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# Transport in Guyana
## Ferries
Ferry services link the primary roads in the coastal area, and Guyana with Suriname. The Government\'s Transport an hid Harbour Department provides scheduled ferry services in the Essequibo and Demerara rivers. Small privately owned river-craft supplement these services. Since the opening of the Berbice River Bridge in December 2008 the Transport and Harbour Department has reduced its service to only one round trip daily between Rosignol and New Amsterdam.
Currently the only ferry service consistently showing profit is The Parika-Adventure. Service for the remainder, in particular The North West services, the Government provides a cross-subsidy funded out of the profits that are always realized by the Harbor Branch of the Transport and Harbors Department. Nevertheless, ferry operations have the potential to be profitable, provided that capital investments are made to improve their physical assets. With the establishment of a Maritime Administration and subsequently a National Sea Ports Authority the ferry operations may be privatized or operated as a commercially viable autonomous agency.
There is also a ferry linking Guyana and Suriname crossing the Corentyne River from Springlands (at Corriverton in Guyana) to Nieuw Nickerie, a town in Suriname. Leaving Rosignol at 8:00hrs and now at 14:30hrs respectively. This service is primarily geared at offsetting the high cost for crossing the Berbice Bridge for school children, public servants and the elderly.
Ultimately, key ferry links were to be replaced with bridges, starting with one from Rosignol to New Amsterdam across the Berbice River.
At the end of 1999 the fleet of ferry vessels owned by the Transport and Harbors Department comprised nine motor vessels, six of which ranged in age from 15 to 55 years. Indeed, two of the vessels were over fifty years of age, and three over 30 years, with an average age of thirty-five. They are in almost continuous need of repair.
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# Transport in Guyana
## Air transportation {#air_transportation}
Air transportation for business and pleasure is readily available for traveling to many parts of the hinterland. Several local airlines depart from both Ogle Airport on the East Coast Demerara, 6 mi south-east of Georgetown and from Cheddi Jagan International Airport, at Timehri, 25 mi south-west of Georgetown.
Air transport plays a vital role in the development of Guyana. Within the country, it provides a link between the coastal areas and communities in the hinterland, many of which are inaccessible by any other means of transportation. Thus, the economic and social well-being of these areas and their integration into the fabric of the nation are critically dependent on the availability of air transport. Externally, passengers are moved to and from the country almost entirely by air. In addition, the potential of this mode of transport for the carriage of cargo, especially exports, continues to increase.
The first airplane flight took place in Guyana in March 1913 when George Schmidt, a German, flew a machine over Georgetown, taking off from the Bel Air Park Race Course.
In September 1929, the first airmail service to Guyana began.
The famous American flier, Colonel Charles Lindbergh, arrived in the Demerara River with his flying boat (an amphibian craft) on September 22, 1929. The first regular flights to the interior started in 1939.
Although air transport in Guyana had its beginnings in the 1920s when the first \"bush\" services were introduced, Government\'s earnest participation can be dated from 1947 when a Director of Civil Aviation was appointed to regulate the industry. Regular shipments of beef from the Rupununi to Georgetown by air began on 9 July 1948. Amphibian aircraft have been vital to the development of the country as they are able land both on airstrips and on water.
The development of air transport in Guyana owes much to Arthur \"Art\" James Williams, a pilot and mechanic from the United States. He arrived in British Guiana in August 1934, and returned to the United States in October 1955. Over this period, except for the war years, during which he served with the United States Air Force, he developed British Guiana Airways Ltd. (registered 27 May 1938) and operating regular internal services since 1939.
On 15 July 1955, the Government purchased British Guiana Airways. However, external services continued to be supplied almost exclusively by foreign airlines until Guyana Airways Corporation commenced regional air services in 1979. Subsequently, restrictions on the repatriation of profits in foreign exchange and other circumstances contributed to the withdrawal of services to Guyana by foreign airlines, with the exception of BWIA. Guyana Airways Corporation was therefore obliged to fill the breach by commencing jet operations to Miami and New York in the US and Toronto, Ontario in Canada.
In the 1980s Guyana Airways Corporation\'s domestic operations started to deteriorate for a number of reasons, not least among them the unrealistically low fares it was required to charge and the lack of access to foreign exchange for imported aircraft parts and other requirements. The private sector therefore began to fill the gap and by 1991 three major domestic charter operators had emerged. In the meantime, Guyana Airways Corporation\'s domestic service continued to deteriorate and, by 1993, possessed only one Twin Otter DHC-6 to service the entire country. Under new management it was revitalized and saw a partial return to its original domestic role with the reintroduction of several domestic scheduled routes, because of the addition of two Shorts Skyvan SC7 aircraft, and a second Twin Otter DHC-6 aircraft.
In 2010, the International Civil Aviation Organization (ICAO) conferred \"international\" status to the air terminal at Ogle (IATA: OGL, ICAO: SYGO), a former sugarcane airstrip just a few kilometres south of Georgetown\'s center. In anticipation of increased regional air traffic to the facility, an EU-subsidized construction project began in January of that year, intended to upgrade the terminal building and extend the primary paved runway to a usable length of 4000 feet. Ogle is the hub for domestic flights to Guyana\'s interior and offers once-daily service to the in-town airstrip in Paramaribo, capital of neighboring Suriname.
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# Transport in Guyana
## Challenges and future development {#challenges_and_future_development}
The gross inadequacy of Guyana\'s transportation system militates against its social and economic development in several ways. First, it increases production costs and, therefore, reduces competitiveness, particularly in the mining and forestry sectors. Second, it inhibits the capacity to fully utilise those natural resources (gold, timber, diamonds, soils suitable for agriculture) that are not located on the coastland. Third, by severely limiting communication between those who live on the coast and those who inhabit the hinterland, it effectively divides the country into two almost unbridgeable cultures. Fourth, it acts as a barrier to the unity of the country in both a physical and spiritual sense: because they are not unified physically, Guyanese seem to find it difficult to think as Guyanese, to act as if they are one nation. Fifth, it restricts the coastal population\'s penetration of the interior, and forces coastlanders to live in a cramped and crowded manner on the coast, struggling and competing for land-space and other amenities, while more suitable areas are available farther south. And sixth, failure to occupy the greater part of the country, might tend to bolster some of the claims of Guyana\'s neighbours to its territory.
The government of Guyana and Brazil signed a Memorandum of Understanding in 2012 to explore the development of Hydro Power, Linden-Lethem Road and Deep Water Harbour to boost bilateral trade and cooperation. This network would have enabled easy access by road to the neighbouring countries of Brazil, Venezuela and Surinam; reduced the costs of utilising the country\'s timber and natural resources, thus making them more competitive in international markets; diversified agricultural development by making more easily available suitable areas in the hinterland, particularly in the Intermediate and Rupununi savannahs; relieved the over-crowded coastland of a significant proportion of its population, thus improving the quality of life of the inhabitants of both the coastal and interior areas; and made more feasible the equitable distribution of economic activity, not only in the agricultural but also in the manufacturing and small- industries sector.
A high-span fixed bridge is currently being studied to replace the existing DHB; a series of bridges and causeways linking the islands in the mouth of the Essequibo River to Morasi on the East Bank and Supenaam on the West Bank; and another high-span bridge across the Essequibo River at Monkey Jump.
Construction of a bridge across the Berbice River at Crab Island and D\'Edwards on the East and West banks of Berbice River was completed in 2008.
In 2012, The Government of Guyana signed a contract with CHEC of China for the expansion of the runway at the CJIA and the construction of a modern terminal building at an estimated cost of 131Million US Dollars. Moreover, the airstrip at Timehri Airport would have been extended, and the entire Airport refurbished to accommodate an increasing number of passengers. The airport at Ogle would have been privatised, and much improved and extended.
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# Transport in Guyana
## Statistics
### Railways
*Total:* 187 km (all dedicated to ore transport)\
*Standard gauge:* 139 km; `{{RailGauge|ussg}}`{=mediawiki}\
*Narrow gauge:* 48 km; `{{RailGauge|3ft|lk=on}}`{=mediawiki} gauge
### Highways
*Total:* 7,970 km\
*Paved:* 590 km\
*Unpaved:* 7,380 km (1996 est.)
- Driving is on the left, a practice inherited from United Kingdom colonial authorities. Guyana and Suriname are the only two countries on the (in-land) American continent who still drive on the left.
### Waterways
Guyana has 5900 km total of navigable waterways; Berbice River, Demerara River, and Essequibo River are navigable by oceangoing vessels for 150 , respectively.
### Seaports and harbors {#seaports_and_harbors}
- Bartica
- Georgetown
- Linden
- New Amsterdam
- Parika
### Merchant marine {#merchant_marine}
*total:* 1 ship (`{{GT|1,000|disp=long}}`{=mediawiki} or over) totaling `{{GT|1,023}}`{=mediawiki}/`{{DWT|1,972|long|disp=long}}`{=mediawiki}\
*ships by type:* (1999 est.)
- cargo ship 1
### Airports
51 (1999 est.)
**International Airport:** Cheddi Jagan International Airport
**Other Major Airport/s:** Eugene F. Correia International Airport
**Airports - with paved runways:**\
*total:* 9\
*1,524 to 2,437 m:* 2\
*914 to 1,523 m:* 1\
*under 914 m:* 2 (1999 est.)
**Airports - with unpaved runways:**\
*total:* 84\
*1,524 to 2,437 m:* 2\
*914 to 1,523 m:* 7\
*under 914 m:* 37 (1999 est
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# Great man theory
The **great man theory** is an approach to the study of history popularised in the 19th century according to which history can be largely explained by the impact of *great men*, or heroes: highly influential and unique individuals who, due to their natural attributes, such as superior intellect, heroic courage, extraordinary leadership abilities, or divine inspiration, have a decisive historical effect. The theory is primarily attributed to the Scottish essayist, historian, and philosopher Thomas Carlyle, who gave a series of lectures on heroism in 1840, later published as *On Heroes, Hero-Worship, & the Heroic in History*, in which he states:
This theory is usually contrasted with people\'s history, which emphasizes the life of the masses creating overwhelming waves of smaller events which carry leaders along with them. Another contrasting school is historical materialism.
## Overview
thumb\|left\|upright=.7\|Bust of Thomas Carlyle by Thomas Woolner Carlyle stated that \"The History of the world is but the Biography of great men\", reflecting his belief that heroes shape history through both their personal attributes and divine inspiration. In his book *Heroes and Hero-Worship*, Carlyle saw history as having turned on the decisions, works, ideas, and characters of \"heroes\", giving detailed analysis of six types: The hero as divinity (such as Odin), prophet (such as Muhammad), poet (such as Shakespeare), priest (such as Martin Luther), man of letters (such as Rousseau), and king (such as Napoleon). Carlyle also argued that the study of great men was \"profitable\" to one\'s own heroic side; that by examining the lives led by such heroes, one could not help but uncover something about one\'s own true nature.
As Sidney Hook notes, a common misinterpretation of the theory is that \"all factors in history, save great men, were inconsequential\", whereas Carlyle is instead claiming that great men are the decisive factor, owing to their unique genius. Hook then goes on to emphasize this uniqueness to illustrate the point: \"Genius is not the result of compounding talent. How many battalions are the equivalent of a Napoleon? How many minor poets will give us a Shakespeare? How many run of the mine scientists will do the work of an Einstein?\"
American scholar Frederick Adams Woods supported the great man theory in his work *The Influence of Monarchs: Steps in a New Science of History*. Woods investigated 386 rulers in Western Europe from the 12th century until the French Revolution in the late 18th century and their influence on the course of historical events.
The Great Man approach to history was most fashionable with professional historians in the 19th century; a popular work of this school is the *Encyclopædia Britannica Eleventh Edition* (1911) which contains lengthy and detailed biographies about the great men of history, but very few general or social histories. For example, all information on the post-Roman \"Migrations Period\" of European History is compiled under the biography of Attila the Hun. This heroic view of history was also strongly endorsed by some philosophers, such as Léon Bloy, Søren Kierkegaard, Oswald Spengler and Max Weber.
Georg Wilhelm Friedrich Hegel, proceeding from providentialist theory, argued that \"what is real is reasonable\" and World-Historical individuals are World-Spirit\'s agents. Hegel wrote: \"Such are great historical men---whose own particular aims involve those large issues which are the will of the World-Spirit.\" Thus, according to Hegel, a great man does not create historical reality himself but only uncovers the inevitable future.
In *Untimely Meditations*, Friedrich Nietzsche writes that \"the goal of humanity lies in its highest specimens\". Although Nietzsche\'s body of work shows some overlap with Carlyle\'s line of thought, Nietzsche expressly rejected Carlyle\'s hero cult in *Ecce Homo*.`{{Page needed|date=September 2022}}`{=mediawiki}
### Assumptions
This theory rests on two main assumptions, as pointed out by Villanova University:
1. Every great leader is born already possessing certain traits that will enable them to rise and lead on instinct.
2. The need for them has to be great for these traits to then arise, allowing them to lead.
This theory, and history, claims these great leaders as heroes that were able to rise against the odds to defeat rivals while inspiring followers along the way. Theorists say that these leaders were then born with a specific set of traits and attributes that make them ideal candidates for leadership and roles of authority and power. This theory relies then heavily on born rather than made, nature rather than nurture and cultivates the idea that those in power deserve to lead and shouldn\'t be questioned because they have the unique traits that make them suited for the position.
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# Great man theory
## Responses
thumb\|upright=.7\|Herbert Spencer was a contemporary critic of Carlyle\'s great man theory.
### Herbert Spencer\'s critique {#herbert_spencers_critique}
One of the most forceful critics of Carlyle\'s formulation of the great man theory was Herbert Spencer, who believed that attributing historical events to the decisions of individuals was an unscientific position. He believed that the men Carlyle supposed \"great men\" are merely products of their social environment:
### William James\' defence {#william_james_defence}
William James, in his 1880 lecture \"Great Men, Great Thoughts, and the Environment\", published in the *Atlantic Monthly*, forcefully defended Carlyle and refuted Spencer, condemning what James viewed as an \"impudent\", \"vague\", and \"dogmatic\" argument. thumb\|upright=.7\|William James was a 19th-century philosopher and psychologist.\|left
James\' defence of the great man theory can be summarized as follows: The unique physiological nature of the individual is the deciding factor in making the great man, who, in turn, is the deciding factor in changing his environment in a unique way, without which the new environment would not have come to be, wherein the extent and nature of this change is also dependent on the reception of the environment to this new stimulus. To begin his argument, he first sardonically claims that these inherent physiological qualities have as much to do with \"social, political, geographical \[and\] anthropological conditions\" as the \"conditions of the crater of Vesuvius has to do with the flickering of this gas by which I write\".
James argues that genetic anomalies in the brains of these *great men* are the decisive factor by introducing an original influence into their environment. They might therefore offer original ideas, discoveries, inventions and perspectives which \"would not, in the mind of another individual, have engendered just that conclusion \... It flashes out of one brain, and no other, because the instability of that brain is such as to tip and upset itself in just that particular direction.\"
James then argues that these spontaneous variations of genius, i.e. the *great men*, which are causally independent of their social environment, subsequently influence that environment which in turn will either preserve or destroy the newly encountered variations in a form of evolutionary selection. If the great man is preserved then the environment is changed by his influence in \"an entirely original and peculiar way. He acts as a ferment, and changes its constitution, just as the advent of a new zoological species changes the faunal and floral equilibrium of the region in which it appears.\" Each ferment, each great man, exerts a new influence on their environment which is either embraced or rejected and if embraced will in turn shape the crucible for the selection process of future geniuses.
In the words of William James, \"If we were to remove these geniuses or alter their idiosyncrasies, what increasing uniformities would the environment exhibit?\" James challenges Mr. Spencer or anyone else to provide a reply. According to James, there are two distinct factors driving social evolution: personal agents and the impact of their unique qualities on the overall course of events.
He thus concludes: \"Both factors are essential to change. The community stagnates without the impulse of the individual. The impulse dies away without the sympathy of the community.\"
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# Great man theory
## Responses
### Other responses {#other_responses}
Before the 19th century, Blaise Pascal begins his *Three Discourses on the Condition of the Great* (written it seems for a young duke) by telling the story of a castaway on an island whose inhabitants take him for their missing king. He defends in his parable of the shipwrecked king, that the legitimacy of the greatness of *great men* is fundamentally custom and chance. A coincidence that gives birth to him in the right place with noble parents and arbitrary custom deciding, for example, on an unequal distribution of wealth in favor of the nobles.
Leo Tolstoy\'s *War and Peace* features criticism of great-man theories as a recurring theme in the philosophical digressions. According to Tolstoy, the significance of great individuals is imaginary; as a matter of fact they are only \"history\'s slaves,\" realizing the decree of Providence.
Jacob Burckhardt affirmed the historical existence of great men in politics, even excusing the rarity among them to possess \"greatness of soul\", or magnanimity: \"Contemporaries believe that if people will only mind their own business political morality will improve of itself and history will be purged of the crimes of the \'great men.\' These optimists forget that the common people too are greedy and envious and when resisted tend to turn to collective violence.\" Burckhardt predicted that the belittling of great men would lead to a lowering of standards and rise in mediocrity generally.
Mark Twain suggests in his essay \"The United States of Lyncherdom\" that \"moral cowardice\" is \"the commanding feature of the make-up of 9,999 men in the 10,000\" and that \"from the beginning of the world no revolt against a public infamy or oppression has ever been begun but by the one daring man in the 10,000, the rest timidly waiting, and slowly and reluctantly joining, under the influence of that man and his fellows from the other ten thousands.\"
In 1926, William Fielding Ogburn noted that Great Men history was being challenged by newer interpretations that focused on wider social forces. While not seeking to deny that individuals could have a role or show exceptional qualities, he saw Great Men as inevitable products of productive cultures. He noted for example that if Isaac Newton had not lived, calculus would have still been discovered by Gottfried Leibniz, and suspected that if neither man had lived, it would have been discovered by someone else. Among modern critics of the theory, Sidney Hook is supportive of the idea; he gives credit to those who shape events through their actions, and his book *The Hero in History* is devoted to the role of the hero and in history and influence of the outstanding persons.
In the introduction to a new edition of *Heroes and Hero-Worship*, David R. Sorensen notes the modern decline in support for Carlyle\'s theory in particular but also for \"heroic distinction\" in general. He cites Robert K. Faulkner as an exception, a proponent of Aristotelian magnanimity who in his book *The Case for Greatness: Honorable Ambition and Its Critics*, criticizes the political bias in discussions on greatness and heroism, stating: \"the new liberalism's antipathy to superior statesmen and to human excellence is peculiarly zealous, parochial, and antiphilosophic.\"
Ian Kershaw wrote in 1998 that \"The figure of Hitler, whose personal attributes -- distinguished from his political aura and impact -- were scarcely noble, elevating or enriching, posed self-evident problems for such a tradition.\" Some historians like Joachim Fest responded by arguing that Hitler had a \"negative greatness\". By contrast, Kershaw rejects the Great Men theory and argues that it is more important to study wider political and social factors to explain the history of Nazi Germany. Kershaw argues that Hitler was an unremarkable person, but his importance came from how people viewed him, an example of Max Weber\'s concept of charismatic leadership
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# GURPS
The ***Generic Universal Role Playing System**\'\', or***GURPS**\'\', is a tabletop role-playing game system published by Steve Jackson Games. The system is designed to run any genre using the same core mechanics. The core rules were first written by Steve Jackson and published in 1986, at a time when most such systems were story- or genre-specific. Since then, four editions have been published. The current line editor is Sean Punch.
Sessions are run by a game master (GM), who controls the world and adjudicates the rules, with any number of players controlling the actions of a character. Most actions are resolved by rolling three six-sided dice (3d6), trying to roll below a certain number, usually a skill. GURPS uses a point-based character creation system; characters are represented by four basic stats (Strength, Dexterity, IQ and Health), and players can buy any number of advantages, disadvantages, perks, quirks and skills.
GURPS consists of a GURPS Basic Set, which contains the core rules required to run most games. In addition, more than a hundred supplemental books provide optional rules and details about different settings and genres (GURPS Martial Arts, for example). By adapting the various optional rules and systems, GURPS can be run with as much or as little detail as required, and can accommodate virtually any genre, character or style of play.
*GURPS* won the Origins Award for *Best Roleplaying Rules of 1988*, and in 2000 it was inducted into the Origins Hall of Fame. Many of its expansions have also won awards.
## Precursors
Prior to *GURPS*, most roleplaying games (RPGs) of the 1970s and early 1980s were developed especially for certain gaming environments, and they were largely incompatible with one another. For example, TSR published its *Dungeons & Dragons* game specifically for a fantasy environment. Another game from the same company, *Star Frontiers*, was developed for science fiction--based role-playing. TSR produced other games for other environments, such as *Gamma World* (post-apocalyptic adventures), *Top Secret* (spies and secret agents), *Gangbusters* (Roaring Twenties adventures), and *Boot Hill* (American Old West). Each of these games was set with its own self-contained rules system, and the rules for playing each game differed greatly from one game to the next. Attempts were made in *Advanced Dungeons and Dragons* to allow cross-genre games using *Gamma World* and *Boot Hill* rules; however, characters could only be used in a new genre by converting their statistics. Although GURPS was preceded by *Basic Role-Playing* (Chaosium, 1980) and the Hero System (Hero Games, a system that expanded to multiple genres starting in 1982), *GURPS* was the most commercially successful generic role-playing game system to allow players to role-play in any environment they please while still using the same set of core rules. This flexibility of environment is greatly aided by the use of technology levels (or \"tech-levels\") that allow a campaign to be set from the Stone Age (TL-0) to the Digital Age (TL-8) or beyond.
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# GURPS
## Development and publication {#development_and_publication}
The immediate mechanical antecedents of *GURPS* were Steve Jackson\'s microgames *Melee* and *Wizard*, both published by Metagaming Concepts, which eventually combined them along with another Jackson game, *In the Labyrinth*, to form *The Fantasy Trip* (*TFT*), an early role-playing game. Several of the core concepts of *GURPS* first appeared in *TFT*, including the inclusion of Strength, Dexterity and Intelligence as the core abilities scores of each character.
By April 1984, the core rules for *GURPS* (at that point referred to as the \"Great Unnamed Universal Role-Playing System\") was being playtested in preparation for a GURPS question-and-answer seminar at Origins 1984 in Dallas. The combat system for GURPS was published in 1985 as *Man to Man: Fantasy Combat from GURPS* to meet the deadline for Origins 1985 and was followed up later that year by the adventure supplement *Orcslayer*.thumb\|upright\|*GURPS* first edition box set
The *Basic GURPS* set was published in 1986 and 1987 and included two booklets, one for developing characters and one for Adventuring.
