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Great Belt Bridge

The Great Belt Bridge (Storebæltsbroen) or Great Belt fixed link (Storebæltsforbindelsen) is a multi-element fixed link crossing the Great Belt strait between the Danish islands of Zealand and Funen. It consists of a road suspension bridge and a railway tunnel between Zealand and the small island Sprogø in the middle of the Great Belt, and a box-girder bridge for both road and rail traffic between Sprogø and Funen. The total length is 18 km.

The term Great Belt Bridge commonly refers to the suspension bridge, although it may also be used to mean the box-girder bridge or the link in its entirety. Officially named the East Bridge, the suspension bridge was designed by the Danish firms COWI and Ramboll, and the architecture firm Dissing+Weitling. It has the world's sixth-longest main span (1.6 km). At the time of the opening of the bridge it was the second longest, beaten by the Akashi Kaikyō Bridge opened a few months previously.

Together with the New Little Belt Bridge, the Great Belt link provides a continuous road and rail connection between Copenhagen and the Danish mainland. The link replaced the Great Belt ferries service, which had been the primary means of crossing the Great Belt. After more than 50 years of debate, the Danish government decided in 1986 to construct a link; it opened to rail traffic in 1997 and to road traffic in 1998. At an estimated cost of DKK 21.4 billion (EUR 2.8 billion) (1988 prices), the link is the largest construction project in Danish history. It has reduced travel times significantly; previously taking one hour by ferry, the Great Belt can now be crossed in ten minutes. This link, together with the Øresund Bridge (built 1995–1999) and the Little Belt Bridge, have together enabled driving from mainland Europe to Sweden through Denmark.

Operation and maintenance are performed by A/S Storebælt under Sund & Bælt. Construction and maintenance are financed by tolls on vehicles and trains. Cyclists are not permitted to use the bridge, but bicycles may be transported by train or bus.

History
The Great Belt ferries entered service between the coastal towns of Korsør and Nyborg in 1883, connecting the railway lines on either side of the Belt. In 1957, road traffic was moved to the Halsskov–Knudshoved route, about 1.5 kilometres to the north and close to the fixed link.

Construction drafts for a fixed link were presented as early as the 1850s, with several suggestions appearing in the following decades. The Danish State Railways, responsible for the ferry service, presented plans for a bridge in 1934. The concepts of bridges over Øresund (152 million DKK) and Storebælt (257 million DKK) were calculated around 1936. In 1948, the Ministry for Public Works (now the Ministry of Transport) established a commission to investigate the implications of a fixed link.

The first law concerning a fixed link was enacted in 1973, but the project was put on hold in 1978 as the Venstre (Liberal) party demanded postponing public spending. Political agreement to restart work was reached in 1986, with a construction law (anlægslov) being passed in 1987.

The design was carried out by the engineering firms COWI and Ramboll together with Dissing+Weitling architecture practice.

Construction of the link commenced in 1988. In 1991, Finland sued Denmark at the International Court of Justice, on the grounds that Finnish-built mobile offshore drilling units would be unable to pass beneath the bridge. The two countries negotiated a financial compensation of 90 million Danish kroner, and Finland withdrew the lawsuit in 1992.

A European Court of Justice ruling in 1993 found that a contractual condition requiring use of local labour and local materials in constructing the bridge was incompatible with the principles of the EEC Treaty.

The link is estimated to have created a value of 379 billion DKK after 50 years of use.

In 2022, the bridge was crossed as part of the route of Stage 2 of the 2022 Tour de France.

Construction
The construction of the fixed link became the biggest building project in the history of Denmark. In order to connect Halsskov on Zealand with Knudshoved on Funen, 18 km to its west, a two-track railway and a four-lane motorway had to be built, via the small island of Sprogø in the middle of the Great Belt. The project comprised three different tasks: the East Bridge for road transport, the East Tunnel for rail transport and the West Bridge for road and rail transport combined. The construction work was carried out by Sundlink Contractors, a consortium of Skanska, Hochtief, Højgaard & Schultz (which built the West Bridge) and Monberg & Thorsen (which built the 8 km section under the Great Belt). The work of lifting and placing the elements was carried out by Ballast Nedam using a floating crane.

East Bridge
Built between 1991 and 1998 at a cost of US$950 million, the East Bridge (Østbroen) is a suspension bridge between Halsskov and Sprogø. It is 6790 m long with a free span of 1624 m,. The East Bridge had been planned to be completed in time to be the longest bridge in the world, but there were delays in construction. Therefore, it happened that the Akashi-Kaikyo Bridge was opened two months earlier.

The vertical clearance for ships is 65 m, meaning the world's largest cruise ship, an Oasis-class cruise ship, just fits under with its smokestack folded. At 254 m above sea level, the two pylons of the East Bridge are the highest points on self-supporting structures in Denmark. Some radio masts, such as Tommerup transmitter, are taller.

To keep the main cables tensioned, an anchorage structure on each side of the span is placed below the road deck. After 15 years, the cables have no rust. They were scheduled for a 15 million DKK paint job, but due to corroding cables on other bridges, the decision was made to instead install a 70 million DKK sealed de-humidifying system in the cables. This was carried out by UK engineering firm Spencer Group, with help from Danish subcontractors Davai who provided the manpower, and Belvent A/S who provided the dehumidification system. Nineteen concrete pillars (12 on the Zealand side, seven by Sprogø), 193 m apart, carry the road deck outside the span.

West Bridge
The West Bridge (Vestbroen) is a box girder bridge between Sprogø and Knudshoved. It is 6611 m long, and has a vertical clearance for ships of 18 m. It is actually two separate, adjacent bridges: the northern one carries rail traffic and the southern one road traffic. The pillars of the two bridges rest on common foundations below sea level. The West Bridge was built between 1988 and 1994; its road/rail deck comprises 63 sections, supported by 62 pillars.

East Tunnel
The twin bored tunnel tubes of the East Tunnel (Østtunnelen) are each 8024 m long. There are 31 connecting tunnels between the two main tunnels, at 250 m intervals. The equipment that is necessary for train operation in the tunnels is installed in the connecting tunnels, which also serve as emergency escape routes.

There were delays and cost overruns in the tunnel construction. The plan was to open it in 1993, giving the trains a head start of three years over road traffic, but train traffic started in 1997 and road traffic in 1998. During construction the sea bed gave way and one of the tunnels was flooded. The water continued to rise and reached the end at Sprogø, where it continued into the (still dry) other tunnel. The water damaged two of the four tunnel boring machines, but no workers were injured. Only by placing a clay blanket on the sea bed was it possible to dry out the tunnels. The two damaged machines were repaired and the majority of the tunnelling was undertaken from the Sprogø side. The machines on the Zealand side tunnelled through difficult ground and made little progress. A major fire on one of the Zealand machines in June 1994 stopped these drives and the tunnels were completed by the two Sprogø machines.

A total of 320 compressed air workers were involved in 9,018 pressure exposures in the four tunnel-boring machines. The project had a decompression sickness incidence of 0.14% with two workers having long-term residual symptoms.

Traffic implications

Prior to the opening of the link, an average of 8,000 cars used the ferries across the Great Belt every day. The traffic across the strait increased 127 percent over the first year after the link's opening due to the so-called traffic leap: new traffic generated by the improved ease, facility and lower price of crossing the Great Belt. In 2021, an average of 34,100 vehicles used the link each day. On August 7, 2022 a record 61,528 vehicles passed the bridge in 24 hours. The increase in traffic is partly caused by the general growth of traffic, partly diversion of traffic volume from other services via ferry and services.

The fixed link has produced considerable savings in travel time between eastern and western Denmark. Previously, it took approximately 90 minutes on average to cross the Great Belt in a car with transfer by ferry, including the waiting time at the ports. It took considerably longer during peak periods, such as weekends and holidays. With the opening of the link, the journey is now between 10 and 15 minutes.

By train the time savings are significant as well. The journey has been reduced by 60 minutes, and there are many more seats available because more carriages may be added to a train that does not have to fit on a ferry. The seating capacity offered by DSB across the Great Belt on an ordinary Wednesday has risen from 11,060 seats to 37,490 seats. On Fridays the seating capacity exceeds 40,000 seats.

The shortest travel times are: Copenhagen–Odense 1 hour 15 minutes, Copenhagen–Aarhus 2 hours 30 minutes, Copenhagen–Aalborg 3 hours 55 minutes and Copenhagen–Esbjerg 2 hours 35 minutes.

Flights between Copenhagen and Odense, and between Copenhagen and Esbjerg have ceased, and the train now has the largest market share between Copenhagen and Aarhus.

Together with the Øresund Bridge, and the two Little Belt bridges, the link provides a direct fixed connection between western Continental Europe and northern Scandinavia, eventually connecting all parts of the European Union except Ireland, Malta, Cyprus, and outlying islands. Most people from Zealand still prefer to take the ferry between Puttgarden and Rødby, as it is a much shorter distance and provides a needed break for those travelling a long distance.

For freight trains, the fixed links are a large improvement between Sweden and Germany, and between Sweden and the UK. The Sweden-to-Germany ferry system is still used to some extent owing to limited rail capacity, with heavy passenger traffic over the bridges and some single track stretches in southern Denmark and northern Germany.

The Great Belt was used by now defunct night passenger trains between Copenhagen and Germany, which were too long to fit on the ferries. Day trains on the Copenhagen-Hamburg route first continued to use the Fehmarn Belt ferries, utilising short diesel trains, but now also use the Great Belt route, which potentially allows longer trains to be used, increasing capacity.

By 2028, the Fehmarn Belt Fixed Link is expected to be complete with much of the international traffic being shifted from the Great Belt Fixed Link. This more direct route will reduce the rail journey from Hamburg to Copenhagen from 4:45 to 3:30 hours.

Toll charge
In 2019, the vehicle tolls were:

Environmental effects
Environmental considerations have been an integral part of the project, and have been of decisive significance for the choice of alignment and determination of the design. Environmental considerations were the reason why Great Belt A/S established an environmental monitoring programme in 1988, and initiated co-operation with authorities and external consultants on the definition of environmental concerns during the construction work and the professional requirements to the monitoring programme. This co-operation issued in a report published at the beginning of 1997 on the state of the environment in the Great Belt. The conclusion of the report was that the marine environment was at least as good as before construction work began.

