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# K-Meleon
## Customization
Customization of K-Meleon\'s interface is possible using text-format configuration files called configs. The menus, keyboard shortcuts, and more can all be customized via K-Meleon\'s configuration files. These configs can call upon macros, a type of extension that can be opened in a text editor.
A simple \"Hello, World!\" program could be written in K-Meleon\'s macro language that would pop up a small window with the message \"Hello world!\".
``` apache
HelloWorld{
alert("Hello world!");
}
```
To trigger the macro, a keyboard accelerator could be created by adding the code below to the accelerator config, causing the macro to launch if the Ctrl, Alt, and H keys are pressed at the same time.
``` clojurescript
CTRL ALT H = macros(HelloWorld)
```
Custom toolbars offer more options, but the syntax is similar. The example below would create a new toolbar with a button to trigger a macro.
``` Apache
NewToolbar{
!NewButton{
macros(HelloWorld)
}
}
```
This combination of configs and macro modules provides control over much of the browser. It also creates a learning curve for customization that is not present in most browsers. A CNET review criticized K-Meleon because it \"requires some knowledge of computer code to get the most out of it\". Popular browsers use systems like WebExtensions, where there is a separation between users and extension developers.
Because of its flexibility, K-Meleon was useful for environments in which the browser needed to be customized for public use, such as libraries and Internet cafés. It allowed administrators to hide some features from patrons. For example, a library could hide interface elements like the address bar or limit the computer\'s access to an online resource like the library catalog.
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# K-Meleon
## Legacy Windows versions {#legacy_windows_versions}
K-Meleon supports a range of legacy software and hardware. Version 76 supports Windows XP (2001) and Windows Vista (2006). Windows XP and its Windows Embedded POSReady 2009 variant have been unsupported since 2019. The latest major browser releases to support these operating systems are Microsoft\'s Internet Explorer 8 (2014), Google Chrome 49.0.2623.112 (2016), and Mozilla Firefox 52.9.0 (2018).
Web browsers cannot access secure websites if they do not support Transport Layer Security (TLS) encryption. As of 2018, most major web sites use TLS encryption via HTTPS. Early versions of K-Meleon for Windows 2000 and Windows 9X receive occasional updates for TLS certificates. K-Meleon 74 can access secure websites on Windows 2000 using an old version of the Goanna engine combined with up-to-date ciphers. K-Meleon 1.5 can run on Windows 95, Windows 98, and Windows Me. Occasional TLS updates allow version 1.5 to access secure websites.
## Release history {#release_history}
K-Meleon, which was first released in 2000, has been under development for over 20 years and is still maintained. The most-recent version K-Meleon 76 is updated on a rolling release schedule. All versions of K-Meleon are written for Microsoft Windows operating systems.
+---------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------+---------------------------------------------------+---------------------------------------+-------+
| Version | scope=\"col\" data-sort-type=date \|Initial Release | scope=\"col\" data-sort-type=date \|Latest Update | Gecko Version | Notes |
+===========================================================================================================================+=====================================================+===================================================+=======================================+=======+
| | | | | |
+---------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------+---------------------------------------------------+---------------------------------------+-------+
| 0.1 | Aug 21, 2000 | Aug 21, 2000 | data-sort-value=\"0.0.17\"\| M17 | |
+---------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------+---------------------------------------------------+---------------------------------------+-------+
| 0.2 | Nov 26, 2000 | Jan 29, 2001 | data-sort-value=\"0.0.18\"\| M18 | |
+---------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------+---------------------------------------------------+---------------------------------------+-------+
| 0.3 | Feb 13, 2001 | Feb 13, 2001 | 0.8 | |
+---------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------+---------------------------------------------------+---------------------------------------+-------+
| 0.4 | May 11, 2001 | May 11, 2001 | 0.9 | |
+---------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------+---------------------------------------------------+---------------------------------------+-------+
| 0.5 | Sep 27, 2001 | Sep 27, 2001 | 0.9.4 | |
+---------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------+---------------------------------------------------+---------------------------------------+-------+
| 0.6 | Oct 30, 2001 | Oct 30, 2001 | 0.9.5 | |
+---------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------+---------------------------------------------------+---------------------------------------+-------+
| 0.7 | Oct 31, 2002 | Feb 12, 2003 | 1.2b | |
+---------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------+---------------------------------------------------+---------------------------------------+-------+
| 0.8 | Nov 10, 2003 | Dec 23, 2003 | 1.5 | |
+---------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------+---------------------------------------------------+---------------------------------------+-------+
| 0.9 | Jan 18, 2005 | Apr 25, 2006 | 1.7.13 | |
+---------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------+---------------------------------------------------+---------------------------------------+-------+
| 1.0 | Jul 15, 2006 | Sep 22, 2006 | 1.8.0.7 | |
+---------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------+---------------------------------------------------+---------------------------------------+-------+
| 1.1 | May 22, 2007 | Jul 18, 2008 | 1.8.1.17 | |
+---------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------+---------------------------------------------------+---------------------------------------+-------+
| 1.5 | Aug 8, 2008 | Dec 9, 2022 | 1.8.1.24 | |
+---------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------+---------------------------------------------------+---------------------------------------+-------+
| 1.6 | Nov 14, 2010 | Dec 12, 2010 | 1.9.1.20 | |
+---------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------+---------------------------------------------------+---------------------------------------+-------+
| 74.0 | Sep 8, 2014 | Aug 14, 2021 | 24.7 | |
+---------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------+---------------------------------------------------+---------------------------------------+-------+
| 75.0 | Nov 25, 2014 | Jun 24, 2015 | 31.5 | |
+---------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------+---------------------------------------------------+---------------------------------------+-------+
| 75.1 | Sep 19, 2015 | Dec 14, 2022 | 31.8 | |
+---------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------+---------------------------------------------------+---------------------------------------+-------+
| 76.0 RC | May 2, 2016 | Dec 20, 2016 | 38.8 | |
+---------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------+---------------------------------------------------+---------------------------------------+-------+
| 76.G | Nov 28, 2017 | Dec 15, 2018 | data-sort-value=\"52\"\| Goanna 3.x | |
+---------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------+---------------------------------------------------+---------------------------------------+-------+
| 76.2.G | Jan 10, 2019 | Aug 22, 2020 | data-sort-value=\"52\"\| Goanna 3.4.6 | |
+---------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------+---------------------------------------------------+---------------------------------------+-------+
| 76.3.G | Aug 29, 2020 | Feb 5, 2021 | data-sort-value=\"52\"\| Goanna 3.4.6 | |
+---------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------+---------------------------------------------------+---------------------------------------+-------+
| 76.4.G | Feb 12, 2021 | Apr 7, 2023 | data-sort-value=\"52\"\| Goanna 3.4.6 | |
+---------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------+---------------------------------------------------+---------------------------------------+-------+
| 76.5.G | Dec 1, 2024 | Oct 10, 2024 | data-sort-value=\"52\"\| Goanna 3.6.0 | |
+---------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------+---------------------------------------------------+---------------------------------------+-------+
| | | | | |
+---------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------+---------------------------------------------------+---------------------------------------+-------+
| **Notes** | | | | |
| | | | | |
| General references for this table include K-Meleon file releases, release notes, changelogs, and the Announcements forum
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# Katsuhiro Otomo
is a Japanese manga artist, screenwriter, animator, and film director. He first rose to prominence as a pioneer founder of the New Wave in the 1970s. He is best known as the creator of *Akira*, both the original 1982 manga series and the 1988 animated film adaptation. In 2005, Otomo was decorated a *Chevalier* of the French Ordre des Arts et des Lettres, promoted to *Officier* of the order in 2014, and became the fourth manga artist ever inducted into the American Eisner Award Hall of Fame in 2012. Celebrated in Japan, he was also awarded the Purple Medal of Honor from the national government in 2013.
In addition, Otomo later received the Winsor McCay Award at the 41st Annie Awards in 2014 and the 2015 Grand Prix de la ville d\'Angoulême, the first manga artist to receive the award.
## Early life {#early_life}
Katsuhiro Otomo was born in Tome, Miyagi Prefecture and grew up in Tome District. He said that living in the very rural Tōhoku region left him with nothing to do as a child, so he read a lot of manga. As the only boy in a family with older and younger sisters, he enjoyed reading and drawing manga on his own and thought about becoming a manga artist. Limited by his parents to buying one manga book a month, Otomo typically chose Kobunsha\'s *Shōnen* magazine, which included *Astro Boy* by Osamu Tezuka and *Tetsujin 28-go* by Mitsuteru Yokoyama, series which he would copy drawing in elementary school. However, he said it was after reading Shotaro Ishinomori\'s *How to Draw Manga* that he understood how to draw manga properly and started doing so more seriously.
In high school, Otomo developed an interest in movies, that led to his ambition to become an illustrator or film director. At this time, one of his friends introduced him to an editor at Futabasha, who, after seeing Otomo\'s manga, told the high school student to contact him if he moved to Tokyo after graduating. Otomo did exactly that, and began his career in Tokyo as a 19-year old professional manga artist.
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# Katsuhiro Otomo
## Career
### Manga
On October 4, 1973, Otomo published his first work, a manga adaptation of Prosper Mérimée\'s short story *Mateo Falcone*, titled *A Gun Report*.
In 1979, after writing multiple short-stories for the magazine *Weekly Manga Action*, Otomo created his first science-fiction work, titled *Fireball*. Although the manga was never completed, it is regarded as a milestone in Otomo\'s career as it contained many of the same themes he would explore in his later, more successful manga such as *Dōmu*. *Dōmu* began serialization in January 1980 and ran until July 1981. It was not published in book form until 1983, when it won the Nihon SF Taisho Award. It also won the 1984 Seiun Award for Best Comic.
In a collaboration with writer Toshihiko Yahagi, Otomo illustrated *Kibun wa mō Sensō* about a fictional war that erupts in the border between China and the Soviet Union. It was published in *Weekly Manga Action* from 1980 to 1981 and collected into one volume in 1982. It won the 1982 Seiun Award for Best Comic. 38 years later, the two created the one-shot sequel *Kibun wa mō Sensō 3 (Datta Kamo Shirenai)* for the April 16, 2019 issue of the magazine.
Also in 1981, Otomo drew *A Farewell to Weapons* for the November 16 issue of Kodansha\'s *Young Magazine*. It was later included in the 1990 short story collection *Kanojo no Omoide\...*
In 1982, Otomo began what would become his most acclaimed and famous work: *Akira*. Kodansha had been asking him to write a series for their new *Young Magazine* for some time, but he had been busy with other work. From the first meeting with the publisher, *Akira* was to be only about ten chapters \"or something like that,\" so Otomo said he was really not expecting it to be a success. It was serialized for eight years and 2000 pages of artwork.
In 1990, Otomo did a brief interview with MTV for a general segment on the Japanese manga scene at the time. Otomo created the one-shot *Hi no Yōjin* about people who put out fires in Japan\'s Edo period for the debut issue of *Comic Cue* in January 1995.
Otomo wrote the 2002 picture book *Hipira: The Little Vampire*, which was illustrated by Shinji Kimura.
Otomo created the full-color work *DJ Teck no Morning Attack* for the April 2012 issue of *Geijutsu Shincho*.
Following the 2011 Tōhoku earthquake and tsunami, Otomo, a native of the Tōhoku region, designed a relief that features a boy riding a robot goldfish in rough seas, while flanked by Fūjin and Raijin. Intended to capture the region\'s will to overcome the natural disaster, it has been located on the first floor of the terminal building at Sendai Airport since March 2015.
Otomo was initially reported in 2012 to be working on his first long-form manga since *Akira*. Planning to draw the work that is set during Japan\'s Meiji period without assistants, he was initially targeting a younger audience, but said the story had developed more towards an older one. Although planned to begin in fall 2012, Otomo revealed in November of that year that the series had been delayed. By 2018, Otomo said he was doing a full-length work, but the contents were still secrets. In 2022, Kodansha released Otomo\'s entire body of manga since 1971 as part of \"The Complete Works Project,\" which featured six separate releases of two books each. It was noted that some of his manga were edited when initially compiled into book format, and this new project, personally overseen by Otomo, restored them to how they appeared in their original serialization.
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# Katsuhiro Otomo
## Career
### Film
At the age of 25, Otomo spent about 5 million yen to make a 16 mm live-action film about an hour long. He said that making this private film showed him roughly how to make and direct movies. In 1982, Otomo made his anime debut, working as character designer for the animated film *Harmagedon: Genma Wars*. It was while working on this film that Otomo began to think he could do it by himself.
In 1987, Otomo directed an animated work for the first time: a segment, which he also wrote the screenplay and drew animation for, in the anthology feature *Neo Tokyo*. He followed this up with two segments in another anthology released that year, *Robot Carnival*. In 1988, he directed the animated film adaptation of his manga *Akira*.
Otomo was executive producer of 1995\'s *Memories*, an anthology film based on three of his stories. Additionally, he wrote the script for *Stink Bomb* and *Cannon Fodder*, the latter of which he also directed.
Otomo has worked extensively with the studio Sunrise. In 1998, he directed the CG short *Gundam: Mission to the Rise* to celebrate the 20th anniversary of their *Gundam* franchise. The studio has animated and produced his 2004 feature film *Steamboy*, 2006\'s *Freedom Project*, and 2007\'s *SOS! Tokyo Metro Explorers: The Next*. The last, is based on Otomo\'s 1980 manga *SOS! Tokyo Metro Explorer* and follows the son of its main characters.
The 2001 animated film *Metropolis* features a script written by Otomo that adapts Tezuka\'s manga of the same name.
Otomo directed the 2006 live-action film *Mushishi*, based on Yuki Urushibara\'s manga of the same name.
In 2013, Otomo took part in *Short Peace*, an anthology consisting on 4 short films; he directed *Combustible*, a tragic love story set in the Edo period based on his 1995 manga *Hi no Yōjin*, while Hajime Katoki directed *A Farewell to Weapons*, depicting a battle in a ruined Tokyo based on Otomo\'s 1981 manga of the same name. *Combustible* won the Grand Prize in the Animation category of the Japan Media Arts Festival in 2012, and was even shortlisted for the 2013 Best Animated Short at the 85th Academy Awards.
Otomo directed the music video for Aya Nakano\'s 2016 song \"Juku-Hatachi\". He is a fan of the singer and previously drew the cover to her 2014 album *Warui Kuse*.
Reports have suggested that Otomo will be the executive producer of the live-action film adaptation of *Akira*. In 2019, he announced that he is writing and directing an animated film adaptation of his 2001 manga *Orbital Era* with Sunrise and released a trailer that same year.
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# Katsuhiro Otomo
## Style
Otomo said that when he started his professional career in the late 1970s, \"almost all manga was gekiga like *Golgo 13*. So it was all gekiga or sports manga, nothing to do with science fiction.\" Remembering how much he loved science fiction as a child, Otomo wanted to recreate that kind of excitement; \"That was in part how something like *Domu* came about. \[\...\] There was no hard science fiction manga \[\...\] so I wanted to change that and do something more realistic and believable.\"
Describing his characterization style, Otomo said he first tried to draw and imitate \"very traditional manga-like art,\" such as *Astro Boy*. But by the time he was in high school, illustration work by people like Tadanori Yokoo and Yoshitaro Isaka was popular, so he wanted to create manga characters with this illustrative art style. When asked about how Japanese critics praise him as the first manga artist to draw realistic Japanese faces, Otomo said he always tries to balance fantasy and realism; \"Depicting things too realistically actually damages the social realism of the piece, and if you go too far into the realm of fantasy, that hurts its imaginative ability.\" However, he said the realism of his early works probably came from having used friends as character models. French cartoonist Moebius, who is known for realistic character designs, is often cited as one of Otomo\'s biggest influences. Otomo is considered to be one of the artists of the New Wave in manga in the late 1970s and 1980s especially due to his visual innovation.
Otomo includes homages to his favorite childhood manga in his work, and there were three manga authors that he really respected at that time; Osamu Tezuka, Shotaro Ishinomori and Mitsuteru Yokoyama. He named the main computer in *Fireball* ATOM after Tezuka\'s character of the same name, the character nicknamed Ecchan in *Domu* is a reference to Ishinomori\'s *Sarutobi Ecchan*, and the title character of *Akira* is also known as No. 28 in homage to Yokoyama\'s *Tetsujin 28-go* in addition to the two series having the \"same overall plot.\" Ever since depicting the apartment complex in *Domu*, Otomo has had a large interest in architecture, proclaiming, \"I don\'t think there was anyone before me who put this much effort into their depictions of buildings.\" He believes this habit of drawing detailed backgrounds was influenced by Shigeru Mizuki\'s manga, which showed him how important backdrops are to a story. Otomo strongly praised the framing done by Tetsuya Chiba, whose work he studied a lot out of admiration at a store in Kichijoji, for making it easy to grasp how tangible the backgrounds and characters are. It was taken from Chiba's *Notari Matsutaro,* a seinen sports manga that mainly inspired Otomo to develop his *grammar* for making manga, including *Domu.*
When asked about his influences in designing the mecha in *Farewell to Weapons*, Otomo pointed out that Studio Nue\'s work was popular at the time, specifically mentioning the powered suit designs by Kazutaka Miyatake and Naoyuki Kato. He also stated that he is a fan of mecha by Takashi Watabe and Makoto Kobayashi and is fond of those seen in *Neon Genesis Evangelion*, but explained that all his influences are jumbled and mixed together; \"In short, I digest many different things and ideas tend to pop out from that.\"
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# Katsuhiro Otomo
## Legacy
It was around the 1979 publication of his *Short Peace* short story collection that Otomo\'s work became influential in Japan. Artists influenced by him and his work include Hisashi Eguchi, Naoki Urasawa, Naoki Yamamoto, Makoto Aida and Hiroya Oku. When talking in 1997 about the future of manga, Urasawa opined that
> \[Osamu\] Tezuka created the form that exists today, then caricatures appeared next, and comics changed again when Katsuhiro Otomo came on the scene. I don\'t think there\'s any room left for further changes.
Masashi Kishimoto cited Otomo as one of his two biggest influences, but liked Otomo\'s art style the best and imitated it while trying to develop his own. The Dragon Ball manga creator Akira Toriyama was interviewed on who was his favorite manga artist, and said that he found his peer Otomo to be "incredible."
Otomo\'s manga work also notably influenced a number of Japanese video game designers by the mid-1980s, including Enix\'s Yuji Horii (*The Portopia Serial Murder Case* and *Dragon Quest*), Capcom\'s Noritaka Funamizu (*Gun.Smoke* and *Hyper Dyne Side Arms*), UPL\'s Tsutomu Fujisawa (*Ninja-Kid*), Thinking Rabbit\'s Hiroyuki Imabayashi (*Sokoban*), dB-SOFT\'s Naoto Shinada (*Volguard*), Hot-B\'s Jun Kuriyama (*Psychic City*), and Microcabin\'s Masashi Katou (*Eiyuu Densetsu Saga*).
Director Satoshi Kon, who worked as an assistant to Otomo in both manga and film, cited *Akira* and especially *Domu* as influences. American film director Rian Johnson is a big fan of Otomo and pointed out similarities between how telekinesis is depicted in *Domu* and its depiction in his film *Looper*.
In 2017, the book *Otomo: A Global Tribute to the Mind Behind Akira* was published in Japan, France and the United States, featuring writing and artwork from 80 artists such as Masakazu Katsura, Taiyo Matsumoto, Masamune Shirow, Asaf and Tomer Hanuka, and Stan Sakai. From April 8 to May 8, 2021, comic art collector Phillipe Labaune\'s self-titled art gallery in New York City held \"Good For Health, Bad For Education: A Tribute to Otomo\" as its first exhibition. Including pieces originally curated by Julien Brugeas for the 2016 Angoulême International Comics Festival, it featured a total of 29 Otomo-inspired works by international artists such as Sara Pichelli, Paul Pope, Boulet, François Boucq, Giannis Milonogiannis and Ian Bertram.
## Personal life {#personal_life}
Otomo is married to Yoko Otomo. Together they have one child, a son named Shohei Otomo, who is also an artist.
## Filmography
**Anime features**
Year Title Director Writer
------ --------------- ---------- --------
1988 *Akira*
1991 *Roujin Z*
2001 *Metropolis*
2004 *Steamboy*
TBA *Orbital Era*
**Anime shorts**
+------+-----------------------------------+----------+--------+------------+------------------------------+
| Year | Title | Director | Writer | Executive\ | Notes |
| | | | | Producer | |
+======+===================================+==========+========+============+==============================+
| 1987 | *Construction Cancellation Order* | | | | Segment of *Neo Tokyo* |
+------+-----------------------------------+----------+--------+------------+------------------------------+
| | \"Opening\" and \"Ending\" | | | | Segments of *Robot Carnival* |
+------+-----------------------------------+----------+--------+------------+------------------------------+
| 1995 | *Magnetic Rose* | | | | Segments of *Memories* |
+------+-----------------------------------+----------+--------+------------+------------------------------+
| | *Stink Bomb* | | | | |
+------+-----------------------------------+----------+--------+------------+------------------------------+
| | *Cannon Fodder* | | | | |
+------+-----------------------------------+----------+--------+------------+------------------------------+
| 1998 | *Gundam: Mission to the Rise* | | | | |
+------+-----------------------------------+----------+--------+------------+------------------------------+
| 2013 | *Combustible* | | | | Segment of *Short Peace* |
+------+-----------------------------------+----------+--------+------------+------------------------------+
| | | | | | |
+------+-----------------------------------+----------+--------+------------+------------------------------+
**Live-action**
Year Title Director Writer Producer Notes
------ -------------------------------------- ---------- -------- ---------- -------------------
1979 *High School Erotopia: Red Uniforms* Pornographic film
1982
1991 *World Apartment Horror*
2006 *Mushishi*
**Additional work**
Besides his own animation, Otomo has contributed art designs to *Harmagedon: Genma Wars*, the *Crusher Joe* film, the seven-part OVA series *Freedom Project*, and *Space Dandy* episode 22.
He also oversaw the composition of the *Spriggan* animated film and directed the music video `{{nihongo|''Juku-Hatachi''|じゅうくはたち}}`{=mediawiki} for Aya Nakano
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# Kittiwake
The **kittiwakes** (genus ***Rissa***) are two closely related seabird species in the gull family Laridae, the black-legged kittiwake (*Rissa tridactyla*) and the red-legged kittiwake (*Rissa brevirostris*). The epithets \"black-legged\" and \"red-legged\" are used to distinguish the two species in North America, but in Europe, where *Rissa brevirostris* is not found, the black-legged kittiwake is often known simply as **kittiwake**. The name is derived from its call, a shrill \'kittee-wa-aaake, kitte-wa-aaake\'. The genus name *Rissa* is from the Icelandic name *Rita* for the black-legged kittiwake.
## Description
The two species are physically very similar. They have a white head and body, grey back, grey wings tipped solid black and a bright yellow bill. Black-legged kittiwake adults are somewhat larger (roughly 40 cm in length with a wingspan of 90 --) than red-legged kittiwakes (35 -- in length with a wingspan around 84 --). Other differences include a shorter bill, larger eyes, a larger, rounder head and darker grey wings in the red-legged kittiwake. While most black-legged kittiwakes do, indeed, have dark-grey legs, some have pinkish-grey to reddish legs, making colouration a somewhat unreliable identifying marker.
In contrast to the dappled chicks of other gull species, kittiwake chicks are downy and white since they are under relatively little threat of predation, as the nests are on extremely steep cliffs. Unlike other gull chicks which wander around as soon as they can walk, kittiwake chicks instinctively sit still in the nest to avoid falling off. Juveniles take three years to reach maturity. When in winter plumage, both birds have a dark grey smudge behind the eye and a grey hind-neck collar. The sexes are visually indistinguishable.
## Distribution and habitat {#distribution_and_habitat}
Kittiwakes are coastal breeding birds ranging in the North Pacific, North Atlantic, and Arctic oceans. They form large, dense, noisy colonies during the summer reproductive period, often sharing habitat with murres. They are the only gull species that are exclusively cliff-nesting. A colony of kittiwakes living in Newcastle upon Tyne and Gateshead in the north east of England has made homes on both the Tyne Bridge and Baltic Centre for Contemporary Art. This colony is notable because it is the furthest inland colony of kittiwakes in the world.
## Species
## Photo gallery {#photo_gallery}
<File:Kittiwake> w.jpg\|Kittiwake -- winter Ireland <File:Kittiwake> with young chick.jpg\|Kittiwake with chicks, Iceland <File:Rissa> tridactyla -Staple Island, Farne Islands, Northumberland, England -adult and chicks-8
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# Kimberly Beck
**Kimberly Beck** is a former American actress, model and singer. She is best known for her role as Trish Jarvis in Joseph Zito\'s *Friday the 13th: The Final Chapter* (1984). Her other film roles include Alfred Hitchcock\'s *Marnie* (1964), Luc Besson\'s *The Big Blue* (1988), George T. Miller\'s *Frozen Assets* (1992), and Roland Emmerich\'s *Independence Day* (1996).
## Life and career {#life_and_career}
Kimberly Beck was born to the actress Cindy Robbins. As a child, she appeared in Alfred Hitchcock\'s *Marnie* and television commercials for such products as Mattel\'s Barbie and Chatty dolls. She had a very brief appearance on *The Munsters* as a transformed Eddie Munster after Eddie (Butch Patrick) drank the rest of Grandpa (Al Lewis)\'s Texas Playgirl Potion in season 1, episode 33 \"Lily Munster, Girl Model\".
In 1968, Beck and her stepfather Tommy Leonetti, then working in Australia, recorded the single \"Let\'s Take a Walk\", released under the name of \"Tommy Leonetti and his daughter Kim\". It charted at #4 on the Melbourne charts.
Beck starred in such movies as *Massacre at Central High*, *Roller Boogie*, and *Friday the 13th: The Final Chapter*. Among her notable television credits are*General Hospital*, *Capitol* (billed as Kimberly Beck-Hilton), *Fantasy Island*, *Buck Rogers in the 25th Century* (as Alison Michaels, one side of a Jekyll-and-Hyde character, whose counterpart Sabrina was played by Trisha Noble), *Westwind*, *The Brady Bunch*, *Dynasty*, *Lucas Tanner* and *Peyton Place* (as the character Kim Schuster). Beck starred on the pilot episode of *Eight Is Enough* as Nancy Bradford, the role that, in the series, went to Dianne Kay. She also had the role of Diane Porter in *Rich Man, Poor Man Book II* with Peter Strauss and appeared in a host of other well-received television miniseries productions.
Beck was previously married to William Barron Hilton, Jr., son of Barron Hilton and a member of the Hilton family, from 1978 to 1985. In 1988, Beck married producer Jason Clark and they had two sons. She appeared in the documentary *Crystal Lake Memories: The Complete History of Friday the 13th* in 2013 and reprised her role as Trish Jarvis from the Friday the 13th franchise in a voiceover role for the fan film short *Victim No More* in 2022.
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# Kimberly Beck
## Filmography
### Film
Year Title Role Notes
------ -------------------------------------- --------------------------- -------------------------------------
1958 *Torpedo Run* Dede Doyle Uncredited
1959 *The FBI Story* Jennie Hardesty (age 2) Uncredited
1963 *The Courtship of Eddie\'s Father* Child Party Guest Uncredited
1964 *Marnie* Jessica \"Jessie\" Cotton Uncredited
1968 *Yours, Mine and Ours* Janette North
1976 *Massacre at Central High* Teresa
1979 *Roller Boogie* Lana
1984 *Friday the 13th: The Final Chapter* Trish Jarvis
1987 *Maid to Order* Kim
1988 *The Big Blue* Sally
*Nightmare at Noon* Cheri Griffiths Alternate title: *Death Street USA*
*Messenger of Death* Piety Beecham
*Private War* Kim
1989 *Playroom* Secretary
1990 *False Identity* Cindy Roger
1991 *Adventures in Dinosaur City* Chanteuse
1992 *Frozen Assets* Voice Actress Voice role
1994 *Killing Zoe* Woman Customer
1996 *Independence Day* Housewife
1999 *The Secret Life of Girls* Mrs. Buchinsky
2009 *Heidi 4 Paws* Clara Sesehound Voice role
2022 *Victim No More* Trish Jarvis-Mahoney Voice role
### Television
Year Title Role Notes
------------ ------------------------------------------ ---------------------- -----------------
1964 *Kraft Suspense Theatre* Child #2 1 episode
1965 *The Munsters* Girl Eddie Munster 1 episode
1965--1966 *Peyton Place* Kim Schuster 34 episodes
1966 *The Virginian* Laura Tedler 1 episode
*I Dream of Jeannie* Gina 1 episode
1969 *Land of the Giants* Giant Girl 1 episode
*My Three Sons* Susan Crawford 1 episode
1970 *Me and Benjie* TV pilot
1971 *Bonanza* Girl 1 episode
1971--1973 *The Brady Bunch* Laura 2 episodes
1974--1975 *Lucas Tanner* Terry Klitsner 21 episodes
1975 *Adam-12* Jo Anne Thompson 1 episode
*General Hospital* Samantha Livingston 1 episode
*Mobile One* Marlene 1 episode
1975--1976 *Westwind* Robin Andrews 13 episodes
1976--1977 *Rich Man, Poor Man Book II* Diane Porter 15 episodes
1977 *Eight Is Enough* Nancy Bradford TV pilot
*The Hardy Boys/Nancy Drew Mysteries* Sue 1 episode
*Murder in Peyton Place* Bonnie Buehler Television film
1978 *Husbands, Wives & Lovers* Amanda 1 episode
*Zuma Beach* Cathy Television film
1979 *B. J. and the Bear* Cindy Smith 1 episode
*Fantasy Island* Cindy 1 episode
*Starting Fresh* Stephanie Harvey TV pilot
*Buck Rogers in the 25th Century* Alison Michaels 1 episode
1980 *The Misadventures of Sheriff Lobo* Vicky Bowers 1 episode
*Scalpels* Nurse Connie Primble TV pilot
*Freebie and the Bean* 1 episode
1981 *Mr. Merlin* Susan 1 episode
1982 *Matt Houston* Laurie Wildcat 1 episode
1982--1983 *Capitol* Julie Clegg 260 episodes
1983 *Webster* Molly 1 episode
1984 *T. J. Hooker* Linda Stevens 1 episode
1985 *Hunter* Marlene 1 episode
*Hollywood Beat* Prostitute 1 episode
*Deadly Intentions* Sally Raynor Television film
1986 *Crazy Like a Fox* Stella Moran 1 episode
*The New Mike Hammer* Lisa Burnett 1 episode
1986--1987 *Dynasty* Claire Prentice 4 episodes
1987 *L.A
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# Karen Kain
**Karen Alexandria Kain** `{{post-nominals|country=CAN|CC|OOnt}}`{=mediawiki} (born March 28, 1951) is a Canadian former ballet dancer and was the Artistic Director of the National Ballet of Canada from 2005 to 2021.
## Early training and childhood {#early_training_and_childhood}
Kain\'s mother enrolled her daughter in ballet training because she believed it would improve her postural alignment, poise, and discipline. The family moved from Ancaster to Erindale Woodlands, Toronto Township when Kain was in grade 6 (age 11, 1962) so she could begin training at the National Ballet School of Canada. (The majority of Toronto Township, including Erindale Woodlands, is now Mississauga.) Upon graduating in 1969, she was invited to join the National Ballet of Canada. She also participated in Girl Guides of Canada programs as a member.
## Career
Kain became a principal dancer in 1971, performing central roles in a wide array of ballets, eventually becoming well known in Canada, with the help of legendary dancer Rudolf Nureyev. She worked as a guest artist with Roland Petit\'s Ballet National de Marseilles, the Bolshoi Ballet, the London Festival Ballet, the Paris Opera Ballet, the Hamburg Ballet, the Vienna State Opera Ballet, and the Eliot Feld Ballet. Kain is a subject of The Portraits of Andy Warhol, c. 1980.
During her career, she performed in many ballets from classical and modern repertoire including among others *Swan Lake* (Erik Bruhn) *Coppélia*, *The Sleeping Beauty* (Rudolph Nureyev), *Giselle*, *Romeo and Juliet* (John Cranko), *La fille mal gardée*, *Onegin* (John Cranko), *The Taming of the Shrew* (John Cranko), *Pastorale* (James Kudelka), *Carmen* (Roland Petit), *Concerto Barocco* (Balanchine), *A Month in the Country* (Frederick Ashton) and *Nutcracker* in which she was often paired with dancer Frank Augustyn. The talent of Kain and Augustyn came to the attention of the public and peers as soon as 1973 when they won prizes at the 1973 Moscow International Ballet Competition.
In 1977, Kain stopped dancing, but started again in 1981 with the National Ballet of Canada, where she performed for 15 more years. In 1996, Kain reunited with Frank Augustyn to appear in her husband Ross Petty\'s panto production of *Robin Hood* at Toronto\'s Elgin Theatre. Kain retired as a professional dancer in 1997.
In 1998, she returned to the National Ballet of Canada as part of the senior management team, in the role of artistic associate. She supported artistic director James Kudelka against principal dancer Kimberley Glasco in a wrongful-dismissal suit. In 2005, she succeeded Kudelka as artistic director. She stepped down from that role in 2021.
Kain served as a president of the jury at the Prix de Lausanne ballet competition in 2009.
Kain was the founding board president of Canada\'s Dancer Transition Resource Centre. Kain\'s autobiography, *Movement Never Lies*, was published in 1994 by McClelland and Stewart.
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# Karen Kain
## Awards
In 1973, she won silver in the women\'s competition and the first prize for best pas de deux (with Frank Augustyn) at the second International Ballet Competition in Moscow dancing the Bluebird pas de deux from Sleeping Beauty. In 1976, she was appointed an Officer of the Order of Canada (OC) and was made a Companion of the Order of Canada (CC) in 1991. She was made a member of the Order of Ontario in 1990. She holds honorary degrees from the University of Toronto, York University, McMaster University, Trent University, and the University of British Columbia. In May 1998, the French Government named her an Officer of the Order of Arts and Letters. Among Kain\'s other honours are the National Arts Centre Award, a companion award of the Governor General\'s Performing Arts Awards (1997) and the Governor General\'s Performing Arts Award for Lifetime Artistic Achievement (2002). In 1996, she became the first Canadian to receive the Cartier Lifetime Achievement Award. The choreographer Marguerite Derricks cited Kain as one of her heroes. in 1989 the Canadian Broadcasting Corporation made a documentary about her, *Karen Kain, Prima Ballerina*. In 2002, she received the Queen Elizabeth II Golden Jubilee Medal.
Kain had an arts based public middle school in Etobicoke named after her (Karen Kain School of the Arts) in 2008. In 2012, Kain received the Queen Elizabeth II Diamond Jubilee Medal. In 1998, she was inducted into Canada\'s Walk of Fame.
### Honorary postage stamp {#honorary_postage_stamp}
In April 2021, Kain was recognized by Canada Post as a \"legend of ballet\" for her lifetime of artistic achievements with a permanent domestic stamp displaying a ballet leap.
## Personal life {#personal_life}
Kain has been married since 1983 to Ross Petty, a stage and film actor, and producer of theatrical pantomime productions in Canada for over 20 years. Kain\'s brother, Kevin Kain, is a noted tropical medicine expert based in Toronto, Ontario; she has three younger siblings and two nephews - Dylan and Taylor Kain.
## Other
In 1976, Kain appeared in a televised version of the ballet *Giselle* in the highly coveted title role, alongside Nadia Potts, Frank Augustyn, and Anne Ditchburn. The production was first shown in 1986. In 1985, Kain starred in an episode of the popular Canadian TV series *Seeing Things*. Kain was also alluded to in the 2003 movie directed by Denys Arcand, *The Barbarian Invasions*, when Rémy Girard reminisced about his past love affairs. Kain did a TV commercial for The Art Shoppe, a furniture store in Toronto during the 1970s
Kain\'s production of *Swan Lake*, her final project as the artistic director for the National Ballet of Canada before her retirement, is profiled in Chelsea McMullan\'s 2023 documentary film *Swan Song*
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# Lynx
A **lynx** (`{{IPAc-en|l|ɪ|ŋ|k|s}}`{=mediawiki} `{{respell|links}}`{=mediawiki}; `{{plural form}}`{=mediawiki}: **lynx** or **lynxes**) is any of the four extant species (the Canada lynx, Iberian lynx, Eurasian lynx and the bobcat) within the medium-sized wild cat genus ***Lynx***. The name originated in Middle English via Latin from the Greek word `{{translit|grc|lynx}}`{=mediawiki} (`{{wikt-lang|el|λύγξ}}`{=mediawiki}), derived from the Indo-European root `{{wikt-lang|ine-pro|*leuk-}}`{=mediawiki} (`{{gloss|light}}`{=mediawiki}, `{{gloss|brightness}}`{=mediawiki}), in reference to the luminescence of its reflective eyes.
## Appearance
Lynx have a short tail, characteristic tufts of black hair on the tips of their ears, large, padded paws for walking on snow and long whiskers on the face. Under their neck, they have a ruff, which has black bars resembling a bow tie, although this is often not visible.
