text:
Newcastle International Airport

Newcastle International Airport is an international airport in Newcastle upon Tyne, England. Located approximately 7.7 mi from Newcastle City Centre, it is the primary and busiest airport in North East England, and the second busiest in Northern England. In 2019, prior to the COVID-19 pandemic, Newcastle International handled 5.2 million passengers annually.

Newcastle Airport has a Civil Aviation Authority Public Use Aerodrome Licence (Number P725) that allows flights for the public transport of passengers or for flying instruction.

In 2019, it was named the best airport in Europe of those serving 5–15million passengers annually by Airports Council International (ACI) for the second consecutive year.

Ownership
The airport is owned by seven local authorities (51%) and AMP Capital (49%). The seven local authorities are: City of Newcastle, City of Sunderland, Durham County Council, Gateshead MBC, North Tyneside MBC, Northumberland County Council, and South Tyneside MBC. In October 2012 Copenhagen Airport sold its stake in the airport to AMP Capital.

Area served
The airport mainly serves the counties of Tyne and Wear, County Durham, and Northumberland in North East England, as well as Cumbria in North West England, and the Scottish Borders area of southern Scotland. The airport competes with the smaller Teesside International Airport for passengers travelling from and to County Durham and the Teesside area of North Yorkshire. The nearest similar-sized airports are Edinburgh, Glasgow and Leeds Bradford.

Early years
In 1929, Newcastle-upon-Tyne City Council set up a special committee to investigate the potential for building an airport to serve the North-East of England, considering 18 locations before selecting a site at Woolsington, about 5 mi northwest of the city centre. The airport was opened on 26 July 1935 as Woolsington Aerodrome by the Secretary of State for Air, Sir Phillip Cunliffe-Lister. Incorporating a clubhouse, hangar, workshops, fuel garage and grass runway, it cost £35,000 to build. The airport became the base for the Newcastle upon Tyne Flying Club, which moved from its previous home at Cramlington Aerodrome and ran the new airport on behalf of the council. On 1 June 1939, No. 43 Elementary and Reserve Flying Training School, operated by Newcastle Flying Club and equipped with a mixture of de Havilland Tiger Moths, Miles Magisters and Hawker Hinds opened at Woolsington, as one of a large number of civil-operated flying schools set up to train aircrew for the RAF. The school was disbanded on 3 September 1939, with the outbreak of the Second World War.

In 1940, the airfield was occasionally used to operate detachments of Supermarine Spitfire fighters from RAF Acklington-based 72 Squadron. On 25 July that year, No. 83 Maintenance Unit RAF, tasked with recovering crashed aircraft and salvaging any usable parts, was formed at Woolsington, remaining operational until April 1946. The airfield was also used as a base for the single Tiger Moth of the Durham University Air Squadron from February 1941, and from 1942 to 1943 by detachments from No. 278 Squadron RAF, operating Westland Lysander and Supermarine Walrus in the air sea rescue role. No. 281 Squadron RAF, another air sea rescue squadron, operated from Woolsington from June to October 1943, while from November 1943 to June 1945, the airfield was used as a satellite field for No. 62 OTU, based at RAF Ouston. Woolsington was handed back to the council in 1946.

In 1967, the construction of a new runway and terminal was completed, along with an apron and a new air traffic control tower. These new additions were officially opened by the Prime Minister, Harold Wilson on 17 February 1967.

In 1978, with passenger figures approaching one million per year, the airport was designated as a regional international hub airport in the UK government's White Paper on Airports Policy, opening the way for further redevelopment; in the same decade it was re-branded as Newcastle Airport. The 1980s saw further investment in check-in, catering and duty-free shops. In 1991, Airport Metro station opened, connecting the airport with Newcastle Newcastle City Centre and Sunderland using the Tyne and Wear Metro system.

Since the 2000s
In August 2004, an extended and refurbished Departure Terminal was opened. The refurbishment included a 3,000 square metre extension with new shops, cafes and 1,200 new seats for waiting passengers.

In 2006, a record 5.4 million passengers used the airport, according to Civil Aviation Authority figures.

Rapid expansion in passenger traffic has led to increasing commercial use of the south side of the airport. This was previously used for general aviation, but is now used for freight, mail and corporate flights. This is partially due to difficulties obtaining departure and arrival slots for light aircraft traffic, which need to be separated from larger aircraft to protect against wake turbulence. As part of the Airport Master Plan, the south-side area is to be expanded with maintenance facilities including new hangar and apron areas.

In January 2007 it was announced that Emirates were to begin a daily non-stop service to Dubai from the airport. This service started on 7 September 2007 and has operated ever since. Until 2012, the route was flown by an Airbus A330. Since September 2012 it has been flown by a Boeing 777. Also in 2007, now defunct carrier Flyglobespan shortly connected Newcastle with Hamilton, Ontario, through this serving the greater Toronto area. Services were discontinued the same summer.

In 2012, Air Transat cut its route linking Newcastle with Toronto-Pearson, which had operated for several years. Through this, Newcastle was left without any transatlantic service.

On 23rd May of 2015, United Airlines commenced its summer seasonal route from Newcastle to New York-Newark, which was a huge achievement for the airport and the region. The service operated five times per week onboard B757-2 through September. However, in August 2016, United Airlines announced it would discontinue its seasonal route from Newark to Newcastle in 2017 after operating for just two consecutive seasons, citing economic reasons.

In July 2017, it was announced that the airport would be investing £3 million on a terminal expansion project which is part of overall £20 million improvement plans running from 2016 to 2017. This £20m improvement plan included a new radar system alongside digital signage in the check-in areas and the installation of new flooring. The £3m plan includes an extension to the terminal by 4,800 sq ft (450 m2) and will increase the equipment in the security hall, bringing in improved technology to speed up procedures there. This was due to be constructed over the winter of 2017/2018.

Until 2019, Jet2.com frequently linked its base in Newcastle with Newark during Christmas time. However, these services have not been resumed since the onset of the COVID-19 pandemic in 2020.

In August 2020, easyJet announced the closure of their crew base in Newcastle due to the financial difficulties from the COVID-19 pandemic which means that the airline only operates domestic flights from the airport after scrapping all of its international routes by 31 August 2020. However, since this decision the airline resumed its operations to Palma de Mallorca and Geneva in 2022 as well as Alicante, Amsterdam and Paris Charles de Gaulle in 2024. As well as introducing a winter seasonal route to Lyon in 2025.

In March 2022, Ryanair opened its new base at Newcastle and announced 10 new routes which meant that the airline would operate a total of 19 routes, with over 130 weekly flights over Summer 2022 using two based aircraft.

In April 2023, TUI announced its biggest ever programme at the airport for Summer 2024, operating up to 84 weekly flights to a total of 31 destinations on offer using an additional fifth aircraft, including new routes to Sal, Cape Verde and Sharm El Sheikh, Egypt.

In May 2023, Jet2.com announced their biggest ever Winter schedule for Newcastle Airport, with over 45 weekly flights. Destinations that have seen increases in the number of flights include Tenerife, Gran Canaria, Lanzarote and Alicante.

Facilities
Newcastle Airport Freight Village is south of the airport and includes Emirates SkyCargo, FedEx, and North East Air Cargo company offices which deal with freight exports and imports and mail. It also houses freight forwarding agents such as Casper Logistics Ltd, Kintetsu World Express, Kuehne + Nagel, Nippon Express, Schenker International, Davis Turner Air Cargo, and Universal Forwarding.

In April 2016, Emirates reported that flown exports have soared to £310m a year since the arrival of the Emirates service from Newcastle to Dubai. The Dubai route contributes some £600m to the economy and has opened unlimited export avenues to North East firms, some of whom have opened offices in the United Arab Emirates.

The airport is also home to the Newcastle Airport Fire Academy. The Newcastle Aviation Academy is also located within this area. When Gill Airways operated, its head office was in the New Aviation House, on the airport property. The south side of the airport also has a base for the National Police Air Service. They normally have one respective helicopter based here at a time but are known to rotate their fleet around bases. The area also holds maintenance workshops for the airport and various other depots for airport-run services like Alpha Catering.

Passenger
The following airlines operate regular scheduled services to and from Newcastle upon Tyne:

Statistics
The airport saw significant growth in the ten years to 2007, when passenger numbers peaked at 5.65 million, more than double the number handled ten years earlier. Passenger numbers declined in the subsequent four years due to the financial crisis of 2007–2010, but later recovered, with around 5.3 million passengers passing through the airport in 2018 (close to the 2006 total), although cargo volumes have broadly increased to record levels since 2005.

Accidents and incidents
On 30 November 2000, a Piper Aerostar registered N64719 en route to Iceland from Newcastle International Airport, crashed close to Fortingall, on the north side of Loch Tay in Perthshire, Scotland, killing the single crewmember. The accident report concluded that the aircraft gradually lost airspeed during an icing encounter, before stalling and the pilot losing control.

Metro
The Newcastle Airport Metro station station is directly connected to the terminal through an indoor walkway. The station is the northern terminus of the green line, with frequent direct services to all the main Newcastle and Sunderland stations (approximately 20 and 50 minutes respectively).

Road transport
The airport is connected to the A1 trunk road by the A696 dual carriageway. A half-hourly bus service links the airport to the nearby villages of Ponteland and Darras Hall, as well as to the City Centre.

title: Newcastle International Airport


text:
Kursk (disambiguation)

Kursk is a city in Russia.

Kursk may also refer to:
 * Kursk Oblast, a federal subject of Russia
 * Kursk crater, a meteorite impact crater in Russia
 * Kursk Magnetic Anomaly
 * Battle of Kursk, the 1943 World War II battle that was Germany's last major offensive in the east and one of the largest tank battles in history
 * Kursk (board game), a 1980 board wargame that simulates the battle
 * Our Lady of Kursk, an Eastern Orthodox icon
 * KYPCK, a Finnish metal band
 * Russian submarine Kursk
 * Kursk submarine disaster (2000)
 * Kursk (play), a play inspired by the sinking of Kursk
 * Kursk (film), a film by Thomas Vinterberg, inspired by the sinking of Kursk

 * Kursk (inhabited locality), several inhabited localities in Russia

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

title: Kursk (disambiguation)


text:
2003 Belgian federal election

Federal elections were held in Belgium on 18 May 2003, the first under a new electoral code. One of the novelties was an electoral threshold of 5, which has cost many seats to the N-VA and the Green parties, Ecolo and Agalev. The Belgian Socialists recovered well; the liberal and nationalist parties increased their vote as well.