In 1990 *GURPS* intersected part of the hacker subculture when the company\'s Austin, Texas, offices were raided by the Secret Service. The target was the author of *GURPS Cyberpunk* in relation to E911 Emergency Response system documents stolen from Bell South. The incident was a direct contributor to the founding of the Electronic Frontier Foundation. A common misconception holds that this raid was part of Operation Sundevil and carried out by the FBI. Operation: Sundevil was in action at the same time, but it was completely separate. See *Steve Jackson Games, Inc. v. United States Secret Service*.
The 1995 supplement *GURPS Illuminati University* introduced Agatha Heterodyne, the character who would go on to star in the popular comic series *Girl Genius* in 2001.
A free PDF version of the *GURPS* rules was released in 1998 as *GURPS Lite*. This limited ruleset was also included with various books such as *GURPS Discworld* and *Transhuman Space*.
Steve Jackson Games released *GURPS Fourth Edition* at the first day of Gen Con on August 19, 2004. It promised to simplify and streamline most areas of play and character creation. The changes include modification of the attribute point adjustments, an edited and rationalized skill list, clarification of the differences between abilities from experience and from inborn talent, more detailed language rules, and revised technology levels. Designed by Sean Punch, the Fourth Edition is sold as two full-color hardcover books as well as in the PDF format.
## Concept
Role-playing games of the 1970s and 1980s, such as *Dungeons & Dragons*, generally used random numbers generated by dice rolls to assign statistics to player characters. In 1978, Jackson designed a new character generation system for the microgames *Melee* and *Wizard* that used a point-buy system: players are given a fixed number of points with which to buy abilities. (The Hero System first used by the *Champions* role-playing game published two years later also used a point-buy system.)
*GURPS*\'s emphasis on its generic aspect has proven to be a successful marketing tactic, as many game series have source engines which can be retrofitted to many styles. Its approach to versatility includes using real world measurements wherever possible (\"reality-checking\" is an important part of any *GURPS* book).
*GURPS* also benefits from the many dozens of worldbooks describing settings or additional rules in all genres including science fiction, fantasy, and historical. Many game designers began their professional careers as *GURPS* writers, including C. J. Carella, Robin Laws, S. John Ross, and Steffan O\'Sullivan.
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# GURPS
## Mechanics of the game {#mechanics_of_the_game}
### Character points {#character_points}
A character in *GURPS* is built with character points. For a beginning character in an average power game, the 4th edition suggests 100--150 points to modify attribute stats, select advantages and disadvantages, and purchase levels in skills. Normal NPCs are built on 25--50 points. Full-fledged heroes usually have 150--250 points, while superheroes are commonly built with 400--800 points. The highest point value recorded for a canon character in a *GURPS* sourcebook is 10,452 for the Harvester (p. 88) in *GURPS Monsters*.
In principle, a Game Master can balance the power of foes to the abilities of the player characters by comparing their relative point values.
### Attributes
Characters in *GURPS* have four basic attributes:
- **Strength (ST)**: A measure of the character\'s physical power and bulk, ability to lift, carry, and do damage
- **Dexterity (DX)**: A measure of the character\'s physical agility, coordination, and manual dexterity
- **Intelligence (IQ)**: A measure of the character\'s mental capacity, acuity and sense of the world
- **Health (HT)**: A measure of the character\'s physical stamina, recovery speed, energy and vitality, ability to resist disease
Each attribute has a number rating assigned to it. Normally they begin at 10, representing typical human ability, but can go as low as 1 for nearly useless, to 20 (or higher) for superhuman power. Anything in the 8 to 12 range is considered to be in the *normal* or *average* area for humans. Basic attribute scores of 6 or less are considered *crippling*---they are so far below the human norm that they are only used for severely handicapped characters. Scores of 15 or more are described as *amazing*---they are immediately apparent and draw constant comment.
Players assign these ratings spending character points. The higher the rating the more points it will cost the player, however, assigning a score below the average 10 gives the player points back to assign elsewhere. Since almost all skills are based on Dexterity or Intelligence, those attributes are twice as expensive (or yield twice the points, if purchased below 10). In earlier editions (pre--4th Edition) all attributes followed the same cost-progression, where higher attributes cost more per increase than attributes close to the average of 10.
Attribute scores also determine several *secondary characteristics*. The four major ones are each directly based on a single attribute:
- **Hit Points (HP)**: how much damage and injury can be sustained, based on *ST* in 4e. In previous editions it was based on HT.
- **Will (Will)**: mental focus and strength, withstanding stress, based on *IQ*.
- **Perception (Per)**: general sensory alertness, based on *IQ*.
- **Fatigue Points (FP)**: a measure of exertion, tiredness, and hunger, based on *HT* in 4e. In previous editions it was based on ST.
The other secondary characteristics (Damage , Basic Lift , Basic Speed, Dodge, Move ) are calculated from one or more attribute values using individual tables or formulae.
### Character advantages and disadvantages {#character_advantages_and_disadvantages}
*GURPS* has a profusion of advantages and disadvantages which enable players or Game Masters to customize their characters. The myriad options available and the rewards the system provides players for carefully creating their characters are attractive to gamers who enjoy a high degree of flexibility in character design.
A player can select numerous Advantages and Disadvantages to differentiate the character; the system supports both mundane traits (such as above-average or below-average Wealth, Status and Reputation) as well as more exotic special abilities and weaknesses. These are categorized as physical, mental or social, and as exotic, supernatural, or mundane. Advantages benefit the character and cost points to purchase. Selecting Disadvantages returns character points and allows players to limit their characters in one way in exchange for being more powerful or gifted in other areas. Disadvantages include such positive attributes as honesty and truthfulness which limit the way a character is played. There are also many Perks and Quirks to choose from which give a character some personality. Perks (minor Advantages) and Quirks (minor Disadvantages) benefit or hinder the character a bit, but they mostly add role-playing flavor.
Enhancements and limitations can tailor an advantage or disadvantage to suit creative players. These modify the effects and point cost of advantages and disadvantages. For example, to create a \"dragon\'s breath\" attack, a player would select the Innate Attack ability (the ability that allows a player to perform an attack most humans could not), and select burning attack 4D (normally 20 points). Then, the player would modify it as follows: cone, 5 yards (+100%); limited use, 3/day (-20%); reduced range, x1/5 (-20%). The final percentage modifier would be +60%, making the final cost 32 points. This addition to the system greatly increases its flexibility while decreasing the number of specific advantages and disadvantages that must be listed. Finally, *mitigators* can themselves tailor advantages and disadvantages (see *GURPS Bio-Tech* for such an example).
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# GURPS
## Mechanics of the game {#mechanics_of_the_game}
### Skills
*GURPS* has a wide variety of skills intended to enable it to support any conceivable genre (such as Acrobatics and Vehicle Piloting). Each skill is tied to at least one attribute, and the characters\' abilities in that skill is a function of their base attributes + or - a certain amount.
The availability of skills depends on the particular genre in which the *GURPS* game is played. For instance, in a generic medieval fantasy setting, skills for operating a computer or flying a fighter jet would not normally be available. Skills are rated by level, and the more levels purchased with character points, the better the characters are at that particular skill relative to their base attribute.
Skills are categorized by difficulty: Easy, Average, Hard, and Very Hard. Easy skills cost few points to purchase levels in, and the cost per skill level increases with each level of difficulty. Game mechanics allow that eventually it may be less expensive to raise the level of the base attribute the skills depend on as opposed to purchasing higher levels of skills. Players can generally purchase a skill for their characters at any level they can afford. The lower a player chooses, the fewer points it costs to buy the skill, while higher levels cost more points. Some skills have default levels, which indicate the level rating a character has when using that skill untrained (i.e. not purchased). For example, a character with a Dexterity of 12, is using the Climbing skill untrained. Climbing has a default of DX-5 or ST-5, which means that using the skill untrained gives him a Climbing skill level of 7 (12--5) if he tied it to the Dexterity stat. If the character had a higher Strength stat, he could have a better chance of success if he tied the Climbing skill there instead.
Some skills also have a Tech Level (TL) rating attached to them, to differentiate between Skills that concern similar concepts, but whose tasks are accomplished in different ways when used with differing levels of technology. This helps during time traveling scenarios, or when characters are forced to deal with particularly outdated or advanced equipment. For instance, a modern boat builder\'s skills will be of less use if he is stuck on a desert island and forced to work with primitive tools and techniques. Thus, the skills he uses are different when in his shop (Shipbuilding/TL8) and when he is on the island (Shipbuilding/TL0).
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# GURPS
## Mechanics of the game {#mechanics_of_the_game}
### Success rolls {#success_rolls}
*GURPS* uses six-sided dice for all game mechanics using standard dice notation. An \"average roll\" of three six sided dice generates a total of 10.5; this makes an \"average\" skill check (a skill of 10, based on an unmodified attribute) equally likely to succeed or fail.
Making statistic and skill checks in *GURPS* is the reverse of the mechanics of most other RPGs, where the higher the total of the die roll, the better. *GURPS* players hope to roll as low as possible under the tested statistic\'s rating or skill\'s level. If the roll is less than or equal to that number, the check succeeds. There is no \"target number\" or \"difficulty rating\" set by the Game Master, as would be the case in many other RPG systems. Instead the GM will apply various modifiers to add or subtract to the skill level. In this way, positive modifiers increase the chance for success by adding to the stat or skill level the player must roll under while negative modifiers deduct from it, making things more difficult.
For example: a player makes a pick pocketing test for her character. The character has a Pickpocket skill with a level of 11. Under normal circumstances - i.e., under an *average stressful situation*, according to the manual - the player must roll an 11 or less for the character to succeed. If the player rolls above 11, then the character has failed the attempt at pick pocketing.
There are some exceptions for very high or low rolls, deemed criticals. No matter the level of the skill, a die roll of 18 is always a *critical failure*, and a roll of 3 or 4 is always a critical success (a roll of 17 is a critical failure as well, unless the character relevant skill level is 16 or more). The Game Master may decide in such cases that, in first case (a roll of 18, or 10+ over the modified skill level), the character has failed miserably and caused something disastrous to happen or, in the other case, that he or she succeeds incredibly well and gains some benefit as a result.
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# GURPS
## Mechanics of the game {#mechanics_of_the_game}
### Combat
Combat in *GURPS* is organized in personal turns: i.e., every character gets a turn each second, and during a character\'s turn he or she may take an action, such as attack or move. After all characters have taken their action, one second has elapsed. Free actions are simple actions that can be done at any time. Characters in a party have a set initiative that is entirely based upon their Basic Speed characteristic.
There are two kinds of attacks: Melee (possibly with hand-to-hand weapons, or unarmed combat) and Ranged (bows, guns, thrown weapons, some Innate Attacks, etc.). Attacks made by a character are checked against their skill with the particular weapon they carry. For instance, if a character is using a pistol, as with any other skill, it is beneficial to have a high level in the Guns skill. Like any other skill check, a player must roll equal to or less than the level of the skill to succeed. Failure means a miss, success scores a hit. Similarly, critical hits mean that the blow might inflict significantly more damage to its target; critical misses may lead to a rather unpleasant and unexpected event (such as dropping the weapon or hitting the wrong target). Attack modifiers are set by the GM when factoring in things like distance, speed and cover that make a successful strike more difficult.
After a successful attack, except in the case of a critical hit, the defender usually gets a chance to avoid the blow. This is called an Active Defense, and takes the form of a Dodge (deliberate movement out of the perceived path of the attack), Parry (attempt to deflect or intercept the attack with a limb or weapon), or Block (effort to interpose a shield or similar object between the attack and the defender\'s body). Unlike many RPG systems, an Active Defense is an unopposed check, meaning that in most cases, the success of an attack has no effect on the difficulty of the defense. Dodge is based on the Basic Speed characteristic, while Parry and Block are each based on individual combat skills, such as Fencing, Karate, or Staff for Parry, and Shield or Cloak for Block. A common criticism is that characters can achieve a relatively high Active Defense value, drawing out fights considerably. The only mechanic within the system to address this is the Feint action, which if successful will place the adversary in an unfavorable position, reducing their active defense against that character only, on the subsequent turn.
Skills, advantages, and equipment, can be combined to great effect. For example, a gunslinger from the Old West is facing a foe:
- the Combat Reflexes advantage gives a +1 on Fast-Draw attempts and prevents the gunslinger from being stunned into inaction during a surprise attack;
- a successful Fast-Draw(Pistol) skill roll grants the results of the Ready maneuver instantly;
- the Gunslinger advantage grants the character the benefits of the Aim maneuver instantly;
- the Dual-Weapon Attack(Pistol) technique allows the gunslinger to fire both his guns at once without the -4 penalties.
- the Ambidextrous advantage or the Off-Hand Weapon Training Technique eliminates the -4 penalty for the weapon in the \"off\" hand.
If the gunslinger lacked these advantages, skills, and techniques, then readying, aiming, firing, aiming again, and firing again would take at least 5 seconds. If the gunslinger lacked these traits and tried to shoot two pistols at once:
- it would take 1 second to ready the pistols
- the right hand pistol would be fired with a -4 penalty
- the \"off\" hand pistol would be fired with a -8 penalty
- both attacks would lack the accuracy bonus from the aiming maneuver.
### Damage and defenses {#damage_and_defenses}
Damage from muscle-powered weapons, (clubs, swords, bows, etc.) is calculated based on the character\'s ST rating. The weaker a character is physically, the less damage he or she is capable of inflicting with such a weapon. Purely mechanical weapons (guns, beam sabers, bombs, etc.) have a set damage value.
When damage is inflicted upon characters, it is deducted from their Hit Points, which are calculated with the Strength stat (prior to *GURPS* 4th Edition, Hit Points were derived from the Health stat). Like most other RPGs, a loss of hit points indicates physical harm being inflicted upon a character, which can potentially lead to death. *GURPS* calculates shock penalties when someone is hit, representing the impact it causes and the rush of pain that interferes with concentration. Different weapons can cause different \'types\' of damage, ranging from crushing (a club or mace), impaling (a spear or arrow), cutting (most swords and axes), piercing (bullets), and so on.
One peculiarity about loss of Hit Points is that in GURPS, death is not certain. While a very high amount of total HP loss will cause certain death, there are also several points at which a player must successfully roll HT, with different grades of failure indicating character death or a mortal injury.
Depending on the nature of the attack, there will sometimes be additional effects.
### Advancement
Character advancement follows the same system as character creation. Characters are awarded character points to improve themselves at regular intervals (usually at the end of a game session or story).
GMs are free to distribute experience as they see fit. This contrasts with some traditional RPGs where players receive a predictable amount of experience for defeating foes. The book recommends providing 1-3 points for completing objectives and 1-3 points for good role-playing per game session.
Advancement can also come through study, work, or other activities, either during game play or between sessions. In general, 200 hours of study equals one character point which can be applied for the area being studied. Self-study and on the job experience take more time per character point while high tech teaching aids can reduce the time required.
Some intensive situations let a character advance quickly, as most waking hours are considered study. For instance, characters travelling through the Amazon may count every waking moment as study of jungle survival, while living in a foreign country could count as eight hours per day of language study or more.
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# GURPS
## Licensed works {#licensed_works}
The computer game publisher Interplay licensed *GURPS* as the basis for a post--nuclear war role-playing video game (*Fallout*) in 1995. Late in development, Interplay replaced the *GURPS* character-building system with their own SPECIAL System. Brian Fargo, one of the executive producers of *Fallout*, stated during an interview that Interplay dropped out of the licensing deal, following fundamental disagreements on the game\'s content. \"\[Jackson\] was offended by the nature of the content and where it was going. \... He saw \[the opening cinematic\], and he just wouldn\'t approve it.\" Jackson said \"I made a lot of concessions because I want to save the project\" and that he felt \"all the original problems could be resolved\".
*GURPS for Dummies* (`{{ISBN|0-471-78329-3}}`{=mediawiki}), a guidebook by Stuart J. Stuple, Bjoern-Erik Hartsfvang, and Adam Griffith, was published in 2006.
## Reception
Marcus L. Rowland reviewed *GURPS* in 1986 for *White Dwarf* #83, and stated that \"While I can applaud the idea behind the system, I can\'t really recommend *GURPS* at its present stage of development. In the long run, *GURPS* and all its supplements may cover more ground than other systems, possibly at less expense, but in the short term there isn\'t enough support material to run a fully rounded game of any type, apart from gladiatorial combat and medieval adventures.\"
*The Games Machine* reviewed *GURPS* and stated that \"If the idea of a generic system appeals, or you want a straightforward set of rules with which to run adventures in a setting of your own making, *GURPS* is worth a look.\"
In his 1990 book *The Complete Guide to Role-Playing Games*, game critic Rick Swan called *GURPS* \"an ambitious design by Steve Jackson that attempts to cover every imaginable genre, setting and character type in the same game. That it achieves this goal at all is impressive; that it does so with imagination, elegance, and innovation is stunning.\" Swan liked the \"slick mechanics\", and called the game \"a model of organization and presentation.\" Swan concluded by giving this game a top rating of 4 out of 4, saying, \"Though it\'s amazing that a game so all-encompassing is this smooth, it\'s not intended for beginners. Experienced players, however, owe it to themselves to investigate this landmark design --- it\'s possible *GURPS* may be the only RPG they\'ll ever need.\"
In a 1996 reader poll conducted by the British games magazine *Arcane* to determine the fifty most popular role-playing games, *GURPS* was ranked 14th. Editor Paul Pettengale commented: \"Based around a points system and six-sided dice, *GURPS* succeeds better than most \'generic\' games. The rules are flexible and it\'s well supported -- regardless of what you want to do with it, you\'ll probably find a supplement with some advice and background. The game suffers from being a little too detailed at times, and can get bogged down in numbers. Still, it\'s an adaptable system with some superb supplements.\"
Scott Taylor for *Black Gate* in 2013 rated *GURPS* as #5 in the top ten role-playing games of all time, saying \"*GURPS* is a very cool idea, especially considering it was created during a time of very hard adherence to finding a genre to fill and making a game that holds fast within it. The ability of *GURPS* to allow players to play in any setting with the same set of core rules captured the minds and wallets of many gaming fans during the late 1980s and is still popular today
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# George Whipple
**George Hoyt Whipple** (August 28, 1878 -- February 1, 1976) was an American physician, pathologist, biomedical researcher, and medical school educator and administrator. Whipple shared the Nobel Prize in Physiology or Medicine in 1934 with George Richards Minot and William Parry Murphy \"for their discoveries concerning liver therapy in cases of anemia\". This makes Whipple the first of several Nobel laureates affiliated with the University of Rochester.
## Early life {#early_life}
Whipple was born to Ashley Cooper Whipple and Frances Anna Hoyt in Ashland, New Hampshire. Ashley Cooper Whipple was a physician, and his father (George\'s paternal grandfather) was a physician and President of the New Hampshire Medical Society. Whipple\'s father died from pneumonia or typhoid fever when George was just shy of two years old. His maternal grandfather also died when Whipple was two years old, and his paternal grandfather died a year later. This left Whipple to be raised by his mother, Frances, and grandmother, Frances Moody Hoyt, who impressed on him the value of hard work and education.
Whipple attended Andover prep school and began attending Yale University as an undergraduate in 1896, earning A.B. degree in 1900. During these years, he developed as an outdoorsman, an affinity he would hold lifelong. He wrote in his autobiography about growing up in a lake district, \"I feel very fortunate that I grew up in the country\...I became interested in wild life and camping, also hiking, snowshoeing, skating, bob sledding, canoeing, fishing, hunting---all this was an essential part of my life\". He even credited his love for the outdoors as a contributor to his successes in work, study, and teaching. In the summers of prep school and undergrad, he worked at a drugstore and at Squam Lake and Lake Winnipesaukee in New Hampshire providing help and ferry services to the tourists and campers. Of his summer experiences, Whipple said, \"I sometimes think I learned as much during the summer work periods as during the school terms.\"
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# George Whipple
## Education
As an undergraduate, he became a member of Beta Theta Pi fraternity, and proved to be a prize-winning gymnast, oarsman, and an outstanding science student. His excellence in science was exemplified by his election to Sigma Xi honor society and graduation with senior honors. The interactions Whipple had with biochemists Russell Henry Chittenden and Lafayette Mendel during his senior year at Yale left an indelible mark on his life and career. In his autobiography, Whipple describes Mendel as \"an unusual man who exerted a strong influence on me \... work with him was exciting and never to be forgotten\".
With a shortage of funds to finance further education, Whipple took a year off after graduating Yale. During this year, he worked at Dr. Holbrook Military School in Ossining, New York, teaching mathematics and science, and serving as an athletic coach.
In 1901, under the advice, persuasion, and guidance of his mother, Whipple attended medical school at Johns Hopkins School of Medicine. He received his M.D. degree in 1905. To gain experience and subsidize his medical school studies, Whipple applied for and was accepted to a teaching assistantship in John J. Abel\'s Department of Physiological Chemistry. Later, his performance in his first year anatomy course earned him a second-year appointment as a student instructor in anatomy. During this time, his interest in histology developed. Under the mentorship of William Welch, Eugene Opie, and William McCallum, Whipple was inspired to correlate clinical illness and disease, to the tissue findings discovered on autopsy. Together, McCallum and Welch conspired to offer Whipple a position as junior member of the pathology department with the hope it would lead to Whipple become a pediatric pathologist. Ultimately, Whipple accepted the position which shaped his career aspirations to become a pathologist.
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# George Whipple
## Career
In 1905, Whipple joined the pathology department at Johns Hopkins School of Medicine as an assistant in pathology. He was promoted successively to Assistant, Instructor, Associate and associate professor in pathology until he left in 1914. During this time, he spent a year in Panama at Ancon Hospital as a pathologist. In Panama, he worked with Samuel Darling, a resident pathologist, and General Gorgas to gain experience in tropical diseases. This experience afforded him the opportunity to study massive hemolysis associated with blackwater fever. Before returning to Johns Hopkins School of Medicine after his time in Panama, Whipple traveled to Europe and spent time in the laboratories of Krehl and Morawitz in Heidelberg, where he learned about anemia in rabbits. In 1911, Whipple went to Vienna to study hepatic portal vein blood flow and its effects on hepatic functions in the dog with Hans Meyer.
In 1914, at 34 years old, Whipple married Katherine Ball Waring of Charleston, South Carolina. They had two children. He was also appointed Professor of Research Medicine, and Director of the Hooper Foundation for Medical Research at the University of California San Francisco medical school. He was dean of that medical school in 1920 and 1921.