Body colour varies from medium brown to goldish to beige-white, and is occasionally marked with dark brown spots, especially on the limbs. All species of lynx have white fur on their chests, bellies and on the insides of their legs, fur which is an extension of the chest and belly fur. The lynx\'s colouring, fur length and paw size vary according to the climate in their range. In the Southwestern United States, they are short-haired, dark in colour and their paws are smaller and less padded. In colder northern climates lynx have thicker and lighter fur as well as larger and more padded paws that are well-adapted to snow.
The smallest species are the bobcat and the Canada lynx, while the largest is the Eurasian lynx, with considerable variations within species.
+---------------------+-------+--------+--------+--------------------------------+
| Species | Sex | Weight | Length | Height (standing at shoulders) |
+=====================+=======+========+========+================================+
| Eurasian lynx\ | males | | | |
+---------------------+-------+--------+--------+--------------------------------+
| females | | | | |
+---------------------+-------+--------+--------+--------------------------------+
| Canada lynx\ | Both | | | |
+---------------------+-------+--------+--------+--------------------------------+
| Iberian lynx\ | males | | | |
+---------------------+-------+--------+--------+--------------------------------+
| females | | | | |
+---------------------+-------+--------+--------+--------------------------------+
| Bobcat\ | males | | | |
+---------------------+-------+--------+--------+--------------------------------+
| females | | | | |
+---------------------+-------+--------+--------+--------------------------------+
: Physical characteristics of *Lynx* species
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# Lynx
## Species
All living species of *Lynx* are thought to descend from *Lynx issiodorensis,* which first appeared during the early Pliocene in Africa, around 4 million years ago, shortly afterwards dispersing into Eurasia. The bobcat is thought to have arisen from a dispersal across the Bering Land Bridge during the Early Pleistocene, around 2.5-2.4 million years ago, with the Iberian lynx suggested to have speciated around 1 million years ago, at the end of the Early Pleistocene, the Eurasian lynx is thought to have evolved from Asian populations of *Lynx issidorensis*. The Canada lynx is thought to descend from a separate later migration of Eurasian lynx over the Bering Land Bridge around 200,000 years ago.
The Pliocene felid *Felis rexroadensis* from North America has been proposed as an even earlier ancestor; however, this was larger than any living species, and is not currently classified as a true lynx. Another extinct species of *Lynx*, *L. shansius*, inhabited what is now northern China during the Early Pleistocene, though this species is considered by some researchers to be a junior synonym of *L. issiodorensis*.
### Eurasian lynx {#eurasian_lynx}
*Main article: Eurasian lynx* Of the four lynx species, the Eurasian lynx (*Lynx lynx*) is the largest in size. It is native to European, Central Asian, and Siberian forests. While its conservation status has been classified as \"least concern\", populations of Eurasian lynx have been reduced or extirpated from much of Europe, where it is now being reintroduced. During the summer, the Eurasian lynx has a relatively short, reddish or brown coat which is replaced by a much thicker silver-grey to greyish-brown coat during winter. The lynx hunts by stalking and jumping on its prey, helped by the rugged, forested country in which it resides. A favorite prey for the lynx in its woodland habitat is roe deer. It will feed however on whatever animal appears easiest, as it is an opportunistic predator much like its cousins.
### Canada lynx {#canada_lynx}
*Main article: Canada lynx*
The Canada lynx (*Lynx canadensis*), or Canadian lynx, is a North American felid that ranges in forest and tundra regions across Canada and into Alaska, as well as some parts of the northern United States. Historically, the Canadian lynx ranged from Alaska across Canada and into many of the northern U.S. states. In the eastern states, it resided in the transition zone in which boreal coniferous forests yielded to deciduous forests. By 2010, after an 11-year effort, it had been successfully reintroduced into Colorado, where it had become extirpated in the 1970s. In 2000, the U.S. Fish and Wildlife Service designated the Canada lynx a threatened species in the lower 48 states.
The Canada lynx is a good climber and swimmer; it constructs rough shelters under fallen trees or rock ledges. It has a thick coat and broad paws, and is twice as effective as the bobcat at supporting its weight on the snow. The Canada lynx feeds almost exclusively on snowshoe hares; its population is highly dependent on the population of this prey animal. It will also hunt medium-sized mammals and birds if hare numbers fall.
### Iberian lynx {#iberian_lynx}
*Main article: Iberian lynx*
The Iberian lynx (*Lynx pardinus*) is a vulnerable species native to the Iberian Peninsula in Southern Europe. It was the most endangered cat species in the world, but conservation efforts have changed its status from critical to endangered to vulnerable. The loss of the species would have been the first feline extinction since the *Smilodon* 10,000 years ago. The species used to be classified as a subspecies of the Eurasian lynx, but is now considered a separate species. Both species occurred together in central Europe in the Pleistocene epoch, being separated by habitat choice. The Iberian lynx is believed to have evolved from *Lynx issiodorensis*.
### Bobcat
*Main article: Bobcat*
The bobcat (*Lynx rufus*) is a North American wild cat. With 13 recognized subspecies, the bobcat is common throughout southern Canada, the continental United States, and northern Mexico. Like the Eurasian lynx, its conservation status is \"least concern.\" The bobcat is an adaptable predator that inhabits deciduous, coniferous, or mixed woodlands, but unlike other *Lynx*, does not depend exclusively on the deep forest, and ranges from swamps and desert lands to mountainous and agricultural areas, its spotted coat serving as camouflage. The population of the bobcat depends primarily on the population of its prey. Nonetheless, the bobcat is often killed by larger predators such as coyotes.
The bobcat resembles other species of the genus *Lynx*, but is on average the smallest of the four. Its coat is variable, though generally tan to grayish brown, with black streaks on the body and dark bars on the forelegs and tail. The ears are black-tipped and pointed, with short, black tufts. There is generally an off-white color on the lips, chin, and underparts. Bobcats in the desert regions of the southwest have the lightest-colored coats, while those in the northern, forested regions have the darkest.
## Behavior and diet {#behavior_and_diet}
The lynx is usually solitary, although a small group of lynx may travel and hunt together occasionally. Mating takes place in the late winter and once a year the female gives birth to between one and four kittens. The gestation time of the lynx is about 70 days. The young stay with the mother for one more winter, a total of around nine months, before moving out to live on their own as young adults. The lynx creates its den in crevices or under ledges. It feeds on a wide range of animals from white-tailed deer, reindeer, roe deer, small red deer, and chamois, to smaller, more usual prey: snowshoe hares, fish, foxes, sheep, squirrels, mice, turkeys and other birds, and goats. It also eats ptarmigans, voles, and grouse.
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# Lynx
## Distribution and habitat {#distribution_and_habitat}
The lynx inhabits high altitude forests with dense cover of shrubs, reeds, and tall grass. Although this cat hunts on the ground, it can climb trees and can swim swiftly, catching fish.
### Europe and Asia {#europe_and_asia}
The Eurasian lynx ranges from central and northern Europe across Asia up to Northern Pakistan and India. In Iran, they live in Mount Damavand area. Since the beginning of the 20th century, the Eurasian lynx was considered extinct in the wild in Slovenia and Croatia. A resettlement project, begun in 1973, has successfully reintroduced lynx to the Slovenian Alps and the Croatian regions of Gorski Kotar and Velebit, including Croatia\'s Plitvice Lakes National Park and Risnjak National Park. In both countries, the lynx is listed as an endangered species and protected by law. The lynx was distributed throughout Japan during Jōmon period; with no paleontological evidence thereafter suggesting extinction at that time.
Several lynx resettlement projects begun in the 1970s have been successful in various regions of Switzerland. Since the 1990s, there have been numerous efforts to resettle the Eurasian lynx in Germany, and since 2000, a small population can now be found in the Harz mountains near Bad Lauterberg.
The lynx is found in the Białowieża Forest in northeastern Poland, and in the northern and western parts of China, particularly the Tibetan Plateau. In Romania, the numbers exceed 2,000, the largest population in Europe outside of Russia, although most experts consider the official population numbers to be overestimated.
The lynx is more common in northern Europe, especially in Norway, Sweden, Estonia, Finland, and the northern parts of Russia. The Swedish population is estimated to be 1200--1500 individuals, spread all over the country, but more common in middle Sweden and in the mountain range. The lynx population in Finland was 1900--2100 individuals in 2008, and the numbers have been increasing every year since 1992. The lynx population in Finland is estimated currently to be larger than ever before. Lynx in Britain were wiped out in the 17th century, but there have been calls to reintroduce them to curb the numbers of deer.
The endangered Iberian lynx lives in southern Spain and formerly in eastern Portugal.`{{Update inline|date=September 2022|reason=See [[Iberian lynx]]. As of today, the range of the Iberian lynx also includes Portugal.}}`{=mediawiki} There is an Iberian lynx reproduction center outside Silves in the Algarve in southern Portugal.
### North America {#north_america}
The two *Lynx* species in North America, Canada lynx and bobcats, are both found in the temperate zone. While the bobcat is common throughout southern Canada, the continental United States and northern Mexico, the Canada lynx is present mainly in boreal forests of Canada and Alaska
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# Location parameter
In statistics, a **location parameter** of a probability distribution is a scalar- or vector-valued parameter $x_0$, which determines the \"location\" or shift of the distribution. In the literature of location parameter estimation, the probability distributions with such parameter are found to be formally defined in one of the following equivalent ways:
- either as having a probability density function or probability mass function $f(x - x_0)$; or
- having a cumulative distribution function $F(x - x_0)$; or
- being defined as resulting from the random variable transformation $x_0 + X$, where $X$ is a random variable with a certain, possibly unknown, distribution. See also `{{Slink||Additive noise}}`{=mediawiki}.
A direct example of a location parameter is the parameter $\mu$ of the normal distribution. To see this, note that the probability density function $f(x | \mu, \sigma)$ of a normal distribution $\mathcal{N}(\mu,\sigma^2)$ can have the parameter $\mu$ factored out and be written as:
$$g(x' = x - \mu | \sigma) = \frac{1}{\sigma \sqrt{2\pi} } \exp\left(-\frac{1}{2}\left(\frac{x'}{\sigma}\right)^2\right)$$ thus fulfilling the first of the definitions given above.
The above definition indicates, in the one-dimensional case, that if $x_0$ is increased, the probability density or mass function shifts rigidly to the right, maintaining its exact shape.
A location parameter can also be found in families having more than one parameter, such as location--scale families. In this case, the probability density function or probability mass function will be a special case of the more general form
$$f_{x_0,\theta}(x) = f_\theta(x-x_0)$$ where $x_0$ is the location parameter, *θ* represents additional parameters, and $f_\theta$ is a function parametrized on the additional parameters.
## Definition
Source:
Let $f(x)$ be any probability density function and let $\mu$ and $\sigma > 0$ be any given constants. Then the function
$g(x| \mu, \sigma)= \frac{1}{\sigma}f\left(\frac{x-\mu}{\sigma}\right)$
is a probability density function.
The location family is then defined as follows:
Let $f(x)$ be any probability density function. Then the family of probability density functions $\mathcal{F} = \{f(x-\mu) : \mu \in \mathbb{R}\}$ is called the location family with standard probability density function $f(x)$, where $\mu$ is called the **location parameter** for the family.
## Additive noise {#additive_noise}
An alternative way of thinking of location families is through the concept of additive noise. If $x_0$ is a constant and *W* is random noise with probability density $f_W(w),$ then $X = x_0 + W$ has probability density $f_{x_0}(x) = f_W(x-x_0)$ and its distribution is therefore part of a location family.
## Proofs
For the continuous univariate case, consider a probability density function $f(x | \theta), x \in [a, b] \subset \mathbb{R}$, where $\theta$ is a vector of parameters. A location parameter $x_0$ can be added by defining:
$$g(x | \theta, x_0) = f(x - x_0 | \theta), \; x \in [a + x_0, b + x_0]$$ it can be proved that $g$ is a p.d.f. by verifying if it respects the two conditions $g(x | \theta, x_0) \ge 0$ and $\int_{-\infty}^{\infty} g(x | \theta, x_0) dx = 1$. $g$ integrates to 1 because:
$$\int_{-\infty}^{\infty} g(x | \theta, x_0) dx = \int_{a + x_0}^{b + x_0} g(x | \theta, x_0) dx = \int_{a + x_0}^{b + x_0} f(x - x_0 | \theta) dx$$ now making the variable change $u = x - x_0$ and updating the integration interval accordingly yields:
$$\int_{a}^{b} f(u | \theta) du = 1$$ because $f(x | \theta)$ is a p.d.f. by hypothesis. $g(x | \theta, x_0) \ge 0$ follows from $g$ sharing the same image of $f$, which is a p.d.f. so its range is contained in $[0, 1]$
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# Larry Wall
**Larry Arnold Wall** (born September 27, 1954) is an American computer programmer, linguist, and author known for creating the Perl programming language and the patch tool.
## Early life and education {#early_life_and_education}
Wall grew up in Los Angeles and Bremerton, Washington. He started higher education at Seattle Pacific University in 1976, majoring in chemistry and music and later pre-medicine. After a hiatus of several years working in the university\'s computing center, he graduated with a bachelor\'s degree in Natural and Artificial Languages.
While in graduate school at the University of California, Berkeley, Wall and his wife were studying linguistics with the intention of finding an unwritten language, perhaps in Africa, and creating a writing system for it. They would then use this new writing system to translate various texts into the language, among them the Bible. For health reasons these plans were cancelled, and they remained in the United States, where Wall instead joined the NASA Jet Propulsion Laboratory after he finished graduate school.
## Career
Wall is the author of the `rn` Usenet client and the widely used `patch` program. He has won the International Obfuscated C Code Contest twice and was the recipient of the first Free Software Foundation Award for the Advancement of Free Software in 1998.
Wall developed the Perl interpreter and language while working for System Development Corporation, which later became part of Burroughs and then Unisys. He is the co-author of *Programming Perl* (often referred to as the *Camel Book* and published by O\'Reilly), which is the definitive resource for Perl programmers; and edited the *Perl Cookbook*. He then became employed full-time by O\'Reilly Media to further develop Perl and write books on the subject.
Wall\'s training as a linguist is apparent in his books, interviews, and lectures. He often compares Perl to a natural language and explains his decisions in Perl\'s design with linguistic rationale. He also often uses linguistic terms for Perl language constructs, so instead of traditional terms such as \"variable\", \"function\", and \"accessor\" he sometimes says \"noun\", \"verb\", and \"topicalizer\".
## Personal life {#personal_life}
Wall is an active member of the New Life, Church of the Nazarene. He also works with his local church for Bible Quizzing for the Nor-Cal district.
Wall\'s Christian faith has influenced some of the terminology of Perl, such as the name itself, a biblical reference to the \"pearl of great price\" (Matthew 13:46). Similar references are the function name *bless*, and the organization of Raku (previously known as Perl 6) design documents with categories such as *apocalypse* and *exegesis*. Wall has also alluded to his faith when speaking at conferences, including at the Perl Conference 3.0 on August 23, 1999
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# Lorisidae
**Lorisidae** (or sometimes **Loridae**) is a family of strepsirrhine primates. The **lorisids** are all slim arboreal animals and comprise the lorises, pottos, and angwantibos. Lorisids live in tropical, central Africa as well as in south and southeast Asia.
## Classification
There are five genera and sixteen species of lorisid.
- Order Primates
- Suborder Strepsirrhini: non-tarsier prosimians
- Infraorder Lemuriformes
- Superfamily Lemuroidea
- Superfamily Lorisoidea
- **Family Lorisidae**
- Subfamily Perodicticinae
- Genus *Arctocebus*, angwantibos
- Genus *Perodicticus*, pottos
- Subfamily Lorisinae
- Genus *Loris*, slender lorises
- Genus *Nycticebus*, slow lorises
- Genus *Xanthonycticebus*, pygmy slow loris
- Family Galagidae: galagos
- Suborder Haplorrhini: tarsiers, monkeys and apes
## Description
Lorisids have a close, woolly fur, which is usually grey or brown, darker on the top side. The eyes are large and face forward. The ears are small and often partially hidden in the fur. The thumbs are opposable and the index finger is short. The second toe of the hind legs has a fine claw for grooming, typical for strepsirrhines. Their tails are short or are missing completely. They grow to a length of 17 to 40 cm and a weight of between 0.3 and 2 kg, depending on the species. Their dental formula is similar to that of lemurs: `{{DentalFormula|upper=2.1.3.3|lower=2.1.3.3}}`{=mediawiki}
## Behavior and ecology {#behavior_and_ecology}
Lorisids are nocturnal and arboreal. Unlike the closely related galagos, lorisids never jump. Some have slow deliberate movements, whilst others can move with some speed across branches. It was previously thought that all lorisids moved slowly, but investigations using red light proved this to be wrong. Nonetheless, even the faster species freeze or move slowly if they hear or see any potential predator. This habit of remaining motionless whilst in danger is successful only because of the leafy environment of their jungle home, which helps to conceal their true position. With their strong hands they clasp at the branches and cannot be removed without significant force. Most lorisids are solitary or live in small family groups.
Slow lorises from southeast Asia produce a secretion from their brachial gland (a scent gland on the upper arm, between the axilla and elbow), that is licked and mixed with their saliva to form a toxin which may be used for defense. The slender lorises from Sri Lanka and South India also possess these brachial glands, but it is uncertain whether they also synthesize the toxin. The potto (*Perodicticus potto*) is thought to lack brachial glands, though it produces similar toxic excretions with its anal glands.
Lorisids have a gestation period of four to six months and give birth to two young. These often clasp themselves to the belly of the mother or wait in nests, while the mother goes to search for food. After three to nine months - depending on the species - they are weaned and are fully mature within 10 to 18 months. The life expectancy of lorises can be to up to 20 years.
Lorisids consume insects, bird eggs and small vertebrates as well as fruits and gums
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# Logrolling
**Logrolling** is the trading of favors, or *quid pro quo*, such as vote trading by legislative members to obtain passage of actions of interest to each legislative member. In organizational analysis, it refers to a practice in which different organizations promote each other\'s agendas, each in the expectation that the other will reciprocate. In an academic context, the *Nuttall Encyclopedia* describes logrolling as \"mutual praise by authors of each other\'s work\". Where intricate tactics or strategy are involved, the process may be called horse trading.
## Concept and origin {#concept_and_origin}
There are three types of logrolling:
- Logrolling in direct democracies: a few individuals vote openly, and votes are easy to trade, rearrange, and observe. Direct democracy is pervasive in representative assemblies and small-government units
- Implicit logrolling: large bodies of voters decide complex issues and trade votes without a formal vote trade (Buchanan and Tullock 1962)
- Distributive logrolling: enables policymakers to achieve their public goals. These policymakers logroll to ensure that their district policies and pork barrel packages are put into practice regardless of whether their policies are actually efficient (Evans 1994 and Buchanan and Tullock 1962).
Distributive logrolling is the most prevalent kind of logrolling found in a democratic system of governance.
*Quid pro quo* sums up the concept of logrolling in the United States\' political process today. Logrolling is the process by which politicians trade support for one issue or piece of legislation in exchange for another politician\'s support, especially by means of legislative votes (Holcombe 2006). If a legislator logrolls, he initiates the trade of votes for one particular act or bill in order to secure votes on behalf of another act or bill. Logrolling means that two parties will pledge their mutual support, so both bills can attain a simple majority. For example, a vote on behalf of a tariff may be traded by a congressman for a vote from another congressman on behalf of an agricultural subsidy to ensure that both acts will gain a majority and pass through the legislature (Shughart 2008). Logrolling cannot occur during presidential elections, where a vast voting population necessitates that individual votes have little political power, or during secret-ballot votes (Buchanan and Tullock 1962). Because logrolling is pervasive in the political process, it is important to understand which external situations determine when, why, and how logrolling will occur, and whether it is beneficial, efficient, or neither.
### Origins
The widest accepted origin is the old custom of neighbors assisting each other with the moving of logs. If two neighbors had cut a lot of timber that needed to be moved, it made more sense for them to work together to roll the logs. In this way, it is similar to a barn-raising where a neighbor comes and helps a family build their barn, and, in turn, that family goes and returns the favor, helping him build his. Here is an example of the term\'s original use:
> \"A family comes to sit in the forest,\" wrote an observer in 1835; \"Their neighbors lay down their employments, shoulder their axes, and come in to the log-rolling. They spend the day in hard labor, and then retire, leaving the newcomers their good wishes, and a habitation.\"
American frontiersman Davy Crockett was one of the first to apply the term to legislation:
> The first known use of the term was by Congressman Davy Crockett, who said on the floor (of the U.S. House of Representatives) in 1835, \"my people don\'t like me to log-roll in their business, and vote away pre-emption rights to fellows in other states that never kindle a fire on their own land.\"
### Choice to logroll {#choice_to_logroll}
Human beings, whether ignorant or informed, rational or irrational, logical or illogical, determine individual and group action through choices. Economics studies these choices, including the choice to logroll, and their particular influence within the market sector (Schwartz 1977). In America, political and economic decisions are usually made by politicians elected to legislative assemblies, and not directly by the citizenry (Buchanan and Tullock 1962). Although legislative votes are recorded and are available to the American public, legislators can exchange their votes on issues they do not care much about for votes on other issues that are more important to their personal agendas (Holcombe 2006). In *The Calculus of Consent*, James M. Buchanan and Gordon Tullock explore the relationship between individual choice in the voting process and in the marketplace, specifically within logrolling. Logrolling vote trades, like any activity within the marketplace, must be mutually beneficial (Buchanan and Tullock 1962).
A vote trade is like a legislative IOU. When a legislator needs a few more votes to acquire a simple majority, he will seek support through a vote exchange. He will promise a fellow legislator an IOU vote for another piece of legislation in return for a vote on his own act or bill. Legislators who logroll within a small body, for example, the U.S. House or Senate, have incentive to honor their IOU votes because they cannot have their reputations tainted if they wish to be effective politicians (Holcombe 2006).
### Logrolling and the role of preference {#logrolling_and_the_role_of_preference}
People have varying preferences, and make decisions at the margin to maximize their utility and improve their welfare. The same is true for legislators, who all enter office with different agendas, passions, and goals. Ideological diversity plays a significant role in the result of a vote and carries with it a significant cost. In addition, legislators will favor interests that offer them the most support. Legislative votes are determined by the intensity of personal preference, desires of constituents, and, ultimately, what will lead to the particular legislator\'s greatest utility. When people have ideologies at opposite ends of the political spectrum, it\'s difficult to ensure a simple majority, so buying a supermajority vote through logrolling may be the most cost effective (Buchanan and Tullock 1962).
In the General Possibility Theorem, Kenneth Arrow argues that if a legislative consensus can be reached through a simple majority, then minimum conditions must be satisfied, and these conditions must provide a superior ranking to any subset of alternative votes (Arrow 1963). A bill must be attractive to a legislator, or else he will not cast his vote for it. A vote, by the pure nature of the voting process, demonstrates explicit interest in whatever is voted upon. In logrolling, a superior ranking means that the marginal benefit of the vote is greater than any alternatives, so exchanging votes is worthwhile. The General Possibility Theorem necessitates that allocating one vote for another must constitute true utility and a sincere vote. Arrow\'s theory may place more restrictions and limitations on an individual voter\'s preferences than Buchanan and Tullock\'s; regardless, individuals will always choose the option they value most.
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# Logrolling
## Concept and origin {#concept_and_origin}
### Logrolling to reach the optimal decision {#logrolling_to_reach_the_optimal_decision}
Decisions reach an optimum only when they are unanimous, when votes are not coerced and everyone has veto power (Buchanan and Tullock 1962). Unanimous votes, however, are not required for the American voting process. This is why some logrolling advocates argue that logrolling must be allowed within a democracy---sometimes there may not be a \"best\" or \"most efficient\" option on a vote.
Logrolling creates a market within which votes are exchanged as a sort of currency, and thus, facilitates the political process that produces the highest valued outcomes (Holcombe 2006). If individual participants recognize the value of their own vote, they are motivated to trade. When methods of trade do not conflict with given standards or ethical procedures, individuals naturally seek mutually advantageous vote trades. An individual may effectually, but imperfectly, \"sell\" his vote on a particular issue to, in return, secure votes from other individuals on behalf of legislation he prefers (Buchanan and Tullock 1962).
Logrolling has one necessary condition: benefits from the public activity must be significantly more concentrated or localized than the costs. In economics, decisions are made at the margin. Logrolling depends on the reality that the marginal benefit (or utility) of at least some elected officials, or the citizenry, will increase when the legislation is passed (Buchanan and Tullock 1962). Any economist will consider the immediate opportunity cost of the logrolling procedure within the legislative body, as well as the external cost of the vote (the cost to enact and see the bill through to fruition).
When transaction costs are low and parties involved are perfectly informed, a mutually beneficial agreement will occur: whoever values the property the highest will end up with it. This is what Ronald H. Coase proposed in his *Theory of Property Rights* in 1960. This theory holds true within the world of economics. In the American system of government, legislators have the incentive to logroll because transaction costs are low. When transaction costs are low, the Coase theorem says that the political marketplace (the decisions of the legislatures) will allocate resources to the highest valued point (Coase 1960).
Typically, logrolling is a mechanism used to gain support for special interest and minority groups. However, because of the ideological mix that already exists within the legislature itself, minority views are often represented, even if only marginally. With low transaction costs, the Coase theorem will come into play. The highest valued outcome is chosen by the legislature, regardless the member\'s ideological stance or political affiliation (Holcombe 2006).
The problem of cyclical majorities may arise with the absence of logrolling. The cyclical majority problem occurs when voters are faced with multiple voting options but cannot choose the option they most prefer, since it is not available. Voters must consider whether the alternative option is closer to their original preference (Bara and Weale 2006). However, when logrolling is allowed, the highest valued outcome is secure without the threat of a cyclical majority. For example, suppose a country road in West Virginia is in disrepair. The local congressman proposes a bill to have the main road in his community resurfaced and paved. The road leads to a town of merely 600 residents. Thus, the other legislators will vote against the measure because the funding is not worthwhile to their constituents. In a logrolling system, the local legislator can use his vote to bargain with his fellow legislators. He will exchange his vote for his fellow legislators\' bills to promote, for instance, the construction of new hospitals and the increase of veteran\'s benefits, in return for their votes to repair the road (Buchanan and Tullock 1962).
### Logrolling: An example {#logrolling_an_example}
Agriculture Tax Vote School Tax Vote Fire Tax Vote
--------- ------------- ------- ------------- -------- ------- ------------- ------- ------- -------------
Tanya \$300 \$200 Y \$150 \$200 N \$100 \$200 N
Alvin \$150 \$200 N \$350 \$200 Y \$150 \$200 N
Rebecca \$100 \$200 N \$50 \$200 N \$225 \$200 Y
Total \$550 \$600 Inefficient \$550 \$600 Inefficient \$475 \$600 Inefficient
: Table 1-1
**Table 1-1** explains another example of logrolling. In the example, we have three individuals: Tanya, Alvin, and Rebecca. Tanya favors subsidies for agriculture, Alvin favors school construction, and Rebecca favors the recruitment of more firefighters. It seems as if the proposals are doomed to fail because each is opposed by a majority of voters. Even so, this may not be the outcome. Tanya may visit Rebecca and tell her that she will vote for Rebecca\'s bill to recruit more firefighters so long as Rebecca votes for her policy, subsidies for agriculture, in return. Now both proposals will win because they have gained a simple majority (**Table 1-2**), even though in reality the subsidy is opposed by two of the three voters. It\'s easy to see the Coase theorem at work in examples like this. Here, transaction costs are low, so mutually beneficial agreements are found, and the person who values the service the most will hold it (Browning and Browning 1979). Still, outcomes may be inefficient. \|last1= \|first1= \|last2=
### Efficient logrolling {#efficient_logrolling}
Agriculture Tax Vote School Tax Vote Fire Tax Vote
--------- ------------- ------- ----------- -------- ------- ------------- ------- ------- -----------
Tanya \$350 \$200 Y \$150 \$200 N \$100 \$200 Y
Alvin \$150 \$200 N \$350 \$200 Y \$200 \$200 N
Rebecca \$125 \$200 Y \$50 \$200 N \$300 \$200 Y
Example \$625 \$600 Efficient \$550 \$600 Inefficient \$600 \$600 Efficient
: Table 1-2
If the sum of the total benefit of the legislation for all the voters is less than the cost of the legislation itself, the legislation is inefficient. Despite its inefficiency, however, it still may pass if logrolling is permitted. If Tanya trades her vote to recruit more firemen to Rebecca in exchange for Rebecca\'s vote in favor of agriculture subsidies, a mutually beneficial agreement will be reached, even though the outcome is inefficient. On the other hand, if the sum of the total benefit of the legislation for all voters is greater than the cost of the legislation itself, the legislation is efficient. If Tanya trades her vote once again for Rebecca\'s vote, both parties will reach a mutually beneficial agreement and an efficient outcome.
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# Logrolling
## Concept and origin {#concept_and_origin}
### Minimum winning coalitions and logrolling {#minimum_winning_coalitions_and_logrolling}
A minimum winning coalition is the smallest number of votes required to win the passage of a piece of legislation. Minimum winning coalitions demonstrate the importance of logrolling within a democracy, because the minimal winning coalition may be overthrown with the sway of a single vote. As previously mentioned, coalitions will buy a supermajority of votes if the support for the proposed legislation sways. If a legislator logrolls a few votes beyond the minimal winning coalition to his side, he will ensure that the final vote will be in favor of his legislation. In a way, vote trading does combine positions on distinct issues to form single legislative votes and packages (Stratmann 1992). Logrolled votes transcend affiliations and party lines and become feasible outcomes preferred by a majority or winning coalition (Schwartz 1977).
### Logrolling in real politics {#logrolling_in_real_politics}
A problem in research is that it is impossible to identify vote trading directly within the House of Representatives or the Senate because roll call votes on specific goods are not observed (Irwin and Kroszner 1996). However, examples of refurbished bills can shed some light on the working-out of logrolling within the legislature. For example, in 1930, the Smoot-Hawley tariff, the second-highest tariff in U.S. history, passed the House and Senate. Congress voted to increase tariffs exponentially, which worked to push the United States from a stagnant recession into a plummeting depression (Irwin and Kroszner 1996). Strict party line votes suggest that partisan polarization in 1929 prevented the Smoot-Hawley bill from passing through Congress. The bill, however, was revamped, and legislators used logrolling to pass it through both chambers in 1930.
Omnibus bills can be an alternative market to logrolling. Various clauses are added to a bill to satisfy all involved parties sufficiently. However, large bills, like the Patient Protection and Affordable Care Act, require an in depth knowledge of 1,000 plus pages. Many sections of these types of bills are initially opposed but are later supported because of special benefit clauses (Evans 1994).
Because logrolling allows special-interest groups a voice in the political process, programs that benefit a minority group can get the approval of a majority. However, this may not be in the best interest of the majority. Special-interest groups typically do not represent the typical voter, but rather, small branches of minority ideologies (Holcombe 2006). Voting results with or without logrolling will differ only if the minority is more interested in an issue than the majority, enough to separate the marginal voters from the majority. Studies show that lobbying and political pressure exerted by special-interest groups are not atypical behavior in a modern democracy (Buchanan and Tullock 1962). Conditions imposed upon the social choice of the legislature imply a more severe restriction on the individual voter\'s preferences than the theory of logrolling presented by Buchanan and Tullock and presumed by Arrow\'s General Possibility Theory (Wilson 1969).
Critics reproach members of Congress for protecting their own electoral interests at the expense of the general welfare. Congressmen tend to distribute specialized benefits at a great cost and ignore the particular costs the legislation bears upon the taxpayers (Evans 1994). Legislators, who seek their personal benefit via logrolling even though it may not benefit those who must pay for the measure, are known as maximizers. Maximizers only take into account their personal cost and electability, instead of the effects of their actions on other parties involved. In short, other taxpayers will pay for the policy even if it does not affect them (Buchanan and Tullock 1962). Initially, maximizers will encourage other legislators to have the same selfish behavior because significant gains can be accrued in the short run. Buchanan and Tullock state that within a system of maximizers, all individuals are worse off than if they had all adopted Kantian norms of behavior.
Legislative bodies can expect higher government spending and taxation when logrolling is allowed to flourish. Logrolling does not imply excessive spending; members can trade tax reductions just as easily as they can trade pork barrel policies. The problem is that benefits of a vote only reach a particular portion of the population, while the tax costs that pay for the vote are spread throughout the entire populace, especially when the act depends on revenue from sales or income taxes. Benefits are concentrated in localities, and the costs are dispersed throughout the nation. Committee members can thus exploit pork barrel projects for electoral purposes. The citizenry is seen as a \"common pool,\" used to finance projects through taxes. Somehow the citizens end up paying higher taxes than those who are not in a logroll system (Dalenberg and Duffy-Deno 1991 and Gilligan and Matsusaka 1995). In a system where logrolling is permitted, a third party may bear the cost of the project, rather than those who receive the full benefit of the legislation. This is always inefficient.
The logic of collective action shows that votes for bills are motivated by politicians and are determined by a simple majority (Olson 1971). Politicians are in the game to win it. Collective effort explains why farms acquire government subsidies at the expense of millions of consumers and why those in the textile industry benefit at the expense of clothing buyers (Shughart 2008). Congressional committees ensure that each committee leader will create legislative coalitions to push his policies to fruition. Thus, ceteris paribus, members who receive such projects, are likely to vote in support of their leader\'s wishes (Evans 1994).
Policymakers and congressmen have goals of power, and making their own mark in public policy, not pure aims of reelection (Dodd 1977). Reelection does play a great part in the legislative process as a condition to achieving any other political goal. Thus, logrolling can be a powerful tool for committee chairs, who control the voting agendas (Evans 1994). While committee leaders create the supermajority, they try to achieve their personal goals and help a bare majority of members achieve theirs. A skilled policy-oriented committee leader often seeks to exploit the goals of other members in order to construct legislation he or she will prefer (Arnold 1979 and Strahan 1989).
#### Wafelijzerpolitiek
*Wafelijzerpolitiek* (lit. waffle iron politics) is a form of logrolling used in Belgium. Until the split of the unitary Belgium in several parts, the unitary government decided on the funds given to big projects. As there were usually two opposing groups of about equal size in Belgium, this norm resulted in the approval of two equally sized projects in the two parts of the country, with the funds given to the two projects being equal. As a result, one project was always overfunded. Many see *wafelijzerpolitiek* as the source of Belgium\'s high debt.
After the first state reformation in 1988, many big projects were decided regionally, so the number of *wafelijzer* projects went down. There are still some things that fall under the supervision of the federal government, where *wafelijzerpolitiek* still happens. One example is the Belgian railway network.
Another result of the *wafelijzerpolitiek* is the big useless works. As Flanders is a part of Belgium with many ports (e.g., big ports in Antwerp and Zeebrugge), for every investment in Flemish waterways there had to be an investment in Walloon waterways. Some results are the Ronquières inclined plane and the Strépy-Thieu boat lift.
### Simple referendums {#simple_referendums}
In a referendum on a simple issue, the voter cannot easily trade his own vote for a vote on a reciprocal favor. This is because first, he is unsure as to when and how the other issues will be voted upon, and second, he and his immediate neighbors represent a fraction of the total electorate. Thus, trading may not be worthwhile (Buchanan and Tullock 1962).
Vote trading under a democratic, majority-rule institution is sometimes considered morally reprehensible behavior. However, the only perfect solution to rid the political system of distributive logrolling would be to develop a specific formula to weigh the costs and benefits of legislation perfectly and only allow efficient programs to be enacted (This is inconceivable. Therefore, logrolling must occur, but only by observing the constitutional rules that have been laid down as safeguards of democracy (Buchanan and Tullock 1962).
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# Logrolling
## Concept and origin {#concept_and_origin}
### Summary
The reality is that transaction costs are high, and most voters, who are ignorant of political issues and the political process, see little incentive to attempt to influence their local legislator\'s political decisions (Holcombe 2006). It is also difficult for voters to be informed of their legislator\'s voting habits. Because of this, distributive logrolling will occur in democratic systems. Furthermore, it is the responsibility of the legislator to measure the costs and benefits of legislation and determine what is most efficient for his constituents. Logrolling will occur only if members of the legislature fail to gather enough votes for the passage of specific legislation. In essence, logrolling is a legal way to manipulate voter preference toward either an efficient or an inefficient outcome that would not otherwise be enacted (Browning 1979).
## Legality
Logrolling is illegal in numerous jurisdictions, and in some instances is a crime. Sophisticated computational techniques have been developed for the detection and prosecution of this crime.