With regards to the water flow, the link must comply with the so-called zero-solution. This has been achieved by deepening parts of the Great Belt, so that the water flow cross section has been increased. This excavation compensates for the blocking effect caused by the bridge pylons and approach ramps. The conclusion of the report is that water flows are now almost at the level they were before the bridge was built.

The fixed link has generated increased road traffic volume, which has meant increased air pollution. However, there has been significant savings in the energy consumption by switching from ferries to the fixed link. Train and car ferries consume much energy for propulsion, high-speed ferries consume large amounts of energy at high speeds, and air transport is highly energy consuming. Domestic air travel over the Great Belt was greatly reduced after the opening of the bridge, with the former air travellers now using trains and private cars.

The larger energy consumption by ferries as opposed to via the fixed link is most clearly seen when comparing short driving distances from areas immediately east or west of the link. For more extended driving distances the difference in energy consumption is smaller, but any transport within Denmark across the link shows very clear energy savings.

During 2009, seven large wind turbines, likely Vestas 3MWs totalling 21MW capacity, were erected in the sea north of Sprogø to contribute to the electrical demand of the Great Belt Link. Their hub heights are about the same level as the road deck of the suspension bridge. Part of the project was to showcase sea wind at the December 2009 Copenhagen climate meeting.

Accidents
During construction 479 work-related accidents were reported, of which 53 resulted in serious injuries or death. Seven workers died as a result of work-related accidents.

The West Bridge has been struck by sea traffic twice. While the link was still under construction on 14 September 1993, the ferry M/F Romsø drifted off course in bad weather and hit the West Bridge. At 19:17 on 3 March 2005, the 3,500-ton freighter MV Karen Danielsen crashed into the West Bridge 800 metres from Funen. All traffic across the bridge was halted, effectively cutting Denmark in two. The bridge was re-opened shortly after midnight, after the freighter was pulled free and inspectors had found no structural damage to the bridge.

The East Bridge has so far been in the clear, although on 16 May 2001, the bridge was closed for 10 minutes as the Cambodian 27,000-ton bulk carrier Bella was heading straight for one of the anchorage structures. The ship was deflected by a swift response from the navy.

On 5 June 2006, a maintenance vehicle burst into flames in the east-bound railway tunnel at about 21:30. Nobody was hurt; its crew of three fled to the other tunnel and escaped. The fire was put out shortly before midnight, and the vehicle was removed from the tunnel the next day. Train service resumed on 6 June at reduced speed, and normal service was restored on 12 June.

On 2 January 2019, eight people were killed in a train accident on the West Bridge. A passenger train was hit by a semi-trailer that fell off a freight train travelling in the opposite direction.

In 2023, a 57-year-old truck driver was arrested by police after traffic on the bridge was disrupted due to spilled potatoes. Police stated that they were working on the hypothesis that the potatoes were either planted intentionally or as an accident.

Operations
In 2009, a study characterized the rail tunnel (together with other major projects like the Channel Tunnel between England and France) as financially non-viable.

title: Great Belt Bridge


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Doomsday Clock

The Doomsday Clock is a symbol that represents the likelihood of a human-made global catastrophe, in the opinion of the members of the Bulletin of the Atomic Scientists. Maintained since 1947, the clock is a metaphor, not a prediction, for threats to humanity from unchecked scientific and technological advances. That is, the time on the clock is not to be interpreted as actual time. A hypothetical global catastrophe is represented by midnight on the clock, with the Bulletin's opinion on how close the world is to one represented by a certain number of minutes or seconds to midnight, which is then assessed in January of each year. The main factors influencing the clock are nuclear warfare, climate change, and artificial intelligence. The Bulletin's Science and Security Board monitors new developments in the life sciences and technology that could inflict irrevocable harm to humanity.

The clock's original setting in 1947 was 7 minutes to midnight. It has since been set backward 8 times and forward 17 times. The farthest time from midnight was 17 minutes in 1991, and the nearest is 90 seconds, set on January 2023.

The clock was moved to 150 seconds (2 minute, 30 seconds) in 2017, then forward to 2 minutes to midnight in January 2018, and left unchanged in 2019. In January 2020, it was moved forward to 100 seconds (1 minute, 40 seconds) before midnight. In January 2023, the Clock was moved forward to 90 seconds (1 minute, 30 seconds) before midnight and remained unchanged in January 2024.

History
The Doomsday Clock's origin can be traced to the international group of researchers called the Chicago Atomic Scientists, who had participated in the Manhattan Project. After the atomic bombings of Hiroshima and Nagasaki, they began publishing a mimeographed newsletter and then the magazine, Bulletin of the Atomic Scientists, which, since its inception, has depicted the Clock on every cover. The Clock was first represented in 1947, when the Bulletin co-founder Hyman Goldsmith asked artist Martyl Langsdorf (wife of Manhattan Project research associate and Szilárd petition signatory Alexander Langsdorf, Jr.) to design a cover for the magazine's June 1947 issue. As Eugene Rabinowitch, another co-founder of the Bulletin, explained later:

"The Bulletin's Clock is not a gauge to register the ups and downs of the international power struggle; it is intended to reflect basic changes in the level of continuous danger in which mankind lives in the nuclear age..." Langsdorf chose a clock to reflect the urgency of the problem: like a countdown, the Clock suggests that destruction will naturally occur unless someone takes action to stop it.

In January 2007, designer Michael Bierut, who was on the Bulletin's Governing Board, redesigned the Doomsday Clock to give it a more modern feel. In 2009, the Bulletin ceased its print edition and became one of the first print publications in the U.S. to become entirely digital; the Clock is now found as part of the logo on the Bulletin 's website. Information about the Doomsday Clock Symposium, a timeline of the Clock's settings, and multimedia shows about the Clock's history and culture can also be found on the Bulletin's website.

The 5th Doomsday Clock Symposium was held on November 14, 2013, in Washington, D.C.; it was a day-long event that was open to the public and featured panelists discussing various issues on the topic "Communicating Catastrophe". There was also an evening event at the Hirshhorn Museum and Sculpture Garden in conjunction with the Hirshhorn's current exhibit, "Damage Control: Art and Destruction Since 1950". The panel discussions, held at the American Association for the Advancement of Science, were streamed live from the Bulletin's website and can still be viewed there. Reflecting international events dangerous to humankind, the Clock has been adjusted 25 times since its inception in 1947, when it was set to "seven minutes to midnight".

Basis for settings
"Midnight" has a deeper meaning besides the constant threat of war. There are various elements taken into consideration when the scientists from The Bulletin of the Atomic Scientists decide what Midnight and "global catastrophe" really mean in a particular year. They might include "politics, energy, weapons, diplomacy, and climate science"; potential sources of threat include nuclear threats, climate change, bioterrorism, and artificial intelligence. Members of the board judge Midnight by discussing how close they think humanity is to the end of civilization. In 1947, at the beginning of the Cold War, the Clock was started at seven minutes to midnight.

Fluctuations and threats
Before January 2020, the two tied-for-lowest points for the Doomsday Clock were in 1953 (when the Clock was set to two minutes until midnight, after the U.S. and the Soviet Union began testing hydrogen bombs) and in 2018, following the failure of world leaders to address tensions relating to nuclear weapons and climate change issues. In other years, the Clock's time has fluctuated from 17 minutes in 1991 to 2 minutes 30 seconds in 2017. Discussing the change to $2 1⁄2$ minutes in 2017, the first use of a fraction in the Clock's history, Lawrence Krauss, one of the scientists from the Bulletin, warned that political leaders must make decisions based on facts, and those facts "must be taken into account if the future of humanity is to be preserved". In an announcement from the Bulletin about the status of the Clock, they went as far to call for action from "wise" public officials and "wise" citizens to make an attempt to steer human life away from catastrophe while humans still can.

On January 24, 2018, scientists moved the clock to two minutes to midnight, based on threats greatest in the nuclear realm. The scientists said, of recent moves by North Korea under Kim Jong-un and the administration of Donald Trump in the U.S.: "Hyperbolic rhetoric and provocative actions by both sides have increased the possibility of nuclear war by accident or miscalculation".

The clock was left unchanged in 2019 due to the twin threats of nuclear weapons and climate change, and the problem of those threats being "exacerbated this past year by the increased use of information warfare to undermine democracy around the world, amplifying risk from these and other threats and putting the future of civilization in extraordinary danger".

On January 23, 2020, the Clock was moved to 100 seconds (1 minute, 40 seconds) before midnight. The Bulletin's executive chairman, Jerry Brown, said "the dangerous rivalry and hostility among the superpowers increases the likelihood of nuclear blunder... Climate change just compounds the crisis". The "100 seconds to midnight" setting remained unchanged in 2021 and 2022.

On January 24, 2023, the Clock was moved to 90 seconds (1 minute, 30 seconds) before midnight, the closest it has ever been set to midnight since its inception in 1947. This adjustment was largely attributed to the risk of nuclear escalation that arose from the Russian invasion of Ukraine. Other reasons cited included climate change, biological threats such as COVID-19, and risks associated with disinformation and disruptive technologies.

Reception
The Doomsday Clock has become a universally recognized metaphor according to The Two-Way, an NPR blog. According to the Bulletin, the Clock attracts more daily visitors to the Bulletin 's site than any other feature.

Anders Sandberg of the Future of Humanity Institute has stated that the "grab bag of threats" currently mixed together by the Clock can induce paralysis. People may be more likely to succeed at smaller, incremental challenges; for example, taking steps to prevent the accidental detonation of nuclear weapons was a small but significant step towards avoiding nuclear war. Alex Barasch in Slate argues that "Putting humanity on a permanent, blanket high-alert isn't helpful when it comes to policy or science", and criticizes the Bulletin for neither explaining nor attempting to quantify their methodology.