In 1921, through the persistence of University of Rochester President Benjamin Rush Rhees, Whipple agreed to become a Professor and Chairman of Pathology, and the founding Dean of the yet-to-be-built medical school (URMC). Rhees was so determined to recruit Whipple, he personally flew to UC San Francisco to offer him the opportunity to build the medical school from the ground up. Whipple found this offer attractive because it would fulfil his passion to create a program which fostered an exchange between clinical and preclinical disciplines. His vision for the school included housing the medical school and hospital at the same site to facilitate this exchange. The first students entered URMC in 1925.
Whipple categorically discriminated against African-American students during his time as dean, and would send a form letter to applicants rejecting their admission and requesting they apply elsewhere. In 1939, A commission of the New York State Legislature found this practice to be in violation of New York\'s anti-discrimination laws, after which the URMC began to admit African-American medical students.
## Retirement
In 1953, at 75 years old, Whipple retired from the Deanship, and retirement from the university would follow in 1955. He was remembered as a superb teacher. In his autobiography, *A Dozen Doctors*, Whipple wrote, \"I would be remembered as a teacher\". He spent his retirement years dabbling in pathology department and medical school activities at the University of Rochester, but returned to his outdoors-man roots, filling his time with pheasant hunting, salmon fishing on the Margaree River, and tarpon fishing off the coast in Florida.
Whipple died in 1976 at the age of 97 and his ashes were scattered in Rochester\'s Mount Hope Cemetery.
Though he was not related to Allen Whipple, who described the Whipple procedure and Whipple\'s triad, the two were lifelong friends. The Whipples also had a deep friendship with George Eastman, founder of Rochester-based Eastman Kodak.
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# George Whipple
## Whipple\'s research {#whipples_research}
Over the course of his career, Whipple authored or co-authored more than 300 publications.
Whipple\'s research interests during his career primarily included anemia and the physiology and pathology of the liver. But he also researched and made significant contributions to tuberculosis, pancreatitis, chloroform poisoning in animals, the metabolism of bile pigments and iron, the constituents of the bile, and the regeneration of plasma protein, protein metabolism, and the stroma of the red blood cells.
One of his first publications described the role of the lungs, lymphatic system, and gastrointestinal tract in the spread of tubercle bacillus causing tuberculosis. Another one of his early publications described autopsy results from a patient with an accumulation of fatty acids in the walls of the small intestine and lymph nodes. He named this abnormality lipodystrophia intestinalis (intestinal lipodystrophy), and correctly pointed to the bacterial cause of the lipid deposits, resulting in the disease being named Whipple\'s disease.
When Whipple first joined Johns Hopkins School of Medicine as an assistant, he worked under William H. Welch, focusing on the repair and regeneration of liver cells. His research in dogs demonstrated that liver cells had an almost unlimited ability to regenerate. Through his chloroform liver injury studies, Whipple demonstrated that the liver was the site of fibrinogen synthesis. His research elucidated the route by which bile pigments enter circulation and produce jaundice in various parts of the body.
Later, he studied bile pigments and their production outside the liver by way of bile fistulas at the Hooper Foundation at UC San Francisco. His interests soon extended to understanding the production of hemoglobin to gain a better understand of how it is metabolized into bile pigments. Co-authored with Hooper, Whipple published 12 papers, from 1915 to 1917, reporting the following:
- Bile pigment bilirubin was a breakdown product of muscle hemoglobin, though red blood cell hemoglobin was the major normal source.
- Bile pigment was not reabsorbed and reused in the production of new red blood cells.
- The heme moiety of hemoglobin could be converted to bilirubin in both the pleural and peritoneal cavities, in addition to the liver.
- Normal liver function was essential for the excretion of bilirubin.
- The curve of red blood cell regeneration in anemia, as influenced by dietary factors, like sugar, amino acids and starvation.
At the University of Rochester, Whipple\'s research focus became studying the various factors in diets which contributed to recovery of long-term anemia, particularly in anemic dogs. Along with his research assistant, Frieda Robscheit-Robbins (formally Frieda Robbins), they co-authored 21 publications, from 1925 to 1930, reporting the following:
- Circulating plasma and hemoglobin volumes
- The effects of dietary and other factors on bile salt production and secretion
- Measurements of blood fibrinogen
- The effects of diet, hemorrhage, liver injury, and other factors on plasma fibrinogen levels
- Blood regeneration following simple anemia
Whipple and Robscheit-Robbins were regarded as having one of the \"great creative partnerships in medicine\".
In his landmark studies, published as a series \"Blood Regeneration in Severe Anemia\" beginning in 1925, Whipple demonstrated that raw liver fed to anemic dogs was the most effective diet additive for reversing the anemia by boosting the production of red blood cells. He would go on to show that foods derived from animal tissue, and cooked apricots also had a positive effect of increasing red blood cells during anemia. Based on these data, Whipple associated the iron content in these dietary factors to the potency of red blood cell regeneration. This data led directly to successful liver treatment of pernicious anemia by George R. Minot and William P. Murphy, despite the main therapeutic mechanism being through B12 rather than iron. This was a remarkable discovery since previously, pernicious anemia was invariably fatal at a young age. For his contribution to this body of work, he was jointly awarded the Nobel Prize in physiology or medicine in 1934 along with Minot and Murphy.
In 1937, Whipple collaborated with William B. Hawkins to determine the life-span of the red blood cell in dogs. Simultaneously, with the advent of radioactive iron, Whipple, Paul F. Hahn, and William F. Bale collaborated to study iron absorption and utilization. They demonstrated that iron absorption was highly regulated in the small intestine and was influenced by the amount of iron stores in the body. They also demonstrated that insignificant amounts of iron were normally excreted or lost in the urine, feces, or bile. During this time, Whipple also formulated his theory on \"the dynamic equilibrium between blood and tissue proteins\" based on earlier plasmapheresis experiments he had performed (in the early 1930s) which demonstrated the importance of dietary protein on production of plasma proteins. This formed the foundation of research into mammalian protein metabolism, and led Rudolf Schoenheimer to write *The Dynamic State of the Body Constituents,* marking the modern era of biochemistry and biology.
Between 1939 and 1943 Leon L. Miller and Whipple collaborated to study the hepato-toxic effects of chloroform anesthesia on dogs. They found that dogs in a protein depleted state sustained lethal liver injury from within anesthesia fifteen minutes; but that feeding these depleted dogs a protein rich meal, particularly rich in L-methionine or L-cystine, prior to anesthesia was protective. This and other studies, led Whipple to the conclusion that S-containing amino acids are protective against liver against toxic agents.
During World War II, Whipple tested combinations of dietary amino acids, administered, orally or parenterally, and their effects on plasma protein synthesis. He was able to characterize amino acid mixtures that could satisfy the metabolic requirements necessary to maintain weight, nitrogen balance, and plasma protein and hemoglobin regeneration in the dog. This would ultimately led to human clinical trials which demonstrated that these amino acid mixtures, along with enzymatic digest of casein, could sustain nourishment in patients who could not intake nutrients through the normal gastrointestinal route for extended periods. Intravenous nutrition, referred to as parenteral nutrition, is routinely used today.
## Nobel Prize, honors and distinctions {#nobel_prize_honors_and_distinctions}
Whipple shared the Nobel Prize in Physiology or Medicine in 1934 with George R. Minot and William P. Murphy \"for their discoveries concerning liver therapy in cases of anemia\".
In presenting the Nobel Prize, Professor I. Holmgren of the Nobel committee observed that \"Of the three prize winners, it was Whipple who first occupied himself with the investigations for which the prize is now awarded. \... Whipple\'s experiments were planned exceedingly well, and carried out very accurately, and consequently their results can lay claim to absolute reliability. These investigations and results of Whipple\'s gave Minot and Murphy the idea that an experiment could be made to see whether favorable results might also be obtained in the case of pernicious anemia\...by making use of the foods of the kind that Whipple had found to yield favorable results in his experiments regarding anemia from loss of blood.\"
Whipple received honorary doctorates from several American and international Universities, including the Universities of Athens and Glasgow. In 1930, along with Minot, he received the Popular Science Monthly Gold Medal and Annual Award. In 1934, he was awarded the William Wood Gerhard Gold Medal of the Pathological Society of Philadelphia.
He also was a member of the following organizations:
- Rockefeller Foundation, Trustee
- Association of Physicians in Vienna, Corresponding Member
- Royal Society of Physicians in Budapest
- European Society of Haematology
- British Medical Association, Foreign Corresponding Member
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# German Unity Day
**German Unity Day** (*Tag der Deutschen Einheit*, `{{IPA|de|ˈtaːk deːɐ̯ ˈdɔʏtʃn̩ ˈʔaɪnhaɪt|pron|audio=De-Tag der Deutschen Einheit.ogg}}`{=mediawiki}) is the national day of Germany, celebrated on 3 October as a public holiday. It commemorates German Reunification in 1990 when the German Democratic Republic (East Germany) joined the Federal Republic of Germany (West Germany), so that for the first time since 1945 there existed a single German state. German Unity Day on 3 October has been the German national holiday since 1990, when the reunification was formally completed.
An alternative choice to commemorate the reunification could have been the day the Berlin Wall came down: 9 November 1989, which coincided with the anniversary of the proclamation of the German Republic in 1918, and the defeat of Hitler\'s first coup in 1923. However, 9 November was also the anniversary of the first large-scale Nazi-led pogroms against Jews in 1938 (*Kristallnacht*), so the day was considered racist as a national holiday (see 9 November in German history). Therefore, 3 October 1990, the day of the formal reunification, was chosen instead. It replaced the \"German Unity Day\" on 17 June, the national holiday of the Federal Republic of Germany from 1954.
## History
Germany has historically associated various dates with its nationhood and unity.
### Imperial Germany {#imperial_germany}
Before 1871, in the area where the single state of Germany now exists, different kingdoms and principalities existed. After the unification of Germany, and the Founding of the Empire 1871, there was still no common national holiday. The Sedantag was, however, celebrated every year on 2 September, recalling the decisive victory in the Franco-Prussian War on 2 September 1870.
Before the Empire was founded in 1872, there were calls for a national holiday, and there were three suggestions. No decision was made. Until 1873, the Sedantag was moved to 18 January or the day of the Frankfurt Treaty (10 May 1871). The Sedantag would soon also be celebrated at the universities and in many German cities. It never occurred to them to think about \"Empire Parade\" or \"Emperor\'s Birthday\". Some Culture Ministers of the states, especially in Prussia, decided that the Sedantag would be an official festival in schools. Upon many suggestions, the date of the Emperor\'s proclamation on 18 January would be established as day of remembrance. Emperor Wilhelm I declined this: \"This was also the day of the first Prussian coronation of the king, which should not fall into the shadow of a united German holiday.\"
Despite this, the Day of the founding of the German Empire was still celebrated locally and nationally to some degree. These celebrations continued in the Weimar Republic and Nazi Germany. Following World War II, East Germany completely abandoned the holiday, while West Germany still celebrated it on a smaller scale. West Germany did acknowledge the centennial of the German Empire as the founding of the German state in 1871.
### Weimar Republic {#weimar_republic}
On 31 July 1919, the Weimar Constitution would be accepted in its form by the Weimar National Congress. In memorial of this \"Hour of birth of democracy\", 11 August was created as Constitution Day, because the President of Germany Friedrich Ebert, signed the constitution on this day.
### National Socialism {#national_socialism}
Shortly after the Nazis took power in 1933 (the so-called *\[\[Machtergreifung\]\]*), May Day (1 May) was established as a national holiday in the *German Reich*. It was already celebrated as a \"Day of the Labor Movement\" since 1890, and also was part of the tradition for the May dance commemorating the Walpurgis Night. Immediately after the establishment of the holiday in 1933, the Nazis banned trade unions on 2 May 1933 and occupied their buildings as offices for the Nazi Movement. On 1 March 1939, Hitler declared 9 November (the day of the failed Beer Hall Putsch in 1923) as the \"Memorial Day for the movement\" as the national holiday.
### Federal Republic of Germany {#federal_republic_of_germany}
From 1954 to 1990, 17 June was an official holiday in the Federal Republic of Germany to commemorate the East German uprising of 1953, even with the name \"German Unity Day\". Since 1963, it was proclaimed by the President of the Federal Republic as \"National Day of Memorial of the German People\". However, by the mid-1960s as hope faded that the two Germanys would ever be re-united, this date became more of a holiday and day of recreation than a day to consider national unity. In the year 1990, the \"German Unity Day\" was celebrated twice, on this date and on 3 October.
### German Democratic Republic {#german_democratic_republic}
In East Germany, the Founding Day in 1949 was celebrated on 7 October as Republic Day, until the 40th anniversary in 1989.
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# German Unity Day
## Decision for GDR\'s unity with the Federal Republic {#decision_for_gdrs_unity_with_the_federal_republic}
The motive for setting the date of 3 October as the possible Day of Unity was decided by the Volkskammer, the East German parliament, on the impending economical and political collapse of the GDR. The Helsinki Conference was set for 2 October, at which the foreign ministers would be informed of the results of the Two-plus-Four talks.
At the beginning of July, the governments of both German states decided on the schedule: State elections in the GDR would be held on 14 October, and a Bundestag election for the entire country on 2 December.
The decision on the date was finally made on 22 August by the GDR\'s Minister-President, Lothar de Maizière, at a special session of the Volkskammer, which began at 9 p.m. After a heated debate, the President of the Volkskammer, Sabine Bergmann-Pohl, announced the results at 2:30 a.m. on 23 August:
Gregor Gysi, Chairman of the SED-PDS, was visibly moved and made a personal statement: \"Madame President! The Parliament has no more and no less decided on the downfall of the German Democratic Republic as of 3 October 1990\". This statement was met by jubilant cheers from the CDU/DA, DSU and SPD.
### Attempt to change the date of Unity Day {#attempt_to_change_the_date_of_unity_day}
On 3 November 2004, the Federal Chancellor, Gerhard Schröder, suggested that the \"German Unity Day\" be celebrated on a Sunday, for economic reasons. Instead of 3 October, the National Reunification should be celebrated on the first Sunday of October. This suggestion received a lot of criticism from many sides, amongst them from Federal President Horst Köhler as well as the President of the Bundestag, Wolfgang Thierse. The demand worried a part of the population because of discontent for increased working hours would be seen as a provocation and devaluing the national holiday. In addition, fixing the Unity Day on the first Sunday of October would have meant that it would sometimes fall on 7 October, which happens to have been the national day of East Germany; this date would thus have been seen as commemorating the division of Germany rather than the reunification. The idea was dropped after a short but angry debate.
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# German Unity Day
## Celebrations
The Day of German Unity is celebrated each year with a ceremonial act and a citizen\'s festival (**Bürgerfest**).
The celebrations are hosted by a major city, usually the state capital, in the German state presiding over the Bundesrat in the respective year (a sequence determined by the Königstein Agreement). After Bonn in 2011, Frankfurt am Main was the second non-state capital to host the celebrations in 2015; however, both cities are significant in German political history (Bonn as former capital of West Germany and Frankfurt as the place of the Frankfurt Parliament of 1848--49).
+-----------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| - 1990 in Berlin, capital of Germany, reunited that year | - 2010 in Bremen |
| - 1991 in Hamburg | - 2011 in Bonn, former federal capital, instead of the state capital of North Rhine-Westphalia, Düsseldorf (Motto: \"Freiheit Einheit Freude -- Bewegt mehr\" - \"Liberty Unity Joy - Make a bigger difference\") |
| - 1992 in Schwerin, state capital of Mecklenburg-Vorpommern | - 2012 in Munich, state capital of Bavaria |
| - 1993 in Saarbrücken, state capital of Saarland | - 2013 in Stuttgart, state capital of Baden-Württemberg |
| - 1994 in Bremen, state capital of Bremen | - 2014 in Hannover, state capital of Lower Saxony (Motto: \"Einheit in Vielfalt\" - \"Unity in Diversity\") |
| - 1995 in Düsseldorf, state capital of North Rhine-Westphalia | - 2015 in Frankfurt, largest city of Hesse (Motto: \"Grenzen überwinden\" - \"Overcoming borders\") |
| - 1996 in Munich, state capital of Bavaria | - 2016 in Dresden, state capital of Saxony (Motto: \"Brücken bauen\" - \"Building bridges\") |
| - 1997 in Stuttgart, state capital of Baden-Württemberg | - 2017 in Mainz, state capital of Rhineland-Palatinate (Motto: \"Zusammen sind wir Deutschland\" - \"Together we are Germany\") |
| - 1998 in Hannover, state capital of Lower Saxony | - 2018 in Berlin |
| - 1999 in Wiesbaden, state capital of Hesse | - 2019 in Kiel, state capital of Schleswig-Holstein |
| - 2000 in Dresden, state capital of Saxony | - 2020 in Potsdam, state capital of Brandenburg |
| - 2001 in Mainz, state capital of Rhineland-Palatinate | - 2021 in Halle, largest city of Saxony-Anhalt |
| - 2002 in Berlin | - 2022 in Erfurt, state capital of Thuringia |
| - 2003 in Magdeburg, state capital of Saxony-Anhalt | - 2023 in Hamburg |
| - 2004 in Erfurt, state capital of Thuringia | - 2024 in Schwerin, state capital of Mecklenburg-Vorpommern |
| - 2005 in Potsdam, state capital of Brandenburg | |
| - 2006 in Kiel, state capital of Schleswig-Holstein | |
| - 2007 in Schwerin, state capital of Mecklenburg-Vorpommern | |
| - 2008 in Hamburg | |
| - 2009 in Saarbrücken, state capital of Saarland | |
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In addition, various celebrations are held in the federal capital Berlin, mainly based on the Straße des 17. Juni and around the Brandenburg Gate. State capitals and also other cities often have additional festivities. Furthermore, the Oktoberfest beer festival in Munich, which traditionally runs until the first Sunday in October, now runs until 3 October, if the Sunday in question falls on the first or second day of October. The celebrations in the host city always includes a festival and fireworks show.
### Zipfelbund: compass communities {#zipfelbund_compass_communities}
At the 1999 Day of German Unity celebration in Wiesbaden the `{{Interlanguage link multi|Zipfelbund|de}}`{=mediawiki} (Compass Confederation) was formalised. The Zipfelbund are the four communities at the cardinal compass points of Germany: North -- List on the island of Sylt, West -- Selfkant, South -- Oberstdorf and East -- Görlitz. Together, they always participate in the respective annual celebration to represent the modern borders of Germany
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# Gheorghe Zamfir
**Gheorghe Zamfir** (`{{IPA|ro|ˈɡe̯orɡe zamˈfir|-|Ro-Gheorghe Zamfir.ogg}}`{=mediawiki}; born April 6, 1941) is a Romanian nai (pan flute) musician.
Zamfir is known for playing an expanded version of normally 20-pipe nai, with 22, 25, 28 or even 30 pipes, to increase its range, and obtaining as many as eight overtones (additional to the fundamental tone) from each pipe by changing his embouchure. He is known as \"The Master of the Pan Flute\".
## Career
Zamfir came to the public eye when he was approached by Swiss ethnomusicologist Marcel Cellier, who extensively researched Romanian folk music in the 1960s. The composer Vladimir Cosma brought Zamfir with his pan flute to Western European countries for the first time in 1972 as the soloist in Cosma\'s original music for the movie *Le grand blond avec une chaussure noire*. The movie received several awards, including the *Top Foreign Film* from the National Board of Review in 1973. Zamfir continued to perform as a soloist in movie soundtracks by composers Francis Lai, Ennio Morricone and many others. Largely through television commercials where he was billed as \"Zamfir, Master of the Pan Flute\", he introduced the folk instrument to a modern audience and revived it from obscurity.
In 1966, Zamfir was appointed conductor of the \"Ciocîrlia Orchestra\", one of the most prestigious state ensembles of Romania, destined for concert tours abroad. This created the opportunity for composition and arranging. In 1969 he left Ciocîrlia and started his own *taraf* (small band) and in 1970 he had his first longer-term contract in Paris. Zamfir discovered the much greater freedom for artistic adventure. His taraf consisted of: Ion Drăgoi (violin), Ion Lăceanu (flutes), Dumitru Fărcaș (tarogato), Petre Vidrean (double bass) and Tony Iordache (cymbalom) all number one soloists in their country. This taraf made some excellent recordings (CD Zamfir a Paris). He changed the composition of the band soon after: Efta Botoca (violin), Marin Chisar (flutes), Dorin Ciobaru and Pavel Cebzan (clarinet and tarogato), Vasile Pandelescu (accordion), Petre Vidrean (bass) and Pantelimon Stînga (cymbalom). It is said that this change was made to increase the command of Zamfir and have more artistic freedom. A turning point was the recording of Zamfir\'s composition \"Messe pour la Paix\" (Philips). His taraf joined a choir and a symphonic orchestra. This was evidence of the growing ambition. While the Philips recordings of that time were rather conservative, Zamfir preached revolution in the concert halls with daring performances. In 1977, he recorded \"The Lonely Shepherd\" with James Last. Zamfir put himself on the world map and since then his career became highly varied, hovering over classical repertoire, easy listening and pop music.
Between 1976 and 1983, Zamfir had six albums peak within the Australian top 100 albums charts, with *The Flutes of Pan*, his best, peaking at number 26 in 1980.
Zamfir\'s big break in the English-speaking world came when the BBC religious television program, *The Light of Experience*, adopted his recording of \"Doina De Jale\", a traditional Romanian funeral song, as its theme. Epic Records released the tune as a single in 1976, and it climbed to number four on the UK Singles chart. It would prove to be his only UK hit single, but it helped pave the way for a consistent stream of album sales in Britain. His song \"Summer Love\" reached number 9 in South Africa in November 1976. In 1983, he scored a No. 3 hit on the Canadian Adult Contemporary chart with \"Blue Navajo,\" \"Senatorial Samba\" in honor of his lifelong friend and confidant The Senator, and several of his albums (including 1982\'s *Romance* and 1983\'s *Childhood Dreams*) have charted in Canada as well. His 1985 album, *Atlantis*, contained tracks composed by Jacques Brel and Eric Satie, plus music from films and Zamfir\'s version of \"Stranger on the Shore\".
After nearly a decade-long absence, Zamfir returned to Canada in January 2006 for a seven-city tour with the Traffic Strings quintet. The program included a world premiere of Vivaldi\'s Four Seasons for pan flute and string quintet arranged by Lucian Moraru, jazz standards, and well-known favorites.
In 2009, Zamfir was sampled by Animal Collective in the song \"Graze\" on their EP *Fall Be Kind*. In 2012, he performed at the opening ceremony of the 11th Conference of Parties to the Ramsar Convention at the Palace of the Parliament in Bucharest, Romania.
