
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# List of laser applications
## Military
### Directly as an energy weapon {#directly_as_an_energy_weapon}
A **laser weapon** is directed-energy weapon based on lasers.`{{summarize|from|Laser weapon|date=December 2022}}`{=mediawiki}
### Defensive countermeasures {#defensive_countermeasures}
Defensive countermeasure applications can range from compact, low power infrared countermeasures to high power, airborne laser systems. IR countermeasure systems use lasers to confuse the seeker heads on infrared homing missiles.
### Disorientation
Some weapons simply use a laser to disorient a person. One such weapon is the Thales Green Laser Optical Warner.
### Guidance
Laser guidance is a technique of guiding a missile or other projectile or vehicle to a target by means of a laser beam.
### Target designator {#target_designator}
Another military use of lasers is as a *laser target designator*. This is a low-power laser pointer used to indicate a target for a precision-guided munition, typically launched from an aircraft. The guided munition adjusts its flight-path to home in to the laser light reflected by the target, enabling a great precision in aiming. The beam of the laser target designator is set to a pulse rate that matches that set on the guided munition to ensure munitions strike their designated targets and do not follow other laser beams which may be in use in the area. The laser designator can be shone onto the target by an aircraft or nearby infantry. Lasers used for this purpose are usually infrared lasers, so the enemy cannot easily detect the guiding laser light.
### Firearms
#### Laser sight {#laser_sight}
The laser has in most firearms applications been used as a tool to enhance the targeting of other weapon systems. For example, a **laser sight** is a small, usually visible-light laser placed on a handgun or a rifle and aligned to emit a beam parallel to the barrel. Since a laser beam has low divergence, the laser light appears as a small spot even at long distances; the user places the spot on the desired target and the barrel of the gun is aligned (but not necessarily allowing for bullet drop, windage, distance between the direction of the beam and the axis of the barrel, and the target mobility while the bullet travels).
Most laser sights use a red laser diode. Others use an infrared diode to produce a dot invisible to the naked human eye but detectable with night vision devices. The firearms adaptive target acquisition module LLM01 laser light module combines visible and infrared laser diodes. In the late 1990s, green diode pumped solid state laser (DPSS) laser sights (532 nm) became available.
#### Eye-targeted lasers {#eye_targeted_lasers}
A less-lethal laser weapon was developed by the U.S. Air Force to temporarily impair an adversary\'s ability to fire a weapon or to otherwise threaten enemy forces. This unit illuminates an opponent with harmless low-power laser light and can have the effect of dazzling or disorienting the subject or causing them to flee. Several types of dazzlers are now available, and some have been used in combat.
There remains the possibility of using lasers to blind, since this requires relatively low power levels and is easily achievable in a man-portable unit. However, most nations regard the deliberate permanent blinding of the enemy as forbidden by the rules of war (see Protocol on Blinding Laser Weapons). Although several nations have developed blinding laser weapons, such as China\'s ZM-87, none of these are believed to have made it past the prototype stage.
In addition to the applications that cross over with military applications, a widely known law enforcement use of lasers is for lidar to measure the speed of vehicles.
#### Holographic weapon sight {#holographic_weapon_sight}
A holographic weapon sight uses a laser diode to illuminate a hologram of a reticle built into a flat glass optical window of the sight. The user looks through the optical window and sees a cross hair reticle image superimposed at a distance on the field of view.
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# List of laser applications
## Medical
- Cosmetic surgery (removing tattoos, scars, stretch marks, sunspots, wrinkles, birthmarks, and hair): see laser hair removal. Laser types used in dermatology include ruby (694 nm), alexandrite (755 nm), pulsed diode array (810 nm), Nd:YAG (1064 nm), Ho:YAG (2090 nm), and Er:YAG (2940 nm).
- Eye surgery and refractive surgery
- Soft tissue surgery: CO~2~, Er:YAG laser
- Laser scalpel (General surgery, gynecological, urology, laparoscopic)
- Photobiomodulation (i.e. laser therapy)
- \"No-Touch\" removal of tumors, especially of the brain and spinal cord.
- In dentistry for caries removal, endodontic/periodontic procedures, tooth whitening, and oral surgery
- Cancer treatment
- Burn and surgical scar management: scar contracture `{{CO2}}`{=mediawiki} (especially the newer fractionated `{{CO2}}`{=mediawiki} lasers), redness and itch (Pulsed Dye laser - PDL), post-inflammatory hyper-pigmentation (Q-switched lasers :Ruby, Alexandrite), burn scar unwanted hair growth and trapped hairs (Ruby, IPL and numerous hair removal lasers)
## Industrial and commercial {#industrial_and_commercial}
Industrial laser applications can be divided into two categories depending on the power of the laser: material processing and micro-material processing.
In material processing, lasers with average optical power above 1 kilowatt are used mainly for industrial materials processing applications. Beyond this power threshold there are thermal issues related to the optics that separate these lasers from their lower-power counterparts. Laser systems in the 50-300W range are used primarily for pumping, plastic welding and soldering applications. Lasers above 300W are used in brazing, thin metal welding, and sheet metal cutting applications. The required brightness (as measured in by the beam parameter product) is higher for cutting applications than for brazing and thin metal welding. High power applications, such as hardening, cladding, and deep penetrating welding, require multiple kW of optical power, and are used in a broad range of industrial processes.
Micro material processing is a category that includes all laser material processing applications under 1 kilowatt. The use of lasers in Micro Materials Processing has found broad application in the development and manufacturing of screens for smartphones, tablet computers, and LED TVs.
A detailed list of industrial and commercial laser applications includes:
- Laser cutting
- Laser welding
- Laser drilling
- Laser marking
- Laser cleaning
- Laser cladding, a surface engineering process applied to mechanical components for reconditioning, repair work or hardfacing
- Photolithography
- Optical communications over optical fiber or in free space
- Laser peening
- Guidance systems (e.g., ring laser gyroscopes)
- Laser rangefinder / surveying,
- Lidar / pollution monitoring,
- Digital minilabs
- Barcode readers
- Laser engraving of printing plate
- Laser bonding of additive marking materials for decoration and identification,
- Laser pointers
- Laser mice
- Laser accelerometers
- OLED display manufacturing
- Holography
- Bubblegrams
- Optical tweezers
- Writing subtitles onto motion picture films.
- Power beaming, which is a possible solution to transfer energy to the climber of a Space elevator
- 3D laser scanners for accurate 3D measurement
- Laser line levels are used in surveying and construction. Lasers are also used for guidance for aircraft.
- Extensively in both consumer and industrial imaging equipment.
- In laser printers: gas and diode lasers play a key role in manufacturing high resolution printing plates and in image scanning equipment.
- Diode lasers are used as a lightswitch in industry, with a laser beam and a receiver which will switch on or off when the beam is interrupted, and because a laser can keep the light intensity over larger distances than a normal light, and is more precise than a normal light it can be used for product detection in automated production.
- Laser alignment
- Additive manufacturing
- Plastic welding
- Metrology - handheld and robotic laser systems for Aerospace, Automotive and Rail applications
- To store and retrieve data in optical discs, such as CDs and DVDs
- Blu-ray
### Entertainment and recreation {#entertainment_and_recreation}
- Laser lighting displays accompany many music concerts
- Laser tag
- Laser harp: a musical instrument were the strings are replaced with laser beams
- As a light source for digital cinema projectors
### Surveying and ranging {#surveying_and_ranging}
## Images
<File:Laser> module.jpg\|Laser models in different colours <File:Laser> pens.jpeg\|Q-line Lasers <File:Laser> effects.jpg\|Lasers were used in the 2005 Classical Spectacular concert <File:Przestrzen> wolnosci harfa laserowa.jpg\|A laser harp <File:Carbon> Dioxide Laser At The Laser Effects Test Facility.jpg\|The surface of a test target is instantly vaporized and bursts into flame upon irradiation by a high power continuous wave carbon dioxide laser emitting tens of kilowatts of far infrared light. Note the operator is standing behind sheets of plexiglas, which is opaque in the far infrared
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# Laser construction
A **laser is constructed** from three principal parts:
- An energy source (usually referred to as the *pump* or *pump source*),
- A *gain medium* or *laser medium*, and
- Two or more mirrors that form an *optical resonator*.
## Pump source {#pump_source}
The *pump source* is the part that provides energy to the laser system. Examples of pump sources include electrical discharges, flashlamps, arc lamps, light from another laser, chemical reactions and even explosive devices. The type of pump source used principally depends on the *gain medium*, and this also determines how the energy is transmitted to the medium. A helium--neon (HeNe) laser uses an electrical discharge in the helium-neon gas mixture, a Nd:YAG laser uses either light focused from a xenon flash lamp or diode lasers, and excimer lasers use a chemical reaction.
## Gain medium / Laser medium {#gain_medium_laser_medium}
The *gain medium* is the major determining factor of the wavelength of operation, and other properties, of the laser. *Gain media* in different materials have linear spectra or wide spectra. *Gain media* with wide spectra allow tuning of the laser frequency. There are hundreds if not thousands of different gain media in which laser operation has been achieved (see list of laser types for a list of the most important ones). The gain medium is excited by the pump source to produce a population inversion, and it is in the gain medium where spontaneous and stimulated emission of photons takes place, leading to the phenomenon of optical gain, or amplification.
Examples of different gain media include:
- Liquids, such as dye lasers. These are usually organic chemical solvents, such as methanol, ethanol or ethylene glycol, to which are added chemical dyes such as coumarin, rhodamine, and fluorescein. The exact chemical configuration of the dye molecules determines the operation wavelength of the dye laser.
- Gases, such as carbon dioxide, argon, krypton and mixtures such as helium--neon. These lasers are often pumped by electrical discharge.
- Solids, such as crystals and glasses. The solid *host* materials are usually doped with an impurity such as chromium, neodymium, erbium or titanium ions. Typical hosts include YAG (yttrium aluminium garnet), YLF (yttrium lithium fluoride), sapphire (aluminium oxide) and various glasses. Examples of solid-state laser media include Nd:YAG, Ti:sapphire, Cr:sapphire (usually known as ruby), Cr:LiSAF (chromium-doped lithium strontium aluminium fluoride), Er:YLF, Nd:glass, and Er:glass. Solid-state lasers are usually pumped by flashlamps or light from another laser.
- Semiconductors, a type of solid, crystal with uniform dopant distribution or material with differing dopant levels in which the movement of electrons can cause laser action. Semiconductor lasers are typically very small, and can be pumped with a simple electric current, enabling them to be used in consumer devices such as compact disc players. See laser diode.
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# Laser construction
## Optical resonator {#optical_resonator}
The *optical resonator*, or *optical cavity*, in its simplest form is two parallel mirrors placed around the gain medium, which provide feedback of the light. The mirrors are given optical coatings which determine their reflective properties. Typically, one will be a high reflector, and the other will be a partial reflector. The latter is called the output coupler, because it allows some of the light to leave the cavity to produce the laser\'s output beam.
Light from the medium, produced by spontaneous emission, is reflected by the mirrors back into the medium, where it may be amplified by stimulated emission. The light may reflect from the mirrors and thus pass through the gain medium many hundreds of times before exiting the cavity. In more complex lasers, configurations with four or more mirrors forming the cavity are used. The design and alignment of the mirrors with respect to the medium is crucial for determining the exact operating wavelength and other attributes of the laser system.
Other optical devices, such as spinning mirrors, modulators, filters, and absorbers, may be placed within the optical resonator to produce a variety of effects on the laser output, such as altering the wavelength of operation or the production of pulses of laser light.
Some lasers do not use an optical cavity, but instead rely on very high optical gain to produce significant amplified spontaneous emission (ASE) without needing feedback of the light back into the gain medium. Such lasers are said to be superluminescent, and emit light with low coherence but high bandwidth. Since they do not use optical feedback, these devices are often not categorized as lasers
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# Logical conjunction
Circumflex Agent (\^)\|Lambda{{!}}Capital Lambda (Λ)\|Turned v{{!}}Turned V (Λ)\|Exterior algebra {{!}}Exterior Product (∧)}} `{{Infobox logical connective
| title = Logical conjunction
| other titles = AND
| Venn diagram = Venn0001.svg
| wikifunction = Z10174
| definition = <math>xy</math>
| truth table = <math>(1000)</math>
| logic gate = AND_ANSI.svg
| DNF = <math>xy</math>
| CNF = <math>xy</math>
| Zhegalkin = <math>xy</math>
| 0-preserving = yes
| 1-preserving = yes
| monotone = no
| affine = no
| self-dual = no
}}`{=mediawiki} `{{Logical connectives sidebar}}`{=mediawiki}
In logic, mathematics and linguistics, *and* ($\wedge$) is the truth-functional operator of **conjunction** or **logical conjunction**. The logical connective of this operator is typically represented as $\wedge$ or $\&$ or $K$ (prefix) or $\times$ or $\cdot$ in which $\wedge$ is the most modern and widely used.
The *and* of a set of operands is true if and only if *all* of its operands are true, i.e., $A \land B$ is true if and only if $A$ is true and $B$ is true.
An operand of a conjunction is a **conjunct**.
Beyond logic, the term \"conjunction\" also refers to similar concepts in other fields:
- In natural language, the denotation of expressions such as English \"and\";
- In programming languages, the short-circuit and control structure;
- In set theory, intersection.
- In lattice theory, logical conjunction (greatest lower bound).
## Notation
**And** is usually denoted by an infix operator: in mathematics and logic, it is denoted by a \"wedge\" $\wedge$ (Unicode `{{unichar|2227|Logical And}}`{=mediawiki}), $\&$ or $\times$; in electronics, $\cdot$; and in programming languages **`&`**, **`&&`**, or **`and`**. In Jan Łukasiewicz\'s prefix notation for logic, the operator is $K$, for Polish *koniunkcja*.
In mathematics, the conjunction of an arbitrary number of elements $a_1, \ldots, a_n$ can be denoted as an iterated binary operation using a \"big wedge\" ⋀ (Unicode `{{unichar|22C0|N-Ary Logical And}}`{=mediawiki}):
$\bigwedge_{i=1}^{n} a_i = a_1 \wedge a_2 \wedge \ldots a_{n-1} \wedge a_{n}$
## Definition
In classical logic, **logical conjunction** is an operation on two logical values, typically the values of two propositions, that produces a value of *true* if and only if (also known as iff) both of its operands are true.
The conjunctive identity is true, which is to say that AND-ing an expression with true will never change the value of the expression. In keeping with the concept of vacuous truth, when conjunction is defined as an operator or function of arbitrary arity, the empty conjunction (AND-ing over an empty set of operands) is often defined as having the result true.
### Truth table {#truth_table}
The truth table of $A \land B$:
### Defined by other operators {#defined_by_other_operators}
In systems where logical conjunction is not a primitive, it may be defined as
$$A \land B = \neg(A \to \neg B)$$ It can be checked by the following truth table (compare the last two columns):
or
$$A \land B = \neg(\neg A \lor \neg B).$$ It can be checked by the following truth table (compare the last two columns):
## Introduction and elimination rules {#introduction_and_elimination_rules}
As a rule of inference, conjunction introduction is a classically valid, simple argument form. The argument form has two premises, $A$ and $B$. Intuitively, it permits the inference of their conjunction.
$$A$$,
$$B$$.
: Therefore, *A* and *B*.
or in logical operator notation, where \\vdash expresses provability:
$$\vdash A,$$
$$\vdash B$$
$$\vdash A \land B$$
Here is an example of an argument that fits the form *conjunction introduction*:
: Bob likes apples.
: Bob likes oranges.
: Therefore, Bob likes apples and Bob likes oranges.
Conjunction elimination is another classically valid, simple argument form. Intuitively, it permits the inference from any conjunction of either element of that conjunction.
$$A$$ and $B$.
: Therefore, $A$.
\...or alternatively,
$$A$$ and $B$.
: Therefore, $B$.
In logical operator notation:
$$\vdash A \land B$$
$$\vdash A$$
\...or alternatively,
$$\vdash A \land B$$
$$\vdash B$$
## Negation
### Definition {#definition_1}
A conjunction $A\land B$ is proven false by establishing either $\neg A$ or $\neg B$. In terms of the object language, this reads
$$\neg A\to\neg(A\land B)$$
This formula can be seen as a special case of
$$(A\to C) \to ( (A\land B)\to C )$$
when $C$ is a false proposition.
### Other proof strategies {#other_proof_strategies}
If $A$ implies $\neg B$, then both $\neg A$ as well as $A$ prove the conjunction false:
$$(A\to\neg{}B)\to\neg(A\land B)$$ In other words, a conjunction can actually be proven false just by knowing about the relation of its conjuncts, and not necessary about their truth values.
This formula can be seen as a special case of
$$(A\to(B\to C))\to ( (A\land B)\to C )$$
when $C$ is a false proposition.
Either of the above are constructively valid proofs by contradiction.
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# Logical conjunction
## Properties
**commutativity: yes**
------------- --------------------------- ------------------ -- --------------------------- --
$A \land B$ $\Leftrightarrow$ $B \land A$ \|-y $\Leftrightarrow$
------------- --------------------------- ------------------ -- --------------------------- --
**associativity: yes**
------ --------------- --------------- --------------------------- -- --------------------------- --------------- --------------- ------
$~A$ $~~~\land~~~$ $(B \land C)$ $\Leftrightarrow$ $(A \land B)$ $~~~\land~~~$ $~C$
$~~~\land~~~$ $\Leftrightarrow$ $\Leftrightarrow$ $~~~\land~~~$
------ --------------- --------------- --------------------------- -- --------------------------- --------------- --------------- ------
**distributivity:** with various operations, especially with *or*
------ --------- -------------- --------------------------- -- --------------------------- --------------- -------- ---------------
$~A$ $\land$ $(B \lor C)$ $\Leftrightarrow$ $(A \land B)$ $\lor$ $(A \land C)$
$\land$ $\Leftrightarrow$ $\Leftrightarrow$ $\lor$
------ --------- -------------- --------------------------- -- --------------------------- --------------- -------- ---------------
+-------------------------------------------------------------------------------------------------------------------------------------------------------+
| others |
+=======================================================================================================================================================+
| with exclusive or: |
| |
| ------ --------- ---------------- --------------------------- -- --------------------------- --------------- ---------- --------------- |
| $~A$ $\land$ $(B \oplus C)$ $\Leftrightarrow$ $(A \land B)$ $\oplus$ $(A \land C)$ |
| |
| $\land$ $\Leftrightarrow$ $\Leftrightarrow$ $\oplus$ |
| ------ --------- ---------------- --------------------------- -- --------------------------- --------------- ---------- --------------- |
| |
| with material nonimplication: |
| |
| ------ --------- ---------------------- --------------------------- -- --------------------------- --------------- ---------------- --------------- |
| $~A$ $\land$ $(B \nrightarrow C)$ $\Leftrightarrow$ $(A \land B)$ $\nrightarrow$ $(A \land C)$ |
| |
| $\land$ $\Leftrightarrow$ $\Leftrightarrow$ $\nrightarrow$ |
| ------ --------- ---------------------- --------------------------- -- --------------------------- --------------- ---------------- --------------- |
| |
| with itself: |
| |
| ------ --------- --------------- --------------------------- -- --------------------------- --------------- --------- --------------- |
| $~A$ $\land$ $(B \land C)$ $\Leftrightarrow$ $(A \land B)$ $\land$ $(A \land C)$ |
| |
| $\land$ $\Leftrightarrow$ $\Leftrightarrow$ $\land$ |
| ------ --------- --------------- --------------------------- -- --------------------------- --------------- --------- --------------- |
+-------------------------------------------------------------------------------------------------------------------------------------------------------+
**idempotency: yes**\
{\| style=\"text-align: center; border: 1px solid darkgray;\" \|- \|$~A~$ \|$~\land~$ \|$~A~$ \| $\Leftrightarrow$ \|$A~$ \|- \| \|$~\land~$ \| \| $\Leftrightarrow$ \| \|}
**monotonicity: yes**
------------------- ----------------------- -- --------------------------- --------------- --------------- ---------------
$A \rightarrow B$ $\Rightarrow$ $(A \land C)$ $\rightarrow$ $(B \land C)$
$\Rightarrow$ $\Leftrightarrow$ $\rightarrow$
------------------- ----------------------- -- --------------------------- --------------- --------------- ---------------
**truth-preserving: yes**\
When all inputs are true, the output is true.
------------- ----------------------- -------------
$A \land B$ $\Rightarrow$ $A \land B$
$\Rightarrow$
------------- ----------------------- -------------
**falsehood-preserving: yes**\
When all inputs are false, the output is false.
------------- ----------------------- ------------
$A \land B$ $\Rightarrow$ $A \lor B$
$\Rightarrow$
------------- ----------------------- ------------
**Walsh spectrum: (1,-1,-1,1)**
**Nonlinearity: 1** (the function is bent)
If using binary values for true (1) and false (0), then *logical conjunction* works exactly like normal arithmetic multiplication.
## Applications in computer engineering`{{anchor|software_AND}}`{=mediawiki} {#applications_in_computer_engineering}
In high-level computer programming and digital electronics, logical conjunction is commonly represented by an infix operator, usually as a keyword such as \"`AND`\", an algebraic multiplication, or the ampersand symbol `&` (sometimes doubled as in `&&`). Many languages also provide short-circuit control structures corresponding to logical conjunction.
Logical conjunction is often used for bitwise operations, where `0` corresponds to false and `1` to true:
- `0 AND 0` = `0`,
- `0 AND 1` = `0`,
- `1 AND 0` = `0`,
- `1 AND 1` = `1`.
The operation can also be applied to two binary words viewed as bitstrings of equal length, by taking the bitwise AND of each pair of bits at corresponding positions. For example:
- `11000110 AND 10100011` = `10000010`.
This can be used to select part of a bitstring using a bit mask. For example, `1001`**`1`**`101 AND 0000`**`1`**`000` = `0000`**`1`**`000` extracts the fourth bit of an 8-bit bitstring.
In computer networking, bit masks are used to derive the network address of a subnet within an existing network from a given IP address, by ANDing the IP address and the subnet mask.
Logical conjunction \"`AND`\" is also used in SQL operations to form database queries.
The Curry--Howard correspondence relates logical conjunction to product types.
## Set-theoretic correspondence {#set_theoretic_correspondence}
The membership of an element of an intersection set in set theory is defined in terms of a logical conjunction: $x\in A\cap B$ if and only if $(x\in A)\wedge (x\in B)$. Through this correspondence, set-theoretic intersection shares several properties with logical conjunction, such as associativity, commutativity and idempotence.
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# Logical conjunction
## Natural language {#natural_language}
As with other notions formalized in mathematical logic, the logical conjunction *and* is related to, but not the same as, the grammatical conjunction *and* in natural languages.
English \"and\" has properties not captured by logical conjunction. For example, \"and\" sometimes implies order having the sense of \"then\". For example, \"They got married and had a child\" in common discourse means that the marriage came before the child.
The word \"and\" can also imply a partition of a thing into parts, as \"The American flag is red, white, and blue.\" Here, it is not meant that the flag is *at once* red, white, and blue, but rather that each color is a part of the flag
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# Logical connective
In logic, a **logical connective** (also called a **logical operator**, **sentential connective**, or **sentential operator**) is a logical constant. Connectives can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary connective $\lor$ can be used to join the two atomic formulas $P$ and $Q$, rendering the complex formula $P \lor Q$.
Common connectives include negation, disjunction, conjunction, implication, and equivalence. In standard systems of classical logic, these connectives are interpreted as truth functions, though they receive a variety of alternative interpretations in nonclassical logics. Their classical interpretations are similar to the meanings of natural language expressions such as English \"not\", \"or\", \"and\", and \"if\", but not identical. Discrepancies between natural language connectives and those of classical logic have motivated nonclassical approaches to natural language meaning as well as approaches which pair a classical compositional semantics with a robust pragmatics.
## Overview
In formal languages, truth functions are represented by unambiguous symbols. This allows logical statements to not be understood in an ambiguous way. These symbols are called *logical connectives*, *logical operators*, *propositional operators*, or, in classical logic, *truth-functional connectives*. For the rules which allow new well-formed formulas to be constructed by joining other well-formed formulas using truth-functional connectives, see well-formed formula.
Logical connectives can be used to link zero or more statements, so one can speak about *`{{mvar|n}}`{=mediawiki}-ary logical connectives*. The boolean constants *True* and *False* can be thought of as zero-ary operators. Negation is a unary connective, and so on.
+---------------------------------+-----------------------------------------------------+--------+
| Symbol, name | | Truth\ |
| | | table |
+=================================+=====================================================+========+
| Zeroary connectives (constants) | | |
+---------------------------------+-----------------------------------------------------+--------+
| $\top$ | style=\"text-align:left; \| Truth/tautology | 1 |
+---------------------------------+-----------------------------------------------------+--------+
| $\bot$ | style=\"text-align:left; \| Falsity/contradiction | 0 |
+---------------------------------+-----------------------------------------------------+--------+
| Unary connectives | | |
+---------------------------------+-----------------------------------------------------+--------+
| $p$ = | | 0 |
+---------------------------------+-----------------------------------------------------+--------+
| | style=\"text-align:left; \| Proposition $p$ | 0 |
+---------------------------------+-----------------------------------------------------+--------+
| $\neg$ | style=\"text-align:left; \| Negation | 1 |
+---------------------------------+-----------------------------------------------------+--------+
| Binary connectives | | |
+---------------------------------+-----------------------------------------------------+--------+
| $p$ = | | 0 |
+---------------------------------+-----------------------------------------------------+--------+
| $q$ = | | 0 |
+---------------------------------+-----------------------------------------------------+--------+
| $\and$ | Conjunction | 0 |
+---------------------------------+-----------------------------------------------------+--------+
| $\uparrow$ | Alternative denial | 1 |
+---------------------------------+-----------------------------------------------------+--------+
| $\vee$ | style=\"text-align:left; \| Disjunction | 0 |
+---------------------------------+-----------------------------------------------------+--------+
| $\downarrow$ | style=\"text-align:left; \| Joint denial | 1 |
+---------------------------------+-----------------------------------------------------+--------+
| $\nleftrightarrow$ | style=\"text-align:left; \| Exclusive or | 0 |
+---------------------------------+-----------------------------------------------------+--------+
| $\leftrightarrow$ | style=\"text-align:left; \| Biconditional | 1 |
+---------------------------------+-----------------------------------------------------+--------+
| $\rightarrow$ | style=\"text-align:left; \| Material conditional | 1 |
+---------------------------------+-----------------------------------------------------+--------+
| $\nrightarrow$ | style=\"text-align:left; \| Material nonimplication | 0 |
+---------------------------------+-----------------------------------------------------+--------+
| $\leftarrow$ | style=\"text-align:left; \| Converse implication | 1 |
+---------------------------------+-----------------------------------------------------+--------+
| $\nleftarrow$ | style=\"text-align:left; \| Converse nonimplication | 0 |
+---------------------------------+-----------------------------------------------------+--------+
| More information | | |
+---------------------------------+-----------------------------------------------------+--------+
### List of common logical connectives {#list_of_common_logical_connectives}
Commonly used logical connectives include the following ones.
- Negation (not): $\neg$, $\sim$, $N$ (prefix) in which $\neg$ is the most modern and widely used, and $\sim$ is also common;
- Conjunction (and): $\wedge$, $\&$, $K$ (prefix) in which $\wedge$ is the most modern and widely used;
- Disjunction (or): $\vee$, $A$ (prefix) in which $\vee$ is the most modern and widely used;
- Implication (if\...then): $\to$, $\supset$, $\Rightarrow$, $C$ (prefix) in which $\to$ is the most modern and widely used, and $\supset$ is also common;
- Equivalence (if and only if): $\leftrightarrow$, $\subset\!\!\!\supset$, $\Leftrightarrow$, $\equiv$, $E$ (prefix) in which $\leftrightarrow$ is the most modern and widely used, and $\subset\!\!\!\supset$ is commonly used where $\supset$ is also used.
For example, the meaning of the statements *it is raining* (denoted by $p$) and *I am indoors* (denoted by $q$) is transformed, when the two are combined with logical connectives:
- It is ***not*** raining ($\neg p$);
- It is raining ***and*** I am indoors ($p \wedge q$);
- It is raining ***or*** I am indoors ($p \lor q$);
- ***If**\'\' it is raining,***then**\'\' I am indoors ($p \rightarrow q$);
- ***If**\'\' I am indoors,***then**\'\' it is raining ($q \rightarrow p$);
- I am indoors ***if and only if*** it is raining ($p \leftrightarrow q$).
It is also common to consider the *always true* formula and the *always false* formula to be connective (in which case they are nullary).
- True formula: $\top$, $1$, $V$ (prefix), or $\mathrm{T}$;
- False formula: $\bot$, $0$, $O$ (prefix), or $\mathrm{F}$.
This table summarizes the terminology:
Connective In English Noun for parts Verb phrase
--------------- --------------------------- ------------------------ ------------------------
Conjunction Both A and B conjunct A and B are conjoined
Disjunction Either A or B, or both disjunct A and B are disjoined
Negation It is not the case that A negatum/negand A is negated
Conditional If A, then B antecedent, consequent B is implied by A
Biconditional A if, and only if, B equivalents A and B are equivalent
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# Logical connective
## Overview
### History of notations {#history_of_notations}
- Negation: the symbol $\neg$ appeared in Heyting in 1930Denis Roegel (2002),
*[A brief survey of 20th century logical notations](https://members.loria.fr/Roegel/loc/symboles-logiques-eng.pdf)* (see chart on page 2).