Cognitive psychologist Steven Pinker harshly criticized the Doomsday Clock as a political stunt, pointing to the words of its founder that its purpose was "to preserve civilization by scaring men into rationality". He stated that it is inconsistent and not based on any objective indicators of security, using as an example its being farther from midnight in 1962 during the Cuban Missile Crisis than in the "far calmer 2007". He argued it was another example of humanity's tendency toward historical pessimism, and compared it to other predictions of self-destruction that went unfulfilled.

Conservative media outlets have often criticized the Bulletin and the Doomsday Clock. Keith Payne writes in the National Review that the Clock overestimates the effects of "developments in the areas of nuclear testing and formal arms control". Tristin Hopper in the National Post acknowledges that "there are plenty of things to worry about regarding climate change", but states that climate change is not in the same league as total nuclear destruction. In addition, some critics accuse the Bulletin of pushing a political agenda.

In popular culture

 * "Seven Minutes to Midnight", a 1980 single by Wah! Heat, refers to that year's change of the Doomsday Clock from nine to seven minutes to midnight.
 * Australian rock band Midnight Oil's 1984 LP Red Sails in the Sunset features a song called "Minutes to Midnight", and the album's cover shows an aerial-view rendering of Sydney after a nuclear strike.
 * The title of Iron Maiden's 1984 song "2 Minutes to Midnight" is a reference to the Doomsday Clock.
 * The Doomsday Clock appears in the beginning of the 1985 music video for "Russians" by Sting.
 * The 1986 short story "The End of the Whole Mess" by Stephen King refers to the Doomsday Clock being set at fifteen seconds before midnight due to elevated geopolitical tension.
 * The Doomsday Clock was a recurring visual theme in Alan Moore and Dave Gibbons's seminal Watchmen graphic novel series (1986–87), its 2009 film adaptation, and its 2019 television miniseries sequel. Additionally its sequel series, which takes place in the main DC Universe, borrows the title.
 * The title of Linkin Park's 2007 album Minutes to Midnight is a reference to the Doomsday Clock. Their music video for "Shadow of the Day" from Minutes to Midnight, represents the Doomsday Clock as an actual clock with it reaching midnight at the end of the video.
 * In the Flobots' song "The Circle in the Square", the lyrics say "the clock is now 11:55 on the big hand", which was the Doomsday Clock's setting in 2012 when the song was released.
 * The title of the 1982 Doctor Who episode "Four to Doomsday" references the Doomsday Clock. In the 2017 episode "The Pyramid at the End of the World", the Monks changed every clock in the world to three minutes to midnight as a warning about what will happen if humanity does not accept their help. Representatives of the three most powerful armies on Earth agreed not to fight each other, believing a potential war is the catastrophe. However, the clock remained displaying two minutes to midnight. After the Doctor averted the true catastrophe - an accidental bacteriological disaster, the clock began moving backwards.
 * The Doomsday Clock is featured in Yael Bartana's What if Women Ruled the World, which premiered on July5, 2017 at the Manchester International Festival.
 * One minute to midnight on the Doomsday Clock is heavily referenced in the grime/punk crossover song "Effed" by Nottingham rapper Snowy and Jason Williamson of Sleaford Mods. Because of the track's political content, there was an initial reluctance from mainstream radio stations to play the track before the 2019 United Kingdom general election. However, the track was later championed by a number of BBC Radio DJs, including punk innovator Iggy Pop.
 * In the Criminal Minds season 13 episode "The Bunker", the unsubs abduct women using the Doomsday Clock.
 * The Madam Secretary season 2 episode "On the Clock" features the Doomsday Clock, as the characters try to keep it from moving forward.

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

title: Doomsday Clock


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Hexactinellid

Hexactinellid sponges are sponges with a skeleton made of four- and/or six-pointed siliceous spicules, often referred to as glass sponges. They are usually classified along with other sponges in the phylum Porifera, but some researchers consider them sufficiently distinct to deserve their own phylum, Symplasma. Some experts believe glass sponges are the longest-lived animals on earth; these scientists tentatively estimate a maximum age of up to 15,000 years.

Biology
Glass sponges are relatively uncommon and are mostly found at depths from 450 to 900 m below sea level. Although the species Oopsacas minuta has been found in shallow water, others have been found much deeper. They are found in all oceans of the world, although they are particularly common in Antarctic and Northern Pacific waters.

They are more-or-less cup-shaped animals, ranging from 10 to 30 cm in height, with sturdy skeletons made of glass-like silica spicules, fused to form a lattice. In some glass sponges such as members of the genus Euplectela, these structures are aided by a protein called glassin. It helps accelerate the production of silicas from the silicic acid absorbed from the surrounding seawater. The body is relatively symmetrical, with a large central cavity that, in many species, opens to the outside through a sieve formed from the skeleton. Some species of glass sponges are capable of fusing together to create reefs or bioherms. They are generally pale in colour, ranging from white to orange.

Much of the body is composed of syncitial tissue, extensive regions of multinucleate cytoplasm. The epidermal cells characteristic of other sponges are absent, being replaced by a syncitial net of amoebocytes, through which the spicules penetrate. Unlike other sponges, they do not possess the ability to contract.

Their body comprises three parts: the inner and outer peripheral trabecular networks, and the choanosome, which is used for feeding purposes. The choanosome acts as the mouth for the sponge while the inner and outer canals that meet at the choanosome are passages for the food, creating a consumption path for the sponge.

All hexactinellids have the potential to grow to different sizes, but the average maximum growth is estimated to be around 32 centimeters long. Some grow past that length and continue to extend their length up to 1 meter long. The estimated life expectancy for hexactinellids that grow around 1 meter is approximately 200 years (Plyes).

Glass sponges possess a unique system for rapidly conducting electrical impulses across their bodies, making it possible for them to respond quickly to external stimuli. In the case Rhabdocalyptus dawsoni, the sponge uses electrical neuron signaling to detect outside stimuli, such as sediments, and then send a signal through its body system to alert the organism to no longer be actively feeding. Another glass sponge species in the same experiment of R. dawsoni, showed that the electrical conduction system for this class of sponges all has its own threshold of how much outside stimuli, sediments, etc, it can endure before it will stop its feeding process. Species like "Venus' flower basket" have a tuft of fibers that extends outward like an inverted crown at the base of their skeleton. These fibers are 50 to 175 mm long and about the thickness of a human hair.

Syncytia
Bodies of glass sponges are different from those other sponges in various other ways. For example, most of their cytoplasm is not divided into separate cells by membranes, but forms a syncytium or continuous mass of cytoplasm with many nuclei (e.g., Reiswig and Mackie, 1983); it is held suspended like a cobweb by a scaffolding-like framework made of silica spicules. The remaining cells are connected to the syncytium by bridges of cytoplasmic "rivers" that transport nuclei, organelles ("organs" within cells) and other substances. Instead of choanocytes, these bridges have further syncytia, known as choanosyncytia, which form bell-shaped chambers where water enters via perforations. The insides of these chambers are lined with "collar bodies", each consisting of a collar and flagellum but without a nucleus of its own. The motion of the flagella sucks water through passages in the "cobweb" and expels it via the open ends of the bell-shaped chambers.

Some types of cells have a single nucleus and membrane each but are connected to other single-nucleus cells and to the main syncytium by "bridges" made of cytoplasm. The sclerocytes that build spicules have multiple nuclei, and in glass sponge larvae they are connected to other tissues by cytoplasm bridges; such connections between sclerocytes have not so far been found in adults, but this may simply reflect the difficulty of investigating such small-scale features. The bridges are controlled by "plugged junctions" that apparently permit some substances to pass while blocking others.

This physiology is what allows for a greater flow of ions and electrical signals to move throughout the organism, with around 75% of the sponge tissue being fused in this way. Another way is their role in the nutrient cycles of deep-sea environments. One species for example, Vazella pourtalesii, has an abundance of symbiotic microbes which aid in the nitrification and denitrification of the communities in which they are present. These interactions help the sponges survive in the low-oxygen conditions of the depths.

Longevity
These creatures are long-lived, but the exact age is hard to measure; one study based on modelling gave an estimated age of a specimen of Scolymastra joubini as 23,000 years (with a range from 13,000 to 40,000 years). However, due to changes in sea levels since the Last Glacial Maximum, its maximum age is thought to be no more than 15,000 years, hence its listing of c. 15,000 years in the AnAge Database. The shallow-water occurrence of hexactinellids is rare worldwide. In the Antarctic, two species occur as shallow as 33 meters under the ice. In the Mediterranean, one species occurs as shallow as 18 m in a cave with deep water upwelling (Boury-Esnault & Vacelet (1994))

Reefs
The sponges form reefs (called sponge reefs) off the coast of British Columbia, southeast Alaska and Washington state, which are studied in the Sponge Reef Project. In the case of Sarostegia oculata, this species almost always hosts symbiotic zoanthids, which cause the hexactinellid sponge to imitate the appearance and structure of coral reefs. Only 33 species of this sponge have ever been reported in the South Atlantic until 2017 when the Shinkai 6500 submersible went on an expedition through the Rio Grande Rise. Reefs discovered in Hecate Strait, British Columbia, have grown to up to 7 kilometres long and 20 metres high. Prior to these discoveries, sponge reefs were thought to have died out in the Jurassic period.

Reports of glass sponges have also been recorded on the HMCS Saskatchewan and HMCS Cape Breton wrecks off the coast of Vancouver Island. Species of zoantharin that rely on hexactinellid have also been found off the coast of the Japanese island of Minami-Torishima. Unidentified species of zoanthids have also been found in Australian waters, if these are identified as the same as the ones found in Minami-Torishima, this could potentially be proof of hexactinellids existing in all of the Pacific Ocean.

Conservation
Most hexactinellids live in deep waters that are not impacted by human activities. However, there are glass sponge reefs off the coast of British Columbia. The Canadian government designated 2140 km² of the Hecate strait and Queen Charlotte sound as a marine protected area. This area contains four glass sponge reefs. The new regulations prohibit bottom contact fishing within 200 meters of the sponge reefs. Although human activities only affect a small portion of glass sponges, they are still subject to the threat of climate changes. Experiments using the species Aphrocallistes vastus have shown that increases in temperature and acidification can lead to weakened skeletal strength and stiffness. In 1995, an Antarctic ice shelf collapsed due to climate change. Since then, studies of the area have shown that hexactinellid reefs have been increasing in size despite the changes in climate.