Zamfir played \"Silent Night\" at the opening of Concerto di Natale (The Christmas Concert) on 15 December 2018 at the Vatican Aula Jean Paul the II. Concerto di Natale is an international event where artists from all over the world meet for a special concert to raise as much money as possible for charity projects in Africa and poor regions of the world. He performed with Anastacia, the Italian singer Alessandra Amoroso, and the Italian flautist Andrea Griminelli. Zamfir and Andrea Griminelli appeared again to perform "The Lonely Shepherd".
## Soundtracks
His first appearance as soloist interpreter in a movie soundtrack was in Vladimir Cosma\'s 1972 *Le grand blond avec une chaussure noire*, whose soundtrack became a worldwide hit.
Another of his notable contributions was to the soundtrack of the classic 1975 Australian film *Picnic at Hanging Rock*. His other film scores include *La guerre du pétrole n\'aura pas lieu* (1975) and the Moroccan film *Bodas de Sangre* (1977).
He was asked by Ennio Morricone to perform the pieces \"Childhood Memories\" and \"Cockeye\'s Song\" for the soundtrack of Sergio Leone\'s 1984 gangster film *Once Upon a Time in America*. His performance can also be heard throughout the 1984 film *The Karate Kid* plus the sequels.
One of Zamfir\'s most famous pieces is \"The Lonely Shepherd\", which was written by James Last and recorded with the James Last Orchestra, and first included on Last\'s 1977 album *Russland Erinnerungen* (Memories of Russia); it was also released as a single. \"The Lonely Shepherd\" was used as the theme for the 1979 Australian miniseries *Golden Soak*. It was also featured in Ishu Patel\'s 1984 Oscar-nominated short film Paradise, Quentin Tarantino\'s 2003 film *Kill Bill: Volume 1* and in Nikolas Grasso\'s 2010 short film *Doina*.
His song \"Frunzuliță Lemn Adus Cântec De Nuntă\" (\"Fluttering Green Leaves Wedding Song\") appears in the 1991 Studio Ghibli film *Only Yesterday*.
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# Gheorghe Zamfir
## Personal life {#personal_life}
Zamfir was born in Găeşti, Romania, on April 6, 1941. Although initially interested in becoming an accordionist, at the age of 14 he began his pan flute studies with Fănică Luca at the Special Musical School no. 1 in Bucharest. Later he attended the Ciprian Porumbescu Conservatory. He currently`{{When|date=November 2010}}`{=mediawiki} resides and teaches pan flute in Bucharest. His son, Emmanuel Teodor (who resides in Montreal, Canada), is also a drummer/musician
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# Gaudy Night
***Gaudy Night*** (1935) is a mystery novel by Dorothy L. Sayers, the tenth featuring Lord Peter Wimsey, and the third including Harriet Vane.
The dons of Harriet Vane\'s *alma mater*, the all-female Shrewsbury College, Oxford (based on Sayers\' own Somerville College), have invited her back to attend the annual Gaudy celebrations. However, the mood turns sour when someone begins a series of malicious acts including poison-pen messages, obscene graffiti, and wanton vandalism. Despite the dons\' reluctance to share the secret with an outsider, Harriet convinces them to let her bring in Lord Peter Wimsey to assist the investigation -- but his involvement is not without complications, both personal and professional.
## Plot
Harriet Vane returns with trepidation to her *alma mater*, Shrewsbury College, Oxford to attend the Gaudy dinner. Expecting hostility because of her notoriety (she had stood trial for murder in an earlier novel, *Strong Poison*), she is surprised to be welcomed warmly by most of the dons, and rediscovers her old love of academic life. Harriet\'s short stay is, however, marred by her discovery of a sheet of paper with an offensive drawing, and a poison pen message referring to her as a \"dirty murderess\".
Some time later the Dean of Shrewsbury writes to ask for her help. There has been an outbreak of vandalism and anonymous letters, and fearing for the college\'s reputation if this becomes public knowledge, the Dean wants someone to investigate confidentially. Harriet, herself a victim of poison-pen letters since her trial, reluctantly agrees, and returns to spend some months in residence, ostensibly to do research on Sheridan Le Fanu and to assist a don with her book. The timing of the first poison pen message during the gaudy, and the use of a Latin quotation from the *Aeneid* during one disturbance, focuses suspicion on the Senior Common Room dons, causing escalating tensions.
As Harriet wrestles with the case, trying to narrow down the list of suspects who might be responsible for poison-pen messages, obscene graffiti, wanton vandalism including the destruction of a set of scholarly proofs, and the crafting of vile effigies, she is forced to examine her ambivalent feelings about Wimsey, love and marriage, and her attraction to academia as an intellectual and emotional refuge. Wimsey eventually arrives in Oxford to help, and she gains a new perspective from those who know him, including his nephew, an undergraduate at the university.
The attacks build to a crisis. There is an attempt to drive a vulnerable student to suicide and a physical assault on Harriet that almost kills her. The perpetrator is finally unmasked as Annie Wilson, one of the college scouts, revealed to be the widow of a disgraced University of York academic. Her husband\'s academic fraud had been exposed by an examiner, destroying his career and driving him to suicide; his suicide note used the Latin quote eventually used by Wilson. The examiner later moved to Shrewsbury College, and the widow\'s campaign has been her revenge against the examiner in particular and more generally against intellectual women who move outside what she sees as their proper domestic sphere.
At the end of the book, Wimsey admits his own faults in his attempts at courtship, and Harriet comes to terms with her own feelings, finally accepting Wimsey\'s proposal of marriage.
## Principal characters {#principal_characters}
- Harriet Vane -- protagonist, a mystery writer
- Lord Peter Wimsey -- protagonist, an aristocratic amateur detective
- Letitia Martin -- Dean of Shrewsbury College
- Helen de Vine -- new Research Fellow at Shrewsbury College
- Miss Lydgate -- Harriet\'s former tutor
- Dr Baring -- Warden of Shrewsbury College
- Miss Hillyard -- history don at Shrewsbury College
- Phoebe Tucker -- Harriet\'s old college friend
- Viscount Saint-George -- Lord Peter\'s nephew, an undergraduate at Christ Church, Oxford
- Reggie Pomfret -- undergraduate at Queen\'s College
- Miss Burrows -- College librarian
- Annie Wilson -- scout at Shrewsbury College
- Padgett -- Head Porter at Shrewsbury College
- Bunter -- Lord Peter\'s manservant
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# Gaudy Night
## Title
A \"gaudy\", at the University of Oxford, is a college feast, typically a reunion for its alumni. The term \"gaudy night\" appears in Shakespeare\'s *Antony and Cleopatra*: \"Let\'s have one other gaudy night: call to me / All my sad captains; fill our bowls once more / Let\'s mock the midnight bell\".
## Reception
Writing in 1936, George Orwell disagreed with the opinion of an *Observer* critic who felt that *Gaudy Night* had put Miss Sayers \"definitely among the great writers\". Orwell concluded, to the contrary, that \"her slickness in writing has blinded many readers to the fact that her stories, considered as detective stories, are very bad ones. They lack the minimum of probability that even a detective story ought to have, and the crime is always committed in a way that is incredibly tortuous and quite uninteresting\".
In a letter to his son Christopher from May 1944, J. R. R. Tolkien wrote: \"I could not stand Gaudy Night. I followed P. Wimsey from his attractive beginnings so far, by which time I conceived a loathing for him (and his creatrix) not surpassed by any other character in literature known to me, unless by his Harriet. The honeymoon one (Busman\'s H\[oneymoon\].?) was worse. I was sick.\"
Jacques Barzun stated that \"*Gaudy Night* is a remarkable achievement. Harriet Vane and Saint-George, the undergraduate nephew of Lord Peter, help give variety, and the college setting justifies good intellectual debate. The motive is magnificently orated on by the culprit in a scene that is a striking set-piece. And though the Shrewsbury dons are sometimes hard to distinguish one from another, the College architecture is very good\".
## Themes
Although no murder occurs in *Gaudy Night*, it includes a great deal of suspense and psychological thrills. The narrative is interwoven with a love story and an examination of women\'s struggles to enlarge their roles and achieve some independence within the social climate of 1930s England, and the novel has been described as \"the first feminist mystery novel\".
The novel deals with a number of philosophical themes, including the right relation between love and independence, and between principles and personal loyalties. Susan Haack has an essay on *Gaudy Night* as a philosophical novel.
The issue of women\'s right to academic education is central to the book\'s plot. Sayers had herself been one of the first women to obtain an Oxford University degree, having been awarded first-class honours in the mediaeval literature examinations of 1915. She attended Somerville College, the basis for the fictional Shrewsbury College of the plot.
## Adaptations
The book was adapted as a three-part series for BBC television in 1987, starring Edward Petherbridge as Wimsey and Harriet Walter as Harriet.
In 2005 a dramatisation of the novel was released on CD by the BBC Radio Collection, with Joanna David as Harriet and Ian Carmichael as Wimsey. In 2010 the dramatisation was broadcast on BBC Radio 7
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# Gamma
**Gamma** (`{{IPAc-en|'|g|æ|m|ə|audio=LL-Q1860 (eng)-Flame, not lame-Gamma.wav}}`{=mediawiki}; uppercase `{{Script|Grek|'''Γ'''}}`{=mediawiki}, lowercase `{{Script|Grek|'''γ'''}}`{=mediawiki}; *gámma*) is the third letter of the Greek alphabet. In the system of Greek numerals it has a value of 3. In Ancient Greek, the letter gamma represented a voiced velar stop `{{IPA|el|ɡ|IPA}}`{=mediawiki}. In Modern Greek, this letter normally represents a voiced velar fricative `{{IPA|el|ɣ|IPA}}`{=mediawiki}, except before either of the two front vowels (/e/, /i/), where it represents a voiced palatal fricative `{{IPA|el|ʝ|IPA}}`{=mediawiki}; while /g/ in foreign words is instead commonly transcribed as γκ).
In the International Phonetic Alphabet and other modern Latin-alphabet based phonetic notations, it represents the voiced velar fricative.
## History
The Greek letter Gamma Γ is a grapheme derived from the Phoenician letter `{{Script|Phnx|𐤂}}`{=mediawiki} (*gīml*) which was rotated from the right-to-left script of Canaanite to accommodate the Greek language\'s writing system of left-to-right. The Canaanite grapheme represented the /g/ phoneme in the Canaanite language, and as such is cognate with *gimel* ג of the Hebrew alphabet.
Based on its name, the letter has been interpreted as an abstract representation of a camel\'s neck, but this has been criticized as contrived, and it is more likely that the letter is derived from an Egyptian hieroglyph representing a club or throwing stick.
In Archaic Greece, the shape of gamma was closer to a classical lambda (Λ), while lambda retained the Phoenician L-shape (`{{Script|Phnx|𐌋}}`{=mediawiki}).
Letters that arose from the Greek gamma include Etruscan (Old Italic) 𐌂, Roman C and G, Runic *kaunan* `{{Script|Runr|ᚲ}}`{=mediawiki}, Gothic *geuua* `{{Script|Goth|𐌲}}`{=mediawiki}, the Coptic Ⲅ, and the Cyrillic letters Г and Ґ.
## Greek phoneme {#greek_phoneme}
The Ancient Greek /g/ phoneme was the voiced velar stop, continuing the reconstructed proto-Indo-European *\*g*, *\*ǵ*.
The modern Greek phoneme represented by gamma is realized either as a voiced palatal fricative (`{{IPA|/ʝ/}}`{=mediawiki}) before a front vowel (/e/, /i/), or as a voiced velar fricative `{{IPA|/ɣ/}}`{=mediawiki} in all other environments. Both in Ancient and in Modern Greek, before other velar consonants (κ, χ, ξ -- that is, *k, kh, ks*), gamma represents a velar nasal `{{IPA|/ŋ/}}`{=mediawiki}. A double gamma γγ (e.g., άγγελος, \"angel\") represents the sequence `{{IPA|/ŋɡ/}}`{=mediawiki} (phonetically varying `{{IPA|[ŋɡ~ɡ]}}`{=mediawiki}) or `{{IPA|/ŋɣ/}}`{=mediawiki}.
## Phonetic transcription {#phonetic_transcription}
Lowercase Greek gamma is used in the Americanist phonetic notation and Uralic Phonetic Alphabet to indicate voiced consonants.
The gamma was also added to the Latin alphabet, as Latin gamma, in the following forms: majuscule Ɣ, minuscule ɣ, and superscript modifier letter ˠ.
In the International Phonetic Alphabet the minuscule letter is used to represent a voiced velar fricative and the superscript modifier letter is used to represent velarization. It is not to be confused with the character `{{IPA|ɤ}}`{=mediawiki}, which looks like a lowercase Latin gamma that lies above the baseline rather than crossing, and which represents the close-mid back unrounded vowel. In certain nonstandard variations of the IPA, the uppercase form is used.
It is as a full-fledged majuscule and minuscule letter in the alphabets of some of languages of Africa such as Dagbani, Dinka, Kabye, and Ewe, and Berber languages using the Berber Latin alphabet.
It is sometimes also used in the romanization of Pashto.
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# Gamma
## Mathematics and science {#mathematics_and_science}
### Lowercase
The lowercase letter $\gamma$ is used as a symbol for:
- Chromatic number of in graph theory
- Gamma radiation in nuclear physics
- Shear strain in physics
- Surface tension in physics
- The photon, the elementary particle of light and other electromagnetic radiation
- The 434 nm spectral line in the Balmer series
- Surface energy in materials science
- The Lorentz factor in the theory of relativity
- In mathematics, the lower incomplete gamma function
- The heat capacity ratio `{{math|''C<sub>p</sub>''{{hairsp}}/''C<sub>v</sub>''}}`{=mediawiki} in thermodynamics
- The activity coefficient in thermodynamics
- The gyromagnetic ratio in electromagnetism
- Gamma waves in neuroscience
- Gamma motor neurons in neuroscience
- A non-SI metric unit of measure of mass equal to one microgram (1 μg). This always-rare use is deprecated.
- A non-SI unit of measure of magnetic flux density, sometimes used in geophysics, equal to 10^−5^ gauss (G), or 1 nanotesla (nT).
- The power by which the luminance of an image is increased in gamma correction
- In civil and mechanical engineering:
- Specific weight
- The shear rate of a fluid is represented by a lowercase gamma with a dot above it: $\dot \gamma$
- Austenite (also known as γ-iron), a metallic non-magnetic allotrope or solid solution of iron.
- The gamma carbon, the third carbon attached to a functional group in organic chemistry and biochemistry; see Alpha and beta carbon
- Hermite constant
- The Euler's Constant also known as Euler--Mascheroni constant ≈ 0.57721566490153286
- Stieltjes constants
- Chvátal--Sankoff constants
The lowercase Latin gamma ɣ can also be used in contexts (such as chemical or molecule nomenclature) where gamma must not be confused with the letter y, which can occur in some computer typefaces.
### Uppercase
The uppercase letter $\Gamma$ is used as a symbol for:
- In mathematics, the gamma function (usually written as $\Gamma$-function) is an extension of the factorial to complex numbers
- In mathematics, the upper incomplete gamma function
- The Christoffel symbols in differential geometry
- In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions
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# George Pappas
**George Sotiros Pappas** (born 1942) is a professor of philosophy at Ohio State University. Pappas specializes in epistemology, the history of early modern philosophy, philosophy of religion and metaphysics. He is of Greek and English origin.
He is the author of the *Stanford Encyclopedia of Philosophy* entry on \"Internalist versus Externalist\" conceptions of epistemic justification.
He was co-editor (with Marshall Swain) of *Essays on Knowledge and Justification* (1978), an anthology of essays relating to the Gettier problem used as a core text in undergraduate epistemology courses.
Pappas is an editorial consultant of Berkeley Studies.
## Studies in Berkeley\'s philosophy {#studies_in_berkeleys_philosophy}
Pappas is known`{{by whom|date=August 2019}}`{=mediawiki} to be a leading Berkeley scholar; his essay \"Berkeley and Scepticism\" was in 1993 awarded the International Berkeley Prize. Pappas is a regular participant of International Berkeley Conferences. At one such conference, celebrating the 300th anniversary of George Berkeley\'s birth, Pappas propounded a new approach to the relationship between Berkeley\'s anti-abstractionism and \"esse est percipi\" principle. On Pappas\' reading, Berkeley\'s two theses --- that there are no abstract ideas and that sensible objects must be perceived in order to exist --- entail one another.
Pappas\' interpretation of Berkeley\'s **esse*is*percipi** thesis has sparked much discussion. In 1989, the Garland Publishing Company brought out a 15-volume collection of major works on Berkeley; Pappas\' paper \"Abstract ideas and the \'esse is percipi\' thesis\" was included in the third volume, as it was considered to be a significant contribution to Berkeley scholarship.
Pappas developed his treatment of Berkeley\'s \"esse est percipi\" principle to repudiate the \"inherence interpretation of Berkeley\", upon which Edwin E. Allaire, among others, elaborated.
> That account is put forward to answer an extremely perplexing question in the history of philosophy: Why did Berkeley embrace idealism, i. e., why did he hold that esse est percipi, that to be is to be perceived? `{{harv|Hausman|1984|pp=421–2}}`{=mediawiki}
After emerging in the early 1960s, the \"inherence account\" attracted numerous proponents and became an influential element of contemporary Berkeley scholarship. In his paper \"Ideas, minds, and Berkeley\" Pappas revealed some discrepancies between fountain-head evidences and Allaire\'s approach to a reconstruction of Berkeley\'s idealism. Pappas\' critical examination of the \"inherence account\" is greatly appreciated by Berkeley scholars. Pappas\' penetrating remarks compelled Edwin B. Allaire to revise and improve his conception. Even those who share Allaire\'s account of Berkeley\'s idealism acknowledge Pappas\' article to be \"an excellent review and critique of the IA \[inherence account\].\"
In 2000, Pappas published his monograph *Berkeley\'s thought* in which some parts were based on earlier papers of his. While writings by A. A. Luce or Geoffrey Warnock are long outdated, *Berkeley\'s thought* is often included in lists of recommended literature on Berkeley\'s philosophy
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# Gordon Banks
**Gordon Banks** `{{post-nominals|country=GBR|size=100%|OBE}}`{=mediawiki} (30 December 1937 -- 12 February 2019) was an English professional footballer who played as a goalkeeper. Widely regarded as one of the greatest goalkeepers of all time, he made 679 appearances during a 20-year professional career, and won 73 caps for England, highlighted by starting every game of the nation\'s 1966 World Cup victory.
Banks joined Chesterfield in March 1953 and played for their youth team in the 1956 FA Youth Cup final. He made his first-team debut in November 1958 and was sold to Leicester City for £7,000 in July 1959. He played in four cup finals for the club, as they were beaten in the 1961 and 1963 FA Cup finals before winning the League Cup in 1964 and finishing as finalists in 1965. Despite this success and his World Cup win in 1966, Banks was dropped by Leicester and sold on to Stoke City for £50,000 in April 1967. In the 1970 World Cup, he made one of the game\'s greatest saves to prevent a Pelé goal, but was absent due to illness as England were beaten by West Germany in the quarter-finals.
Banks was Stoke City\'s goalkeeper in the 1972 League Cup win, the club\'s only major honour. He was still Stoke\'s and England\'s number one when a car crash in October 1972 cost him both the sight in his right eye and, eventually, his professional career. He played two last seasons in the United States for the Fort Lauderdale Strikers in 1977 and 1978, and despite only having the vision in one eye, was NASL Goalkeeper of the Year in 1977 after posting the best defensive record in the league. He briefly entered management with Telford United but left the game in December 1980.
Banks was named FWA Footballer of the Year in 1972 and was named FIFA Goalkeeper of the Year on six occasions. The IFFHS named Banks the second-best goalkeeper of the 20th century, after Lev Yashin.
## Early life {#early_life}
Banks was born in Abbeydale, Sheffield, on 30 December 1937, and brought up in the working-class area of Tinsley. The family later moved to the village of Catcliffe after his father set up a (then-illegal) betting shop. This brought greater prosperity but also misery; one day, Banks\'s disabled brother was mugged for the shop\'s daily takings and died of his injuries some weeks later. Banks left school in December 1952, aged 15, and took up employment as a bagger with a local coal merchant, which helped to build up his upper body strength. He spent a season playing for amateur side Millspaugh after their regular goalkeeper failed to turn up for a match; the club\'s trainer spotted Banks amongst the spectators and invited him to play in goal as he was aware that Banks had previously played for Sheffield Schoolboys. His performances there earned him a game in the Yorkshire League for Rawmarsh Welfare. However, a 12--2 defeat to Stocksbridge Works on his debut was followed by a 3--1 home defeat, and he was dropped by Rawmarsh and returned to Millspaugh. Still aged 15, he then switched jobs to become a hod carrier.
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# Gordon Banks
## Club career {#club_career}
### Chesterfield
Banks was scouted by Chesterfield whilst playing for Millspaugh and offered a six-game trial in the youth team in March 1953. He impressed enough in these games to be offered a part-time £3-a-week contract by manager Teddy Davison in July 1953. The reserve team were placed in the Central League on account of a powerful club director rather than on merit, and Banks conceded 122 goals in the 1954--55 season as the \"Spireites\" finished in last place with only three victories. Banks was posted to Germany with the Royal Signals on national service, and won the Rhine Cup with his regimental team. He recovered from a fractured elbow to help the Chesterfield youth team to the 1956 final of the FA Youth Cup. There they were beaten 4--3 on aggregate by Manchester United\'s famous \"Busby Babes\"---a team that included both Wilf McGuinness and Bobby Charlton.
Banks was given his first-team debut by manager Doug Livingstone, at the expense of long-serving Ron Powell, in a Third Division game against Colchester United at Saltergate in November 1958. The game ended 2--2, and Banks kept his place against Norwich City in the following match; by the end of the 1958--59 season, he had missed only three games, those owing to injury. With no goalkeeping coach to guide him, Banks had to learn from his mistakes on the pitch, and he soon developed into a modern vocal goalkeeper who ordered the players in front of him into a more effective defence. Having just 23 league and three cup appearances to his name, it came as a surprise to Banks when Matt Gillies, manager of First Division club Leicester City, bought him from Chesterfield for £7,000 in July 1959; this also meant a wage increase to £15 a week.