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# Logrolling
## Other usages {#other_usages}
*Spy Magazine* ran a feature entitled \"Logrolling in Our Time\" that cited suspicious or humorous examples of mutually admiring book jacket blurbs by pairs of authors. *Private Eye* magazine regularly draws attention to alleged logrolling by authors in \"books of the year\" features published by British newspapers and magazines.`{{Full citation needed|date=July 2022}}`{=mediawiki}
Log rolling or a hodgepodge legislation in the Philippines also refers to any legislation that have several subjects on unrelated matters combined together. It is expressed in Article 6 Section 26.1 of the 1987 Philippine Constitution as a guarantee to prevent surprise or fraud from the legislature
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# Playing by ear
*Playing by Ear* }} **Playing** or **learning by ear** is the ability of a performing musician to reproduce a piece of music they have heard, without having seen it notated in any form of sheet music. It is considered to be a desirable skill among musical performers, especially for those that play in a musical tradition where notating music is not the norm***.***
It is a misconception that musicians who play by ear do not have or do not require musical education, or have no theoretical understanding of the music they are playing.
Playing by ear is often also used to refer more generally to making music without using musical notation, perhaps using (elements of) improvisation and instant composition.
Blues, pop, jazz, and many forms of non-western music are fundamentally rooted in the concept of playing by ear, where musical compositions are passed down from generation to generation. In this respect, playing by ear can also be seen as a music-specific example of oral tradition.
The concept of playing by ear has led to the development of the idiom to play by ear or \"play *it* by ear.\"
## Method
One learns a piece of music by ear by repeatedly listening to it performed, memorizing it, and then trying to recreate what one has heard. This requires the use of several related skills such as ear training, musical perception, tonal memory, audiation, music theory, techniques, and knowledge about the culture of the music one is trying to learn. As such, learning to play by ear involves training those skills as well.
To practice playing music by ear, music teachers often have a student listen to short musical examples which the student will have to write out in musical notation, play back on an instrument, sing, or describe using note names or a solfège system. Musicians will also train their playing by ear skills by taking recordings of full songs and pieces, figuring out the notes by ear, and either transcribing or memorizing them. According to studies playing by ear is associated with a higher level of creativity and musical intelligence.
Audiation is a vital skill for playing music by ear. Edwin Gordon, originator of the term, describes audiation as: \"the foundation of musicianship. It takes place when we hear and comprehend music for which the sound is no longer or may never have been present.\" It is often described as the ability to hear music in your head. In this sense, audiation is to music what thought is to language.
Learning to play by ear, in the sense of making music without notation, is often compared to learning to speak a language. When sufficiently mastered, playing music by ear should be as comfortable and easy as having a conversation. We speak and react to what we hear, without having to think too deeply about every word we use. The same would be true when playing by ear. A musician can produce a sound at the same time they think of it, without having to consider every separate note they play.
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# Playing by ear
## Existence in musical traditions {#existence_in_musical_traditions}
In most instances, traditions in which music is primarily learned by ear do not use musical notation in any form. Some examples are early Blues guitarists and pianists, Romani fiddlers, and folk music guitarists. One particularly prominent example is Indian classical music: the teaching methods of its two major strands (*Hindustani* and *Carnatic*) are almost exclusively oral.
### In the West {#in_the_west}
Historically, the Western classical music tradition has been based on the process of learning new pieces from musical notation, and hence playing by ear has a lower importance in musical training. Before the widespread use of sheet music, much early medieval Western music was learnt by ear, particularly in monasteries.
However, many teaching methods in this tradition incorporate playing by ear in some form. For instance, \"ear training\" courses are a standard part of conservatory or college music programs (including use of Solfège), and the Suzuki method, which incorporates a highly developed focus on playing by ear from a very young age.
In the West, learning by ear is also used heavily in the genres of folk music, blues, rock, pop, funk, reggae, and jazz. While most professional musicians currently active in these genres are capable of reading musical notation, playing by ear is still widely practiced for a number of reasons. Among those are ease and speed of learning songs, flexibility while improvising and playing variations, and working around the limitations of western musical notation.
Since western musical notation was developed for classical music, musicians sometimes run into issues when musical expressions are commonly used in the genre they are performing but not in classical music. Examples of this are percussion instruments in Afro-Cuban music, where different strokes and techniques are used to produce different tones and timbres, or improvised music like jazz and classical Indian music, where large parts of the composition consists of guidelines for improvisation. Western musical notation can be ill-suited for these situations, and although supplements to musical notation can be invented to try to accommodate this, playing by ear and oral learning are often preferred because of readability, ease, and tradition
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# Linear equation
In mathematics, a **linear equation** is an equation that may be put in the form $a_1x_1+\ldots+a_nx_n+b=0,$ where $x_1,\ldots,x_n$ are the variables (or unknowns), and $b,a_1,\ldots,a_n$ are the coefficients, which are often real numbers. The coefficients may be considered as parameters of the equation and may be arbitrary expressions, provided they do not contain any of the variables. To yield a meaningful equation, the coefficients $a_1, \ldots, a_n$ are required to not all be zero.
Alternatively, a linear equation can be obtained by equating to zero a linear polynomial over some field, from which the coefficients are taken.
The solutions of such an equation are the values that, when substituted for the unknowns, make the equality true.
In the case of just one variable, there is exactly one solution (provided that $a_1\ne 0$). Often, the term *linear equation* refers implicitly to this particular case, in which the variable is sensibly called the *unknown*.
In the case of two variables, each solution may be interpreted as the Cartesian coordinates of a point of the Euclidean plane. The solutions of a linear equation form a line in the Euclidean plane, and, conversely, every line can be viewed as the set of all solutions of a linear equation in two variables. This is the origin of the term *linear* for describing this type of equation. More generally, the solutions of a linear equation in `{{mvar|n}}`{=mediawiki} variables form a hyperplane (a subspace of dimension `{{math|''n'' − 1}}`{=mediawiki}) in the Euclidean space of dimension `{{mvar|n}}`{=mediawiki}.
Linear equations occur frequently in all mathematics and their applications in physics and engineering, partly because non-linear systems are often well approximated by linear equations.
This article considers the case of a single equation with coefficients from the field of real numbers, for which one studies the real solutions. All of its content applies to complex solutions and, more generally, to linear equations with coefficients and solutions in any field. For the case of several simultaneous linear equations, see system of linear equations.
## One variable {#one_variable}
A linear equation in one variable `{{Mvar|x}}`{=mediawiki} can be written as $ax+b=0,$ with $a\neq 0$.
The solution is $x=-\frac ba$.
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# Linear equation
## Two variables {#two_variables}
A linear equation in two variables `{{mvar|x}}`{=mediawiki} and `{{mvar|y}}`{=mediawiki} can be written as $ax+by+c=0,$ where `{{mvar|a}}`{=mediawiki} and `{{mvar|b}}`{=mediawiki} are not both `{{math|0}}`{=mediawiki}.
If `{{mvar|a}}`{=mediawiki} and `{{mvar|b}}`{=mediawiki} are real numbers, it has infinitely many solutions.
### Linear function {#linear_function}
If `{{math|''b'' ≠ 0}}`{=mediawiki}, the equation
$$ax+by+c=0$$ is a linear equation in the single variable `{{mvar|y}}`{=mediawiki} for every value of `{{mvar|x}}`{=mediawiki}. It therefore has a unique solution for `{{mvar|y}}`{=mediawiki}, which is given by
$$y=-\frac ab x-\frac cb.$$
This defines a function. The graph of this function is a line with slope $-\frac ab$ and `{{mvar|y}}`{=mediawiki}-intercept $-\frac cb.$ The functions whose graph is a line are generally called *linear functions* in the context of calculus. However, in linear algebra, a linear function is a function that maps a sum to the sum of the images of the summands. So, for this definition, the above function is linear only when `{{math|1=''c'' = 0}}`{=mediawiki}, that is when the line passes through the origin. To avoid confusion, the functions whose graph is an arbitrary line are often called *affine functions*, and the linear functions such that `{{math|1=''c'' = 0}}`{=mediawiki} are often called *linear maps*.
### Geometric interpretation {#geometric_interpretation}
Each solution `{{math|(''x'', ''y'')}}`{=mediawiki} of a linear equation
$$ax+by+c=0$$ may be viewed as the Cartesian coordinates of a point in the Euclidean plane. With this interpretation, all solutions of the equation form a line, provided that `{{mvar|a}}`{=mediawiki} and `{{mvar|b}}`{=mediawiki} are not both zero. Conversely, every line is the set of all solutions of a linear equation.
The phrase \"linear equation\" takes its origin in this correspondence between lines and equations: a *linear equation* in two variables is an equation whose solutions form a line.
If `{{math|''b'' ≠ 0}}`{=mediawiki}, the line is the graph of the function of `{{mvar|x}}`{=mediawiki} that has been defined in the preceding section. If `{{math|1=''b'' = 0}}`{=mediawiki}, the line is a *vertical line* (that is a line parallel to the `{{mvar|y}}`{=mediawiki}-axis) of equation $x=-\frac ca,$ which is not the graph of a function of `{{mvar|x}}`{=mediawiki}.
Similarly, if `{{math|''a'' ≠ 0}}`{=mediawiki}, the line is the graph of a function of `{{mvar|y}}`{=mediawiki}, and, if `{{math|1=''a'' = 0}}`{=mediawiki}, one has a horizontal line of equation $y=-\frac cb.$
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# Linear equation
## Two variables {#two_variables}
### Equation of a line {#equation_of_a_line}
There are various ways of defining a line. In the following subsections, a linear equation of the line is given in each case.
#### Slope--intercept form or Gradient-intercept form {#slopeintercept_form_or_gradient_intercept_form}
A non-vertical line can be defined by its slope `{{mvar|m}}`{=mediawiki}, and its `{{mvar|y}}`{=mediawiki}-intercept `{{math|''y''{{sub|0}}}}`{=mediawiki} (the `{{mvar|y}}`{=mediawiki} coordinate of its intersection with the `{{mvar|y}}`{=mediawiki}-axis). In this case, its *linear equation* can be written
$$y=mx+y_0.$$
If, moreover, the line is not horizontal, it can be defined by its slope and its `{{mvar|x}}`{=mediawiki}-intercept `{{math|''x''{{sub|0}}}}`{=mediawiki}. In this case, its equation can be written
$$y=m(x-x_0),$$ or, equivalently,
$$y=mx-mx_0.$$
These forms rely on the habit of considering a nonvertical line as the graph of a function. For a line given by an equation
$$ax+by+c = 0,$$ these forms can be easily deduced from the relations
$$\begin{align}
m&=-\frac ab,\\
x_0&=-\frac ca,\\
y_0&=-\frac cb.
\end{align}$$
#### Point--slope form or Point-gradient form {#pointslope_form_or_point_gradient_form}
A non-vertical line can be defined by its slope `{{mvar|m}}`{=mediawiki}, and the coordinates $x_1, y_1$ of any point of the line. In this case, a linear equation of the line is
$$y=y_1 + m(x-x_1),$$ or
$$y=mx +y_1-mx_1.$$
This equation can also be written
$$y-y_1=m(x-x_1)$$ to emphasize that the slope of a line can be computed from the coordinates of any two points.
#### Intercept form {#intercept_form}
A line that is not parallel to an axis and does not pass through the origin cuts the axes into two different points. The intercept values `{{math|''x''{{sub|0}}}}`{=mediawiki} and `{{math|''y''{{sub|0}}}}`{=mediawiki} of these two points are nonzero, and an equation of the line is
$$\frac{x}{x_0} + \frac{y}{y_0} = 1.$$ (It is easy to verify that the line defined by this equation has `{{math|''x''{{sub|0}}}}`{=mediawiki} and `{{math|''y''{{sub|0}}}}`{=mediawiki} as intercept values).
#### Two-point form {#two_point_form}
Given two different points `{{math|(''x''{{sub|1}}, ''y''{{sub|1}})}}`{=mediawiki} and `{{math|(''x''{{sub|2}}, ''y''{{sub|2}})}}`{=mediawiki}, there is exactly one line that passes through them. There are several ways to write a linear equation of this line.
If `{{math|''x''{{sub|1}} ≠ ''x''{{sub|2}}}}`{=mediawiki}, the slope of the line is $\frac{y_2 - y_1}{x_2 - x_1}.$ Thus, a point-slope form is
$$y - y_1 = \frac{y_2 - y_1}{x_2 - x_1} (x - x_1).$$
By clearing denominators, one gets the equation
$$(x_2 - x_1)(y - y_1) - (y_2 - y_1)(x - x_1)=0,$$ which is valid also when `{{math|1=''x''{{sub|1}} = ''x''{{sub|2}}}}`{=mediawiki} (to verify this, it suffices to verify that the two given points satisfy the equation).
This form is not symmetric in the two given points, but a symmetric form can be obtained by regrouping the constant terms:
$$(y_1-y_2)x + (x_2-x_1)y + (x_1y_2 - x_2y_1) =0$$ (exchanging the two points changes the sign of the left-hand side of the equation).
#### Determinant form {#determinant_form}
The two-point form of the equation of a line can be expressed simply in terms of a determinant. There are two common ways for that.
The equation $(x_2 - x_1)(y - y_1) - (y_2 - y_1)(x - x_1)=0$ is the result of expanding the determinant in the equation
$$\begin{vmatrix}x-x_1&y-y_1\\x_2-x_1&y_2-y_1\end{vmatrix}=0.$$
The equation $(y_1-y_2)x + (x_2-x_1)y + (x_1y_2 - x_2y_1)=0$ can be obtained by expanding with respect to its first row the determinant in the equation
$$\begin{vmatrix}
x&y&1\\
x_1&y_1&1\\
x_2&y_2&1
\end{vmatrix}=0.$$
Besides being very simple and mnemonic, this form has the advantage of being a special case of the more general equation of a hyperplane passing through `{{mvar|n}}`{=mediawiki} points in a space of dimension `{{math|''n'' − 1}}`{=mediawiki}. These equations rely on the condition of linear dependence of points in a projective space.
## More than two variables {#more_than_two_variables}
A linear equation with more than two variables may always be assumed to have the form
$$a_1 x_1 + a_2 x_2 + \cdots + a_n x_n + b=0.$$
The coefficient `{{mvar|b}}`{=mediawiki}, often denoted `{{math|''a''{{sub|0}}}}`{=mediawiki} is called the *constant term* (sometimes the *absolute term* in old books). Depending on the context, the term *coefficient* can be reserved for the `{{math|''a''{{sub|''i''}}}}`{=mediawiki} with `{{math|''i'' > 0}}`{=mediawiki}.
When dealing with $n=3$ variables, it is common to use $x,\; y$ and $z$ instead of indexed variables.
A solution of such an equation is a `{{mvar|n}}`{=mediawiki}-tuple such that substituting each element of the tuple for the corresponding variable transforms the equation into a true equality.
For an equation to be meaningful, the coefficient of at least one variable must be non-zero. If every variable has a zero coefficient, then, as mentioned for one variable, the equation is either *inconsistent* (for `{{mvar|''b'' ≠ 0}}`{=mediawiki}) as having no solution, or all `{{nowrap|{{mvar|n}}-tuples}}`{=mediawiki} are solutions.
The `{{mvar|n}}`{=mediawiki}-tuples that are solutions of a linear equation in `{{nowrap|{{mvar|n}} variables}}`{=mediawiki} are the Cartesian coordinates of the points of an `{{math|(''n'' − 1)}}`{=mediawiki}-dimensional hyperplane in an `{{nowrap|{{mvar|n}}-dimensional}}`{=mediawiki} Euclidean space (or affine space if the coefficients are complex numbers or belong to any field). In the case of three variables, this hyperplane is a plane.
If a linear equation is given with `{{math|''a''{{sub|''j''}} ≠ 0}}`{=mediawiki}, then the equation can be solved for `{{math|''x''{{sub|''j''}}}}`{=mediawiki}, yielding
$$x_j = -\frac b{a_j} -\sum_{i\in \{1,\ldots,n\}, i\ne j} \frac {a_i}{a_j}x_i .$$ If the coefficients are real numbers, this defines a real-valued function of `{{mvar|n}}`{=mediawiki} real variables
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# Limousine liberal
**Limousine liberal** and **latte liberal** are pejorative U.S. political terms used to illustrate perceived hypocritical behavior by affluent political liberals and other left-leaning people of upper class or upper middle class status. Related terms are Champagne socialist, silver-spoon socialist, Mercedes Marxist, and Red Nobility.
## Formation and early use {#formation_and_early_use}
### Procaccino campaign {#procaccino_campaign}
Democratic New York City mayoral hopeful Mario Procaccino coined the term \"limousine liberal\" to characterize incumbent Mayor John Lindsay and his wealthy Manhattan backers during a heated 1969 campaign. Historian David Callahan says that Procaccino:
It was a populist and producerist epithet, carrying an implicit accusation that the people it described were insulated from all negative consequences of their programs purported to benefit the poor and that the costs and consequences of such programs would be borne in the main by working class or lower middle class people who were not so poor as to be beneficiaries themselves. In particular, Procaccino criticized Lindsay for favoring unemployed minorities, ex. blacks and Hispanics, over working-class white ethnics.
One Procaccino campaign memo criticized \"rich super-assimilated people who live on Fifth Avenue and maintain some choice mansions outside the city and have no feeling for the small middle class shopkeeper, home owner, etc. They preach the politics of confrontation and condone violent upheaval in society because they are not touched by it and are protected by their courtiers\". *The Independent* later stated that \"Lindsay came across as all style and no substance, a \'limousine liberal\' who knew nothing of the concerns of the same \'silent majority\' that was carrying Richard Nixon to the White House at the very same time.\"
### Desegregation
After the U.S. Supreme Court ruled against school integration delays in *Alexander v. Holmes County Board of Education*, former Alabama Governor George Wallace denounced the court\'s decision and called the Justices \"limousine hypocrites\". Wallace continued this line of attack when he ran for governor again in 1970, as Steve Fraser notes:`{{blockquote|[H]e railed against "rich folks" in their country clubs and "big old houses" drinking "those martinis with their little fingers up in the air" who were calling for integrated schools. "And guess where their children go to school. They go to lily white private school. They've bought above it all."<ref>{{cite book|last=Fraser|first=Steve|title=The Limousine Liberal: How an Incendiary Image United the Right and Fractured America|year=2016|publisher=Basic Books|url=https://books.google.com/books?id=cpzSDQAAQBAJ&pg=PA136|page=136|isbn=978-0465055661}}</ref>}}`{=mediawiki}
## Later use {#later_use}
*The New York Observer* applied the term to 2008 Democratic presidential candidate John Edwards who paid \$400 (`{{Inflation|US|400|2007|fmt=eq|r=-1}}`{=mediawiki}) for a haircut and, according to the newspaper, \"lectures about poverty while living in gated opulence\".
Civil rights leader Al Sharpton used the term *latte liberal* to criticize (mostly white and high-income) left-leaning people \"sit\[ing\] around the Hamptons\" who advocated for the defund the police movement and ignored the concerns of African-Americans that suffer under high crime rates and rely on a strong police force
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# Longitude
thumb\|upright=0.9\|right\|A graticule on the Earth as a sphere or an ellipsoid. The lines from pole to pole are lines of constant longitude, or meridians. The circles parallel to the Equator are circles of constant latitude, or parallels. The graticule shows the latitude and longitude of points on the surface. In this example, meridians are spaced at 6° intervals and parallels at 4° intervals. `{{longlat}}`{=mediawiki}`{{Geodesy|notshowfig=1}}`{=mediawiki}
**Longitude** (`{{IPAc-en|ˈ|l|ɒ|n|dʒ|ᵻ|tj|uː|d}}`{=mediawiki}, `{{small|AU and UK also}}`{=mediawiki} `{{IPAc-en|ˈ|l|ɒ|ŋ|ɡ|ᵻ|-}}`{=mediawiki}) is a geographic coordinate that specifies the east-west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek letter lambda (λ). Meridians are imaginary semicircular lines running from pole to pole that connect points with the same longitude. The prime meridian defines 0° longitude; by convention the International Reference Meridian for the Earth passes near the Royal Observatory in Greenwich, south-east London on the island of Great Britain. Positive longitudes are east of the prime meridian, and negative ones are west.
Because of the Earth\'s rotation, there is a close connection between longitude and time measurement. Scientifically precise local time varies with longitude: a difference of 15° longitude corresponds to a one-hour difference in local time, due to the differing position in relation to the Sun. Comparing local time to an absolute measure of time allows longitude to be determined. Depending on the era, the absolute time might be obtained from a celestial event visible from both locations, such as a lunar eclipse, or from a time signal transmitted by telegraph or radio. The principle is straightforward, but in practice finding a reliable method of determining longitude took centuries and required the effort of some of the greatest scientific minds.
A location\'s north-south position along a meridian is given by its *latitude*, which is approximately the angle between the equatorial plane and the normal from the ground at that location.
Longitude is generally given using the geodetic normal or the gravity direction. The **astronomical longitude** can differ slightly from the ordinary longitude because of *vertical deflection*, small variations in Earth\'s gravitational field (see astronomical latitude).
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# Longitude
## History
The concept of longitude was first developed by ancient Greek astronomers. Hipparchus (2nd century BC) used a coordinate system that assumed a spherical Earth, and divided it into 360° as we still do today. His prime meridian passed through Alexandria. He also proposed a method of determining longitude by comparing the local time of a lunar eclipse at two different places, thus demonstrating an understanding of the relationship between longitude and time.`{{r|Dicks|p=11}}`{=mediawiki} Claudius Ptolemy (2nd century AD) developed a mapping system using curved parallels that reduced distortion. He also collected data for many locations, from Britain to the Middle East. He used a prime meridian through the Canary Islands, so that all longitude values would be positive. While Ptolemy\'s system was sound, the data he used were often poor, leading to a gross over-estimate (by about 70%) of the length of the Mediterranean.
After the fall of the Roman Empire, interest in geography greatly declined in Europe. Hindu and Muslim astronomers continued to develop these ideas, adding many new locations and often improving on Ptolemy\'s data. For example, al-Battānī used simultaneous observations of two lunar eclipses to determine the difference in longitude between Antakya and Raqqa with an error of less than 1°. This is considered to be the best that can be achieved with the methods then available: observation of the eclipse with the naked eye, and determination of local time using an astrolabe to measure the altitude of a suitable \"clock star\".
In the later Middle Ages, interest in geography revived in the west, as travel increased, and Arab scholarship began to be known through contact with Spain and North Africa. In the 12th century, astronomical tables were prepared for a number of European cities, based on the work of al-Zarqālī in Toledo. The lunar eclipse of September 12, 1178 was used to establish the longitude differences between Toledo, Marseilles, and Hereford.
Christopher Columbus made two attempts to use lunar eclipses to discover his longitude, the first in Saona Island, on 14 September 1494 (second voyage), and the second in Jamaica on 29 February 1504 (fourth voyage). It is assumed that he used astronomical tables for reference. His determinations of longitude showed large errors of 13° and 38° W respectively. Randles (1985) documents longitude measurement by the Portuguese and Spanish between 1514 and 1627 both in the Americas and Asia. Errors ranged from 2° to 25°.
The telescope was invented in the early 17th century. Initially an observation device, developments over the next half century transformed it into an accurate measurement tool. The pendulum clock was patented by Christiaan Huygens in 1657 and gave an increase in accuracy of about 30 fold over previous mechanical clocks. These two inventions would revolutionise observational astronomy and cartography.
On land, the period from the development of telescopes and pendulum clocks until the mid-18th century saw a steady increase in the number of places whose longitude had been determined with reasonable accuracy, often with errors of less than a degree, and nearly always within 2° to 3°. By the 1720s errors were consistently less than 1°. At sea during the same period, the situation was very different. Two problems proved intractable; the first was the need of a navigator for immediate results, and the second was the marine environment. Making accurate observations in an ocean swell is much harder than on land, and pendulum clocks do not work well in these conditions.
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# Longitude
## History
### The Chronometer {#the_chronometer}
thumb\|upright=1.2\|The clockwork in John Harrison\'s H4 marine chronometer on display at the Royal Observatory, Greenwich In response to the problems of navigation, a number of European maritime powers offered prizes for a method to determine longitude at sea. The best-known of these is the Longitude Act passed by the British parliament in 1714. It offered two levels of rewards, for solutions within 1° and 0.5°. Rewards were given for two solutions: lunar distances, made practicable by the tables of Tobias Mayer developed into an nautical almanac by the Astronomer Royal Nevil Maskelyne; and for the chronometers developed by the Yorkshire carpenter and clock-maker John Harrison. Harrison built five chronometers over more than three decades. This work was supported and rewarded with thousands of pounds from the Board of Longitude, but he fought to receive money up to the top reward of £20,000, finally receiving an additional payment in 1773 after the intervention of Parliament.`{{r|"Siegel"|p=26}}`{=mediawiki} It was some while before either method became widely used in navigation. In the early years, chronometers were very expensive, and the calculations required for lunar distances were still complex and time-consuming. Lunar distances came into general use after 1790. Chronometers had the advantages that both the observations and the calculations were simpler, and as they became cheaper in the early 19th century they started to replace lunars, which were seldom used after 1850.
The first working telegraphs were established in Britain by Wheatstone and Cooke in 1839, and in the US by Morse in 1844. It was quickly realised that the telegraph could be used to transmit a time signal for longitude determination. The method was soon in practical use for longitude determination, especially in North America, and over longer and longer distances as the telegraph network expanded, including western Europe with the completion of transatlantic cables. The United States Coast Survey, renamed the United States Coast and Geodetic Survey in 1878, was particularly active in this development, and not just in the United States. The Survey established chains of mapped locations through Central and South America, and the West Indies, and as far as Japan and China in the years 1874--90. This contributed greatly to the accurate mapping of these areas.
While mariners benefited from the accurate charts, they could not receive telegraph signals while under way, and so could not use the method for navigation. This changed when wireless telegraphy (radio) became available in the early 20th century. Wireless time signals for the use of ships were transmitted from Halifax, Nova Scotia, starting in 1907 and from the Eiffel Tower in Paris from 1910. These signals allowed navigators to check and adjust their chronometers frequently.
Radio navigation systems came into general use after World War II. The systems all depended on transmissions from fixed navigational beacons. A ship-board receiver calculated the vessel\'s position from these transmissions. They allowed accurate navigation when poor visibility prevented astronomical observations, and became the established method for commercial shipping until replaced by GPS in the early 1990s.
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# Longitude
## Determination
The main conventional methods for determining longitude are listed below. With one exception (magnetic declination), they all depend on a common principle, which is to determine the time for an event or measurement and to compare it with the time at a different location. Longitude, being up to 180° east or west of a prime meridian, is mathematically related to time differences up to 12 hours by a factor of 15. Thus, a time differential (in hours) between two points is multiplied by 15 to obtain a longitudinal difference (in degrees).
Historically, times used for calculating longitude have included apparent solar time, local mean time, and ephemeris time, with mean time being the one most used for navigation of the sea. See also the equation of time for details on the differences.
- Lunar distances and moon culminations. In its orbit around the Earth, the Moon moves relative to the stars at a rate of just over 0.5°/hour. The angle between the limb of the Moon and a suitable star, planet, or sun is measured with a sextant, and, after consulting ephemeris tables, a value for the mean time at a reference meridian, usually Greenwich, can be calculated. For a culmination, the observer simply records the time and compares it with the reference time in the ephemerides after correcting for refraction and other errors. This method was established by Nathaniel Pigott around 1786. The Nautical Almanac was published in the UK beginning in 1767 and the American Ephemeris and Nautical Almanac starting in 1852.
- Satellites of Jupiter. Galileo proposed that with sufficiently accurate knowledge of the orbits of the satellites, their positions could provide a measure of absolute time. The method requires a telescope, as the moons are not visible to the naked eye. Ephemeris tables are employed for comparison to a reference meridian.
- Appulses, occultations, transits, and eclipses. An appulse is the least apparent distance between two objects (the Moon, a star or a planet); an occultation occurs when a star or planet passes behind the Moon --- essentially a type of eclipse. Lunar eclipses continued to be used. The times of these events are compared to those of a reference meridian. Major observatories used the transit circle or meridian circle to establish very accurate longitude values for their country, often establishing their own prime meridian at the longitude of the instrument.
- Transport of chronometers. A clock is set to the local time of a starting point whose longitude is known, and the longitude of any other place can be determined by comparing its local mean time with the clock time. While marine chronometers are relatively stable, they are also relatively large and expensive. Prior to the quartz crystal, chronometers were susceptible to time drift from temperature fluctuations and vibration.
- Signals. Rockets and lights were occasionally used in the 18th and 19th century, although the method is impractical except for short distances and demonstrations. It was a rudimentary form of synchronizing time and establishing longitude. However, signaling by \"ball drop\" was extensively used in the US Navy and Royal Navy in the 19th century. In each case, there were observatories near bodies of water that would drop a ball from a tower, alerting the ships of the correct time, and hence enabling them to maintain stable longitudinal position fixes while at sea.
- Telegraphic determination of longitude. First suggested by the American astronomer Sears Cook Walker, the United States Coast Survey began deploying it in 1849. Europe quickly followed. As the American West was settled, mapping and surveying was greatly improved by the use of the telegraph to determine time and longitude differences between stations. The laying of transatlantic telegraph cables also helped establish coordinated global mapping and navigation.
- Magnetic declination. A compass needle does not in general point true north. The variation from true north varies with location, and it was suggested that this could provide a basis for determination of longitude.
With the exception of magnetic declination, all proved practicable methods. Developments on land and sea, however, were very different.
Several newer methods for navigation, location finding, and the determination of longitude exist. Radio navigation, satellite navigation, and Inertial navigation systems, along with celestial navigation, are a few of the more prevalent ones.
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# Longitude
## Values
Longitude is given as an angular measurement with 0° at the Prime Meridian, ranging from −180° westward to +180° eastward. The Greek letter λ (lambda) is used to denote the location of a place on Earth east or west of the Prime Meridian.
Each degree of longitude is sub-divided into 60 minutes, each of which is divided into 60 seconds. A longitude is thus specified in sexagesimal notation as, for example, 23° 27′ 30″ E. For higher precision, the seconds are specified with a decimal fraction. An alternative representation uses degrees and minutes, and parts of a minute are expressed in decimal notation, thus: 23° 27.5′ E. Degrees may also be expressed as a decimal fraction: 23.45833° E. For calculations, the angular measure may be converted to radians, so longitude may also be expressed in this manner as a signed fraction of `{{pi}}`{=mediawiki} (pi), or an unsigned fraction of 2`{{pi}}`{=mediawiki}.
For calculations, the west/east suffix is replaced by a negative sign in the western hemisphere. The international standard convention (ISO 6709)---that east is positive---is consistent with a right-handed Cartesian coordinate system, with the North Pole up. A specific longitude may then be combined with a specific latitude (positive in the northern hemisphere) to give a precise position on the Earth\'s surface. Confusingly, the convention of negative for east is also sometimes seen, most commonly in the United States; the Earth System Research Laboratories used it on an older version of one of their pages, in order \"to make coordinate entry less awkward\" for applications confined to the Western Hemisphere. They have since shifted to the standard approach.
The longitude is singular at the Poles and calculations that are sufficiently accurate for other positions may be inaccurate at or near the Poles. Also the discontinuity at the ±180° meridian must be handled with care in calculations. An example is a calculation of east displacement by subtracting two longitudes, which gives the wrong answer if the two positions are on either side of this meridian. To avoid these complexities, some applications use another horizontal position representation.
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# Longitude
## Length of a degree of longitude {#length_of_a_degree_of_longitude}
The length of a degree of longitude (east--west distance) depends only on the radius of a circle of latitude. For a sphere of radius `{{mvar|a}}`{=mediawiki} that radius at latitude `{{mvar|φ}}`{=mediawiki} is `{{math|''a'' [[cosine|cos]] ''φ''}}`{=mediawiki}, and the length of a one-degree (or `{{sfrac|{{pi}}|180}}`{=mediawiki} radian) arc along a circle of latitude is $\Delta^1_{\rm long}= \frac{\pi}{180}a \cos \phi$
----- ------------ ------------
0° 110.574 km 111.320 km
15° 110.649 km 107.551 km
30° 110.852 km 96.486 km
45° 111.133 km 78.847 km
60° 111.412 km 55.800 km
75° 111.618 km 28.902 km
90° 111.694 km 0.000 km
----- ------------ ------------
When the Earth is modelled by an ellipsoid this arc length becomes $\Delta^1_{\rm long}=\frac{\pi a\cos\phi}{180 \sqrt{1 - e^2 \sin^2 \phi}}$ where `{{mvar|e}}`{=mediawiki}, the eccentricity of the ellipsoid, is related to the major and minor axes (the equatorial and polar radii respectively) by $e^2=\frac{a^2-b^2}{a^2}$
An alternative formula is $\Delta^1_{\rm long}= \frac{\pi}{180}a \cos \beta \quad \mbox{where }\tan \beta = \frac{b}{a} \tan \phi$
Here $\beta$ is the so-called *parametric* or *reduced* latitude.
cos `{{mvar|φ}}`{=mediawiki} decreases from 1 at the equator to 0 at the poles, which measures how circles of latitude shrink from the equator to a point at the pole, so the length of a degree of longitude decreases likewise. This contrasts with the small (1%) increase in the length of a degree of latitude (north--south distance), equator to pole. The table shows both for the WGS84 ellipsoid with `{{mvar|a}}`{=mediawiki} = `{{val|6378137.0|u=m}}`{=mediawiki} and `{{mvar|b}}`{=mediawiki} = `{{val|6356752.3142|u=m}}`{=mediawiki}. The distance between two points 1 degree apart on the same circle of latitude, measured along that circle of latitude, is slightly more than the shortest (geodesic) distance between those points (unless on the equator, where these are equal); the difference is less than 0.6 m.
A geographical mile is defined to be the length of one minute of arc along the equator (one equatorial minute of longitude) therefore a degree of longitude along the equator is exactly 60 geographical miles or 111.3 kilometers, as there are 60 minutes in a degree. The length of 1 minute of longitude along the equator is 1 geographical mile or 1.855 km, while the length of 1 second of it is 0.016 geographical mile or 30.916 m
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# Lunar Society of Birmingham
The **Lunar Society of Birmingham** was a British dinner club and informal learned society of prominent figures in the Midlands Enlightenment, including industrialists, natural philosophers and intellectuals, who met regularly between 1765 and 1813 in Birmingham. At first called the Lunar Circle, \"Lunar Society\" became the formal name by 1775. The name arose because the society would meet during the full moon, as the extra light made the journey home easier and safer in the absence of street lighting. The members cheerfully referred to themselves as *\"lunaticks\"*, a contemporary spelling of lunatics. Venues included Erasmus Darwin\'s home in Lichfield, Matthew Boulton\'s home, Soho House, Bowbridge House in Derbyshire, and Great Barr Hall.
## Membership and status {#membership_and_status}
The Lunar Society evolved through various degrees of organisation over a period of up to fifty years, but was only ever an informal group. No constitution, minutes, publications or membership lists survive from any period, and evidence of its existence and activities is found only in the correspondence and notes of those associated with it. Historians therefore disagree on what qualifies as membership of the Lunar Society, who can be considered to have been members, and even when the society can be said to have existed. Josiah Wedgwood, for example, is described by some commentators as being one of five \"principal members\" of the society, while others consider that he \"cannot be recognized as \[a\] full member\" at all. Dates given for the establishment of the society range from \"sometime before 1760\" to 1775. Some historians argue that it had ceased to exist by 1791; others that it was still operating as late as 1813.
Despite this uncertainty, fourteen individuals have been identified as having verifiably attended Lunar Society meetings regularly over a long period during its most productive eras: these are Matthew Boulton, Erasmus Darwin, Thomas Day, Richard Lovell Edgeworth, Samuel Galton, Jr., Robert Augustus Johnson, James Keir, Joseph Priestley, William Small, Jonathan Stokes, James Watt, Josiah Wedgwood, John Whitehurst and William Withering.
While the society\'s meetings provided its name and social focus, however, they were relatively unimportant in its activities, and far more activity and communication took place outside the meetings themselves -- members local to Birmingham were in almost daily contact, more distant ones in correspondence at least weekly. A more loosely defined group has therefore been identified over a wider geographical area and longer time period, who attended meetings occasionally and who corresponded or co-operated regularly with multiple other members on group activities. These include Joseph Pickford, Richard Kirwan, John Smeaton, Henry Moyes, John Michell, Pieter Camper, R. E. Raspe, John Baskerville, Thomas Beddoes, John Wyatt, William Thomson, Cyril Jackson, Jean-André Deluc, John Wilkinson, John Ash, Samuel More, Robert Bage, James Brindley, Ralph Griffiths, John Roebuck, Thomas Percival, Joseph Black, James Hutton, Benjamin Franklin, Joseph Banks, James Lind, William Herschel, Daniel Solander, John Warltire, George Fordyce, Alexander Blair, Samuel Parr, Louis Joseph d\'Albert d\'Ailly, William Emes, the seventh Duke of Chaulnes, Barthélemy Faujas de Saint-Fond, Grossart de Virly, Johann Gottling. and Joseph Wright.