Classification
The earliest known hexactinellids are from the earliest Cambrian or late Neoproterozoic eras. They are fairly common relative to demosponges as fossils, but this is thought to be, at least in part, because their spicules are sturdier than spongin and fossilize better. Like almost all sponges, the hexactinellids draw water in through a series of small pores by the whip-like beating of a series of hairs or flagella in chambers which in this group line the sponge wall.

The class is divided into two subclasses and several orders:

Class Hexactinellida
 * Subclass Amphidiscophora
 * Order Amphidiscosida
 * Order †Hemidiscosa
 * Order †Reticulosa
 * Subclass Hexasterophora
 * Incertae sedis
 * Dactylocalycidae Gray, 1867
 * Order Lychniscosida
 * Order Lyssacinosida
 * Order Sceptrulophora

title: Hexactinellid


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Talk:Glossary of topology

Untitled
I think it is a good idea to have pages like this, where many short descriptions of related terms are put on a single page, instead of on separate pages. It looks more substantive and makes for better readability. -Joel Schlosberg

- I moved this from the subject page:

 * For instance, {x: 0<|x|<1} is a punctured neighbourhood of 0 in the real line, because {x : 0 ≤ |x| < 1} is a neighbourhood of 0.
 * Is this example correct? The explanation of open set seems to mean that the given neighbourhood of 0 is not open, but the explanation of Neighbourhood from above states that the neighbourhood of a point contains an open set containing the 1-point set {p}. But The example cannot contain such an open set because 0 is the boundary.

The given neighborhood of 0 is in fact open. It is the open interval (-1,+1). 0 is not in the boundary. Maybe you missed the absolute value sign. AxelBoldt 17:36 Oct 31, 2002 (UTC)

Is the definition of simply connected correct? I thought the base point had to be fixed for all time. Revolver

 * It doesn't make any difference (although this is not obvious). --Zundark

 * Thanks. I asked a couple topologists, who said that it didn't matter, although it's sometimes defined this way, you go on to prove afterward that it doesn't matter.  Funny...no one ever told me that before! Revolver

I'm wondering some things --

Just how "comprehensive" should this glossary be? Potentially, there are many definitions that could be included (say, separation axioms, etc.) that aren't here. It seems that the current glossary is evolving into a "general topology" glossary (i.e. there aren't any definitions of manifolds or homotopy groups, etc.) Certainly manifold theory and algebraic topology have enough terms to warrant their own glossaries as well (eventually!)  Also, as the number of entries of this glossary increases, it becomes hard to find something, if one comes here from another article, esp. the first part. While the entries are logically arranged, it's not easy to find a particular entry. This would be fixed by an alphabetical ordering, but this would lose the nice logical arrangement. Could there be 2 articles (one arranged logically, the other alphabetically)? or can both arrangements be incorporated into a single article? Also, it seems that as the number of math articles/content grows (the math content is large compared to other areas, not necc. by # of articles, but by length of content, scope of content) there will be a number of "glossaries" in the math area. I don't even know how many of these are already in existence. Given that one could be made for any number of areas (number theory, geometry, analysis, differential equations, logic, etc.) maybe there could be a meta-link to the glossaries, maybe on the general math article? Revolver

Glossaries bad?
Thank you, thank you, thank you. To all of you who have contributed to this page: you have done more for my understanding of topology than four different books and a whole lot of papers. This page is a miracle -- nothing else like it exists, anywhere (and believe me, I've been looking for a long time!).

The crucial reasons why glossary style works is that it effectively requires each term have a definition which:

 * is one line long
 * uses only general knowledge and other terms on the same page ("closed under definition-lookup")

I actually favor some technical changes to the wikipedia codebase that would push all pages towards including something similar (so you could build automatic glossaries), but until something like that is implemented, I think this is great.

Megacz 07:36, 31 October 2005 (UTC)

- I think a lot of subjects on this page could benefit from a longer, more involved explanation with examples. My fear this is:

 * People may be linking directly to the glossary page, and these links would have to be fixed.
 * A lot of writers might feel there's no need to write a more complete page when the term is listed here.

Also, the inability (or maybe I haven't figured out how) to link to the middle of a page makes the glossary somewhat inconvenient for readers coming in via links. Is there anything nice we can do for them? Maybe a compact index near the top?

Deco 02:34, 29 Nov 2003 (UTC)

Regarding the subjects on the page requiring more explanations and examples, I think this is the point. Saying too much would defeat the purpose. As I understand it, the purpose of a glossary page like this is so that people have quick access to definitions without constantly jumping to dozens and dozens of separate pages. I think it's intended for someone to use as a reference while reading other articles. If someone wants to look into a particular definition more, there will probably be a link to the appropriate article in the definition itself, (or if not, this can be easily added). It's true that many of the definitions in this glossary could have their own page (and many already do have substantial articles), but I don't see why having them listed here would cause people to think a more complete page is not needed. If anything, it might give someone an idea to write more (in essence, they might have the same thought you did).

The other problems you point out are definitely problems. I'm not sure what to say on, e.g. finding particular defs on a page with dozens. Either they can be all alphabetized somewhere, or else the user would need to be aware of the organisation of the defs. Making a compact index (i.e. further breakdowns into categories) might be nice, but it might not help someone who isn't already familiar with the general classification of defs anyway.

As far as fixing links, maybe this is something we should think about, what the purpose of a glossary like this is. Within an article, when you use a term, but don't want to explain it, should you link to a page with just a definition, or an entire article? Or should every page using general topological terms have a short statement somewhere giving a link to the glossary? I know that a page like this is very useful to me, if I keep a separate window open to it, when reading other articles. This could be true in a lot of subjects. It seems that it should be most useful to people exploring articles on their own, but who know enough to learn definitions on their own as well. I think the potential audience for this use is enough to justify it. How it might all turn out in the end, I don't know. Revolver

Two other points I thought of:

 * There are some defs that will probably never justify their own articles (e.g. "subcover", "refinement", etc.) since they are either used in service of other major concepts or just aren't that interesting.

 * Another major purpose of a glossary like this is to provide a standardised set of definitions for wikipedia itself. This is especially important in mathematics, when defs may not always be standard.  Here, people would come not only to learn defs, but to learn what the standard defs are for the wiki, which have to be uniform for every article in the entire wiki.  This is important, e.g. for the separation axioms.  People need to have places to come to to know what standards are in use. Revolver

I took the liberty of organising part 1, it was just getting out of hand. Feel free to move stuff around if you think I put something in the wrong place, it's just a start. Revolver

Removal of basis
I strongly disagree with the removal of the term basis from the dictionary, because:

 * The page "basis (topology)" redirects to here.
 * It's the only term I knew it by when I arrived; it took me a long time to find the entry for base and realise it was the same thing.

Could this be added back?

Derrick Coetzee 01:26, 1 Dec 2003 (UTC)

I agree. Although I've always been aware of both terms (base and basis), I've heard basis used at least as much as base, if not more. A quick couple of searches on google confirms it's standard terminology. I've changed it back. Revolver

Alphabetical index
Okay...I know I was very "bold" (to use the wikipedia suggestion) in throwing out the thematic organisation of the glossary in favor of a single alphabetical listing, but I have several reasons why I think this is a much better solution.

Here is the trade-off, as I (and some other real-life individuals I talked to) see it: you can go with a thematic organisation, and this has the advantage that similarly defined or conceptually similar definitions are listed in proximity to each other. So, e.g. you can "view" all the various compactness definitions in a single place, with your eye, and also see how the definitions interact thematically. Another advantage is that the definitions tend to increase in terms of "nested-ness", i.e. they read in roughly the order you would get them in a textbook, so all the terms needed are listed previously. This also has some drawbacks. Despite these advantages, I think alphabetic is better, and here are several reasons I have:

 * Easy to find definitions -- Definitions and terms are quickly and easily located, no matter how familiar or unfamiliar they are to the reader. Compare to thematic organisation; with thematic organisation, if the reader is somewhat unfamiliar with a particular definition or term, then he/she may have a very difficult time locating something. Which section to look in? Often, a scan of the entire glossary would be needed. This is both frustrating and time-wasting.

 * Non-linear logical dependence of definitions -- under thematic organisation, it was very tempting to try to only define something if it was in terms of previous definitions; I think this is a mistake, for reasons I'll go into later. But I ran into this problem with "connected component"; it should obviously go in part 1, since it's not a type of space, yet to define it requires the definition of "connected", which isn't until part 2. So, a linear ordering of the definitions is probably impossible in any case.

 * Alternative terminology/spellings are easily accomodated -- if I say "Kolmogorov" and you say "T0", and I don't know what T0 is, I might have trouble finding it, given that I don't even know the name of what it is I'm supposed to be looking for. With alphabetical listing, all alternative terminology can be listed with "links" to a main entry. Thus, no one is left sorting through the entire glossary to find their definition. (I believe this has already happened in the case of base/basis for some people.)

 * Addition of entries is easily accomodated -- entries can easily be added without making the glossary much more difficult to use. This can't be said for the thematic organisation.

 * What is the raison d'etre? -- The thematic organisation would make more sense if the glossary's purpose was to teach someone, but I don't think that's the purpose. The articles themselves should teach; the glossary is really just a reference for people to quickly look up terms when they don't know (or can't remember) a particular definition. The articles are the main expository meat, I doubt anyone would learn anything directly simply by reading the glossary from top to bottom, without going to the articles themselves. An alphabetic listing makes sense seeing the glossary as a reference.

I already find the alphabetical listing easier to use and visually easier on the eyes than it was before. But I'm interested what others think.