(compare to Frege\'s symbol ⫟ in his Begriffsschrift); the symbol $\sim$ appeared in Russell in 1908; an alternative notation is to add a horizontal line on top of the formula, as in $\overline{p}$; another alternative notation is to use a prime symbol as in $p'$.
- Conjunction: the symbol $\wedge$ appeared in Heyting in 1930 (compare to Peano\'s use of the set-theoretic notation of intersection $\cap$); the symbol $\&$ appeared at least in Schönfinkel in 1924; the symbol $\cdot$ comes from Boole\'s interpretation of logic as an elementary algebra.
- Disjunction: the symbol $\vee$ appeared in Russell in 1908 (compare to Peano\'s use of the set-theoretic notation of union $\cup$); the symbol $+$ is also used, in spite of the ambiguity coming from the fact that the $+$ of ordinary elementary algebra is an exclusive or when interpreted logically in a two-element ring; punctually in the history a $+$ together with a dot in the lower right corner has been used by Peirce.
- Implication: the symbol $\to$ appeared in Hilbert in 1918; $\supset$ was used by Russell in 1908 (compare to Peano\'s Ɔ the inverted C); $\Rightarrow$ appeared in Bourbaki in 1954.
- Equivalence: the symbol $\equiv$ in Frege in 1879; $\leftrightarrow$ in Becker in 1933 (not the first time and for this see the following); $\Leftrightarrow$ appeared in Bourbaki in 1954; other symbols appeared punctually in the history, such as $\supset\subset$ in Gentzen, $\sim$ in Schönfinkel or $\subset\supset$ in Chazal,
- True: the symbol $1$ comes from Boole\'s interpretation of logic as an elementary algebra over the two-element Boolean algebra; other notations include $\mathrm{V}$ (abbreviation for the Latin word \"verum\") to be found in Peano in 1889.
- False: the symbol $0$ comes also from Boole\'s interpretation of logic as a ring; other notations include $\Lambda$ (rotated $\mathrm{V}$) to be found in Peano in 1889.
Some authors used letters for connectives: $\operatorname{u.}$ for conjunction (German\'s \"und\" for \"and\") and $\operatorname{o.}$ for disjunction (German\'s \"oder\" for \"or\") in early works by Hilbert (1904); $Np$ for negation, $Kpq$ for conjunction, $Dpq$ for alternative denial, $Apq$ for disjunction, $Cpq$ for implication, $Epq$ for biconditional in Łukasiewicz in 1929.
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# Logical connective
## Overview
### Redundancy
Such a logical connective as converse implication \"$\leftarrow$\" is actually the same as material conditional with swapped arguments; thus, the symbol for converse implication is redundant. In some logical calculi (notably, in classical logic), certain essentially different compound statements are logically equivalent. A less trivial example of a redundancy is the classical equivalence between $\neg p\vee q$ and $p\to q$. Therefore, a classical-based logical system does not need the conditional operator \"$\to$\" if \"$\neg$\" (not) and \"$\vee$\" (or) are already in use, or may use the \"$\to$\" only as a syntactic sugar for a compound having one negation and one disjunction.
There are sixteen Boolean functions associating the input truth values $p$ and $q$ with four-digit binary outputs. These correspond to possible choices of binary logical connectives for classical logic. Different implementations of classical logic can choose different functionally complete subsets of connectives.
One approach is to choose a *minimal* set, and define other connectives by some logical form, as in the example with the material conditional above. The following are the minimal functionally complete sets of operators in classical logic whose arities do not exceed 2:
One element: $\{\uparrow\}$, $\{\downarrow\}$.\
Two elements: $\{\vee, \neg\}$, $\{\wedge, \neg\}$, $\{\to, \neg\}$, $\{\gets, \neg\}$, $\{\to, \bot\}$, $\{\gets, \bot\}$, $\{\to, \nleftrightarrow\}$, $\{\gets, \nleftrightarrow\}$, $\{\to, \nrightarrow\}$, $\{\to, \nleftarrow\}$, $\{\gets, \nrightarrow\}$, $\{\gets, \nleftarrow\}$, $\{\nrightarrow, \neg\}$, $\{\nleftarrow, \neg\}$, $\{\nrightarrow, \top\}$, $\{\nleftarrow, \top\}$, $\{\nrightarrow, \leftrightarrow\}$, $\{\nleftarrow, \leftrightarrow\}$.\
Three elements: $\{\lor, \leftrightarrow, \bot\}$, $\{\lor, \leftrightarrow, \nleftrightarrow\}$, $\{\lor, \nleftrightarrow, \top\}$, $\{\land, \leftrightarrow, \bot\}$, $\{\land, \leftrightarrow, \nleftrightarrow\}$, $\{\land, \nleftrightarrow, \top\}$.
Another approach is to use with equal rights connectives of a certain convenient and functionally complete, but *not minimal* set. This approach requires more propositional axioms, and each equivalence between logical forms must be either an axiom or provable as a theorem.
The situation, however, is more complicated in intuitionistic logic. Of its five connectives, {∧, ∨, →, ¬, ⊥}, only negation \"¬\" can be reduced to other connectives (see `{{Section link|False (logic)|False, negation and contradiction}}`{=mediawiki} for more). Neither conjunction, disjunction, nor material conditional has an equivalent form constructed from the other four logical connectives.
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# Logical connective
## Natural language {#natural_language}
The standard logical connectives of classical logic have rough equivalents in the grammars of natural languages. In English, as in many languages, such expressions are typically grammatical conjunctions. However, they can also take the form of complementizers, verb suffixes, and particles. The denotations of natural language connectives is a major topic of research in formal semantics, a field that studies the logical structure of natural languages.
The meanings of natural language connectives are not precisely identical to their nearest equivalents in classical logic. In particular, disjunction can receive an exclusive interpretation in many languages. Some researchers have taken this fact as evidence that natural language semantics is nonclassical. However, others maintain classical semantics by positing pragmatic accounts of exclusivity which create the illusion of nonclassicality. In such accounts, exclusivity is typically treated as a scalar implicature. Related puzzles involving disjunction include free choice inferences, Hurford\'s Constraint, and the contribution of disjunction in alternative questions.
Other apparent discrepancies between natural language and classical logic include the paradoxes of material implication, donkey anaphora and the problem of counterfactual conditionals. These phenomena have been taken as motivation for identifying the denotations of natural language conditionals with logical operators including the strict conditional, the variably strict conditional, as well as various dynamic operators.
The following table shows the standard classically definable approximations for the English connectives.
English word Connective Symbol Logical gate
---------------- ------------------------- -------------------- --------------
not negation $\neg$ NOT
and conjunction $\and$ AND
or disjunction $\vee$ OR
if\...then material implication $\rightarrow$ IMPLY
\...if converse implication $\leftarrow$
either\...or exclusive disjunction $\nleftrightarrow$ XOR
if and only if biconditional $\leftrightarrow$ XNOR
not both alternative denial $\uparrow$ NAND
neither\...nor joint denial $\downarrow$ NOR
but not material nonimplication $\nrightarrow$ NIMPLY
not\...but converse nonimplication $\nleftarrow$
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# Logical connective
## Properties
Some logical connectives possess properties that may be expressed in the theorems containing the connective. Some of those properties that a logical connective may have are:
Associativity: Within an expression containing two or more of the same associative connectives in a row, the order of the operations does not matter as long as the sequence of the operands is not changed.\
Commutativity:The operands of the connective may be swapped, preserving logical equivalence to the original expression.\
Distributivity: A connective denoted by · distributes over another connective denoted by +, if `{{math|1=''a'' · (''b'' + ''c'') = (''a'' · ''b'') + (''a'' · ''c'')}}`{=mediawiki} for all operands `{{mvar|a}}`{=mediawiki}, `{{mvar|b}}`{=mediawiki}, `{{mvar|c}}`{=mediawiki}.\
Idempotence: Whenever the operands of the operation are the same, the compound is logically equivalent to the operand.\
Absorption: A pair of connectives ∧, ∨ satisfies the absorption law if $a\land(a\lor b)=a$ for all operands `{{mvar|a}}`{=mediawiki}, `{{mvar|b}}`{=mediawiki}.\
Monotonicity: If *f*(*a*~1~, \..., *a*~*n*~) ≤ *f*(*b*~1~, \..., *b*~*n*~) for all *a*~1~, \..., *a*~*n*~, *b*~1~, \..., *b*~*n*~ ∈ {0,1} such that *a*~1~ ≤ *b*~1~, *a*~2~ ≤ *b*~2~, \..., *a*~*n*~ ≤ *b*~*n*~. E.g., ∨, ∧, ⊤, ⊥.\
Affinity: Each variable always makes a difference in the truth-value of the operation or it never makes a difference. E.g., ¬, ↔, $\nleftrightarrow$, ⊤, ⊥.\
Duality: To read the truth-value assignments for the operation from top to bottom on its truth table is the same as taking the complement of reading the table of the same or another connective from bottom to top. Without resorting to truth tables it may be formulated as `{{math|1=''g̃''(¬''a''<sub>1</sub>, ..., ¬''a''<sub>''n''</sub>) = ¬''g''(''a''<sub>1</sub>, ..., ''a''<sub>''n''</sub>)}}`{=mediawiki}. E.g., ¬.\
Truth-preserving: The compound all those arguments are tautologies is a tautology itself. E.g., ∨, ∧, ⊤, →, ↔, ⊂ (see validity).\
Falsehood-preserving: The compound all those argument are contradictions is a contradiction itself. E.g., ∨, ∧, $\nleftrightarrow$, ⊥, ⊄, ⊅ (see validity).\
Involutivity (for unary connectives): `{{math|1=''f''(''f''(''a'')) = ''a''}}`{=mediawiki}. E.g. negation in classical logic.
For classical and intuitionistic logic, the \"=\" symbol means that corresponding implications \"\...→\...\" and \"\...←\...\" for logical compounds can be both proved as theorems, and the \"≤\" symbol means that \"\...→\...\" for logical compounds is a consequence of corresponding \"\...→\...\" connectives for propositional variables. Some many-valued logics may have incompatible definitions of equivalence and order (entailment).
Both conjunction and disjunction are associative, commutative and idempotent in classical logic, most varieties of many-valued logic and intuitionistic logic. The same is true about distributivity of conjunction over disjunction and disjunction over conjunction, as well as for the absorption law.
In classical logic and some varieties of many-valued logic, conjunction and disjunction are dual, and negation is self-dual, the latter is also self-dual in intuitionistic logic.
## Order of precedence {#order_of_precedence}
As a way of reducing the number of necessary parentheses, one may introduce precedence rules: ¬ has higher precedence than ∧, ∧ higher than ∨, and ∨ higher than →. So for example, $P \vee Q \and{\neg R} \rightarrow S$ is short for $(P \vee (Q \and (\neg R))) \rightarrow S$.
Here is a table that shows a commonly used precedence of logical operators.
Operator Precedence
------------------- ------------
$\neg$ 1
$\and$ 2
$\vee$ 3
$\rightarrow$ 4
$\leftrightarrow$ 5
However, not all compilers use the same order; for instance, an ordering in which disjunction is lower precedence than implication or bi-implication has also been used. Sometimes precedence between conjunction and disjunction is unspecified requiring to provide it explicitly in given formula with parentheses. The order of precedence determines which connective is the \"main connective\" when interpreting a non-atomic formula.
## Table and Hasse diagram {#table_and_hasse_diagram}
The 16 logical connectives can be partially ordered to produce the following Hasse diagram. The partial order is defined by declaring that $x \leq y$ if and only if whenever $x$ holds then so does $y.$
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# Logical connective
## Applications
Logical connectives are used in computer science and in set theory.
### Computer science {#computer_science}
A truth-functional approach to logical operators is implemented as logic gates in digital circuits. Practically all digital circuits (the major exception is DRAM) are built up from NAND, NOR, NOT, and transmission gates; see more details in Truth function in computer science. Logical operators over bit vectors (corresponding to finite Boolean algebras) are bitwise operations.
But not every usage of a logical connective in computer programming has a Boolean semantic. For example, lazy evaluation is sometimes implemented for `{{math|''P'' ∧ ''Q''}}`{=mediawiki} and `{{math|''P'' ∨ ''Q''}}`{=mediawiki}, so these connectives are not commutative if either or both of the expressions `{{mvar|P}}`{=mediawiki}, `{{mvar|Q}}`{=mediawiki} have side effects. Also, a conditional, which in some sense corresponds to the material conditional connective, is essentially non-Boolean because for `if (P) then Q;`, the consequent Q is not executed if the antecedent P is false (although a compound as a whole is successful ≈ \"true\" in such case). This is closer to intuitionist and constructivist views on the material conditional--- rather than to classical logic\'s views.
### Set theory {#set_theory}
Logical connectives are used to define the fundamental operations of set theory, as follows:
Set operation Connective Definition
--------------- --------------- ----------------------------------------------------------------------
Intersection Conjunction $A \cap B = \{x : x \in A \land x \in B \}$
Union Disjunction $A \cup B = \{x : x \in A \lor x \in B \}$
Complement Negation $\overline{A} = \{x : x \notin A \}$
Subset Implication $A \subseteq B \leftrightarrow (x \in A \rightarrow x \in B)$
Equality Biconditional $A = B \leftrightarrow (\forall X)[A \in X \leftrightarrow B \in X]$
: Set theory operations and connectives
This definition of set equality is equivalent to the axiom of extensionality
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# Lemuridae
**Lemuridae** is a family of strepsirrhine primates native to Madagascar and the Comoros. They are represented by the Lemuriformes in Madagascar with one of the highest concentration of the lemurs. One of five families commonly known as lemurs, these animals were once thought to be the evolutionary predecessors of monkeys and apes, but this is no longer considered correct. They are formally referred to as **lemurids**.
## Classification
The family Lemuridae contains 21 extant species in five genera.
**Family Lemuridae**
- Genus *Lemur*
- *Lemur catta* (ring-tailed lemur)
- Genus *Eulemur*, true lemurs
- *Eulemur fulvus* (common brown lemur)
- *Eulemur sanfordi* (Sanford\'s brown lemur)
- *Eulemur albifrons* (white-headed lemur)
- *Eulemur rufus* (red lemur)
- *Eulemur rufifrons* (red-fronted lemur)
- *Eulemur collaris* (collared brown lemur)
- *Eulemur cinereiceps* (gray-headed lemur)
- *Eulemur macaco* (black lemur)
- *Eulemur flavifrons* (blue-eyed black lemur)
- *Eulemur coronatus* (crowned lemur)
- *Eulemur rubriventer* (red-bellied lemur)
- *Eulemur mongoz* (mongoose lemur)
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- Genus *Varecia*, ruffed lemurs
- *Varecia variegata* (black-and-white ruffed lemur)
- *Varecia rubra* (red ruffed lemur)
- Genus *Hapalemur*, bamboo lemurs
- *Hapalemur griseus* (Eastern lesser bamboo lemur or gray gentle bamboo lemur)
- *Hapalemur meridionalis* (Southern lesser bamboo lemur)
- *Hapalemur occidentalis* (Western lesser bamboo lemur)
- *Hapalemur alaotrensis* (Lac Alaotra gentle lemur)
- *Hapalemur aureus* (golden bamboo lemur)
- *Hapalemur simus* (greater bamboo lemur)
- Genus †*Pachylemur*
- †*Pachylemur insignis*
- †*Pachylemur jullyi*
This family was once broken into two subfamilies, **Hapalemurinae** (bamboo lemurs and the greater bamboo lemur) and **Lemurinae** (the rest of the family), but molecular evidence and the similarity of the scent glands have since placed the ring-tailed lemur with the bamboo lemurs and the greater bamboo lemur.
Lemur species in the genus *Eulemur* are known to interbreed, despite having dramatically different chromosome numbers. Red-fronted (2N=60) and collared brown (2N=50--52) lemurs were found to hybridize at Berenty Reserve, Madagascar.
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# Lemuridae
## Characteristics
Lemurids are medium-sized arboreal primates, ranging from 32 to 56 cm in length, excluding the tail, and weighing from 0.7 to 5 kg. They have long, bushy tails and soft, woolly fur of varying coloration. The hindlegs are slightly longer than the forelegs, although not enough to hamper fully quadrupedal movement (unlike the sportive lemurs). Most species are highly agile, and regularly leap several metres between trees. They have a good sense of smell and binocular vision. All but one species (the ring-tailed lemur) lack a tapetum lucidum, a reflective layer in the eye that improves night vision. Among mammals, activity cycles are either strictly diurnal or nocturnal, however, these can widely vary across species. In general, lemur activity has evolved from nocturnal to diurnal. Some lemurs are also cathemeral, an activity pattern where an animal is neither strictly diurnal nor nocturnal.
Lemurids are herbivorous, eating predominantly fruits and leaves, with some species consuming nectar, gums, and insects. However, the composition of their diets varies greatly depending on the species. Most lemurids have the dental formula `{{DentalFormula|upper=2.1.3.3|lower=2.1.3.3}}`{=mediawiki}. Some subfossil records have contributed to the knowledge of the currently extant lemurs from the Holocene by showing the changes in their dental records in habitats near human activity. This demonstrates that lemur species such as the ring-tailed lemur and the common brown lemur were forced to switch their primary diet to a group of secondary food sources.
With most lemurids, the mother gives birth to one or two young after a gestation period of between 120 and 140 days, depending on species. The ruffed lemur species are the only lemurids that have true litters, consisting of anywhere from two to six offspring. They are generally sociable animals, living in groups of up to thirty individuals in some species. In some cases, such as the ring-tailed lemur, the groups are long-lasting, with distinct dominance hierarchies, while in others, such as the common brown lemur, the membership of the groups varies from day to day, and seems to have no clear social structure.
Some of the lemur traits include low basal metabolic rate, highly seasonal breeders, adaptations to unpredictable climate and female dominance. Female dominance is expressed in lemurs with the females and males being sexually monomorphic and females having priority access to food. Lemurs live in groups of 11 to 17 animals, where females tend to stay within their natal groups and the males migrate. Male lemurs are competitive to win their mates which causes instability among the other organisms. Lemurs are able to mark their territory by using scents from local areas.
A number of lemur species are considered threatened; two species are critically endangered, one species is endangered, and five species are rated as vulnerable.
## Habitat
The highly seasonal dry deciduous forest of Madagascar alternates between dry and wet seasons, making it uniquely suitable for lemurs. Lemur species diversity increases as the number of tree species in an area increase and is also higher in forests that have been disturbed over undisturbed areas. Evidence from the subfossil records show that many of the now extinct lemurs actually lived in much drier climates than the currently extant lemurs
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# Lucent Technologies
**Lucent Technologies, Inc.** was an American multinational telecommunications equipment company headquartered in Murray Hill, New Jersey. It was established on September 30, 1996, through the divestiture of the former AT&T Technologies business unit of AT&T Corporation, which included Western Electric and Bell Labs.
Lucent was acquired by Alcatel SA on December 1, 2006, forming Alcatel-Lucent.
## Name
Lucent means \"light-bearing\" in Latin. The name was applied for in 1996 at the time of the split from AT&T.
The name was widely criticised, as the logo was to be, both internally and externally. Corporate communications and business cards included the strapline \'Bell Labs Innovations\' in a bid to retain the prestige of the internationally famous research lab, within a new business under an as-yet unknown name.
This same linguistic root also gives Lucifer, \"the light bearer\" (from lux, \'light\', and ferre, \'to bear\'), who is also a character in Dante\'s epic poem *Inferno*. Shortly after the Lucent renaming in 1996, Lucent\'s Plan 9 project released a development of their work as the Inferno OS in 1997. This extended the \'Lucifer\' and Dante references as a series of punning names for the components of Inferno - Dis, Limbo, Charon and Styx (9P Protocol). When the rights to Inferno were sold in 2000, the company Vita Nuova Holdings was formed to represent them. This continues the Dante theme, although moving away from his *Divine Comedy* to the poem *La Vita Nuova*.
## Logo
The Lucent logo, the Innovation Ring, was designed by Landor Associates, a prominent San Francisco-based branding consultancy. One source inside Lucent says that the logo is a Zen Buddhist symbol for \"eternal truth\", the Ensō, turned 90 degrees and modified. Another source says it represents the mythic ouroboros, a snake holding its tail in its mouth. Lucent\'s logo also has been said to represent constant re-creating and re-thinking. Carly Fiorina picked the logo because her mother was a painter and she rejected the sterile geometric logos of most high tech companies.
After the logo was compared in the media to the ring a coffee mug leaves on paper, a *Dilbert* comic strip showed Dogbert as an overpaid consultant designing a new company logo; he takes a piece of paper that his coffee cup was sitting on and calls it the \"Brown Ring of Quality\". A telecommunication commentator referred to the logo as \"a big red zero\" and predicted financial losses.
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# Lucent Technologies
## History
One of the primary reasons AT&T Corporation chose to spin off its equipment manufacturing business was to permit it to profit from sales to competing telecommunications providers; these customers had previously shown reluctance to purchase from a direct competitor. Bell Labs brought prestige to the new company, as well as the revenue from thousands of patents.
At the time of its spinoff, Lucent was placed under the leadership of Henry Schacht, who was brought in to oversee its transition from an arm of AT&T into an independent corporation. Richard McGinn, who was serving as president and COO, succeeded Schacht as CEO in 1997 while Schacht remained chairman of the board. Lucent became a \"darling\" stock of the investment community in the late 1990s, and its split-adjusted spinoff price of \$7.56/share rose to a high of \$84. Its market capitalization reached a high of \$258 billion, and it was at the time the most widely held company with 5.3 million shareholders.
In 1995, Carly Fiorina led corporate operations. In that capacity, she reported to Lucent chief executive Henry B. Schacht. She played a key role in planning and implementing the 1996 initial public offering of a successful stock and company launch strategy. Under her guidance, the spin-off raised `{{USD}}`{=mediawiki}3 billion.
Later in 1996, Fiorina was appointed president of Lucent\'s consumer products sector, reporting to president and chief operating officer Rich McGinn. In 1997, she was named group president for Lucent\'s `{{USD}}`{=mediawiki}19 billion global service-provider business, overseeing marketing and sales for the company\'s largest customer segment. That year, Fiorina chaired a `{{USD}}`{=mediawiki}2.5 billion joint venture between Lucent\'s consumer communications and Royal Philips Electronics, under the name Philips Consumer Communications (PCC). The focus of the venture was to bring both companies to the top three in technology, distribution, and brand recognition.
Ultimately, the project struggled, and dissolved a year later after it garnered only 2% market share in mobile phones. Losses were at \$500 million on sales of \$2.5 billion. As a result of the failed joint venture, Philips announced the closure of one-quarter of the company\'s 230 factories worldwide, and Lucent closed down its wireless handset portion of the venture. Analysts suggested that the joint venture\'s failure was due to a combination of technology and management problems. Upon the end of the joint venture, PCC sent 5,000 employees back to Philips, many of which were laid off, and 8,400 employees back to Lucent.
Under Fiorina, the company added 22,000 jobs and revenues seemed to grow from `{{USD}}`{=mediawiki}19 billion to `{{USD}}`{=mediawiki}38 billion. However, the real cause of Lucent spurring sales under Fiorina was by lending money to their own customers. According to *Fortune* magazine, \"In a neat bit of accounting magic, money from the loans began to appear on Lucent\'s income statement as new revenue while the dicey debt got stashed on its balance sheet as an allegedly solid asset\". Lucent\'s stock price grew 10-fold.
In 1997, Lucent acquired Milpitas-based voicemail market leader Octel Communications Corporation for \$1.8 billion, a move which immediately rendered the Business Systems Group profitable. The same year, Lucent acquired Livingston Enterprises Inc. for \$650 million in stock. Livingston was known most for the creation of the RADIUS protocol and their PortMaster product that was used widely by dial-up internet service providers. In 1999, Lucent acquired Ascend Communications, an Alameda, California--based manufacturer of communications equipment for US\$20 billion. Lucent held discussions to acquire Juniper Networks but decided instead to buy Nexabit Networks.
At the start of 2000, Lucent\'s \"private bubble\" burst, while competitors like Nortel Networks and Alcatel were still going strong; it would be many months before the rest of the telecom industry bubble collapsed. Previously Lucent had 14 straight quarters where it exceeded analysts\' expectations, leading to high expectations for the 15th quarter, ending Dec. 31, 1999. On January 6, 2000, Lucent made the first of a string of announcements that it had missed its quarterly estimates, as CEO Rich McGinn grimly announced that Lucent had run into special problems during that quarter---including disruptions in its optical networking business---and reported flat revenues and a big drop in profits. That caused the stock to plunge by 28%, shaving \$64 billion off of the company\'s market capitalization. When it was later revealed that it had used dubious accounting and sales practices to generate some of its earlier quarterly numbers, Lucent fell from grace. It was said that \"Rich McGinn couldn\'t accept Lucent\'s fall from its early triumphs.\" He described himself once as imposing \"audacious\" goals on his managers, believing the stretch for performance would produce dream results. Henry Schacht defended the corporate culture that McGinn created and noted that McGinn did not sell any Lucent shares while serving as CEO. In June 2000, Lucent announced it would acquire Chromartis, an Israeli maker of optical network equipment, for \$4.5 billion In November 2000, the company disclosed to the Securities and Exchange Commission that it had a \$125 million accounting error for the third quarter of 2000, and by December 2000 it reported it had overstated its revenues for its latest quarter by nearly \$700 million. Although no wrongdoing was found on his part, McGinn was forced to resign as CEO and he was replaced by Schacht on an interim basis. Subsequently, its CFO, Deborah Hopkins, left the company in May 2001 with Lucent\'s stock at \$9.06 whereas at the time she was hired it was at \$46.82. In August 2001, Lucent shut down Chromartis.
In 2000, Lucent received the Shingo Prize for Excellence in Manufacturing at the Mount Olive, New Jersey Product Realization Center.
In 2001 there were merger discussions between Lucent and Alcatel, which would have seen Lucent acquired at its current market price without a premium; the newly combined entity would have been headquartered in Murray Hill. However, these negotiations collapsed when Schacht insisted on an equal 7--7 split of the merged company\'s board of directors, while Alcatel chief executive officer Serge Tchuruk wanted 8 of the 14 board seats for Alcatel due to it being in a stronger position. The failure of the merger talks caused Lucent\'s share price to collapse, and by October 2002 the stock price had bottomed at 55 cents per share.
In April 2000, Lucent sold its Consumer Products unit to VTech. In October 2000, Lucent spun off its Business Systems arm into Avaya, Inc., and in June 2002, it spun off its microelectronics division into Agere Systems. The spinoffs of enterprise networking and wireless, the industry\'s key growth businesses from 2003 onward, meant that Lucent no longer had the capacity to serve this market.
Patricia Russo, formerly Lucent\'s EVP of the Corporate Office who then left for Eastman Kodak to serve as COO, was named permanent chairman and CEO of Lucent in 2002, succeeding Schacht who remained on the board of directors.
Lucent was reduced to 30,500 employees, down from about 165,000 employees at its zenith. The layoffs of so many experienced employees meant that the company was in a weakened position and unable to re-establish itself when the market recovered in 2003. By early 2003, Lucent\'s market value was \$15.6 billion (which includes \$6.8 billion of current value for two companies that Lucent had recently spun off, Avaya and Agere Systems), making the shares worth around \$2.13, a far cry from its dotcom bubble peak of around \$84, when Lucent was worth \$258 billion.
Lucent continued to be active in the areas of telephone switching, optical, data and wireless networking.
In 2004, the SEC charged Lucent with a \$25 million fine for the company\'s lack of cooperation in their fraud case.
On April 2, 2006, Lucent announced a merger agreement with Alcatel, which was 1.5 times the size of Lucent. Serge Tchuruk became non-executive chairman, and Russo served as CEO of the newly merged company, Alcatel-Lucent, until they were both forced to resign at the end of 2008. The merger failed to produce the expected synergies, and there were significant write-downs of Lucent\'s assets that Alcatel purchased.
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# Lucent Technologies
## Operations
### Divisions
Lucent was divided into several core groups:
- **Network Solutions Group** served landline/cellular telephone service providers by providing equipment and other solutions necessary to provide telephone service, including networking equipment.
- **Lucent Worldwide Services (LWS)** provided network services to telecom companies and business; clients included AT&T Corporation and Verizon. Divisions of LWS included the AT&T Customer Business Unit, known as ACBU; and another group for Southwestern Bell and other Bell companies. Both divisions were responsible for the installation of telecom equipment ranging from 2-pair copper to multi-wire fiber optics. Each group also installed the first true national cellular service with LTE speeds in the 1990s.
- **Bell Labs** was created in 1925 as the R&D firm of the Bell System. It was an AT&T subsidiary set up as dual ownership by AT&T and Western Electric, the manufacturing arm of AT&T.
### Murray Hill facility {#murray_hill_facility}
The Murray Hill facility in New Providence, New Jersey was the global headquarters for Lucent Technologies. There was a cricket field in the grounds. The Murray Hill anechoic chamber, built in 1940, is the world\'s oldest wedge-based anechoic chamber. The interior room measures approximately 30 ft high by 28 ft wide by 32 ft deep. The exterior concrete and brick walls are about 3 ft thick to keep outside noise from entering the chamber. The chamber absorbs over 99.995% of the incident acoustic energy above 200 Hz. At one time the Murray Hill chamber was cited in the Guinness Book of World Records as the world\'s quietest room.