### Leicester City {#leicester_city}
Banks faced competition from five other goalkeepers, including 30-year-old Scotland international Johnny Anderson and 25-year-old Dave MacLaren. He started the 1959--60 season as the reserve team\'s goalkeeper. This, in effect, made him the club\'s second-choice, ahead of four of his rivals but behind first-team choice MacLaren. He had played four reserve team games when MacLaren picked up an injury, and manager Matt Gillies selected Banks for his Leicester debut against Blackpool at Filbert Street on 9 September. The match finished 1--1, with Jackie Mudie\'s strike cancelling out Ken Leek\'s opener. Banks retained his place for the 2--0 loss to Newcastle United at St James\' Park three days later. With McLaren fit again, Banks was sent back to the reserves, but after the first team conceded 14 goals in the next five games, he was recalled and became the first-choice goalkeeper for the remainder of the season. The defensive record did not improve at first, with Banks conceding six in a heavy defeat by Everton at Goodison Park. Still, he improved in each match, and the Foxes settled for a comfortable 12th-place finish. In training, he worked extensively on improving his weaknesses, such as coming for crosses. He put in extra hours during training and came up with practice sessions to improve his skills -- this was largely unique in an era where there were no specialized goalkeeping coaches. In the summer, both Anderson and MacLaren departed, leaving Banks as the club\'s undisputed number one ahead of a group of understudies.
Leicester finished sixth in 1960--61, and managed to beat champions Tottenham Hotspur at White Hart Lane. Yet their greatest accomplishment was in reaching the final of the FA Cup, with Banks conceding only five goals in their nine games *en route* to the final, and keeping three clean sheets in the semi-final and two replays against Sheffield United. Their opponents in the final at Wembley were Tottenham, who had already won the First Division title by an eight-point margin. Right-back Len Chalmers picked up a severe injury early in the match, and with Ken Leek dropped for disciplinary reasons in favour of rookie Hughie McIlmoyle, City were effectively playing with ten men and offered little threat going forward. Bobby Smith and Terry Dyson gave Spurs a 2--0 win and the first \"double\" of the 20th century, with Banks unable to prevent either goal.
The 1961--62 season proved to be highly disappointing, as Leicester finished 14th in the league and exited the FA Cup at the hands of Stoke City. The only highlight was the club\'s participation in the European Cup Winners\' Cup, which put Banks in the difficult position of choosing to play for his club against Spanish club Atlético Madrid or choosing to attend the England versus Portugal match as a non-playing squad member. He elected to attend both games, leaving London at full-time to reach Leicester 30 minutes before the kick-off against Madrid. A last-minute goal earned the Spaniards a 1--1 draw at Filbert Street. In the return leg, Banks saved an Enrique Collar penalty, but Atlético were awarded a second penalty which Collar converted, and Leicester lost the game 2--0 (losing the tie 3--1 on aggregate).
Banks broke his nose at Craven Cottage on the opening day of the 1962--63 season, in a 2--1 defeat by Fulham. Leicester went to chase a possible double, reaching the FA Cup semi-finals whilst sitting on top of the table in April. City beat Liverpool 1--0 at Hillsborough to reach the final, with Banks keeping a clean sheet despite his goal being under a near-constant siege from the Merseyside club. The *News of the World* reported that Liverpool had had 34 attempts on goal to Leicester\'s one, and Banks later stated that it was his finest performance at club level. Unluckily, Banks then broke a finger in a 2--1 defeat by West Bromwich Albion at The Hawthorns, and was out injured as Leicester lost their final three league games, ending the season in a disappointing fourth place. In the 1963 FA Cup final Banks and the rest of the team underperformed, and lost the game 3--1 to Manchester United.
City ended the 1963--64 season in 11th place, having been inconsistent all season. Success instead came through the League Cup, as they beat West Ham United 6--3 over two legs in the semi-finals to reach the final against Stoke City. The opening tie at the Victoria Ground finished 1--1 in extremely muddy conditions as Banks spilled a shot from Bill Asprey, with Keith Bebbington pouncing on the rebound. Back at Filbert Street, goals from Mike Stringfellow, Dave Gibson and Howard Riley won the game for Leicester 3--2 and settled the tie at 4--3.
Banks started the 1964--65 season on wages of £40 a week, and the club only agreed to pay £60 a week in December. These miserly wages made it difficult for the club to spend the £80,000 it received from the sale of Frank McLintock -- he had put in a transfer request over dissatisfaction with his pay and quality replacements were reluctant to join a club that paid full internationals like Banks and McLintock no more than the base rate that rival clubs paid to average players. Leicester finished 18th in the league and were knocked out of the FA Cup by Liverpool at Anfield in the sixth round. In the League Cup, City struggled to get past Peterborough United (in a replay), Grimsby Town and Crystal Palace (in a replay), before they recorded an 8--1 victory over Coventry City at Highfield Road. After easing past Plymouth Argyle in the semi-finals, Banks found himself playing in another League Cup final. However, Chelsea won the final after successfully defending their 3--2 win at Stamford Bridge with a goalless draw at Filbert Street.
Banks missed the first nine games of the 1965--66 season after breaking his wrist when diving at the feet of Northampton Town\'s Joe Kiernan in a pre-season friendly. Leicester finished the season in seventh spot and exited both cup competitions at the hands of Manchester City.
Despite being a World Cup winner in the summer of 1966, Banks was dropped towards the end of the 1966--67 season in favour of highly promising teenage reserve Peter Shilton. Manager Matt Gillies was blunt, telling Banks \"we \[Gillies and the club\'s directors\] think your best days are behind you, and you should move on\". Teammate Richie Norman told Banks that Gillies was pressured into the decision, Shilton having told the board he would leave the club unless he was given first-team football. Banks was transfer listed at £50,000, the same price the club received for Derek Dougan in March 1967. However, many of the big clubs were unwilling to spend such a sum on a goalkeeper. Liverpool manager Bill Shankly showed strong interest, but could not convince the club\'s board of directors to agree to such a large fee for a goalkeeper. West Ham United manager Ron Greenwood was prepared to match the fee, but instead signed Kilmarnock\'s Bobby Ferguson for £65,000 because he had already agreed terms with Kilmarnock and did not want to go back on his word. Terms were instead agreed with Stoke City, a mid-table First Division side.
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# Gordon Banks
## Club career {#club_career}
### Stoke City {#stoke_city}
On leaving Filbert Street, Banks requested a loyalty bonus from Leicester and was told by Matt Gillies, \"We\'ve decided not to pay you a penny. There\'s to be no compensation payment and that\'s final.\" Banks then refused the move until Stoke boss Tony Waddington seemingly negotiated a £2,000 payment out of Leicester. It was only some years later that Banks was informed that Stoke had made the payment, not Leicester. Waddington valued good goalkeepers highly, and the two built up a close relationship. During this time, Banks moved to Madeley, Staffordshire. He replaced John Farmer as the club\'s number one, and kept goal in the last four games of the 1966--67 season, making his home debut at the Victoria Ground in a 3--1 win over his former club Leicester.
Banks fitted in well at Stoke, as Waddington built a team of veteran players who were judged by some to be past their best. The Potters struggled near the foot of the First Division table in the 1967--68 and 1968--69 campaigns, before rising to ninth place in the 1969--70 season. Banks remained a reliable stopper for the club. However, on 1 March 1969, he was knocked unconscious at Roker Park by Sunderland\'s Malcolm Moore, and his replacement David Herd conceded four goals in a 4--1 defeat. Banks also played a season for the Cleveland Stokers of the American United Soccer Association in the summer of 1968: he played seven of the short-lived club\'s 12 games in Cleveland, Ohio.
Banks made what he believed to be three of the best saves of his career in a Stoke shirt. In the first instance, he saved and caught a powerful and well-placed header from Manchester City\'s Wyn Davies from 8 yd out; in the second case he saved a Francis Lee header at Maine Road; and he made his third great save for the club by catching a volley from Tottenham Hotspur\'s Alan Gilzean that had been hit from 6 yd out at White Hart Lane.
Stoke began to compete for honours in the 1970--71 season, though despite impressive victories against the top two clubs---Arsenal and Leeds United---City ended the season in mid-table obscurity. The club\'s great achievement was in reaching the semi-finals of the FA Cup, beating Millwall, Huddersfield Town, Ipswich Town and Hull City *en route*. Facing Arsenal at Hillsborough in the semi-finals, they lost a two-goal lead to draw 2--2, and were then beaten 2--0 in the replay at Villa Park.
Despite another mid-table finish in 1971--72, Stoke beat Chesterfield, Tranmere Rovers, Hull City and Manchester United to reach another FA Cup semi-final. They again faced Arsenal, and once more, a draw at Villa Park meant a replay at Goodison Park. The Gunners\' goals in a 2--1 victory came from a disputed Frank McLintock penalty and a John Radford goal that television replays showed was clearly offside. In a May 2011 interview, Banks said that he still felt \"cheated\" out of a chance to play for the club in an FA Cup final. Stoke and Banks found solace in the League Cup, though it took them 11 matches to reach the final after overcoming Southport, then Oxford United in a replay, Manchester United in a second replay, Bristol Rovers, and then West Ham United in a second replay following an aggregate draw after two legs. In extra time of the second leg with West Ham, Banks fouled Harry Redknapp, conceding a penalty, and then saved Geoff Hurst\'s powerful spot-kick to keep City in the competition. They then faced Chelsea in the final at Wembley. Peter Osgood beat Banks with a hooked shot just before half-time, but goals from Terry Conroy and George Eastham won Stoke the game 2--1. At the end of the season, Banks was named the FWA Footballer of the Year, becoming the first goalkeeper to receive the honour since Bert Trautmann in 1956.
On 22 October 1972, while driving home from a session of work on his injured shoulder with the Stoke physiotherapist, Banks lost control of his new Ford Consul (a re-badged Ford Granada Mk I) car, which ended up in a ditch. He had attempted to overtake a car on a sharp bend and collided with an oncoming Austin A60 van. He was taken to the North Staffordshire Hospital and, during an operation, received 200 stitches in his face and over 100 micro-stitches inside the socket of his right eye, and was told the chances of saving the sight in his eye were 50--50. His sight never returned, and as the loss of binocular vision severely limited his abilities as a goalkeeper, he retired from professional football the following summer.
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# Gordon Banks
## Club career {#club_career}
### Fort Lauderdale Strikers {#fort_lauderdale_strikers}
In April 1977, he went on to play as a named superstar in the North American Soccer League (NASL) for Fort Lauderdale Strikers. The Strikers won their division in 1977, and Banks was named NASL Goalkeeper of the Year after he conceded only 29 goals in 26 games---the best defensive record in the NASL. He also played one League of Ireland game for St Patrick\'s Athletic, keeping a clean sheet in a 1--0 win over Shamrock Rovers at Richmond Park on 2 October 1977. He returned to Fort Lauderdale and played 11 games in the 1978 season.
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# Gordon Banks
## International career {#international_career}
Banks was capped twice for the England under-23 side, in matches against Wales and Scotland in 1961.
Ron Springett was the goalkeeper for England as Banks rose to prominence. Still, after the 1962 World Cup in Chile, a new coach was appointed in former England right-back Alf Ramsey. Ramsey demanded sole control of the team and began looking towards the next World Cup. Banks won his first cap on 6 April 1963 against Scotland at Wembley, after Springett was dropped following a poor performance. England lost 2--1, though Banks was blameless as Scotland\'s goals came firstly from an error by Jimmy Armfield and then secondly from the penalty spot. He was picked for the next match against Brazil, which ended in a creditable 1--1 draw after Bryan Douglas cancelled out Pepe\'s opener. Banks continued to play consistently to become established as England\'s first-choice goalkeeper. In 1963, he was picked to play against the Rest of the World, in a celebration match to mark 100 years of The Football Association.
Banks also played in two of England\'s three games at the \"Little World Cup\" in Brazil in the summer of 1964, a 1--1 draw with Portugal and a 1--0 defeat to Argentina. Blackpool\'s Tony Waiters won five caps in the England goal in 1964 but found that his challenge to Banks\'s first-team place came to an end after he conceded five goals to Brazil. During England\'s summer of 1965 tour he built up a solid understanding with his defenders---George Cohen, Jack Charlton, Bobby Moore, and Ray Wilson---as he only conceded two goals in four matches against Hungary, Yugoslavia, West Germany, and Sweden. They then played seven friendlies in 1966 in the build-up to the World Cup, though the team passed their biggest test of character in the British Home Championship, beating Scotland 4--3 in front of a crowd of over 130,000 at Hampden Park. Going into the competition, the only defeat in 21 matches since the \"Little World Cup\" came against Austria, in a game that Banks missed due to injury.
### 1966 World Cup {#world_cup}
Banks entered the 1966 FIFA World Cup as England\'s first-choice goalkeeper, and his understudies Ron Springett and Peter Bonetti never took to the field during the tournament. England opened the tournament with a goalless draw against Uruguay, with Banks a virtual spectator as the highly defensive Uruguayans rarely ventured out of their half. They then defeated Mexico 2--0, with Banks again rarely troubled throughout. A 2--0 win over France then took England through the group stage without Banks conceding a goal.
England beat Argentina 1--0 in the last eight, with Geoff Hurst scoring with a header; the match was sullied by the first-half sending off of Argentinian midfielder Antonio Rattín, who refused to leave the pitch after being dismissed for dissent. In contrast to the previous games, the semi-final against Portugal proved to be a fair contest between two sides of talented players eager to attack from the start of the match. Yet there was panic in the buildup to the game as trainer Harold Shepherdson forgot to buy chewing gum, which Banks used to make his hands stickier and better able to handle the ball, and so Shepherdson had to run to a nearby newsagents to purchase gum as the teams were in the tunnel. Bobby Charlton scored two goals, but Portugal made a strong finish and won a penalty on 82 minutes after Jack Charlton handled the ball in the penalty area. Eusébio converted the penalty after sending Banks the wrong way, and the game finished 2--1 in England\'s favour. This was the first goal Banks had conceded for England in 721 minutes of regular play since giving up Scotland\'s last goal after 81 minutes of the Home International clash in April. This remained a record for an England goalkeeper until 2021 when it was broken by Jordan Pickford.
England\'s opponents in the final were West Germany. It was England who dominated the final, but it was Banks who was beaten first. A weak header from Ray Wilson handed a chance to Helmut Haller, who sent an accurate but relatively weak shot into the corner of the net; Banks had been unsighted by Jack Charlton, and he failed to adjust his position in time to reach the ball. England equalised through a Geoff Hurst header within six minutes and went ahead late in the second half through Martin Peters. With seconds left in the game, Lothar Emmerich sent a free kick into the England penalty area, and the ball fell to Wolfgang Weber, who guided the ball over a lunging Ray Wilson and an outstretched Banks into the net to take the game into extra-time. In extra time, the Germans sent shots in at the England goal, which Banks managed to catch and control without any great danger. Hurst scored two goals to complete his hat-trick, and though many claimed his second goal never crossed the line Banks always maintained his belief that the officials called the decision correctly. Between these goals, Banks had to deal with a fiery shot from Sigfried Held and was later exposed only for Uwe Seeler to come just centimetres away from connecting with the ball.
### Euro 1968 {#euro_1968}
Scotland were the first team to beat the world champions, as goals from Denis Law, Bobby Lennox and Jim McCalliog secured a 3--2 victory at Wembley on 15 April 1967. Despite this set-back, England qualified for UEFA Euro 1968, which consisted of just four teams: England, Italy (hosts), the Soviet Union, and Yugoslavia. England played just two games at the tournament, losing 1--0 to Yugoslavia, and then beating the Soviets 2--0 in the third-place play-off.
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# Gordon Banks
## International career {#international_career}
### 1970 World Cup {#world_cup_1}
Banks went into the 1970 World Cup as England\'s number one with 59 caps to his name, and had Peter Bonetti (six caps) and Alex Stepney (one cap) as his understudies. He found the heat and altitude at Guadalajara, Mexico difficult to cope with. The team\'s efforts at acclimatisation were not helped when Bobby Moore was falsely accused of stealing the infamous \"Bogotá Bracelet\". Despite this, a Geoff Hurst goal was enough to beat their first opponents, Romania. A far tougher test awaited on 7 June, when England faced Brazil. The day before the match, Banks was informed that he had been awarded an OBE.
Playing at pace, Brazil were putting England under enormous pressure and an attack was begun by captain Carlos Alberto who sent a low ball down the right flank for the speedy Jairzinho to latch on to. The Brazilian winger sped past left-back Terry Cooper and crossed the ball into the six-yard box, where Pelé connected with a powerful header to send the ball low towards the right-hand corner of the goal. In the knowledge that his header was placed to perfection, Pelé immediately shouted \"Gol!\" (Brazilian Portuguese for goal).
The split-second incident only allowed Banks time for one conscious thought -- that the shot was impossible to catch, and the only way to prevent Pelé from following up on the rebound would be to parry the ball over the bar. The ball bounced 2 yd in front of the goal-line, and Banks managed to make contact with the ball with the fingers of his right hand and rolled his hand slightly to angle the ball over the crossbar. He landed in the inner netting of the goal and knew he had saved the ball after seeing Pelé\'s reaction. Banks then rose to his feet to defend the corner and broke into laughter after the following exchange:
: \"I thought that was a goal.\" (Pelé)
: \"You and me both.\" (Banks)
: \"You\'re getting old, Banksy, you used to hold on to them.\" (Bobby Moore)
Pelé and numerous journalists and pundits would later describe the save as the greatest in the game\'s history. Banks later said \"They won\'t remember me for winning the World Cup, it\'ll be for that save. That\'s how big a thing it is. People just want to talk about that save.\" In 2002 the UK public voted the save No. 41 in the list of the 100 Greatest Sporting Moments.
Brazil won 1--0 after Jairzinho beat Banks in the second half. England ultimately joined Brazil in the last eight after a win in the final group game against Czechoslovakia. The reward was a rematch of the 1966 final against West Germany.
The day before the West Germany game, England\'s hopes of making further inroads into the World Cup were dented when Banks complained of an upset stomach. He became affected by violent stomach cramps and aching limbs and spent his time in the bathroom sweating, shivering and vomiting. He passed an extremely undemanding fitness test but suffered a relapse shortly before the game, and Ramsey was forced to rest him and play Peter Bonetti in his place. Ramsey remarked that \"of all the players to lose, we had to lose him.\" Banks watched the game on television at the hotel as England lost a two-goal lead to be eliminated 3--2 after extra time. Due to a delay in the broadcast, he switched the television off, with England 2--0 in the lead, as Bobby Moore returned to the hotel to break the news of the defeat. Suspicions later surfaced that Banks had been poisoned to take him out of the game, but with no evidence to support them, Banks never believed in them.
### Final years {#final_years}
Only four teams competed in UEFA Euro 1972: Belgium (hosts), Hungary, the Soviet Union, and West Germany. England came close to qualifying but lost 3--1 to West Germany in the final round of qualifying.
On 15 May 1971, Banks was involved in a notorious incident with George Best who, while playing against England for Northern Ireland, flicked the ball out of Banks\'s hands and headed it into the net. The move was audacious, but was disallowed by the referee, who judged it to be dangerous play. Banks played his 73rd and final game for England on 27 May 1972, in a 1--0 win over Scotland at Hampden Park. During his 73 international games, he kept 35 clean sheets and lost just nine games.
## Coaching career {#coaching_career}
In December 1977, he was appointed as a coach at Port Vale by manager Dennis Butler, being demoted to reserve coach in October 1978 by new boss Alan Bloor. Banks enjoyed coaching but soon resigned his position, feeling that players such as Bernie Wright refused to take his advice on board. He applied for the vacant management positions at Lincoln City and Rotherham United, but was rejected. He instead accepted the role as manager of Alliance Premier League part-time club Telford United. He signed a goalkeeper, centre-half and centre-forward from Bangor City for £1,500, as well as former Stoke striker John Ruggiero. The \"Bucks\" finished in 13th place in 1979--80.
In November 1980, he left Jackie Mudie in temporary charge of team affairs whilst he underwent surgery and led the club to defeat in the FA Trophy at the hands of a lower league club. On his return to the club Banks was sacked. He was offered the position of raffle ticket seller and accepted the post in the belief that it would entitle him to the money owed to him in the terms of his management contract; he eventually had to settle for 50% of his contract. He later stated that \"It broke my heart \... I did not want to stay in the game.\"
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# Gordon Banks
## Style of play {#style_of_play}
An excellent, consistent, and instinctive goalkeeper who possessed significant physical strength, athleticism, and excellent shot-stopping abilities, Banks is regarded as one of the greatest players of all time in his position. He possessed an excellent positional sense, which he felt to be one of his best assets, and was also known for his handling, awareness, composure, and mental strength, as well as his agility, speed, and quick reflexes, which enabled him to produce acrobatic saves, such as his famous stop from Pelé\'s header against Brazil at the 1970 World Cup in Mexico.
## Personal life and health {#personal_life_and_health}
Banks first met his wife, Ursula, during his national service in Germany in 1955. They married in 1957 and had three children: Robert, Julia and Wendy. He separated from Ursula during his time in America. Still, the couple reunited when Banks returned to England.
In October 1972, Banks was involved in a car crash in his Ford Consul while driving on the wrong side of the road, close to his home in Madeley Heath. Fragments of glass had perforated his right eye and damaged the retina, requiring 100 micro stitches to the eye and a further 200 to his face.
Banks\'s nephew is Nick Banks, drummer of the band Pulp.
Shortly after his retirement, Banks was surprised by Eamonn Andrews for an episode of *This Is Your Life*. He later fronted a Leicester-based hospitality company. He lost a significant sum of money when the business failed but was helped out by Leicester City, who offered him a belated testimonial match. He was appointed as Stoke City\'s president following the death of Stanley Matthews. From the 1980s he was a member of the three-man pools panel.
In 2001, he sold his World Cup winners medal at Christie\'s for £124,750, and his international cap from the final was also sold for £27,025. Banks was an Inaugural Inductee to the English Football Hall of Fame in 2002. In March 2004, he was named by Pelé as one of the world\'s 125 greatest living footballers. He was awarded an honorary doctorate from Keele University in February 2006. In May 2006, Banks was the first \'legend\' to be inducted into a new Walk of Fame, by having a plaque installed in the pavement in front of Sheffield Town Hall. In July 2008, Pelé unveiled a statue of Banks making his famous 1970 World Cup save outside the Britannia Stadium. In March 2011, he was also inducted into the City of Stoke-on-Trent Hall of Fame, along with Roy Sproson. Pelé became a good friend of Banks and following his death the Brazilian described Banks as a \"goalkeeper with magic\".
In 1980, Banks published his first autobiography, *Banks of England*. He published a more comprehensive autobiography in 2002: *Banksy: My Autobiography*. Irish investigative author, Don Mullan, published a boyhood memoir in 2006 called *Gordon Banks -- A Hero Who Could Fly* in which he wrote about the influence of the England goalkeeper on his life.