The Flemish Greens lost all their seats. The Greens were attacked on two fronts: some, including their coalition partners, accused them of being too fundamentalist, while others said that they had betrayed their ideals. The resignation of a Walloon green minister (Isabelle Durant), one week before the elections, probably didn't do them much good either. Although it was predicted in some opinion polls, the gains of the Front National were surprising, considering that it seldom appeared in the media. The most important trend was the recovery of the Flemish social-democrats, led by the popular (some would say populist) Steve Stevaert. The fact that Elio Di Rupo was learning Dutch caused rumours that he hoped to become prime minister, if the social-democrats would turn out to be the largest political family.

Themes that probably influenced the election results in some way were the government's opposition to the 2003 invasion of Iraq, the controversy around the nuisance around the airport of Zaventem, the controversy surrounding the banning of tobacco publicity, and unemployment, but a general dominating theme was lacking.

title: 2003 Belgian federal election


text:
1891 in film

The following is an overview of the events of 1891 in film, including a list of films released and notable births.

Events

 * William K. L. Dickson, an assistant to Thomas Edison, supervises the construction of the first film studio, the Black Maria, in West Orange, New Jersey which produces many of the early Kinetoscope short films of the 1890s later seen in penny arcades the following year after the studio is completed.
 * March – William K. L. Dickson successfully develops a working prototype of the Kinetoscope which moves horizontally.
 * May 20 – First public display of Thomas Edison's prototype horizontal kinetoscope: Dickson Greeting is shown at Edison's Laboratory for a convention of the National Federation of Women's Clubs in West Orange, New Jersey.
 * August 24 – Thomas Edison files for a patent for the motion picture camera (which he receives in 1897).

Films released in 1891

 * Dickson Greeting, starring and directed by William K. L. Dickson.
 * Duncan and Another, Blacksmith Shop, directed by William K. L. Dickson and William Heise and starring James C. Duncan.
 * Duncan Smoking, directed by William K. L. Dickson and William Heise and starring James C. Duncan.
 * Duncan or Devonald with Muslin Cloud, directed by William K. L. Dickson and William Heise and starring Fred C. Devonald and James C. Duncan.
 * Men Boxing, directed by William K. L. Dickson and William Heise.
 * Monkey and Another, Boxing, directed by William K. L. Dickson and William Heise.
 * Newark Athlete, directed by William K. L. Dickson.
 * Je vous aime, starring and directed by Georges Demenÿ.
 * La vague, directed by Étienne-Jules Marey.
 * Two Fencers, directed by Étienne-Jules Marey.

title: 1891 in film


text:
Charles Read (naval officer)

Charles William Read (May 12, 1840 – January 25, 1890), known commonly as "Savez", was an officer in the antebellum United States Navy and then in the Confederate Navy during the American Civil War. He was nicknamed the "Seawolf of the Confederacy" for his exploits and daring.

Early life and career
Charles William Read was born in Satartia, Mississippi in 1840. He was appointed to the United States Naval Academy in 1856 and graduated in 1860. He served briefly aboard USS Powhatan after graduation.

American Civil War
At the outbreak of the American Civil War Read resigned his commission with the United States Navy and accepted a position with the Confederate States Navy. Read was initially assigned to the CSS McRae at New Orleans, Louisiana as a midshipman and participated in the battle between batteries on Ship Island and the USS Massachusetts (1860) on July 9, 1861. On October 12, 1861, he participated in the attack on the Union blockading squadron at Head of the Passes on the Mississippi River. When the commander of the CSS McRae was wounded on April 24, 1862, Read took command of the ship.

Read then served as executive officer of the CSS Arkansas during its actions against a blockading fleet of over 30 ships on the Mississippi River near Vicksburg, Mississippi on 13 July 1862. Read served as acting commander of the Arkansas during her final battle supporting the Confederate Army assaulting Baton Rouge, Louisiana on 6 August 1862. After the sinking of the Arkansas, Read travelled by foot to Port Hudson, Louisiana and assisted with the emplacement of shore guns there.

Read was soon ordered to Mobile, Alabama and was assigned to the CSS Florida which set sail on 15 January 1863. He transferred to the CSS Clarence, a captured prize of the Florida, and set out on his own. During this raiding mission, which lasted from 6 June 1863 to 27 June 1863, Read transferred his command to prize vessels twice more, once to the CSS Tacony and finally to the CSS Archer.

At the end of the raid, Lieutenant Read had captured or destroyed twenty-two United States vessels. He and his crew were captured off Portland, Maine on June 27, 1863, while attempting to take the USRC Caleb Cushing. Read was held at Fort Warren, Massachusetts, until he was exchanged at Cox Wharf, Virginia, on October 18, 1864.

After his release, Read participated in naval and land operations on the James River, he commanded the CSS Scorpion and two other torpedo boats at the Battle of Trent's Reach. In January 1865, he was assigned to the CSS Webb at Shreveport, Louisiana with the intention that she become a raider in the Pacific Ocean. Read did not reach the Webb until 22 April 1865. Read attempted to break out to the Gulf of Mexico but grounded in shallow waters near New Orleans on April 23, 1865. Read fired the ship to prevent its capture by Federal forces. Read surrendered to Federal naval authorities in New Orleans and was transported again to Fort Warren. He was released on July 24, 1865.

Later life
In 1867, Read was second officer aboard a ship involved in an effort to help Cuban rebels overthrow the Spanish government of the island. Read and others were arrested by the US government but were quickly released.

He was later hired by Charles Flynt to train Peru in the use of torpedoes. Read was commissioned as an Commander in the Peruvian Navy and much like John Randolph Tucker, received disdain from within the Peruvian Navy due to their jealousy of a foreigner being hired in a position of command.

Read earned his nickname "Savvy" or "Savez" due to his constant use of the term.

Charles Read died on January 25, 1890, in Meridian, Mississippi, and was interred at Rose Hill Cemetery.

title: Charles Read (naval officer)


text:
Köthen (district)

Köthen was a district (Kreis) in the middle of Saxony-Anhalt, Germany. Neighboring districts were (from north clockwise) Anhalt-Zerbst, Schönebeck, Anhalt-Zerbst, the district-free city Dessau, Bitterfeld, Saalkreis and Bernburg.

History
In 1603 the principality of Anhalt-Köthen was created, when the principality of Anhalt was split in five parts. In 1665 it merged with Anhalt-Plötzkau, and in 1807 it became a duchy. 1847 it was divided between Anhalt-Dessau and Anhalt-Bernburg, and in 1853 it was merged with Anhalt-Dessau to form the Duchy of Anhalt-Dessau-Köthen.

When in 1863 the various parts of Anhalt were reunited, the district was created. At first the district Dessau-Köthen did cover the area surrounding the two district-free cities Dessau and Köthen. In 1950 the city of Köthen was added to the district, and it was renamed after its capital. As result of the district reform of 2007, the area was merged into the new district of Anhalt-Bitterfeld with the city of Köthen as its capital.

Geography
The district is located in the Magdeburger Börde, with soft hills from the moraines from the last ice age. The river Elbe forms part of the northern boundary of the district.

title: Köthen (district)


text:
Man About the House

Man About the House is a British sitcom created by Brian Cooke and Johnnie Mortimer. It starred Richard O'Sullivan, Paula Wilcox, Sally Thomsett, Yootha Joyce and Brian Murphy. Six series were broadcast on ITV from 15 August 1973 to 7 April 1976. The series was considered daring at the time because it featured a man sharing a London flat with two single women. The show was made by Thames Television and recorded at its Teddington Studios in Greater London. It is regularly repeated on ITV3.

Two spin-off series were later made: George and Mildred and Robin's Nest. In 2004, Man About the House placed 69th in a poll to find Britain's Best Sitcom. The series was remade in the United States as Three's Company in 1977. A film version was released in 1974.

Main stars

 * Richard O'Sullivan as Robin Tripp
 * Paula Wilcox as Chrissy Plummer
 * Sally Thomsett as Jo

Co-stars

 * Yootha Joyce as Mildred Roper
 * Brian Murphy as George Roper
 * Doug Fisher as Larry Simmonds

Recurring cast

 * Roy Kinnear as Jerry (series 3 to 5)
 * Daphne Oxenford as Mrs Plummer (series 1, 4 and 6)

Plot
Chrissy and Jo live in a London flat together and work for the same firm. The women find a stranger, student chef Robin Tripp, asleep in their bath the morning after the farewell party for their departed flatmate Eleanor. When he meets the two girls, Robin has been in London two days, having moved from Southampton to attend university. The girls are unimpressed with Gabrielle (Helen Fraser) as a potential replacement for Eleanor, but they are impressed by Robin's culinary skills, as they cannot cook at all. Learning that Robin has been staying at the YMCA, they convince him to move in, on the understanding that it will be a platonic relationship.

Chrissy tells landlord George Roper that Robin is gay to eliminate George's objections to the mixed-sex living arrangement. George, in truth a subletting landlord placed by the council, is a miserly, spiteful and unkempt man under the thumb of his domineering and sexually frustrated wife Mildred.

In the second episode, Robin's true sexuality becomes known to Mildred. She takes out her frustrations with George's lack of class and sexual inadequacy by making suggestive remarks to Robin and frequently siding with the tenants against George. Mildred openly flirts with Robin, and Robin frequently flirts with Chrissy and Jo. The girls, adhering to their pledge to maintain a platonic relationship with Robin, spurn his mild advances and adapt to his presence in the flat. Chrissy occasionally shows attraction to Robin, but the two never pursue any romantic interaction.

Robin's friend Larry, a lovable rogue, appears on a recurring basis throughout the series. In the third series, he moves into the loft apartment above the trio's apartment and is a frequent source of trouble. Another occasional cast member is George's friend, the dodgy builder Jerry (Roy Kinnear). Jerry is the only supporting character to reappear in the spin-off George and Mildred.

Robin's brother Norman Tripp (Norman Eshley) appears in the final three episodes of the sixth and final series, and starts a romance with Chrissy. The series ends with Norman and Chrissy marrying. Eshley had a previous guest role in the episode "In Praise of Older Men" (Series 2, Episode 3), and would subsequently appear as another character, the Ropers' neighbour, in George and Mildred.