This lack of a defined membership has led some historians to criticise a Lunar Society \"legend\", leading people to \"confuse it and its efforts with the general growth of intellectual and economic activities in the provinces of eighteenth century Britain\". Others have seen this both as real and as one of the society\'s main strengths: a paper read at the Science Museum in London in 1963 claimed that
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# Lunar Society of Birmingham
## Development
### Origins 1755--1765 {#origins_17551765}
The origins of the Lunar Society lie in a pattern of friendships that emerged in the late 1750s. Matthew Boulton and Erasmus Darwin met some time between 1757 and 1758, possibly through family connections, as Boulton\'s mother\'s family were patients of Darwin; or possibly though shared friendships, as both were admirers of the printer John Baskerville and friends of the astronomer and geologist John Michell, a regular visitor to Darwin\'s house in Lichfield. Darwin was a physician and poet who had studied at Cambridge and Edinburgh; Boulton had left school at fourteen and started work in his father\'s business making metal goods in Birmingham at the age of 21. Despite their different backgrounds they shared a common interest in experiment and invention, and their activities would show Darwin\'s theoretical understanding and Boulton\'s practical experience to be complementary. Soon they were visiting each other regularly and conducting investigations into scientific subjects such as electricity, meteorology and geology.
Around the same time the Derby-based clockmaker John Whitehurst became a friend, first of Boulton and subsequently of Darwin, through his business supplying clock movements to Boulton\'s ormolu manufacturing operation. Although older than both Boulton and Darwin, by 1758 Whitehurst was writing to Boulton telling excitedly of a pyrometer he had built, and looking forward to visiting Birmingham \"to spend one day with you in trying all necessary experiments\".
Boulton, Darwin and Whitehurst were in turn introduced by Michell to Benjamin Franklin when he travelled to Birmingham in July 1758 \"to improve and increase Acquaintance among Persons of Influence\", and Franklin returned in 1760 to conduct experiments with Boulton on electricity and sound. Although Michell seems to have withdrawn slightly from the group when he moved to Thornhill (near Dewsbury) in 1767, Franklin was to remain a common link among many of the early members.
### The Lunar Circle 1765--1775 {#the_lunar_circle_17651775}
The nature of the group was to change significantly with the move to Birmingham in 1765 of the Scottish physician William Small, who had been Professor of Natural Philosophy at The College of William & Mary in Williamsburg, Virginia. There he had taught and been a major influence over Thomas Jefferson, and had formed the focus of a local group of intellectuals. His arrival with a letter of introduction to Matthew Boulton from Benjamin Franklin was to have a galvanising effect on the existing circle, which began to explicitly identify itself as a group and actively started to attract new members.
The first of these was Josiah Wedgwood, who became a close friend of Darwin in 1765 while campaigning for the building of the Trent and Mersey Canal and subsequently closely modelled his large new pottery factory at Etruria, Staffordshire on Boulton\'s Soho Manufactory. Another new recruit, Richard Lovell Edgeworth, met Darwin, Small and Boulton in 1766 through a shared interest in carriage design, and he in turn introduced his friend and fellow Rousseau-admirer Thomas Day, with whom he had studied at Corpus Christi College, Oxford. In 1767 James Keir visited Darwin in Lichfield, where he was introduced to Boulton, Small, Wedgwood and Whitehurst and subsequently decided to move to Birmingham.
The Lunar Circle also attracted more distant involvement. Joseph Priestley, then living in Leeds and a close friend of John Michell, became associated with the Society in 1767 when Darwin and Wedgwood became involved with his work on electricity. In the same year James Watt visited Birmingham on the recommendation of his business patron John Roebuck, being shown around the Soho Manufactory by Small and Darwin in Boulton\'s absence. Although neither Priestley nor Watt were to move to Birmingham for several years, both were to be in constant communication with the Birmingham members and central to the circle\'s activities from 1767.
By 1768 the core group of nine individuals who would form the nucleus of the Lunar Society had come together with Small at their heart. The group at this time is sometimes referred to as the \"Lunar circle\", though this is a later description used by historians, and the group themselves used a variety of less specific descriptions, including \"Birmingham Philosophers\" or simply \"fellow-schemers\".
### The Lunar Society 1775--1780 {#the_lunar_society_17751780}
If William Small\'s arrival in 1765 had been the catalyst to the development of the Lunar Circle as a cohesive group, his death -- probably from malaria -- in 1775 was to mark another change in its structure. Small had been the key link between the members, and in his absence those remaining moved to place the group on a more organised footing. Meetings were to be held on the Sunday nearest the full moon, lasting from two o\'clock in the afternoon until eight o\'clock in the evening. The first was probably that held on 31 December 1775, and the \"Lunar\" name is first recorded in 1776.
The era also saw significant changes in membership. William Withering -- like Small, a physician -- was already an acquaintance of Darwin, Boulton and Wedgwood when he moved from Stafford to Birmingham and became a member of the Society in 1776. John Whitehurst\'s move to London in 1775 had a less dramatic effect: he kept in regular contact with other members of the society and remained an occasional attender of meetings.
The leading figure behind the establishment of the society as a more organised body during this early period seems to have been Matthew Boulton: his home at Soho House in Handsworth was the principal venue for meetings, and in 1776 he is recorded as planning \"to make many Motions to the Members respecting new Laws, and regulations, such as will tend to prevent the decline of a society which I hope will be lasting.\" This reliance on Boulton was also to prove a weakness, however, as the period coincided with the peak of his work building up his steam engine business and he was frequently absent. Although the 1770s was one of the society\'s richest eras in terms of its collaborative achievements, the society\'s meetings declined from regular occurrences in 1775 to infrequent ones by the end of the decade.
### Heyday of the Society 1780--1789 {#heyday_of_the_society_17801789}
In late 1780 the nature of the society was to change again with the move to Birmingham of Joseph Priestley. Priestley had been closely associated with the group\'s activities for over a decade and was a strong advocate of the benefits of scientific societies. Shortly after his arrival Lunar meetings moved from Sunday afternoons to Mondays to accommodate Priestley\'s duties as a clergyman, while the society\'s dependence on Matthew Boulton was lessened by holding meetings at other members\' houses in addition to Soho House. The result was to be the society\'s most productive era.
Several other major new figures became associated with the society during this period. Samuel Galton, Jr., unusual as a Quaker who was also a gun-manufacturer, appears in the letters of other Lunar members as attending meetings from July 1781, and his daughter Mary Anne Schimmelpenninck was to provide one of the few first-hand accounts of the Lunar Society\'s activities. The botanist and physician Jonathan Stokes, who had known William Withering as a child, moved to Stourbridge and started attending Lunar Society meetings from 1783. His contribution to the society was significant but short-lived: after collaborating with Withering on his *Botanical Arrangement of British Plants* the two quarrelled bitterly and Stokes severed his relations with the main Lunar members by 1788.
The society also lost several major figures over the period: Richard Lovell Edgeworth ceased regular involvement in the society\'s activities when he returned to Ireland in 1782, John Whitehurst died in London in 1788, and Thomas Day died the following year. Most significantly, Erasmus Darwin moved to Derby in 1781, but although he complained of being \"cut off from the milk of science\", he continued to attend Lunar Society meetings at least until 1788.
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# Lunar Society of Birmingham
## Development
### Decline 1789--1813 {#decline_17891813}
The outbreak of the French Revolution in 1789 caused political strains between members of the society, but it was the Priestley riots of 1791 in Birmingham itself that saw a decisive falling off of the society\'s spirit and activities. Joseph Priestley himself was driven from the town, leaving England entirely for the United States in 1794, William Withering\'s house was invaded by rioters and Matthew Boulton and James Watt had to arm their employees to protect the Soho Manufactory. Lunar meetings were continued by the younger generation of the families of earlier Lunar members, including Gregory Watt, Matthew Robinson Boulton, Thomas Wedgwood and James Watt junior, and possibly Samuel Tertius Galton. Regular meetings are recorded into the nineteenth century -- eight in 1800, five or six before August 1801 and at least one in 1802, while as late as 1809 Leonard Horner was describing \"the remnant of the Lunar Society\" as being \"very interesting\". While individual members continued to produce work of importance, however, the collaborative activity that marked the heyday of the society was noticeably absent.
The society had definitely collapsed by 1813, however: in August of that year Samuel Galton, Jr. is recorded as having won a ballot for possession of the scientific books from the society\'s library.
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# Lunar Society of Birmingham
## Modern Lunar Societies {#modern_lunar_societies}
Among memorials to the Society and its members are the Moonstones; two statues of Watt and a statue of *Boulton, Watt and Murdoch* by William Bloye; and the museum at Soho House -- all in Birmingham.
A new Lunar Society was formed in Birmingham by a group led by Dame Rachel Waterhouse. Its aim was to play a leading part in the development of the city and the wider region. Clive Stone was elected as Chair of the Lunar Society in July 2023. The society was still in operation in 2024.
**Outside Birmingham**
In Australia, The Lunaticks Society of Newcastle was formed by leading digital entrepreneurs, software developers, educators, film producers, creatives, investors to encourage creative thinking and new ideas in a digital age.
### University of Birmingham Lunar Society {#university_of_birmingham_lunar_society}
In the latter part of the 20th century, the University of Birmingham Lunar Society met every Thursday to debate and discuss all manner of topics in the Guild bar. In 2011, steps were undertaken to reform the discussion society as an alternative to the more regulated debate options available at the university. This was agreed by the University\'s Guild of Students in autumn 2012. The society now hosts symposiums every two weeks. Any member has always been welcome to suggest a topic for discussion. These meetings occur in a variety of environments from University rooms to local bars. In 2013 the society attempted to change the name of one of the rooms in the Guild of Students to \'The Lunar Room\' in honour of the original Birmingham Lunar Society. Like the Oxford Union, the society has always traditionally put a huge emphasis on freedom of speech. The society has similar aims to The Speculative Society of Edinburgh University.`{{Primary source inline|date=June 2018}}`{=mediawiki} In 2019, the society was rebranded as the Devil\'s Advocate Society, and retained the goals of the Lunar Society whilst changing much of its branding.
Today, the society is an informal academic association open to both undergraduate and graduate students, as well as professional academics, from the University of Birmingham.
## Archives
Historical material related to the Lunar Society is held in multiple collections. The University of Birmingham\'s Cadbury Research Library holds a series of portraits of the original Lunar Society members. The Library of Birmingham holds a large collection of Joseph Priestley\'s publications. Both archives also hold various letters of society members
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# Law of noncontradiction
In logic, the **law of noncontradiction** (**LNC**; also known as the **law of contradiction**, **principle of non-contradiction** (**PNC**), or the **principle of contradiction**) states that for any given proposition, the proposition and its negation cannot both be simultaneously true, e.g. the proposition \"*the house is white*\" and its negation \"*the house is not white*\" are mutually exclusive. Formally, this is expressed as the tautology ¬(p ∧ ¬p). The law is not to be confused with the law of excluded middle which states that at least one of two propositions like \"the house is white\" and \"the house is not white\" holds.
One reason to have this law is the principle of explosion, which states that anything follows from a contradiction. The law is employed in a *reductio ad absurdum* proof.
To express the fact that the law is tenseless and to avoid equivocation, sometimes the law is amended to say \"contradictory propositions cannot both be true \'at the same time and in the same sense\'\".
It is one of the so called three laws of thought, along with its complement, the law of excluded middle, and the law of identity. However, no system of logic is built on just these laws, and none of these laws provide inference rules, such as *modus ponens* or De Morgan\'s laws.
The law of non-contradiction and the law of excluded middle create a dichotomy in a so-called logical space, the points in which are all the consistent combinations of propositions. Each combination would contain exactly one member of each pair of contradictory propositions, so the space would have two parts which are mutually exclusive and jointly exhaustive. The law of non-contradiction is merely an expression of the mutually exclusive aspect of that dichotomy, and the law of excluded middle is an expression of its jointly exhaustive aspect.
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# Law of noncontradiction
## Interpretations
One difficulty in applying the law of non-contradiction is ambiguity in the propositions. For instance, if it is not explicitly specified as part of the propositions A and B, then *A* may be *B* at one time, and not at another. A and B may in some cases be made to sound mutually exclusive linguistically even though *A* may be partly *B* and partly not *B* at the same time. However, it is impossible to predicate of the same thing, at the same time, and in the same sense, the absence and the presence of the same fixed quality.
### Indian philosophy {#indian_philosophy}
The Buddhist Tripitaka attributes to Nigaṇṭha Nātaputta, who lived in the 6th century BCE, the implicit formulation of the law of noncontradiction, "'See how upright, honest and sincere Citta, the householder, is'; and, a little later, he also says: 'See how Citta, the householder, is not upright, honest or sincere.' To this, Citta replies: 'if your former statement is true, your latter statement is false and if your latter statement is true, your former statement is false.'" Early explicit formulations of the law of noncontradiction were ontic, with later 2nd century Buddhist philosopher Nagarjuna stating "when something is a single thing, it cannot be both existent and non-existent" similar to Aristotle's own ontic formulation that "that a thing cannot at the same time be and not be".
### Heraclitus
According to both Plato and Aristotle, Heraclitus was *said* to have denied the law of non-contradiction. This is quite likely if, as Plato pointed out, the law of non-contradiction does not hold for changing things in the world. If a philosophy of Becoming is not possible without change, then (the potential of) what is to become must already exist in the present object. In \"We step and do not step into the same rivers; we are and we are not\", both Heraclitus\'s and Plato\'s object simultaneously must, in some sense, be both what it now is and have the potential (dynamic) of what it might become.
So little remains of Heraclitus\' aphorisms that not much about his philosophy can be said with certainty. He seems to have held that strife of opposites is universal both within and without, therefore *both* opposite existents or qualities must simultaneously exist, although in some instances in different respects. \"The *road up and down are one and the same*\" implies either the road leads both ways, or there can be no road at all. This is the logical complement of the law of non-contradiction. According to Heraclitus, change, and the constant conflict of opposites is the universal logos of nature.
### Protagoras
Personal subjective perceptions or judgments can only be said to be true at the same time in the same respect, in which case, the law of non-contradiction must be applicable to personal judgments. The most famous saying of Protagoras is: \"Man is the measure of all things: of things which are, that they are, and of things which are not, that they are not\". However, Protagoras was referring to things that are used by or in some way related to humans. This makes a great difference in the meaning of his aphorism. Properties, social entities, ideas, feelings, judgments, etc. originate in the human mind. However, Protagoras has never suggested that man must be the measure of stars or the motion of the stars.
### Parmenides
Parmenides employed an ontological version of the law of non-contradiction to prove that being is and to deny the void, change, and motion. He also similarly disproved contrary propositions. In his poem On Nature, he said, `{{Quotation|the only routes of inquiry there are for thinking:<br>
the one that [it] is and that [it] cannot not be<br>
is the path of Persuasion (for it attends upon truth)<br>
the other, that [it] is not and that it is right that [it] not be,<br>
this I point out to you is a path wholly inscrutable<br>
for you could not know what is not (for it is not to be accomplished)<br>
nor could you point it out... For the same thing is for thinking and for being}}`{=mediawiki}
The nature of the \'is\' or what-is in Parmenides is a highly contentious subject. Some have taken it to be whatever exists, some to be whatever is or can be the object of scientific inquiry.
### Socrates
In Plato\'s early dialogues, Socrates uses the elenctic method to investigate the nature or definition of ethical concepts such as justice or virtue. Elenctic refutation depends on a dichotomous thesis, one that may be divided into exactly two mutually exclusive parts, only one of which may be true. Then Socrates goes on to demonstrate the contrary of the commonly accepted part using the law of non-contradiction. According to Gregory Vlastos, the method has the following steps:
1. Socrates\' interlocutor asserts a thesis, for example, \"Courage is endurance of the soul\", which Socrates considers false and targets for refutation.
2. Socrates secures his interlocutor\'s agreement to further premises, for example, \"Courage is a fine thing\" and \"Ignorant endurance is not a fine thing\".
3. Socrates then argues, and the interlocutor agrees, that these further premises imply the contrary of the original thesis, in this case, it leads to: \"courage is not endurance of the soul\".
4. Socrates then claims that he has shown that his interlocutor\'s thesis is false and that its negation is true.
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# Law of noncontradiction
## Interpretations
### Plato\'s synthesis {#platos_synthesis}
Plato\'s version of the law of non-contradiction states that \"The same thing clearly cannot act or be acted upon in the same part or in relation to the same thing at the same time, in contrary ways\" (The *Republic* (436b)). In this, Plato carefully phrases three axiomatic restrictions on *action* or reaction: in the same part, in the same relation, at the same time. The effect is to momentarily create a frozen, timeless state, somewhat like figures frozen in action on the frieze of the Parthenon.
This way, he accomplishes two essential goals for his philosophy. First, he logically separates the Platonic world of constant change from the formally knowable world of momentarily fixed physical objects. Second, he provides the conditions for the dialectic method to be used in finding definitions, as for example in the *Sophist*. So Plato\'s law of non-contradiction is the empirically derived necessary starting point for all else he has to say.
In contrast, Aristotle reverses Plato\'s order of derivation. Rather than starting with *experience*, Aristotle begins *a priori* with the law of non-contradiction as the fundamental axiom of an analytic philosophical system. This axiom then necessitates the fixed, realist model. Now, he starts with much stronger logical foundations than Plato\'s non-contrariety of action in reaction to conflicting demands from the three parts of the soul.
### Aristotle\'s contribution {#aristotles_contribution}
The traditional source of the law of non-contradiction is Aristotle\'s *Metaphysics* where he gives three different versions.
- Ontological: \"It is impossible that the same thing belong and not belong to the same thing at the same time and in the same respect.\" (1005b19-20)
- Psychological: \"No one can believe that the same thing can (at the same time) be and not be.\" (1005b23--24)
- Logical (aka the medieval *Lex Contradictoriarum*): \"The most certain of all basic principles is that contradictory propositions are not true simultaneously.\" (1011b13-14)
Aristotle attempts several proofs of this law. He first argues that every expression has a single meaning (otherwise we could not communicate with one another). This rules out the possibility that by \"to be a man\", \"not to be a man\" is meant. But \"man\" means \"two-footed animal\" (for example), and so if anything is a man, it is necessary (by virtue of the meaning of \"man\") that it must be a two-footed animal, and so it is impossible at the same time for it *not* to be a two-footed animal. Thus \"it is not possible to say truly at the same time that the same thing is and is not a man\" (*Metaphysics* 1006b 35). Another argument is that anyone who believes something cannot believe its contradiction (1008b):
: Why does he not just get up first thing and walk into a well or, if he finds one, over a cliff? In fact, he seems rather careful about cliffs and wells.
### Avicenna
Avicenna\'s commentary on the *Metaphysics* illustrates the common view that the law of non-contradiction \"and their like are among the things that do not require our elaboration.\" Avicenna\'s words for \"the obdurate\" are quite facetious: \"he must be subjected to the conflagration of fire, since \'fire\' and \'not fire\' are one. Pain must be inflicted on him through beating, since \'pain\' and \'no pain\' are one. And he must be denied food and drink, since eating and drinking and the abstention from both are one \[and the same\].\"
### Thomas Aquinas {#thomas_aquinas}
Thomas Aquinas argued that the principle of non-contradiction is essential to the reasoning of human beings (\"One cannot reasonably hold two mutually exclusive beliefs at the same time\"). He argued that human reasoning without the principle of non-contradiction is utterly impossible because reason itself can\'t function with two contradictory ideas. Aquinas argued that this is the same both for moral arguments as well as theological arguments and even machinery ("the parts must work together, the machine can't work if two parts are incompatible").
### Leibniz and Kant {#leibniz_and_kant}
Leibniz and Kant both used the law of non-contradiction to define the difference between analytic and synthetic propositions. For Leibniz, analytic statements follow from the law of non-contradiction, and synthetic ones from the principle of sufficient reason.
### Russell
The principle was stated as a theorem of propositional logic by Russell and Whitehead in *Principia Mathematica* as:
:
: $\mathbf{*3\cdot24}. \ \ \vdash. \thicksim(p.\thicksim p)$
### Dialetheism
Graham Priest advocates the view that *under some conditions*, some statements can be both true and false simultaneously, or may be true and false at different times. Dialetheism arises from formal logical paradoxes, such as the Liar\'s paradox and Russell\'s paradox, even though it isn\'t the only solution to them.
## Alleged impossibility of its proof or denial {#alleged_impossibility_of_its_proof_or_denial}
The law of non-contradiction is alleged to be neither verifiable nor falsifiable, on the ground that any proof or disproof must use the law itself prior to reaching the conclusion. In other words, in order to verify or falsify the laws of logic one must resort to logic as a weapon, an act that is argued to be self-defeating. Since the early 20th century, certain logicians have proposed logics that deny the validity of the law.
Logics known as \"paraconsistent\" are inconsistency-tolerant logics in that there, from P together with ¬P, it does not imply that any proposition follows. Nevertheless, not all paraconsistent logics deny the law of non-contradiction and some such logics even prove it.
Some, such as David Lewis, have objected to paraconsistent logic on the ground that it is simply impossible for a statement and its negation to be jointly true. A related objection is that \"negation\" in paraconsistent logic is not really *negation*; it is merely a subcontrary-forming operator.`{{full citation needed|date=July 2016}}`{=mediawiki}`{{full citation needed|date=July 2016}}`{=mediawiki} Those who (like the dialetheists) claim that the Law of Non-Contradiction can be violated are in fact using a different definition of negation, and therefore talking about something else other than the Law of Non-Contradiction which is based on a particular definition of negation and therefore cannot be violated.
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# Law of noncontradiction
## In popular culture {#in_popular_culture}
The *Fargo* episode \"The Law of Non-Contradiction\", which takes its name from the law, was noted for its several elements relating to the law of non-contradiction, as the episode\'s main character faces several paradoxes. For example, she is still the acting chief of police while having been demoted from the position, and tries to investigate a man that both was and was not named Ennis Stussy, and who both was and was not her stepfather. It also features the story of a robot who, after having spent millions of years unable to help humanity, is told that he greatly helped mankind all along by observing history
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# Law of excluded middle
In logic, the **law of excluded middle** or the **principle of excluded middle** states that for every proposition, either this proposition or its negation is true. It is one of the three laws of thought, along with the law of noncontradiction and the law of identity; however, no system of logic is built on just these laws, and none of these laws provides inference rules, such as modus ponens or De Morgan\'s laws. The law is also known as the **law**/**principle** **of the excluded third**, in Latin ***principium tertii exclusi**\'\'. Another Latin designation for this law is***tertium non datur**\'\' or \"no third \[possibility\] is given\". In classical logic, the law is a tautology.
In contemporary logic the principle is distinguished from the semantical principle of bivalence, which states that every proposition is either true or false. The principle of bivalence always implies the law of excluded middle, while the converse is not always true. A commonly cited counterexample uses statements unprovable now, but provable in the future to show that the law of excluded middle may apply when the principle of bivalence fails.
## History
### Aristotle
The earliest known formulation is in Aristotle\'s discussion of the principle of non-contradiction, first proposed in *On Interpretation,* where he says that of two contradictory propositions (i.e. where one proposition is the negation of the other) one must be true, and the other false. He also states it as a principle in the *Metaphysics* book 4, saying that it is necessary in every case to affirm or deny, and that it is impossible that there should be anything between the two parts of a contradiction.
Aristotle wrote that ambiguity can arise from the use of ambiguous names, but cannot exist in the facts themselves:
Aristotle\'s assertion that \"it will not be possible to be and not to be the same thing\" would be written in propositional logic as \~(*P* ∧ \~*P*). In modern so called classical logic, this statement is equivalent to the law of excluded middle (*P* ∨ \~*P*), through distribution of the negation in Aristotle\'s assertion. The former claims that no statement is *both* true and false, while the latter requires that any statement is *either* true or false.
But Aristotle also writes, \"since it is impossible that contradictories should be at the same time true of the same thing, obviously contraries also cannot belong at the same time to the same thing\" (Book IV, CH 6, p. 531). He then proposes that \"there cannot be an intermediate between contradictories, but of one subject we must either affirm or deny any one predicate\" (Book IV, CH 7, p. 531). In the context of Aristotle\'s traditional logic, this is a remarkably precise statement of the law of excluded middle, *P* ∨ \~*P*.
Yet in *On Interpretation* Aristotle seems to deny the law of excluded middle in the case of future contingents, in his discussion on the sea battle.
### Leibniz
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# Law of excluded middle
## History
### Bertrand Russell and *Principia Mathematica* {#bertrand_russell_and_principia_mathematica}
The principle was stated as a theorem of propositional logic by Russell and Whitehead in *Principia Mathematica* as:
$\mathbf{*2\cdot11}. \ \ \vdash . \ p \ \vee \thicksim p$.
So just what is \"truth\" and \"falsehood\"? At the opening *PM* quickly announces some definitions:
This is not much help. But later, in a much deeper discussion (\"Definition and systematic ambiguity of Truth and Falsehood\" Chapter II part III, p. 41 ff), *PM* defines truth and falsehood in terms of a relationship between the \"a\" and the \"b\" and the \"percipient\". For example \"This \'a\' is \'b{{\'\"}} (e.g. \"This \'object a\' is \'red{{\'\"}}) really means {{\"\'}}object a\' is a sense-datum\" and {{\"\'}}red\' is a sense-datum\", and they \"stand in relation\" to one another and in relation to \"I\". Thus what we really mean is: \"I perceive that \'This object a is red{{\'\"}} and this is an undeniable-by-3rd-party \"truth\".
*PM* further defines a distinction between a \"sense-datum\" and a \"sensation\": `{{quote|That is, when we judge (say) "this is red", what occurs is a relation of three terms, the mind, and "this", and "red". On the other hand, when we perceive "the redness of this", there is a relation of two terms, namely the mind and the complex object "the redness of this" (pp. 43–44).}}`{=mediawiki}
Russell reiterated his distinction between \"sense-datum\" and \"sensation\" in his book *The Problems of Philosophy* (1912), published at the same time as *PM* (1910--1913): `{{quote|Let us give the name of "sense-data" to the things that are immediately known in sensation: such things as colours, sounds, smells, hardnesses, roughnesses, and so on. We shall give the name "sensation" to the experience of being immediately aware of these things … The colour itself is a sense-datum, not a sensation. (p. 12)}}`{=mediawiki}
Russell further described his reasoning behind his definitions of \"truth\" and \"falsehood\" in the same book (Chapter XII, *Truth and Falsehood*).
#### Consequences of the law of excluded middle in *Principia Mathematica* {#consequences_of_the_law_of_excluded_middle_in_principia_mathematica}
From the law of excluded middle, formula ✸2.1 in *Principia Mathematica,* Whitehead and Russell derive some of the most powerful tools in the logician\'s argumentation toolkit. (In *Principia Mathematica,* formulas and propositions are identified by a leading asterisk and two numbers, such as \"✸2.1\".)
✸2.1 \~*p* ∨ *p* \"This is the Law of excluded middle\" (*PM*, p. 101).
The proof of ✸2.1 is roughly as follows: \"primitive idea\" 1.08 defines *p* → *q* = \~*p* ∨ *q*. Substituting *p* for *q* in this rule yields *p* → *p* = \~*p* ∨ *p*. Since *p* → *p* is true (this is Theorem 2.08, which is proved separately), then \~*p* ∨ *p* must be true.
✸2.11 *p* ∨ \~*p* (Permutation of the assertions is allowed by axiom 1.4)\
✸2.12 *p* → \~(\~*p*) (Principle of double negation, part 1: if \"this rose is red\" is true then it\'s not true that {{\"\'}}this rose is not-red\' is true\".)\
✸2.13 *p* ∨ \~{\~(\~*p*)} (Lemma together with 2.12 used to derive 2.14)\
✸2.14 \~(\~*p*) → *p* (Principle of double negation, part 2)\
✸2.15 (\~*p* → *q*) → (\~*q* → *p*) (One of the four \"Principles of transposition\". Similar to 1.03, 1.16 and 1.17. A very long demonstration was required here.)\
✸2.16 (*p* → *q*) → (\~*q* → \~*p*) (If it\'s true that \"If this rose is red then this pig flies\" then it\'s true that \"If this pig doesn\'t fly then this rose isn\'t red.\")\
✸2.17 ( \~*p* → \~*q* ) → (*q* → *p*) (Another of the \"Principles of transposition\".)\
✸2.18 (\~*p* → *p*) → *p* (Called \"The complement of *reductio ad absurdum*. It states that a proposition which follows from the hypothesis of its own falsehood is true\" (*PM*, pp. 103--104).)
Most of these theorems---in particular ✸2.1, ✸2.11, and ✸2.14---are rejected by intuitionism. These tools are recast into another form that Kolmogorov cites as \"Hilbert\'s four axioms of implication\" and \"Hilbert\'s two axioms of negation\" (Kolmogorov in van Heijenoort, p. 335).
Propositions ✸2.12 and ✸2.14, \"double negation\": The intuitionist writings of L. E. J. Brouwer refer to what he calls \"the *principle of the reciprocity of the multiple species*, that is, the principle that for every system the correctness of a property follows from the impossibility of the impossibility of this property\" (Brouwer, ibid, p. 335).
This principle is commonly called \"the principle of double negation\" (*PM*, pp. 101--102). From the law of excluded middle (✸2.1 and ✸2.11), *PM* derives principle ✸2.12 immediately. We substitute \~*p* for *p* in 2.11 to yield \~*p* ∨ \~(\~*p*), and by the definition of implication (i.e. 1.01 p → q = \~p ∨ q) then \~p ∨ \~(\~p)= p → \~(\~p). QED (The derivation of 2.14 is a bit more involved.)
### Reichenbach
It is correct, at least for bivalent logic---i.e. it can be seen with a Karnaugh map---that this law removes \"the middle\" of the inclusive-or used in his law (3). And this is the point of Reichenbach\'s demonstration that some believe the *exclusive*-or should take the place of the *inclusive*-or.
About this issue (in admittedly very technical terms) Reichenbach observes:
:
: The tertium non datur
: 29\. (*x*)\[*f*(*x*) ∨ \~*f*(*x*)\]
: is not exhaustive in its major terms and is therefore an inflated formula. This fact may perhaps explain why some people consider it unreasonable to write (29) with the inclusive-\'or\', and want to have it written with the sign of the *exclusive*-\'or\'
```{=html}
<!-- -->
```
:
: 30\. (*x*)\[*f*(*x*) ⊕ \~*f*(*x*)\], where the symbol \"⊕\" signifies exclusive-or
: in which form it would be fully exhaustive and therefore nomological in the narrower sense. (Reichenbach, p. 376)
In line (30) the \"(x)\" means \"for all\" or \"for every\", a form used by Russell and Reichenbach; today the symbolism is usually $\forall$ *x*. Thus an example of the expression would look like this:
- (*pig*): (*Flies*(*pig*) ⊕ \~*Flies*(*pig*))
- (For all instances of \"pig\" seen and unseen): (\"Pig does fly\" or \"Pig does not fly\" but not both simultaneously)
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# Law of excluded middle
## History
### Formalists versus Intuitionists {#formalists_versus_intuitionists}
From the late 1800s through the 1930s, a bitter, persistent debate raged between Hilbert and his followers versus Hermann Weyl and L. E. J. Brouwer. Brouwer\'s philosophy, called intuitionism, started in earnest with Leopold Kronecker in the late 1800s.
Hilbert intensely disliked Kronecker\'s ideas:
The debate had a profound effect on Hilbert. Reid indicates that Hilbert\'s second problem (one of Hilbert\'s problems from the Second International Conference in Paris in 1900) evolved from this debate (italics in the original):
:
: In his second problem, \[Hilbert\] had asked for a *mathematical proof* of the consistency of the axioms of the arithmetic of real numbers.
: To show the significance of this problem, he added the following observation:
: \"If contradictory attributes be assigned to a concept, I say that *mathematically the concept does not exist*\" (Reid p. 71)
Thus, Hilbert was saying: \"If *p* and \~*p* are both shown to be true, then *p* does not exist\", and was thereby invoking the law of excluded middle cast into the form of the law of contradiction.
The rancorous debate continued through the early 1900s into the 1920s; in 1927 Brouwer complained about \"polemicizing against it \[intuitionism\] in sneering tones\" (Brouwer in van Heijenoort, p. 492). But the debate was fertile: it resulted in *Principia Mathematica* (1910--1913), and that work gave a precise definition to the law of excluded middle, and all this provided an intellectual setting and the tools necessary for the mathematicians of the early 20th century:
Brouwer reduced the debate to the use of proofs designed from \"negative\" or \"non-existence\" versus \"constructive\" proof:
:
: According to Brouwer, a statement that an object exists having a given property means that, and is only proved, when a method is known which in principle at least will enable such an object to be found or constructed ...
: Hilbert naturally disagreed.
: \"pure existence proofs have been the most important landmarks in the historical development of our science,\" he maintained. (Reid p. 155)
```{=html}
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```
:
: Brouwer refused to accept the logical principle of the excluded middle, His argument was the following:
```{=html}
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```
:
: \"Suppose that A is the statement \"There exists a member of the set *S* having the property *P*.\" If the set is finite, it is possible---in principle---to examine each member of *S* and determine whether there is a member of *S* with the property *P* or that every member of *S* lacks the property *P*.\" For finite sets, therefore, Brouwer accepted the principle of the excluded middle as valid. He refused to accept it for infinite sets because if the set *S* is infinite, we cannot---even in principle---examine each member of the set. If, during the course of our examination, we find a member of the set with the property *P*, the first alternative is substantiated; but if we never find such a member, the second alternative is still not substantiated.
: Since mathematical theorems are often proved by establishing that the negation would involve us in a contradiction, this third possibility which Brouwer suggested would throw into question many of the mathematical statements currently accepted.
: \"Taking the Principle of the Excluded Middle from the mathematician,\" Hilbert said, \"is the same as ... prohibiting the boxer the use of his fists.\"
: \"The possible loss did not seem to bother Weyl ... Brouwer\'s program was the coming thing, he insisted to his friends in Zürich.\" (Reid, p. 149)
In his lecture in 1941 at Yale and the subsequent paper, Gödel proposed a solution: \"that the negation of a universal proposition was to be understood as asserting the existence ... of a counterexample\" (Dawson, p. 157)
Gödel\'s approach to the law of excluded middle was to assert that objections against \"the use of \'impredicative definitions{{\'\"}} had \"carried more weight\" than \"the law of excluded middle and related theorems of the propositional calculus\" (Dawson p. 156). He proposed his \"system Σ ... and he concluded by mentioning several applications of his interpretation. Among them were a proof of the consistency with intuitionistic logic of the principle \~ (∀A: (A ∨ \~A)) (despite the inconsistency of the assumption ∃ A: \~ (A ∨ \~A))\" (Dawson, p. 157)
The debate seemed to weaken: mathematicians, logicians and engineers continue to use the law of excluded middle (and double negation) in their daily work.
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# Law of excluded middle
## History
### Intuitionist definitions of the law (principle) of excluded middle {#intuitionist_definitions_of_the_law_principle_of_excluded_middle}
The following highlights the deep mathematical and philosophic problem behind what it means to \"know\", and also helps elucidate what the \"law\" implies (i.e. what the law really means). Their difficulties with the law emerge: that they do not want to accept as true implications drawn from that which is unverifiable (untestable, unknowable) or from the impossible or the false. (All quotes are from van Heijenoort, italics added).
*Brouwer* offers his definition of \"principle of excluded middle\"; we see here also the issue of \"testability\":
:
: On the basis of the testability just mentioned, there hold, for properties conceived within a specific finite main system, the \"principle of excluded middle\", that is, *the principle that for every system every property is either correct \[richtig\] or impossible*, and in particular the principle of the reciprocity of the complementary species, that is, the principle that for every system the correctness of a property follows from the impossibility of the impossibility of this property. (335)
*Kolmogorov*\'s definition cites Hilbert\'s two axioms of negation
5. *A* → (\~*A* → *B*)
6. (*A* → *B*) → { (\~*A* → *B*) → *B*}
:
: Hilbert\'s first axiom of negation, \"anything follows from the false\", made its appearance only with the rise of symbolic logic, as did the first axiom of implication ... while ... the axiom under consideration \[axiom 5\] asserts something about the consequences of something impossible: we have to accept *B* if the true judgment *A* is regarded as false ...
: Hilbert\'s second axiom of negation expresses the principle of excluded middle. The principle is expressed here in the form in which is it used for derivations: if *B* follows from *A* as well as from \~*A*, then *B* is true. Its usual form, \"every judgment is either true or false\" is equivalent to that given above\".
: From the first interpretation of negation, that is, the interdiction from regarding the judgment as true, it is impossible to obtain the certitude that the principle of excluded middle is true ... Brouwer showed that in the case of such transfinite judgments the principle of excluded middle cannot be considered obvious
: footnote 9: \"This is Leibniz\'s very simple formulation (see *Nouveaux Essais*, IV,2). The formulation \"*A* is either *B* or not-*B*\" has nothing to do with the logic of judgments.
: footnote 10: \"Symbolically the second form is expressed thus
: *A* ∨ \~*A*
where ∨ means \"or\". The equivalence of the two forms is easily proved (p. 421)
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# Law of excluded middle
## Examples
For example, if *P* is the proposition:
: *Socrates is mortal.*
then the law of excluded middle holds that the logical disjunction:
: *Either Socrates is mortal, or it is not the case that Socrates is mortal.*
is true by virtue of its form alone. That is, the \"middle\" position, that Socrates is neither mortal nor not-mortal, is excluded by logic, and therefore either the first possibility (*Socrates is mortal*) or its negation (*it is not the case that Socrates is mortal*) must be true.