In December 2015, it was announced Banks was receiving treatment for kidney cancer. He died from cancer in his sleep at his home in Madeley, Staffordshire, 12 February 2019 at the age of 81. Banks\'s funeral took place on 4 March 2019 at Stoke Minster. His pallbearers were goalkeepers representing his former teams; Joe Anyon (Chesterfield), Jack Butland (Stoke City), Joe Hart (England) and Kasper Schmeichel (Leicester City).
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# Gordon Banks
## Career statistics {#career_statistics}
### Club
Club Season League FA Cup League Cup
------------------------------- ---------- ------------------------------ ------ ------- -------- ------- ------------
Division Apps Goals Apps Goals Apps Goals Apps
Chesterfield 1958--59 Third Division 23 0 3 0 ---
Leicester City 1959--60 First Division 32 0 4 0 ---
1960--61 First Division 40 0 10 0 1
1961--62 First Division 41 0 2 0 1
1962--63 First Division 38 0 6 0 2
1963--64 First Division 36 0 1 0 8
1964--65 First Division 38 0 6 0 9
1965--66 First Division 32 0 4 0 1
1966--67 First Division 36 0 1 0 3
Total 293 0 34 0 25
Stoke City 1966--67 First Division 4 0 0 0 0
1967--68 First Division 39 0 2 0 4
1968--69 First Division 30 0 4 0 0
1969--70 First Division 38 0 3 0 1
1970--71 First Division 39 0 10 0 1
1971--72 First Division 36 0 8 0 11
1972--73 First Division 8 0 0 0 2
Total 194 0 27 0 19
Cleveland Stokers (loan) 1967 United Soccer Association 7 0 --- ---
Hellenic (loan) 1971 National Football League 3 0 --- ---
Fort Lauderdale Strikers 1977 North American Soccer League 26 0 --- ---
1978 North American Soccer League 11 0 --- ---
Total 37 0 --- ---
St Patrick\'s Athletic (loan) 1977--78 League of Ireland 1 0 0 0 0
Career total 558 0 64 0 44
: Appearances and goals by club, season and competition
### International
National team Year Apps Goals
--------------- ------ ------ -------
England 1963 7 0
1964 7 0
1965 7 0
1966 15 0
1967 4 0
1968 6 0
1969 6 0
1970 10 0
1971 7 0
1972 4 0
Total 73 0
: Appearances and goals by national team and year
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# Gordon Banks
## Honours
**Leicester City**
- Football League Cup: 1963--64
- FA Cup runner-up: 1960--61, 1962--63
**Stoke City**
- Football League Cup: 1971--72
**England**
- FIFA World Cup: 1966
- UEFA European Championship third-place: 1968
- British Home Championship: 1964 (shared), 1965, 1966, 1968, 1969, 1970 (shared), 1971, 1972
**Individual**
- FIFA Goalkeeper of the Year: 1966, 1967, 1968, 1969, 1970, 1971
- FIFA World Cup All-Star Team: 1966
- Ballon d\'Or Nominated: 1966, 1970, 1972
- World XI: 1969, 1971, 1972
- *FUWO European Team of the Season*: 1969, 1970
- *Rothmans Golden Boots Awards*: 1970, 1971, 1972
- Officer of the Order of the British Empire: 1970
- *Daily Express* Sportsmen of the Year: 1971, 1972
- *Sport Ideal European XI*: 1971, 1972
- FWA Footballer of the Year: 1972
- Football League 100 Legends: 1998
- English Football Hall of Fame: 2002
- NASL All-Stars: 1977
- NASL Goalkeeper of the Year: 1977
- *World Soccer* Greatest Players of the 20th Century: 32nd
- FIFA 100: 2004
- PFA Team of the Century (1907--1976): 2007
- Freedom of the City of Stoke-on-Trent 16 October 2014.
- Freedom of the Borough of Newcastle-under-Lyme 23 February 2018
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# Ganglion
A **ganglion** (`{{plural form}}`{=mediawiki}: **ganglia**) is a group of neuron cell bodies in the peripheral nervous system. In the somatic nervous system, this includes dorsal root ganglia and trigeminal ganglia among a few others. In the autonomic nervous system, there are both sympathetic and parasympathetic ganglia which contain the cell bodies of postganglionic sympathetic and parasympathetic neurons respectively.
A **pseudoganglion** looks like a ganglion, but only has nerve fibers and has no nerve cell bodies.
## Structure
Ganglia are primarily made up of somata and dendritic structures, which are bundled or connected. Ganglia often interconnect with other ganglia to form a complex system of ganglia known as a plexus. Ganglia provide relay points and intermediary connections between different neurological structures in the body, such as the peripheral and central nervous systems.
Among vertebrates there are three major groups of ganglia:
- Dorsal root ganglia (also known as the spinal ganglia) contain the cell bodies of sensory (afferent) neurons.
- Cranial nerve ganglia contain the cell bodies of cranial nerve neurons.
- Autonomic ganglia contain the cell bodies of autonomic nerves.
In the autonomic nervous system, fibers from the central nervous system to the ganglia are known as preganglionic fibers, while those from the ganglia to the effector organ are called postganglionic fibers.
### Basal ganglia {#basal_ganglia}
The term \"ganglion\" refers to the peripheral nervous system.
However, in the brain (part of the central nervous system), the basal ganglia are a group of nuclei interconnected with the cerebral cortex, thalamus, and brainstem, associated with a variety of functions: motor control, cognition, emotions, and learning.
Partly due to this ambiguity, the *Terminologia Anatomica* recommends using the term \'basal nuclei\' instead of \'basal ganglia\'; however, this usage has not been generally adopted.
### Pseudoganglion
A pseudoganglion is a localized thickening of the main part or trunk of a nerve that has the appearance of a ganglion but has only nerve fibers and no nerve cell bodies.
Pseudoganglia are found in the teres minor muscle and radial nerve
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# Gamma World
***Gamma World*** is a post-apocalyptic science fantasy role-playing game in which player characters explore Earth centuries after the collapse of civilization, searching for artifacts from the time before \"The Great Upheaval\". The game was originally designed by James M. Ward and Gary Jaquet, and first published by TSR in 1978. It borrows heavily from Ward\'s earlier role-playing game, *Metamorphosis Alpha*.
## Setting
*Gamma World* takes place in the mid-25th century, more than a century after a second nuclear war had destroyed human civilization. This war is only vaguely described in most editions of the game, and what details are provided change from version to version:
The first two editions explained that ever-increasing material prosperity and leisure had led to ever-more radical and violent social movements, culminating in a final war in the years AD 2309--2322, and ascribe the final annihilation to a terrorist group called \"The Apocalypse\" and the ensuing retaliation by surviving factions.
Later versions would alter the reason for the collapse. The 2000 *Alternity* edition explained this as caused by the arrival of aliens and nuclear response. The 2003 *d20 Modern* iteration explained collapse as due to uncontrolled nanotechnology and AI. The 2010 edition attributes the destruction of civilization to the activation of the Large Hadron Collider, which caused multiple realities to exchange features in an event known as the Big Mistake.
All backstories agree that the cataclysm destroyed all government and society beyond a village scale, plunging the world into a Dark Age. In many editions of the game, technology is at best quasi-medieval (in the first edition, the crossbow is described as \"the ultimate weapon\" for most Gamma World societies). Some, such as the 2003 and, to a lesser degree the 2010 edition, feature advanced technology that is well known and often easily available. In contrast, super-science artifacts in earlier editions were risky to use due to the average Gamma World character not knowing how to properly operate such devices, or possibly even what the device is at all. The post-apocalyptic inhabitants of Earth now refer to their planet as \"Gamma World\", or, in later edition, \"Gamma Terra\".
The setting is chaotic and dangerous and little resembles pre-apocalyptic Earth. The weapons unleashed during the final war were strong enough to alter coastlines, level cities, and leave large areas of land lethally radioactive. These future weapons bathed the surviving life of Earth in unspecified forms of radiation and biochemical agents, producing widespread, permanent mutations among humans, animals, and plants. This has caused mutations such as additional limbs, super-strength, and psychic powers. (Random tables of such improbable mutations are a hallmark of every edition of *Gamma World*.) Many animals and plants are sentient, semi-civilized species competing with surviving humans. Both humans and non-humans have lost most knowledge of the pre-war humans, whom Gamma World\'s inhabitants call \"the Ancients\". The only group with significant knowledge of the Ancients are isolated robots and other AIs that survived the war. These machines tend to be damaged, in ill repair, and/or hostile to organic beings.
Player characters include unmutated humans (referred to as \"Pure Strain Humans\" in most editions), mutated humans, sentient animals or plants, and androids. Characters explore ruins and strange post-apocalyptic societies to gain knowledge of the Ancients and social status for themselves. Common adventure themes involve protecting fragile post-apocalypse societies, retrieving such Ancient \"artifacts\" fiction as power armor, laser pistols, and anti-grav sleds), or mere survival against the multifarious dangers of the future such as gun-toting mutant rabbits, death machines, and other, more hostile, Gamma Worlders.
A recurrent source of conflict on Gamma World is the rivalry among the Cryptic Alliances, semi-secret societies whose ideological agendas, sometimes monomaniacal ones, often bring them into conflict with the rest of the Gamma World. The Pure Strain Humans\' Knights of Genetic Purity, for example, wish for genocide on mutants, Iron Society seeks the same for baseline humans.. Other rivalries involve attitudes towards Ancient technology. The Restorationists seek to rebuild Ancient society while others the Seekers, wish to destroy it.
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# Gamma World
## System
Throughout the game\'s many editions, *Gamma World* has almost always remained strongly compatible with the then-current edition of *Dungeons & Dragons* (*D&D*). Attribute generation is much the same for instance with a range of 3 to 18, randomly generated by rolling three six-sided dice. The attributes themselves are the same, but with occasional name changes such as Physical Strength instead of Strength and Mental Strength instead of Wisdom. This allows Gamma World and D&D characters to potentially cross over genres.
Character generation is mostly random, and features one of the game\'s most distinctive mechanics, the mutation tables. Players who choose to play mutants roll dice to randomly determine their characters\' mutations. All versions of *Gamma World* eschew a realistic portrayal of genetic mutation to one degree or another, instead giving characters fantastic abilities like psychic powers, laser beams, force fields, life draining and others. Other mutations are extensions or extremes of naturally existing features transposed from different species, such as electrical generation, infravision, quills, extra limbs, dual brains, carapaces, gills, etc. These were offset with defects that also ranged from the fantastical---such as skin that dissolves in water, or a scent that attracts monsters---to the mundane, such as seizures, madness and phobias.
Characters in most versions of *Gamma World* earn experience points during their adventures, which cause the character\'s Rank (in some editions, Level) to increase. Unlike *D&D*, however, the first two editions of *Gamma World* do not use a concept of true level or character class, and increases in Rank do not affect the character\'s skills or combat abilities. In fact, in the first three editions of the game, character rank is primarily a measure of the character\'s social prestige.
The game mechanics used for resolving character actions, on the other hand, greatly varied between *Gamma World* editions. The first two editions, like the early editions of *D&D*, depend heavily on matrix-based mechanics, where two factors (one representing the actor or attacker, and one representing the opponent) are cross-referenced on a chart. For some actions, such as attacks, the number located on the matrix represents a number the acting player must roll. For other actions (such as determining the result of radiation exposure), the matrix result indicates a non-negotiable result. *Gamma* World\'s first two editions had a variety of specialized matrices for different situations (again, closely resembling *D&D*).
The third edition rules replace specialized matrices with the Action Control Table (ACT), a single, color-coded chart that allowed players to determine whether a character action succeeded, and the degree of success, with a single roll. (The ACT concept is drawn from the *Marvel Super Heroes* game published by TSR shortly before development of *Gamma World*\'s third edition.) The ACT requires the referee to cross-reference the difficulty of a character action with the ability score used to complete that action, determining which column of the ACT is used for that action. The character\'s player then rolls percentile dice; the result is compared to appropriate column, determining a degree of success or failure and eliminating the need for second result roll (e.g. the damage roll that many games require after a successful combat action).
The fourth edition was directly compatible with 2nd Edition AD&D with some minor differences in mechanics. The fifth and sixth editions though would relegate Gamma World to that of a Campaign Setting and require the core books to play. 5th uses the Alternity system which is mostly represented in the book but required the core rules in order to resolve some factors. 6th Edition though was fully incomplete on its own and required the d20 Modern rulebook in order to play the game.
The seventh version uses a streamlined version of *D&D 4th edition* mechanics. Character generation choice though was nearly fully removed. Instead of choosing a character class, a player had to roll a twenty-sided die two times and consult an accompanying character origin table. For example, a player might obtain the result \"Radioactive Yeti\" and gain the powers associated with the \"Radioactive\" and \"Yeti\" origins. Attributes, mutations, and skills were also randomly assigned. Two decks of cards comprising the core of a *Collectible Card Game* are included with the game. One deck represented random Alpha Mutations, which could be drawn to gain temporary powers, and the other contained various Omega Tech, powerful technological devices that could possibly backfire on those that used them. Some 4th edition rules enhancements for the setting include new damage types such as \"Radiation\", Gamma World-specific skills, and increased lethality. Despite these differences, it is possible to use characters and monsters from a *D&D* game in *Gamma World* and vice versa.
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# Gamma World
## History
### First Edition (1978) {#first_edition_1978}
The original *Gamma World* boxed set (containing a 56-page rulebook, a map of a devastated North America, and dice) was released in 1978. TSR went on to publish three accessories for the 1st edition of the game:
- GW1, *Legion of Gold* by Gary Gygax, Luke Gygax, and Paul Reiche III
- GW2, *Famine In Far-Go* by Michael Price
- *Gamma World Referee\'s Screen*
Grenadier Miniatures also supported the game, with a line of licensed miniatures.
At least one other TSR product was announced \-- *Metamorphosis Alpha to Omega*, an adaptation of *Metamorphosis Alpha\'s* campaign setting to *Gamma World\'s* rules (Anon 1981). Work on the adaptation was halted when a 2nd edition of *Gamma World* was announced. This was later released as *Metamorphosis Alpha to Omega* using the *Amazing Engine* Rules.
### Second Edition (1983) {#second_edition_1983}
The second edition *Gamma World* boxed set (with rules designed by Ward, Jaquet, and David James Ritchie) was released in 1983. Two modules and two accessories were released for this version:
- GW3, *The Cleansing War of Garik Blackhand* by Michael Pierre Price and Garry Spiegle
- GW4, *The Mind Masters* by Philip Taterczynski
- GWAC1, *Gamma World Referee\'s Screen and Mini-Module*
- GWAC2, *Gamma World Character Sheets*
TSR also produced four packs of *Gamma World* miniatures. TSR started production on a third adventure module, which was to be assigned the identification code GW5 and had the working title *Rapture of the Deep*. This module was not published. However, a \'ghost\' Second Edition GW5 *Rapture of the Deep* module was produced in 2007.
### Third Edition (1986) {#third_edition_1986}
The 3rd edition of *Gamma World* was another boxed set, credited to James M. Ward. It introduced the Action Control Table, a color-coded table used to resolve nearly all actions in the game. (Color-coded tables were something of a trend at TSR in the mid-1980s. After 1984\'s *Marvel Super Heroes* proved the viability of the concept, TSR revised *Gamma World*, *Star Frontiers*, and *Top Secret* to use similar tables.) Unfortunately for TSR, this version of the rules became notorious for the number of editorial mistakes, including cross-references to rules that didn\'t appear in the boxed set. The errors were serious enough that TSR published a *Gamma World Rules Supplement* containing the \"missing\" rules. The *Rules Supplement* was sent to gamers who requested it by mail, and included in reprintings of the boxed set.
The five modules TSR published for *Gamma World\'s* 3rd edition introduced the setting\'s first multi-module metaplot, which involved rebuilding an ancient \'sky chariot\':
- GW6, *Alpha Factor* by Kim Eastland
- GW7, *Beta Principle* by Bruce Nesmith
- GW8, *Gamma Base* by Kim Eastland
- GW9, *Delta Fragment* by Kim Eastland
- GW10, *Epsilon Cyborgs* by Kim Eastland
TSR dropped the 3rd edition of *Gamma World* from its product line before the multi-module storyline could be completed. In 2003 an unofficial conclusion to the series was published under the title GW11 *Omega Project*.
Despite its editorial issues, the 3rd edition rules were well-received enough to win the 1986/1987 Gamer\'s Choice Award for \"Best Science-Fiction Roleplaying Game\".
Scott Taylor of *Black Gate* in 2015 rated the GW6-GW10 series as #7 in \"The Top 10 Campaign Adventure Module Series of All Time, saying \"if you are ever in the mood to crack out *Gamma World*, or just have a great campaign setting for any post-apocalyptic campaign, this super series could be for you.\"
### Fourth Edition (1992) {#fourth_edition_1992}
The 4th edition of *Gamma World* was a 192-page softcover book, written by Bruce Nesmith and James M. Ward, published in May 1992 by TSR. This version of the game abandoned the 3rd edition\'s Action Control Table for mechanics resembling *2nd Edition Advanced Dungeons & Dragons*. TSR published five accessories for the 4th edition:
- GWA1, *Treasures of the Ancients* by Dale \"Slade\" Henson (`{{ISBN|1-56076-577-1}}`{=mediawiki})
- GWA2, *The Overlord of Bonparr* by Jack A. Barker (`{{ISBN|1-56076-599-2}}`{=mediawiki})
- GWQ1, *Mutant Master* by Bruce Nesmith (`{{ISBN|1-56076-411-2}}`{=mediawiki})
- GWQ2, *All Animals Are Equal* by Dale \"Slade\" Henson (`{{ISBN|1-56076-638-7}}`{=mediawiki})
- GWQ3, *Home Before the Sky Falls* by Tim Beach, Paul Riegel, Drew Bittner, and Kim Eastland (`{{ISBN|1-56076-674-3}}`{=mediawiki})
TSR\'s *Gamma World* development team announced at Gen Con 1993 that no further products would be released for the 4th edition. They also announced that TSR had restarted development of *Metamorphosis Alpha to Omega*, but that the manuscript would be completed using the *Amazing Engine* rules.
### Fifth Edition (2000) {#fifth_edition_2000}
The 5th version of *Gamma World* was a supplement for the science-fiction game *Alternity*. (In a nod to *Gamma World*\'s reputation for being repeatedly revised, the book\'s back cover states \"That\'s right, it\'s the return of the *Gamma World*\".) The *Gamma World Campaign Setting* (`{{ISBN|0-7869-1629-X}}`{=mediawiki}) was a 192-page softcover book written by Andy Collins and Jeff Grubb, published in 2000 by Wizards of the Coast (WOTC), only a month after WOTC announced its cancellation of the *Alternity* line. This version of *Gamma World* is unique as the only one not to have accessories or supplements.
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# Gamma World
## History
### *Omega World* (2002) {#omega_world_2002}
In September 2002, *Omega World*, a *d20 System* mini-game based on *Gamma World* and written by Jonathan Tweet, was published in *Dungeon* 94/*Polyhedron* 153. Tweet does not plan any expansions for the game, although it received a warm reception from *Gamma World* fans and players new to the concept alike.
### Sixth Edition (2003) {#sixth_edition_2003}
In November 2002, Sword & Sorcery Studios (SSS) announced that it had licensed the *Gamma World* setting from WOTC in order to produce a sixth version of the game. SSS\'s version of the game, which reached the market in 2003, used the *d20 Modern* system, and mimicked *D&D*\'s \"three core book\" model with three hardcover manuals:
- *Gamma World Player\'s Handbook* by Bruce Baugh, Ian Eller, Mikko Rautalahti, and Geoff Skellams
- *Gamma World Game Master\'s Guide* by Bruce Baugh, Werner Hager, Lizard, and Doug Oglesby
- *Gamma World Machines and Mutants* by David Bolack, Gareth Hanrahan, Patrick O\'Duffy, and Chuck Wendig
Sword & Sorcery Studios also published three paperback supplements for the d20 version of *Gamma World*:
- *Gamma World Beyond the Horizon* by Ellen Kiley
- *Gamma World Cryptic Alliances and Unknown Enemies* by Owen K.C. Stephens, Alejandro Melchor, and Geoff Skellams
- *Gamma World Out of the Vaults* by James Maliszewski, John Snead, and Ellen P. Kiley
This new version of the game presented a more sober and serious approach to the concept of a post-nuclear world, at odds with the more light-hearted and adventurous approach taken by previous editions; it was also the first edition of the game to include fantastical nanotechnology on a large scale. In August 2005, White Wolf announced that it was reverting the rights to publish *Gamma World* products back to Wizards of the Coast, putting the game out of print again. Several critics and fans considered Tweet\'s *Omega World* to be a superior d20 System treatment of the *Gamma World* concept.
### *Mutant Future* (2008 and 2010) {#mutant_future_2008_and_2010}
An unofficial open gaming version published in 2008 and in revised form in 2010.
### Seventh Edition (2010) {#seventh_edition_2010}
At the Dungeons & Dragons Experience fan convention in early 2010, Wizards of the Coast announced a new version titled *D&D Gamma World*, eventually released in October of that year. The game is compatible with the D&D 4th Edition rules and the System Reference Document, but is not considered a separate D&D setting.
The basic box included 80 non-random cards. In addition, random \"boosters\" of \"Alpha Mutation\" and \"Omega Tech\" cards for players are sold separately in packs of eight.
This edition of *Gamma World* includes the following three boxed sets (one core set and two expansion kits):
- *D&D Gamma World Roleplaying Game* by Richard Baker and Bruce R. Cordell
- *D&D Gamma World Expansion Kit: Famine in Far-go* by Robert J. Schwalb
- *D&D Gamma World Expansion Kit: Legion of Gold* by Richard Baker and Bruce Cordell
Additional content was released for the 7th Edition of *Gamma World* at Game Day 2010 and at the 2010 Penny Arcade Expo, Trouble in Freesboro and Pax Extraterrestria respectively. In addition, a Christmas themed adventure and vehicular combat rules were released online.
Additionally, two novels were published in the setting. *Sooner Dead* by Mel Odom was published February 1, 2011, and *Red Sails in the Fallout* by Pauli Kidd, published July 5, 2011.
### *Mutant Crawl Classics* (2018) {#mutant_crawl_classics_2018}
A open gaming unofficial release from Goodman Games.