### Mount Olive facility {#mount_olive_facility}
The Mount Olive Product Realization Center (MTO-PRC) facility in Mount Olive, New Jersey was part of the Wireless Networks Group business unit. The 252,000 square-feet building was constructed for AT&T Corp. in 1994. The two leased buildings were located at the International Trade Center (New Jersey) and one building was used for warehousing and the other used for wireless products manufacturing since 1995. An additionally built wireless products manufacturing, PRC, was located in Piscataway, New Jersey also independently of AT&T creation.
This system integration plant was a manufacturing location with the business unit under one roof. This allowed, the development, design, business functions for manufacturing cellular phone parts and between 1996 and 1999, the production of first generation CDMA (Code-division multiple access) minicells needed for cellular phone carriers. A 1,015-lb second generation Flexent Modcell cabinet was introduced in October 1999 for production as PCS (1.9 gigahertz) and TDMA (time-division multiple access) cellular (850 MHz) versions.
From 1996 to 1999, PRC achieved and reduced with this new facility the following production metrics and lean manufacturing statistics: product-development cycle time reduced over 50%, material cost reduced 43%, cost of goods by 68%, assembly productivity increased close to 150%, assembly defects reduced by 80%, manufacturing inventory reduced 70%, and 100% on-time delivery. The facility introduced several self-managed work teams called PODs (Production On Demand) to assemble and test 50 Flexent Modcells daily.
The location was also active in research and development of CDMA minicells for future global market growth and third generation W-CDMA (Wideband Code-Division Multiple Access) innovation. Expansion was evident with minicell lines for the South America market with cross-training technicians from Brazil on the product and the W-CDMA product for Japan\'s cellular carrier, NTT DoCoMo.
The facility was awarded various awards and prizes for the lean manufacturing of products and excellence in work methods.
In June 2002, Lucent announced closure of the manufacturing building by the end of the year, due to the telecommunication losses in operations. Of the remaining 530 employees at the facility. 170 were employee layoffs and the other 360 employees would mostly transfer to Lucent\'s Whippany, New Jersey location. The manufacturing of cell based systems would transfer to the Columbus, Ohio facility without employees. In the prior year. the warehouse building had closed for consolidation of facilities and cost reduction.
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# Lucent Technologies
## Operations
### Notable buildings {#notable_buildings}
During its expansion in the late 1990s, Lucent commissioned several large office buildings. The architectural firm, Kevin Roche, John Dinkeloo, and Associates (KRJDA) designed five structures clad in energy-efficient, tinted, low-E glass.
- **Westminster** -- built between 1997 and 2001, the Westminster, Colorado building was a 480,000 ft² research and development facility for 1,350 employees. Its design is similar to the Lisle, Illinois building, with two four-story wings arranged with an entrance resembling a glass satellite dish. The building was an expansion to the existing Westminster building via pedestrian bridge.
- **Naperville** -- in 2000, the 600,000 ft² Naperville, Illinois five-story structure was completed for 2000 employees. It had a pedestrian bridge to the existing Indian Hill research and development building. In April 2023, the building was sold for \$4.8 million by Nokia to a developer and the new ownership began demolition in August 2023 of those structures formerly called \'Indian Hill New\' by Lucent and Alcatel-Lucent.
- **Lisle** -- in 2001, the Network Software Center in Lisle, Illinois was also completed in a similar design of a five-story three building with wings and two parking garages. This research and development building was a 600,000 ft² glass building for 2,000 employees. A pedestrian bridge over an existing lake linked it to the Network Software Center, built in the 1970s.
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- **Nuremberg** -- completed in 2002, the Nuremberg, Germany \"serpentine\" five-story building was a 215,000 ft² expansion for two existing buildings, with the same aesthetic design as the United States projects. It included a customer center and training area.
- **Agere Hanover** -- the last project was completed in 2002 in Hanover Township, Allentown, Pennsylvania. The project was called the Agere Systems Expansion, which was a three-story administration, research and development building for 2,000 employees with 560,000 ft² of space. These buildings also included parking garages with about 2,000 parking spaces. The new structures were planned in 1998 by Lucent Technologies, before Agere was incorporated on August 1, 2000, and Agere was spun off by Lucent Technologies on June 1, 2002. Built at a cost of \$165 million, it became the Agere world headquarters in 2003 with consolidation of offices, research and development operations from former AT&T/Lucent Technologies locations at Allentown, Breinigsville, and Muhlenberg.
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# Lucent Technologies
## Operations
### Leased locations {#leased_locations}
To meet customer and business needs, further locations were built and leased for Lucent, rather than built as corporate assets. At September, 1997 Lucent reported that future non-cancelable lease payments totaled \$1,037 million.
- **Oklahoma City** -- in 1997, Adevco Corp. of Norcross, Ga., built the \$8 million building for a Lucent customer center to employ 400 people in Oklahoma City, Oklahoma. Additionally, \$4 million was added to the cost for components, communications systems, and technology of the 10 year contracted lease. The location was to provide support in orders, billing, and scheduled service for over 1.5 million customers. The 57,000-square-foot building was at 14400 Hertz Quail Springs Parkway and was the largest of four customer care locations. The other three centers being opened were in Tucson, Arizona; Atlanta, Georgia; and Parsippany, New Jersey.
- **Altamonte Springs** -- in 1997, an international telecommunications training center was being constructed for potentially 20,000 yearly students learning the network and computerized phone switches. The Altamonte Springs, Florida 100,000-square-foot center would have approximately 100 employees and consolidate the Northlake Boulevard Altamonte Springs training center with 20 employees. The building was located near Interstate 4 and Central Parkway, and leased from Emerson International. State and city officials gave Lucent a \$348,600 four-year incentive packages to build the center at that city. The address was 240 East Central Parkway and considered as Centerpointe building. The training courses were hands-on, lab-based training of company products in data-networking, network-management, optical-networking, wireless, and wireline technologies in either international or domestic markets. The location also provided Navis Optical EMS (Element Management System) System User and Administration Training Using the GUI optical courses. The Customer Training and Information Products at Lucent Technologies facility continued to be known later as Alcatel-Lucent University upon the merger.
- **Coppell** -- in 1998, consolidation of six office buildings, with seven business units, were planned for a new building in Coppell, Texas. A business communications systems division and various local area administration, service, and sales employees were moved to the building. The 100,000-square-foot constructed building was a two-story office building at address, 1111 Freeport Parkway. Catellus Management Corporation was the developer on the project and Compass Management & Leasing was the lessor for Lucent. Lucent\'s real estate costs for Carrollton and Las Colinas buildings were eliminated with this new building constructed. Also, additional buildings at the following locations were moved as planned: 1841 Hutton in Valwood, 4006 Belt Line Road, 4100 Bryan, 5429 LBJ Freeway, 5501 LBJ Freeway, and 17950 Preston Road. In 1999, Townsend Capital purchased the building and Lucent was subletting the building to Avaya.
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- **Highlands Ranch** -- in 1999, Lucent moved its regional headquarters into the recently built Highlands Ranch Business Park at Highlands Ranch, Colorado. Shea Properties constructed the center and anticipated Lucents\' decision by changing the name of Highlands Ranch Boulevard to Lucent Boulevard in 1997. The address was 8740-8744 Lucent Blvd and there was 600,000 square feet of office space to consolidate 3,200 employees from 13 sites near Denver. The 37-acre campus of three white precast buildings was built by Citadel National Construction Group in 21 months and Townsend Capital, LLC was the lessor for Lucent\'s project. The 8744 Lucent Blvd building was later used by Avaya.
- **Miramar** -- in 2000, Lucent announced the Miramar, Florida, 240,000 square foot Caribbean & Latin American division (CALA) regional headquarters, to be built at a cost of \$40 million. Opening was expected in summer 2001 at 2400 SW 145th Avenue, to consolidate 1,200 employees from 13 South Florida locations. Clayco built and developed the four-story, V-shaped building, including two wings for Rockefeller Group Development Corporation, the lessor of the building for Lucent\'s 15-year contract. About 2,500 square feet of lab space was planned for product development as part of this project. In 2002, Lucent\'s technology bubble burst and it relinquished 150,000 square feet of unused space. Within 24 months, the company recovered \$20 million or more from subleasing the former space to new tenants. Alcatel-Lucent continued to use the building for CALA operations after the Lucent merger.
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# Lucent Technologies
## Operations
### International locations {#international_locations}
- **Bangalore** - in 1997, Bell Labs R&D was opened in Bangalore, India and after four years of operation, Lucent announced the closure of Bell Labs in India. In August 2001, during the announcement, up to 500 employees were at Bangalore and Hyderabad locations. Lucent planned a \$2 billion improvement in capital with restructuring on a global plan. On July 9, 2000, a year earlier, Lucent had hired five Indian teenagers Bangalore jobs as they were considered, the "best and brightest minds" of Chennai and Bangalore.
- **Singapore** -- in 1998, an \$8 million education and training center was planned for the Asia Pacific region. The Singapore location would have 20,000 square feet of space with allocation of about 5,000 square feet of lab and equipment areas. The ten classrooms were for training customers on telecommunications services and products.
- **Madrid** -- in 2000, the microelectronics unit of Lucent Technologies located at Tres Cantos, Madrid, Spain was ending production of integrated circuits under Agere. The facility was installed by AT&T in 1987 and became Lucent in 1996. During Lucent\'s creation of Agere as a subsidiary, the facility became Agere and was later acquired by BP Solar to manufacture photovoltaic panels. Lucent sold the facility in restructuring efforts to reduce staff and reduce the value of manufacturing assets. The location was called Lucent Technologies Madrid or Tres Cantos. Although the facility had a record of turnover production in November 2000 of 180 million euros and 18 million euros in income, it sold after June 2001 to BP due to not exceeding 25% production demand.
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- **Hyderabad** - in 2001, Lucent announced the closure of Bell Labs in India at the Bangalore and Hyderabad, India R&D locations.
- **Gurgaon** - in 2001, Lucent announced the Bangalore and Hyderabad Bell Labs locations of India to close. The Gurgaon, India location was not in the August 2001 announcement and stated there were about 500 employees at the location supporting networking, marketing, and sales and not associated with the Bell Labs or R&D aspects.
- **Hilversum** - in 2002, the Hilversum, Netherlands announced a closure of the facility. The closure would result in 300 employees in the Research and Development manufacturing sector. The Hilversum telecommunications operations were originally sold to AT&T from Philips in 1989.
- **Bangalore** - in 2004, Lucent announced a Bell Research Center in Bangalore, India with development on data and networking management software. The scientists at Bell Labs Research would work on computer algorithms and switch architectures for wireless, optical, or data networking.
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# Lucent Technologies
## Operations
### Domestic manufacturing locations {#domestic_manufacturing_locations}
Many of the following manufacturing locations were transferred to other subsidiaries during Lucent\'s existence, closed, or sold years later. These facilities were established by Western Electric before the 1983 Bell System break-up. AT&T operated and managed these locations from 1984 until 1996. After the AT&T spin-off of Lucent, the telecommunications equipment being manufactured at these locations became products of Lucent Technologies.
Name Location Address Established Products Notes
------------------------ ------------------------------- ---------------------------------- ------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Allentown Works Allentown, Pennsylvania 555 Union Blvd. 1948 microelectronics 1,036,000 sq. ft. /later Agere Systems. Agere Systems, Inc. and LSI Logic Corporation merged and operated under a new name LSI Corporation effective April 2, 2007. Closed, several buildings demolished of manufacturing, and sold historical building for charter school.
Atlanta Works Norcross, Georgia 2000 Northeast Expressway 1969 undersea cables, later fiber-optic cables Lucent closed in 2001 the Optical Fiber Solutions (OFS) business and sold it to Furukawa Electric Co., Ltd. at \$2.525 billion. Additionally, Corning Incorporated paid Lucent \$225 million for Lucent Technologies Beijing Fiber Optic Cable Co., Ltd. and Lucent Technologies Shanghai Fiber Optic Co. Ltd. of China in this deal.
Columbus Works Columbus, Ohio 6200 E. Broad St. 1959 switching equipment 1,661,000 sq. ft./ Closed in 2010/2011 under Alcatel-Lucent, sold, and demolished by new owners. From 1957 Western Electric move-in until Bell Labs 1959 move-in, plant reached 3,100 employees. During Western Electric mid 1970s, plant reached 12,000 employees. Between 1984 and 1996, AT&T owned and managed the facility products. From 1996 until 2000, Lucent Technologies changed production with employees concerned of plant operations. About 5,500 employees were in 2000, then Lucent decided to sell in 2001 to Celestica the plant and employees, who did not take severance packages. In 2002 Lucent re-purchased the plant from Celestica. Shortly in 2003, with 1,470 employees in R&D mostly left, Lucent decided to sell the plant. Merger in 2006 with Alcatel-Lucent. In October 2007, Alcatel-Lucent to cease productions and release 230 positions. Alcatel-Lucent in 2009, had 700 employees in non-manufacturing activities. On October 17, 2012, new owners purchased the 84-acre property for \$2.3 million and decided to demolish 943,000 square feet of manufacturing space. The historical administration office building later was used as offices.
Dallas Works Mesquite, Texas 3000 Skyline Drive 1970 electronic switches and power equipment/supplies Closed and sold.
Denver Works Westminster, Colorado 12110 Pecos St. 1972 Dimension and Horizon business PBX systems Closed and sold.
Greensboro Shops Greensboro, North Carolina 801 Merritt Dr. 1950 military equipment 336,000 sq. ft./ Closed and sold.
Indianapolis Works Indianapolis, Indiana 2525 Shadeland Ave. 1950 consumer telephone sets 1,824,000 sq. ft. / Closed and sold.
Kansas City Works Lee\'s Summit, Missouri 777 N. Blue Pkwy 1961 electronics, switching equipment 1,517,000 sq. ft./ Closed and sold.
Merrimack Valley Works North Andover, Massachusetts 1600 Osgood St. 1956 transmission equipment 1,565,000 sq. ft./ Closed and sold.
Oklahoma City Works Oklahoma City, Oklahoma 7725 W Reno Ave 1961 payphones, switching equipment Closed and sold.
Omaha Works Omaha, Nebraska 132nd and L Streets 1958 crossbar, dial, and PBX equipment, cable, relays \"Two key buildings that were part of the original complex: Building 20 (the property\'s iconic office building) and Building 30 (a former manufacturing/warehouse facility).\" were purchased upon the closure in November 2011. Closed and sold.
Orlando Works Orlando, Florida 9701 and 9333 John Young Parkway early 1980s microelectronics 1,307,000 sq. ft. /later Agere Systems Closed 2005, demolished, and sold 2007.
Phoenix Works Phoenix, Arizona 505 N. 51 Ave. 1967 cable and wire 850,000 sq. ft./ Closed and sold.
Reading Works Reading, Pennsylvania 2525 North 12th St 1962 microelectronics 1,214,000 sq. ft./later Agere Systems Closed and sold.
Richmond Works Richmond, Virginia 4500 Laburnum Ave 1973 printed circuit technology 400,000 sq. ft./ In 1979, Fortune Magazine designated as one of the 10 best-managed American factories. Sold in 1996 to Viasystems Group, Inc. and closed the circuit board plant. During Viasystems, the manufacturing operations ceased in June 2001 and the facility was idle up-to the sale on August 23, 2006. The new ownership, Laburnum Investments, LLC, planned the White Oak Village Shopping Center. Although, the site was sold, Lucent and Alcatel-Lucent were involved in the Environmental Protection Agency (EPA) remediation of chemicals underground from Western Electric/AT&T operations. Afterwards, when the EPA ordered remediation clean-up in 1996 under Lucent, several companies were later created and responsibility for the cleanup was the following: Agere in 2001, LSI in 2007, Avago in 2014, and Broadcom in 2016.
Shreveport Works Shreveport, Louisiana 9595 Mansfield Rd 1967 business and consumer telephone sets, payphones 1,206,000 sq. ft./Closed and sold.
Winston-Salem Works Winston-Salem, North Carolina 3300 Lexington Rd. S.E. 1954 broadband carrier equipment, inbound signaling, telephone and telegraph repeaters, capacitors, thin film resistors, sealed contacts, magnetic apparatus, mainly military and wave guide equipment 1,084,000/ Closed and sold.
### Awards
- 1997, the Primetime Engineering Emmy Awards from the Academy of Television Arts and Sciences for work done by formerly AT&T Bell Labs and Microelectronics Group on the Grand Alliance (HDTV) project for digital television.
- 1998\. the Adjunct Physics Director at Lucent Bell Labs, Horst Stormer, received the Nobel Prize in Physics with former AT&T Bell Labs scientists Daniel C. Tsui and Robert B. Laughlin. Their research work was done on fractional quantum hall effect during their tenure at AT&T Bell Labs.
- 1998, Lucent received the INFORMS Prize, for its work in the companies operations research, presented by Institute for Operations Research and the Management Sciences.
- 1999\. the Wireless Networks Group at the Mount Olive, New Jersey Product Realization Center, received the 1999 New Jersey Governor\'s Gold Award for Performance Excellence.
- 2000, the Shingo Prize for Excellence in Manufacturing was awarded at the Mount Olive Product Realization Center
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# Lupercalia
**Lupercalia**, also known as **Lupercal**, was a pastoral festival of Ancient Rome observed annually on February 15 to purify the city, promoting health and fertility. Lupercalia was also known as *dies Februatus*, after the purification instruments called *februa*, the basis for the month named *Februarius*.
## Name
The festival was originally known as Februa (\"Purifications\" or \"Purgings\") after the **februum** which was used on the day. It was also known as **Februatus** and gave its name variously, as epithet to Juno Februalis, Februlis, or Februata in her role as patron deity of that month; to a supposed purification deity called Februus; and to February (**mensis Februarius**), the month during which the festival occurred. Ovid connects **februare** to an Etruscan word for \"purging\".
The name *Lupercalia* was believed in antiquity to evince some connection with the Ancient Greek festival of the Arcadian Lykaia, a wolf festival (*λύκος*, *lýkos*; *lupus*), and the worship of *Lycaean Pan*, assumed to be a Greek equivalent to Faunus, as instituted by Evander. Justin describes a cult image of \"the Lycaean god, whom the Greeks call Pan and the Romans Lupercus\", as nude, save for a goatskin girdle.
The statue stood in the Lupercal, the cave where tradition held that Romulus and Remus were suckled by the she-wolf (Lupa). The cave lay at the foot of the Palatine Hill, on which Romulus was thought to have founded Rome. The name of the festival most likely derives from *lupus*, \"wolf\", though both the etymology and its significance are obscure. The wolf appellation may have to do with the fact that an animal predator plays a key role in male rites of passage. Despite Justin\'s assertion, no deity named \"Lupercus\" has been identified.
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# Lupercalia
## Rites
### Locations
The rites were confined to the Lupercal cave, the Palatine Hill, and the Forum, all of which were central locations in Rome\'s foundation myth. Near the cave stood a sanctuary of Rumina, goddess of breastfeeding; and the wild fig-tree (*Ficus Ruminalis*) to which Romulus and Remus were brought by the divine intervention of the river-god Tiberinus; some Roman sources name the wild fig tree *caprificus*, literally \"goat fig\". Like the cultivated fig, its fruit is pendulous, and the tree exudes a milky sap if cut, which makes it a good candidate for a cult of breastfeeding.
### Priesthoods
The Lupercalia had its own priesthood, the *Luperci* (\"brothers of the wolf\"), whose institution and rites were attributed either to the Arcadian culture-hero Evander, or to Romulus and Remus, erstwhile shepherds who had each established a group of followers. The *Luperci* were young men (*iuvenes*), usually between the ages of 20 and 40. They formed two religious *collegia* (associations) based on ancestry; the *Quinctiliani* (named after the *gens* Quinctia) and the *Fabiani* (named after the *gens* Fabia). Each college was headed by a *magister*.
In 44 BC, a third college, the *Juliani*, was instituted in honor of Julius Caesar; its first *magister* was Mark Antony. The college of *Juliani* disbanded or lapsed following the Assassination of Julius Caesar, and was not re-established in the reforms of his successor, Augustus. In the Imperial era, membership of the two traditional *collegia* was opened to *iuvenes* of equestrian status.
### Sacrifice and fertility rites {#sacrifice_and_fertility_rites}
At the Lupercal altar, a male goat (or goats) and a dog were sacrificed by one or another of the *Luperci*, under the supervision of the Flamen dialis, Jupiter\'s chief priest. An offering was also made of salted mealcakes, prepared by the Vestal Virgins.`{{failed verification|date=February 2023}}`{=mediawiki} After the blood sacrifice, two *Luperci* approached the altar. Their foreheads were anointed with blood from the sacrificial knife, then wiped clean with wool soaked in milk, after which they were expected to laugh.
The sacrificial feast followed, after which the Luperci cut thongs (known as **februa**) from the flayed skin of the animal, and ran with these, naked or near-naked, along the old Palatine boundary, in an anticlockwise direction around the hill. In Plutarch\'s description of the Lupercalia, written during the early Roman Empire, `{{quote|...many of the noble youths and of the magistrates run up and down through the city naked, for sport and laughter striking those they meet with shaggy thongs. And many women of rank also purposely get in their way, and like children at school present their hands to be struck, believing that the [[pregnant]] will thus be helped in [[Childbirth|delivery]], and the barren to pregnancy.<ref>{{cite book| url= https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Plutarch/Lives/Caesar*.html#61 | author= Plutarch| title= Life of Caesar| language= en| via= uchicago.edu| access-date= }}</ref>}}`{=mediawiki} The *Luperci* completed their circuit of the Palatine, then returned to the *Lupercal* cave.
While sometimes repeated uncritically by modern sources, there is no ancient evidence for any kind of lottery or sortition scheme pairing couples for sex. The first descriptions of this fictitious lottery appeared in the 15th century in relation to Valentine\'s Day, with a connection to the Lupercalia first asserted in 18th century antiquarian works, such as those by Alban Butler and Francis Douce.
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# Lupercalia
## History
The Februa was of ancient and possibly Sabine origin. After February was added to the Roman calendar, Februa occurred on its fifteenth day (**a.d. XV Kal. Mart.**). Of its various rituals, the most important came to be those of the Lupercalia. The Romans themselves attributed the instigation of the Lupercalia to Evander, a culture hero from Arcadia who was credited with bringing the Olympic pantheon, Greek laws and alphabet to Italy, where he founded the city of Pallantium on the future site of Rome, 60 years before the Trojan War.
Lupercalia was celebrated in parts of Italy; *Luperci* are attested by inscriptions at Velitrae, Praeneste, Nemausus (modern Nîmes) and elsewhere. The ancient cult of the Hirpi Sorani (\"wolves of Soranus\", from Sabine *hirpus* \"wolf\"), who practiced at Mt. Soracte, 45 km north of Rome, had elements in common with the Roman Lupercalia.
Descriptions of the Lupercalia festival of 44 BC attest to its continuity. During the festival, Julius Caesar publicly refused a golden crown offered to him by Mark Antony. The Lupercal cave was restored or rebuilt by Augustus, and has been speculated to be identical with a grotto discovered in 2007, 50 ft below the remains of Augustus\' residence; according to scholarly consensus, the grotto is a nymphaeum, not the Lupercal. The Lupercalia festival is marked on a calendar of 354 alongside traditional and Christian festivals.
Despite the banning in 391 of all non-Christian cults and festivals, the Lupercalia was celebrated by the nominally Christian populace on a regular basis into the reign of the emperor Anastasius. Pope Gelasius I (494--96) claimed that only the \"vile rabble\" were involved in the festival and sought its forceful abolition; the Roman Senate protested that the Lupercalia was essential to Rome\'s safety and well-being. This prompted Gelasius\' scornful suggestion that \"If you assert that this rite has salutary force, celebrate it yourselves in the ancestral fashion; run nude yourselves that you may properly carry out the mockery\".
There is no contemporary evidence to support the popular notions that Gelasius abolished the Lupercalia, or that he, or any other prelate, replaced it with the Feast of the Purification of the Blessed Virgin Mary. A literary association between the Lupercalia and the romantic elements of Saint Valentine\'s Day dates back to Chaucer and poetic traditions of courtly love.
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# Lupercalia
## Legacy
Horace\'s Ode III, 18 alludes to the Lupercalia. The festival or its associated rituals gave its name to the Roman month of February (**mensis Februarius**) and thence to the modern month. The Roman god Februus personified both the month and purification, but seems to postdate both.
William Shakespeare\'s play *Julius Caesar* begins during the Lupercalia. Mark Antony is instructed by Caesar to strike his wife Calpurnia, in the hope that she will be able to conceive.
Research published in 2019 suggests that the word Leprechaun derives from *Lupercus*
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# Lists of atheists
Atheism, in the broadest sense, is an absence of belief in the existence of deities. In a narrower sense, atheism is simply the absence of belief that any deities exist. This is a compilation of the various **lists of atheists** with articles on Wikipedia by category. Living people in these lists are those whose atheism is relevant to their notable activities or public life, and who have publicly identified themselves as atheists
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# Body relative direction
**Body relative directions** (also known as **egocentric coordinates**) are geometrical orientations relative to a body such as a human person\'s body or a road sign. The most common ones are: **left** and **right**; **forward** and **backward**; **up** and **down**. They form three pairs of orthogonal axes.
## Traditions and conventions {#traditions_and_conventions}
Since definitions of left and right based on the geometry of the natural environment are unwieldy, in practice, the meaning of relative direction words is conveyed through tradition, acculturation, education, and direct reference. One common definition of up and down uses the gravity of Earth as a frame of reference. Since there is a very noticeable force of gravity acting between the Earth and any other nearby object, down is defined as that direction consistent with the local gravitational field unit vector, in other words, the direction which an object moves in reference to the Earth when the object is allowed to fall freely. Up is then defined as the opposite direction of down. Another common definition uses a human body, standing upright, as a frame of reference. In that case, up is defined as the direction from feet to head, perpendicular to the surface of the Earth. In most cases, up is a directionally oriented position generally opposite to that of the pull of gravity.
In situations where a common frame of reference is needed, it is most common to use an egocentric view. A simple example is road signage. Another example is stage blocking, where \"stage left\" \"stage right\" are, by convention, defined from the point of view of actors facing the audience. \"Upstage\" and \"downstage\" do not follow gravity but by convention mean away from and towards the audience. An example of a non-egocentric view is page layout, where the relative terms \"upper half\" \"left margin,\" etc. are defined in terms of the observer but employed in reverse for a type compositor, returning to an egocentric view. In medicine and science, where precise definitions are crucial, relative directions (left and right) are the sides of the organism, not those of the observer. The same is true in heraldry, where left and right in a coat of arms is treated as if the shield were being held by the armiger. To avoid confusion, Latin terminology is employed: *dexter* and *sinister* for right and left. Proper right and proper left are terms mainly used to describe artistic images, and overcome the potential confusion that a figure\'s \"own\" right or \"proper right\" hand is on the left hand as the viewer sees it from the front.
Forward and backward may be defined by referring to an object\'s or organism\'s motion. Forward is defined as the direction in which the object is moving. Backward is then defined as the opposite direction to forward. Alternatively, \'forward\' may be the direction pointed by the observer\'s nose, defining \'backward\' as the direction from the nose to the sagittal border in the observer\'s skull. With respect to a ship \'forward\' would indicate the relative position of any object lying in the direction the ship is pointing. For symmetrical objects, it is also necessary to define forward and backward in terms of expected direction. Many mass transit trains are built symmetrically with paired control booths, and definitions of forward, backward, left, and right are temporary.
Given significant distance from the magnetic poles, one can figure which hand is which using a magnetic compass and the sun. Facing the sun, before noon, the north pointer of the compass points to the \"left\" hand. After noon, it points to the \"right\".
## Geometry of the natural environment {#geometry_of_the_natural_environment}
A right-hand rule is one common way to relate three principal directions. For many years a fundamental question in physics was whether a left-hand rule would be equivalent. Many natural structures, including human bodies, follow a certain \"handedness\", but it was widely assumed that nature did not distinguish the two possibilities. This changed with the discovery of parity violations in particle physics. If a sample of cobalt-60 atoms is magnetized so that they spin counterclockwise around some axis, the beta radiation resulting from their nuclear decay will be preferentially directed opposite that axis. Since counter-clockwise may be defined in terms of up, forward, and right, this experiment unambiguously differentiates left from right using only natural elements: if they were reversed, or the atoms spun clockwise, the radiation would follow the spin axis instead of being opposite to it.
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# Body relative direction
## Nautical terminology {#nautical_terminology}
Bow, stern, port, starboard, fore and aft are nautical terms that convey an impersonal relative direction in the context of the moving frame of persons aboard a ship. The need for impersonal terms is most clearly seen in a rowing shell where the majority of the crew face aft (\"backwards\"), hence the oars to their right are actually on the port side of the boat. Rowers eschew the terms left, right, port and starboard in favor of stroke-side and bow-side. The usage derives from the tradition of having the stroke (the rower closest to the stern of the boat) oar on the port side of the boat.
## Cultures without relative directions {#cultures_without_relative_directions}
Most human cultures use relative directions for reference, but there are exceptions. Some Australian Aboriginal languages like Guugu Yimithirr, Kayardild and Kuuk Thaayorre have no words denoting the egocentric directions; instead, speakers exclusively refer to cardinal directions, even when describing small-scale spaces. For instance, if they wanted someone to move over on the car seat to make room, they might say \"move a bit to the east\". To tell someone where exactly they left something in their house, they might say, \"I left it on the southern edge of the western table.\" Or they might warn a person to \"look out for that big ant just north of your foot\". Other peoples \"from Polynesia to Mexico and from Namibia to Bali\" similarly have predominantly \"geographic languages\". American Sign Language makes heavy use of geographical direction through absolute orientation
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# List of deists
This is a partial list of people who have been categorized as Deists, the belief in a deity based on natural religion only, or belief in religious truths discovered by people through a process of reasoning, independent of any revelation through scriptures or prophets. They have been selected for their influence on Deism or for their notability in other areas.