An example of an argument that depends on the law of excluded middle follows. We seek to prove that
: there exist two irrational numbers $a$ and $b$ such that $a^b$ is rational.
It is known that $\sqrt{2}$ is irrational (see proof). Consider the number
$$\sqrt{2}^{\sqrt{2}}$$.
Clearly (excluded middle) this number is either rational or irrational. If it is rational, the proof is complete, and
$$a=\sqrt{2}$$ and $b=\sqrt{2}$.
But if $\sqrt{2}^{\sqrt{2}}$ is irrational, then let
$$a=\sqrt{2}^{\sqrt{2}}$$ and $b=\sqrt{2}$.
Then
$$a^b = \left(\sqrt{2}^{\sqrt{2}}\right)^{\sqrt{2}} = \sqrt{2}^{\left(\sqrt{2}\cdot\sqrt{2}\right)} = \sqrt{2}^2 = 2$$,
and 2 is certainly rational. This concludes the proof.
In the above argument, the assertion \"this number is either rational or irrational\" invokes the law of excluded middle. An intuitionist, for example, would not accept this argument without further support for that statement. This might come in the form of a proof that the number in question is in fact irrational (or rational, as the case may be); or a finite algorithm that could determine whether the number is rational.
### Non-constructive proofs over the infinite {#non_constructive_proofs_over_the_infinite}
The above proof is an example of a *non-constructive* proof disallowed by intuitionists: `{{quote|The proof is non-constructive because it doesn't give specific numbers <math>a</math> and <math>b</math> that satisfy the theorem but only two separate possibilities, one of which must work. (Actually <math>a=\sqrt{2}^{\sqrt{2}}`{=mediawiki} is irrational but there is no known easy proof of that fact.) (Davis 2000:220)}} (Constructive proofs of the specific example above are not hard to produce; for example $a=\sqrt{2}$ and $b=\log_2 9$ are both easily shown to be irrational, and $a^b=3$; a proof allowed by intuitionists).
By *non-constructive* Davis means that \"a proof that there actually are mathematic entities satisfying certain conditions would not have to provide a method to exhibit explicitly the entities in question.\" (p. 85). Such proofs presume the existence of a totality that is complete, a notion disallowed by intuitionists when extended to the *infinite*---for them the infinite can never be completed:
David Hilbert and Luitzen E. J. Brouwer both give examples of the law of excluded middle extended to the infinite. Hilbert\'s example: \"the assertion that either there are only finitely many prime numbers or there are infinitely many\" (quoted in Davis 2000:97); and Brouwer\'s: \"Every mathematical species is either finite or infinite.\" (Brouwer 1923 in van Heijenoort 1967:336). In general, intuitionists allow the use of the law of excluded middle when it is confined to discourse over finite collections (sets), but not when it is used in discourse over infinite sets (e.g. the natural numbers). Thus intuitionists absolutely disallow the blanket assertion: \"For all propositions *P* concerning infinite sets *D*: *P* or \~*P*\" (Kleene 1952:48).
Putative counterexamples to the law of excluded middle include the liar paradox or Quine\'s paradox. Certain resolutions of these paradoxes, particularly Graham Priest\'s dialetheism as formalised in LP, have the law of excluded middle as a theorem, but resolve out the Liar as both true and false. In this way, the law of excluded middle is true, but because truth itself, and therefore disjunction, is not exclusive, it says next to nothing if one of the disjuncts is paradoxical, or both true and false.
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# Law of excluded middle
## Criticisms
The Catuṣkoṭi (tetralemma) is an ancient alternative to the law of excluded middle, which examines all four possible assignments of truth values to a proposition and its negation. It has been important in Indian logic and Buddhist logic as well as the ancient Greek philosophical school known as Pyrrhonism.
Many modern logic systems replace the law of excluded middle with the concept of negation as failure. Instead of a proposition\'s being either true or false, a proposition is either true or not able to be proved true. These two dichotomies only differ in logical systems that are not complete. The principle of negation as failure is used as a foundation for autoepistemic logic, and is widely used in logic programming. In these systems, the programmer is free to assert the law of excluded middle as a true fact, but it is not built-in *a priori* into these systems.
Mathematicians such as L. E. J. Brouwer and Arend Heyting have also contested the usefulness of the law of excluded middle in the context of modern mathematics.
### In mathematical logic {#in_mathematical_logic}
In modern mathematical logic, the excluded middle has been argued to result in possible self-contradiction. It is possible in logic to make well-constructed propositions that can be neither true nor false; a common example of this is the \"Liar\'s paradox\", the statement \"this statement is false\", which is argued to itself be neither true nor false. Arthur Prior has argued that The Paradox is not an example of a statement that cannot be true or false. The law of excluded middle still holds here as the negation of this statement \"This statement is not false\", can be assigned true. In set theory, such a self-referential paradox can be constructed by examining the set \"the set of all sets that do not contain themselves\". This set is unambiguously defined, but leads to a Russell\'s paradox: does the set contain, as one of its elements, itself? However, in the modern Zermelo--Fraenkel set theory, this type of contradiction is no longer admitted. Furthermore, paradoxes of self reference can be constructed without even invoking negation at all, as in Curry\'s paradox.
## Analogous laws {#analogous_laws}
Some systems of logic have different but analogous laws. For some finite *n*-valued logics, there is an analogous law called the *law of excluded*n*+1th*. If negation is cyclic and \"∨\" is a \"max operator\", then the law can be expressed in the object language by (P ∨ \~P ∨ \~\~P ∨ \... ∨ \~\...\~P), where \"\~\...\~\" represents *n*−1 negation signs and \"∨ \... ∨\" *n*−1 disjunction signs. It is easy to check that the sentence must receive at least one of the *n* truth values (and not a value that is not one of the *n*).
Other systems reject the law entirely.`{{specify|date=August 2020}}`{=mediawiki}
### Law of the weak excluded middle {#law_of_the_weak_excluded_middle}
A particularly well-studied intermediate logic is given by De Morgan logic, which adds the axiom $\neg P \lor \neg\neg P$ to intuitionistic logic, which is sometimes called the law of the weak excluded middle
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# Line of scrimmage
In gridiron football, a **line of scrimmage** is an invisible transverse line (across the width of the field) beyond which a team cannot cross until the next play has begun. Its location is based on the spot where the ball is placed after the end of the most recent play and following the assessment of any penalty yards.
## History
The line of scrimmage first came into use in 1880. Developed by Walter Camp (who introduced many innovations that are part of the modern game of American football), it replaced a contested scrimmage that had descended from the game\'s rugby roots. This uncontested line of scrimmage would set into motion many more rules that led to the formation of the modern form of gridiron football (although the Canadian rules were developed independently of the American game, despite their similarities).
## Dimensions
A line of scrimmage is parallel to the goal lines and touches one edge of the ball where it sits on the ground before the snap. In American football, the set distance of the line of scrimmage between the offense and defense is 11 in, the length of the ball. In Canadian football, the set distance of the line of scrimmage is 1 yd, more than three times as long as the American line.
Under NCAA, and NFHS rules, there are two lines of scrimmage at the outset of each play: one that restricts the offense and one that restricts the defense. The area between the two lines (representing the length of the ball as extended to both sidelines) is called the *neutral zone*.
## Rules regarding the line of scrimmage {#rules_regarding_the_line_of_scrimmage}
- Only the offensive player who snaps the ball (usually the center or long snapper) is allowed to have any part of his body in the neutral zone.
- For there to be a legal beginning of a play, at least seven players on the offensive team, including two eligible receivers, must be at, on, or within a few inches of their line of scrimmage.
- Beginning in 2019, high school football will allow as few as five players on a line of scrimmage, but in practice, the limits will remain the same since teams will still be limited to four persons behind the line of scrimmage; the difference would only come into play if a team plays offense with fewer than 11 players.
## Presentation during broadcasts {#presentation_during_broadcasts}
Modern video techniques enable broadcasts of American football to display a visible line on the screen representing the line of scrimmage. The line is tapered according to the camera angle and gets occluded by players and other objects as if the line were painted on the field. The line may represent the line of scrimmage or the minimum distance that the ball must be moved for the offensive team to achieve a first down.
## Misnomers
Many fans and commentators refer colloquially to the entire neutral zone as the \"line of scrimmage\", although this is technically incorrect. In the NFL rulebook, only the defensive-side restraining line is officially considered a line of scrimmage
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# Laurales
The **Laurales** are an order of flowering plants. They are magnoliids, related to the Magnoliales.
The order includes about 2500--2800 species from 85 to 90 genera, which comprise seven families of trees and shrubs. Most of the species are tropical and subtropical, though a few genera reach the temperate zone. The best known species in this order are those of the Lauraceae (for example bay laurel, cinnamon, avocado, and *Sassafras*), and the ornamental shrub *Calycanthus* of the Calycanthaceae.
The earliest lauraceous fossils are from the early Cretaceous. It is possible that the ancient origin of this order is one of the reasons for its highly diverged morphology. Presently no single morphological property is known, which would unify all the members of Laurales. The presently accepted classification is based on molecular and genetic analysis.
## Classification
The first botanist to think of the Laurales as a natural group was H. Hallier in 1905. He viewed them as being derived from the Magnoliales. During some or all of the 20th century, the Laurales generally included *Amborella* and the plants now classified in Austrobaileyales and Chloranthaceae. They were not removed until the advent of molecular data in the late 20th century; their previous inclusion made it harder to determine the relationships within the Laurales and between the Laurales and other groups.
The following families are included in the Angiosperm Phylogeny Group system (APG III):
<table>
<tbody>
<tr class="odd">
<td style="background:#fff; padding:2.5px"><p>order <strong>Laurales</strong></p>
<dl>
<dt></dt>
<dd>
family Atherospermataceae
</dd>
<dd>
family Calycanthaceae
</dd>
<dd>
family Gomortegaceae
</dd>
<dd>
family Hernandiaceae
</dd>
<dd>
family Lauraceae
</dd>
<dd>
family Monimiaceae
</dd>
<dd>
family Siparunaceae
</dd>
</dl></td>
<td><p>{{clade| style=font-size:75%;line-height:75%</p></td>
<td><p>label1=Magnoliids</p></td>
<td><p>1={{clade</p></td>
<td><p>1={{clade</p></td>
<td><p>1=Canellales</p></td>
<td><p>2=Piperales</p>
<p><code> }}</code></p></td>
<td><p>2={{clade</p></td>
<td><p>1={{clade</p></td>
<td><p>label1=<strong>Laurales</strong></p></td>
<td><p>1={{clade</p></td>
<td><p>1=Calycanthaceae</p></td>
<td><p>2={{clade</p></td>
<td><p>1={{clade</p></td>
<td><p>1=Siparunaceae</p></td>
<td><p>2={{clade</p></td>
<td><p>1=Atherospermataceae</p></td>
<td><p>2=Gomortegaceae</p>
<p><code> }}</code><br />
<code> }}</code></p></td>
<td><p>2={{clade</p></td>
<td><p>1=Hernandiaceae</p></td>
<td><p>2={{clade</p></td>
<td><p>1=Monimiaceae</p></td>
<td><p>2=Lauraceae</p>
<p><code> }}</code><br />
<code> }}</code><br />
<code> }}</code><br />
<code> }}</code><br />
<code> }}</code></p></td>
<td><p>2=Magnoliales</p>
<p><code> }}</code><br />
<code> }}</code></p>
<p>}}</p></td>
</tr>
<tr class="even">
<td colspan="2"><p>The current composition and phylogeny of the Laurales.</p></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
Under the older Cronquist system, the Laurales included a slightly different set of families (current placement, where different, in brackets):
- Family Amborellaceae (Family Amborellaceae, unplaced)
- Family Calycanthaceae
- Family Gomortegaceae
- Family Hernandiaceae
- Family Idiospermaceae (= Calycanthaceae *pro parte*)
- Family Lauraceae
- Family Monimiaceae (Cronquist included Atherospermataceae and Siparunaceae in Monimiaceae)
- Family Trimeniaceae (Austrobaileyales)
The extinct family Araripiaceae (containing only the genus *Araripia*) is known from the Aptian of Brazil
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# Lamiales
The **Lamiales** (also known as the **mint order**) are an order of flowering plants in the asterids clade of the Eudicots. Under the APG IV system of flowering plant classification the order consists of 24 families, and includes about 23,810 species and 1,059 genera with representatives found all over the world. Well-known or economically important members of this order include aromatic, culinary, and medicinal herbs such as basil, mint, rosemary, sage, savory, marjoram, oregano, hyssop, thyme, lavender, perilla, lemon verbena, catnip, bee balm, wild dagga, and oriental motherwort, as well as olives, ash trees, teak, foxgloves, lilacs, jasmine, snapdragons, African violets, Jacarandas, Paulownias, butterfly bushes, sesame, and psyllium.
## Description
Plant species within the order Lamiales are eudicots and are herbaceous or have woody stems. Zygomorphic flowers are common, having five petals with an upper lip of two petals and lower lip of three petals, but actinomorphic flowers are also seen. Species potentially have five stamens, but these are typically reduced to two or four. Lamiales also produce a single style attached to an ovary typically containing two carpels. The ovary is mostly observed to be superior. The inflorescence is typically seen as cyme, raceme or spike. The fruit type is usually dehiscent capsules. Glandular hairs are present on the plants. A number of species of carnivorous plants are found in the families Lentibulariaceae and Byblidaceae. Protocarnivorous plant species have also been found in the order, specifically in the Martyniaceae family. Parasitic plant species are found in the order, belonging to the family Orobanchaceae. These parasitic plants can either be hemi-parasites or holoparasites.
## Taxonomy
### Phylogeny
The APG IV system gives the following cladogram for Lamiales.`{{r|APG4}}`{=mediawiki}
The Lamiales previously had a restricted circumscription (e.g., by Arthur Cronquist) that included the major families Lamiaceae (Labiatae), Verbenaceae, and Boraginaceae, plus a few smaller families. In the classification system of Dahlgren the Lamiales were in the superorder Lamiiflorae (also called Lamianae). Recent phylogenetic work has shown the Lamiales are polyphyletic with respect to order Scrophulariales and the two groups are now usually combined in a single order that also includes the former orders Hippuridales and Plantaginales. Lamiales has become the preferred name for this much larger combined group. The placement of the Boraginaceae is unclear, but phylogenetic work shows this family does not belong in Lamiales.
Also, the circumscription of family Scrophulariaceae, formerly a paraphyletic group defined primarily by plesiomorphic characters and from within which numerous other families of the Lamiales were derived, has been radically altered to create a number of smaller, better-defined, and putatively monophyletic families.
### Dating
Much research has been conducted in recent years regarding the dating the Lamiales lineage, although there still remains some ambiguity. A 2004 study, on the molecular phylogenetic dating of asterid flowering plants, estimated 106 million years (MY) for the stem lineage of Lamiales. A similar study in 2009 estimated 80 million years. Another 2009 study gives several reasons why the issue is particularly difficult to solve.
## Habitat
The Lamiales order can be found in almost all kinds of habitats world-wide. These habitats include forests, valleys, grasslands, rocky terrain, rainforests, the tropics, temperate regions, marshes, coastlines, and even frozen areas.
## Uses
The order Lamiales has a variety of species with anthropogenic uses, the most popular belonging to the Lamiaceae and Acanthaceae families. Many of these species in the order Lamiales produce medicinal properties from alkaloids and saponins to help a variety of infections and diseases. These alkaloids and saponins may help with digestion, the common cold or flu, asthma, liver infections, pulmonary infections and contain antioxidant properties.
Species within the order are also known to have properties to repel insects and help control harmful diseases from insects, such as Malaria from mosquitos. Plants of the family Acanthaceae have bioactive secondary metabolites within their mature leaves, which have been found to be toxic to insect larvae. Botanical derived insecticides are a good alternate for chemical or synthetic insecticides as it is inexpensive, abundant and safe for other plants, non-target organisms and the environment.
Many species within the order are used as decorations, flavouring agents, cosmetics and fragrances. Natural dyes can also be extracted from Lamiales species. For example, in Sardinia culture, the most common Lamiales plant species used for natural dyes is *Lavandula stoechas,* where a light-green dye is extracted from the stem
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# Letterboxing (hobby)
**Letterboxing** is an outdoor hobby that combines elements of orienteering, art, and puzzle solving. Letterboxers hide small, weatherproof boxes in publicly accessible places (like parks) and distribute clues to finding the box in printed catalogs, on one of several websites, or by word of mouth. Individual letterboxes contain a notebook and a rubber stamp, preferably hand carved or custom made. Finders make an imprint of the letterbox\'s stamp in their personal notebook, and leave an impression of their personal signature stamp on the letterbox\'s \"visitors\' book\" or \"logbook\" --- as proof of having found the box and letting other letterboxers know who has visited. Many letterboxers keep careful track of their \"find count\".
## History
The origin of letterboxing can be traced to Dartmoor, Devon, England in 1854. William Crossing in his *Guide to Dartmoor* states that a well known Dartmoor guide (James Perrott) placed a bottle for visiting cards at Cranmere Pool on the northern moor in 1854. From this hikers on the moors began to leave a letter or postcard inside a box along the trail (sometimes addressed to themselves, sometimes a friend or relative)---hence the name \"letterboxing\". The next person to discover the site would collect the postcards and post them. In 1938 a plaque and letterbox in Crossing\'s memory were placed at Duck\'s Pool on southern Dartmoor.
The first Dartmoor letterboxes were so remote and well-hidden that only the most determined walkers found them, allowing weeks to pass before the letter made its way home. Until the 1970s there were no more than a dozen sites around the moor, usually in the most inaccessible locations. Increasingly, however, letterboxes have been located in relatively accessible sites and today there are thousands of letterboxes, many within easy walking distance of the road. As a result, the tradition of leaving a letter or postcard in the box has been forgotten.
Membership of the \"100 Club\" is open to anyone who has found at least 100 letterboxes on Dartmoor. Clues to the locations of letterboxes are published by the \"100 Club\" in an annual catalogue. Some letterboxes however remain \"word of mouth\" and the clues to their location can only be obtained from the person who placed the box. Some clues may also be found in other letterboxes or on the Internet, but this is more commonly for letterboxes in places other than Dartmoor, where no \"100 Club\" or catalogue exist.
Letterboxing has become a popular sport, with thousands of walkers gathering for \'box-hunts\', and while in some areas of Dartmoor it is particularly popular amongst children, some of the more difficult to find boxes and tougher terrain are better suited to more experienced adults.
Letterboxes can be found in other areas of the United Kingdom, including the North York Moors, and have spread all over the world. The Scottish artist Alec Finlay has placed letterboxes with rubber stamp circle poems at locations around the world, including Yorkshire Sculpture Park.
Interest in letterboxing in the US is generally considered to have started with a feature article in the *Smithsonian* magazine in April 1998. Much of the terminology below is associated with letterboxing in the US and would be unfamiliar to UK letterboxers. The growing popularity of the somewhat similar activity of geocaching during the 2000s has increased interest in letterboxing as well.
## Gatherings
Letterboxers organise events, usually called *meets* or *gatherings*. The first letterbox meet was held on Dartmoor, and they are now held twice-yearly on \"clock change days\" (in March and October). Gatherings in the US are usually at parks or places with enough space for a large group of letterboxers to meet up and do exchanges (exchanging of personal stamps and/or personal travelers), as well as talk and discuss box ideas. Gatherings in the US usually have a special, one-day \"Event stamp.\" At some gatherings, boxes are created or donated to be planted nearby specifically for the gathering attendees to find.
The first gathering in North America was held in November, 1999, at The Inn at Long Trail in Killington, Vermont.
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# Letterboxing (hobby)
## Types
There are now many different kinds of letterboxes, each with some specific distinction. While purists recognise only those letterboxes planted in the wild, many new variations exist. The kinds include:
Traditional box
: A normal letterbox, hidden and uses clue to find it.
```{=html}
<!-- -->
```
Mystery box
: These are usually traditional boxes, but these \"mystery\" boxes have either vague starting areas, no starting areas, no descriptions, no clue -- any number of things to make the box extremely hard to find.
```{=html}
<!-- -->
```
Bonus box
: The clues for these are usually found in a traditional box as an extra one to find. Usually planted in the same area as the traditional that hosts its clue. Clues can be distributed in any way.
```{=html}
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Word of mouth box (WOM)
: The clue is given by word of mouth, or typed up, but a letterboxer can only receive the clue from the planter.
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Cuckoo clue
: A clue without a home. The clue is hidden in another letterbox (similar to clues for a bonus boxes), but the letterboxer that finds the clue is expected to move the clue to another nearby letterbox. The cuckoo clue typically contains directions to limit how far the clue should travel to find a new home.
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Hitchhiker
: A traveling letterbox, it is placed in a traditional letterbox for another letterboxer to find. When found, it is stamped like a traditional letterbox, but is then carried by the letterboxer to the next letterbox they find and then left in that letterbox for the next finder. The hitchhiker\'s stamp should also be recorded in the host letterbox\'s logbook, and vice versa.
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Personal traveller
: Much like a traditional box, but instead of being planted, the box is kept with the creator at all times. If another letterboxer is met on the trail or at a meet it is attainable if requested. In the US this box is usually only attainable if the other letterboxer knows the password or passphrase which is sometimes cryptic, straightforward, almost non-existent, or silly.
In the US, letterboxes have developed new forms:
Cootie
: Much like a hitchhiker, except instead of being carried from letterbox to letterbox, a letterboxer passes it to another letterboxer. It can be passed in a personal traveller, or planted on another letterboxer or their unattended bags on the trails or at gatherings. Most people are subtle about planting them---but not all.
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Flea
: Like a combination of a hitchhiker and a cootie. Either put in a traditional letterbox, like a hitchhiker, or put it on a person, like a cootie.
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Hitchhiker hostel
: This is a traditional letterbox with special qualities. Namely, it is a \"hostel\" for hitchhikers, sized and specially designated to hold multiple hitchhikers at one time. Normally, there are at least one or two hitchhikers in the box at all times, and any letterboxer who takes a hitchhiker out is required to leave a new one in its place. A hitchhiker hostel has its own stamp and logbook, just like a traditional letterbox, and any hitchhiker that is placed within it should be stamped and recorded within the logbook, preferably with both the date of its being added to the hostel (in order to make it easier to move the older hitchhikers out), and the date it is removed.
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American parasite (these should not be confused with English parasites)
: A parasite is very much like a hitchhiker except, instead of being carried by a letterboxer between letterboxes on its own, it is carried along with a hitchhiker. When a letterboxer joins a parasite to a hitchhiker (\"infecting\" it), it is stamped into the hitchhiker. The parasite\'s stamp is also recorded in the logbook of the letterbox that a hitchhiker is placed in, \"infecting\" the letterbox, as well. In the event of being placed in a letterbox that has multiple hitchhikers in it (such as a hitchhiker hostel), the parasite \"infects\" all of the hitchhikers inside. The letterboxer that has done the moving also has the choice of sending the parasite along with a different hitchhiker. (This is a relatively new variation of letterbox, and has only just recently`{{When|date=August 2024}}`{=mediawiki} begun to take off.)
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Virtual
: Online letterboxes; A scavenger hunt of sorts for an image of a letterbox through different websites, collecting answers to questions posted as the clues to the box. Answers sometimes are unscrambled or emailed to the creator; the final answer is put in a blank in a web address, which takes the finder to an image of the letterbox online.
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Limited time box
: A letterbox that has only been planted for a short amount of time. (A few days or a week, any time length the planter wants.)
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Postal (PLB)
: Boxes that are made like traditional letterboxes, but instead of being planted in the wild, they are sent via postal mail to the people on sign-up lists for the box, or around a \"ring\" of people in a postal ring, which is usually focused on a theme of some sort. Postals are also very often very well-designed and organised, as well as ornate.
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Circle poem
: A circle poem is a kind of \'art\' letterbox developed in Britain. There are one hundred planned boxes, each of which contains a rubber stamp circle poem by the Scottish poet and artist, Alec Finlay. These are sited at locations around the world, and each has its own nominated keeper.
## Find counts {#find_counts}
A letterboxer\'s *find count* or *PFX count* is organised as follows:
- The *P* (\"plants\") count is the number of boxes the letterboxer has made and placed.
- The *F* (\"finds\") count is the number of boxes the letterboxer has found in the wild.
- The *X* (\"exchanges\") count is the number of exchanges the letterboxer has.
Some boxers list individual types of boxes in their PFX counts (e.g.: `P12 F76 X45 E4 HH21 V4` would mean 12 plants, 76 finds, 45 exchanges, four events or event stamps, 21 hitchhikers, and four virtuals). Some include virtuals, hitchhikers, and other non-traditional boxes in a single find count, while some exclude them. Many letterboxers do not bother to keep count at all.
The \"PFX count\" is not a term associated with Dartmoor Letterboxing.
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# Letterboxing (hobby)
## Questing
**Questing** is a game played across a community or geographic place. Originally coined in the US, it is similar to the concept of letterboxing where clues lead to sealed boxes to be found in a type of treasure hunt.
Vital Communities, a non-profit organization in White River Junction, Vermont established the Valley Quest program as a sense-of-place education program in 1995. Valley quests map and share the Upper Valley region\'s special places. Created by school groups, scout groups, historical societies and others, there are now over 200 quests across Vermont and New Hampshire. Questing has spread to other communities, too. There is a South Shore Quests program in Hingham, Massachusetts along with programs in Keene, New Hampshire and on Martha\'s Vineyard
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# Legal technicality
The term **legal technicality** is a casual or colloquial phrase referring to a technical aspect of law. The phrase is not a term of art in the law; it has no exact meaning, nor does it have a legal definition. In public perception, it typically refers to \"procedural rules that can dictate the outcome of a case without having anything to do with the merits of that case.\" However, as a vague term, the definition of a technicality varies from person to person, and it is often simply used to denote any portion of the law that interferes with the outcome desired by the user of the term.An example: In the case of U.S. v. Shipp, 214 US 386 (1909), the U.S. Supreme Court quoted a local newspaper as follows:
- "In the News, published the evening of March 19, there was an editorial reviewing the local proceedings, which concluded: \'All of this delay is aggravating to the community. The people of Chattanooga believe that Johnson is guilty, and that he ought to suffer the penalty of the law as speedily as possible. If by legal technicality the case is prolonged and the culprit finally escapes, there will be no use to plead with a mob here if another such crime is committed. Such delays are largely responsible for mob violence all over the country.\'"(U.S. v. SHIPP, 1909) The newspaper plainly was using the phrase \"legal technicality\" to refer to technical aspects of the law which the newspaper\'s editorial staff saw as an obstacle to its preferred outcome.
Some legal technicalities govern legal procedure, enable or restrict access to courts, and/or enable or limit the discretion of a court in handing down judgment. These are aspects of procedural law. Other legal technicalities deal with aspects of substantive law, that is, aspects of the law that articulate specific criteria that a court uses to assess a party\'s compliance with or violation of, for example, one or more criminal laws or civil laws.In the U.S., for example, the Supreme Court has used the informal phrase \"legal technicality\" in its decisions 13 times in the last century. In every case the use of the words refers to merely \"technicalities of the law\". The three most recent uses are illustrative:
- \(1\) "The function of counsel as a guide through complex legal technicalities long has been recognized by this Court." (U.S. v. Ash, 1973)
- \(2\) "Furthermore, during the federal habeas corpus hearing Davis showed his awareness of legal technicalities."(used in a footnote, Davis v. North Carolina, 1966)
- \(3\) "If recovery were denied in this case, the railroads, by the simple expedient of doing each other\'s work, could tie their employees up in legal technicalities\...\" (Shenker v. Baltimore and Ohio R.Co., 1963)
In some cases, people may regard legal protections such as the exclusionary rule as legal technicalities.
In the introduction to *A Dictionary of Human Rights*, David Robertson states (emphasis in original): `{{quote|"One cannot dismiss legal technicalities and cut through legal language entirely, because [[Human rights|rights]] basically ''are'' legal technicalities. What cannot be expressed with some clarity in a legal document will not be preserved and protected."<ref name="Robertson2004">{{cite book | author = David Robertson | date = 25 November 2004 | title = A Dictionary of Human Rights | publisher = Routledge | pages = | isbn = 978-1-136-95872-4 | url = https://books.google.com/books?id=jatlAgAAQBAJ}}</ref>}}`{=mediawiki}
In 1928, William W. Brewton wrote that the law is inevitably technical because a relatively small number of laws have to account for a much larger number of possible situations. Since the rules and principles of law are expected to apply to many different cases, they cannot always account for the exact circumstances, which can result in failures of justice in individual cases even when the greatest possible overall justice is being achieved. He said that people mistakenly criticize the technicalities, which are both \"necessary and inevitable\", when they should focus instead on preventing the original causes of litigation and crime.
Brewton wrote that the rules of procedure are complex because there is no simplified approach that would be sufficient
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# Lionhead Studios
**Lionhead Studios Limited** was a British video game developer founded in July 1997 by Peter Molyneux, Mark Webley, Tim Rance, and Steve Jackson. The company is best known for the *Black & White* and *Fable* series. Lionhead started as a breakaway from developer Bullfrog Productions, which was also founded by Molyneux. Lionhead\'s first game was *Black & White*, a god game with elements of artificial life and strategy games. *Black & White* was published by Electronic Arts in 2001. Lionhead Studios is named after Webley\'s hamster, which died not long after the naming of the studio, as a result of which the studio was very briefly renamed to Redeye Studios.
*Black & White* was followed up with the release of an expansion pack named *Black & White: Creature Isle*. Lionhead released *Fable*, from satellite developer Big Blue Box. In 2005, Lionhead released *The Movies* and *Black & White 2*. Lionhead was acquired by Microsoft Studios in April 2006 due to encountering financial difficulties. Many Lionhead developers left around this time, including co-founder Jackson and several developers who left to found Media Molecule. Molyneux left Lionhead in early 2012 (shortly after the resignation of another group of developers who were dissatisfied with the company) to found 22cans because he wanted to be more creative. After Molyneux\'s departure, Microsoft had Lionhead switch to developing games as a service games. As a result, there were many changes within the studio.
In early March 2016, Microsoft announced that it had proposed closing Lionhead Studios and that the planned game *Fable Legends* would be cancelled; Lionhead was closed down almost two months later, on 29 April. A few months after Lionhead\'s closure, two key people (Webley and Gary Carr, who was Lionhead\'s creative director) founded Two Point Studios.
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# Lionhead Studios
## History
### Founding
Peter Molyneux founded Bullfrog Productions in 1987, which was later acquired by Electronic Arts (EA) in 1995. Around 1996, Molyneux had contemplated leaving Bullfrog, as he felt limited in his creative freedom under Electronic Arts. He along with Lionhead\'s eventual co-founders, Mark Webley, Tim Rance and Steve Jackson, started developing plans for a new studio. In 1997, due to a series of events and from issues arising between Molyneux and Electronic Arts, he ultimately left the company in July 1997, co-founding Lionhead shortly after that, along with Mark Webley, Tim Rance, and Steve Jackson (who co-founded Games Workshop and co-authored the *Fighting Fantasy* series). On his recruitment, Jackson said \"It was an offer I couldn\'t refuse\", as he wanted to get back to making games instead of writing about them (Jackson had interviewed Molyneux about Bullfrog and *Dungeon Keeper*, but for much of it, they discussed German board games instead. This led to them meeting frequently for an event called \"Games Night\"). Molyneux assured him that his lack of programming knowledge was an asset rather than a problem. Lionhead is the second Bullfrog break-off group, after Mucky Foot Productions (founded in February 1997). According to Glenn Corpes (who co-founded another: Lost Toys), Lionhead was Molyneux\'s \"take on what Bullfrog used was\".
The idea of the company was to develop quality games without growing too large. On the differences between Lionhead and Bullfrog, Molyneux said: \"This time round we\'re a professionally run company. Gone are the days of shooting work experience people with guns\". He also said that Lionhead would develop only one game at a time. Early Lionhead employees included Demis Hassabis, Mark Healey (Lionhead\'s first artist), and Alex Evans.
The name Lionhead came from Webley\'s pet hamster, who had died the week prior to the foundation. The hamster\'s death was taken as a bad sign, so other names, including Black Box, Red Rocket, Midnight, and Hurricane were considered but none had unanimous support. The name Red Eye was then suggested, and everyone liked it (the decision needed to be quick as Molyneux was to be interviewed by *Edge*). However, for reasons including the name being in use by many other companies, the domains redeye.com and redeye.co.uk being taken and lionhead.co.uk had already been registered by Rance, the company already having Lionhead business cards, and the possibility of the name Red Eye having drinking connotations, the name was reverted to Lionhead. By the time the name was reverted, it was too late for *Edge* to amend their interview, so it was published with the company being referred to as Redeye Studios. In the interview, Molyneux stated that his ambition for the company was to \"make it a world-renowned software development house -- known in Europe, Japan and America for top-quality games\".
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# Lionhead Studios
## History
### Early years {#early_years}
Word about Lionhead began spreading quickly. Within the first month, companies including Sega, Nintendo, Eidos, GTI, and Lego had arranged meetings. One day, \"a major Japanese console manufacturer\" had come to present plans for a \"next generation console\", but by then, Lionhead\'s first game had already been committed.
By the end of July, Lionhead had signed a one-game contract with Electronic Arts. The studio was initially run out of Molyneux\'s mansion in Elstead, before relocating to the University of Surrey Research Park in 1998. According to Jackson, it was \"a mere stone\'s throw from Bullfrog\'s old lily pad on the very same estate\". For the staff who had come from Bullfrog, it was \"a little like coming home\". Six companies were competing for a space, and Lionhead won due to Molyneux and Bullfrog\'s reputation.
Lionhead had originally intended to make their first public appearance at the E3 trade show in May 1997. This was cancelled at the last minute because there was not yet any deal with Electronic Arts, and there was the possibility of not being able to discuss Lionhead. The debut was made in September at the European Computer Trade Show instead. According to Jackson, \"Everyone\" was interested in Lionhead: journalists from many major European magazines frequently turned up at Lionhead\'s suite.
By August 1998, after the studio placed a job advertisement in *Edge* which received over 100 applications, Russell Shaw had been hired as Head of Music. Lionhead\'s first title was *Black & White*, which was published by Electronic Arts under terms of Molyneux\'s severance package from departing Bullfrog. It was released in 2001 to widespread critical acclaim. It won BAFTA Awards for Interactivity and Moving Images in 2001, and Academy of Interactive Arts & Sciences awards for Computer Innovation and Computer Game of the Year the following year. An expansion pack *Black & White: Creature Isle*, was released the following year. In Lionhead\'s early years, Jackson wrote columns about the company and the development of *Black & White* for magazines such as *PC Zone* and *Génération 4*. The articles were also published on Lionhead\'s website.
According to Eurogamer, Lionhead \"was a continuation of the culture and development ethic of Bullfrog\", which included the playing of pranks. One such prank was one \"that would go down in Lionhead history\". It involved a visit from the Mayor of Guildford during the development of *Black & White*: Healey had inserted a couple of wires into a woollen glove with the other ends put into a floppy drive. Molyneux was forced to explain to the Mayor how the game\'s on-screen hand was controlled by the glove (which Healey was wearing), when it was actually being controlled by a mouse with Healey\'s other hand, which were hidden. The Mayor fell for the trick.
By June 2002, Lionhead had established satellite companies, including Big Blue Box Studios, Intrepid Computer Entertainment (also called Intrepid Developments), and Black & White Studios. Lionhead and its satellite studios had 107 employees and were developing six games: *Fable*, *The Movies*, a project called *Creation* (also called *Dimitri*), *Black & White NG* (*Black & White Next Generation*), *Black & White 2*, and *BC*, despite Molyneux\'s earlier statement that Lionhead would only work on one at a time. The idea to form these satellite studios came from Jackson during the development of *Black & White*. Big Blue Box Studios was founded in July 1998 by Ian Lovett and Simon and Dene Carter, because of a desire to leave Electronic Arts and \"the sadly ravaged corpse of Bullfrog it had left behind\". Intrepid Computer Entertainment was founded by Joe Rider and Matt Chilton, and Black & White Studios was headed by Jonty Barnes, who was a programmer on *Dungeon Keeper* and *Black & White*. According to Molyneux, *The Movies* came about because Lionhead listened to some financial advisers after the release of *Black & White*, who said that the company would die if it did not float on the stock market. The company then went for initial public offering, which Molyneux said was \"The most stupid thing that ever happened\" because it meant having to expand quickly and develop more games. In the early 2000s, Lionhead was \"growing very fast\". The company was nominated for the 2002 Golden Joystick Awards British Developer of the Year award.