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# Gamma World
## Reception
In Issue 41 of *Moves*, Steve List reviewed the first edition and commented, \"*Gamma World* is not a game for those who take their science fiction, science, or technology seriously, but it is a good set of rules for role-playing, provided an energetic referee can be found to run the show.\"
Don Turnbull reviewed the first edition of *Gamma World* for *White Dwarf* #10, giving it an overall rating of 9 out of 10, and stated that \"*Gamma World* is good quality - let there be no mistake. This has not been thrown together in haste by earnest amateurs over glasses of cheap booze. It is a thoroughly professional job which deserves a place on the shelf (and the playing table) of anyone remotely interested in the science fiction game-setting.\"
In the 1979 book *The Playboy Winner\'s Guide to Board Games, John Jackson reviewed the first edition, and noted that \"*Gama World*could draw on a hundred science-fiction novels for material. It seems to be better organized than its cousin \[*Metamorphosis Alpha\'\'\], and the campaign map of an altered America is almost worth the cost of the game itself.\"
Ronald Pehr reviewed the first edition of *Gamma World* in *The Space Gamer* No. 32 and commented \"If you liked its progenitors, *Gamma World* is an interesting variant. Beginning players should find it easy to learn, and referees are challenged to create a playable, balanced world. It\'s somewhat expensive and the sudden-death power of futuristic weaponry and the lack of character \'levels\' may put you off, but if the basic premise is appealing you\'ll probably enjoy *Gamma World*.\"
In the July 1980 issue of *Fantastic Science Fiction*, Greg Costikyan called the rules of the first edition \"reasonably well written, if poorly organized; they are sufficient to base a campaign upon.\" However, Costikyan was appalled by the lack of hard science, calling the game \"idiotic pseudo-science\". Costikyan concluded, \"I\'m surprised that even TSR would attempt to foist junk like *Gamma World* off on an unsuspecting public.\"
In the 1980 book *The Complete Book of Wargames*, game designer Jon Freeman reviewed the first edition and commented, \"This is in every sense an improved version of *Metamorphosis Alpha*. Rules have been tightened and elaborated, and the organization is clearly superior.\" Freeman concluded, \"While it\'s not quite as open-ended in scope as *Dungeons & Dragons*, it has plenty of potential. It\'s hardly flawless, but *Gamma World* is one of the best things TSR has produced.\"
In Issue 11 of the French games magazine *Jeu et Stratégie*, Michel Brassinne found the game mechanics only ordinary, but noted \"the mutation table is a gem worth its weight in gold, it is indeed sometimes hilarious.\" Brassinne pointed out that because of similarities in rules, this game could theoretically be combined with other TSR games such as *AD&D*, but he warned, \"be careful, because this is not a walk of pleasure --- I experienced it with characters from *D&D* and I can assure you that I will not do it again soon.\" Brassinne concluded, \"Given dice, cards, modules, pencils and time, the result will be long, exciting sleepless nights.\"
Chris Baylis reviewed the second edition for *Imagine* magazine, and stated that \"For a post nuclear holocaust role-playing game, *Gamma World* game has just about all the right ingredients, in the correct proportions. It is a very good introduction into the fantasy world of role-playing, and should seriously rival all other RPGs.\"
In the August 1984 issue of *Asimov\'s Science Fiction*, Dana Lombardy called the redesign of the 2nd edition \"so extensive it should be considered a new game \... *Gamma World* offers one of the more bizarre and hostile environments to role-play in.\" Lombardy did note that \"the technology is disjointed. You can have a dog-man with a spear fighting alongside a robot with a laser, allied against humanoids with pistols and swords.\" Lombardy concluded, \"If you prefer more straightforward science fiction with known and approximately equal abilities and weapons, then *Gamma World* may not be for you. It\'s a topsy-turvy world, where the average pure-strain human is hard-pressed to exist among plants and animals mutated by humanity\'s wars. But if you like a challenge, and want to role-play something really different --- *Gamma World* could be it.\"
In Issue 37 of the French games magazine *Casus Belli*, Denis Beck found many improvements in the third edition, writing, \"Even if *Gamma World* sometimes reminds us of a transposition of *AD&D* into the future, this new version --- where we do not find the many problems that handicapped the previous editions --- really looks good alongside other post-apocalypse games.\" Beck concluded, \"It may not be the game of the year, but fans of The Great Upheaval will find plenty to enjoy here.\"
In his 1990 book *The Complete Guide to Role-Playing Games*, game critic Rick Swan reviewed the 3rd edition and commented \"Though *Gamma World* may sound like a loony-bin version of *Twilight: 2000*, it makes for some exciting adventures as the PCs explore a high-tech wonderland of mysterious landmarks and artifacts\". Swan concluded by giving the game a rating of 3 out of 4, saying, \"It\'s a bang-up job \[\...\] that is, if you don\'t take your nuclear holocausts too seriously.\"
Gene Alloway reviewed the Complete 4th Edition Game of *Gamma World* in *White Wolf* #36 (1993), rating it a 3 out of 5 and stated that \"*Gamma World* has not undergone a massive overhaul from the third edition. But it does seem better to me and to those around me familiar with both versions. It is an enjoyable, entertaining trip through an America that isn\'t quite what it used to be. If you like science fiction that takes some latitude with the laws of nature, you should visit *Gamma World, Fourth Edition*: it\'ll be a fun \'wahoo experience.\'\"
Scott Taylor for *Black Gate* in 2013 rated *Gamma World* as #8 in the top ten role-playing games of all time, saying \"There seems to be an innate fascination with the end of the world, be it from a global thermal nuclear war, zombie outbreak, alien invasion, or super-bug and *Gamma World* finds a way to bring the fantastic to this type of setting. It has survived seven editions and three companies, but still, *Gamma World* remains a fun and functional game in the current RPG marketplace.\"
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# Gamma World
## Other reviews and commentary {#other_reviews_and_commentary}
- *Polyhedron* #1
## Cancelled video game {#cancelled_video_game}
In 2011, a video game adaptation was announced at E3 called *Gamma World: Alpha Mutation* for the Xbox 360, PlayStation 3 and PC. It was to be developed by Bedlam Games and published by Atari. Unfortunately, due to unknown reasons, it was cancelled.
## Legacy
The Swedish role playing game *Mutant*, released in 1984 by Äventyrsspel, was first pitched to its future writer as \"Gamma World, set in Sweden\".
The post-apocalyptic premise of the 1997 computer game *Fallout* was inspired by *Gamma World.* Game creator Tim Cain said it was not the most balanced RPG but it had a good spirit to it.
*Gamma World* was cited as a source of inspiration for the procedurally generated world-building in Caves of Qud
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# Great Plague of London
The **Great Plague of London**, lasting from 1665 to 1666, was the most recent major epidemic of the bubonic plague to occur in England. It happened within the centuries-long Second Pandemic, a period of intermittent bubonic plague epidemics that originated in Central Asia in 1331 (the first year of the Black Death), and included related diseases such as pneumonic plague and septicemic plague, which lasted until 1750.
The Great Plague killed an estimated 100,000 people---almost a quarter of London\'s population---in 18 months. The plague was caused by the *Yersinia pestis* bacterium, which is usually transmitted to a human by the bite of a flea or louse.
The 1665--66 epidemic was on a much smaller scale than the earlier Black Death pandemic. It became known afterwards as the \"great\" plague mainly because it was the last widespread outbreak of bubonic plague in England during the 400-year Second Pandemic.
## London in 1665 {#london_in_1665}
thumb\|right\|upright=1.3\|The \"Woodcut\" map of London, dating from the 1560s thumb\|right\|upright=1.3\|Map of London by Wenceslaus Hollar, c. 1665 The plague was endemic in 17th-century London, as it was in other European cities at the time. The disease periodically erupted into massive epidemics. There were 30,000 deaths due to the plague in 1603, 35,000 in 1625, 10,000 in 1636, and smaller numbers in other years.
In late 1664, a bright comet was seen in the sky, and the people of London became fearful, wondering what evil event it portended. London at that time was a city of about 448 acres surrounded by a city wall that had originally been built to keep out raiding bands, and, in the south, by the River Thames. There were gates in the wall at Ludgate, Newgate, Aldersgate, Cripplegate, Moorgate, Bishopsgate and Aldgate, and the Thames was crossable at London Bridge. In the poorer parts of the city, filled with overcrowded tenements and garrets, hygiene was impossible to maintain. There was no sanitation, and open drains flowed along the centre of winding streets. The cobbles were slippery with animal droppings, rubbish and the slops thrown out of the houses; they were muddy and buzzing with flies in summer, and awash with sewage in winter. The City Corporation employed \"rakers\" to remove the worst of the filth, and it was transported to mounds outside the walls, where it accumulated and continued to decompose. The stench was overwhelming, and people walked around with handkerchiefs or nosegays pressed against their nostrils.
Some of the city\'s necessities, such as coal, arrived by barge, but most came by road. Carts, carriages, horses and pedestrians were crowded together, and the gateways in the wall formed bottlenecks through which it was difficult to progress. The nineteen-arch London Bridge was even more congested. Those who were better-off used hackney carriages and sedan chairs to get to their destinations without getting filthy. The poor walked, and might be drenched by water tossed up by wheeled vehicles, slops thrown into the street, or water pouring off overhanging roofs. Another hazard was the choking black smoke belching forth from soap factories, breweries, iron smelters and about 15,000 households that were burning coal to heat their homes.
Outside the city walls, shanty towns with wooden shacks and no sanitation had sprung up, providing homes for the craftsmen and tradespeople who had flocked to the already overcrowded city. The government had tried to limit the development of these \"suburbs\", but had failed: Over a quarter of a million people lived in them. When Royalists had fled the country during the Commonwealth, they had left many fine town houses vacant, and some immigrants to London had crowded into them, converting them into tenements that housed different families in every room. These properties were soon vandalised and became rat-infested.
The City of London proper was administered by the Lord Mayor, the Aldermen and the common councillors, but some parts of the greater metropolitan area were not legally part of the city. Some of these areas, both inside the City walls and outside its boundaries, had long been organised into districts of various sizes, called \"liberties\", that had historically been granted rights to self-government. (Many had originally been associated with the religious institutions that were abolished in the Dissolution of the Monasteries, whereupon their historic rights and property had been transferred to secular owners.)
By 1665, the walled City was surrounded by a ring of liberties which had come under its authority, and these had come to be referred to collectively as \'the City and Liberties\'. However, this area was surrounded by additional suburbs with other independent administrations. For example, Westminster was an independent town with its own liberties, joined to London by urban development, and the Tower of London was an independent liberty. Areas that were not part of any of these various independent administrations came under the authority of the county of Middlesex if they were north of the river, and under the authority of Surrey if they were south of the river.
At that time, bubonic plague was a much feared disease, but its cause was not understood. Many mistakenly blamed emanations from the earth, \"pestilential effluvia\", unusual weather, sickness in livestock, abnormal behaviour of animals or an increase in the numbers of moles, frogs, mice or flies. It was not until 1894 that its causal agent, the bacterium *Yersinia pestis*, was identified by Alexandre Yersin, and its transmission by rat fleas became known. Although the Great Plague in London was long assumed to be bubonic plague, caused by *Yersinia pestis*, this was only confirmed (by DNA analysis) in 2016. It is now believed that human body lice also played a key role in causing infections, perhaps more so than rats.
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# Great Plague of London
## The recording of deaths {#the_recording_of_deaths}
In order to judge the severity of an epidemic, it is first necessary to know how big the population was in which it occurred. There was no official census of the population to provide this figure, and the best contemporary count comes from the work of John Graunt (1620--1674), who was one of the earliest Fellows of the Royal Society and one of the first demographers, bringing a scientific approach to the collection of statistics. In 1662, he estimated that 384,000 people lived in the City of London, the Liberties, Westminster and the out-parishes, based on figures in the Bills of Mortality published each week in the capital. These different districts with different administrations constituted the officially recognized extent of London as a whole. In 1665, he revised his estimate to \"not above 460,000\". Other contemporaries put the figure higher (the French Ambassador, for example, suggested 600,000), but with no mathematical basis to support their estimates. The next largest city in the kingdom was Norwich, with a population of 30,000.
There was no duty to report a death to anyone in authority. Instead, each parish appointed two or more \"searchers of the dead\", whose duty was to inspect a corpse and determine the cause of death. A searcher was entitled to charge a small fee from relatives for each death they reported, and so habitually the parish would appoint someone to the post who would otherwise be destitute and would be receiving support from the parish poor rate. Typically, this meant searchers would be old women who were illiterate, might know little about identifying diseases and who would be open to dishonesty. Searchers would typically learn about a death either from the local sexton who had been asked to dig a grave or from the tolling of a church bell. Anyone who did not report a death to their local church, such as Quakers, Anabaptists, other non-Anglican Christians or Jews, frequently did not get included in the official records. Searchers during times of plague were required to live apart from the community, avoid other people and carry a white stick to warn of their occupation when outdoors, and stay indoors except when performing their duties, to avoid spreading the diseases. Searchers reported to the Parish Clerk, who made a return each week to the Company of Parish Clerks in Brode Lane. Figures were then passed to the Lord Mayor and then to the Minister of State once plague became a matter of national concern. The reported figures were used to compile the Bills of Mortality, which listed total deaths in each parish and whether by the plague. The system of Searchers to report the cause of death continued until 1836.
Graunt recorded the incompetence of the Searchers at identifying true causes of death, remarking on the frequent recording of \'consumption\' rather than other diseases which were recognized then by physicians. He suggested a cup of ale and a doubling of their fee to two groats rather than one was sufficient for Searchers to change the cause of death to one more convenient for the householders. No one wished to be known as having had a death by plague in their household, and Parish Clerks, too, connived in covering up cases of plague in their official returns. Analysis of the Bills of Mortality during the months plague took hold shows a rise in deaths other than by plague well above the average death rate, a tell-tale sign of misrepresentation of the true cause of death. As plague spread, a system of quarantine was introduced, whereby any house where someone had died from plague would be locked up and no one allowed to enter or leave for 40 days. This frequently led to the deaths of the other inhabitants, by neglect if not from the plague, and provided ample incentive not to report the disease. The official returns record 68,596 cases of plague, but a reasonable estimate suggests this figure is 30,000 short of the true total. A plague house was marked with a red cross on the door with the words \"Lord have mercy upon us\", and a watchman stood guard outside.
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# Great Plague of London
## Preventive measures {#preventive_measures}
Reports of plague around Europe began to reach England in the 1660s, causing the Privy Council to consider what steps might be taken to prevent it crossing to England. Quarantining (isolation) of ships had been used during previous outbreaks and was again introduced for ships coming to London in November 1663, following outbreaks in Amsterdam and Hamburg. Two naval ships were assigned to intercept any vessels entering the Thames estuary. Ships from infected ports were required to moor at Hole Haven on Canvey Island for a *trentine* -- period of 30 days -- before being allowed to travel up-river. Ships from ports free of plague or completing their isolation period were given a certificate of health and allowed to travel on. A second inspection line was established between the forts on opposite banks of the Thames at Tilbury and Gravesend with instructions to pass only ships with a certificate.
The isolation period was increased to forty days -- a *quarantine* -- in May 1664 as the continental plague worsened, and the areas subject to quarantine changed with the news of the spread of plague to include all of Holland, Zeeland and Friesland (all regions of the Dutch Republic); restrictions on Hamburg were removed in November. Quarantine measures against ships coming from the Dutch Republic were put in place in 29 other ports from May, starting with Great Yarmouth. The Dutch ambassador objected at the constraint of trade with his country, but England responded that it had been one of the last countries introducing such restrictions. Regulations were enforced quite strictly, so that people or houses where voyagers had come ashore without serving their quarantine were also subjected to 40 days of quarantine.
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# Great Plague of London
## Outbreak
Plague was one of the hazards of life in Britain from its dramatic appearance in 1348 with the Black Death. The Bills of Mortality began to be published regularly in 1603, in which year 33,347 deaths were recorded from plague. Between then and 1665, only four years had no recorded cases. In 1563, a thousand people were reportedly dying in London each week. In 1593, there were 15,003 deaths, 1625 saw 41,313 dead, between 1640 and 1646 came 11,000 deaths, culminating in 3,597 for 1647. The 1625 outbreak was recorded at the time as the \'Great Plague\', until deaths from the plague of 1665 surpassed it. These official figures are likely to under-report actual numbers.
### Early days {#early_days}
Plague was sufficiently uncommon that medical practitioners might have had no personal experience of seeing the disease; medical training varied from those who had attended the college of physicians, to apothecaries who also acted as doctors, to charlatans. Other diseases abounded, such as an outbreak of smallpox the year before, and these uncertainties all added to difficulties identifying the true start of the epidemic. Contemporary accounts suggest cases of plague occurred through the winter of 1664--65, some of which were fatal but a number of which did not display the virulence of the later epidemic. The winter was cold, the ground frozen from December to March, river traffic on the Thames twice blocked by ice, and it may be that the cold weather held back its spread.
This outbreak of bubonic plague in England is thought to have spread from the Netherlands, where the disease had been occurring intermittently since 1599. It is unclear exactly where the disease first struck but the initial contagion may have arrived with Dutch trading ships carrying bales of cotton from Amsterdam, which was ravaged by the disease in 1663--64, with a mortality given of 50,000. The first areas to be struck are believed to be the dock areas just outside London, and the parish of St Giles. In both of these localities, poor workers were crowded into ill-kept structures. Two suspicious deaths were recorded in St Giles parish in 1664 and another in February 1665. These did not appear as plague deaths on the Bills of Mortality, so no control measures were taken by the authorities, but the total number of people dying in London during the first four months of 1665 showed a marked increase. By the end of April, only four plague deaths had been recorded, two in the parish of St. Giles, but total deaths per week had risen from around 290 to 398.
There had been three official cases in April, a level of plague which in earlier years had not induced any official response, but the Privy Council now acted to introduce household quarantine. Justices of the Peace in Middlesex were instructed to investigate any suspected cases and to shut up the house if it was confirmed. Shortly after, a similar order was issued by the King\'s Bench to the City and Liberties. A riot broke out in St. Giles when the first house was sealed up; the crowd broke down the door and released the inhabitants. Rioters caught were punished severely. Instructions were given to build pest-houses, which were essentially isolation hospitals built away from other people where the sick could be cared for (or stay until they died). This official activity suggests that despite the few recorded cases, the government was already aware that this was a serious outbreak of plague. With the arrival of warmer weather, the disease began to take a firmer hold. In the week 2--9 May, there were three recorded deaths in the parish of St Giles, four in neighbouring St Clement Danes and one each in St Andrew Holborn and St Mary Woolchurch Haw. Only the last was actually inside the city walls. A Privy Council committee was formed to investigate methods to best prevent the spread of plague, and measures were introduced to close some of the ale houses in affected areas and limit the number of lodgers allowed in a household. In the city, the Lord Mayor issued a proclamation that all householders must diligently clean the streets outside their property, which was a householder\'s responsibility, not a state one (the city employed scavengers and rakers to remove the worst of the mess). Matters just became worse, and Aldermen were instructed to find and punish those failing their duty. As cases in St. Giles began to rise, an attempt was made to quarantine the area and constables were instructed to inspect everyone wishing to travel and contain inside vagrants or suspect persons.
People began to be alarmed. Samuel Pepys, who had an important position at the Admiralty, stayed in London and provided a contemporary account of the plague through his diary. On 30 April he wrote: \"Great fears of the sickness here in the City it being said that two or three houses are already shut up. God preserve us all!\" Another source of information on the time is *A Journal of the Plague Year*, which was written by Daniel Defoe and published in 1722. He had been only five when the plague struck but made use of his family\'s recollections (his uncle was a saddler in East London and his father a butcher in Cripplegate), interviews with survivors and sight of such official records as were available.
The onset of the disease was recalled two years later by Puritan minister Thomas Vincent:`{{blockquote|It was in the month of May that the Plague was first taken notice of; our Bill of Mortality did let us know but of three which died of the disease in the whole year before; but in the beginning of May the bill tells us of nine...fear quickly begins to creep upon peoples hearts; great thoughts and discourse there is in Town about the Plague, and they cast in their minds whether they should go if the Plague should increase. Yet when the next weeks Bill signifieth to them the disease from nine to three their minds are something appeased; discourse of that subject cools; fears are hushed, and hopes take place, that the black cloud did but threaten, and give a few drops; but the wind would drive it away. But when in the next Bill the number of the dead by the Plague is mounted from three to fourteen, and in the next to seventeen, and in the next to forty-three, and the disease begins so much to increase, and disperse. Now secure sinners begin to be startled, and those who would have slept at quiet still in their nests, are unwillingly awakened.<ref name="Vincent">{{cite book |last1=Vincent |first1=Thomas |author-link1=Thomas Vincent (minister) |title=God's Terrible Voice in the City |date=1667 |publisher=George Calvert |location=London |url=https://quod.lib.umich.edu/e/eebo/A64990.0001.001?view=toc |access-date=22 November 2020}}</ref>}}`{=mediawiki}
### Exodus from the city {#exodus_from_the_city}
thumb\|right\|upright=1.5\|Scenes in London during the plague By July 1665, plague was rampant in the City of London. The rich ran away, including King Charles II of England, his family and his court, who left the city for Salisbury, moving on to Oxford in September when some cases of plague occurred in Salisbury. The aldermen and most of the other city authorities opted to stay at their posts. The Lord Mayor of London, Sir John Lawrence, also decided to stay in the city. Businesses were closed when merchants and professionals fled. Defoe wrote \"Nothing was to be seen but wagons and carts, with goods, women, servants, children, coaches filled with people of the better sort, and horsemen attending them, and all hurrying away\". As the plague raged throughout the summer, only a small number of clergymen, physicians and apothecaries remained to cope with an increasingly large number of victims. Ellen Cotes, author of *London\'s Dreadful Visitation*, expressed the hope that \"Neither the Physicians of our Souls or Bodies may hereafter in such great numbers forsake us\".
The poorer people were also alarmed by the contagion and some left the city, but it was not easy for them to abandon their accommodation and livelihoods for an uncertain future elsewhere. Before exiting through the city gates, they were required to possess a certificate of good health signed by the Lord Mayor and these became increasingly difficult to obtain. As time went by and the numbers of plague victims rose, people living in the villages outside London began to resent this exodus and were no longer prepared to accept townsfolk from London, with or without a certificate. The refugees were turned back, were not allowed to pass through towns and had to travel across country, and were forced to live rough on what they could steal or scavenge from the fields. Many died in wretched circumstances of starvation and dehydration in the hot summer that was to follow.