Episodes
First airing on 15 August 1973, Man About the House ran until 7 April 1976, spanning 39 episodes in six series. In addition, on Christmas Day 1973, a short special aired as part of All-star Comedy Carnival.

Theme music
Written by Johnny Hawksworth and entitled "Up to Date", the theme song was not specially commissioned for the show, but rather was provided via the production music company De Wolfe Music. It also appeared on the 1996 compilation CD The Sound Gallery – Volume Two, but credited to the Simon Park Orchestra.

Film
A 1974 film version of the show starred all of the main cast members. It was the last in a series of movie screen adaptations of popular TV shows made by Hammer Films, though a George and Mildred film (featuring Yootha Joyce and Brian Murphy) would be made in 1980 by another studio.

Spin-offs and remakes
After the series ended in 1976, two successful spin-off series followed:

 * George and Mildred, in which the Ropers move to the suburbs.
 * Robin's Nest, in which Robin gets married and opens a bistro.

The format of Man About the House was sold internationally, and it was remade in the United States as Three's Company in 1976; in the Netherlands as Sam Sam in 1994; in Sweden as En fyra för tre in 1996; in Norway as Tre på toppen in 1997; in Portugal as Não Há Duas Sem Três in 1997; in Poland as Lokatorzy in 2000; in Russia as Troe sverhy in 2006; in Ecuador as El hombre de la casa and in Chile as Tres son multitud, both in 2007.

The American Three's Company adaptation also spawned the same spin-offs as had Man About the House: Three's a Crowd (based on Robin's Nest) and The Ropers (based upon George and Mildred).

Two and a half decades after the original ended, there were plans for Man About the House to return to British TV screens in the early 2000s with a new cast consisting of Johnny Vaughan, Amanda Holden and Jane Wall as the new main stars of the show, but those plans were scrapped before getting past the pre-planning stage.

Home media
All six series have been released on DVD in the UK by Network DVD, as have George and Mildred and Robin's Nest.

Region 2 Releases:
 * Series 1 - 2005 (reissued on 8 April 2013)
 * Series 2–30 January 2006
 * Series 3–20 March 2006
 * Series 4–7 August 2006
 * Series 5–22 January 2007
 * Series 6–14 May 2007
 * The Complete Series (features the six individual seasons in a box) - 24 September 2007
 * The Complete Series (in slimmer packaging) - 26 May 2008

Series 1 and 2 have had a US release as part of a two-disc set by FremantleMedia.

Series 1 and 2 were released in Australia in 2004, but a delay was encountered in releasing further series because of contract renegotiations (the same problem affected releases of George and Mildred and Bless This House). Series 3 was finally released on 16 July 2008, and Series 4 on 5 November 2008. Series 5 and 6 are yet to be released. Series 1 was re-released on 2 April 2009, now with the same cover art as the UK edition. Fremantle Media re-released series 1 on 3 March 2011 with new cover art. Re-releases have continued with Series 2 on 3 October 2012, Series 3 on 1 May 2013, and Series 4 on 1 May 2013. Series 5 and Series 6 finally received a release on 7 August 2013. Via Vision Entertainment announced "The Complete Series" will be released on October 21, 2020, which will be the first time this series will be released as a collection.

In 2019, a 19-disc DVD set (Region 2) was issued by Network/Fremantle containing every episode of Man About the House, George and Mildred and Robin's Nest.

title: Man About the House


text:
Spark gap

A spark gap consists of an arrangement of two conducting electrodes separated by a gap usually filled with a gas such as air, designed to allow an electric spark to pass between the conductors. When the potential difference between the conductors exceeds the breakdown voltage of the gas within the gap, a spark forms, ionizing the gas and drastically reducing its electrical resistance. An electric current then flows until the path of ionized gas is broken or the current reduces below a minimum value called the "holding current". This usually happens when the voltage drops, but in some cases occurs when the heated gas rises, stretching out and then breaking the filament of ionized gas. Usually, the action of ionizing the gas is violent and disruptive, often leading to sound (ranging from a snap for a spark plug to thunder for a lightning discharge), light, and heat.

Spark gaps were used historically in early electrical equipment, such as spark gap radio transmitters, electrostatic machines, and X-ray machines. Their most widespread use today is in spark plugs to ignite the fuel in internal combustion engines, but they are also used in lightning arresters and other devices to protect electrical equipment from high-voltage transients.

Breakdown voltage
For air, the breakdown strength is about 30 kV/cm at sea level.

Spark visibility
The light emitted by a spark does not come from the current of electrons itself, but from the material medium fluorescing in response to collisions from the electrons. When electrons collide with molecules of air in the gap, they excite their orbital electrons to higher energy levels. When these excited electrons fall back to their original energy levels, they emit energy as light. It is impossible for a visible spark to form in a vacuum. Without intervening matter capable of electromagnetic transitions, the spark will be invisible (see vacuum arc).

Applications
Spark gaps are essential to the functioning of a number of electronic devices.

Ignition devices

A spark plug uses a spark gap to initiate combustion. The heat of the ionization trail, but more importantly, UV radiation and hot free electrons (both cause the formation of reactive free radicals) ignite a fuel-air mixture inside an internal combustion engine, or a burner in a furnace, oven, or stove. The more UV radiation is produced and successfully spread into the combustion chamber, the further the combustion process proceeds.

The Space Shuttle Main Engine hydrogen oxygen propellant mixture was ignited with a spark igniter.

Protective devices

Spark gaps are frequently used to prevent voltage surges from damaging equipment. Spark gaps are used in high-voltage switches, large power transformers, in power plants and electrical substations. Such switches are constructed with a large, remote-operated switching blade with a hinge as one contact and two leaf springs holding the other end as second contact. If the blade is opened, a spark may keep the connection between blade and spring conducting. The spark ionizes the air, which becomes conductive and allows an arc to form, which sustains ionization and hence conduction. A Jacob's ladder on top of the switch will cause the arc to rise and eventually extinguish. One might also find small Jacob's ladders mounted on top of ceramic insulators of high-voltage pylons. These are sometimes called horn gaps. If a spark should ever manage to jump over the insulator and give rise to an arc, it will be extinguished.

Smaller spark gaps are often used to protect sensitive electrical or electronic equipment from high-voltage surges. In sophisticated versions of these devices (called gas tube arresters), a small spark gap breaks down during an abnormal voltage surge, safely shunting the surge to ground and thereby protecting the equipment. These devices are commonly used for telephone lines as they enter a building; the spark gaps help protect the building and internal telephone circuits from the effects of lightning strikes. Less sophisticated (and much less expensive) spark gaps are made using modified ceramic capacitors; in these devices, the spark gap is simply an air gap sawn between the two lead wires that connect the capacitor to the circuit. A voltage surge causes a spark that jumps from lead wire to lead wire across the gap left by the sawing process. These low-cost devices are often used to prevent damaging arcs between the elements of the electron gun(s) within a cathode ray tube (CRT).

Small spark gaps are very common in telephone switchboards, as the long phone cables are very susceptible to induced surges from lightning strikes. Larger spark gaps are used to protect power lines.

Spark gaps are sometimes implemented on Printed Circuit Boards in electronics products using two closely spaced exposed PCB traces. This is an effectively zero cost method of adding crude over-voltage protection to electronics products.

Transils and trisils are the solid-state alternatives to spark gaps for lower-power applications. Neon bulbs are also used for this purpose.

High speed photography

A triggered spark gap in an air-gap flash is used to produce photographic light flashes in the sub-microsecond domain.

Radio transmitters
A spark radiates energy throughout the electromagnetic spectrum. Nowadays, this is usually regarded as illegal radio frequency interference and is suppressed, but in the early days of radio communications (1880–1920), this was the means by which radio signals were transmitted, in the unmodulated spark-gap transmitter. Many radio spark gaps include cooling devices, such as the rotary gap and heat sinks, since the spark gap becomes quite hot under continuous use at high power.

Sphere gap for voltage measurement
A calibrated spherical spark gap will break down at a highly repeatable voltage, when corrected for air pressure, humidity and temperature. A gap between two spheres can provide a voltage measurement without any electronics or voltage dividers, to an accuracy of about 3%. A spark gap can be used to measure high voltage AC, DC, or pulses, but for very short pulses, an ultraviolet light source or radioactive source may be put on one of the terminals to provide a source of electrons.

Power-switching devices
Spark gaps may be used as electrical switches because they have two states with significantly different electrical resistance. Resistance between the electrodes may be as high as 10$12$ ohms when the electrodes are separated by gas or vacuum which means that little current flows even when a high voltage exists between the electrodes. Resistance drops as low as a 10$-3$ ohms low when the electrodes are connected by plasma which means that power dissipation is low even at high current. This combination of properties has led to the use of spark gaps as electrical switches in pulsed power applications where energy is stored at high voltage in a capacitor and then discharged at high current. Examples include pulsed lasers, railguns, Marx generators, fusion, ultrastrong pulsed magnetic field research, and nuclear bomb triggering.

When a spark gap consists of only two electrodes separated by gas, the transition between the non-conducting and conducting states is governed by Paschen's law. At typical pressure and electrode distance combinations, Paschen's law says that Townsend discharge will fill the gap between the electrodes with conductive plasma whenever the ratio of the electric field strength to the pressure exceeds a constant value determined by the composition of the gas. The speed with which pressure can be reduced is limited by choked flow, while increasing the electric field in a capacitor discharge circuit is limited by the capacitance in the circuit and the current available for charging the capacitance. These limitations on the speed with which discharge may be initiated mean that spark gaps with two electrodes typically have high jitter.

Triggered spark gaps are a class of devices with some additional means of triggering to achieve low jitter. Most commonly, this is a third electrode, as in a trigatron. The voltage of the trigger electrode can be changed quickly because the capacitance between it and the other electrodes is small. In a triggered spark gap, gas pressure is optimized to minimize jitter while also avoiding unintentional triggering. Triggered spark gaps are made in permanently sealed versions with limited voltage range and in user-pressurized versions with voltage range proportional to the available pressure range. Triggered spark gaps share many similarities with other gas-filled tubes such as thyratrons, krytrons, ignitrons, and crossatrons.