Before *Fable* shipped, Lionhead purchased Big Blue Box and Intrepid. The decision to merge Big Blue Box with Lionhead was made to accelerate the completion of the game. *Fable* was released in 2004 for the Xbox, and won AIAS awards for Outstanding Achievement in Character or Story Development and Outstanding Achievement in Original Musical Composition in 2005. *Dimitri* was cancelled. In 2003, Gary Carr joined Lionhead. Due to the stock market crash in the aftermath of 9/11, Lionhead sought investments from venture capitalists. Deals with various firms were signed in July 2004. This came at a time when the company needed money for the development of five games to be released by different publishers.
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# Lionhead Studios
## History
### Acquisition by Microsoft {#acquisition_by_microsoft}
In 2005, Lionhead released two titles: *Black & White 2* and *The Movies*. Around this time, Lionhead had roughly 220 employees. These titles did not achieve a massive impact in sales (Molyneux described *The Movies* as \"a disaster\" due to lack of playtesting. However, it won a BAFTA Award for Simulation in 2006.), and Lionhead soon afterwards encountered financial difficulty. Due to this, on 6 April 2006, Lionhead Studios was acquired by Microsoft. Ubisoft was another contender for the acquisition of Lionhead, but Molyneux believed Microsoft to be \"perfect\", and said people wanted \"the safety and security of being part of something bigger\". Microsoft wanted the *Fable* series to be an Xbox exclusive, and knew that if Ubisoft had acquired Lionhead, it would have gone to the PlayStation 3 instead, a conclusion that Webley concurred with. Lionhead were concerned with securing the company\'s future and protecting jobs and spent \"months\" preparing for the acquisition. Some, such as Andy Robson (Head of Testing), were dissatisfied with the deal. He claimed Lionhead were trying to cheat him out of money he was owed. Molyneux believed that Microsoft were pleased with the deal, and said that they made their money back due to the release of the \"fantastically successful\" *Fable II* (it won a BAFTA Award for Action and Adventure in 2009) for the Xbox 360 in 2008. In late 2005, Healey left Lionhead with Evans and a couple of other developers to found Media Molecule. Jackson also left in 2006 when Microsoft took over.
The general consensus amongst Lionhead was that the buyout \"benefited Lionhead greatly\". Microsoft purchased a lease that enabled Lionhead to expand to multiple floors, a canteen, and an office revamp. According to *Fable* franchise director Ted Timmins, the improvements felt like Lionhead was \"a real developer\". The pranks were also reduced. During the development of *Fable II*, Lionhead received death threats because the game featured a gay character and some of the leading characters were black. Microsoft, for the most part, left Lionhead alone during the development of *Fable II*, but did ask them to change the icon of a condom (the game featured a dog who was able to dig them up) to a modern one, despite the game being set in an earlier era. Lionhead and Microsoft conflicted over the game\'s marketing: Microsoft believed that role-playing games were about dragons and wanted to market the game as such, despite Lionhead\'s insistence that the game was \"a Monty Python-esque comedy\". According to *Fable* art director John McCormack, the marketing was \"shit\" and that dragons were *Dungeons & Dragons* fare and had nothing to do with *Fable*. Despite the row, most of the *Fable II* team thought highly of the relationship between Lionhead and Microsoft, and after the game\'s release, Lionhead won a BAFTA Award for the best action adventure game. There was also a dispute over *Fable III*{{\'}}s box art. The game was developed and released in 18 months, but fell short of the expectations set by the previous installment. Six months before its release, Lionhead attempted to integrate Kinect into the game, but failed. In June 2009, Molyneux became creative director of Microsoft Studios\' European division, a position he held concurrently with the head of Lionhead.
Another Kinect-based project, *Milo & Kate* was in development but was cancelled. Molyneux blamed the cancellation on Kinect\'s technology and Microsoft\'s attitude towards their target market. Its development team moved to *Fable: The Journey*, another Kinect game that was released in 2012 and was \"disastrous\".
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# Lionhead Studios
## History
### Molyneux\'s departure {#molyneuxs_departure}
By early 2012, Lionhead were suffering what had been described as \"Black Monday\". Several Lionhead veterans, dissatisfied with the way the company was heading, resigned on the same day. According to McCormack, Molyneux \"lost it\" and ordered them to leave the premises immediately. Molyneux apologised for this outburst, and soon afterwards, in March, he too left Lionhead and founded 22cans, along with Rance, who had ceased being Lionhead\'s chief technology officer sometime prior. He was also joined by Paul McLaughlin, who was Lionhead\'s head of art. Webley then temporarily took over as head of the studio, before being replaced by Scott Henson early the following year. Molyneux said he left Lionhead because he wanted to increase his creativity. He also said that after 12 years (the series began in 2000 by Big Blue Box Studios), everyone was \"tired\" of the *Fable* series. Craig Oman, producer of *Fable Anniversary*, said that Molyneux\'s departure gave Lionhead an opportunity to reidentify itself.
Molyneux\'s departure had a much greater impact than those of other veterans who had already left the company. Lionhead became more professional and organised according to some staff. One said that Molyneux had the power to keep Microsoft at bay, and his departure left the remaining staff vulnerable. Around this time, Microsoft insisted that Lionhead make a games as a service *Fable* game to reinvigorate interest in the series or face closure. Due to the switch to service based model, the idea of *Fable IV* was rejected, and experts in monetisation and competitive game design were hired to assist the transition. At some point, John Needham became head of Lionhead. Creative director Carr (who had played major roles in *Milo & Kate*, *The Movies*, and *Fable: The Journey*) left in September 2015, and a new one, David Eckelberry, was brought in. Lionhead encountered difficulty in this project, *Fable Legends*, because they had not done anything like it before.
### Closure
On 7 March 2016, Microsoft announced the cancellation of *Fable Legends* and a proposed closure of Lionhead Studios. The closure came as a shock to some staff, who had suspected Microsoft were concerned but did not think Lionhead would be shut down: it was thought that the worst-case scenario would be that *Fable Legends*{{\'}}s assets would be used for *Fable IV*. Some staff put the closure down to \"a string of bad decisions and mismanagement\". The game was supposed to be released in summer 2015, after the release of Windows 10, and some said Lionhead had failed to meet their own targets. To comply with UK employment law, there was a consultation period and the *Fable Legends* servers were not shut down until mid-April so that customers could get refunds. There was a small \"live operations\" team that conducted this process, but for others, work was optional. An attempt to save the project was made, under the name of *Project Phoenix*. This would have involved developing it with a new studio under licence from Microsoft, who supported the idea, but it failed due to lack of time and the fact that many Lionhead employees had found new jobs. On 29 April 2016, Lionhead closed down. One Lionhead developer, Charlton Edwards (the only one remaining who had worked on *Black & White*), said there was a giveaway and he received some of the \"trophies\". Both current and former Lionhead developers gave the studio a send-off at a pub. On 26 July, Webley and Carr founded Two Point Studios, a studio that some former Lionhead developers later joined.
In the 2021 documentary *Power On: The Story of Xbox*, Microsoft admitted that their handling of Lionhead Studios was a mistake. Phil Spencer, the current head of Xbox at Microsoft, admitted that forcing Lionhead to work on Kinect and the impact of that on the quality of their games was at fault. Spencer said \"You acquire a studio for what they\'re great at now, and your job is to help them accelerate how they do what they do, not them accelerate what you do
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# Leading question
A **leading question** is a question that suggests a particular answer and contains information the examiner is looking to have confirmed. The use of leading questions in court to elicit testimony is restricted in order to reduce the ability of the examiner to direct or influence the evidence presented. Depending on the circumstances, leading questions can be objectionable or proper.
The propriety of leading questions generally depends on the relationship of the witness to the party conducting the examination. An examiner may generally ask leading questions of a hostile witness or on cross-examination (\"Will help to elicit the testimony of a witness who, due to age, incapacity, or limited intelligence, is having difficulty communicating their evidence\"), but not on direct examination (to \"coach\" the witness to provide a particular answer).
Cairns-Lee, Lawley & Tosey have reviewed the role of leading questions in research interviews and proposed a typology and a \'cleanness rating\' to facilitate researchers to review and assess the influence of their interview questions.
## Example
Leading questions may often be answerable with a yes or no (though not all yes--no questions are leading). Leading questions are distinct from loaded questions, which are objectionable because they contain implicit assumptions (such as \"Have you stopped beating your wife?\" indirectly asserting that the subject both *has* a wife, and *has* beaten her at some point).
Leading question: \"Mr. Smith\'s car was traveling 20 miles over the speed limit when he lost control of his vehicle and slammed into the victim\'s car, right?\" (Leads the witness to the conclusion that Mr. Smith was speeding, and as a result lost control of his vehicle, leading to the accident, which was clearly his fault.)
Neutral question: \"How fast would you estimate Mr. Smith\'s car was traveling before the collision?\"
Even neutral questions can lead witnesses to answers based on word choice, response framing, assumptions made, and form. The words \"fast\", \"collision\" and \"How\", for example, can alter speed estimates provided by respondents.
When someone asks a leading question, they expect the other person to agree with the leading question.
\"Our company has the best sandwiches, right?\"
They expect the answer to agree that the sandwiches are the best.
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# Leading question
## United States {#united_states}
While each state has its own rules of evidence, many states model their rules on the Federal Rules of Evidence, which themselves relate closely to the common-law mode of examination. Rule 611(c) of the Federal Rules of Evidence provides that:
Leading questions are the primary mode of examination of witnesses who are hostile to the examining party, and are not objectionable in that context. Examination of hostile witnesses usually takes place on cross-examination. As the rule recognizes, the examination of a \"hostile witness, an adverse party, or a witness identified with an adverse party\" will sometimes take place on direct examination, and leading questions are permitted.
In practice, judges will sometimes permit leading questions on direct examination of friendly witnesses with respect to preliminary matters that are necessary to provide background or context, and which are not in dispute; for example, a witness\'s employment or education. Leading questions may also be permitted on direct examination when a witness requires special handling, for example a child. However, the court must take care to be sure that the examining attorney is not *coaching* the witness through leading questions. Courts may also cite the various editions of McCormick\'s and Wigmore\'s treatises on evidence to answer whether a closed-ended question is inherently leading.
Although Rule 611(c) of the Federal Rules of Evidence (and comparable rules of many states) do not prohibit leading questions on re-direct, some`{{Which|date=July 2012}}`{=mediawiki} states have expressly limited the use of leading questions on re-direct. As a practical matter, it rests within the trial court\'s discretion as to what leading questions may be asked on re-direct. Generally speaking, leading questions will be more liberally permitted on re-direct in order to establish a foundation and call the attention of the witness to specific testimony elicited on cross examination. Additionally, on re-direct, an interrogator will often ask questions which specifically seek to elicit whether an inference resulting from questioning on cross examinations is accurate. Although these types of questions will likely result in a \"yes\" or \"no\" response, they are properly understood to be direct questions, not leading questions, and are permissible.
Exceptions to general restrictions against leading questions may arise,
- Where the witness is hostile to the examiner, or reluctant or unwilling to testify, in which situation the witness is unlikely to accept being \"coached\" by the questioner.
- To bring out preliminary matters (name, occupation, and other pedigree information).
- Where the memory of the witness has been exhausted and there is still information to be elicited
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# Relativist fallacy
The **relativist fallacy**, also known as the **subjectivist fallacy**, is claiming that something is true for one person but not true for someone else, when in fact that thing is an objective fact. The fallacy rests on the law of noncontradiction. The fallacy applies only to objective facts, or what are alleged to be objective facts, rather than to facts about personal tastes or subjective experiences, and only to facts regarded in the same sense and at the same time.
## Interpretations
There are at least two ways to interpret the relativist fallacy: either as identical to relativism (generally), or as the ad hoc adoption of a relativist stance purely to defend a controversial position.
On the one hand, discussions of the relativist fallacy that portray it as *identical to* relativism (e.g., linguistic relativism or cultural relativism) are themselves committing a commonly identified fallacy of informal logic---namely, begging the question against an earnest, intelligent, logically competent relativist. It is itself a fallacy to describe a controversial view as a \"fallacy\"---not, at least, without arguing that it is a fallacy. In any event, it does not do to argue as follows:
1. To advocate relativism, even some sophisticated relativism, is to commit the relativist fallacy.
2. If one commits a fallacy, one says something false or not worth serious consideration.
3. Therefore, to advocate relativism, even some sophisticated relativism, is to say something false or not worth serious consideration.
This is an example of circular reasoning. The second step includes an argument from fallacy.
On the other hand, if someone adopts a simple relativist stance as an ad hoc defense of a controversial or otherwise compromised position---saying, in effect, that \"what is true for you is not necessarily true for me,\" and thereby attempting to avoid having to mount any further defense of the position---one might be said to have committed a fallacy. The accusation of having committed a fallacy might rest on either of two grounds: (1) the relativism on which the bogus defense rests is so simple and meritless that it straightforwardly contradicts the law of noncontradiction; or (2) the defense (and thus the fallacy itself) is an example of ad hoc reasoning. It puts one in the position of asserting or implying that truth or standards of logical consistency are relative to a particular thinker or group and that under some other standard, the position is correct despite its failure to stand up to logic.
Determining whether someone has committed a relativist fallacy---by any interpretation---requires distinguishing between things that are true *for* a particular person, and things that are true *about* that person. Take, for example, the statement proffered by Alice: \"More Americans than ever are overweight.\" One may introduce arguments for and against this proposition, based upon such things as standards of statistical analysis, the definition of \"overweight,\" etc. The position answers to objective logical debate. If Bob answers Alice, saying \"That may be true for you, but it is not true for me,\" he has given an answer that is fallacious as well as somewhat meaningless in the context of Alice\'s original statement.
Conversely, take the new statement by Alice, who is 5 ft tall, \"270 lb is grossly overweight.\" Bob, who is 6 ft, and weighs an exact, well-conditioned 270 lb, replies, \"That may be true for you, but it is not true for me.\" In this context, Bob\'s reply is both meaningful and arguably accurate. As he is discussing something that is true *about* himself, he is not barred from making an argument that considers subjective facts, and so he does not commit the fallacy
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# Equivocation
In logic, **equivocation** (\"calling two different things by the same name\") is an informal fallacy resulting from the use of a particular word or expression in multiple senses within an argument.
It is a type of ambiguity that stems from a phrase having two or more distinct meanings, not from the grammar or structure of the sentence.
## Fallacy of four terms {#fallacy_of_four_terms}
Equivocation in a syllogism (a chain of reasoning) produces a fallacy of four terms (*quaternio terminorum*). Below is an example:
: Since only man \[human\] is rational.
: And no woman is a man \[male\].
: Therefore, no woman is rational.
The first instance of \"man\" implies the entire human species, while the second implies just those who are male.
## Motte-and-bailey fallacy {#motte_and_bailey_fallacy}
Equivocation can also be used to conflate two positions which share similarities, one modest and easy to defend and one much more controversial. The arguer advances the controversial position, but when challenged, they insist that they are only advancing the more modest position
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# No true Scotsman
**No true Scotsman** or **appeal to purity** is an informal fallacy in which one modifies a prior claim in response to a counterexample by asserting the counterexample is excluded by definition. Rather than admitting error or providing evidence to disprove the counterexample, the original claim is changed by using a non-substantive modifier such as \"true\", \"pure\", \"genuine\", \"authentic\", \"real\", or other similar terms.
Philosopher Bradley Dowden explains the fallacy as an \"ad hoc rescue\" of a refuted generalization attempt. The following is a simplified rendition of the fallacy:
Person A: \"No Scotsman puts sugar on his porridge.\" Person B: \"But my uncle Angus is a Scotsman and he puts sugar on his porridge.\" Person A: \"But no `{{em|true}}`{=mediawiki} Scotsman puts sugar on his porridge.\"
## Occurrence
The \"no true Scotsman\" fallacy is committed when the arguer satisfies the following conditions:
- not publicly retreating from the initial, falsified *a posteriori* assertion
- offering a modified assertion that definitionally excludes a targeted unwanted counterexample
- using rhetoric to signal the modification
An appeal to purity is commonly associated with protecting a preferred group. Scottish national pride may be at stake if someone regularly considered to be Scottish commits a heinous crime. To protect people of Scottish heritage from a possible accusation of guilt by association, one may use this fallacy to deny that the group is associated with this undesirable member or action. \"No `{{em|true}}`{=mediawiki} Scotsman would do something so undesirable\"; i.e., the people who would do such a thing are tautologically (definitionally) excluded from being part of our group such that they cannot serve as a counterexample to the group\'s good nature.
## Origin and philosophy {#origin_and_philosophy}
The description of the fallacy in this form is attributed to the British philosopher Antony Flew, who wrote, in his 1966 book *God & Philosophy*,
In his 1975 book *Thinking About Thinking*, Flew wrote:
David P. Goldman, writing under his pseudonym \"Spengler\", compared distinguishing between \"mature\" democracies, which never start wars, and \"emerging democracies\", which may start them, with the \"no true Scotsman\" fallacy. Spengler alleges that political scientists have attempted to save the \"US academic dogma\" that democracies never start wars against other democracies from counterexamples by declaring any democracy which does indeed start a war against another democracy to be flawed, thus maintaining that no `{{em|true and mature}}`{=mediawiki} democracy starts a war against a fellow democracy.
Cognitive psychologist Steven Pinker has suggested that phrases like \"no true Christian ever kills, no true communist state is repressive and no true Trump supporter endorses violence\" exemplify the fallacy
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# Slippery slope
*The Slippery Slope*\|the film\|Slippery Slope{{!}}*Slippery Slope*}} `{{Use dmy dates|date=May 2024}}`{=mediawiki} In a **slippery slope argument**, a course of action is rejected because the slippery slope advocate believes it will lead to a chain reaction resulting in an undesirable end or ends. The core of the slippery slope argument is that a specific decision under debate is likely to result in unintended consequences. The strength of such an argument depends on whether the small step really is likely to lead to the effect. This is quantified in terms of what is known as the warrant (in this case, a demonstration of the process that leads to the significant effect).
This type of argument is sometimes used as a form of fearmongering in which the probable consequences of a given action are exaggerated in an attempt to scare the audience. When the initial step is not demonstrably likely to result in the claimed effects, this is called the **slippery slope fallacy**. This is a type of informal fallacy, and is a subset of continuum fallacy, in that it ignores the possibility of middle ground and assumes a discrete transition from category A to category B. Other idioms for the slippery slope fallacy are the **thin edge of the wedge**, **domino fallacy** (as a form of domino effect argument) or *dam burst* , and various other terms that are sometimes considered distinct argument types or reasoning flaws, such as the *camel\'s nose in the tent*, *parade of horribles*, *boiling frog*, and *snowball effect*.
## Slopes, arguments, and fallacies {#slopes_arguments_and_fallacies}
Some writers distinguish between a slippery slope `{{em|event}}`{=mediawiki} and a slippery slope `{{em|argument}}`{=mediawiki}. A slippery slope `{{em|event}}`{=mediawiki} can be represented by a series of conditional statements, namely:
The idea being that through a series of intermediate steps, `{{var|p}}`{=mediawiki} will imply `{{var|z}}`{=mediawiki}. Some writers point out that strict necessity isn\'t required and it can still be characterized as a slippery slope if at each stage the next step is plausible. With strict implication, `{{var|p}}`{=mediawiki} will imply `{{var|z}}`{=mediawiki}, but if at each step the probability is 90%, for example, then the more steps there are, the less likely it becomes that `{{var|p}}`{=mediawiki} will cause `{{var|z}}`{=mediawiki}.
A slippery slope `{{em|argument}}`{=mediawiki} is typically a negative argument where there is an attempt to discourage someone from taking a course of action because if they do it will lead to some unacceptable conclusion. Some writers point out that an argument with the same structure might be used in a positive way in which someone is encouraged to take the first step because it leads to a desirable conclusion.
If someone is `{{em|accused}}`{=mediawiki} of using a slippery slope argument then it is being suggested they are guilty of fallacious reasoning, and while they are claiming that `{{var|p}}`{=mediawiki} implies `{{var|z}}`{=mediawiki}, for whatever reason, this is not the case. In logic and critical thinking textbooks, slippery slopes and slippery slope arguments are normally discussed as a form of `{{em|fallacy}}`{=mediawiki}, although there may be an acknowledgement that non-fallacious forms of the argument can also exist.
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# Slippery slope
## Types of argument {#types_of_argument}
Different writers have classified slippery slope arguments in different and often contradictory ways, but there are two basic types of argument that have been described as slippery slope arguments. One type has been called *the causal slippery slope*, and the distinguishing feature of this type is that the various steps leading from p to z are events with each event being the cause of the next in the sequence. The second type might be called *the judgmental slippery slope* with the idea being that the \'slope\' does not consist of a series of events but is such that, for whatever reason, if a person makes one particular judgment they will rationally have to make another and so on. The judgmental type may be further sub-divided into conceptual slippery slopes and decisional slippery slopes.
Conceptual slippery slopes, which Trudy Govier calls *the fallacy of slippery assimilation*, are closely related to the sorites paradox. So, in the context of talking about slippery slopes, Merilee Salmon writes: \"The slippery slope is an ancient form of reasoning. According to van Fraassen (*The Scientific Image*), the argument is found in Sextus Empiricus that incest is not immoral, on the grounds that \'touching your mother\'s big toe with your little finger is not immoral, and all the rest differs only by degree.{{\'\"}}
Decisional slippery slopes are similar to conceptual slippery slopes in that they rely on there being a continuum with no clear dividing lines such that if you decide to accept one position or course of action then there will, either now or in the future, be no rational grounds for not accepting the next position or course of action in the sequence.
The difficulty in classifying slippery slope arguments is that there is no clear consensus in the literature as to how terminology should be used. It has been said that whilst these two fallacies \"have a relationship which may justify treating them together\", they are also distinct, and \"the fact that they share a name is unfortunate\". Some writers treat them side by side but emphasize how they differ. Some writers use the term *slippery slope* to refer to one kind of argument but not the other, but don\'t agree on which one, whilst others use the term to refer to both. So, for example:
- Christopher Tindale gives a definition that only fits the causal type. He says: \"Slippery Slope reasoning is a type of negative reasoning from consequences, distinguished by the presence of a causal chain leading from the proposed action to the negative outcome.\"
- Merrilee Salmon describes the fallacy as a failure to recognise that meaningful distinctions can be drawn and even casts the \"domino theory\" in that light.
- Douglas N. Walton says that an essential feature of slippery slopes is a \"loss of control\" and this only fits with the decisional type of slippery slope. He says that, \"The domino argument has a sequence of events in which each one in the sequence causes the next one to happen in such a manner that once the first event occurs it will lead to the next event, and so forth, until the last event in the sequence finally occurs...(and)...is clearly different from the slippery slope argument, but can be seen as a part of it, and closely related to it.\"
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# Slippery slope
## Metaphor and its alternatives {#metaphor_and_its_alternatives}
The metaphor of the \"slippery slope\" dates back at least to Cicero\'s essay *Laelius de Amicitia* (XII.41). The title character Gaius Laelius Sapiens uses the metaphor to describe the decline of the Republic upon the impending election of Gaius Gracchus: \"Affairs soon move on, for they glide readily down the path of ruin when once they have taken a start.\"
### Thin end of a wedge {#thin_end_of_a_wedge}
Walton suggests Alfred Sidgwick should be credited as the first writer on informal logic to describe what would today be called a slippery slope argument. Sidgwick wrote in 1910: `{{Blockquote|1=We must not do this or that, it is often said, because if we did we should be logically bound to do something else which is plainly absurd or wrong. If we once begin to take a certain course there is no knowing where we shall be able to stop within any show of consistency; there would be no reason for stopping anywhere in particular, and we should be led on, step by step into action or opinions that we all agree to call undesirable or untrue.}}`{=mediawiki}
Sidgwick says this is \"popularly known as the objection to a thin end of a wedge\" but might be classified now as a decisional slippery slope. However, the wedge metaphor also captures the idea that unpleasant end result is a wider application of a principle associated with the initial decision which is often a feature of decisional slippery slopes due to their incremental nature but may be absent from causal slippery slopes.
### Domino fallacy {#domino_fallacy}
T. Edward Damer, in his book *Attacking Faulty Reasoning*, describes what others might call a causal slippery slope but says:
Instead Damer prefers to call it the *domino fallacy*. Howard Kahane suggests that the domino variation of the fallacy has gone out of fashion because it was tied to the domino theory for the United States becoming involved in the war in Vietnam and although the U.S. lost that war, \"it is primarily communist dominoes that have fallen\".
### Dam burst {#dam_burst}
Frank Saliger notes that \"in the German-speaking world the dramatic image of *the dam burst* seems to predominate, in English speaking circles talk is more of the slippery slope argument\", and that \"in German writing dam burst and slippery slope arguments are treated as broadly synonymous. In particular the structural analyses of slippery slope arguments derived from English writing are largely transferred directly to the dam burst argument.\"
In exploring the differences between the two metaphors, he comments that in the dam burst the initial action is clearly in the foreground and there is a rapid movement towards the resulting events whereas in the slippery slope metaphor the downward slide has at least equal prominence to the initial action and it \"conveys the impression of a slower \'step-by-step\' process where the decision maker as participant slides inexorably downwards under the weight of its own successive (erroneous) decisions\". Despite these differences Saliger continues to treat the two metaphors as being synonymous. Walton argues that although the two are comparable \"the metaphor of the dam bursting carries with it no essential element of a sequence of steps from an initial action through a gray zone with its accompanying loss of control eventuated in the ultimate outcome of the ruinous disaster. For these reasons, it seems best to propose drawing a distinction between dam burst arguments and slippery slope arguments.\"
### Other metaphors {#other_metaphors}
Eric Lode notes that:
Bruce Waller says it is lawyers who often call it the \"parade of horribles\" argument while politicians seem to favor \"the camel\'s nose is in the tent\".
The 1985 best-selling children\'s book *If You Give a Mouse a Cookie* by Laura Joffe Numeroff and Felicia Bond popularized the general idea of the slippery slope for recent generations.
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# Slippery slope
## Defining features of slippery slope arguments {#defining_features_of_slippery_slope_arguments}
Given the disagreement over what constitutes a genuine slippery slope argument, it is to be expected that there are differences in the way they are defined. Lode says that \"although all SSAs share certain features, they are a family of related arguments rather than a class of arguments whose members all share the same form.\"
Various writers have attempted to produce a general taxonomy of these different kinds of slippery slope. Other writers have given a general definition that will encompass the diversity of slippery slope arguments. Eugene Volokh says, \"I think the most useful definition of a slippery slope is one that covers all situations where decision A, which you might find appealing, ends up materially increasing the probability that others will bring about decision B, which you oppose.\"
Those who hold that slippery slopes are causal generally give a simple definition, provide some appropriate examples and perhaps add some discussion as to the difficulty of determining whether the argument is reasonable or fallacious. Most of the more detailed analysis of slippery slopes has been done by those who hold that genuine slippery slopes are of the decisional kind.
Lode, having claimed that SSAs are not a single class of arguments whose members all share the same form, nevertheless goes on to suggest the following common features. `{{Ordered list |list_style_type=upper-alpha
|The series of intervening and gradual steps
|The idea that the slope lacks a non-arbitrary stopping place
|The idea that the practice under consideration is, in itself, unobjectionable
}}`{=mediawiki}
Rizzo and Whitman identify slightly different features. They say, \"Although there is no paradigm case of the slippery slope argument, there are characteristic features of all such arguments. The key components of slippery slope arguments are three:
1. An initial, seemingly acceptable argument and decision;
2. A \"danger case\"---a later argument and decision that are clearly unacceptable;
3. A \"process\" or \"mechanism\" by which accepting the initial argument and making the initial decision raise the likelihood of accepting the later argument and making the later decision.\"
Walton notes that these three features will be common to all slippery slopes but objects that there needs to be more clarity on the nature of the \'mechanism\' and a way of distinguishing between slippery slope arguments and arguments from negative consequences.
Corner et al. say that a slippery slope has \"four distinct components: `{{Ordered list |list_style_type=lower-roman
|An initial proposal (A).
|An undesirable outcome (C).
|The belief that allowing (A) will lead to a re-evaluation of (C) in the future.
|The rejection of (A) based on this belief.
}}`{=mediawiki}
The alleged danger lurking on the slippery slope is the fear that a presently unacceptable proposal (C) will (by any number of psychological processes---see, e.g., `{{harvnb|Volokh|2003}}`{=mediawiki}) in the future be re-evaluated as acceptable.\"
Walton adds the requirement that there must be a loss of control. He says, there are four basic components: `{{blockquote|One is a first step, an action or policy being considered. A second is a sequence in which this action leads to other actions. A third is a so-called gray zone or area of indeterminacy along the sequence where the agent loses control. The fourth is the catastrophic outcome at the very end of the sequence. The idea is that as soon as the agent in question takes the first step he will be impelled forward through the sequence, losing control so that in the end he will reach the catastrophic outcome. Not all of these components are typically made explicit ...
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# Roxen (lake)
**Roxen** (`{{IPA|sv|ˈrɔ̌ksɛn}}`{=mediawiki}) is a medium-sized lake in south-central Sweden, east of Lake Vättern, part of the waterpath Motala ström and the Göta Canal. South of Lake Roxen is the city Linköping.
Roxen, especially the western parts, is very good for birdwatching. There are natural reserves at Kungsbro and Svartåmynningen.
The lake develops in a graben depression
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# Locomotive
Road locomotive\|other uses}} `{{More citations needed|date=August 2022}}`{=mediawiki} `{{Use dmy dates|date=August 2023}}`{=mediawiki}
thumb\|upright=1.2\|A Victorian Railways R class steam locomotive in Australia thumb\|upright=1.2\|A China Railways HXD1D electric locomotive in China `{{train topics}}`{=mediawiki}
A **locomotive** is a rail vehicle that provides the motive power for a train. Traditionally, locomotives pulled trains from the front. However, push--pull operation has become common, and in the pursuit for longer and heavier freight trains, companies are increasingly using distributed power: single or multiple locomotives placed at the front and rear and at intermediate points throughout the train under the control of the leading locomotive.
## Etymology
The word *locomotive* originates from the Latin *loco* \'from a place\', ablative of *locus* \'place\', and the Medieval Latin *motivus* \'causing motion\', and is a shortened form of the term *locomotive engine*, which was first used in 1814 to distinguish between self-propelled and stationary steam engines.
## Classifications
Prior to locomotives, the motive force for railways had been generated by various lower-technology methods such as human power, horse power, gravity or stationary engines that drove cable systems. Few such systems are still in existence today. Locomotives may generate their power from fuel (wood, coal, petroleum or natural gas), or they may take power from an outside source of electricity. It is common to classify locomotives by their source of energy. The common ones include:
### Steam
A steam locomotive is a locomotive whose primary power source is a steam engine. The most common form of steam locomotive also contains a boiler to generate the steam used by the engine. The water in the boiler is heated by burning combustible material -- usually coal, wood, or oil -- to produce steam. The steam moves reciprocating pistons which are connected to the locomotive\'s main wheels, known as the \"driving wheels\". Both fuel and water supplies are carried with the locomotive, either on the locomotive itself, in bunkers and tanks, (this arrangement is known as a \"tank locomotive\") or pulled behind the locomotive, in tenders, (this arrangement is known as a \"tender locomotive\").
The first full-scale working railway steam locomotive was built by Richard Trevithick in 1802. It was constructed for the Coalbrookdale ironworks in Shropshire in England though no record of it working there has survived. On 21 February 1804, the first recorded steam-hauled railway journey took place as another of Trevithick\'s locomotives hauled a train from the Penydarren ironworks, in Merthyr Tydfil, to Abercynon in South Wales. Accompanied by Andrew Vivian, it ran with mixed success. The design incorporated a number of important innovations including the use of high-pressure steam which reduced the weight of the engine and increased its efficiency.
In 1812, Matthew Murray\'s twin-cylinder rack locomotive *Salamanca* first ran on the edge-railed rack-and-pinion Middleton Railway; this is generally regarded as the first commercially successful locomotive. Another well-known early locomotive was *Puffing Billy*, built 1813--14 by engineer William Hedley for the Wylam Colliery near Newcastle upon Tyne. This locomotive is the oldest preserved, and is on static display in the Science Museum, London. George Stephenson built *Locomotion No. 1* for the Stockton & Darlington Railway in the north-east of England, which was the first public steam railway in the world. In 1829, his son Robert built *The Rocket* in Newcastle upon Tyne. Rocket was entered into, and won, the Rainhill Trials. This success led to the company emerging as the pre-eminent early builder of steam locomotives used on railways in the UK, US and much of Europe. The Liverpool & Manchester Railway, built by Stephenson, opened a year later making exclusive use of steam power for passenger and goods trains.
The steam locomotive remained by far the most common type of locomotive until after World War II. Steam locomotives are less efficient than modern diesel and electric locomotives, and a significantly larger workforce is required to operate and service them. British Rail figures showed that the cost of crewing and fuelling a steam locomotive was about two and a half times larger than the cost of supporting an equivalent diesel locomotive, and the daily mileage they could run was lower. Between about 1950 and 1970, the majority of steam locomotives were retired from commercial service and replaced with electric and diesel--electric locomotives. While North America transitioned from steam during the 1950s, and continental Europe by the 1970s, in other parts of the world, the transition happened later. Steam was a familiar technology that used widely-available fuels and in low-wage economies did not suffer as wide a cost disparity. It continued to be used in many countries until the end of the 20th century. By the end of the 20th century, almost the only steam power remaining in regular use around the world was on heritage railways. `{{gallery
|File:Locomotive trevithick.svg|Trevithick's 1802 locomotive
|File:Locomotion No. 1..jpg|The ''[[Locomotion No. 1]]'' at Darlington Railway Centre and Museum}}`{=mediawiki}
### Internal combustion {#internal_combustion}
*Main article: Internal combustion locomotive* Internal combustion locomotives use an internal combustion engine, connected to the driving wheels by a transmission. They typically keep the engine running at a near-constant speed whether the locomotive is stationary or moving. Internal combustion locomotives are categorised by their fuel type and sub-categorised by their transmission type.
The first internal combustion rail vehicle was a kerosene-powered draisine built by Gottlieb Daimler in 1887, but this was not technically a locomotive as it carried a payload.
The earliest gasoline locomotive in the western United States was built by the Best Manufacturing Company in 1891 for San Jose and Alum Rock Railroad. It was only a limited success and was returned to Best in 1892.
The first commercially successful petrol locomotive in the United Kingdom was a petrol--mechanical locomotive built by the Maudslay Motor Company in 1902, for the Deptford Cattle Market in London. It was an 80 hp locomotive using a three-cylinder vertical petrol engine, with a two speed mechanical gearbox.
In 1903, the Hungarian Weitzer railmotor was the world\'s first petrol electric locomotive.
#### Diesel
Diesel locomotives are powered by diesel engines. In the early days of diesel propulsion development, various transmission systems were employed with varying degrees of success, with electric transmission proving to be the most popular. In 1914, Hermann Lemp, a General Electric electrical engineer, developed and patented a reliable direct current electrical control system (subsequent improvements were also patented by Lemp). Lemp\'s design used a single lever to control both engine and generator in a coordinated fashion, and was the prototype for all diesel--electric locomotive control. In 1917--18, GE produced three experimental diesel--electric locomotives using Lemp\'s control design. In 1924, a diesel--electric locomotive (E^el^2 original number Юэ 001/Yu-e 001) started operations. It had been designed by a team led by Yury Lomonosov and built 1923--1924 by Maschinenfabrik Esslingen in Germany. It had five driving axles (1\'E1\'). After several test rides, it hauled trains for almost three decades from 1925 to 1954.
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# Locomotive
## Classifications
### Electric
An electric locomotive is a locomotive powered only by electricity. Electricity is supplied to moving trains with a (nearly) continuous conductor running along the track that usually takes one of three forms: an overhead line, suspended from poles or towers along the track or from structure or tunnel ceilings; a third rail mounted at track level; or an onboard battery. Both overhead wire and third-rail systems usually use the running rails as the return conductor but some systems use a separate fourth rail for this purpose. The type of electrical power used is either direct current (DC) or alternating current (AC).
Various collection methods exist: a trolley pole, which is a long flexible pole that engages the line with a wheel or shoe; a bow collector, which is a frame that holds a long collecting rod against the wire; a pantograph, which is a hinged frame that holds the collecting shoes against the wire in a fixed geometry; or a contact shoe, which is a shoe in contact with the third rail. Of the three, the pantograph method is best suited for high-speed operation.
Electric locomotives almost universally use axle-hung traction motors, with one motor for each powered axle. In this arrangement, one side of the motor housing is supported by plain bearings riding on a ground and polished journal that is integral to the axle. The other side of the housing has a tongue-shaped protuberance that engages a matching slot in the truck (bogie) bolster, its purpose being to act as a torque reaction device, as well as a support. Power transfer from motor to axle is effected by spur gearing, in which a pinion on the motor shaft engages a bull gear on the axle. Both gears are enclosed in a liquid-tight housing containing lubricating oil. The type of service in which the locomotive is used dictates the gear ratio employed. Numerically high ratios are commonly found on freight units, whereas numerically low ratios are typical of passenger engines.