## Born before 1700 {#born_before_1700}
- Al-Maʿarri (973--1058), was a blind Arab philosopher, poet and writer, and a controversial rationalist.
- Leonardo da Vinci (1452--1519), Italian Renaissance polymath: painter, sculptor, architect, musician, scientist, mathematician, engineer, inventor, anatomist, geologist, cartographer, botanist, and writer. Described as a deist by some sources, most historians have deemed him a Roman Catholic.
- Edward Herbert, 1st Baron Herbert of Cherbury (1583--1648), British soldier, diplomat, historian, poet and religious philosopher
- Gottfried Leibniz (1646--1716), German mathematician and philosopher. He is best known for developing infinitesimal calculus independently of Isaac Newton, and his mathematical notation has been widely used ever since it was published. He has also been labeled a Christian as well.
- Matthew Tindal (1657--1733), controversial English author whose works were influential on Enlightenment thinking
- Voltaire (1694--1778), French Enlightenment writer and philosopher
- William Hogarth (1697--1764), English painter, visual artist and pioneering cartoonist
- Colin Maclaurin (1698--1746), Scottish mathematician who made important contributions to geometry and algebra. The Maclaurin series, a special case of the Taylor series, are named after him.
## Born 1700--1800 {#born_17001800}
- Benjamin Franklin (1706--1790), American polymath; one of the Founding Fathers of the United States
- Émilie du Châtelet (1706--1749), French mathematician, physicist, and author during the Age of Enlightenment. Her crowning achievement is considered to be her translation and commentary on Isaac Newton\'s work *Principia Mathematica*.
- Mikhail Lomonosov (1711--1765), Russian polymath, scientist and writer, who made important contributions to literature, education, and science. Among his discoveries was the atmosphere of Venus. His spheres of science were natural science, chemistry, physics, mineralogy, history, art, philology, optical devices and others. Lomonosov was also a poet and influenced the formation of the modern Russian literary language.
- Jean le Rond d\'Alembert (1717--1783), French mathematician, mechanician, physicist, philosopher, and music theorist. He was also co-editor with Denis Diderot of the *Encyclopédie*.
- Adam Smith (1723--1790), Scottish philosopher and economist; considered the father of modern economics
- James Hutton (1726--1797), Scottish physician, geologist, naturalist, chemical manufacturer and experimental agriculturalist. His work helped to establish the basis of modern geology. His theories of geology and geologic time, also called deep time, came to be included in theories which were called plutonism and uniformitarianism.
- Gotthold Ephraim Lessing (1729--1781), German writer, philosopher, dramatist, publicist, and art critic
- Moses Mendelssohn (1729--1796), German philosopher influential in the Jewish Haskalah
- George Washington (1732--1799), American soldier, statesman, and Founding Father, who served as the first president of the United States from 1789 to 1797
- James Watt (1736--1819), Scottish inventor and mechanical engineer whose improvements to the Newcomen steam engine were fundamental to the changes brought by the Industrial Revolution in both his native Great Britain and the rest of the world.
- Thomas Paine (1737--1809), English pamphleteer, revolutionary, radical, inventor, and intellectual, and one of the Founding Fathers of the United States
- Ethan Allen (1738--89), early American revolutionary and guerrilla leader
- Thomas Jefferson (1743--1826), author of the Jefferson Bible, an American Founding Father, the principal author of the U.S. Declaration of Independence, and the third President of the United States.
- Jean-Baptiste Lamarck (1744--1829), French naturalist. He was a soldier, biologist, academic, and an early proponent of the idea that evolution occurred and proceeded in accordance with natural laws.
- Johann Adam Weishaupt (1748--1830), Bavarian philosopher, canon law professor and founder of the Illuminati
- James Madison (1751--1836), \"Father of the United States Constitution\", one of the Founding Fathers of the United States, and the 4th President of the United States
- James Monroe (1758--1831), Founding Father of the United States and fifth president of the United States; held various other roles in the government of the United States. Monroe almost never discussed religion but used Deist language in speeches and was a Freemason, who were largely Deists at the time.
- Friedrich Schiller (1759--1805), German poet, philosopher, historian, and playwright.
- Maximilien Robespierre (1758--1794), French revolutionary and lawyer
- Elihu Palmer (1764--1806), American author and advocate of deism
- Carl Friedrich Gauss (1777--1855), German mathematician and physical scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.
- Humphry Davy (1778--1829), British chemist and inventor.
- Charles Lyell (1797--1875), British lawyer and the foremost geologist of his day. He is best known as the author of *Principles of Geology*, which popularised James Hutton\'s concepts of uniformitarianism.
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# List of deists
## Born 1800--1900 {#born_18001900}
- Victor Hugo (1802--1885), French writer, artist, activist and statesman
- William Lloyd Garrison (1805--1879), American abolitionist, journalist, and social reformer. He is best known as the editor of the abolitionist newspaper *The Liberator*, and was one of the founders of the American Anti-Slavery Society, he promoted \"immediate emancipation\" of slaves in the United States.
- Lysander Spooner (1808--1887), American anarchist, philosopher and abolitionist
- Henrik Wergeland (1808--1845), Norwegian poet and theologist (by self-definition).
- Abraham Lincoln (1809--1865), sixteenth president of the United States. He never joined any church and has been described as a \"Christian deist\". As a young man, he was religiously skeptical and sometimes ridiculed revivalists. During his early years, Lincoln enjoyed reading the works of deists such as Thomas Paine and Voltaire. He drafted a pamphlet incorporating such ideas but did not publish it. After charges of hostility to Christianity almost cost him a congressional bid, he kept his unorthodox beliefs private. James Adams labelled Lincoln as a deist. In 1834, Lincoln reportedly wrote a manuscript essay challenging Christianity modelled on Paine\'s book *The Age of Reason*, which a friend supposedly burned to protect him from ridicule. He seemed to believe in an all-powerful God, who shaped events and, by 1865, was expressing those beliefs in major speeches.
- Jules Verne (1828--1905), French author who pioneered the science fiction genre in Europe. He is best known for his novels *Twenty Thousand Leagues Under the Seas*, *Journey to the Center of the Earth*, and *Around the World in Eighty Days*.
- Dmitri Mendeleev (1834--1907), Russian chemist and inventor. He is credited as being the creator of the first version of the periodic table of elements.
- Simon Newcomb (1835--1909), Canadian-American astronomer and mathematician.
- Mark Twain (1835--1910), American author and humorist
- Alfred M. Mayer (1836--1897), American physicist.
- Charles Sanders Peirce (1839--1914), American philosopher, logician, mathematician, and scientist, sometimes known as \"the father of pragmatism\". He was educated as a chemist and employed as a scientist for 30 years. Today he is appreciated largely for his contributions to logic, mathematics, philosophy, scientific methodology, and semiotics, and for his founding of pragmatism.
- Ludwig Boltzmann (1844--1906), Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics.
- Thomas Alva Edison (1847--1931), American inventor and businessman.
- Max Planck (1858--1947), German physicist, regarded as the founder of quantum theory.
- José Rizal (1861--1896), a Filipino patriot, philosopher, medical doctor, poet, journalist, novelist, political scientist, painter and polyglot. Considered to be one of the Philippines\' most important heroes and martyrs whose writings and execution contributed to the igniting of the Philippine Revolution. He is also considered as Asia\'s first modern non-violent proponent of freedom.
- Ernest Rutherford (1871--1937), New Zealand chemist and \"father\" of nuclear physics, who was awarded the Nobel Prize in Chemistry in 1908 \"for his investigations into the disintegration of the elements, and the chemistry of radioactive substances\".
- Max Born (1882--1970), German-British physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics and supervised the work of a number of notable physicists in the 1920s and 30s. Born won the 1954 Nobel Prize in Physics (shared with Walther Bothe).
- Hermann Weyl (1885--1955), German mathematician and theoretical physicist.
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# List of deists
## Born after 1900 {#born_after_1900}
- Wolfgang Pauli (1900--1958), Austrian theoretical physicist. In 1945, he received the Nobel Prize in Physics. He is best known for his work on Pauli principle and spin theory.
- Luis Walter Alvarez (1911--1988), American experimental physicist and inventor, who spent nearly all of his long professional career on the faculty of the University of California, Berkeley. He was awarded the Nobel Prize in Physics in 1968, and took out over 40 patents, some of which led to commercial products.
- Martin Gardner (1914--2010), American popular mathematics and science writer specializing in recreational mathematics, but with interests encompassing micromagic, stage magic, literature (especially the writings of Lewis Carroll and G. K. Chesterton), philosophy, scientific skepticism, and religion.
- Antony Flew (1923--2010), British analytic philosopher and prominent former atheist; during his last years he openly made an allegiance to Deism and stated to have acknowledged the existence of an Intelligent Creator of the universe, the Aristotelian God.
- Walter Kohn (1923--2016), Austrian-born American theoretical physicist. He was awarded, with John Pople, the Nobel Prize in Chemistry in 1998.
- Harish-Chandra (1923--1983), Indian mathematician, who did fundamental work in representation theory, especially Harmonic analysis on semisimple Lie groups.
- Neil Armstrong (1930--2012), American NASA astronaut, test pilot, aerospace engineer, university professor, United States Naval Aviator, and the first person to set foot upon the Moon.
- James Heckman (born 1944), American economist who shared the Nobel Memorial Prize in Economic Sciences in 2000 for his pioneering work in econometrics and microeconomics.
- Rodrigo Duterte (born 1945), 16th President of the Philippines.
- Paul Davies (born 1946), British physicist and science writer and broadcaster
- Nick Cave (born 1957), Australian musician, songwriter, poet, author and actor.
- Brett Gurewitz (born 1962), guitarist and songwriter for the American punk rock band Bad Religion
- Tammy Duckworth (born 1968), United States Senator for Illinois, member of United States House of Representatives, Army National Guard lieutenant colonel
- Harmony Korine (born 1973), American film director, producer, screenwriter, and author.
- Rosalia (Born 1992) Spanish singer
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# Lossy compression
In information technology, **lossy compression** or **irreversible compression** is the class of data compression methods that uses inexact approximations and partial data discarding to represent the content. These techniques are used to reduce data size for storing, handling, and transmitting content. Higher degrees of approximation create coarser images as more details are removed. This is opposed to lossless data compression (reversible data compression) which does not degrade the data. The amount of data reduction possible using lossy compression is much higher than using lossless techniques.
Well-designed lossy compression technology often reduces file sizes significantly before degradation is noticed by the end-user. Even when noticeable by the user, further data reduction may be desirable (e.g., for real-time communication or to reduce transmission times or storage needs). The most widely used lossy compression algorithm is the discrete cosine transform (DCT), first published by Nasir Ahmed, T. Natarajan and K. R. Rao in 1974.
Lossy compression is most commonly used to compress multimedia data (audio, video, and images), especially in applications such as streaming media and internet telephony. By contrast, lossless compression is typically required for text and data files, such as bank records and text articles. It can be advantageous to make a master lossless file which can then be used to produce additional copies from. This allows one to avoid basing new compressed copies on a lossy source file, which would yield additional artifacts and further unnecessary information loss.
## Types
It is possible to compress many types of digital data in a way that reduces the size of a computer file needed to store it, or the bandwidth needed to transmit it, with no loss of the full information contained in the original file. A picture, for example, is converted to a digital file by considering it to be an array of dots and specifying the color and brightness of each dot. If the picture contains an area of the same color, it can be compressed without loss by saying \"200 red dots\" instead of \"red dot, red dot, \...(197 more times)\..., red dot.\"
The original data contains a certain amount of information, and there is a lower bound to the size of a file that can still carry all the information. Basic information theory says that there is an absolute limit in reducing the size of this data. When data is compressed, its entropy increases, and it cannot increase indefinitely. For example, a compressed ZIP file is smaller than its original, but repeatedly compressing the same file will not reduce the size to nothing. Most compression algorithms can recognize when further compression would be pointless and would in fact increase the size of the data.
In many cases, files or data streams contain more information than is needed. For example, a picture may have more detail than the eye can distinguish when reproduced at the largest size intended; likewise, an audio file does not need a lot of fine detail during a very loud passage. Developing lossy compression techniques as closely matched to human perception as possible is a complex task. Sometimes the ideal is a file that provides exactly the same perception as the original, with as much digital information as possible removed; other times, perceptible loss of quality is considered a valid tradeoff.
The terms \"irreversible\" and \"reversible\" are preferred over \"lossy\" and \"lossless\" respectively for some applications, such as medical image compression, to circumvent the negative implications of \"loss\". The type and amount of loss can affect the utility of the images. Artifacts or undesirable effects of compression may be clearly discernible yet the result still useful for the intended purpose. Or lossy compressed images may be \'visually lossless\', or in the case of medical images, so-called diagnostically acceptable irreversible compression (DAIC) may have been applied.
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# Lossy compression
## Transform coding {#transform_coding}
Some forms of lossy compression can be thought of as an application of transform coding, which is a type of data compression used for digital images, digital audio signals, and digital video. The transformation is typically used to enable better (more targeted) quantization. Knowledge of the application is used to choose information to discard, thereby lowering its bandwidth. The remaining information can then be compressed via a variety of methods. When the output is decoded, the result may not be identical to the original input, but is expected to be close enough for the purpose of the application.
The most common form of lossy compression is a transform coding method, the discrete cosine transform (DCT), which was first published by Nasir Ahmed, T. Natarajan and K. R. Rao in 1974. DCT is the most widely used form of lossy compression, for popular image compression formats (such as JPEG), video coding standards (such as MPEG and H.264/AVC) and audio compression formats (such as MP3 and AAC).
In the case of audio data, a popular form of transform coding is perceptual coding, which transforms the raw data to a domain that more accurately reflects the information content. For example, rather than expressing a sound file as the amplitude levels over time, one may express it as the frequency spectrum over time, which corresponds more accurately to human audio perception. While data reduction (compression, be it lossy or lossless) is a main goal of transform coding, it also allows other goals: one may represent data more accurately for the original amount of space -- for example, in principle, if one starts with an analog or high-resolution digital master, an MP3 file of a given size should provide a better representation than a raw uncompressed audio in WAV or AIFF file of the same size. This is because uncompressed audio can only reduce file size by lowering bit rate or depth, whereas compressing audio can reduce size while maintaining bit rate and depth. This compression becomes a selective loss of the least significant data, rather than losing data across the board. Further, a transform coding may provide a better domain for manipulating or otherwise editing the data -- for example, equalization of audio is most naturally expressed in the frequency domain (boost the bass, for instance) rather than in the raw time domain.
From this point of view, perceptual encoding is not essentially about *discarding* data, but rather about a *better representation* of data. Another use is for backward compatibility and graceful degradation: in color television, encoding color via a luminance-chrominance transform domain (such as YUV) means that black-and-white sets display the luminance, while ignoring the color information. Another example is chroma subsampling: the use of color spaces such as YIQ, used in NTSC, allow one to reduce the resolution on the components to accord with human perception -- humans have highest resolution for black-and-white (luma), lower resolution for mid-spectrum colors like yellow and green, and lowest for red and blues -- thus NTSC displays approximately 350 pixels of luma per scanline, 150 pixels of yellow vs. green, and 50 pixels of blue vs. red, which are proportional to human sensitivity to each component.
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# Lossy compression
## Information loss {#information_loss}
Lossy compression formats suffer from generation loss: repeatedly compressing and decompressing the file will cause it to progressively lose quality. This is in contrast with lossless data compression, where data will not be lost via the use of such a procedure. Information-theoretical foundations for lossy data compression are provided by rate-distortion theory. Much like the use of probability in optimal coding theory, rate-distortion theory heavily draws on Bayesian estimation and decision theory in order to model perceptual distortion and even aesthetic judgment.
There are two basic lossy compression schemes:
- In *lossy transform codecs*, samples of picture or sound are taken, chopped into small segments, transformed into a new basis space, and quantized. The resulting quantized values are then entropy coded.
- In *lossy predictive codecs*, previous and/or subsequent decoded data is used to predict the current sound sample or image frame. The error between the predicted data and the real data, together with any extra information needed to reproduce the prediction, is then quantized and coded.
In some systems the two techniques are combined, with transform codecs being used to compress the error signals generated by the predictive stage.
## Comparison
The advantage of lossy methods over lossless methods is that in some cases a lossy method can produce a much smaller compressed file than any lossless method, while still meeting the requirements of the application. Lossy methods are most often used for compressing sound, images or videos. This is because these types of data are intended for human interpretation where the mind can easily \"fill in the blanks\" or see past very minor errors or inconsistencies -- ideally lossy compression is transparent (imperceptible), which can be verified via an ABX test. Data files using lossy compression are smaller in size and thus cost less to store and to transmit over the Internet, a crucial consideration for streaming video services such as Netflix and streaming audio services such as Spotify.
### Transparency
When a user acquires a lossily compressed file, (for example, to reduce download time) the retrieved file can be quite different from the original at the bit level while being indistinguishable to the human ear or eye for most practical purposes. Many compression methods focus on the idiosyncrasies of human physiology, taking into account, for instance, that the human eye can see only certain wavelengths of light. The psychoacoustic model describes how sound can be highly compressed without degrading perceived quality. Flaws caused by lossy compression that are noticeable to the human eye or ear are known as compression artifacts.
### Compression ratio {#compression_ratio}
The compression ratio (that is, the size of the compressed file compared to that of the uncompressed file) of lossy video codecs is nearly always far superior to that of the audio and still-image equivalents.
- Video can be compressed immensely (e.g., 100:1) with little visible quality loss
- Audio can often be compressed at 10:1 with almost imperceptible loss of quality
- Still images are often lossily compressed at 10:1, as with audio, but the quality loss is more noticeable, especially on closer inspection.
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# Lossy compression
## Transcoding and editing {#transcoding_and_editing}
An important caveat about lossy compression (formally transcoding), is that editing lossily compressed files causes digital generation loss from the re-encoding. This can be avoided by only producing lossy files from (lossless) originals and only editing (copies of) original files, such as images in raw image format instead of JPEG. If data which has been compressed lossily is decoded and compressed losslessly, the size of the result can be comparable with the size of the data before lossy compression, but the data already lost cannot be recovered. When deciding to use lossy conversion without keeping the original, format conversion may be needed in the future to achieve compatibility with software or devices (format shifting), or to avoid paying patent royalties for decoding or distribution of compressed files.
### Editing of lossy files {#editing_of_lossy_files}
By modifying the compressed data directly without decoding and re-encoding, some editing of lossily compressed files without degradation of quality is possible. Editing which reduces the file size as if it had been compressed to a greater degree, but without more loss than this, is sometimes also possible.
#### JPEG
The primary programs for lossless editing of JPEGs are `jpegtran`, and the derived `exiftran` (which also preserves Exif information), and [Jpegcrop](http://sylvana.net/jpegcrop/) (which provides a Windows interface).
These allow the image to be cropped, rotated, flipped, and flopped, or even converted to grayscale (by dropping the chrominance channel). While unwanted information is destroyed, the quality of the remaining portion is unchanged.
Some other transforms are possible to some extent, such as joining images with the same encoding (composing side by side, as on a grid) or pasting images such as logos onto existing images (both via [Jpegjoin](http://sylvana.net/jpegcrop/jpegjoin/)), or scaling.
Some changes can be made to the compression without re-encoding:
- Optimizing the compression (to reduce size without change to the decoded image)
- Converting between progressive and non-progressive encoding.
The freeware Windows-only IrfanView has some lossless JPEG operations in its `JPG_TRANSFORM` plugin.
#### Metadata
Metadata, such as ID3 tags, Vorbis comments, or Exif information, can usually be modified or removed without modifying the underlying data.
#### Downsampling/compressed representation scalability {#downsamplingcompressed_representation_scalability}
One may wish to downsample or otherwise decrease the resolution of the represented source signal and the quantity of data used for its compressed representation without re-encoding, as in bitrate peeling, but this functionality is not supported in all designs, as not all codecs encode data in a form that allows less important detail to simply be dropped. Some well-known designs that have this capability include JPEG 2000 for still images and H.264/MPEG-4 AVC based Scalable Video Coding for video. Such schemes have also been standardized for older designs as well, such as JPEG images with progressive encoding, and MPEG-2 and MPEG-4 Part 2 video, although those prior schemes had limited success in terms of adoption into real-world common usage. Without this capacity, which is often the case in practice, to produce a representation with lower resolution or lower fidelity than a given one, one needs to start with the original source signal and encode, or start with a compressed representation and then decompress and re-encode it (transcoding), though the latter tends to cause digital generation loss.
Another approach is to encode the original signal at several different bitrates, and then either choose which to use (as when streaming over the internet -- as in RealNetworks\' \"SureStream\" -- or offering varying downloads, as at Apple\'s iTunes Store), or broadcast several, where the best that is successfully received is used, as in various implementations of hierarchical modulation. Similar techniques are used in mipmaps, pyramid representations, and more sophisticated scale space methods. Some audio formats feature a combination of a lossy format and a lossless correction which when combined reproduce the original signal; the correction can be stripped, leaving a smaller, lossily compressed, file. Such formats include MPEG-4 SLS (Scalable to Lossless), WavPack, OptimFROG DualStream, and DTS-HD Master Audio in lossless (XLL) mode).
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# Lossy compression
## Methods
### Graphics
#### Image
- Discrete cosine transform (DCT)
- JPEG
- WebP (high-density lossless or lossy compression of RGB and RGBA images)
- High Efficiency Image Format (HEIF)
- Better Portable Graphics (BPG) (lossless or lossy compression)
- JPEG XR, a successor of JPEG with support for high-dynamic range, wide gamut pixel formats (lossless or lossy compression)
- Wavelet compression
- JPEG 2000, JPEG\'s successor format that uses wavelets (lossless or lossy compression)
- DjVu
- ICER, used by the Mars Rovers, related to JPEG 2000 in its use of wavelets
- PGF, Progressive Graphics File (lossless or lossy compression)
- Cartesian Perceptual Compression, also known as CPC
- Fractal compression
- JBIG2 (lossless or lossy compression)
- S3TC texture compression for 3D computer graphics hardware
#### 3D computer graphics {#d_computer_graphics}
- glTF
#### Video
- Discrete cosine transform (DCT)
- H.261
- Motion JPEG
- MPEG-1 Part 2
- MPEG-2 Part 2 (H.262)
- MPEG-4 Part 2 (H.263)
- Advanced Video Coding (AVC / H.264 / MPEG-4 AVC) (may also be lossless, even in certain video sections)
- High Efficiency Video Coding (HEVC / H.265)
- Ogg Theora (noted for its lack of patent restrictions)
- VC-1
- Wavelet compression
- Motion JPEG 2000
- Dirac
- Sorenson video codec
### Audio
#### General
- Modified discrete cosine transform (MDCT)
- Dolby Digital (AC-3)
- Adaptive Transform Acoustic Coding (ATRAC)
- MPEG Layer III (MP3)
- Advanced Audio Coding (AAC / MP4 Audio)
- Vorbis
- Windows Media Audio (WMA) (Standard and Pro profiles are lossy. WMA Lossless is also available.)
- LDAC
- Opus (Notable for lack of patent restrictions, low delay, and high quality speech and general audio.)
- Adaptive differential pulse-code modulation (ADPCM)
- Master Quality Authenticated (MQA)
- MPEG-1 Audio Layer II (MP2)
- Musepack (based on Musicam)
- aptX/ aptX-HD
#### Speech
- Linear predictive coding (LPC)
- Adaptive predictive coding (APC)
- Code-excited linear prediction (CELP)
- Algebraic code-excited linear prediction (ACELP)
- Relaxed code-excited linear prediction (RCELP)
- Low-delay CELP (LD-CELP)
- Adaptive Multi-Rate (used in GSM and 3GPP)
- Codec2 (noted for its lack of patent restrictions)
- Speex (noted for its lack of patent restrictions)
- Modified discrete cosine transform (MDCT)
- AAC-LD
- Constrained Energy Lapped Transform (CELT)
- Opus (mostly for real-time applications)
### Other data {#other_data}
Researchers have performed lossy compression on text by either using a thesaurus to substitute short words for long ones, or generative text techniques, although these sometimes fall into the related category of lossy data conversion.
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# Lossy compression
## Lowering resolution {#lowering_resolution}
A general kind of lossy compression is to lower the resolution of an image, as in image scaling, particularly decimation. One may also remove less \"lower information\" parts of an image, such as by seam carving. Many media transforms, such as Gaussian blur, are, like lossy compression, irreversible: the original signal cannot be reconstructed from the transformed signal. However, in general these will have the same size as the original, and are not a form of compression. Lowering resolution has practical uses, as the NASA New Horizons craft transmitted thumbnails of its encounter with Pluto-Charon before it sent the higher resolution images. Another solution for slow connections is the usage of Image interlacing which progressively defines the image. Thus a partial transmission is enough to preview the final image, in a lower resolution version, without creating a scaled and a full version too
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# Lossless compression
**Lossless compression** is a class of data compression that allows the original data to be perfectly reconstructed from the compressed data with no loss of information. Lossless compression is possible because most real-world data exhibits statistical redundancy. By contrast, lossy compression permits reconstruction only of an approximation of the original data, though usually with greatly improved compression rates (and therefore reduced media sizes).
By operation of the pigeonhole principle, no lossless compression algorithm can shrink the size of all possible data: Some data will get longer by at least one symbol or bit.
Compression algorithms are usually effective for human- and machine-readable documents and cannot shrink the size of random data that contain no redundancy. Different algorithms exist that are designed either with a specific type of input data in mind or with specific assumptions about what kinds of redundancy the uncompressed data are likely to contain.
Lossless data compression is used in many applications. For example, it is used in the ZIP file format and in the GNU tool gzip. It is also often used as a component within lossy data compression technologies (e.g. lossless mid/side joint stereo preprocessing by MP3 encoders and other lossy audio encoders).
Lossless compression is used in cases where it is important that the original and the decompressed data be identical, or where deviations from the original data would be unfavourable. Common examples are executable programs, text documents, and source code. Some image file formats, like PNG or GIF, use only lossless compression, while others like TIFF and MNG may use either lossless or lossy methods. Lossless audio formats are most often used for archiving or production purposes, while smaller lossy audio files are typically used on portable players and in other cases where storage space is limited or exact replication of the audio is unnecessary.
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# Lossless compression
## Techniques
Most lossless compression programs do two things in sequence: the first step generates a *statistical model* for the input data, and the second step uses this model to map input data to bit sequences in such a way that \"probable\" (i.e. frequently encountered) data will produce shorter output than \"improbable\" data.
The primary encoding algorithms used to produce bit sequences are Huffman coding (also used by the deflate algorithm) and arithmetic coding. Arithmetic coding achieves compression rates close to the best possible for a particular statistical model, which is given by the information entropy, whereas Huffman compression is simpler and faster but produces poor results for models that deal with symbol probabilities close to 1.
There are two primary ways of constructing statistical models: in a *static* model, the data is analyzed and a model is constructed, then this model is stored with the compressed data. This approach is simple and modular, but has the disadvantage that the model itself can be expensive to store, and also that it forces using a single model for all data being compressed, and so performs poorly on files that contain heterogeneous data. *Adaptive* models dynamically update the model as the data is compressed. Both the encoder and decoder begin with a trivial model, yielding poor compression of initial data, but as they learn more about the data, performance improves. Most popular types of compression used in practice now use adaptive coders.
Lossless compression methods may be categorized according to the type of data they are designed to compress. While, in principle, any general-purpose lossless compression algorithm (*general-purpose* meaning that they can accept any bitstring) can be used on any type of data, many are unable to achieve significant compression on data that are not of the form for which they were designed to compress. Many of the lossless compression techniques used for text also work reasonably well for indexed images.
### Multimedia
These techniques take advantage of the specific characteristics of images such as the common phenomenon of contiguous 2-D areas of similar tones. Every pixel but the first is replaced by the difference to its left neighbor. This leads to small values having a much higher probability than large values. This is often also applied to sound files, and can compress files that contain mostly low frequencies and low volumes. For images, this step can be repeated by taking the difference to the top pixel, and then in videos, the difference to the pixel in the next frame can be taken.
A hierarchical version of this technique takes neighboring pairs of data points, stores their difference and sum, and on a higher level with lower resolution continues with the sums. This is called discrete wavelet transform. JPEG2000 additionally uses data points from other pairs and multiplication factors to mix them into the difference. These factors must be integers, so that the result is an integer under all circumstances. So the values are increased, increasing file size, but the distribution of values could be more peaked.
The adaptive encoding uses the probabilities from the previous sample in sound encoding, from the left and upper pixel in image encoding, and additionally from the previous frame in video encoding. In the wavelet transformation, the probabilities are also passed through the hierarchy.
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# Lossless compression
## Techniques
### Historical legal issues {#historical_legal_issues}
Many of these methods are implemented in open-source and proprietary tools, particularly LZW and its variants. Some algorithms are patented in the United States and other countries and their legal usage requires licensing by the patent holder. Because of patents on certain kinds of LZW compression, and in particular licensing practices by patent holder Unisys that many developers considered abusive, some open source proponents encouraged people to avoid using the Graphics Interchange Format (GIF) for compressing still image files in favor of Portable Network Graphics (PNG), which combines the LZ77-based deflate algorithm with a selection of domain-specific prediction filters. However, the patents on LZW expired on June 20, 2003.