Triggered vacuum gaps, or sprytrons, resemble triggered spark gaps both in appearance and construction but rely on a different operating principle. A triggered vacuum gap consists of three electrodes in an airtight glass or ceramic envelope that has been evacuated. This means that, unlike a triggered spark gap, a triggered vacuum gap operates in the parameter space to the left of the Paschen minimum where breakdown is promoted by increasing pressure. Current between the electrodes is limited to a small value by field emission in the non-conducting state. Breakdown is initiated by rapidly evaporating material from a trigger electrode or an adjacent resistive coating. Once the vacuum arc is initiated, a triggered vacuum gap is filled with conductive plasma as in any other spark gap. A triggered vacuum gap has a larger operating voltage range than a sealed triggered spark gap because Paschen curves are much steeper to the left of the Paschen minimum than at higher pressures. Triggered vacuum gaps are also rad hard because in the non-conducting state they do not contain any gas that could be ionized by radiation.

Insect control
They are also used as insect zappers. The two electrodes are implemented as metal lattices placed a slightly too far apart for the voltage to jump. When an insect ventures between the electrodes the gap distance is reduced by the insects body, being conductive, and a spark discharge occurs to electrocute and burn the insect.

In this use the spark gap mechanism is often used in conjunction with a bait, such as a light, to attract the insect into the spark gap.

title: Spark gap


text:
Capgras delusion

Capgras delusion or Capgras syndrome is a psychiatric disorder in which a person holds a delusion that a friend, spouse, parent, another close family member, or pet has been replaced by an identical impostor. It is named after Joseph Capgras (1873–1950), the French psychiatrist who first described the disorder.

The Capgras delusion is classified as a delusional misidentification syndrome, a class of delusional beliefs that involves the misidentification of people, places, or objects. It can occur in acute, transient, or chronic forms. Cases in which patients hold the belief that time has been "warped" or "substituted" have also been reported.

The delusion most commonly occurs in individuals diagnosed with a psychotic disorder, usually schizophrenia, but has also been seen in brain injury, dementia with Lewy bodies, and other forms of dementia. It presents often in individuals with a neurodegenerative disease, particularly at an older age; it has also been reported as occurring in association with diabetes, hypothyroidism, and migraine attacks. In one isolated case, the Capgras delusion was temporarily induced in a healthy subject by administration of ketamine. It occurs more frequently in females, with a female to male ratio of approximately.

Signs and symptoms
Compared to other delusional misidentification syndromes, like the Fregoli delusion, the Capgras delusion is more widely documented. The following two case reports are examples of the Capgras delusion in a psychiatric setting:

"Mrs. D, a 74-year-old married housewife, recently discharged from a local hospital after her first psychiatric admission, presented to our facility for a second opinion. At the time of her admission earlier in the year, she had received the diagnosis of atypical psychosis because of her belief that her husband had been replaced by another unrelated man. She refused to sleep with the impostor, locked her bedroom and door at night, asked her son for a gun, and finally fought with the police when attempts were made to hospitalise her. At times she believed her husband was her long deceased father. She easily recognised other family members and would misidentify her husband only."

"Diane was a 28-year-old single woman who was seen for an evaluation at a day hospital program in preparation for discharge from a psychiatric hospital. This was her third psychiatric admission in the past five years. Always shy and reclusive, Diane first became psychotic at age 23. Following an examination by her physician, she began to worry that the doctor had damaged her internally and that she might never be able to become pregnant. The patient's condition improved with neuroleptic treatment but deteriorated after discharge because she refused medication. When she was admitted eight months later, she presented with delusions that a man was making exact copies of people—'screens'—and that there were two screens of her, one evil and one good. The diagnosis was schizophrenia with Capgras delusion. She was disheveled and had a bald spot on her scalp from self-mutilation."

The following case is an instance of the Capgras delusion resulting from a neurodegenerative disease:

"Fred, a 59-year-old man with a high school qualification, was referred for neurological and neuropsychological evaluation because of cognitive and behavioural disturbances. He had worked as the head of a small unit devoted to energy research until a few months before. His past medical and psychiatric history was uneventful. [...] Fred's wife reported that about 15 months from onset he began to see her as a 'double' (her words). The first episode occurred one day when, after coming home, Fred asked her where Wilma was. On her surprised answer that she was right there, he firmly denied that she was his wife Wilma, whom he 'knew very well as his sons' mother', and went on plainly commenting that Wilma had probably gone out and would come back later. [...] Fred presented progressive cognitive deterioration characterised both by severity and fast decline. Apart from [Capgras disorder], his neuropsychological presentation was hallmarked by language disturbances suggestive of frontal-executive dysfunction. His cognitive impairment ended up in a severe, all-encompassing frontal syndrome."

Causes
It is generally agreed that the Capgras delusion has a complex and organic basis caused by structural damage to organs and can be better understood by examining neuroanatomical damage associated with the syndrome.

In one of the first papers to consider the cerebral basis of the Capgras delusion, Alexander, Stuss and Benson pointed out in 1979 that the disorder might be related to a combination of frontal lobe damage causing problems with familiarity and right hemisphere damage causing problems with visual recognition.

Further clues to the possible causes of the Capgras delusion were suggested by the study of brain-injured patients who had developed prosopagnosia. In this condition, patients are unable to recognize faces consciously, despite being able to recognize other types of visual objects. However, a 1984 study by Bauer showed that even though conscious face recognition was impaired, patients with the condition showed autonomic arousal (measured by a galvanic skin response measure) to familiar faces, suggesting there are two pathways to face recognition—one conscious and one unconscious.

In a 1990 paper published in the British Journal of Psychiatry, psychologists Hadyn Ellis and Andy Young hypothesized that patients with Capgras delusion may have a "mirror image" or double dissociation of prosopagnosia, in that their conscious ability to recognize faces was intact, but they might have damage to the system which produces the automatic emotional arousal to familiar faces. This might lead to the experience of recognizing someone while feeling something was not "quite right" about them. In 1997, Ellis and his colleagues published a study of five patients with Capgras delusion (all diagnosed with schizophrenia) and confirmed that although they could consciously recognize the faces, they did not show the normal automatic emotional arousal response. The same low level of autonomic response was shown in the presence of strangers. Young (2008) has theorized that this means that patients with the disease experience a "loss" of familiarity, not a "lack" of it. Further evidence for this explanation comes from other studies measuring galvanic skin responses (GSR) to faces. A patient with Capgras delusion showed reduced GSRs to faces in spite of normal face recognition. This theory for the causes of Capgras delusion was summarised in Trends in Cognitive Sciences in 2001.

William Hirstein and Vilayanur S. Ramachandran reported similar findings in a paper published on a single case of a patient with Capgras delusion after brain injury. Ramachandran portrayed this case in his book Phantoms in the Brain and gave a talk about it at TED 2007. Since the patient was capable of feeling emotions and recognizing faces but could not feel emotions when recognizing familiar faces, Ramachandran hypothesizes the origin of Capgras syndrome is a disconnection between the temporal cortex, where faces are usually recognized (see temporal lobe), and the limbic system, involved in emotions. More specifically, he emphasizes the disconnection between the amygdala and the inferotemporal cortex.

In 2010, Hirstein revised this theory to explain why a person with Capgras syndrome would have the particular reaction of not recognizing a familiar person. Hirstein explained the theory as follows:

"my current hypothesis on Capgras, which is a more specific version of the earlier position I took in the 1997 article with V. S. Ramachandran. According to my current approach, we represent the people we know well with hybrid representations containing two parts. One part represents them externally: how they look, sound, etc. The other part represents them internally: their personalities, beliefs, characteristic emotions, preferences, etc. Capgras syndrome occurs when the internal portion of the representation is damaged or inaccessible. This produces the impression of someone who looks right on the outside, but seems different on the inside, i.e., an impostor. This gives a much more specific explanation that fits well with what the patients actually say. It corrects a problem with the earlier hypothesis in that there are many possible responses to the lack of an emotion upon seeing someone."

Furthermore, Ramachandran suggests a relationship between the Capgras syndrome and a more general difficulty in linking successive episodic memories because of the crucial role emotion plays in creating memories. Since the patient could not put together memories and feelings, he believed objects in a photograph were new on every viewing, even though they normally should have evoked feelings (e.g., a person close to him, a familiar object, or even himself). Others like Merrin and Silberfarb (1976) have also proposed links between the Capgras syndrome and deficits in aspects of memory. They suggest that an important and familiar person (the usual subject of the delusion) has many layers of visual, auditory, tactile, and experiential memories associated with them, so the Capgras delusion can be understood as a failure of object constancy at a high perceptual level.

Most likely, more than a mere impairment of the automatic emotional arousal response is necessary to form the Capgras delusion, as the same pattern has been reported in patients showing no signs of delusions. Ellis suggested that a second factor explains why this unusual experience is transformed into a delusional belief; this second factor is thought to be an impairment in reasoning, although no specific impairment has been found to explain all cases. Many have argued for the inclusion of the role of patient phenomenology in explanatory models of the Capgras syndrome in order to better understand the mechanisms that enable the creation and maintenance of delusional beliefs.

Capgras syndrome has also been linked to reduplicative paramnesia, another delusional misidentification syndrome in which a person believes a location has been duplicated or relocated. Since these two syndromes are highly associated, it has been proposed that they affect similar areas of the brain and therefore have similar neurological implications. Reduplicative paramnesia is understood to affect the frontal lobe, and thus it is believed that Capgras syndrome is also associated with the frontal lobe. Even if the damage is not directly to the frontal lobe, an interruption of signals between other lobes and the frontal lobe could result in Capgras syndrome. Some authors have highlighted cannabis consumption as a trigger for Capgras syndrome.

Diagnosis
Because it is a rare and poorly understood condition, there is no established way to diagnose the Capgras delusion. Diagnosis is primarily made on a psychiatric evaluation of the patient, who is most likely brought to a psychiatrist's attention by a family member or friend believed to be an imposter by the person under the delusion. The patient may undergo mental skills tests to check for dementia or other conditions, and brain imaging tests like MRI or EEG that look for lesions or other brain changes.