Electricity is typically generated in large and relatively efficient generating stations, transmitted to the railway network and distributed to the trains. Some electric railways have their own dedicated generating stations and transmission lines but most purchase power from an electric utility. The railway usually provides its own distribution lines, switches and transformers.
Electric locomotives usually cost 20% less than diesel locomotives, their maintenance costs are 25--35% lower, and cost up to 50% less to run.
#### Direct current {#direct_current}
The earliest systems were DC systems. The first electric passenger train was presented by Werner von Siemens at Berlin in 1879. The locomotive was driven by a 2.2 kW, series-wound motor, and the train, consisting of the locomotive and three cars, reached a speed of 13 km/h. During four months, the train carried 90,000 passengers on a 300 m circular track. The electricity (150 V DC) was supplied through a third insulated rail between the tracks. A contact roller was used to collect the electricity. The world\'s first electric tram line opened in Lichterfelde near Berlin, Germany, in 1881. It was built by Werner von Siemens (see Gross-Lichterfelde Tramway and Berlin Straßenbahn). The Volk\'s Electric Railway opened in 1883 in Brighton, and is the oldest surviving electric railway. Also in 1883, Mödling and Hinterbrühl Tram opened near Vienna in Austria. It was the first in the world in regular service powered from an overhead line. Five years later, in the U.S. electric trolleys were pioneered in 1888 on the Richmond Union Passenger Railway, using equipment designed by Frank J. Sprague.
The first electrically worked underground line was the City & South London Railway, prompted by a clause in its enabling act prohibiting use of steam power. It opened in 1890, using electric locomotives built by Mather & Platt. Electricity quickly became the power supply of choice for subways, abetted by the Sprague\'s invention of multiple-unit train control in 1897.
The first use of electrification on a main line was on a four-mile stretch of the Baltimore Belt Line of the Baltimore & Ohio (B&O) in 1895 connecting the main portion of the B&O to the new line to New York through a series of tunnels around the edges of Baltimore\'s downtown. Three Bo+Bo units were initially used, at the south end of the electrified section; they coupled onto the locomotive and train and pulled it through the tunnels.
DC was used on earlier systems. These systems were gradually replaced by AC. Today, almost all main-line railways use AC systems. DC systems are confined mostly to urban transit such as metro systems, light rail and trams, where power requirement is less.
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# Locomotive
## Classifications
### Electric
#### Alternating current {#alternating_current}
The first practical AC electric locomotive was designed by Charles Brown, then working for Oerlikon, Zürich. In 1891, Brown had demonstrated long-distance power transmission, using three-phase AC, between a hydro-electric plant at Lauffen am Neckar and Frankfurt am Main West, a distance of 280 km. Using experience he had gained while working for Jean Heilmann on steam--electric locomotive designs, Brown observed that three-phase motors had a higher power-to-weight ratio than DC motors and, because of the absence of a commutator, were simpler to manufacture and maintain. However, they were much larger than the DC motors of the time and could not be mounted in underfloor bogies: they could only be carried within locomotive bodies.
In 1894, Hungarian engineer Kálmán Kandó developed a new type 3-phase asynchronous electric drive motors and generators for electric locomotives. The new 3-phase asynchronous electric drive motors were more effective than the synchronous electric motors of earlier locomotive designs. Kandó\'s early 1894 designs were first applied in a short three-phase AC tramway in Evian-les-Bains (France), which was constructed between 1896 and 1898. In 1918, Kandó invented and developed the rotary phase converter, enabling electric locomotives to use three-phase motors whilst supplied via a single overhead wire, carrying the simple industrial frequency (50 Hz) single phase AC of the high voltage national networks.
In 1896, Oerlikon installed the first commercial example of the system on the Lugano Tramway. Each 30-tonne locomotive had two 110 kW motors run by three-phase 750 V 40 Hz fed from double overhead lines. Three-phase motors run at constant speed and provide regenerative braking, and are well suited to steeply graded routes, and the first main-line three-phase locomotives were supplied by Brown (by then in partnership with Walter Boveri) in 1899 on the 40 km Burgdorf---Thun line, Switzerland. The first implementation of industrial frequency single-phase AC supply for locomotives came from Oerlikon in 1901, using the designs of Hans Behn-Eschenburg and Emil Huber-Stockar; installation on the Seebach-Wettingen line of the Swiss Federal Railways was completed in 1904. The 15 kV, 50 Hz 345 kW, 48 tonne locomotives used transformers and rotary converters to power DC traction motors.
Italian railways were the first in the world to introduce electric traction for the entire length of a main line rather than just a short stretch. The 106 km Valtellina line was opened on 4 September 1902, designed by Kandó and a team from the Ganz works. The electrical system was three-phase at 3 kV 15 Hz. The voltage was significantly higher than used earlier and it required new designs for electric motors and switching devices. The three-phase two-wire system was used on several railways in Northern Italy and became known as \"the Italian system\". Kandó was invited in 1905 to undertake the management of Società Italiana Westinghouse and led the development of several Italian electric locomotives.
#### Battery--electric
A battery--electric locomotive (or battery locomotive) is an electric locomotive powered by onboard batteries; a kind of battery electric vehicle.
Such locomotives are used where a conventional diesel or electric locomotive would be unsuitable. An example is maintenance trains on electrified lines when the electricity supply is turned off. Another use is in industrial facilities where a combustion-powered locomotive (i.e., steam- or diesel-powered) could cause a safety issue due to the risks of fire, explosion or fumes in a confined space. Battery locomotives are preferred for mines where gas could be ignited by trolley-powered units arcing at the collection shoes, or where electrical resistance could develop in the supply or return circuits, especially at rail joints, and allow dangerous current leakage into the ground. Battery locomotives in over-the-road service can recharge while absorbing dynamic-braking energy.
The first known electric locomotive was built in 1837 by chemist Robert Davidson of Aberdeen, and it was powered by galvanic cells (batteries). Davidson later built a larger locomotive named *Galvani*, exhibited at the Royal Scottish Society of Arts Exhibition in 1841. The seven-ton vehicle had two direct-drive reluctance motors, with fixed electromagnets acting on iron bars attached to a wooden cylinder on each axle, and simple commutators. It hauled a load of six tons at four miles per hour (6 kilometers per hour) for a distance of 1+1/2 mi. It was tested on the Edinburgh and Glasgow Railway in September of the following year, but the limited power from batteries prevented its general use.
Another example was at the Kennecott Copper Mine, Latouche, Alaska, where in 1917 the underground haulage ways were widened to enable working by two battery locomotives of `{{frac|4|1|2}}`{=mediawiki} tons. In 1928, Kennecott Copper ordered four 700-series electric locomotives with on-board batteries. These locomotives weighed 85 tons and operated on 750-volt overhead trolley wire with considerable further range whilst running on batteries. The locomotives provided several decades of service using Nickel--iron battery (Edison) technology. The batteries were replaced with lead-acid batteries, and the locomotives were retired shortly afterward. All four locomotives were donated to museums, but one was scrapped. The others can be seen at the Boone and Scenic Valley Railroad, Iowa, and at the Western Railway Museum in Rio Vista, California. The Toronto Transit Commission previously operated a battery electric locomotive built by Nippon Sharyo in 1968 and retired in 2009.
London Underground regularly operates battery--electric locomotives for general maintenance work.
### Other types {#other_types}
#### Fireless
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# Locomotive
## Classifications
### Electric
#### Atomic--electric
In the early 1950s, Lyle Borst of the University of Utah was given funding by various US railroad line and manufacturers to study the feasibility of an electric-drive locomotive, in which an onboard atomic reactor produced the steam to generate the electricity. At that time, atomic power was not fully understood; Borst believed the major stumbling block was the price of uranium. With the Borst atomic locomotive, the center section would have a 200-ton reactor chamber and steel walls 5 feet thick to prevent releases of radioactivity in case of accidents. He estimated a cost to manufacture atomic locomotives with 7000 h.p. engines at approximately \$1,200,000 each. Consequently, trains with onboard nuclear generators were generally deemed unfeasible due to prohibitive costs.
#### Fuel cell--electric {#fuel_cellelectric}
In 2002, the first 3.6 tonne, 17 kW hydrogen-(fuel-cell)--powered mining locomotive was demonstrated in Val-d\'Or, Quebec. In 2007 the educational mini-hydrail in Kaohsiung, Taiwan went into service. The Railpower GG20B finally is another example of a fuel cell--electric locomotive.
#### Hybrid locomotives {#hybrid_locomotives}
There are many different types of hybrid or dual-mode locomotives using two or more types of motive power. The most common hybrids are electro-diesel locomotives powered either from an electricity supply or else by an onboard diesel engine. These are used to provide continuous journeys along routes that are only partly electrified. Examples include the EMD FL9 and Bombardier ALP-45DP
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# Locomotive
## Use
There are three main uses of locomotives in rail transport operations: hauling passenger trains, freight trains, and switching (UK English: shunting).
Freight locomotives are normally designed to deliver high starting tractive effort and high sustained power. This allows them to start and move long, heavy trains, but usually comes at the cost of relatively low maximum speeds. Passenger locomotives usually develop lower starting tractive effort but are able to operate at the high speeds required to maintain passenger schedules. Mixed-traffic locomotives (US English: general purpose or road switcher locomotives) meant for both passenger and freight trains do not develop as much starting tractive effort as a freight locomotive but are able to haul heavier trains than a passenger locomotive.`{{Dubious|reason=Over-simplified; not current; incorrect|date=March 2025}}`{=mediawiki}
Most steam locomotives have reciprocating engines, with pistons coupled to the driving wheels by means of connecting rods, with no intervening gearbox. This means the combination of starting tractive effort and maximum speed is greatly influenced by the diameter of the driving wheels. Steam locomotives intended for freight service generally have smaller diameter driving wheels than passenger locomotives.
In diesel-electric and electric locomotives the control system between the traction motors and axles adapts the power output to the rails for freight or passenger service. Passenger locomotives may include other features, such as head-end power (also referred to as hotel power or electric train supply) or a steam generator.
Some locomotives are designed specifically to work steep grade railways, and feature extensive additional braking mechanisms and sometimes rack and pinion. Steam locomotives built for steep rack and pinion railways frequently have the boiler tilted relative to the locomotive frame, so that the boiler remains roughly level on steep grades.
Locomotives are also used on some high-speed trains. Some of them are operated in push-pull formation with trailer control cars at another end of a train, which often have a cabin with the same design as a cabin of locomotive; examples of such trains with conventional locomotives are Railjet and Intercity 225.
Also many high-speed trains, including all TGV, many Talgo (250 / 350 / Avril / XXI), some Korea Train Express, ICE 1/ICE 2 and Intercity 125, use dedicated power cars, which do not have places for passengers and technically are special single-ended locomotives. The difference from conventional locomotives is that these power cars are integral part of a train and are not adapted for operation with any other types of passenger coaches. On the other hand, many high-speed trains such as the Shinkansen network never use locomotives. Instead of locomotive-like power-cars, they use electric multiple units (EMUs) or diesel multiple units (DMUs) -- passenger cars that also have traction motors and power equipment. Using dedicated locomotive-like power cars allows for a high ride quality and less electrical equipment; but EMUs have less axle weight, which reduces maintenance costs, and EMUs also have higher acceleration and higher seating capacity. Also some trains, including TGV PSE, TGV TMST and TGV V150, use both non-passenger power cars and additional passenger motor cars.
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# Locomotive
## Operational role `{{anchor|role}}`{=mediawiki} {#operational_role}
Locomotives occasionally work in a specific role, such as:
- **Train engine** is the technical name for a locomotive attached to the front of a railway train to haul that train. Alternatively, where facilities exist for push-pull operation, the train engine might be attached to the rear of the train;
- Pilot engine -- a locomotive attached in front of the train engine, to enable double-heading;
- Banking engine -- a locomotive temporarily assisting a train from the rear, due to a difficult start or a sharp incline gradient;
- Light engine -- a locomotive operating without a train behind it, for relocation or operational reasons. Occasionally, a light engine is referred to as a train in and of itself.
- Station pilot -- a locomotive used to shunt passenger trains at a railway station.
## Wheel arrangement {#wheel_arrangement}
The wheel arrangement of a locomotive describes how many wheels it has; common methods include the AAR wheel arrangement, UIC classification, and Whyte notation systems.
## Remote control locomotives {#remote_control_locomotives}
In the second half of the twentieth century remote control locomotives started to enter service in switching operations, being remotely controlled by an operator outside of the locomotive cab. The main benefit is one operator can control the loading of grain, coal, gravel, etc. into the cars. In addition, the same operator can move the train as needed. Thus, the locomotive is loaded or unloaded in about a third of the time
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# Lysator
**Lysator** is an academic computer club at Linköping University, Sweden with almost 600 members. It is an independent non-profit society, separate from the students\' union and the faculties of the university.
## History
Lysator was founded on 29 March 1973. The first computer used at Lysator was a Datasaab D21, delivered to Lysator on 25 May 1973. Later in the decade, members of Lysator developed and initially built a microcomputer, the LYS-16, which was advanced for its time due to its 16-bit word size.
In February 1993, Lysator put up the first web server in Sweden, among the first 10--15 in the world.
On 30 July 2010, Lysator began migrating to a new 3U home rack, increasing their available storage space from 700GB to 13TB
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# Library of Alexandria
Alexandria Library}} `{{Redirect|Great Library|the library of Quebec in Montreal|Grande Bibliothèque|the library of Baghdad during the Islamic Golden Age|House of Wisdom}}`{=mediawiki} `{{pp-move}}`{=mediawiki} `{{Good article}}`{=mediawiki} `{{Use dmy dates|date=October 2019}}`{=mediawiki}
The **Great Library of Alexandria** in Alexandria, Egypt, was one of the largest and most significant libraries of the ancient world. The library was part of a larger research institution called the Mouseion, which was dedicated to the Muses, the nine goddesses of the arts. The idea of a universal library in Alexandria may have been proposed by Demetrius of Phalerum, an exiled Athenian statesman living in Alexandria, to Ptolemy I Soter, who may have established plans for the Library, but the Library itself was probably not built until the reign of his son Ptolemy II Philadelphus. The Library quickly acquired many papyrus scrolls, owing largely to the Ptolemaic kings\' aggressive and well-funded policies for procuring texts. It is unknown precisely how many scrolls were housed at any given time, but estimates range from 40,000 to 400,000 at its height.
Alexandria came to be regarded as the capital of knowledge and learning, in part because of the Great Library. Many important and influential scholars worked at the Library during the third and second centuries BC, including: Zenodotus of Ephesus, who worked towards standardizing the works of Homer; Callimachus, who wrote the *Pinakes*, sometimes considered the world\'s first library catalog; Apollonius of Rhodes, who composed the epic poem the *Argonautica*; Eratosthenes of Cyrene, who calculated the circumference of the earth within a few hundred kilometers of accuracy; Hero of Alexandria, who invented the first recorded steam engine; Aristophanes of Byzantium, who invented the system of Greek diacritics and was the first to divide poetic texts into lines; and Aristarchus of Samothrace, who produced the definitive texts of the Homeric poems as well as extensive commentaries on them. During the reign of Ptolemy III Euergetes, a daughter library was established in the Serapeum, a temple to the Greco-Egyptian god Serapis.
The influence of the Library declined gradually over the course of several centuries. This decline began with the purging of intellectuals from Alexandria in 145 BC during the reign of Ptolemy VIII Physcon, which resulted in Aristarchus of Samothrace, the head librarian, resigning and exiling himself to Cyprus. Many other scholars, including Dionysius Thrax and Apollodorus of Athens, fled to other cities, where they continued teaching and conducting scholarship. The Library, or part of its collection, was accidentally burned by Julius Caesar during his civil war in 48 BC, but it is unclear how much was actually destroyed and it seems to have either survived or been rebuilt shortly thereafter. The geographer Strabo mentions having visited the Mouseion in around 20 BC, and the prodigious scholarly output of Didymus Chalcenterus in Alexandria from this period indicates that he had access to at least some of the Library\'s resources.
The Library dwindled during the Roman period, from a lack of funding and support. Its membership appears to have ceased by the 260s AD. Between 270 and 275 AD, Alexandria saw a Palmyrene invasion and an imperial counterattack that probably destroyed whatever remained of the Library, if it still existed. The daughter library in the Serapeum may have survived after the main Library\'s destruction. The Serapeum, mainly used as a gathering place for Neoplatonist philosophers following the teachings of Iamblichus, was vandalized and demolished in 391 AD under a decree issued by bishop Theophilus of Alexandria.
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# Library of Alexandria
## Historical background {#historical_background}
The Library of Alexandria was not the first library of its kind. A long tradition of libraries existed in both Greece and in the ancient Near East. The earliest recorded archive of written materials comes from the ancient Sumerian city-state of Uruk in around 3400 BC, when writing had only just begun to develop. Scholarly curation of literary texts began in around 2500 BC. The later kingdoms and empires of the ancient Near East had long traditions of book collecting. The ancient Hittites and Assyrians had massive archives containing records written in many different languages. The most famous library of the ancient Near East was the Library of Ashurbanipal in Nineveh, founded in the seventh century BC by the Assyrian king Ashurbanipal (ruled 668--c. 627 BC). A large library also existed in Babylon during the reign of Nebuchadnezzar II (c. 605--c. 562 BC). In Greece, the Athenian tyrant Pisistratus was said to have founded the first major public library in the sixth century BC. It was out of this mixed heritage of both Greek and Near Eastern book collections that the idea for the Library of Alexandria may have been born through Alexander.
Following the death of Alexander the Great in 323 BC, there was a power grab for his empire among his top-ranking officers. The empire was divided into three: the Antigonid dynasty controlled Greece; the Seleucid dynasty, who had their capitals at Antioch and Seleucia, controlled large areas of Asia Minor, Syria, and Mesopotamia; and the Ptolemaic dynasty controlled Egypt with Alexandria as its capital. The Macedonian kings who succeeded Alexander the Great as rulers of the Near East wanted to promote Hellenistic culture and learning throughout the known world. These rulers, therefore, had a vested interest in collecting and compiling information from both the Greeks and the far more ancient kingdoms of the Near East. Libraries enhanced a city\'s prestige, attracted scholars, and provided practical assistance in ruling and governing the kingdom. Eventually, for these reasons, every major Hellenistic urban center would have a royal library. The Library of Alexandria, however, was unprecedented because of the scope and scale of the Ptolemies\' ambitions; unlike their predecessors and contemporaries, the Ptolemies wanted to produce a repository of all knowledge. To support this endeavor, they were well positioned as Egypt was the ideal habitat for the papyrus plant, which provided an abundant supply of materials needed to amass their knowledge repository.
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# Library of Alexandria
## Under Ptolemaic patronage {#under_ptolemaic_patronage}
### Founding
The Library was one of the largest and most significant libraries of the ancient world, but details about it are a mixture of history and legend. The earliest known surviving source of information on the founding of the Library of Alexandria is the pseudepigraphic *Letter of Aristeas*, which was composed between c. 180 and c. 145 BC. It claims the Library was founded during the reign of Ptolemy I Soter (c. 323--c. 283 BC) and that it was initially organized by Demetrius of Phalerum, a student of Aristotle who had been exiled from Athens and taken refuge in Alexandria within the Ptolemaic court. Nonetheless, the *Letter of Aristeas* is very late and contains information that is now known to be inaccurate. According to Diogenes Laertius, Demetrius was a student of Theophrastus, a student of Aristotle. Other sources claim that the Library was instead created under the reign of Ptolemy I\'s son Ptolemy II Philadelphus (283--246 BC).
Modern scholars agree that, while it is possible that Ptolemy I, who was a historian and author of an account of Alexander\'s campaign, may have laid the groundwork for the Library, it probably did not come into being as a physical institution until the reign of Ptolemy II. By that time, Demetrius of Phalerum had fallen out of favor with the Ptolemaic court. He probably would not, therefore, have had any role in establishing the Library as an institution. Stephen V. Tracy, however, argues that it is highly probable that Demetrius played an important role in collecting at least some of the earliest texts that would later become part of the Library\'s collection. In around 295 BC, Demetrius may have acquired early texts of the writings of Aristotle and Theophrastus, which he would have been uniquely positioned to do since he was a distinguished member of the Peripatetic school.
The Library was built in the Brucheion (Royal Quarter) as part of the Mouseion. Its main purpose was to show off the wealth of Egypt, with research as a lesser goal, but its contents were used to aid the ruler of Egypt. The exact layout of the library is not known, but ancient sources describe the Library of Alexandria as comprising a collection of scrolls, Greek columns, a `{{wikt-lang|en|Peripatetic|peripatos}}`{=mediawiki} walk, a room for shared dining, a reading room, meeting rooms, gardens, and lecture halls, creating a model for the modern university campus. A hall contained shelves for the collections of papyrus scrolls known as *bibliothekai* (*βιβλιοθῆκαι*). According to popular description, an inscription above the shelves read: \"The place of the cure of the soul.\"
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# Library of Alexandria
## Under Ptolemaic patronage {#under_ptolemaic_patronage}
### Early expansion and organization {#early_expansion_and_organization}
thumb\|upright=1.5\|Map of ancient Alexandria. The Mouseion was located in the royal Broucheion quarter (listed on this map as \"Bruchium\") in the central part of the city near the Great Harbor (\"Portus Magnus\" on the map).
The Ptolemaic rulers intended the Library to be a collection of all knowledge and they worked to expand the Library\'s collections through an aggressive and well-funded policy of book purchasing. They dispatched royal agents with large amounts of money and ordered them to purchase and collect as many texts as they possibly could, about any subject and by any author. Older copies of texts were favored over newer ones, since it was assumed that older copies had undergone less copying and that they were therefore more likely to more closely resemble what the original author had written. This program involved trips to the book fairs of Rhodes and Athens. According to the Greek medical writer Galen, under the decree of Ptolemy II, any books found on ships that came into port were taken to the library, where they were copied by official scribes. The original texts were kept in the library, and the copies delivered to the owners. The Library particularly focused on acquiring manuscripts of the Homeric poems, which were the foundation of Greek education and revered above all other poems. The Library therefore acquired many different manuscripts of these poems, tagging each copy with a label to indicate where it had come from.
In addition to collecting works from the past, the Mouseion which housed the Library also served as home to a host of international scholars, poets, philosophers, and researchers, who, according to the first-century BC Greek geographer Strabo, were provided with a large salary, free food and lodging, and exemption from taxes. They had a large, circular dining hall with a high domed ceiling in which they ate meals communally. There were also numerous classrooms, where the scholars were expected to at least occasionally teach students. Ptolemy II Philadelphus is said to have had a keen interest in zoology, so it has been speculated that the Mouseion may have even had a zoo for exotic animals. According to classical scholar Lionel Casson, the idea was that if the scholars were completely freed from all the burdens of everyday life they would be able to devote more time to research and intellectual pursuits. Strabo called the group of scholars who lived at the Mouseion a σύνοδος (*synodos*, \"community\"). As early as 283 BC, they may have numbered between thirty and fifty learned men.
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# Library of Alexandria
## Under Ptolemaic patronage {#under_ptolemaic_patronage}
### Early scholarship {#early_scholarship}
The Library of Alexandria was not affiliated with any particular philosophical school; consequently, scholars who studied there had considerable academic freedom. They were, however, subject to the authority of the king. One likely apocryphal story is told of a poet named Sotades who wrote an obscene epigram making fun of Ptolemy II for marrying his sister Arsinoe II. Ptolemy II is said to have jailed him and, after he escaped and was caught again, sealed him in a lead jar and dropped him into the sea. As a religious center, the Mouseion was directed by a priest of the Muses known as an *epistates*, who was appointed by the king in the same manner as the priests who managed the various Egyptian temples. The Library itself was directed by a scholar who served as head librarian, as well as tutor to the king\'s son.
The first recorded head librarian was Zenodotus of Ephesus (lived c. 325). Zenodotus\' main work was devoted to the establishment of canonical texts for the Homeric poems and the early Greek lyric poets. Most of what is known about him comes from later commentaries that mention his preferred readings of particular passages. Zenodotus is known to have written a glossary of rare and unusual words, which was organized in alphabetical order, making him the first person known to have employed alphabetical order as a method of organization. Since the collection at the Library of Alexandria seems to have been organized in alphabetical order by the first letter of the author\'s name from very early, Casson concludes that it is highly probable that Zenodotus was the one who organized it in this way. Zenodotus\' system of alphabetization, however, only used the first letter of the word and it was not until the second century AD that anyone is known to have applied the same method of alphabetization to the remaining letters of the word.
Meanwhile, the scholar and poet Callimachus compiled the *Pinakes*, a 120-book catalogue of various authors and all their known works. The *Pinakes* has not survived, but enough references to it and fragments of it have survived to allow scholars to reconstruct its basic structure. The *Pinakes* was divided into multiple sections, each containing entries for writers of a particular genre of literature. The most basic division was between writers of poetry and prose, with each section divided into smaller subsections. Each section listed authors in alphabetical order. Each entry included the author\'s name, father\'s name, place of birth, and other brief biographical information, sometimes including nicknames by which that author was known, followed by a complete list of all that author\'s known works. The entries for prolific authors such as Aeschylus, Euripides, Sophocles, and Theophrastus must have been extremely long, spanning multiple columns of text. Although Callimachus did his most famous work at the Library of Alexandria, he never held the position of head librarian there. Callimachus\' pupil Hermippus of Smyrna wrote biographies, Philostephanus of Cyrene studied geography, and Istros (who may have also been from Cyrene) studied Attic antiquities. In addition to the Great Library, many other smaller libraries also began to spring up all around the city of Alexandria.
After Zenodotus either died or retired, Ptolemy II Philadelphus appointed Apollonius of Rhodes (lived c. 295), a native of Alexandria and a student of Callimachus, as the second head librarian of the Library of Alexandria. Philadelphus also appointed Apollonius of Rhodes as the tutor to his son, the future Ptolemy III Euergetes. Apollonius of Rhodes is best known as the author of the *Argonautica*, an epic poem about the voyages of Jason and the Argonauts, which has survived to the present in its complete form. The *Argonautica* displays Apollonius\' vast knowledge of history and literature and makes allusions to a vast array of events and texts while simultaneously imitating the style of the Homeric poems. Some fragments of his scholarly writings have also survived, but he is generally more famous today as a poet than as a scholar.
According to legend, during the librarianship of Apollonius, the mathematician and inventor Archimedes (lived c. 287 --c. 212 BC) came to visit the Library of Alexandria. During his time in Egypt, Archimedes is said to have observed the rise and fall of the Nile, leading him to invent the Archimedes\' screw, which can be used to transport water from low-lying bodies into irrigation ditches. Archimedes later returned to Syracuse, where he continued making new inventions.
According to two late and largely unreliable biographies, Apollonius was forced to resign from his position as head librarian and moved to the island of Rhodes (after which he takes his name) on account of the hostile reception he received in Alexandria to the first draft of his *Argonautica*. It is more likely that Apollonius\' resignation was on account of Ptolemy III Euergetes\' ascension to the throne in 246 BC.
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# Library of Alexandria
## Under Ptolemaic patronage {#under_ptolemaic_patronage}
### Later scholarship and expansion {#later_scholarship_and_expansion}
The third head librarian, Eratosthenes of Cyrene (lived c. 280--c. 194 BC), is best known today for his scientific works, but he was also a literary scholar. Eratosthenes\' most important work was his treatise *Geographika*, which was originally in three volumes. The work itself has not survived, but many fragments of it are preserved through quotation in the writings of the later geographer Strabo. Eratosthenes was the first scholar to apply mathematics to geography and map-making and, in his treatise *Concerning the Measurement of the Earth*, he calculated the circumference of the earth and was only off by less than a few hundred kilometers. Eratosthenes also produced a map of the entire known world, which incorporated information taken from sources held in the Library, including accounts of Alexander the Great\'s campaigns in India and reports written by members of Ptolemaic elephant-hunting expeditions along the coast of East Africa.
Eratosthenes was the first person to advance geography towards becoming a scientific discipline. Eratosthenes believed that the setting of the Homeric poems was purely imaginary and argued that the purpose of poetry was \"to capture the soul\", rather than to give a historically accurate account of actual events. Strabo quotes him as having sarcastically commented, \"a man might find the places of Odysseus\' wanderings if the day were to come when he would find the leatherworker who stitched the goatskin of the winds.\" Meanwhile, scholars at the Library of Alexandria displayed interest in other scientific subjects. Bacchius of Tanagra, a contemporary of Eratosthenes, edited and commented on the medical writings of the Hippocratic Corpus. The doctors Herophilus (lived c. 335--c. 280 BC) and Erasistratus (c. 304--c. 250 BC) studied human anatomy, but their studies were hindered by protests against the dissection of human corpses, which was seen as immoral.
According to Galen, around this time, Ptolemy III requested permission from the Athenians to borrow the original manuscripts of Aeschylus, Sophocles, and Euripides, for which the Athenians demanded the enormous amount of fifteen talents (1000 lbs) of a precious metal as guarantee that he would return them. Ptolemy III had expensive copies of the plays made on the highest quality papyrus and sent the Athenians the copies, keeping the original manuscripts for the library and telling the Athenians they could keep the talents. This story may also be construed erroneously to show the power of Alexandria over Athens during the Ptolemaic dynasty. This detail arises from the fact that Alexandria was a man-made bidirectional port between the mainland and the Pharos island, welcoming trade from the East and West, and soon found itself to be an international hub for trade, the leading producer of papyrus and, soon enough, books. As the Library expanded, it ran out of space to house the scrolls in its collection, so, during the reign of Ptolemy III Euergetes, it opened a satellite collection in the Serapeum of Alexandria, a temple to the Greco-Egyptian god Serapis located near the royal palace.
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# Library of Alexandria
## Under Ptolemaic patronage {#under_ptolemaic_patronage}
### Peak of literary criticism {#peak_of_literary_criticism}
Aristophanes of Byzantium (lived c. 257--c. 180 BC) became the fourth head librarian sometime around 200 BC. According to a legend recorded by the Roman writer Vitruvius, Aristophanes was one of seven judges appointed for a poetry competition hosted by Ptolemy III Euergetes. All six of the other judges favored one competitor, but Aristophanes favored the one whom the audience had liked the least. Aristophanes declared that all of the poets except for the one he had chosen had committed plagiarism and were therefore disqualified. The king demanded that he prove this, so he retrieved the texts that the authors had plagiarized from the Library, locating them by memory. On account of his impressive memory and diligence, Ptolemy III appointed him as head librarian.
The librarianship of Aristophanes of Byzantium is widely considered to have opened a more mature phase of scholarship in the Library of Alexandria\'s history. During this phase, literary criticism reached its peak and came to dominate the Library\'s scholarly output. Aristophanes of Byzantium edited poetic texts and introduced the division of poems into separate lines on the page, since they had previously been written out just like prose. He also invented the system of Greek diacritics, wrote important works on lexicography, and introduced a series of signs for textual criticism. He wrote introductions to many plays, some of which have survived in partially rewritten forms.
The fifth head librarian was an obscure individual named Apollonius Eidographus, who is known by the epithet *ὁ εἰδογράφος* (\"the classifier of forms\"). One late lexicographical source explains this epithet as referring to the classification of poetry on the basis of musical forms.
During the early second century BC, several scholars at the Library of Alexandria studied works on medicine. Zeuxis the Empiricist is credited with having written commentaries on the Hippocratic Corpus and he actively worked to procure medical writings for the Library\'s collection. A scholar named Ptolemy Epithetes wrote a treatise on wounds in the Homeric poems, a subject straddling the line between traditional philology and medicine. However, it was also during the early second century BC that the political power of Ptolemaic Egypt began to decline. After the Battle of Raphia in 217 BC, Ptolemaic power became increasingly unstable. There were uprisings among segments of the Egyptian population and, in the first half of the second century BC, connection with Upper Egypt became largely disrupted. Ptolemaic rulers also began to emphasize the Egyptian aspect of their nation over the Greek aspect. Consequently, many Greek scholars began to leave Alexandria for safer countries with more generous patronages.
Aristarchus of Samothrace (lived c. 216--c. 145 BC) was the sixth head librarian. He earned a reputation as the greatest of all ancient scholars and produced not only texts of classic poems and works of prose, but full *hypomnemata*, or long, free-standing commentaries, on them. These commentaries would typically cite a passage of a classical text, explain its meaning, define any unusual words used in it, and comment on whether the words in the passage were really those used by the original author or if they were later interpolations added by scribes. He made many contributions to a variety of studies, but particularly the study of the Homeric poems, and his editorial opinions are widely quoted by ancient authors as authoritative. A portion of one of Aristarchus\' commentaries on the *Histories* of Herodotus has survived in a papyrus fragment. In 145 BC, however, Aristarchus became caught up in a dynastic struggle in which he supported Ptolemy VII Neos Philopator as the ruler of Egypt. Ptolemy VII was murdered and succeeded by Ptolemy VIII Physcon, who immediately set about punishing all those who had supported his predecessor, forcing Aristarchus to flee Egypt and take refuge on the island of Cyprus, where he died shortly after. Ptolemy VIII expelled all foreign scholars from Alexandria, forcing them to disperse across the Eastern Mediterranean.
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# Library of Alexandria
## Decline
### After Ptolemy VIII\'s expulsions {#after_ptolemy_viiis_expulsions}
Ptolemy VIII Physcon\'s expulsion of the scholars from Alexandria brought about a shift in the history of Hellenistic scholarship. The scholars who had studied at the Library of Alexandria and their students continued to conduct research and write treatises, but most of them no longer did so in association with the Library. Due to this decline in respect and prestige, the Library of Alexandria began a decline. A diaspora of Alexandrian scholarship occurred, in which scholars of the Library dispersed first into the eastern Mediterranean and then into the world of the western Mediterranean as well. Former scholars and their disciples took their scholarly energies elsewhere. For example, Aristarchus\' student Dionysius Thrax (c. 170) established a school on the Greek island of Rhodes. He also wrote the first book on Greek grammar, a succinct guide to speaking and writing clearly and effectively -- a book that remained the primary grammar textbook for Greek schoolboys until as late as the twelfth century AD. Another one of Aristarchus\' pupils, Apollodorus of Athens (c. 180), went to Alexandria\'s greatest rival, Pergamum, where he taught and conducted research. This scholarly diaspora prompted the historian Menecles of Barca to sarcastically comment that Alexandria had become the teacher of all Greeks and barbarians alike.
Meanwhile, in Alexandria, from the middle of the second century BC onwards, Ptolemaic rule in Egypt grew less stable than it had been previously. Confronted with growing social unrest and other major political and economic problems, the later Ptolemies did not devote as much attention towards the Library and the Mouseion as their predecessors had, continuing the decline that had begun under Ptolemy VIII Physcon. The status of both the Library and the head librarian diminished. Several of the later Ptolemies used the position of head librarian as a mere political plum to reward their most devoted supporters. Ptolemy VIII appointed a man named Cydas, one of his palace guards, as head librarian and Ptolemy IX Soter II (ruled 88--81 BC) is said to have given the position to a political supporter. Eventually, the position of head librarian lost so much of its former prestige that even contemporary authors ceased to take interest in recording the terms of office for individual head librarians.
A shift in Greek scholarship at large occurred around the beginning of the first century BC. By this time, all major classical poetic texts had finally been standardized and extensive commentaries had already been produced on the writings of all the major literary authors of the Greek Classical Era. Consequently, there was little original work left for scholars to do with these texts. Many scholars began producing syntheses and reworkings of the commentaries of the Alexandrian scholars of previous centuries, at the expense of their own originalities. Other scholars branched out and began writing commentaries on the poetic works of postclassical authors, including Alexandrian poets such as Callimachus and Apollonius of Rhodes. Meanwhile, Alexandrian scholarship was probably introduced to Rome in the first century BC by Tyrannion of Amisus (c. 100), a student of Dionysius Thrax.
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# Library of Alexandria
## Decline
### Burning by Julius Caesar {#burning_by_julius_caesar}
In 48 BC, during Caesar\'s Civil War, Julius Caesar was besieged at Alexandria. His soldiers set fire to some of the Egyptian ships docked in the Alexandrian port while trying to clear the wharves to block the fleet belonging to Cleopatra\'s brother Ptolemy XIV. This fire purportedly spread to the parts of the city nearest to the docks, causing considerable devastation in that area. The first-century AD Roman playwright and Stoic philosopher Seneca the Younger quotes Livy\'s *\[\[Ab Urbe Condita Libri\]\]*, which was written between 63 and 14 BC, as saying that the fire started by Caesar destroyed 40,000 scrolls from the Library of Alexandria. The Greek Middle Platonist Plutarch (c. 46--120 AD) writes in his *Life of Caesar* that, \"\[W\]hen the enemy endeavored to cut off his communication by sea, he was forced to divert that danger by setting fire to his ships, which, after burning the docks, thence spread on and destroyed the great library.\" The Roman historian Cassius Dio (c. 155), however, writes: \"Many places were set on fire, with the result that, along with other buildings, the dockyards and storehouses of grain and books, said to be great in number and of the finest, were burned.\" However, Florus and Lucan only mention that the flames burned the fleet itself and some \"houses near the sea\".