Revolver

As long as one person is making bold changes (which I admit I agree with), I suggest a change bolder still: the elimination of the glossary page in its entirety. Notice that:

 * We already have a quick way to look up a term: using the Go box at the top of the page. Terms within a page should be able to merely be clicked on.
 * We already have a quick way to send one term to another: redirect pages.

We're reinventing the wheel on a local scale. While some like to have a little collection of short definitions of many related concepts, I would argue that if this exists at all it should be generated, not written by contributors. Unfortunately the Wikipedia lacks this capacity. For lack of this, I think the glossary is harmless to have around, but I strongly believe: nothing should link here, and nothing should redirect here, at least once all the proper articles have been created, even for the simple terms. People need a way to look them up more directly.

I would advocate this as a general policy for glossaries on the Wikipedia.

Deco 05:00, 5 Dec 2003 (UTC)

Some general comments:

The original reason for the topology glossary was simply that the topology article was a mess, and I wanted to sort it out. Creating a topology glossary and moving parts of the topology article there seemed like a good idea, so that's what I did. Articles using topological terms could then link to the glossary for definitions. (There were very few articles on individual topological terms at that time.) Of course, I could instead have created a large number of tiny stub articles, but that would certainly have been frowned upon, especially as some of them would have been orphans.

More than two years after the glossary was created, we still don't have individual articles for many of the terms, because the glossary itself has greatly expanded. So the glossary still serves a purpose, as terms defined here but lacking their own article can be redirected here until someone gets around to writing an article. Direct links to the glossary shouldn't usually be used, of course.

As for the organization of the glossary, the separation into two parts was simply something that was convenient at the time, and Revolver is probably right that an alphabetical ordering is now more appropriate.

--Zundark 12:05, 5 Dec 2003 (UTC)

"As long as one person is making bold changes (which I admit I agree with), I suggest a change bolder still: the elimination of the glossary page in its entirety."

I've been thinking about this and I have to admit I've wondering the same thing, or at least I've been wondering more and more what the point of the glossary is (esp. after looking, working on it for a while). In my mind, (which has changed a lot just recently, it seems) there are a number of things working against (having) the glossary:

 * Links can simply be made within articles to other articles.
 * Links to articles contain more information than definitions.
 * No need for a separate glossary page.

There's still some issues that seem problematic for me, though. Working against not having a glossary:

 * It's not always such a simple matter to hit the "go" button to find a definition of something. Currently, the "go" button is based on google, and we all know the reliability/usability of that. If you want the definition of "X", odds are that you might not hit it on the top search match, or even on the top page of search matches. Evidence of this is that sometimes I've actually had to type in the URL itself to get somewhere. I've heard this is a problem with google, so it might be solved with better and better search engines in the future, of course.

 * Even if you do find just the right article you need, it's not always so easy to visually scan to find the definition immediately. There's usually between a line or two to a paragraph of two of introductory remarks before a formal definition (as recommended by the Math Project guidelines), so you sometimes have to look a while. This is more of an inconvenience for people who just want to find the definition quickly, then go right back to their original article, instead of people wanting to read on. Also, several definitions are often found in a single article, since they might make the most sense to define and explain within another general article topic, (although even this seems to change throughout time), and some of these might never get their own article. So, if something is defined near the middle or end of a lengthy article, it can be difficult for someone to find, even if led to that particular article.

Despite this, I wonder if these problems can't be worked around. Some ways to do this:

 * Who cares about stubs?? I know that stubs are considered "bad" on the wikipedia in general, but maybe we should ask, which is better/worse -- a lot of small definition stubs (that could still grow in the future), or an enormous, unweildy glossary?? I know that "wikipedia is not a dictionary", but in mathematics, definitions themselves have a fundamental role that they don't necessarily have in other areas of knowledge (e.g. literary theory or sociology or even chemistry).

 * A practice that seems to be working well, (one which I haven't followed very well myself!) is to try to make your links go to verbatim what you're saying, and then if there's nothing there, do a redirect to the best substitute. Then, if someone comes along later and finds it's a redirect they could start a new article for, they just go in and take out the redirect and start writing. (Example: Stone-Cech compactification -- it's redirected to compactification, although it easily seems possible that at any time someone could go in and take out the redirect and start writing an article for SC-comp. right there.)

 * There could be some standard notation or visual clue that could be used in all math articles to signal definitions (I mean, beyond headings that say "definition" or "formal definition"). The reasons I have for this, again, are that definitions aren't always easy to visually locate, if they're not right at the top, and another reason is that definitions, esp. of secondary topics or concepts, are sometimes hidden within the text itself and not even prefaced by comments or headings. Maybe all definitions could be set off in a box, or have some other way to uniquely set them apart so they're easy to spot.

Revolver

"While some like to have a little collection of short definitions of many related concepts, I would argue that if this exists at all it should be generated, not written by contributors. Unfortunately the Wikipedia lacks this capacity."

There's a wiktionary, isn't there? Can't math definitions go there? I know it's supposed to be a general dictionary, but isn't any specialised branch of knowledge free to use it as well (physics, chemistry, archaeology, art history, etc., etc.??) This would make it easier for people who wanted to find just a definition quickly. Revolver

--- ''It's not always such a simple matter to hit the "go" button to find a definition of something. Currently, the "go" button is based on google, and we all know the reliability/usability of that.''

This isn't exactly true. The only search we have is based on Google, but I visit most articles directly using the Go button, the button labelled go, which only does exact matching.

There's a wiktionary, isn't there?

As you said, definitions in math are quite different, and I think distinct from definitions of the Wiktionary sort. Open up a random dictionary to "homomorphic" to see what I mean.

As for finding definitions in math pages, I think it's reasonable (if unwieldly to fix) for every math page to have a book-style definition which stands out clearly, such as this:

Definition. A set is said to be compact if each open cover contains a finite subcover.

Moreover, I think an article which requires important concepts, such as compact requiring open cover, should give at least an intuitive definition of the concept therein without having to go afield, while providing a link for more detailed information.

Derrick Coetzee 08:12, 6 Dec 2003 (UTC)

As for finding definitions in math pages, I think it's reasonable (if unwieldly to fix) for every math page to have a book-style definition which stands out clearly, such as this:

Definition. A set is said to be compact if each open cover contains a finite subcover.

 * Yes, this seems like an excellent idea/solution. As for this being "unweildy" to implement or fix, it might not be that much of a problem...there are a lot of people working here. Lots of protocol changes have gone into effect before. And it would be easier to start with it now than later on when there are more articles. Revolver

How about this?:

Definition  Let S = {0,1}. Then T = {{},{1},{0,1}} is a topology on S, and the resulting topological space is called Sierpinski space.

or this?

Definition  Let SL(2,7) denote the group of all 2&times2 matrices of determinant one over the finite field with 7 elements. Then G = PSL(2,7) is defined to be the quotient group SL(2,7) / {I,−I} obtained by identifying I and −I. In this article, we let G denote any group isomorphic to PSL(2,7).

The combination of

along with

Definition  [plus one nbsp]

seems to set things off so its very easy to find, but it doesn't interrupt the flow of most articles. (see Sierpinski space and PSL(2,7)

I have problems with alphabetical lists. They seem to privilege random access to concepts, over being a study guide (that is, taking the chance to group concepts into clusters, impose some sort of reasonable order, and use indentation to show dependencies). I also have a problems with the formal, mathsy style here. It is fine in its place - but that is at most 25% of a good article, sometimes. Discursive is good, in my view.

By the way the

 You can define stuff here

style of display seems to me less intrusive, for boxed-off material needing to be displayed.

Charles Matthews 10:22, 6 Dec 2003 (UTC)

The purpose of experimenting with the above changes wasn't to be formal or mathsy, per se. It was just meant to make it easy to find definitions. I know definitions are a really small part of most articles, and certainly wikipedia articles should strive to be anti-Bourbaki, but there are times when you want to know just exactly what is meant by a certain term, precisely, or you just need to know what a term means, and being able to find definitions quickly helps this. Revolver

Well, yes - that probably does apply to me. It would take me a couple of seconds to do a full text search of a long page for Sierpinski. Have to set that against the needs of a more 'average' reader, though.

Charles Matthews 10:40, 6 Dec 2003 (UTC)

I've experimented with a couple pages to see how different things might look, so others can see. In each of these, if you look at the most recent links in the page history, you can see 3 different versions, one without any "setting off", one with lines, one with box. If the idea doesn't catch on, and people wish to change everything back, it's fine. But at least people can compare the difference here. linear combination Sierpinski space PSL(2,7) Baire space Banach-Mazur game Modular group Gamma Revolver

''Well, yes - that probably does apply to me. It would take me a couple of seconds to do a full text search of a long page for Sierpinski. Have to set that against the needs of a more 'average' reader, though.''

 * Yes, I know what you mean. It's all a matter of good judgment, probably. On the one hand, I would hate to see accessible articles on prime numbers or basic geometry or calculus get bogged down in endless clutter of definitions getting set off...on the other hand, I doubt that anyone who is needing to look up the different between "paracompact" and "locally compact" or forgot the exact definition of "natural transformation of functors" is going to be shocked at the sight of a definition boxed-off occasionally. Revolver

Glossary word links
One problem with the glossary is that it's uncertain which entries already have real articles associated with them and which are still functioning as "mini-stubs" until the article is written. To distinguish these better, for any term which has an article associated with it, I link the bold word beginning that definition directly to its article. I haven't finished doing this though, and any help would be appreciated.

I also added more links while I was at it; considering this may be a page that someone consults when encountering a new term which may in turn require more new terms, I think it's deserving of a high number of (meaningful) links.

Deco 07:41, 19 Dec 2003 (UTC)

I'm late to the conversation, but since I've both created a lot of redirects to this page and written a lot of articles on concepts that were once defined only on this page, I thought that I'd give an opinion.

I think that the glossary, if kept short, can serve a purpose if it's linked to by phrases such as "This article uses terms from topology that may be found in the topology glossary.". But one should never create a link using the pipe trick like "open set"! If the article Open set doesn't exist (of course this example does), then it can be redirected here, but all links should go through that redirect.