Treatment
Treatment of Capgras delusion has not been well studied, so there is no evidence-based approach. Typically, treatment of delusional disorders is challenging due to poor patient insight and lack of empirical data. Treatment is generally therapy, often with support of antipsychotic medication. As manifestation of Capgras delusion is often a symptom rather than a syndrome itself, treatment may focus on the accompanying condition. A study has shown that using medications appropriately to target the underlying disorder's core symptoms can be an effective management strategy. Hospitalization may be necessary, if the patient is engaging in self-harm or violence.

History
Capgras syndrome is named after Joseph Capgras, a French psychiatrist who first described the disorder in 1923 in his paper co-authored by Jean Reboul-Lachaux, on the case of a French woman, "Madame Macabre," who complained that corresponding "doubles" had taken the places of her husband and other people she knew. Capgras and Reboul-Lachaux first called the syndrome "l'illusion des sosies", which can be translated literally as "the illusion of Doppelgänger."

The syndrome was initially considered a purely psychiatric disorder, the delusion of a double seen as symptomatic of schizophrenia, and purely a female disorder (though this is now known not to be the case ) often noted as a symptom of hysteria. Most of the proposed explanations initially following that of Capgras and Reboul-Lachaux were psychoanalytical in nature. It was not until the 1980s that attention turned to the usually co-existing organic brain lesions originally thought to be essentially unrelated or coincidental. Today, the Capgras syndrome is understood as a neurological disorder, in which the delusion primarily results from organic brain lesions or degeneration.

Actual cases of impostors
Historically, there have been many cases of actual impostors, who took over or attempted to take over the life and identity of someone else. The case of Christine Collins resulted in her illegitimate commitment to a mental hospital until the impostor who pretended to be her disappeared son confessed.

Society and culture
The song "Mr. Capgras Encounters a Secondhand Vanity" by Will Wood and the Tapeworms references the disorder, and in it the speaker accuses someone of being replaced by an imposter.

title: Capgras delusion


text:
Petr Beckmann

Petr Beckmann (November 13, 1924 – August 3, 1993) was a professor of electrical engineering and advocate of libertarianism and nuclear power who disputed Albert Einstein's theory of relativity and other accepted theories in modern physics.

Biography
In 1939, when Beckmann was 14, his family fled their home in Prague, Czechoslovakia to escape the Nazis. From 1942 to 1945, he served in a Czech squadron of the Royal Air Force. He worked as a radar mechanic on the newly invented radar systems that helped Britain win the Battle of the Atlantic. He received a B.Sc. in 1949, a Ph.D. in 1955, and a D.Sc. in 1962, all from Prague's Czech Academy of Sciences in electrical engineering. He defected to the United States in 1963 and became a professor (later, emeritus) of electrical engineering at the University of Colorado. In the United States, he became acquainted with novelist Ayn Rand, a contributing editor to a publication devoted to her ideas, The Intellectual Activist, and a speaker at The Thomas Jefferson School, an intellectual conference of similar purpose.

Beckmann was a prolific author; he wrote several electrical engineering textbooks and non-technical works. By 1968, he had founded Golem Press, which published most of his books. The Golem Press books included The Health Hazards of Not Going Nuclear (1976), which argued in favor of nuclear power during the height of the anti-nuclear movement by making "apples-to-apples" comparisons of the risks of nuclear power with the risks in the same terms (e.g., deaths per terawatt hour) of the alternative power sources. Beckmann also wrote A History of $π$, documenting the history of the calculation of $π$. The book also expresses opposition to the Roman culture, Catholicism (and other religions), Nazism, and Communism. He published his own monthly newsletter, Access to Energy, which since September 1993 has been written by biochemist Arthur B. Robinson.

In 1981, he took early retirement with emeritus status, in order to devote himself fully to what he saw as the defense of science, technology and free enterprise, through his newsletter, Access to Energy. He founded the Golem Press in 1967, publishing more than nine books. These included The History of $π$, Einstein Plus Two, and The Health Hazards of Not Going Nuclear (with an Introduction by Edward Teller). He wrote some 60 scientific papers and eight technical books. Beckmann spoke at the 1990 San Francisco Conference of International Society for Individual Liberty (ISIL), where he received a standing ovation for his speech in which he attacked "sham environmentalists".

Beckmann was also a frequent participant in Usenet debates. In them, he claimed to have debunked Albert Einstein's theory of special relativity in his book Einstein Plus Two, as well as in the journal Galilean Electrodynamics, which he also founded.

Books

 * (with coauthor A. Spizzichino)
 * (with coauthor A. Spizzichino)
 * (with coauthor A. Spizzichino)
 * (with coauthor A. Spizzichino)
 * (with coauthor A. Spizzichino)
 * (with coauthor A. Spizzichino)
 * (with coauthor A. Spizzichino)
 * (with coauthor A. Spizzichino)
 * (with coauthor A. Spizzichino)
 * (with coauthor A. Spizzichino)
 * (with coauthor A. Spizzichino)
 * (with coauthor A. Spizzichino)
 * (with coauthor A. Spizzichino)

title: Petr Beckmann


text:
François-Henri de Montmorency, duc de Luxembourg

François Henri de Montmorency-Bouteville, Duke of Piney-Luxembourg, commonly known as Luxembourg (8 January 1628 – 4 January 1695), and nicknamed "The Upholsterer of Notre-Dame" (Le Tapissier de Notre-Dame), was a French general and Marshal of France. A comrade and successor of the Great Condé, he was one of the most accomplished military commanders of the early modern period and is particularly noted for his exploits in the Franco-Dutch War and War of the Grand Alliance. Not imposing physically, as he was a slight man and hunchbacked, Luxembourg was nonetheless one of France's greatest generals.

Early years
François Henri de Montmorency was born in Paris. His father, François de Montmorency-Bouteville, had been executed six months before his birth for participating in a duel against the Marquis de Beuvron. His aunt, Charlotte Marguerite de Montmorency, Princess of Condé, took charge of him and educated him with her son, the Duke of Enghien. The young Montmorency (or Bouteville as he was then called) attached himself to his cousin, and shared his successes and reverses throughout the troubles of the Fronde. He returned to France in 1659 and was pardoned, and Condé, then much attached to the Duchess of Châtillon, Montmorency's sister, contrived the marriage of his adherent and cousin to the greatest heiress in France, Madeleine de Luxembourg, Princess of Tingry and heiress of the Luxembourg dukedom (1661), after which he was created Duke of Luxembourg and peer of France.

War of Devolution and the Franco-Dutch War
At the opening of the War of Devolution (1667–68), Condé, and consequently Luxembourg, had no command, but during the second campaign he served as Condé's lieutenant general in the conquest of Franche-Comté. During the four years of peace which followed, Luxembourg cultivated the favour of Louvois, and in 1672 held a high command against the Dutch during the Franco-Dutch War (1672–1678). He defeated a counterattack by the Prince William III of Orange at Woerden but was blocked by the Dutch Water Line. On 27 December the inundations were frozen over and he began to cross over the ice, but a sudden thaw cut his force in half. Retreating, de Luxembourg found the fortress town of Bodegraven abandoned by its garrison and ordered the entire civilian population to be burned alive with their houses. The Dutch anti-French propaganda quickly exploited this massacre and when de Luxembourg bragged to Louis XIV that he had roasted any Dutchman he could find in the town, he was surprised to find that some at court considered such cruelties unnecessary. In 1673 he made his famous retreat from Utrecht to Maastricht with only 20,000 men in face of 70,000, an exploit which placed him in the first rank of generals. In 1674 he was made captain of the Garde du Corps, and in 1675 Marshal of France.

On 10 March 1676 (N.S.) he was made commander of the Army of the Rhine replacing Condé, who was in bad health. However, he could not relieve the siege of Philippsburg. This fortress had been invested by Imperial troops under Charles V, Duke of Lorraine on 1 May. Luxembourg could neither break through the defenses of Wissembourg established by the Imperials, nor draw them out to do battle. Philippsburg fell on 17 September. In 1677 he stormed Valenciennes and defeated William of Orange again at Cassel. In 1678 William forced Luxembourg from his positions at Saint-Denis after the signature of the Peace of Nijmegen. Despite this his reputation was now high and it is reputed that he quarrelled with Louvois, who managed to involve him in the "Affair of the Poisons" and get him sent to the Bastille. Rousset in his Histoire de Louvois has shown that this quarrel is probably apocryphal. Luxembourg doubtlessly spent some months of 1680 in the Bastille, but on his release took up his post at court as capitaine des gardes.

War of the Grand Alliance 1688-97
By 1690, during the War of the Grand Alliance, Luxembourg was entrusted with the command of King Louis' army in the Spanish Netherlands, superseding Louis de Crevant, Duke of Humières. On 1 July 1690, he won his greatest victory over William's allied commander, the Prince of Waldeck, at Fleurus. Strategically the battle however changed little. In the following year his cavalry showed its superiority at Leuze, despite being eventually thrown back.

In the next campaign he covered the king's 1692 Siege of Namur and repulsed a surprise attack of William at Steenkerque in 1692. On 29 July 1693, won the most famous of his battles over his eternal adversary at Neerwinden, after which he was called "Le Tapissier de Nôtre Dame" (The Upholsterer of Notre Dame) due to the number of captured enemy flags that he sent to the cathedral. However, his last victory would be devoid of strategic results. The heavy losses suffered by his army stalled his campaign and his soldiers mutinied after which Louis XIV ordered Luxembourg to return to the French border. He was received with enthusiasm at Paris by all but the king, who looked coldly on a relative and adherent of the Condés. St-Simon describes in the first volume of his Memoirs how, instead of ranking as eighteenth peer of France according to his patent of 1661, he claimed through his wife to be duc de Piney of an old creation of 1571, which would place him second on the roll. The affair is described with St-Simon's usual interest in the peerage, and was chiefly checked through his assiduity.

In the campaign of 1694, Luxembourg did little in Flanders, except conducting a famous march from Vignemont to Tournai in face of the enemy.

Death
On his return to Versailles for the winter he fell ill, and died. In his last moments he was attended by the famous Jesuit priest Bourdaloue, who said on his death, "I have not lived his life, but I would wish to die his death." Luxembourg was considered immoral, even in those times, but as a general he was Condé's grandest pupil. Though slothful like Condé in the management of a campaign, at the moment of battle he seemed seized with happy inspirations, against which no ardour of William's and no steadiness of Dutch or English soldiers could stand. His death and Catinat's disgrace close the second period of the military history of the reign of Louis XIV.