Many of the lossless compression techniques used for text also work reasonably well for indexed images, but there are other techniques that do not work for typical text that are useful for some images (particularly simple bitmaps), and other techniques that take advantage of the specific characteristics of images (such as the common phenomenon of contiguous 2-D areas of similar tones, and the fact that color images usually have a preponderance of a limited range of colors out of those representable in the color space).
As mentioned previously, lossless sound compression is a somewhat specialized area. Lossless sound compression algorithms can take advantage of the repeating patterns shown by the wave-like nature of the `{{nowrap|data{{px2}}{{mdash}}{{px2}}}}`{=mediawiki}essentially using autoregressive models to predict the \"next\" value and encoding the (possibly small) difference between the expected value and the actual data. If the difference between the predicted and the actual data (called the *error*) tends to be small, then certain difference values (like 0, +1, −1 etc. on sample values) become very frequent, which can be exploited by encoding them in few output bits.
It is sometimes beneficial to compress only the differences between two versions of a file (or, in video compression, of successive images within a sequence). This is called delta encoding (from the Greek letter Δ, which in mathematics, denotes a difference), but the term is typically only used if both versions are meaningful outside compression and decompression. For example, while the process of compressing the error in the above-mentioned lossless audio compression scheme could be described as delta encoding from the approximated sound wave to the original sound wave, the approximated version of the sound wave is not meaningful in any other context.
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# Lossless compression
## Methods
No lossless compression algorithm can efficiently compress all possible data `{{xref|(see {{slink||Limitations}} for more on this)}}`{=mediawiki}. For this reason, many different algorithms exist that are designed either with a specific type of input data in mind or with specific assumptions about what kinds of redundancy the uncompressed data are likely to contain.
Some of the most common lossless compression algorithms are listed below.
### General purpose {#general_purpose}
- ANS -- Entropy encoding, used by LZFSE and Zstandard
- Arithmetic coding -- Entropy encoding
- Burrows--Wheeler transform reversible transform for making textual data more compressible, used by bzip2
- Huffman coding -- Entropy encoding, pairs well with other algorithms
- Lempel-Ziv compression (LZ77 and LZ78) -- Dictionary-based algorithm that forms the basis for many other algorithms
- Deflate -- Combines LZ77 compression with Huffman coding, used by ZIP, gzip, and PNG images
- Lempel--Ziv--Markov chain algorithm (LZMA) -- Very high compression ratio, used by 7zip and xz
- Lempel--Ziv--Storer--Szymanski (LZSS) -- Used by WinRAR in tandem with Huffman coding
- Lempel--Ziv--Welch (LZW) -- Used by GIF images and Unix\'s `compress` utility
- Prediction by partial matching (PPM) -- Optimized for compressing plain text
- Run-length encoding (RLE) -- Simple scheme that provides good compression of data containing many runs of the same value
### Audio
- Adaptive Transform Acoustic Coding (ATRAC)
- Apple Lossless (ALAC -- Apple Lossless Audio Codec)
- Audio Lossless Coding (also known as MPEG-4 ALS)
- Direct Stream Transfer (DST)
- Dolby TrueHD
- DTS-HD Master Audio
- Free Lossless Audio Codec (FLAC)
- Meridian Lossless Packing (MLP)
- Monkey\'s Audio (Monkey\'s Audio APE)
- MPEG-4 SLS (also known as HD-AAC)
- OptimFROG
- Original Sound Quality (OSQ)
- RealPlayer (RealAudio Lossless)
- Shorten (SHN)
- TTA (True Audio Lossless)
- WavPack (WavPack lossless)
- WMA Lossless (Windows Media Lossless)
### Raster graphics {#raster_graphics}
- Lossless only encoding
- BMP
- PNG -- Portable Network Graphics
- GIF -- Graphics Interchange Format
- Lossy and Lossless encoding options
- AVIF -- AV1 Image File Format
- FLIF -- Free Lossless Image Format
- HEIF -- High Efficiency Image File Format, using HEVC
- ILBM -- (RLE compression of Amiga IFF images)
- JBIG2 -- compression of B&W images
- JPEG 2000 -- (via Le Gall--Tabatabai 5/3 reversible integer wavelet transform)
- JPEG-LS
- JPEG XL
- JPEG XR -- formerly *WMPhoto* and *HD Photo*
- LDCT -- Discrete Cosine Transform
- PCX -- PiCture eXchange
- QOI -- Quite OK Image Format
- TGA -- Truevision TGA
- TIFF -- Tag Image File Format
- WebP
### 3D Graphics {#d_graphics}
- OpenCTM -- Lossless compression of 3D triangle meshes
### Video
See list of lossless video codecs
### Cryptography
Cryptosystems often compress data (the \"plaintext\") *before* encryption for added security. When properly implemented, compression greatly increases the unicity distance by removing patterns that might facilitate cryptanalysis. However, many ordinary lossless compression algorithms produce headers, wrappers, tables, or other predictable output that might instead make cryptanalysis easier. Thus, cryptosystems must utilize compression algorithms whose output does not contain these predictable patterns.
### Genetics and genomics {#genetics_and_genomics}
Genetics compression algorithms (not to be confused with genetic algorithms) are the latest generation of lossless algorithms that compress data (typically sequences of nucleotides) using both conventional compression algorithms and specific algorithms adapted to genetic data. In 2012, a team of scientists from Johns Hopkins University published the first genetic compression algorithm that does not rely on external genetic databases for compression. HAPZIPPER was tailored for HapMap data and achieves over 20-fold compression (95% reduction in file size), providing 2- to 4-fold better compression much faster than leading general-purpose compression utilities.
Genomic sequence compression algorithms, also known as DNA sequence compressors, explore the fact that DNA sequences have characteristic properties, such as inverted repeats. The most successful compressors are XM and GeCo. For eukaryotes XM is slightly better in compression ratio, though for sequences larger than 100 MB its computational requirements are impractical.
### Executables
Self-extracting executables contain a compressed application and a decompressor. When executed, the decompressor transparently decompresses and runs the original application. This is especially often used in demo coding, where competitions are held for demos with strict size limits, as small as 1 kilobyte. This type of compression is not strictly limited to binary executables, but can also be applied to scripts, such as JavaScript.
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# Lossless compression
## Benchmarks
Lossless compression algorithms and their implementations are routinely tested in head-to-head benchmarks. There are a number of better-known compression benchmarks. Some benchmarks cover only the data compression ratio, so winners in these benchmarks may be unsuitable for everyday use due to the slow speed of the top performers. Another drawback of some benchmarks is that their data files are known, so some program writers may optimize their programs for best performance on a particular data set. The winners on these benchmarks often come from the class of context-mixing compression software.
Matt Mahoney, in his February 2010 edition of the free booklet *Data Compression Explained*, additionally lists the following:
- The Calgary Corpus dating back to 1987 is no longer widely used due to its small size. Matt Mahoney maintained the Calgary Compression Challenge, created and maintained from May 21, 1996, through May 21, 2016, by Leonid A. Broukhis.
- The Large Text Compression Benchmark and the similar Hutter Prize both use a trimmed Wikipedia XML UTF-8 data set.
- The Generic Compression Benchmark, maintained by Matt Mahoney, tests compression of data generated by random Turing machines.
- Sami Runsas (the author of NanoZip) maintained Compression Ratings, a benchmark similar to Maximum Compression multiple file test, but with minimum speed requirements. It offered the calculator that allowed the user to weight the importance of speed and compression ratio. The top programs were fairly different due to the speed requirement. In January 2010, the top program was NanoZip followed by FreeArc, CCM, flashzip, and 7-Zip.
- The Monster of Compression benchmark by Nania Francesco Antonio tested compression on 1Gb of public data with a 40-minute time limit. In December 2009, the top ranked archiver was NanoZip 0.07a and the top ranked single file compressor was ccmx 1.30c.
The Compression Ratings website published a chart summary of the \"frontier\" in compression ratio and time.
The Compression Analysis Tool is a Windows application that enables end users to benchmark the performance characteristics of streaming implementations of LZF4, Deflate, ZLIB, GZIP, BZIP2 and LZMA using their own data. It produces measurements and charts with which users can compare the compression speed, decompression speed and compression ratio of the different compression methods and to examine how the compression level, buffer size and flushing operations affect the results.
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# Lossless compression
## Limitations
Lossless data compression algorithms cannot guarantee compression for all input data sets. In other words, for any lossless data compression algorithm, there will be an input data set that does not get smaller when processed by the algorithm, and for any lossless data compression algorithm that makes at least one file smaller, there will be at least one file that it makes larger. This is easily proven with elementary mathematics using a counting argument called the pigeonhole principle, as follows:
- Assume that each file is represented as a string of bits of some arbitrary length.
- Suppose that there is a compression algorithm that transforms every file into an output file that is no longer than the original file, and that at least one file will be compressed into an output file that is shorter than the original file.
- Let *M* be the least number such that there is a file *F* with length *M* bits that compresses to something shorter. Let *N* be the length (in bits) of the compressed version of *F*.
- Because *N*\<*M*, **every** file of length *N* keeps its size during compression. There are 2^*N*^ such files possible. Together with *F*, this makes 2^*N*^+1 files that all compress into one of the 2^*N*^ files of length *N*.
- But 2^*N*^ is smaller than 2^*N*^+1, so by the pigeonhole principle there must be some file of length *N* that is simultaneously the output of the compression function on two different inputs. That file cannot be decompressed reliably (which of the two originals should that yield?), which contradicts the assumption that the algorithm was lossless.
- We must therefore conclude that our original hypothesis (that the compression function makes no file longer) is necessarily untrue.
Most practical compression algorithms provide an \"escape\" facility that can turn off the normal coding for files that would become longer by being encoded. In theory, only a single additional bit is required to tell the decoder that the normal coding has been turned off for the entire input; however, most encoding algorithms use at least one full byte (and typically more than one) for this purpose. For example, deflate compressed files never need to grow by more than 5 bytes per 65,535 bytes of input.
In fact, if we consider files of length N, if all files were equally probable, then for any lossless compression that reduces the size of some file, the expected length of a compressed file (averaged over all possible files of length N) must necessarily be *greater* than N.`{{fact|date=January 2025}}`{=mediawiki} So if we know nothing about the properties of the data we are compressing, we might as well not compress it at all. A lossless compression algorithm is useful only when we are more likely to compress certain types of files than others; then the algorithm could be designed to compress those types of data better.
Thus, the main lesson from the argument is not that one risks big losses, but merely that one cannot always win. To choose an algorithm always means implicitly to select a *subset* of all files that will become usefully shorter. This is the theoretical reason why we need to have different compression algorithms for different kinds of files: there cannot be any algorithm that is good for all kinds of data.
The \"trick\" that allows lossless compression algorithms, used on the type of data they were designed for, to consistently compress such files to a shorter form is that the files the algorithms are designed to act on all have some form of easily modeled redundancy that the algorithm is designed to remove, and thus belong to the subset of files that that algorithm can make shorter, whereas other files would not get compressed or even get bigger. Algorithms are generally quite specifically tuned to a particular type of file: for example, lossless audio compression programs do not work well on text files, and vice versa.
In particular, files of random data cannot be consistently compressed by any conceivable lossless data compression algorithm; indeed, this result is used to *define* the concept of randomness in Kolmogorov complexity.
It is provably impossible to create an algorithm that can losslessly compress any data. While there have been many claims through the years of companies achieving \"perfect compression\" where an arbitrary number *N* of random bits can always be compressed to *N* − 1 bits, these kinds of claims can be safely discarded without even looking at any further details regarding the purported compression scheme. Such an algorithm contradicts fundamental laws of mathematics because, if it existed, it could be applied repeatedly to losslessly reduce any file to length 1.
On the other hand, it has also been proven that there is no algorithm to determine whether a file is incompressible in the sense of Kolmogorov complexity. Hence it is possible that any particular file, even if it appears random, may be significantly compressed, even including the size of the decompressor. An example is the digits of the mathematical constant *pi*, which appear random but can be generated by a very small program. However, even though it cannot be determined whether a particular file is incompressible, a simple theorem about incompressible strings shows that over 99% of files of any given length cannot be compressed by more than one byte (including the size of the decompressor).
### Mathematical background {#mathematical_background}
Abstractly, a compression algorithm can be viewed as a function on sequences (normally of octets). Compression is successful if the resulting sequence is shorter than the original sequence (and the instructions for the decompression map). For a compression algorithm to be lossless, the compression map must form an injection from \"plain\" to \"compressed\" bit sequences. The pigeonhole principle prohibits a bijection between the collection of sequences of length *N* and any subset of the collection of sequences of length *N*−1. Therefore, it is not possible to produce a lossless algorithm that reduces the size of every possible input sequence.
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# Lossless compression
## Limitations
### Points of application in real compression theory {#points_of_application_in_real_compression_theory}
Real compression algorithm designers accept that streams of high information entropy cannot be compressed, and accordingly, include facilities for detecting and handling this condition. An obvious way of detection is applying a raw compression algorithm and testing if its output is smaller than its input. Sometimes, detection is made by heuristics; for example, a compression application may consider files whose names end in \".zip\", \".arj\" or \".lha\" uncompressible without any more sophisticated detection. A common way of handling this situation is quoting input, or uncompressible parts of the input in the output, minimizing the compression overhead. For example, the zip data format specifies the \'compression method\' of \'Stored\' for input files that have been copied into the archive verbatim.
### The Million Random Digit Challenge {#the_million_random_digit_challenge}
Mark Nelson, in response to claims of \"magic\" compression algorithms appearing in comp.compression, has constructed a 415,241 byte binary file of highly entropic content, and issued a public challenge of \$100 to anyone to write a program that, together with its input, would be smaller than his provided binary data yet be able to reconstitute it without error. A similar challenge, with \$5,000 as reward, was issued by Mike Goldman
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# LambdaMOO
***LambdaMOO*** is an online community of the variety called a MOO. It is the oldest MOO today.
*LambdaMOO* was founded in 1990 by Pavel Curtis at Xerox PARC. Now hosted in the state of Washington, it is operated and administered entirely on a volunteer basis. Guests are allowed, and membership is free to anyone with an e-mail address.
*LambdaMOO* gained some notoriety when Julian Dibbell wrote a book called *My Tiny Life* describing his experiences there. Over its history, *LambdaMOO* has been highly influential in the examination of virtual-world social issues.
## History
LambdaMOO has its roots in the 1978--1980 work by Roy Trubshaw and Richard Bartle to create and expand the concept of Multi-User Dungeon (MUD) -- virtual communities. Around 1987--1988, the expansion of the global Internet allowed more users to experience the MUD. Pavel Curtis at Xerox PARC noted that they were \"almost exclusively for recreational purposes.\" Curtis determined to explore whether the MUD could be non-recreational. He developed *LambdaMOO* software to run on the LambdaMOO server, which implements the MOO programming language. This software was subsequently made available to the public. Several starter databases, known as cores, are available for MOOs; *LambdaMOO* itself uses the LambdaCore database. The \"Lambda\" name is from Curtis\'s own username on earlier MUD systems.
LambdaMOO can refer to the software, the server, or the community of users.
## Geography
*LambdaMOO* central geography was based on Pavel Curtis\'s California home. New players and guests traditionally connected in \"The Coat Closet\", but a second area, \"The Linen Closet\" (specially programmed as a silent area) was later added as an alternative connection point. The coat closet opens onto the center of the house in The Living Room, a common hangout and place for conversation; its fixtures include a fireplace (where things can be roasted), The Living Room Couch (which periodically causes players\' objects to \'fall through\' to underneath the couch), and a pet Cockatoo who repeats overheard phrases (which is sometimes found with its beak gagged). Occasionally, the Cockatoo is replaced with a more seasonal creature: a Turkey near Thanksgiving, a Raven near Halloween, et cetera.
To the north of the Living Room is the Entrance Hall, the Front Yard, and a limited residential area along LambdaStreet. There is an extensive subterranean complex located down the manhole, including a sewage system. Players walking to the far west along LambdaStreet may be given the option to \'jump off the edge of the world\', which disables access to their account for three months.
To the south of the Living Room is a pool deck, a hot tub, and some of the extensive grounds of the mansion, featuring gardens, hot air balloon landing pads, open fields, fishing holes, and the like.
To the northwest of the living room are the laundry room, garage, dining room, smoking room, drawing room, housekeeper\'s quarters, and kitchen.
To the east of the entry hall, hallways provide access to some individual rooms, the Linen Closet, and to the eastern wing of the house. In the eastern wing can be found the Library of online books, the Museum of generic objects (which account-holders may create instances of), and an extensive area for the *LambdaMOO* RPG.
Since the creation of the original LambdaMOO map, many users have expanded the MOO by making additional rooms with the command \"@dig.\"
## Politics
While most MOOs are run by administrative fiat, in summer of 1993 *LambdaMOO* implemented a petition/ballot mechanism, allowing the community to propose and vote on new policies and other administrative actions. A petition may be created by anyone eligible to participate in politics (those who have maintained accounts at the MOO for at least 30 days), can be signed by other players, and may then be submitted for administrative \'vetting\'. Once vetted, the petition has a limited time to collect enough signatures to become valid and be made into a ballot. Ballots are subsequently voted on; those with a 66% approval rating are passed and will be implemented. This system suffered quite a lot of evolution and eventually passed into a state where wizards took back the power they\'d passed into the hands of the people, but still maintain the ballot system as a way for the community to express its opinions.
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# LambdaMOO
## Demographics
The population of *LambdaMOO* numbered close to 10,000 around 1994, with over 300 actively connected at any time
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# Lorica segmentata
The ***lorica segmentata*** (`{{IPA|la|ɫoːˈriːka}}`{=mediawiki}), also called ***lorica lamminata**\'\', or***banded armour**\'\' is a type of personal armour that was used by soldiers of the Roman army, consisting of metal strips fashioned into circular bands, fastened to internal leather straps.
The *lorica segmentata* has come to be viewed as symbolic of the Roman legions in popular culture.
## Name
thumb\|Roman legionaries marching across a pontoon bridge, a relief scene from the column of Emperor Trajan (r. 98-117 AD) in Rome, Italy (monochrome photographs by Conrad Cichorius)
In Latin, the name *lorica segmentata* translates to \"segmented cuirass.\" However, this name was not given to the armor by the Romans. Instead, it was given by scholars in the 16th century. Despite the lack of knowledge on the Roman name for the armor, scholars can make educated guesses on the Roman name. It is obvious the name had the word *lorica* in it. However, the following part of the name is unknown. Some scholars believe that the name was *lorica lamminata*. This theory is based on the Romans referring to sheets of metal as lamina, although no firm evidence for any theory regarding the name of the armor currently exists.
## History
Despite the armor being commonly associated with the Romans, the technology behind the *lorica segmentata* was old by the time it was introduced into the Roman infantry. The Dendra panoply is an example from the 15th century BC of articulated plate defense using a similar technique of overlapping curved plates. Laminated armor was also used by the Parthians and possibly the Dacians, Scythians, or Sarmatians before the Romans adopted it. Some sets of limb armor of this type combined with scale armor dating back to the 4th century BC have been found in archaeological sites located in the steppe. It is possible the Manica (armguard) was worn by gladiators before it was introduced for military use.
Although the exact time at which the Romans adopted the armor remains unknown, it is possible that the *lorica segmentata* was introduced after Crassus\' defeat at Carrhae in 53 BC. Another possibility is that the armor was adopted in 21 AD after the Revolt of Julius Sacrovir and Julius Florus. Since an archeological research conducted in Kalkriese confirmed that the soldiers at the Battle of the Teutoburg Forest in 9 AD wore the *lorica segmentata*, it is assumed that this armor must have been in use before 9 AD.
Around the middle of the third century the *lorica segmentata* fell out of favor with the Roman army, although it did remain in use during the Late Roman Empire. Soldiers wearing the *lorica segmentata* were depicted on the Arch of Constantine, a monument erected in Rome in 315. However, it has been argued that these depictions are from an earlier monument by Marcus Aurelius, from which Constantine the Great incorporated portions into his Arch. The latest known use of the armor was therefore in the 4th century.
Over time the type of *lorica segmentata* would change. From 9 BC to 43 AD the Roman soldier wore the Dangstetten-Kalkriese-Vindonissa types, from 69 to 100 the Corbridge-Carnuntum type was used. From 164 to 180, the Newstead type was used. The time the armors were used overlapped. It is possible that there was a fourth type, covering the body with segmented armor joined to scale shoulder defenses. However, this is only known from one badly damaged statue originating at Alba Iulia in Romania. This armor was used from about 14 BC to the late 3rd century AD. The *lorica segmentata\'s* use in the Roman army was geographically widespread, but the mail armor *lorica hamata* may have been more common at all times.
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# Lorica segmentata
## Construction
The plates in the *lorica segmentata* armor were made by overlapping ferrous plates that were then riveted to straps made from leather. It is unknown what animal was used to make the leather and if it was tanned or tawed. The plates were made of soft iron on the inside and rolled mild steel on the outside. This made the plates hardened against damage without making them brittle. This case hardening was done by packing organic matter tightly around them and heating them in a forge, transferring carbon from the burnt materials into the surface of the metal. The plates were made from beating out ingots.
The strips were arranged horizontally on the body, overlapping downwards, and they surrounded the torso in two halves, being fastened at the front and back. Additional strips, shoulder guards, breastplates, and backplates were used to protect the upper body and the shoulders. The form of the armor allowed it to be stored very compactly, since it was possible to separate it into four sections, each of which would collapse on itself into a compact mass. The fitments that closed the various plate sections together (buckles, lobate hinges, hinged straps, tie-hooks, tie-rings, etc.) were made of brass. In later variants dating from around 75--80 C.E., the fastenings of the armor were simplified.
Bronze hinges were removed in favor of simple rivets, belt fastenings used small hooks, and the lowest two girdle plates were replaced by one broad plate. The component parts of the *lorica segmentata* moved in synchronization with the other parts. This made the armor more flexible. The armor was very long lasting. The Kalkriese type of armor lasted 55 years, the Corbridge armor lasted 70 years, and the Newstead type lasted 90 years.
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# Lorica segmentata
## Usage
It is unclear who used this armor. On monuments, *Auxilia* are generally shown wearing mail, not cuirasses, and carrying oval shields. Roman depictions of legionaries, such as those found on Trajan\'s column often depict them wearing the *lorica segmentata*. On this basis, it has been supposed that *lorica segmentata* was exclusively used by legionaries and praetorians. However, some historians consider Trajan\'s Column to be inaccurate as a historical source due to its inaccurate and stylized portrayal of Roman armor. These historians also say that \"it is probably safest to interpret the Column reliefs as \'impressions\', rather than accurate representations.\"
The discovery of parts of the *lorica segmentata* at areas where auxiliary soldiers would have been stationed implies that auxiliary troops used the *lorica segmentata*. However, it is entirely possible that the reason behind the presence of the *lorica segmentata* in these areas could be that these areas had a small number of legionaries stationed there. On the Adamclisi *Tropaeum*, the *lorica segmentata* does not appear at all, and legionaries and *auxilia* alike are depicted wearing the *lorica squamata*. Some experts are of the opinion that the Adamclisi monument is a more accurate portrayal of the situation.
It may have been used rarely, maybe only for set-piece battles and parades. This viewpoint considers the figures in Trajan\'s Column to be highly stereotyped, in order to distinguish clearly between different types of troops. It is also debated if the lorica segmentata was only used in the west. All archaeological finds of such armor has been made in 16 countries in the western part of the Roman Empire but never in the east.
## Cultural impact {#cultural_impact}
The tendency to portray Roman legionaries clad in this type of armour often extends to periods of time that are too early or too late in history.
## Gallery
<File:Medinaceli> Actium reliefs 09.jpg\|Relief from the first half of the 1st century depicting the naval battle at Actium <File:047> Conrad Cichorius, Die Reliefs der Traianssäule, Tafel XLVII (Ausschnitt 01).jpg\|Detail of Trajan\'s Column <File:Base> della colonna antonina, decursio sx 04.JPG\|High relief on base of the Column of Antoninus Pius <file:Column> of Marcus Aurelius - detail3.jpg\|Roman legionaries as depicted in relief on the column of Emperor Marcus Aurelius (r. 161--180 AD) in Rome, Italy <File:Arch> of Septimius Severus, Forum Romanum.jpg\|Detail of an Arch of Septimius Severus <File:Roman> soldier in lorica segmentata 1-cropped
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# Libro de los juegos
The ***Libro de los juegos*** (Spanish: \"Book of games\"), or ***Libro de axedrez, dados e tablas*** (\"Book of chess, dice and tables\", in Old Spanish), is a 13th century Spanish treatise of chess that synthesizes the information from Arabic works on this same topic, dice and tables (backgammon forebears) games, commissioned by Alfonso X of Castile, Galicia and León and completed in his scriptorium in Toledo in 1283. It contains the earliest European treatise on chess as well as being the oldest document on European tables games, and is an exemplary piece of the literary legacy of the Toledo School of Translators.
## Significance
The *Libro de los juegos* is one of the most important documents for researching the history of board games. This \"celebrated MS book of games\" has been described as \"one of the choicest treasures of the library of the Escorial\" as well as \"perhaps the greatest source of information on board games ever compiled during the Middle Ages.\" It is both \"the earliest treatise on chess and the oldest document relating to tables which have had their origin in Europe.\"
## Description
The book consists of ninety-seven leaves of parchment, many with color illustrations, and contains 150 miniatures. The text is a treatise that addresses the playing of three game types: a game of skill, or chess; games of chance, or dice; and a third game type, tables, which combines elements of both skill and chance. These games are discussed in the final section of the book at both an astronomical and astrological level. Examining further, the text can also be read as an allegorical initiation tale and as a metaphysical guide for leading a balanced, prudent, and virtuous life. In addition to the didactic, although not overly moralistic, aspect of the text, the manuscript\'s illustrations reveal a rich cultural, social, and religious complexity.
## Location
The earliest manuscript is in the library of the monastery of El Escorial near Madrid in Spain, as manuscript T.I.6. It is bound in sheepskin and is 40 cm high and 28 cm wide (16 in × 11 in). A 1334 copy is held in the library of the Spanish Royal Academy of History in Madrid.
## Background
Alfonso was likely influenced by his contact with scholars in the Arab world. Unlike many contemporary texts on the topic, he does not engage the games in the text with moralistic arguments; instead, he portrays them in an astrological context. He conceives of gaming as a dichotomy between the intellect and chance. The book is divided into three parts reflecting this: the first on chess (a game purely of abstract strategy), the second on dice (with outcomes controlled strictly by chance), and the last on tables (combining elements of both). The first section of the book also speaks of some other games of abstract strategy, notably alquerque and nine men\'s morris, among others. The text may have been influenced by Frederick II\'s text on falconry.
## Chess
The *Libro de los Juegos* contains an extensive collection of writings on chess, with over 100 chess problems and variants. Among its more notable entries is a depiction of what Alfonso calls the *ajedrex de los quatro tiempos* (\"chess of the four seasons\"). This game is a chess variant for four players, described as representing a conflict between the four elements and the four humors. The chessmen are marked correspondingly in green, red, black, and white, and pieces are moved according to the roll of dice. Alfonso also describes a game titled \"astronomical chess\", played on a board of seven concentric circles, divided radially into twelve areas, each associated with a constellation of the Zodiac.
Another variant described in the book is the \"Grant Acedrex\", played over a 12x12 board with alternative pieces as the giraffe and the unicornio.
## Tables
The book describes the rules for a number of games in the tables family. One notable entry is *todas tablas*, the equivalent of the Anglo-Scottish game of Irish, which some scholars have argued has several similarities to modern backgammon including an identical starting position and the same rules for movement and bearing off, albeit the accompanying image has a different opening layout. Alfonso also describes a variant played on a board with seven points in each table. Players rolled seven-sided dice to determine the movement of pieces, an example of Alfonso\'s preference for the number seven.
The tables games described are:
Spanish name Translation Remarks
--------------------------- ------------------------------ ---------------------------------------------
Quinze Tablas Fifteen Pieces
Doce Canes, Doce Hermanos Twelve Dogs, Twelve Brothers
Doblet Doublet Related to the English game of Doublets
Fallas Drop Dead Related to the English game of Fayles
Seys Does e As Six, Two and Ace Related to the English game of Six-Ace
Emperador Emperor
Medio-Emperador Half Emperor
Paireia de Entrada Paired Entry
Cab e Quinal Alongside Fives
Todas Tablas All Pieces Related to the Anglo-Scottish game of Irish
Laquet Related to the French game of Jacquet
Buffa Cortesa Courtly Puff Related to the German game of Puff
Buffa de Baldrac Common Puff
Rencontrat
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# Libro de los juegos
## Art
thumb\|upright=1.45\|right\|A 13th-century illustration in *Libro de los Juegos* of Nine men\'s morris being played with dice The miniatures in the *Libro de juegos* vary between half- and full-page illustrations. The half-page miniatures typically occupy the upper half of a folio, with text explaining the game \"problem\" solved in the image occupying the bottom half. The back or second (verso) side of Folio 1, in a half-page illustration, depicts the initial stages of the creation of the *Libro de juegos*, accompanied by text on the bottom half of the page, and the front or first (recto) side of Folio 2 depicts the transmission of the game of chess from an Indian Philosopher-King to three followers. The full-page illustrations are almost exclusively on the verso side of later folios and are faced by accompanying text on the recto side of the following folio. The significance of the change in miniature size and placement may indicate images of special emphasis, could merely function as a narrative or didactic technique, or could indicate different artisans at work in Alfonso\'s scriptorium as the project developed over time.