Scholars have interpreted Cassius Dio\'s wording to indicate that the fire did not actually destroy the entire Library itself, but rather one or more Library warehouses near the docks. Whatever damage Caesar\'s fire may have caused, evidently the Library was not completely destroyed. The geographer Strabo (c. 63 BC) mentions visiting the Mouseion, the larger research institution to which the Library was attached, in around 20 BC, several decades after Caesar\'s fire, indicating that it either survived the fire or was rebuilt soon afterwards. Nonetheless, Strabo\'s manner of talking about the Mouseion shows that it was nowhere near as prestigious as it had been a few centuries prior. It is unknown whether this was due to historical decline or catastrophic destruction. Despite mentioning the Mouseion, Strabo does not mention the Library separately, perhaps indicating that it had been so drastically reduced in stature and significance that Strabo felt it did not warrant separate mention. It is unclear what happened to the Mouseion after Strabo\'s mention of it.
Furthermore, Plutarch records in his *Life of Mark Antony* that in the years leading up to the Battle of Actium in 33 BC, Mark Antony was rumored to have given Cleopatra all 200,000 scrolls in the Library of Pergamum. Plutarch himself notes that his source for this anecdote was sometimes unreliable and it is possible that the story may be nothing more than propaganda intended to show that Mark Antony was loyal to Cleopatra and Egypt rather than to Rome. Casson, however, argues that even if the story was made up, it would not have been believable unless the Library still existed. Edward J. Watts argues that Mark Antony\'s gift may have been intended to replenish the Library\'s collection after the damage to it caused by Caesar\'s fire roughly a decade and a half prior.
Further evidence for the Library\'s survival after 48 BC comes from the fact that the most notable producer of composite commentaries during the late first century BC and early first century AD was a scholar who worked in Alexandria named Didymus Chalcenterus, whose epithet *Χαλκέντερος* (*Chalkénteros*) means \"bronze guts\". Didymus is said to have produced somewhere between 3,500 and 4,000 books, making him the most prolific known writer in all of antiquity. He was also given the nickname *βιβλιολάθης* (*Biblioláthēs*), meaning \"book-forgetter\" because it was said that even he could not remember all the books he had written. Parts of some of Didymus\' commentaries have been preserved in the forms of later extracts and these remains are modern scholars\' most important sources of information about the critical works of the earlier scholars at the Library of Alexandria. Lionel Casson states that Didymus\' prodigious output \"would have been impossible without at least a good part of the resources of the library at his disposal\".
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# Library of Alexandria
## Decline
### Roman period and destruction {#roman_period_and_destruction}
Very little is known about the Library of Alexandria during the time of the Roman Principate (27 BC -- 284 AD). The emperor Claudius (ruled 41--54 AD) is recorded to have built an extension to the Library, but it seems that the Library of Alexandria\'s general fortunes followed those of the city of Alexandria itself. After Alexandria came under Roman rule, the city\'s status and, consequently that of its famous Library, gradually diminished. While the Mouseion still existed, membership was granted not on the basis of scholarly achievement, but rather on the basis of distinction in government, the military, or even in athletics.
The same was evidently the case even for the position of head librarian; the only known head librarian from the Roman Period was a man named Tiberius Claudius Balbilus, who lived in the middle of the first century AD and was a politician, administrator, and military officer with no record of substantial scholarly achievements. Members of the Mouseion were no longer required to teach, conduct research, or even live in Alexandria. The Greek writer Philostratus records that the emperor Hadrian (ruled 117--138 AD) appointed the ethnographer Dionysius of Miletus and the sophist Polemon of Laodicea as members of the Mouseion, even though neither of these men is known to have ever spent any significant amount of time in Alexandria.
As the reputation of Alexandrian scholarship declined, the reputations of other libraries across the Mediterranean world improved, diminishing the Library of Alexandria\'s former status as the most prominent. Other libraries also sprang up within the city of Alexandria itself and the scrolls from the Great Library may have been used to stock some of these smaller libraries. The Caesareum and the Claudianum in Alexandria are both known to have had major libraries by the end of the first century AD. The Serapeum, originally the \"daughter library\" of the Great Library, probably expanded during this period as well, according to classical historian Edward J. Watts.
By the second century AD, the Roman Empire grew less dependent on grain from Alexandria and the city\'s prominence declined further. The Romans during this period also had less interest in Alexandrian scholarship, causing the Library\'s reputation to continue to decline as well. The scholars who worked and studied at the Library of Alexandria during the time of the Roman Empire were less well known than the ones who had studied there during the Ptolemaic Period. Eventually, the word \"Alexandrian\" itself came to be synonymous with the editing of texts, correction of textual errors, and writing of commentaries synthesized from those of earlier scholars---in other words, taking on connotations of pedantry, monotony, and lack of originality. Mention of both the Great Library of Alexandria and the Mouseion that housed it disappear after the middle of the third century AD. The last known references to scholars being members of the Mouseion date to the 260s.
In 272 AD, the emperor Aurelian fought to recapture the city of Alexandria from the forces of the Palmyrene queen Zenobia. During the course of the fighting, Aurelian\'s forces destroyed the Broucheion quarter of the city in which the main library was located. If the Mouseion and Library still existed at this time, they were almost certainly destroyed or damaged during the attack. If they did survive the attack, whatever was left of them would have been further damaged or destroyed during the emperor Diocletian\'s siege of Alexandria in 297, when the Brouchion quarter was again destroyed.
### Arabic sources on the Arab conquest {#arabic_sources_on_the_arab_conquest}
In 642 AD, Alexandria was captured by an Arab army under the command of Amr ibn al-As. Several later Arabic sources describe the library\'s destruction by the order of Caliph Umar. The earliest was al-Qifti who described the story in a biographical dictionary *History of Learned Men*, written before 1248. Bar-Hebraeus, writing in the thirteenth century, quotes Umar as saying to Yaḥyā al-Naḥwī (John Philoponus): \"If those books are in agreement with the Quran, we have no need of them; and if these are opposed to the Quran, destroy them.\" So, Ibn al Qifti recounts, the general ordered that the books be burned to fuel the fires that heated Alexandria\'s city baths. It is said that they were enough to provide heating for six months.
Later scholars, beginning with Father Eusèbe Renaudot in his 1713 translation of the *History of the Patriarchs of Alexandria*, are skeptical of these stories, given the amount of time that had passed before they were recorded and the political motivations of the various authors. Roy MacLeod, for example, points out that the story first appeared 500 years after the event, that John Philoponus was almost certainly dead by the time of the conquest of Egypt and that both the Great Library of Alexandria and the Mouseion were likely long gone by then. According to Diana Delia, \"Omar\'s rejection of pagan and Christian wisdom may have been devised and exploited by conservative authorities as a moral exemplum for Muslims to follow in later, uncertain times, when the devotion of the faithful was once again tested by proximity to nonbelievers\". The historian Bernard Lewis suggests the myth came into existence during the reign of Saladin in order to justify the Sunni Ayyubids\' breaking up of the Shia Fatimid collections and library at public auction.
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# Library of Alexandria
## Successors to the Mouseion {#successors_to_the_mouseion}
### Serapeum
The Serapeum is often called the \"Daughter Library\" of Alexandria. For much of the late fourth century AD it was probably the largest collection of books in the city of Alexandria. In the 370s and 380s, the Serapeum was still a major pilgrimage site for pagans. It remained a fully functioning temple, and had classrooms for philosophers to teach in. It naturally tended to attract followers of Iamblichean Neoplatonism. Most of these philosophers were primarily interested in theurgy, the study of cultic rituals and esoteric religious practices. The Neoplatonist philosopher Damascius (lived c. 458 --after 538) records that a man named Olympus came from Cilicia to teach at the Serapeum, where he enthusiastically taught his students the rules of traditional divine worship and ancient religious practices. He enjoined his students to worship the old gods in traditional ways, and he may have even taught them theurgy.
Scattered references indicate that, sometime in the fourth century, an institution known as the \"Mouseion\" may have been reestablished at a different location somewhere in Alexandria. Nothing, however, is known about the characteristics of this organization. It may have possessed some bibliographic resources, but whatever they may have been, they were clearly not comparable to those of its predecessor.
Under the Christian rule of Roman emperor Theodosius I, pagan rituals were outlawed, and pagan temples were destroyed. In 391 AD, the bishop of Alexandria, Theophilus, supervised the destruction of an old Mithraeum. They gave some of the cult objects to Theophilus, who had them paraded through the streets so that they could be mocked and ridiculed. The pagans of Alexandria were incensed by this act of desecration, especially the teachers of Neoplatonic philosophy and theurgy at the Serapeum. The teachers at the Serapeum took up arms and led their students and other followers in a guerrilla attack on the Christian population of Alexandria, killing many of them before being forced to retreat. In retaliation, the Christians vandalized and demolished the Serapeum, although some parts of the colonnade were still standing as late as the twelfth century. Whether an actual library still existed at this point, and if so how extensive it was, is not recorded. Jonathan Theodore has stated that by 391/392 AD there was \"no remaining \"Great Library\" in the sense of the iconic vast, priceless collection\". Only Orosius explicitly mentions the destruction of books or scrolls; sources probably written after the Serapeum\'s destruction speak of its collection of literature in the past tense. On the other hand, a recent article identifies the literary evidence suggesting that the original Ptolemaic library collection was moved to the Serapeum by the end of the second century AD and that a library is attested there until the Serapeum was destroyed along with the books it contained.
### School of Theon and Hypatia {#school_of_theon_and_hypatia}
The *Suda*, a tenth-century Byzantine encyclopedia, calls the mathematician Theon of Alexandria (c. AD 335--c. 405) a \"man of the Mouseion\". According to classical historian Edward J. Watts, however, Theon was probably the head of a school called the \"Mouseion\", which was named in emulation of the Hellenistic Mouseion that had once included the Library of Alexandria, but which had little other connection to it. Theon\'s school was exclusive, highly prestigious, and doctrinally conservative. Theon does not seem to have had any connections to the militant Iamblichean Neoplatonists who taught in the Serapeum. Instead, he seems to have rejected the teachings of Iamblichus and may have taken pride in teaching a pure, Plotinian Neoplatonism. In around 400 AD, Theon\'s daughter Hypatia (born c. 350--370; died 415 AD) succeeded him as the head of his school. Like her father, she rejected the teachings of Iamblichus and instead embraced the original Neoplatonism formulated by Plotinus.
Theophilus, the bishop involved in the destruction of the Serapeum, tolerated Hypatia\'s school and even encouraged two of her students to become bishops in territory under his authority. Hypatia was extremely popular with the people of Alexandria and exerted profound political influence. Theophilus respected Alexandria\'s political structures and raised no objection to the close ties Hypatia established with Roman prefects. Hypatia was later implicated in a political feud between Orestes, the Roman prefect of Alexandria, and Cyril of Alexandria, Theophilus\' successor as bishop. Rumors spread accusing her of preventing Orestes from reconciling with Cyril and, in March of 415 AD, she was murdered by a mob of Christians, led by a lector named Peter. She had no successor and her school collapsed after her death.
### Later schools and libraries in Alexandria {#later_schools_and_libraries_in_alexandria}
Nonetheless, Hypatia was not the last pagan in Alexandria, nor was she the last Neoplatonist philosopher. Neoplatonism and paganism both survived in Alexandria and throughout the eastern Mediterranean for centuries after her death. British Egyptologist Charlotte Booth notes that many new academic lecture halls were built in Alexandria at Kom el-Dikka shortly after Hypatia\'s death, indicating that philosophy was clearly still taught in Alexandrian schools. The late fifth-century writers Zacharias Scholasticus and Aeneas of Gaza both speak of the \"Mouseion\" as occupying some kind of a physical space. Archaeologists have identified lecture halls dating to around this time period, located near, but not on, the site of the Ptolemaic Mouseion, which may be the \"Mouseion\" to which these writers refer.
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# Library of Alexandria
## Collection
It is not possible to determine the collection\'s size in any era with certainty. Papyrus scrolls constituted the collection, and although codices were used after 300 BC, the Alexandrian Library is never documented as having switched to parchment, perhaps because of its strong links to the papyrus trade. The Library of Alexandria in fact was indirectly causal in the creation of writing on parchment, as the Egyptians refused to export papyrus to their competitor in the Library of Pergamum. Consequently, the Library of Pergamum developed parchment as its own writing material.
A single piece of writing might occupy several scrolls, and this division into self-contained \"books\" was a major aspect of editorial work. King Ptolemy II Philadelphus (309--246 BC) is said to have set 500,000 scrolls as an objective for the library. The library\'s index, Callimachus\' *Pinakes*, has only survived in the form of a few fragments, and it is not possible to know with certainty how large and how diverse the collection may have been. At its height, the library was said to possess nearly half a million scrolls, and, although historians debate the precise number, the highest estimates claim 900,000 scrolls while the most conservative estimates are as low as 40,000, which is still an enormous collection that required vast storage space.
As a research institution, the library filled its stacks with new works in mathematics, astronomy, physics, natural sciences, and other subjects. Its empirical standards were applied in one of the first and certainly strongest homes for serious textual criticism. As the same text often existed in several different versions, comparative textual criticism was crucial for ensuring their veracity. Once ascertained, canonical copies would then be made for scholars, royalty, and wealthy bibliophiles all over the world, this commerce bringing income to the library.
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# Library of Alexandria
## Legacy
### In antiquity {#in_antiquity}
The Library of Alexandria was one of the largest and most prestigious libraries of the ancient world, but it was far from the only one. By the end of the Hellenistic Period, almost every city in the Eastern Mediterranean had a public library and so did many medium-sized towns. During the Roman Period, the number of libraries only proliferated. By the fourth century AD, there were at least two dozen public libraries in the city of Rome alone. As the Library of Alexandria declined, centers of academic excellence arose in various other capital cities. It is possible most of the material from the Library of Alexandria survived, by way of the Imperial Library of Constantinople, the Academy of Gondishapur, and the House of Wisdom. This material may then have been preserved by the Reconquista, which led to the formation of European universities and the recompilation of ancient texts from formerly scattered fragments.
In late antiquity, as the Roman Empire became Christianized, Christian libraries modeled directly on the Library of Alexandria and other great libraries of earlier pagan times began to be founded all across the Greek-speaking eastern part of the empire. Among the largest and most prominent of these libraries were the Theological Library of Caesarea Maritima, the Library of Jerusalem, and a Christian library in Alexandria. These libraries held both pagan and Christian writings side-by-side and Christian scholars applied to the Christian scriptures the same philological techniques that the scholars of the Library of Alexandria had used for analyzing the Greek classics. Nonetheless, the study of pagan authors remained secondary to the study of the Christian scriptures until the Renaissance.
The survival of ancient texts owes a great deal to the fact that they were exhaustingly copied and recopied. At first, they were copied by professional scribes during the Roman period. Mediaeval Muslim scholars also played a crucial role in preserving and translating the knowledge of the ancient world. The Graeco-Arabic translation movement translated a significant number of ancient texts into Arabic, keeping the texts intact and preserving them. Later, they were translated and re-introduced to Europe. This movement began in earnest under the Abbasid Caliphate where it played a significant role in the Islamic Golden Age. The translation movement encompassed scholars of various religions in the Abbasid empire. For example, under the patronage of Caliph al-Ma\'mun, a Christian scholar and translator named Hunayn ibn Ishaq completed major translation projects of Aristotle, Hypocrates, and Galen so that they remained accessible to scholars. These translations were translated into Latin and re-introduced to Europe. These texts were copied by monks during Middle Ages and Renaissance, making them more easily available to European scholars once more.
### Modern library: Bibliotheca Alexandrina {#modern_library_bibliotheca_alexandrina}
The idea of reviving the ancient Library of Alexandria in the modern era was first proposed in 1974, when Lotfy Dowidar was president of the University of Alexandria. In May 1986, Egypt requested the executive board of UNESCO to allow the international organization to conduct a feasibility study for the project. This marked the beginning of UNESCO and the international community\'s involvement in trying to bring the project to fruition. Starting in 1988, UNESCO and the UNDP worked to support the international architectural competition to design the Library. Egypt devoted four hectares of land for the building of the Library and established the National High Commission for the Library of Alexandria. Egyptian president Hosni Mubarak took a personal interest in the project, which greatly contributed to its advancement. An international architectural competition took place in 1989 with Norwegian architectural firm Snøhetta winning the competition. Completed in 2002, the Bibliotheca Alexandrina now functions as a modern library and cultural center, commemorating the original Library of Alexandria. In line with the mission of the Great Library of Alexandria, the Bibliotheca Alexandrina also houses the International School of Information Science, a school for students preparing for highly specialized post-graduate degrees, whose goal is to train professional staff for libraries in Egypt and across the Middle East
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# Line Islands
The **Line Islands**, **Teraina Islands** or **Equatorial Islands** (*Aono Raina*) are a chain of 11 atolls (with partly or fully enclosed lagoons, except Vostok and Jarvis) and coral islands (with a surrounding reef) in the central Pacific Ocean, south of the Hawaiian Islands. Eight of the atolls are parts of Kiribati. The remaining three---Jarvis Island, Kingman Reef, and Palmyra Atoll---are territories of the United States grouped with the United States Minor Outlying Islands. The Line Islands, all of which were formed by volcanic activity, are one of the longest island chains in the world, stretching 2350 km from northwest to southeast. One of them, Starbuck Island, is near the geographic center of the Pacific Ocean (4.97 S 158.75 W format=dms type:landmark_region:FR_scale:10000 display=inline). Another, Kiritimati, has the largest land area of any atoll in the world. Only Kiritimati, Tabuaeran, and Teraina have a permanent population. Besides the 11 confirmed atolls and islands, Filippo Reef is shown on some maps, but its existence is doubted.
The International Date Line passes through the Line Islands. The ones that are parts of Kiribati are in the world\'s farthest forward time zone, UTC+14:00. The time of day in these atolls is 24 hours ahead of the state of Hawaii in the United States, which uses UTC−10:00, and 26 hours ahead of some other islands in Oceania, such as Baker Island, which uses UTC−12:00.
## Overview
Copra and pet fish are the islands\' main export products (along with seaweed).
Archaeologists have identified the remains of coral Marae platforms and/or village complexes on several of the islands, including the Kiritimati and Tabuaeran atolls, Teraina Island, Malden, Millennium Atoll and Flint Island. These remains are dateable as far back as the 14th century, and show that the inhabitants of the Line Islands were likely permanent or at least semi-permanent.
Most 18th-century visitors to these isles overlooked these telltale signs of former Polynesian settlement. This included Captain Cook, who landed on Christmas Island (now called Kiritimati) in 1777, as well as Captain Fanning, who visited Teraina (Washington Island) and Tabuaeran (Fanning Atoll) in 1798.
In the 19th century, whaling ships were regular visitors to the islands. They came in search of water, wood and provisions. The first whaler recorded to have visited one of them was the *Coquette*, which docked at Kiritimati (then called Christmas Island) in 1822.
In 1888, the United Kingdom was planning to lay the Pacific cable, and annexed the islands with a view to using Tabuaeran (then Fanning Island) as one of the relay stations for the cable. The cable was laid and was operational between 1902 and 1963 (except for a short period in 1914) .
In 1916, the British annexed Fanning and Washington islands, making them part of the British colony of the Gilbert and Ellice Islands. In 1919, they annexed Christmas Island to the same colony. The Line Islands occasionally featured briefly in the biennial reports furnished by the Colony\'s resident commissioner to the Colonial Office and Parliament in London (see, for example, the reports submitted in 1966 and 1967).
The United States contested the British annexations, based on the U.S. Guano Islands Act of 1856, which allowed for very wide-ranging territorial claims. It relinquished these claims only in 1979, when it entered into the Treaty of Tarawa, which recognised Kiribati\'s sovereignty over the majority of the Line Islands chain.
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# Line Islands
## List of atolls, islands and reefs {#list_of_atolls_islands_and_reefs}
Geographically, the Line Islands is divided into three subgroups: the Northern, Central, and Southern Line Islands (however, the Central Line Islands are sometimes grouped with the Southern Line Islands). The table below lists the islands from north to south.
+----------------------------------------------+--------------+----------+------------+-------------+
| Atoll / Island / Reef | Area (km^2^) | | Population | Coordinates |
+==============================================+==============+==========+============+=============+
| Land | Lagoon | | | |
+----------------------------------------------+--------------+----------+------------+-------------+
| **Northern Line Islands** (Fanning\'s Group) | | | | |
+----------------------------------------------+--------------+----------+------------+-------------+
| Kingman Reef | 0.01 | 60 | 0 | |
+----------------------------------------------+--------------+----------+------------+-------------+
| Palmyra Atoll | 3.9 | 8 | 4 | |
+----------------------------------------------+--------------+----------+------------+-------------+
| Teraina\ | 9.55 | 2^\*^ | 1,155 | |
| (Washington Island) | | | | |
+----------------------------------------------+--------------+----------+------------+-------------+
| Tabuaeran\ | 33.73 | 110 | 2,539 | |
| (Fanning Island) | | | | |
+----------------------------------------------+--------------+----------+------------+-------------+
| Kiritimati\ | 388.39 | 217.61 | 5,115 | |
| (Christmas Island) | | | | |
+----------------------------------------------+--------------+----------+------------+-------------+
| **Central Line Islands** | | | | |
+----------------------------------------------+--------------+----------+------------+-------------+
| Jarvis Island | 5 | --- | 0 | |
+----------------------------------------------+--------------+----------+------------+-------------+
| Malden Island | 39.3 | 13^\*^ | 0 | |
+----------------------------------------------+--------------+----------+------------+-------------+
| Filippo Reef\ | --- | 1.5 | 0 | |
| (*existence uncertain*) | | | | |
+----------------------------------------------+--------------+----------+------------+-------------+
| Starbuck Island | 16.2 | 4^\*^ | 0 | |
+----------------------------------------------+--------------+----------+------------+-------------+
| **Southern Line Islands** | | | | |
+----------------------------------------------+--------------+----------+------------+-------------+
| Millennium Island\ | 3.76 | 6.3 | 0 | |
| (Caroline Island) | | | | |
+----------------------------------------------+--------------+----------+------------+-------------+
| Vostok Island | 0.24 | --- | 0 | |
+----------------------------------------------+--------------+----------+------------+-------------+
| Flint Island | 3.2 | 0.01^\*^ | 0 | |
+----------------------------------------------+--------------+----------+------------+-------------+
| **Line Islands** | 503.28 | 422.42 | 8,813 | |
+----------------------------------------------+--------------+----------+------------+-------------+
Note:
^\*^The lagoon areas marked with an asterisk are included in the land areas of the previous column because, unlike typical lagoons in atolls, they are inland waters completely sealed off from the sea.
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# Line Islands
## Time zone realignment {#time_zone_realignment}
On 23 December 1994, the Republic of Kiribati announced a change of time zone for the Line Islands, to take effect from 31 December 1994. This adjustment effectively moved the International Date Line more than 1000 km to the east within Kiribati, which placed all of Kiribati on the Asian or western side of the date line, despite the fact that Millennium Island\'s longitude of 150 degrees west corresponds to UTC−10:00 rather than to its official time zone of UTC+14:00. Millennium Island is now at the same time as the Hawaiian Islands (Hawaii--Aleutian Time Zone), but one day ahead. This move made Millennium Island (then Caroline Island) the easternmost land in the earliest time zone (by some definitions, the easternmost point on Earth), and one of the first points of land which saw sunrise on 1 January 2000 -- at 5:43 am, as measured by local time.
The move was the fulfilment of a campaign promise by Kiribati President Teburoro Tito. Previously, the country straddled the Date Line, thus being constantly in two different days. Kiribati officials later capitalised on the nation\'s new status as owners of the first land to see sunrise in 2000. Other Pacific nations, including Tonga and New Zealand\'s Chatham Islands, protested the move, objecting that it interfered with their own claims to be the first land to see dawn in the year 2000.
In 1999, to further capitalise upon the massive public interest in celebrations marking the arrival of the year 2000, Caroline Island was officially renamed Millennium Island. Although the island is uninhabited, a special celebration was held there to mark the occasion. It featured performances by native Kiribati entertainers and was attended by Kiribati\'s President Tito. Over 70 Kiribati singers and dancers travelled to Millennium Island from the capital, South Tarawa, accompanied by approximately 25 journalists. The celebration, which was broadcast worldwide by satellite, had an estimated audience size of as many as one billion viewers
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# LiveScript (programming language)
**LiveScript** is a functional programming language that transpiles to JavaScript. It was created by Jeremy Ashkenas, the creator of CoffeeScript, along with Satoshi Muramaki, George Zahariev, and many others. (The name may be a homage to the beta name of JavaScript; for a few months in 1995, it was called LiveScript before the official release.)
## Syntax
LiveScript is an indirect descendant of CoffeeScript. The following \"Hello, World!\" program is written in LiveScript, but is also compatible with CoffeeScript:
``` livescript
hello = ->
console.log 'hello, world!'
```
While calling a function can be done with empty parens, `hello()`, LiveScript treats the exclamation mark as a single-character shorthand for function calls with zero arguments: `hello!`
LiveScript introduces a number of other incompatible idioms:
### Name mangling {#name_mangling}
At compile time, the LiveScript parser implicitly converts kebab case (dashed variables and function names) to camel case.
``` livescript
hello-world = ->
console.log 'Hello, World!'
```
With this definition, both the following calls are valid. However, calling using the same dashed syntax is recommended.
``` output
hello-world!
helloWorld!
```
This does not preclude developers from using camel case explicitly or using snake case. Dashed naming is however, common in idiomatic LiveScript
### Pipes
A pipe operator `|>` passes the result of an expression on the left of the operator as an argument to the expression on the right of it. LiveScript supports these, as do some other functional languages such as F# and Elixir; the argument passed in F# is the last one, but in Elixir is the first one.
``` livescript
"hello!" |> capitalize |> console.log
# > Hello!
```
### Operators as functions {#operators_as_functions}
When parenthesized, operators such as `not` or `+` can be included in pipelines or called as if they are functions
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# Low Saxon
**Low Saxon** (*Nedersaksisch*), also known as **West Low German** (*Westniederdeutsch*) are a group of Low German dialects spoken in parts of the Netherlands, northwestern Germany and southern Denmark (in North Schleswig by parts of the German-speaking minority). It is one of two dialect groups, the other being East Low German.
## Extent
The language area comprises the North German states of Lower Saxony, North Rhine-Westphalia (the Westphalian part), Bremen, Hamburg, Schleswig-Holstein and Saxony-Anhalt (the northwestern areas around Magdeburg) as well as the northeast of the Netherlands (i.e. Dutch Low Saxon, spoken in Groningen, Drenthe, Overijssel, northern Gelderland and Urk) and the Schleswigsch dialect spoken by the North Schleswig Germans in the southernmost part of Denmark.
In the south the Benrath line and Uerdingen line isoglosses form the border with the area, where West Central German variants of High German are spoken.
## List of dialects {#list_of_dialects}
### Germany
- West Low German
- Westphalian, including the region around Münster and the Osnabrück region of Lower Saxony
- Eastphalian, spoken in southeastern Lower Saxony (Hanover, Braunschweig, Göttingen) and in the Magdeburg Börde region
- Northern Low Saxon
- East Frisian Low Saxon in East Frisia
- Dithmarsisch
- Schleswig\[i\]sch
- Holsteinisch
- Hamburgisch
- Nordhannoversch
- Emsländisch
- Oldenburgisch in the Oldenburg region
### Netherlands
While Dutch is a Low Franconian language, the Dutch Low Saxon varieties form a dialect continuum with Westphalian. They consist of:
- West Low German, divided into:
- Gronings
- Drents
- Stellingwerfs
- Sallands
- West-Overijssels
- Twents
- Achterhoeks
- Veluws
- Urkers
### Denmark
- West Low German
- Northern Low Saxon
- Schleswigsch dialect spoken in former South Jutland County (the northern part of the former Duchy of Schleswig) around Aabenraa (*Apenrade*)
### Poland
- West Low German
- Westphalian
- Koschneiderisch`{{snd}}`{=mediawiki}extinct dialect possibly related to Westphalian, used by settlers from around Osnabrück in the Koschneiderei region (*Kosznajderia*)
## Situation in the Netherlands {#situation_in_the_netherlands}
A 2005 study found that there were approximately 1.8 million \"daily speakers\" of Low Saxon in the Netherlands. 53% spoke Low Saxon or Low Saxon and Dutch at home and 71% could speak it.`{{page needed |date=July 2023}}`{=mediawiki} According to another study the percentage of speakers among parents dropped from 34% in 1995 to 15% in 2011. The percentage of speakers among their children dropped from 8% to 2% in the same period
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# Mass media in Laos
**Mass media in Laos** are based on a network of telephone lines, radiotelephone communications, and mobile phone infrastructure.
## Infrastructure and statistics {#infrastructure_and_statistics}
In 1997 there were 25,000 telephone lines in use, and in 2007 there were 850,000 mobile cellular subscribers. Laos is served by a Russian Intersputnik satellite that covers the Indian Ocean region.
In 1998 there were 12 AM stations and 1 FM station. In 1997 there were an estimated 730,000 radios in the country. In 2011 Laos had 3 television channels. In 2000 there was 1 Internet service provider, by 2002 serving about 10,000 users. The top-level domain for Laos is .la
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# Transport in Laos
`{{Use mdy dates|date=March 2013}}`{=mediawiki} This article concerns the systems of **transportation in Laos**. Laos is a country in Asia, which possesses a number of modern transportation systems, including several highways and a number of airports. As a landlocked country, Laos possesses no ports or harbours on the sea, and the difficulty of navigation on the Mekong means that this is also not a significant transport route.
## Geography and transport limits {#geography_and_transport_limits}
Because of its mountainous topography and lack of development, Laos has few reliable transportation routes. This inaccessibility has historically limited the ability of any government to maintain a presence in areas distant from the national or provincial capitals and has limited interchange and communication among villages and ethnic groups.
The Mekong and Nam Ou are the only natural channels suitable for large-draft boat transportation, and from December through May, low water limits the size of the draft that may be used over many routes. Laotians in lowland villages located on the banks of smaller rivers have traditionally traveled in pirogues for fishing, trading, and visiting up and down the river for limited distances.
Otherwise, travel is done by ox-cart over level terrain or by foot. The steep mountains and lack of roads have caused upland ethnic groups to rely entirely on pack baskets and horse packing for transportation.
The road system is not extensive. A rudimentary network begun under the French colonial rule and continued from the 1950s, has provided an important means of increased intervillage communication, movement of market goods, and a focus for new settlements. As of mid-1994, travel in most areas of Laos were difficult and expensive, and most Laotians traveled only limited distances, if at all. As a result of ongoing improvements in the road system started during the early 1990s, it is expected that in the future villagers will more easily be able to seek medical care, send children to schools at district centers, and work outside their villages.
Currently, there are several projects to develop transport networks.
## Rail
*Main article: Rail transport in Laos* `{{see also|Boten–Vientiane railway}}`{=mediawiki} Laos has two railway lines: the standard gauge Boten--Vientiane railway spanning northern and central Laos, and a metre gauge spur line connecting Khamsavath with the Thai railway network.
Rail transport has not played a significant part in Laos\'s transport sector, since the country largely lacks the required infrastructure, though that is expected to change after the opening of the Boten--Vientiane railway.
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# Transport in Laos
## Highways
In Laos, there are 59,963 km of roadway, with 1.45% paved with concrete, 12.03% with asphalt concrete and 75.77% with double bituminous surface treatment and 10.75% with gravel road. Right-hand traffic (RHT) is observed in Laos.
Laos constructed a new highway in 2007 connecting Savannakhet to the Vietnamese border at Lao Bao, with funding from the Japanese government. This has greatly improved transport across Laos. This highway can be traversed in a few hours, while in 2002 the trip took over nine hours.
Laos is connected across the Mekong River to Thailand by First and Second Thai-Lao Friendship Bridges. Vientiane is linked to Nong Khai by the First Friendship Bridge. The Third Thai-Lao Friendship Bridge began construction in March 2009 linking Nakhon Phanom Province in northeastern Thailand and Khammouane Province in Laos. It was completed on 11 November 2011.
Laos opened a highway connection to Kunming in April 2008. The Fourth Thai-Lao Friendship Bridge opened to the public on 11 December 2013 linking Kunming to Bokeo, Laos and Chiang Rai. It reduced travel time to five hours.
### Expressway
*Main article: Vientiane-Vang Vieng Expressway* On 20 December 2020, the Vientiane--Vang Vieng Expressway, the first expressway in Laos, was completed. Construction began at the end of 2018 and was initially scheduled to finish in 2021. The road, which includes twin tunnels almost 900 metres long through Phoupha Mountain, shortens the route by 43 km as compared with the existing Route No 13. The expressway toll is 550 kip per kilometre, or about 62,000 kip for a one-way trip between Vientiane and Vang Vieng. The Vientiane-Vang Vieng expressway is the first section of a planned expressway from Vientiane through the northern provinces to Boten in Luang Namtha Province, which borders China.
### National Route list {#national_route_list}
- Route 1: Rantouy, Phongsaly (China)-Attapeu (Cambodia)
- Route 2: Thai Chang border-Muang Ngeun border
- Route 3: Nateuy-Houayxay (Thailand)
- Route 4: Luang Prabang-Kenethao
- Route 5: Tha Heua-Xaysomboun (Vietnam)
- Route 6: Phou Lao-Namsoi
- Route 7: Phou Khoun-Namcan border
- Route 8: Vienkham-Laksao-Namphao border
- Route 9: Savannakhet-Lao Bao (Vietnam)
- Route 10: Vientiane-Bankeun-Phonhone
- Route 11: Vientiane-Paklay
- Route 12: Thakhek-Mụ Giạ Pass(Vietnam)
- Route 13: Boten (China)-Vientiane-Veunkham(Cambodia)
- Route 14: Pakse-Champasak town-Cambodia border
- Route 15: Napong-Salavan-Lalay border
- Route 16: Chongmek-Pakse-Paxong-xekong-Namgiang border
- Route 17: Luang Namtha-Muang Sing-Xieng Kok (Myanmar)
- Route 18: Thang Beng-Attapeu-Phukuea border
- Route 19: Ban Pakha Kao-Boun Neua-Phongsali-Hatsa
- Route 20: Pakse-Salavan
## Water transport {#water_transport}
About 4,600 km of navigable water routes exist in Laos, primarily the Mekong and its tributaries. There are an additional 2,900 km of water routes, which is sectionally navigable by craft drawing less than 0.5 m.
Laos has an ocean-going merchant marine that consisted of one cargo ship of `{{GT|2,370|disp=long}}`{=mediawiki} in 2004, and still consisted of one ship in 2023.
## Pipelines
Laos has 136 km of pipelines for the transport of petroleum products.
## Airports
Laos possesses 52 airports, of which nine have paved runways. Of the airports with paved runways, Wattay International Airport in Vientiane has a runway length of 3,000 m. Of the remainder, four have runways 1,524 m to 2,437 m length, and a further four have lengths between 914 m and 1,523 m.
Of the airports without unpaved runways, one has a runway length of more than 1,524 m. Seventeen have runway lengths between 914 m and 1,523 m, leaving 25 with a lengths below 914 m
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# Geography of Latvia
Latvia lies on the eastern shores of the Baltic Sea on the level northwestern part of the rising East European platform, between Estonia and Lithuania. About 98% of the country lies under 200 m elevation. With the exception of the coastal plains, the ice age divided Latvia into three main regions: the morainic Western and Eastern uplands and the Middle lowlands. Latvia holds over 12,000 rivers, only 17 of which are longer than 100 km, and over 3,000 small lakes, most of which are eutrophic. The major rivers include the Daugava, the Lielupe, the Gauja, the Venta and the Salaca. Woodlands cover around 52% of the country (Pine -- 34%, Spruce -- 18%, Birch -- 30%). Other than peat, dolomite, and limestone, natural resources are scarce. Latvia has 504 km of sandy coastline, and the ports of Liepāja and Ventspils provide important warm-water harbors for the Baltic coast.
Latvia is a small country with a land size of 64,559 km2. However, it is larger than many other European countries (Albania, Belgium, Bosnia and Herzegovina, Croatia, Cyprus, Denmark, Estonia, Luxembourg, North Macedonia, Malta, Montenegro, Netherlands, Slovakia, Slovenia or Switzerland). Its strategic location has instigated many wars between rival powers on its territory. As recently as 1944, the USSR granted Russia the Abrene region, which Latvia contested after the dissolution of the Soviet Union.
## Physical environment {#physical_environment}
Latvia encompasses 64,589 square kilometers and is an extension of the East European Plain. Its flat terrain differs little from that of its surrounding neighbors. Latvia\'s only distinct border is the Baltic Sea coast, which extends for 496 kilometers. Its neighbors include Lithuania on the south (453 kilometers of common border), Estonia on the north (267 kilometers), Russia on the east (217 kilometers), and Belarus on the southeast (141 kilometers). Prior to World War II, Latvia bordered eastern Poland, but as a result of boundary changes by the Soviet Union, this territory was attached to Belarus.
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