Reputation
St-Simon said of Luxembourg: "...in his final calculations no one was ever more conscientious than M. de Luxembourg; no one more brilliant, prudent and far-sighted in the face of the enemy or in battle. He had daring and confidence, and at the same time a cool-headedness that allowed him to observe and foresee in the midst of the fiercest cannonade, in dangerously critical moments. That was when he was truly great. At all other times he was idleness itself; no exercise, except where absolutely necessary; gambling; conversing with intimates; every night a small supper party; nearly always with the same company, and, if they happened to be near a town, an agreeable mingling of the sexes." He was distinguished for a pungent wit. One of his retorts referred to his deformity. "I never can beat that cursed humpback", William was reputed to have said of him. "How does he know I have a hump?" retorted Luxembourg, "he has never seen my back." He left four sons, the youngest of whom was a marshal of France as Marechal de Montmorency.

Marriage and children
On 17 March 1661 François-Henri de Montmorency married Madeleine de Clermont-Tonnerre, duchess of Luxembourg, princess of Tingry, comtess of Ligny, baroness of Dangu, and had 5 children:

 * Charles Frédéric de Montmorency-Luxembourg (1662–1726), duc de Piney-Luxembourg, father of Charles II Frédéric (1702–1764) Marshal of France (1757);
 * Pierre Henri de Montmorency-Luxembourg (1663–1700), abbot of Saint-Michel d'Orcamp;
 * Paul Sigismond de Montmorency-Luxembourg (1664-1731), duc de Châtillon, comte de Luxe and baron d'Apremont;
 * Angelique Cunegonde de Montmorency-Luxembourg (1666–1736), mademoiselle de Luxembourg; married Louis Henri de Bourbon, bâtard de Soissons'', illegitimate son of Louis de Bourbon and had issue; had two children;
 * Christian Louis de Montmorency-Luxembourg (1675–1746), prince de Tingry, comte de Luxe, pair de France, Marshal of France (1734).


text:
Euler–Lagrange equation

In the calculus of variations and classical mechanics, the Euler–Lagrange equations are a system of second-order ordinary differential equations whose solutions are stationary points of the given action functional. The equations were discovered in the 1750s by Swiss mathematician Leonhard Euler and Italian mathematician Joseph-Louis Lagrange.

Because a differentiable functional is stationary at its local extrema, the Euler–Lagrange equation is useful for solving optimization problems in which, given some functional, one seeks the function minimizing or maximizing it. This is analogous to Fermat's theorem in calculus, stating that at any point where a differentiable function attains a local extremum its derivative is zero. In Lagrangian mechanics, according to Hamilton's principle of stationary action, the evolution of a physical system is described by the solutions to the Euler equation for the action of the system. In this context Euler equations are usually called Lagrange equations. In classical mechanics, it is equivalent to Newton's laws of motion; indeed, the Euler-Lagrange equations will produce the same equations as Newton's Laws. This is particularly useful when analyzing systems whose force vectors are particularly complicated. It has the advantage that it takes the same form in any system of generalized coordinates, and it is better suited to generalizations. In classical field theory there is an analogous equation to calculate the dynamics of a field.

History
The Euler–Lagrange equation was developed in the 1750s by Euler and Lagrange in connection with their studies of the tautochrone problem. This is the problem of determining a curve on which a weighted particle will fall to a fixed point in a fixed amount of time, independent of the starting point.

Lagrange solved this problem in 1755 and sent the solution to Euler. Both further developed Lagrange's method and applied it to mechanics, which led to the formulation of Lagrangian mechanics. Their correspondence ultimately led to the calculus of variations, a term coined by Euler himself in 1766.

Statement
Let $$(X,L)$$ be a real dynamical system with $$n$$ degrees of freedom. Here $$X$$ is the configuration space and $$L=L(t,{\boldsymbol q}(t), {\boldsymbol v}(t))$$ the Lagrangian, i.e. a smooth real-valued function such that $${\boldsymbol q}(t) \in X,$$ and $${\boldsymbol v}(t)$$ is an $$n$$-dimensional "vector of speed". (For those familiar with differential geometry, $$X$$ is a smooth manifold, and $$L : {\mathbb R}_t \times TX \to {\mathbb R},$$ where $$TX$$ is the tangent bundle of $$X).$$

Let $${\cal P}(a,b,\boldsymbol x_a,\boldsymbol x_b)$$ be the set of smooth paths $$\boldsymbol q: [a,b] \to X$$ for which $$\boldsymbol q(a) = \boldsymbol x_a$$ and $$\boldsymbol q(b) = \boldsymbol x_b. $$

The action functional $$S : {\cal P}(a,b,\boldsymbol x_a,\boldsymbol x_b) \to \mathbb{R}$$ is defined via $$ S[\boldsymbol q] = \int_a^b L(t,\boldsymbol q(t),\dot{\boldsymbol q}(t))\, dt.$$

A path $$\boldsymbol q \in {\cal P}(a,b,\boldsymbol x_a,\boldsymbol x_b)$$ is a stationary point of $$S$$ if and only if

Here, $$\dot{\boldsymbol q}(t) $$ is the time derivative of $$\boldsymbol q(t).$$ When we say stationary point, we mean a stationary point of $$S$$ with respect to any small perturbation in $$\boldsymbol q$$. See proofs below for more rigorous detail.

$$ $$

Example
A standard example is finding the real-valued function y(x) on the interval [a, b], such that y(a) = c and y(b) = d, for which the path length along the curve traced by y is as short as possible.
 * $$ \text{s} = \int_{a}^{b} \sqrt{\mathrm{d}x^2+\mathrm{d}y^2} = \int_{a}^{b} \sqrt{1+y'^2}\,\mathrm{d}x,$$

the integrand function being $ L(x,y, y') = \sqrt{1+y'^2} $.

The partial derivatives of L are:
 * $$\frac{\partial L(x, y, y')}{\partial y'} = \frac{y'}{\sqrt{1 + y'^2}} \quad \text{and} \quad

\frac{\partial L(x, y, y')}{\partial y} = 0.$$ By substituting these into the Euler–Lagrange equation, we obtain

\begin{align} \frac{\mathrm{d}}{\mathrm{d}x} \frac{y'(x)}{\sqrt{1 + (y'(x))^2}} &= 0 \\ \frac{y'(x)}{\sqrt{1 + (y'(x))^2}} &= C = \text{constant} \\ \Rightarrow y'(x)&= \frac{C}{\sqrt{1-C^2}} =: A \\ \Rightarrow y(x) &= Ax + B \end{align} $$ that is, the function must have a constant first derivative, and thus its graph is a straight line.

Single function of single variable with higher derivatives
The stationary values of the functional

I[f] = \int_{x_0}^{x_1} \mathcal{L}(x, f, f', f'', \dots, f^{(k)})~\mathrm{d}x ~; f' := \cfrac{\mathrm{d}f}{\mathrm{d}x}, ~f'' := \cfrac{\mathrm{d}^2f}{\mathrm{d}x^2}, ~ f^{(k)} := \cfrac{\mathrm{d}^kf}{\mathrm{d}x^k} $$ can be obtained from the Euler–Lagrange equation

\cfrac{\partial \mathcal{L}}{\partial f} - \cfrac{\mathrm{d}}{\mathrm{d} x}\left(\cfrac{\partial \mathcal{L}}{\partial f'}\right) + \cfrac{\mathrm{d}^2}{\mathrm{d} x^2}\left(\cfrac{\partial \mathcal{L}}{\partial f''}\right) - \dots + (-1)^k \cfrac{\mathrm{d}^k}{\mathrm{d} x^k}\left(\cfrac{\partial \mathcal{L}}{\partial f^{(k)}}\right) = 0 $$ under fixed boundary conditions for the function itself as well as for the first $$k-1$$ derivatives (i.e. for all $$f^{(i)}, i \in \{0, ..., k-1\}$$). The endpoint values of the highest derivative $$f^{(k)}$$ remain flexible.

Several functions of single variable with single derivative
If the problem involves finding several functions ($$f_1, f_2, \dots, f_m$$) of a single independent variable ($$x$$) that define an extremum of the functional

I[f_1,f_2, \dots, f_m] = \int_{x_0}^{x_1} \mathcal{L}(x, f_1, f_2, \dots, f_m, f_1', f_2', \dots, f_m')~\mathrm{d}x ~; f_i' := \cfrac{\mathrm{d}f_i}{\mathrm{d}x} $$ then the corresponding Euler–Lagrange equations are

\begin{align} \frac{\partial \mathcal{L}}{\partial f_i} - \frac{\mathrm{d}}{\mathrm{d}x}\left(\frac{\partial \mathcal{L}}{\partial f_i'}\right) = 0 ; \quad i = 1, 2, ..., m  \end{align} $$

Single function of several variables with single derivative
A multi-dimensional generalization comes from considering a function on n variables. If $$\Omega$$ is some surface, then

I[f] = \int_{\Omega} \mathcal{L}(x_1, \dots, x_n, f, f_{1}, \dots , f_{n})\, \mathrm{d}\mathbf{x}\,\! ~;     f_{j} := \cfrac{\partial f}{\partial x_j} $$

is extremized only if f satisfies the partial differential equation

 * $$ \frac{\partial \mathcal{L}}{\partial f} - \sum_{j=1}^{n} \frac{\partial}{\partial x_j}\left(\frac{\partial \mathcal{L}}{\partial f_{j}}\right) = 0. $$

When n = 2 and functional $$\mathcal I$$ is the energy functional, this leads to the soap-film minimal surface problem.