Having multiple artisans working on the *Libro de juegos* would have been a typical practice for medieval chanceries and scriptoria, where the labor of producing a manuscript was divided amongst individuals of varying capacities, for example the positions of scribe, draftsman, and apprentice cutting pages. But in addition to performing different tasks, various artisans could have labored at the same job, such as the work of illustration in the *Libro de juegos*, thereby revealing a variety of hands or styles. The *Libro de Juegos* offers such evidence in the difference in size between the half- and full-page illustrations in addition to changes in framing techniques amongst the folios: geometrical frames with embellished corners, architectural frames established by loosely perspectival rooftops and colonnades, and games played under tents. Other stylistic variances are found in figural representation, in facial types, and in a repertoire of different postures assumed by the players in different folios in the manuscript.
For example, in a comparison of two miniatures, found on Folios 53v and 76r, examples of these different styles are apparent, although the trope of a pair of gamers is maintained. In Folio 53v, two men are playing chess, both wearing turbans and robes. Although they may be seated on rugs on the ground, as suggested by the ceramic containers that are placed on or front of the rug near the man on the right side of the board, the figures\' seated positions, which are full frontal with knees bent at right angles, suggests that they are seated on stools or perhaps upholstered benches. The figures\' robes display a Byzantine conservatism, with their modeled three-dimensionality and allusion to a Classical style, yet the iconic hand gestures are reminiscent of a Romanesque energy and theatricality. Although the figures are seated with their knees and torsos facing front, their shoulders and heads rotate in three-quarter profile toward the center of the page, the chess board, and each other. The proximal, inner arm of each player (the arm that is closest to the board) is raised in a speaking gesture; the distal, outside arms of the players are also raised and are bent at the elbows, creating a partial crossing of each player\'s torso as the hands lift in speaking gestures. The faces reveal a striking specificity of subtle detail, particular to a limited number of miniatures throughout the *Libro de juegos*, perhaps indicative of a particular artist\'s hand. These details include full cheeks, realistic wrinkles around the eyes and across the brow, and a red, full-lipped mouth that hints at the Gothic affectations in figural representation coming out of France during the late twelfth and early thirteenth centuries.
The style in the miniature in Folio 76v is markedly different from the style in Folio 53v. In this case, the framed miniature contains two men, perhaps Spanish, with uncovered wavy light brown hair that falls to the jaw line. The men seem young, as the player on the left has no facial hair and his face is unlined. In both folios, both pairs of players are playing tables and seem to be well-dressed, although there is no addition of gold detailing to their robes as seen in the wardrobes of aristocratic players in other miniatures. These players are seated on the ground, leaning on pillows that are placed next to a tables board. In this miniature, the figure on the left side of the board faces the reader, while the figure on the right leans in to the board with his back to the reader. In other words, each player is leaning on his left elbow, using his right hand to reach across his body to play. In the miniatures of this style, the emphasis seems to be more on the posture of the player than the detail of their faces; this crossed, lounging style is only found in the folios of the *Libro de tablas*, the third section of the *Libro de juegos* which explains tables games, again perhaps indicative of the work of a particular artist.
Other visual details contemporaneous of Alfonso\'s court and social and cultural milieu infuse the *Libro de juegos*. Although some of the miniatures are framed by simple rectangles with corners embellished by the golden castles and lions of Castile and León, other are framed by medieval Spanish architectural motifs, including Gothic and Mudéjar arcades of columns and arches. At times, the figural depictions are hierarchical, especially in scenes with representations of Alfonso, where the king is seated on a raised throne while dictating to scribes or meting out punishments to gamblers. Yet a contemporary atmosphere of Spanish *convivencia* is evoked by the inclusion nobility, rogues, vagrants, young and old, men, women, Christian, Muslim, and Jewish characters. Alfonso himself is depicted throughout the text, both as participant and spectator and as an older man and as a younger. The pages are filled with many social classes and ethnicities in various stages of solving the challenges presented by games.
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# Libro de los juegos
## Iconography
The *Libro de los Juegos* can be divided into three parts: the games and problems it explores textually, the actual illuminations themselves, and the metaphysical allegories, where an analysis of the texts and illuminations reveals the movements of the macrocosmos of the universe and the microcosmos of man. The symbolism within the medieval illuminations, as explained by the accompanying texts, reveal allusions to medieval literature, art, science, law and philosophy. Intended as a didactic text, the manuscript functions as a manual that documents and explains how and why one plays games ranging from pure, intellectual strategy (chess), to games of pure chance (dice), to games that incorporate both elements (tables). Conceivably, Alfonso hoped to elucidate for himself how to better play the game of life, while also providing a teaching tool for others. The game of *ajedrex*, or chess, is not the only game explained in the *Libro de los Juegos*, but it does occupy the primary position in the text and is given the most attention to detail.
In the thirteenth century, chess had been played in Europe for almost two hundred years, having been introduced into Europe by Arabs around the year 1000. The Arabs had become familiar with the game as early as the eighth century when the Islamic empire conquered Persia, where the game of chess was alleged to have been originated. It is said that a royal advisor had invented the game in order to teach his king prudence without having to overtly correct him. As Arab contact with the West expanded, so too did the game and its various permutations, and by the twelfth century, chess was becoming an entertaining diversion among a growing population of Europeans, including some scholars, clergy, the aristocracy, and the merchant classes; thus, by the thirteenth century, the iconography and symbolism associated with chess would have been accessible and familiar to Alfonso and his literate court culture, who may have had access to the private library, and manuscripts, of Alfonso, including the *Libro de los Juegos*.
The *Libro de los Juegos* manuscript was a Castilian translation of Arabic texts, which were themselves translations of Persian manuscripts. The visual trope portrayed in the *Libro de los Juegos* miniatures is seen in other European transcriptions of the Arabic translations, most notably the German Carmina Burana Manuscript: two figures, one on either side of the board, with the board tilted up to reveal to the readers the moves made by the players. The juxtaposition of chess and dice in Arabic tradition, indicating the opposing values of skill (chess) and ignorance (dice), was given a different spin in Alfonso\'s manuscript, however. As Alfonso elucidates in the opening section of the *Libro de los Juegos*, the *Libro de ajedrex* (Book of chess) demonstrates the value of the intellect, the *Libro de los dados* (Book of dice) illustrates that chance has supremacy over pure intellect, and the*Libro de las tablas* (Book of tables) celebrates a conjoined use of both intellect and chance. Further, the iconographic linkage between chess and kingship in the Western tradition continued to evolve and became symbolic of kingly virtues, including skill, prudence, and intelligence.
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# Libro de los juegos
## Literary context {#literary_context}
Most of the work accomplished in Alfonso\'s scriptorium consisted of translations into the Spanish vernacular from Arabic translations of Greek texts or classical Jewish medicinal texts. As a result, very few original works were produced by this scholar-king, relative to the huge amount of work that was translated under his auspices. This enormous focus on translation was perhaps an attempt by Alfonso to continue the legacy of academic openness in Castile, initiated by Islamic rulers in Córdoba, where the emirates had also employed armies of translators in order to fill their libraries with Arabic translations of classic Greek texts. Alfonso was successful in promoting Castilian society and culture through his emphasis on the use of Galaico-Portuguese and Castilian, in academic, juridical, diplomatic, literary, and historical works. This emphasis also had the effect of reducing the universality of his translated works and original academic writings, as Latin was the *lingua franca* in both Iberia and Europe; yet Alfonso never desisted in his promotion of the Castilian vernacular.
## Legacy
In 1217, Alfonso had captured the Kingdom of Murcia, on the Mediterranean coast south of Valencia, for his father, King Alfonso IX, thereby unifying the kingdoms of Castile and León, bringing together the northern half of the Iberian Peninsula under one Christian throne. With the Christian *Reconquista* of the Peninsula underway, inroads into Islamic territories were successfully incorporating lands previously held by the *taifa* kingdoms. The arts and sciences prospered in the Kingdom of Castile under the confluence of Latin and Arabic traditions of academic curiosity as Alfonso sponsored scholars, translators, and artists of all three religions of the Book (Jewish, Christian, and Muslim) in his chanceries and scriptoria. Clerical and secular scholars from Europe turned their eyes to the Iberian Peninsula as the arts and sciences prospered in an early Spanish \"renaissance\" under the patronage of Alfonso X, who was continuing the tradition of (relatively) enlightened and tolerant *convivencia* established by the Muslim emirate several centuries earlier.
As an inheritor of a dynamic mixture of Arabic and Latin culture, Alfonso was steeped in the rich heritage of humanistic philosophy, and the production of his *Libro de los Juegos* reveals the compendium of world views that comprised the eclectic thirteenth-century admixture of faith and science. According to this approach, man\'s actions could be traced historically, and his failures and successes could be studied as lessons to be applied to his future progress. These experiences can be played out and studied as they are lived, or as game moves played and analysed in the pages of the *Libro de los Juegos*. It is a beautiful and luxurious document, rich not only in workmanship but also in the amount of scholarship of multiple medieval disciplines that are integrated in its pages
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# Lithium citrate
**Lithium citrate** (Li~3~C~6~H~5~O~7~) is a lithium salt of citric acid that is used as a mood stabilizer in psychiatric treatment of manic states and bipolar disorder. There is extensive pharmacology of lithium, the active component of this salt.
## History
Lithium citrate was one of the lithium salts used to add lithium to drinks and water (lithia water) in the late 19th century and the early 20th century, when there was a general health craze for lithium with it believed to be a cure-all. The soft drink 7Up was at one point named \"7Up Lithiated Lemon Soda\" when it was formulated in 1929 because it claimed to contain lithium citrate. The beverage was a patent medicine marketed as a cure for hangover. In 1936 the federal government forced the manufacturer to remove a number of health claims, and because \"lithium was not an actual ingredient\", the name was changed to just \"7 Up\" in 1937. Many sources repeat an incorrect version of the story where the name is \"Bib-Label Lithiated Lemon-Lime Soda\" and the removal happened in 1948 due to a Food and Drug Administration ban.
Lithium citrate is used as a mood stabilizer and is used to treat mania, hypomania, depression and bipolar disorder. It can be administered orally in the form of a syrup
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# Lunar Roving Vehicle
The **Lunar Roving Vehicle** (**LRV**) is a battery-powered four-wheeled rover used on the Moon in the last three missions of the American Apollo program (15, 16, and 17) during 1971 and 1972. It is popularly called the **Moon buggy**, a play on the term \"dune buggy\".
Built by Boeing, each LRV has a mass of 462 lb without payload. It could carry a maximum payload of 970 lb, including two astronauts, equipment, and cargo such as lunar samples, and was designed for a top speed of 6 mi/h, although it achieved a top speed of 11.2 mph on its last mission, Apollo 17.
Each LRV was carried to the Moon folded up in the Lunar Module\'s Quadrant 1 Bay. After being unpacked, each was driven an average of 30 km, without major incident. These three LRVs remain on the Moon.
## History
The concept of a lunar rover predated Apollo, with a 1952--1954 series in *Collier\'s Weekly* magazine by Wernher von Braun and others, \"Man Will Conquer Space Soon!\" In this, von Braun described a six-week stay on the Moon, featuring 10-ton tractor-trailers for moving supplies.
In 1956, Mieczysław G. Bekker published two books on land locomotion while he was a University of Michigan professor and a consultant to the U.S. Army Tank-Automotive Command\'s Land Locomotion Laboratory. The books provided much of the theoretical basis for future lunar vehicle development.
In 1959, Georg von Tiesenhausen conceived the lunar rover as a four-wheel-drive vehicle with noninflated, flexible wheels.
### Early lunar mobility studies {#early_lunar_mobility_studies}
In the February 1964 issue of *Popular Science*, von Braun, then director of NASA\'s Marshall Space Flight Center (MSFC), discussed the need for a lunar surface vehicle, and revealed that studies had been underway at Marshall in conjunction with Lockheed, Bendix, Boeing, General Motors, Brown Engineering, Grumman, and Bell Aerospace. Saverio Morea was named LRV Manager at MSFC in 1961. Beginning in the early 1960s, a series of studies centering on lunar mobility were conducted under Marshall. This began with the lunar logistics system (LLS), followed by the mobility laboratory (MOLAB), then the lunar scientific survey module (LSSM), and finally the mobility test article (MTA). In early planning for the Apollo program, it had been assumed that two Saturn V launch vehicles would be used for each lunar mission: one for sending the crew aboard a Lunar Surface Module (LSM) to lunar orbit, landing, and returning, and a second for sending an LSM-Truck (LSM-T) with all of the equipment, supplies, and transport vehicle for use by the crew while on the surface. All of the first Marshall studies were based on this dual-launch assumption, allowing a large, heavy, roving vehicle.
Grumman and Northrop, in late 1962, began to design pressurized-cabin vehicles, with electric motors for each wheel. At about this same time, Bendix and Boeing started their internal studies on lunar transportation systems. Mieczysław Bekker, now with General Motors Defense Research Laboratories at Santa Barbara, California, was completing a study for NASA\'s Jet Propulsion Laboratory on a small, uncrewed lunar roving vehicle for the Surveyor program. Ferenc Pavlics, originally from Hungary, used a wire-mesh design for \"resilient wheels,\" a design that would be followed in future small rovers.
In early 1963, NASA selected Marshall for studies in an Apollo Logistics Support System (ALSS). Following reviews of all earlier efforts, this resulted in a 10-volume report. Included was the need for a pressurized vehicle in the 6490 - weight range, accommodating two men with their expendables and instruments for traverses up to two weeks in duration. In June 1964, Marshall awarded contracts to Bendix and Boeing, with GM\'s lab designated as the vehicle technology subcontractor. Bell Aerospace was already under contract for studies of Lunar Flying Vehicles.
Even as the Bendix and Boeing studies were underway, Marshall was examining a less ambitious surface exploration activity, the LSSM. This would be composed of a fixed, habitable shelter--laboratory with a small lunar-traversing vehicle that could either carry one man or be remotely controlled. This mission would still require a dual launch with the moon vehicle carried on the \"lunar truck\". Marshall\'s Propulsion and Vehicle Engineering (P&VE) lab contracted with Hayes International to make a preliminary study of the shelter and its related vehicle. Because of the potential need for an enclosed vehicle for enlarged future lunar explorations, those design efforts continued for some time and resulted in several full-scale test vehicles.
With pressure from Congress to hold down Apollo costs, Saturn V production was reduced, allowing only a single launch per mission. Any roving vehicle would have to fit on the same lunar module as the astronauts. In November 1964, two-rocket models were put on indefinite hold, but Bendix and Boeing were given study contracts for small rovers. The name of the lunar excursion module was changed to simply the lunar module, indicating that the capability for powered \"excursions\" away from a lunar-lander base did not yet exist. There could be no mobile lab---the astronauts would work out of the LM. Marshall also continued to examine uncrewed robotic rovers that could be controlled from the Earth.
From the beginnings at Marshall, the Brown Engineering Company of Huntsville, Alabama, had participated in all of the lunar mobility efforts. In 1965, Brown became the prime support contractor for Marshall\'s P&VE Laboratory. With an urgent need to determine the feasibility of a two-man self-contained lander, von Braun bypassed the usual procurement process and had P&VE\'s Advanced Studies Office directly task Brown to design, build, and test a prototype vehicle. While Bendix and Boeing would continue to refine concepts and designs for a lander, test model rovers were vital for Marshall human factors studies involving spacesuit-clad astronauts interfacing with power, telemetry, navigation, and life-support rover equipment.
Brown\'s team made full use of the earlier small-rover studies, and commercially available components were incorporated wherever possible. The selection of wheels was of great importance, and almost nothing was known at that time about the lunar surface. The Marshall Space Sciences Laboratory (SSL) was responsible for predicting surface properties, and Brown was also prime support contractor for this lab; Brown set up a test area to examine a wide variety of wheel-surface conditions. To simulate Pavlics\'s \"resilient wheel,\" a four-foot-diameter inner tube wrapped with nylon ski rope was used. On the small test rover, each wheel had a small electric motor, with overall power provided by standard truck batteries. A roll bar gave protection from overturning accidents.
In early 1966, Brown\'s vehicle became available for examining human factors and other testing. Marshall built a small test track with craters and rock debris where several different mock-ups were compared; it became obvious that a small rover would be best for the proposed missions. The test vehicle was also operated in remote mode to determine characteristics that might be dangerous to the driver, such as acceleration, bounce-height, and turn-over tendency as it traveled at higher speeds and over simulated obstacles. The test rover\'s performance under one-sixth gravity was obtained through flights on a KC-135A aircraft in a Reduced Gravity parabolic maneuver; among other things, the need for a very soft wheel and suspension combination was shown. Although Pavlics\' wire-mesh wheels were not initially available for the reduced gravity tests, the mesh wheels were tested on various soils at the Waterways Experiment Station of the U.S. Army Corps of Engineers at Vicksburg, Mississippi. Later, when wire-mesh wheels were tested on low-g flights, the need for wheel fenders to reduce dust contamination was found. The model was also extensively tested at the U.S. Army\'s Yuma Proving Ground in Arizona, as well as the Army\'s Aberdeen Proving Ground in Maryland.
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# Lunar Roving Vehicle
## History
### Lunar Roving Vehicle Project {#lunar_roving_vehicle_project}
During 1965 and 1967, the Summer Conference on Lunar Exploration and Science brought together leading scientists to assess NASA\'s planning for exploring the Moon and to make recommendations. One of their findings was that the LSSM was critical to a successful program and should be given major attention. At Marshall, von Braun established a Lunar Roving Task Team, and in May 1969, NASA approved the Manned Lunar Rover Vehicle Program as a Marshall hardware development. The project was led by Eberhard Rees, Director of Research and Development at Marshall, who oversaw the design and construction of the rover, with Saverio Morea acting as project manager.
On 11 July 1969, just before the successful Moon landing of Apollo 11, a request for proposal for the final development and building the Apollo LRV was released by Marshall. Boeing, Bendix, Grumman, and Chrysler submitted proposals. Following three months of proposal evaluation and negotiations, Boeing was selected as the Apollo LRV prime contractor on 28 October 1969. Boeing would manage the LRV project under Henry Kudish in Huntsville, Alabama. Kudish was replaced the following year in 1970 by LRV Project Manager Earl Houtz. As a major subcontractor, the General Motors Defense Research Laboratories in Santa Barbara, California, would furnish the mobility system (wheels, motors, and suspension); this effort would be led by GM Program Manager Samuel Romano and Ferenc Pavlics. Boeing in Seattle, Washington, would furnish the electronics and navigation system. Vehicle testing would take place at the Boeing facility in Kent, Washington, and the chassis manufacturing and overall assembly would be completed at the Boeing facility in Huntsville.
thumb\|upright=1.3\|Apollo 15 -- Commander David Scott drives the Rover near the LM *Falcon*
The first cost-plus-incentive-fee contract to Boeing was for \$19,000,000 and called for delivery of the first LRV by 1 April 1971. Cost overruns, however, led to a final cost of \$38,000,000, which was about the same as NASA\'s original estimate. Four lunar rovers were built, one each for Apollo missions 15, 16, and 17; and one used for spare parts after the cancellation of further Apollo missions. Other LRV models were built: a static model to assist with human factors design; an engineering model to design and integrate the subsystems; two one-sixth gravity models for testing the deployment mechanism; a one-gravity trainer to give the astronauts instruction in the operation of the rover and allow them to practice driving it; a mass model to test the effect of the rover on the LM structure, balance, and handling; a vibration test unit to study the LRV\'s durability and handling of launch stresses; and a qualification test unit to study integration of all LRV subsystems. A paper by Saverio Morea gives details of the LRV system and its development.thumb\|upright=1.3\|John Young works at the LRV near the LM *Orion* on Apollo 16 in April 1972.LRVs were used for greater surface mobility during the Apollo J-class missions, Apollo 15, Apollo 16, and Apollo 17. The rover was first used on 31 July 1971, during the Apollo 15 mission. This greatly expanded the range of the lunar explorers. Previous teams of astronauts were restricted to short walking distances around the landing site due to the bulky space suit equipment required to sustain life in the lunar environment. The range, however, was operationally restricted to remain within walking distance of the lunar module, in case the rover broke down at any point. The rovers were designed with a top speed of about 8 mph, although Eugene Cernan recorded a maximum speed of 11.2 mph, giving him the (unofficial) lunar land-speed record.
The LRV was developed in only 17 months and performed all its functions on the Moon with no major anomalies. Scientist-astronaut Harrison Schmitt of Apollo 17 said, \"The Lunar Rover proved to be the reliable, safe and flexible lunar exploration vehicle we expected it to be. Without it, the major scientific discoveries of Apollo 15, 16, and 17 would not have been possible; and our current understanding of lunar evolution would not have been possible.\"
The LRVs experienced some minor problems. The rear fender extension on the Apollo 16 LRV was lost during the mission\'s second extra-vehicular activity (EVA) at station 8 when John Young bumped into it while going to assist Charles Duke. The dust thrown up from the wheel covered the crew, the console, and the communications equipment. High battery temperatures and resulting high power consumption ensued. No repair attempt was mentioned.
The fender extension on the Apollo 17 LRV broke when accidentally bumped by Eugene Cernan with a hammer handle. Cernan and Schmitt taped the extension back in place, but due to the dusty surfaces, the tape did not adhere, and the extension was lost after about one hour of driving, causing the astronauts to be covered with dust. For their second EVA, a replacement \"fender\" was made with some EVA maps, duct tape, and a pair of clamps from inside the Lunar Module that were nominally intended for the moveable overhead light. This repair was later undone so that the clamps could be taken inside for the return launch. The maps were brought back to Earth and are now on display at the National Air and Space Museum. The abrasion from the dust is evident on some portions of the makeshift fender. thumb\|upright=1.32\|right\|`{{center|The Lunar Rover Vehicle depicted on the [[U.S. Space Exploration History on U.S. Stamps|Space Achievement]] Decade Issue of 1971}}`{=mediawiki}
The color TV camera mounted on the front of the LRV could be remotely operated by Mission Control in pan and tilt axes as well as zoom. This allowed far better television coverage of the EVA than the earlier missions. On each mission, at the conclusion of the astronauts\' stay on the surface, the commander drove the LRV to a position away from the Lunar Module so that the camera could record the ascent stage launch. The camera operator in Mission Control experienced difficulty in timing the various delays so that the LM ascent stage was in frame through the launch. On the third and final attempt (Apollo 17), the launch and ascent were successfully tracked.
NASA\'s rovers, left behind, are among the artificial objects on the Moon, as are the Soviet Union\'s uncrewed rovers, *Lunokhod 1* and *Lunokhod 2*.
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# Lunar Roving Vehicle
## Features and specifications {#features_and_specifications}
thumb\|upright=1.8\|left\|Eugene Cernan test drives the Apollo 17 lunar rover shortly after unloading it from the LM *Challenger*
The Apollo Lunar Roving Vehicle is a battery electric vehicle designed to operate in the low-gravity vacuum of the Moon and to be capable of traversing the lunar surface, allowing the Apollo astronauts to extend the range of their surface extravehicular activities. Three LRVs were used on the Moon: one on Apollo 15 by astronauts David Scott and Jim Irwin, one on Apollo 16 by John Young and Charles Duke, and one on Apollo 17 by Eugene Cernan and Harrison Schmitt. The mission commander served as the driver, occupying the left-hand seat of each LRV. Features are available in papers by Morea, Baker, and Kudish.
### Mass and payload {#mass_and_payload}
The Lunar Roving Vehicles have a mass of 210 kg, and were designed to hold an additional payload of 230 kg. This resulted in weights in the approximately one-sixth g on the lunar surface of 35 kgf empty (curb weight) and 73 kgf fully loaded (gross vehicle weight). The vehicle frame is 10 ft long with a wheelbase of 7.5 ft. The height of the vehicles is 3.6 ft. The frame is made of 2219 aluminum alloy tubing welded assemblies and consisted of a three-part chassis that was hinged in the center so it could be folded up and hung in the Lunar Module Quadrant 1 bay, which was kept open to space by omission of the outer skin panel. They have two side-by-side foldable seats made of tubular aluminum with nylon webbing and aluminum floor panels. An armrest was mounted between the seats, and each seat had adjustable footrests and a Velcro-fastened seat belt. A large mesh dish antenna was mounted on a mast on the front center of the rover. The suspension consists of a double horizontal wishbone with upper and lower torsion bars and a damper unit between the chassis and upper wishbone. Fully loaded, the LRV has a ground clearance of 14 in.
### Wheels and power {#wheels_and_power}
The wheels were designed and manufactured by General Motors Defense Research Laboratories in Santa Barbara, California. Ferenc Pavlics was given special recognition by NASA for developing the \"resilient wheel\". They consisted of a spun aluminum hub and a 32 in, 9 in tire made of zinc-coated woven 0.033 in steel strands attached to the rim. Titanium chevrons covered 50% of the contact area to provide traction. Inside the tire was a 25.5 in titanium bump stop frame to protect the hub. Dust guards were mounted above the wheels. Each wheel had its own electric drive made by Delco, a brushed DC electric motor capable of 0.25 hp at 10,000 rpm, attached to the wheel via an 80:1 harmonic drive, and a mechanical brake unit. In the case of drive failure, astronauts could remove pins to disengage the drive from the wheel, allowing the wheel to spin freely.
Maneuvering capability was provided through the use of front and rear steering motors. Each series-wound DC steering motor was capable of 0.1 hp. The front and rear wheels could pivot in opposite directions to achieve a tight turning radius of 10 ft, or could be decoupled so only front or rear would be used for steering. The wheels were linked in Ackermann steering geometry, where the inside tires have a greater turn angle than the outside tires, to avoid sideslip.
Power was provided by two 36-volt silver-zinc potassium hydroxide non-rechargeable batteries developed by Eagle-Picher with a charge capacity of 121 A·h each (a total of 242 A·h), yielding a range of 57 mi. These were used to power the drive and steering motors and also a 36-volt utility outlet mounted on the front of the LRV to power the communications relay unit or the TV camera. LRV batteries and electronics were passively cooled, using change-of-phase wax thermal capacitor packages and reflective, upward-facing radiating surfaces. While driving, radiators were covered with mylar blankets to minimize dust accumulation. When stopped, the astronauts would open the blankets, and manually remove excess dust from the cooling surfaces with hand brushes.
### Control and navigation {#control_and_navigation}
A T-shaped hand controller situated between the two seats controlled the four drive motors, two steering motors, and brakes. Moving the stick forward powered the LRV forward, left and right turned the vehicle left or right, and pulling backwards activated the brakes. Activating a switch on the handle before pulling back would put the LRV into reverse. Pulling the handle all the way back activated a parking brake. The control and display modules were situated in front of the handle and gave information on the speed, heading, pitch, and power and temperature levels.
Navigation was based on continuously recording direction and distance through use of a directional gyro and odometer and feeding this data to a computer that would keep track of the overall direction and distance back to the LM. There was also a Sun-shadow device that could give a manual heading based on the direction of the Sun, using the fact that the Sun moved very slowly in the sky.
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# Lunar Roving Vehicle
## Usage
The LRV was used during the lunar surface operations of Apollo 15, 16 and 17, the J missions of the Apollo program. On each mission, the LRV was used on three separate EVAs, for a total of nine lunar traverses, or sorties. During operation, the commander (CDR) always drove, while the Lunar Module Pilot (LMP) was a passenger who assisted with navigation.
Mission Total distance Total time Longest single traverse Maximum range from the LM
------------------- ---------------- ------------ ------------------------- ---------------------------
Apollo 15 (LRV-1) 3 h 02 min
Apollo 16 (LRV-2) 3 h 26 min
Apollo 17 (LRV-3) 4 h 26 min
An operational constraint on the use of the LRV was that the astronauts must be able to walk back to the LM if the LRV were to fail at any time during the EVA (called the \"Walkback Limit\"). Thus, the traverses were limited in the distance they could go at the start and at any time later in the EVA. Therefore, they went to the farthest point away from the LM and worked their way back to it so that, as the life support consumables were depleted, their remaining walk back distance was equally diminished. This constraint was relaxed during the longest traverse on Apollo 17, based on the demonstrated reliability of the LRV and spacesuits on previous missions. A paper by Burkhalter and Sharp provides details on usage.
### Deployment
Astronaut deployment of the Lunar Roving Vehicle from the LM\'s open Quadrant 1 bay was achieved with a system of pulleys and braked reels using ropes and cloth tapes. The rover was folded and stored in the bay with the underside of the chassis facing out. One astronaut would climb the egress ladder on the LM and release the rover, which would then be slowly tilted out by the second astronaut on the ground through the use of reels and tapes. As the rover was let down from the bay, most of the deployment was automatic. The rear wheels folded out and locked in place. When they touched the ground, the front of the rover could be unfolded, the wheels deployed, and the entire frame let down to the surface by pulleys.
The rover components locked into place upon opening. Cabling, pins, and tripods would then be removed and the seats and footrests raised. After switching on all the electronics, the vehicle was ready to back away from the LM.
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# Lunar Roving Vehicle
## Usage
### Locations
Four flight-ready LRVs were manufactured, as well as several others for testing and training. Three were transported to and left on the Moon via the Apollo 15, 16, and 17 missions (LRV-1 to 3), with the fourth (LRV-4) used for spare parts for the first three following the cancellation of Apollo 18.