Also, redirects should go to a more specific page if one exists. Thus if there is no article Perfectly normal space, still that should redirect to Normal space rather than here. That also helps keep the glossary concise; semiregularity is obscure enough that it really doesn't belong here.

So the glossary is a good thing, but it needs to be used wisely. In particular, links should be as specific as possible.

-- Toby Bartels 00:19, 15 Feb 2004 (UTC)

+ Differential topology ??
Do you think it is ok to add here terms from differential topology?

Tosha 19:32, 6 Mar 2004 (UTC)

It is really for general topology. I think it's better to have a number of separate pages. A very long glossary becomes difficult to use.

Charles Matthews 19:50, 6 Mar 2004 (UTC)

Bursting?
I realise, esp. with my recent additions, that the glossary is now officially bursting at the seam. I'm not sure how much of a problem this is...it's true, a "very long glossary" becomes difficult to use. But, this is an area with a ton of definitions. Part of the problem is that general topology is the backbone for so many OTHER areas, that even including the most fundamental "helper" definitions creates a long list (semilocally simply connected, homogeneous, etc.) One can argue not to include "helper" defs at all, but then again, one can argue that general topology itself developed as a result of "helper defs" to other fields, (not counting the recent explosion of study of point-set topology for its own sake, that is...) Maybe things like "TG" and "TVS" can be safely removed, since they aren't strictly topological objects (similarly, I don't think "fundamental group" belongs as an entry, since it's an algebraic object). What do people think. Revolver 14:41, 18 Jun 2004 (UTC)

 * I think the glossary is helpful, and I do not have a problem with the length. I agree that algebraic topology needs its own glossary, and that "fundamental group" does not belong in this one. Rick Norwood 13:41, 31 October 2005 (UTC)

Definition lists
After my indulgences at mathematical jargon I've become fond of definition lists for pages like this. For one, they just look better, and they take up less space in markup as well. One feature I'd love to see, which I don't see, is being able to link to particular items in the list as one would link to sections of the page; this seems uniquely desirable for this particular list but it's not implemented as far as I know. So: if anyone reads this who knows what's what in the universe of Wikipedia development, could you tell me if this can get implemented? And in the mean time, is it worth putting HTML tags tags in front of each definition, so that when we have a cross reference we link there rather than directly to the main page? This sort of centralizes the control of each term. Ryan Reich 16:43, 29 March 2006 (UTC)

Node, vertex, edge
Are these terms from topology I learned at school no longer of any use? Hotlorp 15:31, 27 February 2007 (UTC)

2007-02-7 Automated pywikipediabot message
--CopyToWiktionaryBot 13:32, 7 February 2007 (UTC)

Accessibility
Currently, the wikitext for the definitions on the glossary page uses empty lines in many places to separate consecutive entries. When rendered as HTML by the wiki engine this will cause the entries to be broken up into sequences of singleton lists. E.g.,

;Accessible: See $T_1$. ;Accumulation point: See limit point. ;Alexandrov topology: A space X has the Alexandrov topology (or is finitely generated) if arbitrary intersections of open sets in X are open, or equivalently, if arbitrary unions of closed sets are closed.

(with empty lines between the definitions) will be turned into

 Accessible See .   Accumulation point See limit point.</dd> </dl> <dl> <dt><a href="/wiki/Alexandrov_topology" title="Alexandrov topology">Alexandrov topology</a></dt> <dd>A space X has the <a href="/wiki/Alexandrov_topology" title="Alexandrov topology">Alexandrov topology</a> (or is finitely generated) if arbitrary intersections of open sets in X are open, or equivalently, if arbitrary unions of closed sets are closed.</dd> </dl>

by the wiki engine, where every definition is wrapped by its own definition list. Without the empty lines, i.e., like this

;Accessible: See $T_1$. ;Accumulation point: See limit point. ;Alexandrov topology: A space X has the Alexandrov topology (or is finitely generated) if arbitrary intersections of open sets in X are open, or equivalently, if arbitrary unions of closed sets are closed.

the definition list will be rendered as

<dl> <dt>Accessible</dt> <dd>See <a href="/wiki/T1_space" title="T1 space"><img class="tex" alt="T_1" src="http://upload.wikimedia.org/math/a/5/7/a5749ec33f2c95fe8c19d702d76d4968.png" /></a>.</dd> <dt>Accumulation point</dt> <dd>See <a href="/wiki/Limit_point" title="Limit point">limit point</a>.</dd> <dt><a href="/wiki/Alexandrov_topology" title="Alexandrov topology">Alexandrov topology</a></dt> <dd>A space X has the <a href="/wiki/Alexandrov_topology" title="Alexandrov topology">Alexandrov topology</a> (or is finitely generated) if arbitrary intersections of open sets in X are open, or equivalently, if arbitrary unions of closed sets are closed.</dd> </dl>

with all definitions collected in a single list. Apparantly, people using screen readers can easily navigate between the definitions within a single definition list but not if the list is broken as it is now. See also Accessibility. I would like to remove the empty lines between the entries if nobody objects. — Tobias Bergemann (talk) 10:43, 20 January 2010 (UTC)

Almost discrete
There seem to be several definitions in the literature, none of which are obviously the same as that in the article: Is there a reliable reference that relates these? Junior Wrangler (talk) 19:28, 11 December 2012 (UTC)
 * The only strictly finer topology is the discrete topology
 * Contains no infinite compact subset
 * Exactly one isolated point
 * Hausdorff with exactly one isolated point
 * Every compact subset has an isolated point
 * Punctured neighbourhoods of a point form an ultrrafilter
 * The empty set is the only nowhere dense set
 * Alexandrov and zero-dimensional
 * The set of isolated points is dense

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Flashcards link
We wanted to learn all these terms in a flashcard format so we built one and made it freely available. Thought it would be helpful for anyone who wanted to learn the content of this glossary in a flashcard format like Anki to also be able to discover that they exist and have access to it from the source.

Was going to suggest it to be added in the external links section like the following but as it is linking to our own site, following the instructions of the Wikipedia guidelines, thought it would be best to leave this in the talk page for other contributors to see if it would be relevant or see if there was a better place/format to put it

Darigov Research (talk) 11:33, 21 March 2021 (UTC)
 * Flashcard version of the Wikipedia Glossary of topology in an Anki-readable format

"Punctured plane" listed at Redirects for discussion
The redirect [//en.wikipedia.org/w/index.php?title=Punctured_plane&redirect=no Punctured plane] has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at  until a consensus is reached. 1234qwer1234qwer4 00:47, 26 March 2024 (UTC)

title: Talk:Glossary of topology


text:
Rook (chess)

The rook (♖, ♜) is a piece in the game of chess. It may move any number of squares horizontally or vertically without jumping, and it may an enemy piece on its path; it may participate in castling. Each player starts the game with two rooks, one in each corner on their side of the board.

Formerly, the rook (from Persian رخ rokh/rukh, meaning "chariot")  was alternatively called the tower, marquess, rector, and comes (count or earl). The term "castle" is considered to be informal or old-fashioned.

Placement and movement
The white rooks start on the squares a1 and h1, while the black rooks start on a8 and h8. The rook moves horizontally or vertically, through any number of unoccupied squares. The rook cannot jump over pieces. The rook may capture an enemy piece by moving to the square on which the enemy piece stands, removing it from play. The rook also participates with the king in a special move called castling, wherein it is transferred to the square crossed by the king after the king is shifted two squares toward the rook.

Relative value
The rook is worth about five pawns. In general, rooks are stronger than bishops or knights and are considered greater in value than either of those pieces by nearly two pawns, but less valuable than two minor pieces by approximately a pawn. Two rooks are generally considered to be worth slightly more than a queen (see chess piece relative value). Winning a rook for a bishop or knight is referred to as winning the exchange. Rooks and queens are called major pieces or heavy pieces, as opposed to bishops and knights, the minor pieces.

Development
In the opening, the rooks are blocked in by other pieces and cannot immediately participate in the game, so it is usually desirable to connect one's rooks on the by castling and then clearing all pieces except the king and rooks from the first rank. In that position, the rooks support each other and can more easily move to occupy and control the most favorable.

A common strategic goal is to a rook on the first rank of an open file (i.e., one unobstructed by pawns of either player) or a half-open file (i.e., one unobstructed by friendly pawns). From this position, the rook is relatively unexposed to risk but can exert control on every square on the file. If one file is particularly important, a player might advance one rook on it, then position the other rook behind—doubling the rooks.

A rook on the seventh rank (the opponent's second rank) is typically very powerful, as it threatens the opponent's unadvanced pawns and hems in the enemy king. A rook on the seventh rank is often considered sufficient compensation for a pawn. In the diagrammed position from a game between Lev Polugaevsky and Larry Evans, the rook on the seventh rank enables White to draw, despite being a pawn down.

rooks on the seventh rank are often enough to force victory by the blind swine mate, or at least a draw by perpetual check.

Endgame
Rooks are most powerful towards the end of a game (i.e., the endgame), when they can move unobstructed by pawns and control large numbers of squares. They are somewhat clumsy at restraining enemy pawns from advancing towards promotion unless they can occupy the file behind the advancing pawn. As well, a rook best supports a friendly pawn towards promotion from behind it on the same file (see Tarrasch rule).

In a position with a rook and one or two versus two rooks, generally in addition to pawns, and possibly other pieces, Lev Alburt advises that the player with the single rook should avoid exchanging the rook for one of his opponent's rooks.

The rook is adept at delivering checkmate. Below are a few examples of rook checkmates that are easy to. A single rook can force checkmate while a single minor piece cannot.

History
In the medieval shatranj, the rook symbolized a chariot. The Persian word rukh means "chariot", and the corresponding piece in the original Indian version, chaturanga, has the name ratha (meaning "chariot"). In modern times, it is mostly known as हाथी (elephant) to Hindi-speaking players, while East Asian chess games such as xiangqi and shogi have names also meaning chariot (車) for the same piece.

Persian war chariots were heavily armored, carrying a driver and at least one ranged-weapon bearer, such as an archer. The sides of the chariot were built to resemble fortified stone work, giving the impression of small, mobile buildings, causing terror on the battlefield.