Several functions of several variables with single derivative
If there are several unknown functions to be determined and several variables such that

I[f_1,f_2,\dots,f_m] = \int_{\Omega} \mathcal{L}(x_1, \dots, x_n, f_1, \dots, f_m, f_{1,1}, \dots , f_{1,n}, \dots, f_{m,1}, \dots, f_{m,n}) \, \mathrm{d}\mathbf{x}\,\! ~;     f_{i,j} := \cfrac{\partial f_i}{\partial x_j} $$ the system of Euler–Lagrange equations is

\begin{align} \frac{\partial \mathcal{L}}{\partial f_1} - \sum_{j=1}^{n} \frac{\partial}{\partial x_j}\left(\frac{\partial \mathcal{L}}{\partial f_{1,j}}\right) &= 0_1 \\ \frac{\partial \mathcal{L}}{\partial f_2} - \sum_{j=1}^{n} \frac{\partial}{\partial x_j}\left(\frac{\partial \mathcal{L}}{\partial f_{2,j}}\right) &= 0_2 \\ \vdots \qquad \vdots \qquad &\quad \vdots \\ \frac{\partial \mathcal{L}}{\partial f_m} - \sum_{j=1}^{n} \frac{\partial}{\partial x_j}\left(\frac{\partial \mathcal{L}}{\partial f_{m,j}}\right) &= 0_m. \end{align} $$

Single function of two variables with higher derivatives
If there is a single unknown function f to be determined that is dependent on two variables x1 and x2 and if the functional depends on higher derivatives of f up to n-th order such that

\begin{align} I[f] & = \int_{\Omega} \mathcal{L}(x_1, x_2, f, f_{1}, f_{2}, f_{11}, f_{12}, f_{22},                                       \dots, f_{22\dots 2})\, \mathrm{d}\mathbf{x} \\ & \qquad \quad f_{i} := \cfrac{\partial f}{\partial x_i} \;, \quad f_{ij} := \cfrac{\partial^2 f}{\partial x_i\partial x_j} \;, \;\; \dots \end{align} $$ then the Euler–Lagrange equation is

\begin{align} \frac{\partial \mathcal{L}}{\partial f}   & - \frac{\partial}{\partial x_1}\left(\frac{\partial \mathcal{L}}{\partial f_{1}}\right) - \frac{\partial}{\partial x_2}\left(\frac{\partial \mathcal{L}}{\partial f_{2}}\right) + \frac{\partial^2}{\partial x_1^2}\left(\frac{\partial \mathcal{L}}{\partial f_{11}}\right) + \frac{\partial^2}{\partial x_1\partial x_2}\left(\frac{\partial \mathcal{L}}{\partial f_{12}}\right) + \frac{\partial^2}{\partial x_2^2}\left(\frac{\partial \mathcal{L}}{\partial f_{22}}\right) \\ & - \dots + (-1)^n \frac{\partial^n}{\partial x_2^n}\left(\frac{\partial \mathcal{L}}{\partial f_{22\dots 2}}\right) = 0 \end{align} $$ which can be represented shortly as:

\frac{\partial \mathcal{L}}{\partial f} +\sum_{j=1}^n \sum_{\mu_1 \leq \ldots \leq \mu_j} (-1)^j \frac{\partial^j}{\partial x_{\mu_{1}}\dots \partial x_{\mu_{j}}} \left( \frac{\partial \mathcal{L} }{\partial f_{\mu_1\dots\mu_j}}\right)=0 $$ wherein $$\mu_1 \dots \mu_j$$ are indices that span the number of variables, that is, here they go from 1 to 2. Here summation over the $$\mu_1 \dots \mu_j$$ indices is only over $$\mu_1 \leq \mu_2 \leq \ldots \leq \mu_j$$ in order to avoid counting the same partial derivative multiple times, for example $$f_{12} = f_{21}$$ appears only once in the previous equation.

Several functions of several variables with higher derivatives
If there are p unknown functions fi to be determined that are dependent on m variables x1 ... xm and if the functional depends on higher derivatives of the fi up to n-th order such that

\begin{align} I[f_1,\ldots,f_p] & = \int_{\Omega} \mathcal{L}(x_1, \ldots, x_m; f_1,\ldots,f_p; f_{1,1},\ldots,    f_{p,m}; f_{1,11},\ldots, f_{p,mm};\ldots; f_{p,1\ldots 1}, \ldots, f_{p,m\ldots m})\, \mathrm{d}\mathbf{x} \\ & \qquad \quad f_{i,\mu} := \cfrac{\partial f_i}{\partial x_\mu} \;, \quad f_{i,\mu_1\mu_2} := \cfrac{\partial^2 f_i}{\partial x_{\mu_1}\partial x_{\mu_2}} \;, \;\; \dots \end{align} $$

where $$\mu_1 \dots \mu_j$$ are indices that span the number of variables, that is they go from 1 to m. Then the Euler–Lagrange equation is

\frac{\partial \mathcal{L}}{\partial f_i} +\sum_{j=1}^n \sum_{\mu_1 \leq \ldots \leq \mu_j} (-1)^j \frac{\partial^j}{\partial x_{\mu_{1}}\dots \partial x_{\mu_{j}}} \left( \frac{\partial \mathcal{L} }{\partial f_{i,\mu_1\dots\mu_j}}\right)=0 $$

where the summation over the $$\mu_1 \dots \mu_j$$ is avoiding counting the same derivative $$ f_{i,\mu_1\mu_2} = f_{i,\mu_2\mu_1}$$ several times, just as in the previous subsection. This can be expressed more compactly as

\sum_{j=0}^n \sum_{\mu_1 \leq \ldots \leq \mu_j} (-1)^j \partial_{ \mu_{1}\ldots \mu_{j} }^j \left( \frac{\partial \mathcal{L} }{\partial f_{i,\mu_1\dots\mu_j}}\right)=0 $$

Generalization to manifolds
Let $$M$$ be a smooth manifold, and let $$C^\infty([a,b])$$ denote the space of smooth functions $$f\colon [a,b]\to M$$. Then, for functionals $$S\colon C^\infty ([a,b])\to \mathbb{R}$$ of the form

S[f]=\int_a^b (L\circ\dot{f})(t)\,\mathrm{d} t $$ where $$L\colon TM\to\mathbb{R}$$ is the Lagrangian, the statement $$\mathrm{d} S_f=0$$ is equivalent to the statement that, for all $$t\in [a,b]$$, each coordinate frame trivialization $$(x^i,X^i)$$ of a neighborhood of $$\dot{f}(t)$$ yields the following $$\dim M$$ equations:

\forall i:\frac{\mathrm{d}}{\mathrm{d}t}\frac{\partial L}{\partial X^i}\bigg|_{\dot{f}(t)}=\frac{\partial L}{\partial x^i}\bigg|_{\dot{f}(t)}. $$ Euler-Lagrange equations can also be written in a coordinate-free form as

\mathcal{L}_\Delta \theta_L=dL $$ where $$\theta_L$$ is the canonical momenta 1-form corresponding to the Lagrangian $$L$$. The vector field generating time translations is denoted by $$\Delta$$ and the Lie derivative is denoted by $$\mathcal{L}$$. One can use local charts $$(q^\alpha,\dot{q}^\alpha)$$ in which $$\theta_L=\frac{\partial L}{\partial \dot{q}^\alpha}dq^\alpha$$ and $$\Delta:=\frac{d}{dt}=\dot{q}^\alpha\frac{\partial}{\partial q^\alpha}+\ddot{q}^\alpha\frac{\partial}{\partial \dot{q}^\alpha}$$ and use coordinate expressions for the Lie derivative to see equivalence with coordinate expressions of the Euler Lagrange equation. The coordinate free form is particularly suitable for geometrical interpretation of the Euler Lagrange equations.

title: Euler–Lagrange equation


text:
Charles Taylor (philosopher)

Charles Margrave Taylor (born November 5, 1931) is a Canadian philosopher from Montreal, Quebec, and professor emeritus at McGill University best known for his contributions to political philosophy, the philosophy of social science, the history of philosophy, and intellectual history. His work has earned him the Kyoto Prize, the Templeton Prize, the Berggruen Prize for Philosophy, and the John W. Kluge Prize.

In 2007, Taylor served with Gérard Bouchard on the Bouchard–Taylor Commission on reasonable accommodation with regard to cultural differences in the province of Quebec. He has also made contributions to moral philosophy, epistemology, hermeneutics, aesthetics, the philosophy of mind, the philosophy of language, and the philosophy of action.

Biography
Charles Margrave Taylor was born in Montreal, Quebec, on November 5, 1931, to a Roman Catholic Francophone mother and a Protestant Anglophone father by whom he was raised bilingually. His father, Walter Margrave Taylor, was a steel magnate originally from Toronto while his mother, Simone Marguerite Beaubien, was a dressmaker. His sister was Gretta Chambers. He attended Selwyn House School from 1939 to 1946, followed by Trinity College School from 1946 to 1949, and began his undergraduate education at McGill University where he received a Bachelor of Arts (BA) degree in history in 1952. He continued his studies at the University of Oxford, first as a Rhodes Scholar at Balliol College, receiving a BA degree with first-class honours in philosophy, politics and economics in 1955, and then as a postgraduate student, receiving a Doctor of Philosophy degree in 1961 under the supervision of Sir Isaiah Berlin. As an undergraduate student, he started one of the first campaigns to ban thermonuclear weapons in the United Kingdom in 1956, serving as the first president of the Oxford Campaign for Nuclear Disarmament. Recent research has explored Taylor's engagement with socialist politics during this time.

He succeeded John Plamenatz as Chichele Professor of Social and Political Theory at the University of Oxford and became a fellow of All Souls College.

For many years, both before and after Oxford, he was Professor of Political Science and Philosophy at McGill University in Montreal, where he is now professor emeritus. Taylor was also a Board of Trustees Professor of Law and Philosophy at Northwestern University in Evanston, Illinois, for several years after his retirement from McGill.

Taylor was elected a foreign honorary member of the American Academy of Arts and Sciences in 1986. In 1991, Taylor was appointed to the Conseil de la langue française in the province of Quebec, at which point he critiqued Quebec's commercial sign laws. In 1995, he was made a Companion of the Order of Canada. In 2000, he was made a Grand Officer of the National Order of Quebec. In 2003, he was awarded the Social Sciences and Humanities Research Council's Gold Medal for Achievement in Research, which had been the council's highest honour. He was awarded the 2007 Templeton Prize for progress towards research or discoveries about spiritual realities, which included a cash award of US$1.5 million.

In 2007 he and Gérard Bouchard were appointed to head a one-year commission of inquiry into what would constitute reasonable accommodation for minority cultures in his home province of Quebec.