The rover used on Apollo 15 was left at Hadley-Apennine (26.10 N 3.65 E globe:moon name=Apollo 15 Lunar Roving Vehicle at Hadley--Apennine). The rover used on Apollo 16 was left at Descartes (8.99 S 15.51 E globe:moon name=Apollo 16 Lunar Roving Vehicle at Descartes Highlands). The rover used on Apollo 17 was left at Taurus-Littrow (20.16 N 30.76 E globe:moon name=Apollo 17 Lunar Roving Vehicle at Taurus-Littrow) and was seen by the Lunar Reconnaissance Orbiter during passes in 2009 and 2011. In 2020 the State of Washington designated the flown rovers as historic landmarks.
Since only the upper stages of the lunar excursion modules could return to lunar orbit from the surface, the vehicles, along with the lower stages were abandoned. As a result, the only lunar rovers on display are LRV-4, test vehicles, trainers, and mock-ups.
- Lunar Roving Vehicle 4 (LRV-4)[1](https://commons.wikimedia.org/wiki/Category:Lunar_Roving_Vehicle_4_at_the_Kennedy_Space_Center_Visitor_Complex) is on display at the Kennedy Space Center Visitors Complex in Cape Canaveral, Florida.
- The Engineering Mockup [2](https://commons.wikimedia.org/wiki/Category:Lunar_Roving_Vehicle_at_The_Museum_of_Flight), intended to design and integrate subsystems, is on display at the Museum of Flight in Seattle, Washington.
- The Qualification Test Unit [3](https://commons.wikimedia.org/wiki/Category:Lunar_Roving_Vehicle_at_the_National_Air_and_Space_Museum), designed to study integration of all LRV subsystems, is on display at the National Air and Space Museum in Washington, D.C.
- The Vibration Test Unit [4](https://commons.wikimedia.org/wiki/Category:Lunar_Roving_Vehicle_at_the_U.S._Space_%26_Rocket_Center), intended to study durability and handling of launch stresses, is on display in the Davidson Saturn V Center at the U.S. Space & Rocket Center in Huntsville, Alabama.
- The 1-gravity trainer [5](https://commons.wikimedia.org/wiki/Category:Lunar_Roving_Vehicle_at_Space_Center_Houston) is on display at the Johnson Space Center in Houston, Texas.
As mentioned before, additional test units were built, like a static model, two 1/6 gravity models, a mass model.
<File:Apollo> 15- Follow the Tracks (6816337786).jpg\|LRO image of Apollo 15 site, **LRV-1** is near the right edge <File:Apollo> 16 LS.png\|LRO image of Apollo 16 site, **LRV-2** is near the right edge <File:Apollo> 17 landing site, labeled.jpg\|LRO image of Apollo 17 site, **LRV-3** is in the lower right <File:Lunar> Roving Vehicle no. 4, Boeing, 1971 - Kennedy Space Center - Cape Canaveral, Florida - DSC02871.jpg\|**LRV-4**, KSC Visitors Complex <File:Space> Center Houston March 2022 10 (Lunar Roving Vehicle trainer).jpg\|**LRV** **1-gravity trainer**, Space Center Houston <File:Seattle> (9287877759).jpg\|**LRV** **engineering mockup**, Museum of Flight <File:MSFC> 76545 on display.JPG\|**LRV** **Vibration Test Unit**, U.S. Space & Rocket Center <File:Lunar> Roving Vehicle at SNASM.jpg\|**LRV** **Qualification Test Unit**, National Air and Space Museum
Replicas of rovers are on display at the Johnson Space Center in Houston, Texas, the Kennedy Space Center Visitors Complex in Cape Canaveral, Florida, the National Museum of Naval Aviation in Pensacola, Florida, the Evergreen Aviation & Space Museum in McMinnville, Oregon, the Kansas Cosmosphere and Space Center in Hutchinson, Kansas, and the Omega Museum in Biel, Switzerland. A replica on loan from the Smithsonian Institution is on display at the Mission: Space attraction at Epcot at the Walt Disney World Resort near Orlando, Florida.
## Media
<File:Astronauts> with Lunar Roving Vehicle.jpg\|(from left to right) Astronauts John Young, Eugene Cernan, Fred Haise, Charles Duke, Anthony England, Charles Fullerton, and Donald Peterson await deployment tests of the Lunar Roving Vehicle (LRV) qualification test unit in building 4649 at the Marshall Space Flight Center (MSFC). November 1971. Image:Ap16 rover.ogv\|Apollo 16 Commander John Young drives Lunar Rover 002 Image:Apollo 15 Lunar Rover training
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# List of memorials to Lyndon B. Johnson
This is a list of memorials to Lyndon B. Johnson, the 36th president of the United States.
## Buildings
- Lyndon B. Johnson Student Center, a complex including teaching theaters, shops, a student pool hall, and office space located at the Texas State University in San Marcos, Texas; President Johnson\'s college alma mater.
- Lyndon B. Johnson Tropical Medical Center, a hospital in American Samoa
- Lyndon B. Johnson General Hospital, part of Harris Health System in Houston, Texas
- Lyndon B. Johnson Space Center in Houston, Texas
- Lyndon Baines Johnson Department of Education Building, in Washington, D.C.
- Lyndon Baines Johnson Library and Museum, presidential museum in Austin, Texas
## Military vessels {#military_vessels}
- USS *Lyndon B. Johnson* (DDG-1002)
## Parks and topographical features {#parks_and_topographical_features}
- Lyndon B. Johnson National Historical Park, Johnson City, Texas
- Lyndon B. Johnson State Park and Historic Site, Stonewall, Texas
- Lake Lyndon B. Johnson, a lake in Texas
- Lyndon B. Johnson National Grassland, in Texas
- Lyndon Baines Johnson Memorial Grove on the Potomac, in Washington, D.C.
- FELDA L.B. Johnson, a village settlement in Negeri Sembilan, Malaysia.
## Roads
- Lyndon B. Johnson Freeway (Interstate 635), a freeway in Dallas, Texas
## Schools
- Lyndon B. Johnson Elementary School in Jackson, Kentucky
- Lyndon B. Johnson High School (Austin, Texas)
- Lyndon B. Johnson High School (Johnson City, Texas)
- Lyndon B. Johnson High School (Laredo, Texas)
- Lyndon B. Johnson Middle School in Melbourne, Florida
- Lyndon B. Johnson School of Public Affairs, a public affairs graduate school at the University of Texas at Austin
- Johnson Elementary in Bryan, Texas
## Public monuments {#public_monuments}
- Lyndon B. Johnson Monument - statue monument located in Little Tranquility Park in Houston.
## Clubs and Organizations {#clubs_and_organizations}
- The K5LBJ Amateur Radio Club is operated within LASA High School and is named after LBJ High School in Austin, Texas from its founding when LASA and LBJ were one high school
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# Luxembourgish
**Luxembourgish** (`{{IPAc-en|ˈ|l|ʌ|k|s|əm|b|ɜːr|ɡ|ɪ|ʃ|}}`{=mediawiki} `{{respell|LUK|səm|bur|ghish}}`{=mediawiki}; also *Luxemburgish*, *Luxembourgian*,
-
-
- *Letzebu(e)rgesch*; *Lëtzebuergesch* `{{IPA|lb|ˈlətsəbu̯əjəʃ||lb-lëtzebuergesch.ogg}}`{=mediawiki}) is a West Germanic language that is spoken mainly in Luxembourg. About 400,000 people speak Luxembourgish worldwide.
The language is standardized and officially the national language of the Grand Duchy of Luxembourg. As such, Luxembourgish is different from the German language also used in the Grand Duchy. The German language exists in a national standard variety of Luxembourg, which is slightly different from the standard varieties in Germany, Austria or Switzerland. Another important language of Luxembourg is French, which had a certain influence on both the national language, Luxembourgish, and the Luxembourg national variety of German. Luxembourgish, German and French are the three official languages *(Amtssprachen)* of Luxembourg.
As a standard form of the Moselle Franconian language, Luxembourgish has similarities with other High German dialects and the wider group of West Germanic languages. The status of Luxembourgish as the national language of Luxembourg and the existence there of a regulatory body have removed Luxembourgish, at least in part, from the domain of Standard German, its traditional *Dachsprache\]\]*. It is also related to the Transylvanian Saxon dialect spoken by the Transylvanian Saxons in Transylvania, contemporary central Romania.
## History
Luxembourgish was considered a German dialect like many others until about World War II but then the language underwent ausbau, creating its own standard form in vocabulary, grammar, and spelling and therefore is seen today as an independent language. Luxembourgish managed to gain linguistic autonomy against a vigorous One Standard German Axiom by being framed as an independent language with a name rather than as a national pluricentric standard variety of German.
As Luxembourgish has a maximum of some 285,000 native speakers; resources in the language, like books, newspapers, magazines, television, internet, etc., are limited. Since most Luxembourgers also speak Standard German and French, there is strong competition with these languages, which both have large language resources. Because of this, the use of Luxembourgish remains limited.
## Language family {#language_family}
Luxembourgish belongs to the West Central German group of the High German languages and is the primary example of a Moselle Franconian language. Furthermore, it is closely related to Transylvanian Saxon which has been spoken since the High Middle Ages by the Transylvanian Saxons in Transylvania, present-day central Romania.
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# Luxembourgish
## Speech
Luxembourgish is considered the national language of Luxembourg and also one of the three administrative languages, alongside German and French.
In Luxembourg, 77% of residents can speak Luxembourgish, and it is the primary language of 48% of the population. It is also spoken in the Arelerland region of Belgium (part of the Province of Luxembourg) and in small parts of Lorraine in France.
In the German Eifel and Hunsrück regions, similar local Moselle Franconian dialects of German are spoken. The language is also spoken by a few descendants of Luxembourg immigrants in the United States and Canada.
Other Moselle Franconian dialects are spoken by ethnic Germans long settled in Transylvania, Romania (Siebenbürgen).
Moselle Franconian dialects outside the Luxembourg state border tend to have far fewer French loanwords, and these mostly remain from the French Revolution.
The political party that places the greatest importance on promoting, using and preserving Luxembourgish is the Alternative Democratic Reform Party (ADR) and its electoral success in the 1999 election pushed the CSV-DP government to make knowledge of it a criterion for naturalisation. It is currently also the only political party in Luxembourg that wishes to implement written laws also in Luxembourgish and that wants Luxembourgish to be an officially recognized language of the European Union. In this context, in 2005, then-Deputy Prime Minister Jean Asselborn of the LSAP rejected a demand made by the ADR to make Luxembourgish an official language of the EU, citing financial reasons and the sufficiency of official German and French. A similar proposal by the ADR was rejected by the Chamber of Deputies in 2024.
### Varieties
There are several distinct dialect forms of Luxembourgish including Areler (from Arlon), Eechternoacher (Echternach), Dikrecher (Diekirch), Kliärrwer (Clervaux), Miseler (Moselle), Stater (Luxembourg City), Veiner (Vianden), Minetter (Southwest Luxembourg) and Weelzer (Wiltz). Further small vocabulary differences may be seen even between small villages. These varieties are grouped into North, East, South, and Center dialects which can be automatically categorised with a correctness of about 80%.
Increasing mobility of the population and the dissemination of the language through mass media such as radio and television are leading to a gradual standardisation towards a \"Standard Luxembourgish\" through the process of koineization.
### Surrounding languages {#surrounding_languages}
There is no distinct geographic boundary between the use of Luxembourgish and the use of other closely related High German dialects (for example, Lorraine Franconian); it instead forms a dialect continuum of gradual change.
Spoken Luxembourgish is relatively hard to understand for speakers of German who are generally not familiar with Moselle Franconian dialects (or at least other West Central German dialects). They can usually read the language to some degree. For those Germans familiar with Moselle Franconian dialects, it is relatively easy to understand and speak Luxembourgish as far as the everyday vocabulary is concerned. The large number of French loanwords in Luxembourgish may hamper communication about certain topics or with certain speakers (those who use many terms taken from French).
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# Luxembourgish
## Orthography
### Standardisation
A number of proposals for standardising the orthography of Luxembourgish can be documented, going back to the middle of the 19th century. There was no officially recognised system until the adoption of the \"OLO\" (*ofizjel lezebuurjer ortografi*) on 5 June 1946. This orthography provided a system for speakers of all varieties of Luxembourgish to transcribe words the way they pronounced them, rather than imposing a single, standard spelling for the words of the language. The rules explicitly rejected certain elements of German orthography (`{{abbr|e.g.|for example}}`{=mediawiki}, the use of `{{angbr|[[ä]]}}`{=mediawiki} and `{{angbr|[[ö]]}}`{=mediawiki}, the capitalisation of nouns). Similarly, new principles were adopted for the spelling of French loanwords.
- , *rééjelen*, *shwèzt*, *veinejer* (cf. German `{{wikt-lang|de|vorigen}}`{=mediawiki}, *`{{Wikt-lang|de|Regeln}}`{=mediawiki}*, *`{{Wikt-lang|de|schwätzt}}`{=mediawiki}*, *`{{Wikt-lang|de|weniger}}`{=mediawiki}*)
- , *âprê*, *Shaarel*, *ssistém* (cf. French *`{{Wikt-lang|fr|bulletin}}`{=mediawiki}*, *`{{Wikt-lang|fr|emprunt}}`{=mediawiki}*, *`{{Wikt-lang|fr|Charles}}`{=mediawiki}*, *`{{Wikt-lang|fr|système}}`{=mediawiki}*)
This proposed orthography, so different from existing \"foreign\" standards that people were already familiar with, did not enjoy widespread approval.
A more successful standard eventually emerged from the work of the committee of specialists charged with the task of creating the *Luxemburger Wörterbuch*, published in 5 volumes between 1950 and 1977. The orthographic conventions adopted in this decades-long project, set out in Bruch (1955), provided the basis of the standard orthography that became official on 10 October 1975. Modifications to this standard were proposed by the *Permanent Council of the Luxembourguish language* and adopted officially in the spelling reform of 30 July 1999. A detailed explanation of current practice for Luxembourgish can be found in Schanen & Lulling (2003).
### Alphabet
The Luxembourgish alphabet consists of the 26 Latin letters plus three letters with diacritics: `{{angbr|é}}`{=mediawiki}, `{{angbr|ä}}`{=mediawiki}, and `{{angbr|ë}}`{=mediawiki}. In loanwords from French and Standard German, other diacritics are usually preserved:
- French: *Boîte*, *Enquête*, *Piqûre*, etc.
- German: *blöd*, *Bühn* (from German *Bühne*), etc.
In German loanwords, the digraphs `{{angbr IPA|eu}}`{=mediawiki} and `{{angbr IPA|äu}}`{=mediawiki} indicate the diphthong `{{IPA|/oɪ/}}`{=mediawiki}, which does not appear in native words.
#### Orthography of vowels {#orthography_of_vowels}
: {\| class=\"wikitable\"
\|+ Monophthongs ! Spelling ! IPA ! Example \|- \| rowspan=\"2\" style=\"vertical-align: middle;\" \| a \| `{{IPA link|ɑ}}`{=mediawiki} \| *K\'\'\'a\'\'\'pp* \|- \| rowspan=\"2\" style=\"vertical-align: middle;\" \| `{{IPA link|aː}}`{=mediawiki} \| *K\'\'\'a\'\'\'p* \|- \| aa \| *n\'\'\'aa\'\'\'ss* \|- \| ä \| rowspan=\"2\" style=\"vertical-align: middle;\" \| `{{IPA link|æ}}`{=mediawiki} \| *K\'\'\'ä\'\'\'pp* \|- \| rowspan=\"2\" style=\"vertical-align: middle;\" \| e \| *D\'\'\'e\'\'\'cken* \|- \| rowspan=\"2\" style=\"vertical-align: middle;\" \| `{{IPA link|ə}}`{=mediawiki} \| *lies\'\'\'e\'\'\'n* \|- \| ë \| *h\'\'\'ë\'\'\'llefen* \|- \| é \| `{{IPA link|e}}`{=mediawiki} \| *dr\'\'\'é\'\'\'cken* \|- \| ee \| `{{IPA link|ɪ|eː}}`{=mediawiki} \| *B\'\'\'ee\'\'\'n* \|- \| rowspan=\"2\" style=\"vertical-align: middle;\" \| i \| `{{IPA link|i}}`{=mediawiki} \| *G\'\'\'i\'\'\'tt* \|- \| rowspan=\"2\" style=\"vertical-align: middle;\" \| `{{IPA link|iː}}`{=mediawiki} \| *s\'\'\'i\'\'\'wen* \|- \| ii \| *K\'\'\'ii\'\'\'scht* \|- \| rowspan=\"2\" style=\"vertical-align: middle;\" \| o \| `{{IPA link|o}}`{=mediawiki} \| *S\'\'\'o\'\'\'nn* \|- \| rowspan=\"2\" \| `{{IPA link|ʊ|oː}}`{=mediawiki} \| *dr\'\'\'o\'\'\'leg* \|- \| oo \| *Spr\'\'\'oo\'\'\'ch* \|- \| rowspan=\"2\" style=\"vertical-align: middle;\" \| u \| `{{IPA link|u}}`{=mediawiki} \| *H\'\'\'u\'\'\'tt* \|- \| rowspan=\"2\" style=\"vertical-align: middle;\" \| `{{IPA link|uː}}`{=mediawiki} \| *T\'\'\'u\'\'\'t* \|- \| uu \| *L\'\'\'uu\'\'\'cht* \|} `{{col-break}}`{=mediawiki}
: {\| class=\"wikitable\"
\|+ Diphthongs ! Spelling ! IPA ! Example \|- \| ai \| rowspan=\"2\" style=\"vertical-align: middle;\" \| `{{IPA|ɑɪ̯}}`{=mediawiki} \| *Geb\'\'\'ai\'\'\'* \|- \| ei \| *d\'\'\'ei\'\'\'er* \|- \| äi \| `{{IPA|æːɪ̯}}`{=mediawiki} \| *r\'\'\'äi\'\'\'ch* \|- \| rowspan=\"2\" style=\"vertical-align: middle;\" \| au \| `{{IPA|ɑʊ̯}}`{=mediawiki} \| *M\'\'\'au\'\'\'er* \|- \| `{{IPA|æːʊ̯}}`{=mediawiki} \| *M\'\'\'au\'\'\'l* \|- \| éi \| `{{IPA|əɪ̯}}`{=mediawiki} \| *Schn\'\'\'éi\'\'\'* \|- \| `{{not a typo|ie}}`{=mediawiki} \| rowspan=\"2\" \| `{{IPA|iə}}`{=mediawiki} \| *l\'\'\'ie\'\'\'sen* \|- \| ier \| *B\'\'\'ier\'\'\'gem* \|- \| ou \| `{{IPA|əʊ̯}}`{=mediawiki} \| *Sch\'\'\'ou\'\'\'l* \|- \| ue \| rowspan=\"2\" \| `{{IPA|uə}}`{=mediawiki} \| *B\'\'\'ue\'\'\'dem* \|- \| uer \| *Lëtzeb\'\'\'uer\'\'\'g* \|} `{{col-break}}`{=mediawiki}
: {\| class=\"wikitable\"
\|+ r-vocalization ! Spelling ! IPA ! Example \|- \| ar \| rowspan=\"2\" \| `{{IPA|aː}}`{=mediawiki} \| *D\'\'\'ar\'\'\'* \|- \| aar \| *\'\'\'aar\'\'\'m* \|- \| är \| rowspan=\"2\" \| `{{IPA|ɛːɐ̯}}`{=mediawiki} \| *St\'\'\'är\'\'\'* \|- \| äer \| *P\'\'\'äer\'\'\'d* \|- \| er \| `{{IPA|ɐ}}`{=mediawiki} \| *an\'\'\'er\'\'\'* \|- \| ir \| rowspan=\"2\" \| `{{IPA|iːɐ̯}}`{=mediawiki} \| *St\'\'\'ir\'\'\'* \|- \| ier \| *H\'\'\'ier\'\'\'t* \|- \| or \| rowspan=\"2\" \| `{{IPA|oːɐ̯}}`{=mediawiki} \| *Gef\'\'\'or\'\'\'* \|- \| oer \| *J\'\'\'oer\'\'\'* \|- \| ur \| rowspan=\"2\" \| `{{IPA|uːɐ̯}}`{=mediawiki} \| *B\'\'\'ur\'\'\'* \|- \| uer \| *W\'\'\'uer\'\'\'m* \|} `{{col-end}}`{=mediawiki}
### Eifeler Regel {#eifeler_regel}
Like many other varieties of Western High German, Luxembourgish has a rule of final *n*-deletion in certain contexts. The effects of this rule (known as the \"Eifel Rule\") are indicated in writing, and therefore must be taken into account when spelling words and morphemes ending in `{{angbr|n}}`{=mediawiki} or `{{angbr|nn}}`{=mediawiki}. For example:
- \"when I go\", but *wa mer ginn* \"when we go\"
- \"thirty-five\", but *fënnefavéierzeg* \"forty-five\".
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# Luxembourgish
## Phonology
### Consonants
The consonant inventory of Luxembourgish is quite similar to that of Standard German.
Labial Alveolar Postalveolar Dorsal
------------- -- --------------------------------- --------------------------------- --------------------------------- --------
Nasal
Plosive
Affricate (`{{IPA link|p͡f}}`{=mediawiki})
(`{{IPA link|d͡z}}`{=mediawiki}) (`{{IPA link|d͡ʒ}}`{=mediawiki})
Fricative
Trill
Approximant
: Consonant phonemes of Luxembourgish
- occurs only in loanwords from Standard German. Just as for many native speakers of Standard German, it tends to be simplified to `{{IPA|[f]}}`{=mediawiki} word-initially. For example, *Pflicht* (\'obligation\') is realised as `{{IPA|[fliɕt]}}`{=mediawiki} or, in careful speech, `{{IPA|[p͡fliɕt]}}`{=mediawiki}.
- is realised as `{{IPAblink|w}}`{=mediawiki} when it occurs after `{{IPA|/k, t͡s, ʃ/}}`{=mediawiki}, e.g. *zwee* `{{IPA|[t͡sweː]}}`{=mediawiki} (\'two\').
- appears only in a few words, such as *spadséieren* `{{IPA|/ʃpɑˈd͡zəɪ̯eʀen/}}`{=mediawiki} (\'to go for a walk\').
- occurs only in loanwords from English.
- have two types of allophones: alveolo-palatal `{{IPA|[{{IPAplink|ɕ}}, {{IPAplink|ʑ}}]}}`{=mediawiki} and uvular `{{IPA|[{{IPAplink|χ}}, {{IPAplink|ʁ}}]}}`{=mediawiki}. The latter occur before back vowels, and the former occur in all other positions.
- The `{{IPAblink|ʑ}}`{=mediawiki} allophone appears only in a few words, and speakers increasingly fail to distinguish between the alveolo-palatal allophones of `{{IPA|/χ, ʁ/}}`{=mediawiki} and the postalveolar phonemes `{{IPA|/ʃ, ʒ/}}`{=mediawiki}.
- Younger speakers tend to vocalize a word-final `{{IPA|/ʀ/}}`{=mediawiki} to `{{IPAblink|ɐ}}`{=mediawiki}.
### Vowels
Front
----------- ------- ---------
unrounded rounded
short long short
Close
Close-mid
Open-mid
Open
: Monophthong phonemes
- The front rounded vowels `{{IPA|/y, yː, øː, œ, œː/}}`{=mediawiki} appear only in loanwords from French and Standard German. In loanwords from French, nasal `{{IPA|/õː, ɛ̃ː, ɑ̃ː/}}`{=mediawiki} also occur.
- has two allophones:
- Before velars: close-mid front unrounded `{{IPAblink|e}}`{=mediawiki}, which, for some speakers, may be open-mid `{{IPAblink|ɛ}}`{=mediawiki}, especially before `{{IPA|/ʀ/}}`{=mediawiki}. The same variation in height applies to `{{IPA|/o/}}`{=mediawiki}, which may be as open as `{{IPAblink|ɔ}}`{=mediawiki}.
- All other positions: mid central vowel, more often slightly rounded `{{IPAblink|ə̹}}`{=mediawiki} than unrounded `{{IPAblink|ə̜}}`{=mediawiki}.
- Phonetically, the long mid vowels `{{IPA|/eː, oː/}}`{=mediawiki} are raised close-mid (near-close) `{{IPA|[{{IPAplink|e̝ː}}, {{IPAplink|o̝ː}}]}}`{=mediawiki} and may even overlap with `{{IPA|/iː, uː/}}`{=mediawiki}.
- before `{{IPA|/ʀ/}}`{=mediawiki} is realised as `{{IPAblink|ɛː}}`{=mediawiki}.
- is the long variant of `{{IPA|/ɑ/}}`{=mediawiki}, not `{{IPA|/æ/}}`{=mediawiki}, which does not have a long counterpart.
Ending point
------- --------------
Front Central
Close
Mid
Open
: Diphthong phonemes
- appears only in loanwords from Standard German.
- The first elements of `{{IPA|/æːɪ, æːʊ/}}`{=mediawiki} may be phonetically short `{{IPA|[æ]}}`{=mediawiki} in fast speech or in unstressed syllables.
- The `{{IPA|/æːɪ–ɑɪ/}}`{=mediawiki} and `{{IPA|/æːʊ–ɑʊ/}}`{=mediawiki} contrasts arose from the former lexical tone contrast; the shorter `{{IPA|/ɑɪ, ɑʊ/}}`{=mediawiki} were used in words with Accent 1, and the lengthened `{{IPA|/æːɪ, æːʊ/}}`{=mediawiki} were used in words with Accent 2.
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# Luxembourgish
## Grammar
### Nominal syntax {#nominal_syntax}
Luxembourgish has three genders (masculine, feminine, and neuter), and three cases (nominative, accusative, and dative). These are marked morphologically on determiners and pronouns. As in German, there is no morphological gender distinction in the plural.
The forms of the articles and of some selected determiners are given below:
+-----------------------------------------+-----------------------------------------+
| singular | singular |
| --------------- ---------- ---------- | --------------- ---------- ---------- |
| masculine neuter feminine | masculine neuter feminine |
| definite | definite |
| def. emphatic | def. emphatic |
| demonstrative | demonstrative |
| indefinite | indefinite |
| negative | negative |
| \"his/its\" | \"his/its\" |
| \"her/their\" | \"her/their\" |
| | |
| : nominative/accusative | : dative |
+-----------------------------------------+-----------------------------------------+
As seen above, Luxembourgish has plural forms of *en* (\"a, an\"), namely *eng* in the nominative/accusative and *engen* in the dative. They are not used as indefinite articles, which---as in German and English---do not exist in the plural, but they do occur in the compound pronouns *wéi en* (\"what, which\") and *sou en* (\"such\"). For example: *wéi eng Saachen* (\"what things\"); *sou eng Saachen* (\"such things\"). Moreover, they are used before numbers to express an estimation: *eng 30.000 Spectateuren* (\"some 30,000 spectators\").
Distinct nominative forms survive in a few nominal phrases such as *der Däiwel* (\"the devil\") and *eiser Herrgott* (\"our Lord\"). Rare examples of the genitive are also found: *Enn des Mounts* (\"end of the month\"), *Ufanks der Woch* (\"at the beginning of the week\"). The functions of the genitive are normally expressed using a combination of the dative and a possessive determiner: e.g. *dem Mann säi Buch* (lit. \"to the man his book\", i.e. \"the man\'s book\"). This is known as a periphrastic genitive, and is a phenomenon also commonly seen in dialectal and colloquial German, and in Dutch.
The forms of the personal pronouns are given in the following table (unstressed forms appear in parentheses):
nominative accusative dative
------ ------------ ------------ ---------
1sg (*mer*)
2sg (*de*) (*der*)
3sgm (*en*) (*em*)
3sgn (*et*)
3sgf (*se*) (*er*)
1pl (*mer*) / *eis*
2pl (*der*)
3pl (*se*) (*en*)
The 2pl form is also used as a polite singular (like French *vous*, see T-V distinction); the forms are capitalised in writing:
: (\"How did you \[informal sg.\] like the concert?\")
: (\"How did you \[informal pl.\] like the concert?\")
: (\"How did you \[formal sg. or pl.\] like the concert?\")
Like most varieties of colloquial German, but even more invariably, Luxembourgish uses definite articles with personal names. They are obligatory and not to be translated:
: (\"Serge is in the kitchen.\")
A feature Luxembourgish shares with only some western dialects of German is that women and girls are most often referred to with forms of the *neuter* pronoun *hatt*:
: (\"That\'s Nathalie. She is tired because she has worked a lot in her garden.\")
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# Luxembourgish
## Grammar
### Adjectives
Adjectives show a different morphological behaviour when used attributively and predicatively. In predicative use, e.g. when they occur with verbs like *sinn* (\"to be\"), adjectives receive no extra ending:
- De Mann ass grouss. (*masculine*, \"The man is tall.\")
- D\'Fra ass grouss. (*feminine*, \"The woman is tall.\")
- D\'Meedchen ass grouss. (*neuter*, \"The girl is tall.\")
- D\'Kanner si grouss. (*plural*, \"The children are tall.\")
In attributive use, i.e. when placed before the noun they describe, they change their ending according to the grammatical gender, number and case of the noun:
- de grouss**e** Mann (*masculine*)
- déi grouss Fra (*feminine*)
- dat grouss**t** Meedchen (*neuter*)
- déi grouss Kanner (*plural*)
The definite article changes with the use of an attributive adjective: feminine *d\'* goes to *déi* (or *di*), neuter *d\'* goes to *dat*, and plural *d\'* changes to *déi*.