In Europe, the castle or tower appears for the first time in the 16th century in Vida's 1550 Ludus Scacchia, and then as a tower on the back of an elephant. In time, the elephant disappeared and only the tower was used as the piece.

In the West, the rook is almost universally represented as a crenellated turret. The piece is called torre ("tower") in Italian, Portuguese, Catalan and Spanish; tour in French; toren in Dutch; Turm in German; torn in Swedish; and torni in Finnish. In Hungarian, it is bástya ("bastion") and in Hebrew ,it is called צריח (tsriʾaḥ, meaning "turret"). In the British Museum's collection of the medieval Lewis chess pieces, the rooks appear as stern warders, or wild-eyed berserker warriors.

Rooks are usually similar in appearance to small castles; thus, a rook is sometimes called a "castle", though modern chess literature rarely, if ever, uses this term.

In some languages, the rook is called a ship: Thai เรือ (reūa), Armenian Նավակ (navak), Russian ладья (ladya), Javanese ꦥꦿꦲꦸ (prahu). This may be because of the use of an Arabic style V-shaped rook piece, which some may have mistaken for a ship. It is possible that the rendition comes from Sanskrit roka (ship); however, no chaturanga pieces were ever called a roka. Murray argued that the Javanese could not visualize a chariot moving through the jungles in sweeping fashion as the rook. The only vehicle that moved in straight fashion was ship, thus they replaced it with prahu. Murray, however, did not give an explanation of why the Russians call the piece a "ship".

Peter Tyson suggests that there is a correlation between the name of the piece and the word rukh, a mythical giant bird of prey from Persian mythology.

In South Slavic languages, it is called the "cannon" (Топ, Romanised top).

In Kannada, it is known as ಆನೆ (āāne), meaning "elephant". This is unusual, as the term for elephant is in many other languages applied to the bishop.

Heraldry
Chess rooks frequently occur as heraldic charges. Heraldic rooks are usually shown as they looked in medieval chess sets, with the usual battlements replaced by two outward-curving horns. They occur in arms from around the 13th century onwards.

In Canadian heraldry, the chess rook is the cadency mark of a fifth daughter.

Unicode
Unicode defines three codepoints for a rook:

♖ U+2656 White Chess Rook

♜ U+265C Black Chess Rook

🨂 U+1FA02 Neutral Chess Rook

title: Rook (chess)


text:
Bishop (chess)

The bishop (♗, ♝) is a piece in the game of chess. It moves and captures along without jumping over intervening pieces. Each player begins the game with two bishops. The starting squares are c1 and f1 for White's bishops, and c8 and f8 for Black's bishops.

Placement and movement
The is placed on f1 for White and f8 for Black; the  is placed on c1 for White and c8 for Black.

The bishop has no restrictions in distance for each move but is limited to diagonal movement. It cannot jump over other pieces. A bishop captures by occupying the square on which an enemy piece stands. As a consequence of its diagonal movement, each bishop always remains on one square color. Due to this, it is common to refer to a bishop as a light-squared or dark-squared bishop.

Versus rook
A rook is generally worth about two pawns more than a bishop. The bishop has access to only half of the squares on the board, whereas all squares of the board are accessible to the rook. When unobstructed, a rook attacks fourteen squares regardless of position, whereas a bishop attacks no more than thirteen (from one of four center squares) and sometimes as few as seven (from sides and corners). A king and rook can checkmate against a lone king, whereas a king and bishop cannot. A king and two bishops on opposite-colored squares, however, can force mate.

Versus knight
Knights and bishops are each worth about three pawns. This means bishops are approximately equal in strength to knights, but depending on the game situation, either may have a distinct advantage. In general, the bishop is slightly stronger than the knight.

Less experienced players tend to underrate the bishop compared to the knight because the knight can reach all squares and is more adept at forking. More experienced players understand the power of the bishop.

Bishops usually gain in relative strength towards the endgame as more pieces are captured and more open lines become available on which they can operate. A bishop can easily influence both wings simultaneously, whereas a knight is less capable of doing so. In an open endgame, a pair of bishops is decidedly superior to either a bishop and a knight, or two knights. A player possessing a pair of bishops has a strategic weapon in the form of a long-term threat to trade down to an advantageous endgame.

Two bishops on opposite-colored squares and king can force checkmate against a lone king, whereas two knights cannot. A bishop and knight can force mate, but with far greater difficulty than two bishops.

In certain positions a bishop can by itself lose a move (see triangulation and tempo), while a knight can never do so. The bishop is capable of skewering or pinning a piece, while the knight can do neither. A bishop can in some situations hinder a knight from moving. In these situations, the bishop is said to be "dominating" the knight.

On the other hand, in the opening and middlegame a bishop may be hemmed in by pawns of both players, and thus be inferior to a knight which can jump over them. A knight check cannot be blocked but a bishop check can. Furthermore, on a crowded board a knight has many tactical opportunities to fork two enemy pieces. A bishop can fork, but opportunities are rarer. One such example occurs in the position illustrated, which arises from the Ruy Lopez: 1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Ba4 Nf6 5.0-0 b5 6.Bb3 Be7 7.d4 d6 8.c3 Bg4 9.h3 Bxf3 10.Qxf3 exd4 11.Qg3 g6 12.Bh6

Good bishop and bad bishop
In the middlegame, a player with only one bishop should generally place friendly pawns on squares of the color that the bishop cannot move to. This allows the player to control squares of both colors, allows the bishop to move freely among the pawns, and helps fix enemy pawns on squares on which they can be attacked by the bishop. Such a bishop is often referred to as a "good" bishop.

Conversely, a bishop which is impeded by friendly pawns is often referred to as a "bad bishop" (or sometimes, disparagingly, a "tall pawn"). The black light-squared bishop in the French Defense is a notorious example of this concept. A "bad" bishop, however, need not always be a weakness, especially if it is outside its own. In addition, having a "bad" bishop may be advantageous in an opposite-colored bishops endgame. Even if the bad bishop is passively placed, it may serve a useful defensive function; a well-known quip from GM Mihai Suba is that "Bad bishops protect good pawns."

In the position from the game Krasenkow versus Zvjaginsev, a thicket of black pawns hems in Black's bishop on c8, so Black is effectively playing with one piece fewer than White. Although the black pawns also obstruct the white bishop on e2, it has many more attacking possibilities, and thus is a good bishop vis-à-vis Black's bad bishop. Black resigned after another ten moves.

Fianchetto
A bishop may be fianchettoed, for example after moving the g2 pawn to g3 and the bishop on f1 to g2. This can form a strong defense for the castled king on g1 and the bishop can often exert strong pressure on the long diagonal (here h1–a8). A fianchettoed bishop should generally not be given up lightly, since the resulting in the pawn formation may prove to be serious weaknesses, particularly if the king has castled on that side of the board.

There are nonetheless some modern opening lines where a fianchettoed bishop is given up for a knight in order to double the opponent's pawns, for example 1.d4 g6 2.c4 Bg7 3.Nc3 c5 4.d5 Bxc3+!? 5.bxc3 f5, a sharp line originated by Roman Dzindzichashvili. Giving up a fianchettoed queen's bishop for a knight is usually less problematic. For example, in Karpov–Browne, San Antonio 1972, after 1.c4 c5 2.b3 Nf6 3.Bb2 g6, Karpov gave up his fianchettoed bishop with 4.Bxf6! exf6 5.Nc3, doubling Black's pawns and giving him a hole on d5.

Endgame
An endgame in which each player has only one bishop, one controlling the dark squares and the other the light, will often result in a draw even if one player has a pawn or sometimes two more than the other. The players tend to gain control of squares of opposite colors, and a deadlock results. In endgames with same-colored bishops, however, even a positional advantage may be enough to win.

Bishops on opposite colors
Endgames in which each player has only one bishop (and no other pieces besides the king) and the bishops are on opposite colors are often drawn, even when one side has an extra pawn or two. Many of these positions would be a win if the bishops were on the same color.

The position from Wolf versus Leonhardt (see diagram) shows an important defensive setup. Black can make no progress, since the white bishop ties the black king to defending the pawn on g4 and it also prevents the advance ...f3+ because it would simply the pawn – then either the other pawn is exchanged for the bishop (an immediate draw) or the pawn advances (an easily drawn position). Otherwise the bishop alternates between the squares d1 and e2.

If two pawns are connected, they normally win if they reach their sixth, otherwise the game may be a draw (as above). If two pawns are separated by one they usually draw, but win if they are farther apart.

In some cases with more pawns on the board, it is actually advantageous to have the bishops on opposite colors if one side has weak pawns. In the 1925 game Efim Bogoljubov–Max Blümich (see diagram), White wins because of the bishops being on opposite colors making Black weak on the dark squares, the weakness of Black's isolated pawns on the, and the weak doubled pawns on the. The game continued:

 * 29.Kd2 Ke7 30.Kc3 f6 31.Kd4 Be6 32.Kc5 Kd7 33.Kb6 g5 34.Kxa6 Kc7 35.Bb6+ Kc8 36.Bc5 Kc7 37.Bf8 f5 38.Bxg7 f4 39.Bf6 f3 40.gxf3 exf3 41.Bxg5 Bxh3 42.Bf4+

Wrong bishop
In an endgame with a bishop, in some cases the bishop is the "wrong bishop", meaning that it is on the wrong color of square for some purpose (usually promoting a pawn). For example, with just a bishop and a, if the bishop cannot control the promotion square of the pawn, it is said to be the "wrong bishop" or the pawn is said to be the wrong rook pawn. This results in some positions being drawn (by setting up a fortress) which otherwise would be won.