In June 2008, he was awarded the Kyoto Prize in the arts and philosophy category. The Kyoto Prize is sometimes referred to as the Japanese Nobel. In 2015, he was awarded the John W. Kluge Prize for Achievement in the Study of Humanity, a prize he shared with philosopher Jürgen Habermas. In 2016, he was awarded the inaugural $1-million Berggruen Prize for being "a thinker whose ideas are of broad significance for shaping human self-understanding and the advancement of humanity".

Views
Despite his extensive and diverse philosophical oeuvre, Taylor famously calls himself a "monomaniac," concerned with only one fundamental aspiration: to develop a convincing philosophical anthropology.

In order to understand Taylor's views, it is helpful to understand his philosophical background, especially his writings on Georg Wilhelm Friedrich Hegel, Ludwig Wittgenstein, Martin Heidegger, and Maurice Merleau-Ponty. Taylor rejects naturalism and formalist epistemology. He is part of an influential intellectual tradition of Canadian idealism that includes John Watson, George Paxton Young, C. B. Macpherson, and George Grant.

In his essay "To Follow a Rule," Taylor explores why people can fail to follow rules, and what kind of knowledge it is that allows a person to successfully follow a rule, such as the arrow on a sign. The intellectualist tradition presupposes that to follow directions, we must know a set of propositions and premises about how to follow directions.

Taylor argues that Wittgenstein's solution is that all interpretation of rules draws upon a tacit background. This background is not more rules or premises, but what Wittgenstein calls "forms of life." More specifically, Wittgenstein says in the Philosophical Investigations that "Obeying a rule is a practice." Taylor situates the interpretation of rules within the practices that are incorporated into our bodies in the form of habits, dispositions and tendencies.

Following Heidegger, Merleau-Ponty, Hans-Georg Gadamer, Michael Polanyi, and Wittgenstein, Taylor argues that it is mistaken to presuppose that our understanding of the world is primarily mediated by representations. It is only against an unarticulated background that representations can make sense to us. On occasion we do follow rules by explicitly representing them to ourselves, but Taylor reminds us that rules do not contain the principles of their own application: application requires that we draw on an unarticulated understanding or "sense of things" — the background.

Taylor's critique of naturalism
Taylor defines naturalism as a family of various, often quite diverse theories that all hold "the ambition to model the study of man on the natural sciences." Philosophically, naturalism was largely popularized and defended by the unity of science movement that was advanced by logical positivist philosophy. In many ways, Taylor's early philosophy springs from a critical reaction against the logical positivism and naturalism that was ascendant in Oxford while he was a student.

Initially, much of Taylor's philosophical work consisted of careful conceptual critiques of various naturalist research programs. This began with his 1964 dissertation The Explanation of Behaviour, which was a detailed and systematic criticism of the behaviourist psychology of B. F. Skinner that was highly influential at mid-century.

From there, Taylor also spread his critique to other disciplines. The essay "Interpretation and the Sciences of Man" was published in 1972 as a critique of the political science of the behavioural revolution advanced by giants of the field like David Easton, Robert Dahl, Gabriel Almond, and Sydney Verba. In an essay entitled "The Significance of Significance: The Case for Cognitive Psychology", Taylor criticized the naturalism he saw distorting the major research program that had replaced B. F. Skinner's behaviourism.

But Taylor also detected naturalism in fields where it was not immediately apparent. For example, in 1978's "Language and Human Nature" he found naturalist distortions in various modern "designative" theories of language, while in Sources of the Self (1989) he found both naturalist error and the deep moral, motivational sources for this outlook in various individualist and utilitarian conceptions of selfhood.

Taylor and hermeneutics
Concurrent to Taylor's critique of naturalism was his development of an alternative. Indeed, Taylor's mature philosophy begins when as a doctoral student at Oxford he turned away, disappointed, from analytic philosophy in search of other philosophical resources which he found in French and German modern hermeneutics and phenomenology.

The hermeneutic tradition develops a view of human understanding and cognition as centred on the decipherment of meanings (as opposed to, say, foundational theories of brute verification or an apodictic rationalism). Taylor's own philosophical outlook can broadly and fairly be characterized as hermeneutic and has been called engaged hermeneutics. This is clear in his championing of the works of major figures within the hermeneutic tradition such as Wilhelm Dilthey, Heidegger, Merleau-Ponty, and Gadamer. It is also evident in his own original contributions to hermeneutic and interpretive theory.

Communitarian critique of liberalism
Taylor (as well as Alasdair MacIntyre, Michael Walzer, and Michael Sandel) is associated with a communitarian critique of liberal theory's understanding of the "self". Communitarians emphasize the importance of social institutions in the development of individual meaning and identity.

In his 1991 Massey Lecture The Malaise of Modernity, Taylor argued that political theorists—from John Locke and Thomas Hobbes to John Rawls and Ronald Dworkin—have neglected the way in which individuals arise within the context supplied by societies. A more realistic understanding of the "self" recognizes the social background against which life choices gain importance and meaning.

Philosophy and sociology of religion
Taylor's later work has turned to the philosophy of religion, as evident in several pieces, including the lecture "A Catholic Modernity" and the short monograph "Varieties of Religion Today: William James Revisited".

Taylor's most significant contribution in this field to date is his book A Secular Age which argues against the secularization thesis of Max Weber, Steve Bruce, and others. In rough form, the secularization thesis holds that as modernity (a bundle of phenomena including science, technology, and rational forms of authority) progresses, religion gradually diminishes in influence. Taylor begins from the fact that the modern world has not seen the disappearance of religion but rather its diversification and in many places its growth. He then develops a complex alternative notion of what secularization actually means given that the secularization thesis has not been borne out. In the process, Taylor also greatly deepens his account of moral, political, and spiritual modernity that he had begun in Sources of the Self.

Politics
Taylor was a candidate for the social democratic New Democratic Party (NDP) in Mount Royal on three occasions in the 1960s, beginning with the 1962 federal election when he came in third behind Liberal Alan MacNaughton. He improved his standing in 1963, coming in second. Most famously, he also lost in the 1965 election to newcomer and future prime minister, Pierre Trudeau. This campaign garnered national attention. Taylor's fourth and final attempt to enter the House of Commons of Canada was in the 1968 federal election, when he came in second as an NDP candidate in the riding of Dollard. In 1994 he coedited a paper on human rights with Vitit Muntarbhorn in Thailand.

Taylor served as a vice president of the federal NDP (beginning c. 1965) and was president of its Quebec section.

In 2010, Taylor said multiculturalism was a work in progress that faced challenges. He identified tackling Islamophobia in Canada as the next challenge.

In his 2020 book Reconstructing Democracy he, together with Patrizia Nanz and Madeleine Beaubien Taylor, uses local examples to describe how democracies in transformation might be revitalized by involving citizenship.

Interlocutors

 * Himani Bannerji: "Charles Taylor's Politics of Recognition: A Critique" (2000)
 * Richard Rorty
 * Bernard Williams
 * Alasdair MacIntyre: critique of liberalism
 * Will Kymlicka
 * Martha Nussbaum
 * Kwame Appiah
 * Hubert Dreyfus: co-author
 * Quentin Skinner
 * Talal Asad
 * Marcel Gauchet
 * Arjun Appadurai: on the imaginary
 * Paul Berman
 * William E. Connolly
 * Robert Bellah: on Taylor's A Secular Age
 * John Milbank
 * Stuart Hall
 * Catherine Pickstock
 * James Tully: on Taylor on "Deep Diversity"
 * Jürgen Habermas: shared Kluge prize

Books

 * Multiculturalism and "The Politics of Recognition". Edited by Gutmann, Amy. Princeton, New Jersey: Princeton University Press. 1992.
 * Rapprocher les solitudes: écrits sur le fédéralisme et le nationalisme au Canada [Reconciling the Solitudes: Writings on Canadian Federalism and Nationalism] (in French). Edited by Laforest, Guy. Sainte-Foy, Quebec: Les Presses de l'Université Laval. 1992.
 * English translation: Reconciling the Solitudes: Essays on Canadian Federalism and Nationalism. Edited by Laforest, Guy. Montreal: McGill-Queen's University Press. 1993.
 * Road to Democracy: Human Rights and Human Development in Thailand. With Muntarbhorn, Vitit. Montreal: International Centre for Human Rights and Democratic Development. 1994.

 * Identitet, Frihet och Gemenskap: Politisk-Filosofiska Texter (in Swedish). Edited by Grimen, Harald. Gothenburg, Sweden: Daidalos. 1995.

 * La liberté des modernes (in French). Translated by de Lara, Philippe. Paris: Presses Universitaires de France. 1997.
 * A Catholic Modernity? Edited by Heft, James L. New York: Oxford University Press. 1999.
 * Prizivanje gradjanskog drustva [Invoking Civil Society] (in Serbo-Croatian). Edited by Savic, Obrad.

 * Laïcité et liberté de conscience (in French). With Maclure, Jocelyn. Montreal: Boréal. 2010.
 * English translation: Secularism and Freedom of Conscience. With Maclure, Jocelyn. Translated by Todd, Jane Marie. Cambridge, Massachusetts: Harvard University Press. 2011.

 * Church and People: Disjunctions in a Secular Age. Edited with Casanova, José; McLean, George F. Washington: Council for Research in Values and Philosophy. 2012.
 * Democracia Republicana / Republican Democracy. Edited by Cristi, Renato; Tranjan, J. Ricardo. Santiago: LOM Ediciones. 2012.
 * Boundaries of Toleration. Edited with Stepan, Alfred C. New York: Columbia University Press. 2014.
 * Incanto e Disincanto. Secolarità e Laicità in Occidente (in Italian). Edited and translated by Costa, Paolo. Bologna, Italy: EDB. 2014.
 * La Democrazia e i Suoi Dilemmi (in Italian). Edited and translated by Costa, Paolo. Parma, Italy: Diabasis. 2014.

 * English translation:
 * Retrieving Realism. With Dreyfus, Hubert. Cambridge, Massachusetts: Harvard University Press. 2015.
 * Reconstructing Democracy. How Citizens Are Building from the Ground Up. With Nanz, Patrizia; Beaubien Taylor, Madeleine. Cambridge, Massachusetts: Harvard University Press. 2020
 * Reconstructing Democracy. How Citizens Are Building from the Ground Up. With Nanz, Patrizia; Beaubien Taylor, Madeleine. Cambridge, Massachusetts: Harvard University Press. 2020

title: Charles Taylor (philosopher)