The comparative in Luxembourgish is formed analytically, i.e. the adjective itself is not altered (compare the use of -*er* in German and English; *tall* → *taller*, *klein* → *kleiner*). Instead it is formed using the adverb *méi*: e.g. *schéin* → *méi schéin*
- Lëtzebuerg ass méi schéi wéi Esch. (\"Luxembourg is prettier than Esch.\")
The superlative involves a synthetic form consisting of the adjective and the suffix *-st*: e.g. *schéin* → *schéin**st*** (compare German *schönst*, English *prettiest*). Attributive modification requires the emphatic definite article and the inflected superlative adjective:
- **dee** schéinst**e** Mann (\"the most handsome man\")
- **déi** schéinst Fra (\"the prettiest woman\")
Predicative modification uses either the same adjectival structure or the adverbial structure *am*+ -*sten*: e.g. *schéin* → *am schéinsten*:
- Lëtzebuerg ass dee schéinsten / deen allerschéinsten / am schéinsten. (\"Luxembourg is the most beautiful (of all).\")
Some common adjectives have exceptional comparative and superlative forms:
- gutt, besser, am beschten (\"good, better, best\")
- vill, méi, am meeschten (\"much, more, most\")
- wéineg, manner, am mannsten (\"few, fewer, fewest\")
Several other adjectives also have comparative forms, not commonly used as normal comparatives, but in special senses:
- al (\"old\") → *eeler* Leit (\"elderly people\"), but: *méi al* Leit (\"older people, people older than X\")
- fréi (\"early\") → de *fréiere* President (\"the former president\"), but: e *méi fréien* Termin (\"an earlier appointment\")
- laang (\"long\") → viru *längerer* Zäit (\"some time ago\"), but: eng *méi laang* Zäit (\"a longer period of time\")
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# Luxembourgish
## Grammar
### Word order {#word_order}
Luxembourgish exhibits \"verb second\" word order in clauses. More specifically, Luxembourgish is a V2-SOV language, like German and Dutch. In other words, we find the following finite clausal structures:
- the finite verb in second position in declarative clauses and *wh*-questions
:
: Ech **kafen** en Hutt. Muer **kafen** ech en Hutt. (lit. \"I buy a hat. Tomorrow buy I a hat.)
: Wat **kafen** ech haut? (lit. \"What buy I today?\")
- the finite verb in first position in yes/no questions and finite imperatives
:
: **Bass** de midd? (\"Are you tired?\")
: **Gëff** mer deng Hand! (\"Give me your hand!\")
- the finite verb in final position in subordinate clauses
:
: Du weess, datt ech midd **sinn**. (lit. \"You know, that I tired am.\")
Non-finite verbs (infinitives and participles) generally appear in final position:
- compound past tenses
:
: Ech hunn en Hutt **kaf**. (lit. \"I have a hat bought.\")
- infinitival complements
:
: Du solls net esou vill Kaffi **drénken**. (lit. \"You should not so much coffee drink.\")
- infinitival clauses (e.g., used as imperatives)
:
: Nëmme Lëtzebuergesch **schwätzen**! (lit. \"Only Luxembourgish speak!\")
These rules interact so that in subordinate clauses, the finite verb and any non-finite verbs must all cluster at the end. Luxembourgish allows different word orders in these cases:
:
: Hie freet, ob ech **komme kann**. (cf. German *Er fragt, ob ich kommen kann.*) (lit. \"He asks if I come can.\")
: Hie freet, ob ech **ka kommen**. (cf. Dutch *Hij vraagt of ik kan komen.*) (lit. \"He asks if I can come.\")
This is also the case when two non-finite verb forms occur together:
:
: Ech hunn net **kënne kommen**. (cf. Dutch *Ik heb niet kunnen komen.*) (lit, \"I have not be-able to-come\")
: Ech hunn net **komme kënnen**. (cf. German *Ich habe nicht kommen können.*) (lit, \"I have not to-come be-able\")
Luxembourgish (like Dutch and German) allows prepositional phrases to appear after the verb cluster in subordinate clauses:
:
: alles, wat Der ëmmer wollt wëssen **iwwer Lëtzebuerg**
: (lit. \"everything what you always wanted know about Luxembourg\")
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# Luxembourgish
## Vocabulary
Luxembourgish has borrowed many French words. For example, the word for a bus driver is *Buschauffeur* (as in Dutch and Swiss German), which would be *Busfahrer* in German and *chauffeur de bus* in French.
Some words are different from Standard German, but have equivalents in German dialects. An example is *Gromperen* (potatoes -- German: *Kartoffeln*). Other words are exclusive to Luxembourgish.
### Selected common phrases {#selected_common_phrases}
*Note: Words spoken in sound clip do not reflect all words on this list.*
Dutch Luxembourgish Standard German English
------------------------------------------- ------------------------------------------- ------------------------------------------- ---------------------------------------
Ja. Jo. Ja. *Yes.*
Nee(n). Nee(n). Nein. *No.*
Misschien, wellicht Vläicht. Vielleicht. *Maybe.*
Hallo. (also *moi* in the north and east) Moien. Hallo. (also *Moin* in the north) *Hello.*
Goedemorgen. Gudde Moien. Guten Morgen. *Good morning.*
Goedendag. or Goedemiddag. Gudde Mëtteg. Guten Tag. *Good afternoon.*
Goedenavond. Gudden Owend. Guten Abend. *Good evening.*
Tot ziens. Äddi. Auf Wiedersehen. *Goodbye.*
Dank u or Merci. (Belgium) Merci. Danke. *Thank you.*
Waarom? or Waarvoor? Firwat? Warum? or Wofür? *Why*, *What for*
Ik weet het niet. Ech weess net. Ich weiß nicht. *I don\'t know.*
Ik versta het niet. Ech verstinn net. Ich verstehe nicht. *I don\'t understand.*
Excuseer mij or Wablief? (Belgium) Watgelift? or Entschëllegt? Entschuldigung? *Excuse me?*
Slagerszoon. Metzleschjong. Metzgersohn. / Metzgerjunge. *Butcher\'s son.*
Spreek je Duits/Frans/Engels? Schwätzt dir Däitsch/Franséisch/Englesch? Sprichst du Deutsch/Französisch/Englisch? *Do you speak German/French/English?*
Hoe heet je? Wéi heeschs du? Wie heißt du? *What is your name?*
Hoe gaat het? Wéi geet et? Wie geht\'s? *How are you?*, *How is it going?*
Politiek Fatsoen. Politeschen Anstand. Politischer Anstand. *Political decency*
Zo. Sou. So. *So.*
Vrij. Fräi. Frei. *Free.*
Thuis. Heem. zu Hause. / Heim. *Home.*
Ik. Ech. Ich. *I.*
En. An. Und. *And.*
Mijn. Mäin. Mein. *My.*
Ezel. Iesel. Esel. *donkey*, *ass.*
Met. Mat. Mit. *With.*
Kind. Kand. Kind. *Child, kid*
Weg. Wee. Weg. *Way.*
Aardappel. Gromper. Kartoffel/Erdapfel. *Potato.*
Brood. Brout. Brot. *Bread.*
### Neologisms
Neologisms in Luxembourgish include both entirely new words, and the attachment of new meanings to old words in everyday speech. The most recent neologisms come from the English language in the fields of telecommunications, computer science, and the Internet.
Recent neologisms in Luxembourgish include:
- direct loans from English: *Browser*, *Spam*, *CD*, *Fitness*, *Come-back*, *Terminal*, *Hip*, *Cool*, *Tip-top*
- also found in German: *Sichmaschinn* (search engine, German: *Suchmaschine*), *schwaarzt Lach* (black hole, German: *Schwarzes Loch*), *Handy* (mobile phone), *Websäit* (webpage, German: *Webseite*)
- native Luxembourgish
- *déck* as an emphatic like *ganz* and *voll*, e.g. *Dëse Kuch ass déck gutt!* (\"This cake is really good!\")
- recent expressions, used mainly by teenagers: *oh mëllen!* (\"oh crazy\"), *en décke gelénkt* (\"you\'ve been tricked\") or *cassé* (French for \"(you\'ve been) owned\")
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# Luxembourgish
## Academic projects {#academic_projects}
Between 2000 and 2002, Luxembourgish linguist Jérôme Lulling compiled a lexical database of 125,000-word forms as the basis for the first Luxembourgish spellchecker (Projet C.ORT.IN.A).
The LaF (*Lëtzebuergesch als Friemsprooch* -- Luxembourgish as a Foreign Language) is a set of four language proficiency certifications for Luxembourgish and follows the ALTE framework of language examination standards. The tests are administered by the Institut National des Langues Luxembourg.
The \"Centre for Luxembourg Studies\" at the University of Sheffield was founded in 1995 on the initiative of Professor Gerald Newton. It is supported by the government of Luxembourg which funds an endowed chair in Luxembourg Studies at the university. The first class of students to study the language outside of the country as undergraduate students began their studies at the \'Centre for Luxembourg Studies\' at Sheffield in the academic year 2011--2012.
## Endangered status claims {#endangered_status_claims}
UNESCO declared Luxembourgish to be an endangered language in 2019, adding it to its *Atlas of the World\'s Languages in Danger*.
Additionally, some local media have argued that the Luxembourgish language is at risk of disappearing, and that it should be considered an endangered language. Even though the government claims that more people than ever are able to speak Luxembourgish, these are absolute numbers and often include the many naturalized citizens who have passed the *Sproochentest,* a language test that certifies the knowledge of merely A.2. in speaking and B.1. in understanding.
Luxembourgish language expert and historian Alain Atten argues that not only the absolute number of Luxembourgish speakers should be considered when defining the status of a language, but also the proportion of speakers in a country. Noting that the proportion of native Luxembourgish speakers has decreased in recent decades, Atten believes that Luxembourgish will inevitably disappear, stating:
> It is simple math, if there are about 70% foreigners and about 30% Luxembourgers (which is the case in Luxembourg City), then it cannot possibly be said that Luxembourgish is thriving. That would be very improbable.
Alain Atten also argues that the situation is even more dramatic, since the cited percentages take only the residents of Luxembourg into account, excluding the 200,000 cross-border-workers present in the country on a daily basis. This group plays a major role in the daily use of languages in Luxembourg, thus further lowering the percentage of Luxembourgish speakers present in the country.
The following numbers are based on statistics by *STATEC* (those since 2011) and show that the percentage of the population that is able to speak Luxembourgish has been constantly diminishing for years (The 200,000 cross-border workers are not included in this statistic):
Year Percentage
------ ------------
1846 99.0%
1900 88.0%
1983 80.6%
2011 70.51%
2012 70.07%
2013 69.65%
2014 69.17%
2015 68.78%
2016 68.35%
2017 67.77%
It has also been argued that two very similar languages, Alsatian and Lorraine Franconian, which were very broadly spoken by the local populations at the beginning of the 20th century in Alsace and in Lorraine respectively, have been nearly completely supplanted by French, and that a similar fate could also be possible for Luxembourgish. Another example of the replacement of Luxembourgish by French occurred in Arelerland (historically a part of Luxembourg, today in Belgium), where the vast majority of the local population spoke Luxembourgish as a native language well into the 20th century. Today, Luxembourgish is nearly extinct in this region, having been replaced by French.
According to some Luxembourgish news media and members of Actioun Lëtzebuergesch (an association for the preservation and promotion of the language), the biggest threat to the existence of Luxembourgish is indeed French, since it is the language of most official documents and street signs in Luxembourg; this considerably weakens the possibility for Luxembourgish to be practiced by new speakers and learners. In most cases, this passively forces expats to learn French instead of Luxembourgish.
In 2021 it was announced that public announcements in Luxembourgish (and in German as well) at Luxembourg Airport would cease; it would only be using French and English for future public announcements. This will cause Luxembourgish to go unused at Luxembourg Airport after many decades. Actioun Lëtzebuergesch declared itself to be hugely upset by this new governmental measure, citing that other airports in the world seem to have no problems making public announcements in multiple languages. According to a poll conducted by AL, 92.84% of the Luxembourgish population wished to have public announcements to be made in Luxembourgish at Luxembourg Airport.
ADR politician Fred Keup has claimed that Luxembourgish is already on its way to complete replacement by French
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# Liber Pontificalis
The ***Liber Pontificalis*** (Latin for \'pontifical book\' or *Book of the Popes*) is a book of biographies of popes from Saint Peter until the 15th century. The original publication of the *Liber Pontificalis* stopped with Pope Adrian II (867--872) or Pope Stephen V (885--891), but it was later supplemented in a different style until Pope Eugene IV (1431--1447) and then Pope Pius II (1458--1464). Although quoted virtually uncritically from the 8th to 18th centuries, the *Liber Pontificalis* has undergone intense modern scholarly scrutiny. The work of the French priest Louis Duchesne (who compiled the major scholarly edition), and of others has highlighted some of the underlying redactional motivations of different sections, though such interests are so disparate and varied as to render improbable one populariser\'s claim that it is an \"unofficial instrument of pontifical propaganda.\"
The title *Liber Pontificalis* goes back to the 12th century, although it only became current in the 15th century, and the canonical title of the work since the edition of Duchesne in the 19th century. In the earliest extant manuscripts it is referred to as ***Liber episcopalis in quo continentur acta beatorum pontificum Urbis Romae*** (\'episcopal book in which are contained the acts of the blessed pontiffs of the city of Rome\') and later the ***Gesta**\'\' or***Chronica pontificum**\'\'.
## Authorship
During the Middle Ages, Saint Jerome was considered the author of all the biographies up until those of Pope Damasus I (366--383), based on an apocryphal letter between Saint Jerome and Pope Damasus published as a preface to the Medieval manuscripts. The attribution originated with Rabanus Maurus and is repeated by Martin of Opava, who extended the work into the 13th century. Other sources attribute the early work to Hegesippus and Irenaeus, having been continued by Eusebius of Caesarea. In the 16th century, Onofrio Panvinio attributed the biographies after Damasus until Pope Nicholas I (858--867) to Anastasius Bibliothecarius; Anastasius continued to be cited as the author into the 17th century, although this attribution was disputed by the scholarship of Caesar Baronius, Ciampini, Schelstrate and others. The modern interpretation, following that of Louis Duchesne, is that the *Liber Pontificalis* was gradually and unsystematically compiled, and that the authorship is impossible to determine, with a few exceptions (e.g. the biography of Pope Stephen II (752--757) to papal \"Primicerius\" Christopher; the biographies of Pope Nicholas I and Pope Adrian II (867--872) to Anastasius). Duchesne and others have viewed the beginning of the *Liber Pontificalis* up until the biographies of Pope Felix III (483--492) as the work of a single author, who was a contemporary of Pope Anastasius II (496-498), relying on *Catalogus Liberianus*, which in turn draws from the papal catalogue of Hippolytus of Rome, and the *Leonine Catalogue*, which is no longer extant. Most scholars believe the *Liber Pontificalis* was first compiled in the 5th or 6th century.
Because of the use of the *vestiarium*, the records of the papal treasury, some have hypothesised that the author of the early *Liber Pontificalis* was a clerk of the papal treasury. Edward Gibbon\'s *Decline and Fall of the Roman Empire* (1788) summarised the scholarly consensus as being that the *Liber Pontificalis* was composed by \"apostolic librarians and notaries of the viii^th^ and ix^th^ centuries\" with only the most recent portion being composed by Anastasius.
Duchesne and others believe that the author of the first addition to the *Liber Pontificalis* was a contemporary of Pope Silverius (536--537), and that the author of another (not necessarily the second) addition was a contemporary of Pope Conon (686--687), with later popes being added individually and during their reigns or shortly after their deaths.
## Content
The *Liber Pontificalis* originally only contained the names of the bishops of Rome and the durations of their pontificates. As enlarged in the 6th century, each biography consists of: the birth name of the pope and that of his father, place of birth, profession before elevation, length of pontificate, historical notes of varying thoroughness, major theological pronouncements and decrees, administrative milestones (including building campaigns, especially of Roman churches), ordinations, date of death, place of burial, and the duration of the ensuing *sede vacante*.
Pope Adrian II (867--872) is the last pope for which there are extant manuscripts of the original *Liber Pontificalis*: the biographies of Pope John VIII, Pope Marinus I, and Pope Adrian III are missing and the biography of Pope Stephen V (885--891) is incomplete. From Stephen V through the 10th and 11th centuries, the historical notes are extremely abbreviated, usually with only the pope\'s origin and reign duration.
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# Liber Pontificalis
## Extension
It was only in the 12th century that the *Liber Pontificalis* was systematically continued, although papal biographies exist in the interim period in other sources.
### Petrus Guillermi {#petrus_guillermi}
Duchesne refers to the 12th-century work by Petrus Guillermi in 1142 at the monastery of St. Gilles (Diocese of Reims) as the *Liber Pontificalis of Petrus Guillermi (son of William)*. Guillermi\'s version is mostly copied from other works with small additions or excisions from the papal biographies of Pandulf, nephew of Hugo of Alatri, which in turn was copied almost verbatim from the original *Liber Pontificalis* (with the notable exception of the biography of Pope Leo IX), then from other sources until Pope Honorius II (1124--1130), and with contemporary information from Pope Paschal II (1099--1118) to Pope Urban II (1088--1099).
Duchesne attributes all biographies from Pope Gregory VII to Urban II to Pandulf, while earlier historians like Giesebrecht and Watterich attributed the biographies of Gregory VII, Victor III, and Urban II to Petrus Pisanus, and the subsequent biographies to Pandulf. These biographies until those of Pope Martin IV (1281--1285) are extant only as revised by Petrus Guillermi in the manuscripts of the monastery of St. Gilles having been taken from the Chronicle of Martin of Opava.
Early in the 14th century, an unknown author built upon the continuation of Petrus Guillermi, adding the biographies of popes Martin IV (d. 1285) through John XXII (1316--1334), with information taken from the \"Chronicon Pontificum\" of Bernardus Guidonis, stopping abruptly in 1328.
### Boso
Independently, the cardinal-nephew of Pope Adrian IV, Cardinal Boso intended to extend the *Liber Pontificalis* from where it left off with Stephen V, although his work was only published posthumously as the *Gesta Romanorum Pontificum* alongside the *Liber Censuum* of Pope Honorius III. Boso drew on Bonizo of Sutri for popes from John XII to Gregory VII, and wrote from his own experiences about the popes from Gelasius II (1118--1119) to Alexander III (1179--1181).
### Western Schism {#western_schism}
An independent continuation appeared in the reign of Pope Eugene IV (1431--1447), appending biographies from Pope Urban V (1362--1370) to Pope Martin V (1417--1431), encompassing the period of the Western Schism. A later recension of this continuation was expanded under Pope Eugene IV.
### 15th century {#th_century}
The two collections of papal biographies of the 15th century remain independent, although they may have been intended to be continuations of the *Liber Pontificalis*. The first extends from popes Benedict XII (1334--1342) to Martin V (1417--1431), or in one manuscript to Eugene IV (1431--1447). The second extends from Pope Urban VI (1378--1389) to Pope Pius II (1458--1464).
## Editions
The *Liber Pontificalis* was first edited by Joannes Busaeus under the title *Anastasii bibliothecarii Vitæ seu Gesta Romanorum Pontificum* (Mainz, 1602). A new edition, including the *Historia ecclesiastica* of Anastasius, was edited by Fabrotti (Paris, 1647). Another edition, editing the older *Liber Pontificalis* up to Pope Adrian II and adding Pope Stephen VI, was compiled by Fr. Bianchini (4 vols., Rome, 1718--35; a projected fifth volume did not appear). Muratori reprinted Bianchini\'s edition, adding the remaining popes through John XXII (Scriptores rerum Italicarum, III). Migne also republished Bianchini\'s edition, adding several appendixes (P. L., cxxvii--cxxviii).
Modern editions include those of Louis Duchesne (*Liber Pontificalis. Texte, introduction et commentaire*, 2 vols., Paris, 1886--92) and Theodor Mommsen (*Gestorum Pontificum Romanorum pars I: Liber Pontificalis*, Mon. Germ. hist., Berlin, 1898). Duchesne incorporates the *Annales Romani* (1044--1187) into his edition of the *Liber Pontificalis*, which otherwise relies on the two earliest known recensions of the work (530 and 687). Mommsen\'s edition is incomplete, extending only until 715. Translations and further commentaries appeared throughout the 20th century.
## Editions {#editions_1}
- Davis, Raymond. *The Book of Pontiffs* **(Liber Pontificalis)**. Liverpool: University of Liverpool Press, 1989. `{{ISBN|0-85323-216-4}}`{=mediawiki}. An English translation for general use, but not including scholarly notes.
- Davis, Raymond. *The Book of Pontiffs* **(Liber Pontificalis)**. Second Edition. Liverpool: University of Liverpool Press, 2000. `{{ISBN|0-85323-545-7}}`{=mediawiki}. Stops with Pope Constantine, 708--15; contains an extensive and up to date bibliography,
- Davis, Raymond. \"The Lives of the Eighth Century Popes.\" Liverpool: University of Liverpool Press, 1992. From 715 to 817.
- Davis, Raymond. \"The Lives of the Ninth Century Popes\" Liverpool: University of Liverpool Press, 1989. From 817 to 891
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# Lower Peninsula of Michigan
The **Lower Peninsula of Michigan** -- also known as **Lower Michigan** -- is the larger, southern and less elevated of the two major landmasses that make up the U.S. state of Michigan; the other being the Upper Peninsula, which is separated by the Straits of Mackinac. It is surrounded by water on all sides except its southern border, which it shares with Indiana and Ohio.
Although the Upper Peninsula is commonly referred to as \"the U.P.\", it is uncommon for the Lower Peninsula to be called \"the L.P.\". Because of its recognizable shape, the Lower Peninsula is nicknamed **The Mitten**, with the eastern region identified as \"The Thumb\". This has led to several folkloric creation myths for the area, one being that it is a handprint of Paul Bunyan, a giant lumberjack and popular European-American folk character in Michigan. When asked where they live, Lower Peninsula residents may hold up their right palm and point to a spot on it to indicate the location.
The peninsula is sometimes divided into the Northern Lower Peninsula---which is more sparsely populated and largely forested---and the Southern Lower Peninsula---which is largely urban or farmland. Southern Lower Michigan is sometimes further divided into economic and cultural subregions.
The more culturally and economically diverse Lower Peninsula dominates Michigan politics, and maps of it without the Upper Peninsula are sometimes mistakenly presented as \"Michigan\", which contributes to resentment by \"Yoopers\" (residents of \"the U.P.\"). Yoopers jokingly refer to residents of the Lower Peninsula as \"flat-landers\" (referring to the region\'s less rugged terrain) or \"trolls\" (because, being south of the Mackinac Bridge, they \"live under the bridge\").
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# Lower Peninsula of Michigan
## Geography
The Lower Peninsula is bounded on the west by Lake Michigan and on the northeast by Lake Huron, which connect at the Straits of Mackinac. In the southeast, the waterway consisting of the St. Clair River, Lake St. Clair, Detroit River, and Lake Erie separates it from the province of Ontario, Canada. It is bounded on the south by the states of Indiana and Ohio. This border is irregular: the border with Indiana was moved 10 miles northward from its territorial position to give Indiana more access to Lake Michigan, and its slightly angled border with Ohio was part of the compromise which ended the Toledo War. The Lower Peninsula is a part of the Great Lakes Plain, which include large parts of Wisconsin and Ohio.
At its widest points, the Lower Peninsula is 277 mi long from north to south and 195 mi from east to west. It contains nearly two-thirds of Michigan\'s total land area. The surface of the peninsula is generally level, broken by conical hills and glacial moraines usually not more than a few hundred feet tall, most common in the north. The highest point in the Lower Peninsula is not definitely established, but is either Briar Hill at 1,705 ft, or one of several points nearby in the vicinity of Cadillac. The lowest point is at the shore of Lake Erie at 571 ft. The western coast features extensive sandy beaches and dunes produced by Lake Michigan and the prevailing winds from the west. The relatively shallow Saginaw Bay is surrounded by a similarly shallow drainage basin. Several large river systems flow into the adjacent Great Lakes, including the Kalamazoo, Grand, Muskegon, and Manistee rivers (Lake Michigan), and the Au Sable and Tittabawassee--Shiawassee--Saginaw rivers (Lake Huron). Because of the networks of rivers and numerous lakes, no point on land is more than 6 mi from one of these bodies of water, and at most 85 mi from one of the Great Lakes (near Lansing).
### Flora and fauna {#flora_and_fauna}
The American Bird Conservancy and the National Audubon Society have designated several locations as internationally Important Bird Areas.
### Geology
The Lower Peninsula is dominated by a geological basin known as the Michigan Basin. That feature is represented by a nearly circular pattern of geologic sedimentary strata in the area with a nearly uniform structural dip toward the center of the peninsula. The basin is centered in Gladwin County where the Precambrian basement rocks are 16000 ft deep. Around the margins, such as under Mackinaw City, Michigan, the Precambrian surface is around 4000 ft down. This 4000 ft contour on the bedrock clips the northern part of the lower peninsula and continues under Lake Michigan along the west. It crosses the southern counties of Michigan and continues on to the north beneath Lake Huron.
### Climate
Most monthly temperatures in the lower peninsula range from a low of 14 degrees to a high of 84 degrees Fahrenheit.
## Regions
Michigan\'s Lower Peninsula can be divided into four main regions based on geological, soil, and vegetation differences; amount of urban areas or rural areas; minority populations; and agriculture. The four principal regions listed below can further be separated into sub-regions and overlapping areas.
- Northern Michigan
- Central/Mid-Michigan
- The Thumb
- Tri-Cities
- Southern Michigan
- West Michigan
- Southern Michigan
- Michiana
- Southeast Michigan
- Metro Detroit
## Transportation
### Major airports {#major_airports}
- Alpena County Regional Airport (APN) (Alpena)
- Bishop International Airport (FNT) (Flint)
- Capital Region International Airport (LAN) (Lansing)
- Cherry Capital Airport (TVC) (Traverse City)
- Detroit Metropolitan Wayne County Airport (DTW) (Romulus)
- Gerald R. Ford International Airport (GRR) (Grand Rapids)
- Kalamazoo/Battle Creek International Airport (AZO) (Kalamazoo)
- MBS International Airport (MBS) (Saginaw)
- Pellston Regional Airport (PLN) (Pellston)
### Highways
Interstate Highways in the region include:
-
-
-
-
U.S. Highways in the region include:
-
-
-
-
-
-
-
-
The Great Lakes Circle Tour is a designated scenic road system connecting all of the Great Lakes and the St. Lawrence River.
### Passenger rail {#passenger_rail}
The Lower Peninsula is served by three Amtrak routes that travel up to 110 mph:
- *Wolverine*
- *Pere Marquette*
- *Blue Water*
### Intercity Bus {#intercity_bus}
Various intercity buses transport people across the Lower Peninsula, including the Michigan Flyer that travels from Lansing to the Detroit Airport with stops in Brighton and Ann Arbor, and the D2A2 nonstop bus from Detroit to Ann Arbor
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# Lamorna Birch
**Samuel John** \"**Lamorna**\" **Birch**, RA, RWS (7 June 1869 -- 7 January 1955) was an English artist in oils and watercolours. At the suggestion of fellow artist Stanhope Forbes, Birch adopted the *soubriquet* \"Lamorna\" to distinguish himself from Lionel Birch, an artist who was also working in the area at that time.
## Biography
Lamorna Birch was born in Egremont, Cheshire, England. He was self-taught as an artist, except for a brief period of study at the Académie Colarossi in Paris during 1895.
Birch settled in Lamorna, Cornwall in 1892, initially lodging at nearby Boleigh Farm. Many of his most famous pictures date from this time and the beautiful Lamorna Cove is usually their subject matter. He was attracted to Cornwall by the Newlyn group of artists but he ended up starting a second group based around his adopted home of Lamorna. He married Houghton (Mouse) Emily Vivian, the daughter of a mining agent from Camborne and they lived at Flagstaff Cottage, Lamorna.
In 1936, Birch embarked on an extensive painting and lecture tour in New Zealand. He was accompanied on his visit by fellow artists Kathleen Airini Vane and Russell Clark. Birch would paint many of the scenic areas of Northland together with Vane, and embark on skiing expeditions with Clark. At the end of his visit, Vane would present several works by Birch to the Christchurch Art Gallery which remain in its collection.
## Personal life {#personal_life}
Greta Valentine met Birch when she was 28 and she was on holiday with her parents in Cornwall. Lamorna was married but he was intrigued by Greta. He would write her poetry and create paintings for her. Symbolism within the paintings expressed his love for her.
## Exhibitions
He exhibited at the Royal Academy from 1893, was elected as an Associate (ARA) in 1926 and made a Royal Academician (RA) in 1934, and showed more than two hundred paintings there. He held his first one-man exhibition at the Fine Art Society in 1906 and is said to have produced more than 20,000 pictures. Like a number of his contemporaries, he was profiled as an \'Artist of Note\' in *The Artist* magazine, by Richard Seddon, in the June 1944 edition.
- *Shades of British Impressionism Lamorna Birch and his Circle* was shown at Warrington Museum & Art Gallery in the Mezzanine in October 2004. This details his links with Henry Scott Tuke and Thomas Cooper Gotch and many others who settled in the artists\' colony in the 1880s and 1890s. \"These painters helped to change the face of British art. Their emphasis on colour and light, truth and social realism brought about a revolution in British art.\" says the catalogue for the show.
- *Entranced by a Special Place: The Art of S J Lamorna Birch* -- at Penlee House, Penzance, part of the Royal Academy\'s 250th anniversary celebrations.
## Today
Birch has paintings at Penlee House and in the collection of Derby Art Gallery. Christchurch Art Gallery also holds the aforementioned works presented by Kathleen Airini Vane and works acquired through other means
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