History

The bishop's predecessor in medieval chess, shatranj (originally chaturanga), was the alfil, meaning "elephant", which could leap two squares along any diagonal, and could jump over an intervening piece. As a consequence, each fil was restricted to eight squares, and no fil could attack another. The modern bishop first appeared shortly after 1200 in Courier chess. A piece with this move, called a cocatriz or crocodile, is part of the Grande Acedrex in the Libro de los juegos compiled in 1283 for King Alfonso X of Castile. The game is attributed to "India", then a very vague term. About half a century later Muḥammad ibn Maḥmud al-Āmulī, in his Treasury of the Sciences, describes an expanded form of chess with two pieces moving "like the rook but obliquely". The bishop was also independently invented in Japan at about the same time (the 13th century), where it formed part of sho shogi and dai shogi; it remains present in modern shogi as the direct descendant of sho shogi.

Derivatives of alfil survive in the languages of the two countries where chess was first introduced within Western Europe—Italian (alfiere) and Spanish (alfil). It was known as the aufin in French, or the aufin, alphin, or archer in early English.

The earliest references to bishops on the chessboard are two 13th-century Latin texts, De Vetula and Quaedam moralitas de scaccario. The etymology of "bishop" comes from Old English bisceop "bishop, high priest," from Late Latin episcopus, from Greek episkopos "watcher, overseer." The term "bishop" as applied specifically to the chess piece was first recorded in the 16th century, with the first known written example dating back to the 1560s. In all other Germanic languages, except for Icelandic, it is called various names, all of which directly translate to English as "runner" or "messenger". In Icelandic, however, it is called "biskup", with the same meaning as in English. The use of the term in Icelandic predates that of the English language, as the first mentioning of "biskup" in Icelandic texts dates back to the early part of the 14th century, while the 12th-century Lewis Chessmen portray the bishop as an unambiguously ecclesiastical figure. In the Saga of Earl Mágus, which was written in Iceland somewhere between 1300–1325, it is described how an emperor was checkmated by a bishop. This has led to some speculations as to the origin of the English use of the term "bishop".

The canonical chessmen date back to the Staunton chess set of 1849. The piece's deep groove symbolizes a bishop's (or abbot's) mitre. Some have written that the groove originated from the original form of the piece, an elephant with the groove representing the elephant's tusks. The English apparently chose to call the piece a bishop because the projections at the top resembled a mitre. This groove was interpreted differently in different countries as the game moved to Europe; in France, for example, the groove was taken to be a jester's cap, hence in France the bishop is called fou, the "jester" and in Romania the nebun (madman).

In some Slavic languages (e.g. Czech/Slovak) the bishop is called střelec/strelec, which directly translates to English as a "shooter" meaning an archer, while in others it is still known as "elephant" (e.g. Russian slon). In South Slavic languages it is usually known as lovac, meaning "hunter", or laufer, taken from the German name for the same piece (laufer is also a co-official Polish name for the piece alongside goniec). An alternative name for bishop in Russian is "officer" (офицер); it is also called αξιωματικός (axiomatikos) in Greek, афіцэр (afitser) in Belarusian and oficeri in Albanian.

In Mongolian and several Indian languages it is called the "camel".

In Lithuanian it is the rikis, a kind of military commander in medieval Lithuania.

In Latvia it is known as laidnis, a term for the wooden handle part of some firearms.

Unicode
Unicode defines three codepoints for a bishop:

♗ U+2657 White Chess Bishop

♝ U+265D Black Chess Bishop

🨃 U+1FA03 Neutral Chess Bishop

title: Bishop (chess)


text:
Rook

Rook or rooks may refer to:

Animals

 * Rook (bird) (Corvus frugilegus), a bird of the corvid family

Games

 * Rook (chess), a piece in chess
 * Rook (card game), a trick-taking card game

Military

 * Sukhoi Su-25 or Rook, a close air support aircraft
 * USS Rooks (DD-804), a destroyer launched in 1944

Places

 * Montes Rook, a mountain range on the Moon
 * Rooks County, Kansas
 * Rook Mountain, a summit in Alaska

Fictional entities

 * The Rook (comics), a comic book character from Eerie magazine
 * Rook (G.I. Joe), a character in the G.I. Joe universe
 * Rook, an Utrom in Teenage Mutant Ninja Turtles season 4
 * Rook Blonko, a character in Ben 10: Omniverse

Other uses

 * Rook (album), 2008 album by Shearwater
 * The Rook (novel), a 2011 supernatural thriller by Daniel O'Malley
 * The Rook (TV series), a TV series on Starz
 * Rook (piercing), a piercing on the anti-helix of the ear
 * Rook (rocket), a British rocket launched between 1959 and 1972
 * Rook (surname)
 * Qolla l-Bajda Battery or Rook, a discothèque in Żebbuġ, Gozo, Malta
 * Rook, an 1874 South Devon Railway 0-4-0 locomotive

title: Rook


text:
Chess piece

A chess piece, or chessman, is a game piece that is placed on a chessboard to play the game of chess. It can be either white or black, and it can be one of six types: king, queen, rook, bishop, knight, or pawn.

Chess sets generally come with sixteen pieces of each color. Additional pieces, usually an extra queen per color, may be provided for use in promotion.

Number
Each player begins with sixteen pieces (but see the subsection below for other usage of the term piece). The pieces that belong to each player are distinguished by color: the lighter colored pieces are referred to as "white" and the player that controls them as "White", whereas the darker colored pieces are referred to as "black" and the player that controls them as "Black".

In a standard game, each of the two players begins with the following sixteen pieces:
 * 1 king
 * 1 queen
 * 2 rooks
 * 2 bishops
 * 2 knights
 * 8 pawns

Definitions
The word "piece" has three meanings, depending on the context.
 * 1) It may mean any of the physical pieces of the set, including the pawns. When used this way, "piece" is synonymous with "chessman" or simply "man".  Chess sets have been made in a variety of styles, sometimes for decorative or artistic purposes rather than practical play, but the Staunton pattern is standard for competition.
 * 2) In play, the term is usually used to exclude pawns, referring only to a queen, rook, bishop, knight, or king. In this context, the pieces can be broken down into three groups: major pieces (queen and rooks), minor pieces (bishops and knights), and the king.
 * 3) In phrases such as "winning a piece", "losing a piece" or "sacrificing a piece" and other related contexts, it refers only to minor pieces (bishops or knights). By convention, the queen, rooks, and pawns are specified by name in these cases – for example, "winning a queen", "losing a rook", or "sacrificing a pawn".

Moves
The rules of chess prescribe the moves each type of chess piece can make. During play, the players take turns moving their own chess pieces.
 * The rook may move any number of squares vertically or horizontally without jumping. It also takes part, along with the king, in castling.
 * The bishop may move any number of squares diagonally without jumping. Consequently, a bishop stays on squares of the same color throughout the game.
 * The queen may move any number of squares vertically, horizontally, or diagonally without jumping.
 * The king may move to any adjoining square. No move may be made such that the king is placed or left in check. The king may participate in castling, which is a move consisting of the king moving two squares toward a same-colored rook on the same rank and the rook moving to the square crossed by the king. Castling may only be performed if the king and rook involved are unmoved, if the king is not in check, if the king would not travel through or into check, and if there are no pieces between the rook and the king.
 * The knight moves from one corner of any two-by-three rectangle to the opposite corner. Consequently, the knight alternates its square color each time it moves. It is not obstructed by other pieces.
 * The pawn may move forward one square, and one or two squares when on its starting square, toward the opponent's side of the board. When there is an enemy piece one square diagonally ahead of a pawn, then the pawn may capture that piece. A pawn can perform a special type of capture of an enemy pawn called en passant ("in passing"), wherein it captures a horizontally adjacent enemy pawn that has just advanced two squares as if that pawn had only advanced one square. If the pawn reaches a square on the of the opponent, it promotes to the player's choice of a queen, rook, bishop, or knight of the same color.

Pieces other than pawns capture in the same way that they move. A capturing piece replaces the opponent piece on its square, except for an en passant capture by a pawn. Captured pieces are immediately removed from the game. A square may hold only one piece at any given time. Except for castling and the knight's move, no piece may jump over another piece.

Relative value
The value assigned to a piece attempts to represent the potential strength of the piece in the game. As the game develops, the relative values of the pieces will also change. For example, in an, bishops are relatively more valuable; they can be positioned to control long, open diagonal spaces. In a with lines of protected pawns blocking bishops, knights usually become relatively more potent. Similar ideas apply to placing rooks on open files and knights on active,. The standard valuation is one point for a pawn, three points for a knight or bishop, five points for a rook, and nine points for a queen. These values are reliable in endgames, particularly with a limited number of pieces. But these values can change depending on the position or the phase of the game (opening, middle game, or ending). A for example, is worth an additional half-pawn on average. In specific circumstances, the values may be quite different: sometimes a knight can be more valuable than a queen if a particular angle is required for a mating attack, such as certain smothered mates. The humble pawn becomes more and more valuable the closer it is to securing a queen promotion for another example.

History
Chess evolved over time from its earliest versions in India and Persia to variants that spread both West and East. Pieces changed names and rules as well; the most notable changes was the Vizir (or Firz) becoming the Queen, and the Elephant becoming the Bishop in European versions of chess. The movement patterns for Queens and Bishops also changed, with the earliest rules restricting elephants to just two squares along a diagonal, but allowing them to "jump" (seen in the fairy chess piece the alfil); and the earliest versions of queens could only move a single square diagonally (the fairy chess piece Ferz). The modern bishop's movement was popularized in the 14th and 15th centuries, and the modern queen was popularized in the 15th and 16th centuries, with versions with the more powerful modern queen eclipsing older variants.

Names
The characters implied by pieces' names vary between languages. For example, in many languages, the piece known in English as the "knight" frequently translates as "horse", and the English "bishop" frequently translates as "elephant" in language areas that adapted the modern bishop's movement pattern, but not its new name.

Variants
Chess variants sometimes include new, non-standard, or even old pieces. For example, Courier Chess, a predecessor of modern chess dating from the 12th century, was played on an 8×12 board and used all six modern chess piece types, plus three additional types of pieces: Courier, Mann (or rath or sage), and Jester. Variants of "old" chess might use the old rules for bishops/elephants with the alfil piece, or old rules for Queens with the ferz. Many modern variants with unorthodox pieces exist, such as Berolina chess which uses custom pawns that advance diagonally and capture vertically.

title: Chess piece