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# Great Plague of London
## Outbreak
### Height of the epidemic {#height_of_the_epidemic}
In the last week of July, the London Bill of Mortality showed 3,014 deaths, of which 2,020 had died from the plague. The number of deaths as a result of plague may have been underestimated, as deaths in other years in the same period were much lower, at around 300. As the number of victims affected mounted up, burial grounds became overfull, and pits were dug to accommodate the dead. Drivers of dead-carts travelled the streets calling \"Bring out your dead\" and carted away piles of bodies. The authorities became concerned that the number of deaths might cause public alarm and ordered that body removal and interment should take place only at night. As time went on, there were too many victims, and too few drivers, to remove the bodies which began to be stacked up against the walls of houses. Daytime collection was resumed and the plague pits became mounds of decomposing corpses. In the parish of Aldgate, a great hole was dug near the churchyard, fifty feet long and twenty feet wide. Digging was continued by labourers at one end while the dead-carts tipped in corpses at the other. When there was no room for further extension it was dug deeper until ground water was reached at twenty feet. When finally covered with earth it housed 1,114 corpses.
Plague doctors traversed the streets diagnosing victims, many of them without formal medical training. Several public health efforts were attempted. Physicians were hired by city officials and burial details were carefully organized, but panic spread through the city and, out of the fear of contagion, bodies were hastily buried in overcrowded pits. The means of transmission of the disease were not known but thinking they might be linked to the animals, the City Corporation ordered a cull of dogs and cats. This decision may have extended the length of the epidemic since those animals could have helped keep in check the rat population carrying the fleas which transmitted the disease. Thinking bad air was involved in transmission, the authorities ordered giant bonfires to be burned in the streets and house fires to be kept burning night and day, in the hope that the air would be cleansed. Tobacco was thought to be a prophylactic and it was later said that no London tobacconist had died from the plague during the epidemic. Trade and business had dried up, and the streets were empty of people except for the dead-carts and the dying victims, as witnessed and recorded by Samuel Pepys in his diary: \"Lord! How empty the streets are and how melancholy, so many poor sick people in the streets full of sores... in Westminster, there is never a physician and but one apothecary left, all being dead.\" That people did not starve was down to the foresight of Sir John Lawrence and the Corporation of London who arranged for a commission of one farthing to be paid above the normal price for every quarter of corn landed in the Port of London. Another food source was the villages around London which, denied of their usual sales in the capital, left vegetables in specified market areas, negotiated their sale by shouting, and collected their payment after the money had been left submerged in a bucket of vinegar to \"disinfect\" the coins.
Records state that plague deaths in London and the suburbs crept up over the summer from 2,000 people per week to over 7,000 per week in September. These figures are likely to be a considerable underestimate. Many of the sextons and parish clerks who kept the records themselves died. Quakers refused to co-operate and many of the poor were just dumped into mass graves unrecorded. It is not clear how many people caught the disease and made a recovery because only deaths were recorded and many records were destroyed in the Great Fire of London the following year. In the few districts where intact records remain, plague deaths varied between 30% and over 50% of the total population.
Vincent wrote:`{{blockquote|it was very dismal to behold the red crosses, and read in great letters "LORD, HAVE MERCY UPON US" on the doors, and watchmen standing before them with halberds...people passing by them so gingerly, and with such fearful looks as if they had been lined with enemies in ambush to destroy them...a man at the corner of Artillery-wall, that as I judge, through the dizziness of his head with the disease, which seized upon him there, had dasht his face against the wall; and when I came by, he lay hanging with his bloody face over the rails, and bleeding upon the ground...I went and spoke to him; he could make no answer, but rattled in the throat, and as I was informed, within half an hour died in the place. It would be endless to speak of what we have seen and heard, of some in their frenzy, rising out of their beds, and leaping about their rooms; others crying and roaring at their windows; some coming forth almost naked, and running into the streets...scarcely a day passed over my head for, I think, a month or more together, but I should hear of the death of some one or more that I knew. The first day that they were smitten, the next day some hopes of recovery, and the third day, that they were dead.<ref name="Vincent" />}}`{=mediawiki}
The outbreak was concentrated in London, but it affected other areas as well. Perhaps the best known example occurred in the village of Eyam in Derbyshire. The plague allegedly arrived with a merchant carrying a parcel of cloth sent from London. The villagers imposed a quarantine on themselves to stop the further spread of the disease. This prevented the disease from moving into surrounding areas, but around 33% of the village\'s inhabitants died over a period of fourteen months. Other places hit hard included Derby and Norwich. In Bristol strenuous efforts by the City Council seems to have limited the death rate to c.0.6 per cent during an outbreak lasting from April to September 1666.
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# Great Plague of London
## Aftermath
By late autumn, the death toll in London and the suburbs began to slow until, in February 1666, it was considered safe enough for the King and his entourage to come back to the city. With the return of the monarch, others began to return: The gentry returned in their carriages accompanied by carts piled high with their belongings. The judges moved back from Windsor to sit in Westminster Hall; Parliament, which had been prorogued in April 1665, did not reconvene until September 1666. Trade recommenced and businesses and workshops opened up. London was the goal of a new wave of people who flocked to the city in expectation of making their fortunes. Writing at the end of March 1666, Lord Clarendon, the Lord Chancellor, stated \"\... the streets were as full, the Exchange as much crowded, the people in all places as numerous as they had ever been seen \...\".
Plague cases continued to occur sporadically at a modest rate until mid-1666. That September, the Great Fire of London destroyed much of the City of London, and some people believed that the fire put an end to the epidemic. It is now thought that the plague had largely subsided before the fire took place. Most of the later cases of plague were found in the suburbs, and it was the City of London that was destroyed by the fire.
According to the Bills of Mortality, there were in total 68,596 deaths in London from the plague in 1665. Lord Clarendon estimated that the true number of mortalities was probably twice that figure. 1666 saw further deaths in other cities but on a lesser scale. Dr Thomas Gumble, chaplain to the Duke of Albemarle, both of whom had stayed in London for the whole of the epidemic, estimated that the total death count for the country from plague during 1665 and 1666 was about 200,000. Among the more notable death victims were Samuel Fisher, John Godwin, John Lewger and George Starkey.
The Great Plague of 1665/1666 was the most recent major outbreak of bubonic plague in Great Britain. The last recorded death from plague came in 1679, and it was removed as a specific category in the Bills of Mortality after 1703. It spread to other towns in East Anglia and the southeast of England but fewer than ten per cent of parishes outside London had a higher than average death rate during those years. Urban areas were more affected than rural ones; Norwich, Ipswich, Colchester, Southampton and Winchester were badly affected, while the west of England and areas of the English Midlands escaped altogether.
The population of England in 1650 was approximately 5.25 million, which declined to about 4.9 million by 1680, recovering to just over 5 million by 1700. Other diseases, such as smallpox, took a high toll on the population without the contribution by plague. The higher death rate in cities, both generally and specifically from the plague, was made up by continuous immigration, from small towns to larger ones and from the countryside to the towns.
There were no contemporary censuses of London\'s population, but available records suggest that the population returned to its previous level within a couple of years. Burials in 1667 had returned to 1663 levels, Hearth Tax returns had recovered, and John Graunt contemporarily analysed baptism records and concluded they represented a recovered population. Part of this could be accounted for by the return of wealthy households, merchants and manufacturing industries, all of which needed to replace losses among their staff and took steps to bring in necessary people. Colchester had suffered more severe depopulation, but manufacturing records for cloth suggested that production had recovered or even increased by 1669, and the total population had nearly returned to pre-plague levels by 1674. Other towns did less well: Ipswich was affected less than Colchester, but in 1674, its population had dropped by 18%, more than could be accounted for by the plague deaths alone.`{{dubious|date=July 2018}}`{=mediawiki}
As a proportion of the population who died, the London death toll was less severe than in some other towns. The total of deaths in London was greater than in any previous outbreak for 100 years, though as a proportion of the population, the epidemics in 1563, 1603 and 1625 were comparable or greater. Perhaps around 2.5% of the English population died.
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# Great Plague of London
## Impact
The plague in London largely affected the poor, as the rich were able to leave the city by either retiring to their country estates or residing with kin in other parts of the country. The subsequent Great Fire of London ruined many city merchants and property owners. As a result of these events, London was largely rebuilt and Parliament enacted the Rebuilding of London Act 1666. The street plan of the capital remained relatively unchanged, but some improvements were made: streets were widened, pavements were created, open sewers abolished, wooden buildings and overhanging gables forbidden, and the design and construction of buildings controlled. The use of brick or stone was mandatory and many gracious buildings were constructed. Not only was the capital rejuvenated, but it became a healthier environment in which to live. Londoners had a greater sense of community after they had overcome the great adversities of 1665 and 1666.
Rebuilding took over ten years and was supervised by Robert Hooke as Surveyor of London. The architect Sir Christopher Wren was involved in the rebuilding of St Paul\'s Cathedral and more than fifty London churches. King Charles II did much to foster the rebuilding work. He was a patron of the arts and sciences and founded the Royal Observatory and supported the Royal Society, a scientific group whose early members included Robert Hooke, Robert Boyle and Sir Isaac Newton. In fact, out of the fire and pestilence flowed a renaissance in the arts and sciences in England.
Plague pits have been archaeologically excavated during underground construction work. Between 2011 and 2015, 3,500 burials from the \'New Churchyard\' or \'Bethlam burial ground\' were discovered during the construction of the Crossrail railway at Liverpool Street. *Yersinia pestis* DNA was found in the teeth of individuals found buried in pits at the site, confirming they had died of bubonic plague
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# Gamete
A **gamete** (`{{IPAc-en|ˈ|ɡ|æ|m|iː|t}}`{=mediawiki} `{{respell|GAM|eet}}`{=mediawiki}) is a haploid cell that fuses with another haploid cell during fertilization in organisms that reproduce sexually. Gametes are an organism\'s **reproductive cells**, also referred to as **sex cells**. The name gamete was introduced by the German cytologist Eduard Strasburger in 1878.
Gametes of both mating individuals can be the same size and shape, a condition known as isogamy. By contrast, in the majority of species, the gametes are of different sizes, a condition known as anisogamy or heterogamy that applies to humans and other mammals. The human ovum has approximately 100,000 times the volume of a single human sperm cell. The type of gamete an organism produces determines its sex and sets the basis for the sexual roles and sexual selection.
In humans and other species that produce two morphologically distinct types of gametes, and in which each individual produces only one type, a female is any individual that produces the larger type of gamete called an ovum, and a male produces the smaller type, called a sperm cell or spermatozoon. Sperm cells are small and motile due to the presence of a tail-shaped structure, the flagellum, that provides propulsion. In contrast, each egg cell or ovum is comparably large and non-motile.
Oogenesis, the process of female gamete formation in animals, involves meiosis (including meiotic recombination) of a diploid primary oocyte to produce a haploid ovum. Spermatogenesis, the process of male gamete formation in animals, involves meiosis in a diploid primary spermatocyte to produce haploid spermatozoa. In animals, ova are produced in the ovaries of females and sperm develop in the testes of males. During fertilization, a spermatozoon and an ovum, each carrying half of the genetic information of an individual, unite to form a zygote that develops into a new diploid organism.
## Evolution
It is generally accepted that isogamy is the ancestral state from which anisogamy and oogamy evolved, although its evolution has left no fossil records. There are almost invariably only two gamete types, all analyses showing that intermediate gamete sizes are eliminated due to selection. Since intermediate sized gametes do not have the same advantages as small or large ones, they do worse than small ones in mobility and numbers, and worse than large ones in supply.
## Differences between gametes and somatic cells {#differences_between_gametes_and_somatic_cells}
In contrast to a gamete, which has only one set of chromosomes, a diploid somatic cell has two sets of homologous chromosomes, one of which is a copy of the chromosome set from the sperm and one a copy of the chromosome set from the egg cell. Recombination of the genes during meiosis ensures that the chromosomes of gametes are not exact duplicates of either of the sets of chromosomes carried in the parental diploid chromosomes but a mixture of the two.
## Artificial gametes {#artificial_gametes}
Artificial gametes, also known as in vitro derived gametes (IVD), stem cell-derived gametes (SCDGs), and in vitro generated gametes (IVG), are gametes derived from stem cells. The use of such artificial gametes would \"necessarily require IVF techniques\". Research shows that artificial gametes may be a reproductive technique for same-sex male couples, although a surrogate mother would still be required for the gestation period. Women who have passed menopause may be able to produce eggs and bear genetically related children with artificial gametes. Robert Sparrow wrote, in the Journal of Medical Ethics, that embryos derived from artificial gametes could be used to derive new gametes and this process could be repeated to create multiple human generations in the laboratory. This technique could be used to create cell lines for medical applications and for studying the heredity of genetic disorders. Additionally, this technique could be used for human enhancement by selectively breeding for a desired genome or by using recombinant DNA technology to create enhancements that have not arisen in nature.
## Plants
Plants that reproduce sexually also produce gametes. However, since plants have a life cycle involving alternation of diploid and haploid generations some differences from animal life cycles exist. Plants use meiosis to produce spores that develop into multicellular haploid gametophytes which produce gametes by mitosis. In animals there is no corresponding multicellular haploid phase. The sperm of plants that reproduce using spores are formed by mitosis in an organ of the gametophyte known as the antheridium and the egg cells by mitosis in a flask-shaped organ called the archegonium. Plant sperm cells are their only motile cells, often described as flagellate, but more correctly as ciliate.
Bryophytes have 2 flagella, horsetails have up to 200 and the mature spermatozoa of the cycad *Zamia pumila* has up to 50,000 flagella. Cycads and *Ginkgo biloba* are the only gymnosperms with motile sperm.
In the flowering plants, the female gametophyte is produced inside the ovule within the ovary of the flower. When mature, the haploid gametophyte produces female gametes which are ready for fertilization. The male gametophyte is produced inside a pollen grain within the anther and is non-motile, but can be distributed by wind, water or animal vectors. When a pollen grain lands on a mature stigma of a flower it germinates to form a pollen tube that grows down the style into the ovary of the flower and then into the ovule.
The pollen then produces non-motile sperm nuclei by mitosis that are transported down the pollen tube to the ovule where they are released for fertilization of the egg cell
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# Gregory Chaitin
**Gregory John Chaitin** (`{{IPAc-en|ˈ|tʃ|aɪ|t|ɪ|n}}`{=mediawiki} `{{respell|CHY|tin}}`{=mediawiki}; born 25 June 1947) is an Argentine-American mathematician and computer scientist. Beginning in the late 1960s, Chaitin made contributions to algorithmic information theory and metamathematics, in particular a computer-theoretic result equivalent to Gödel\'s incompleteness theorem. He is considered to be one of the founders of what is today known as algorithmic (Solomonoff--Kolmogorov--Chaitin, Kolmogorov or program-size) complexity together with Andrei Kolmogorov and Ray Solomonoff. Along with the works of e.g. Solomonoff, Kolmogorov, Martin-Löf, and Leonid Levin, algorithmic information theory became a foundational part of theoretical computer science, information theory, and mathematical logic. It is a common subject in several computer science curricula. Besides computer scientists, Chaitin\'s work draws attention of many philosophers and mathematicians to fundamental problems in mathematical creativity and digital philosophy.
## Mathematics and computer science {#mathematics_and_computer_science}
Gregory Chaitin is Jewish. He attended the Bronx High School of Science and the City College of New York, where he (still in his teens) developed the theory that led to his independent discovery of algorithmic complexity.
Chaitin has defined Chaitin\'s constant Ω, a real number whose digits are equidistributed and which is sometimes informally described as an expression of the probability that a random program will halt. Ω has the mathematical property that it is definable, with asymptotic approximations from below (but not from above), but not computable.
Chaitin is also the originator of using graph coloring to do register allocation in compiling, a process known as Chaitin\'s algorithm.
He was formerly a researcher at IBM\'s Thomas J. Watson Research Center in New York. He has written more than 10 books that have been translated to about 15 languages. He is today interested in questions of metabiology and information-theoretic formalizations of the theory of evolution, and is a member of the Institute for Advanced Studies at Mohammed VI Polytechnic University.
## Other scholarly contributions {#other_scholarly_contributions}
Chaitin also writes about philosophy, especially metaphysics and philosophy of mathematics (particularly about epistemological matters in mathematics). In metaphysics, Chaitin claims that algorithmic information theory is the key to solving problems in the field of biology (obtaining a formal definition of \'life\', its origin and evolution) and neuroscience (the problem of consciousness and the study of the mind).
In recent writings, he defends a position known as digital philosophy. In the epistemology of mathematics, he claims that his findings in mathematical logic and algorithmic information theory show there are \"mathematical facts that are true for no reason, that are true by accident\". Chaitin proposes that mathematicians must abandon any hope of proving those mathematical facts and adopt a quasi-empirical methodology.
## Honors
In 1995 he was given the degree of doctor of science *honoris causa* by the University of Maine. In 2002 he was given the title of honorary professor by the University of Buenos Aires in Argentina, where his parents were born and where Chaitin spent part of his youth. In 2007 he was given a Leibniz Medal by Wolfram Research. In 2009 he was given the degree of doctor of philosophy *honoris causa* by the National University of Córdoba. He was formerly a researcher at IBM\'s Thomas J. Watson Research Center and a professor at the Federal University of Rio de Janeiro
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# Gestation
**Gestation** is the period of development during the carrying of an embryo, and later fetus, inside viviparous animals (the embryo develops within the parent). It is typical for mammals, but also occurs for some non-mammals. Mammals during pregnancy can have one or more gestations at the same time, for example in a multiple birth.
The time interval of a gestation is called the *gestation period*. In obstetrics, *gestational age* refers to the time since the onset of the last menses, which on average is fertilization age plus two weeks.
## Mammals
In mammals, pregnancy begins when a zygote (fertilized ovum) implants in the female\'s uterus and ends once the fetus leaves the uterus during labor or an abortion (whether induced or spontaneous).
### Humans
alt=Timeline of human fertilization, ending with implantation of the blastocyst eight to nine days after fertilization.\|thumb\|upright=1.5\|Timeline of human fertilization In humans, pregnancy can be defined clinically, biochemically or biologically. Clinically, pregnancy starts from first day of the mother\'s last period. Biochemically, pregnancy starts when a woman\'s human chorionic gonadotropin (hCG) levels rise above 25 mIU/mL. Biologically, pregnancy starts at implantation of the fertilized egg.
Human pregnancy can be divided into three trimesters, each approximately three months long: the first, second, and third trimester. The first trimester is from the last menstrual period through the 13th week, the second trimester is 14th--28/29th week, and the third trimester is 29/30th--42nd week. Birth normally occurs at a gestational age of about 40 weeks, though it is common for births to occur from 37 to 42 weeks. Labor occurring prior to 37 weeks gestation is considered preterm labor and can result from multiple factors, including previous preterm deliveries.
Prenatal care is important for the maintenance of a healthy pregnancy and surveillance of related complications. In high-income countries, prenatal care typically involves monthly visits during the first two trimesters, with an increasing number of visits closer to delivery. At these visits, healthcare providers will evaluate a variety of parental and fetal metrics, including fetal growth and heart rate, birth defects, maternal blood pressure, among others.
After birth, health care providers will measure the baby\'s weight, vital signs, reflexes, head circumference, muscle tone, and posture to help determine the gestational age.
Various factors can influence the duration of gestation, including diseases in pregnancy and adequate prenatal care. The rates of morbidity and pre-existing diseases that predispose mothers to life-threatening, pregnancy-related complications in the United States are increasing. Inaccessibility of prenatal care may partially explain this ongoing disparity.
### Placental mammals {#placental_mammals}
During gestation in placental mammals, there is a gradual physiological increase in senescence in the maternal decidua (the specialized layer of endometrium that forms the base of the placental bed) and in placental cells. This increase in senescence is associated with a gradual physiological increase in DNA damage during gestation. A positive correlation between the gestation period and maximum lifespan was observed across 740 mammalian species. It was postulated that the rates of DNA damage and senescence may impact the gestation period as well as lifespan.
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# Gestation
## Non-mammals {#non_mammals}
In viviparous animals, the embryo develops inside the body of the mother, as opposed to outside in an egg (oviparity). The mother then gives live birth. The less developed form of viviparity is called ovoviviparity, in which the mother carries embryos inside eggs. Most vipers exhibit ovoviviparity. The more developed form of viviparity is called placental viviparity; mammals are the best example, but it has also evolved independently in other animals, such as in scorpions, some sharks, and in velvet worms. Viviparous offspring live independently and require an external food supply from birth. Certain lizards also employ this method such as the genera *Tiliqua* and *Corucia.* The placenta is attached directly to the mother in these lizards which is called viviparous matrotrophy.
Ovoviviparous animals develop within eggs that remain within the mother\'s body up until they hatch or are about to hatch. It is similar to viviparity in that the embryo develops within the mother\'s body. Unlike the embryos of viviparous species, ovoviviparous embryos are nourished by the egg yolk rather than by the mother\'s body. However, the mother\'s body does provide gas exchange. The young of ovoviviparous amphibians are sometimes born as larvae, and undergo metamorphosis outside the body of the mother.
The fish family Syngnathidae has the unique characteristic whereby females lay their eggs in a brood pouch on the male\'s chest, and the male incubates the eggs. Fertilization may take place in the pouch or before implantation in the water. Included in Syngnathidae are seahorses, the pipefish, and the weedy and leafy sea dragons. Syngnathidae is the only family in the animal kingdom to which the term \"male pregnancy\" has been applied
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# Georges Braque
**Georges Braque** (`{{IPAc-en|b|r|ɑː|k|,_|b|r|æ|k}}`{=mediawiki} `{{respell|BRA(H)K}}`{=mediawiki}; `{{IPA|fr|ʒɔʁʒ bʁak|lang}}`{=mediawiki}; 13 May 1882 -- 31 August 1963) was a major 20th-century French painter, collagist, draughtsman, printmaker and sculptor. His most notable contributions were in his alliance with Fauvism from 1905, and the role he played in the development of Cubism. Braque\'s work between 1908 and 1912 is closely associated with that of his colleague Pablo Picasso. Their respective Cubist works were indistinguishable for many years, yet the quiet nature of Braque was partially eclipsed by the fame and notoriety of Picasso.
## Early life {#early_life}
Georges Braque was born on 13 May 1882 in Argenteuil, Val-d\'Oise. He grew up in Le Havre and trained to be a house painter and decorator like his father and grandfather. However, he also studied artistic painting during evenings at the École supérieure d\'art et design Le Havre-Rouen, previously known as the École supérieure des Arts in Le Havre, from about 1897 to 1899. In Paris, he apprenticed with a decorator and was awarded his certificate in 1902. The next year, he attended the Académie Humbert, also in Paris, and painted there until 1904. It was here that he met Marie Laurencin and Francis Picabia.
## Fauvism
Braque\'s earliest works were impressionistic, but after seeing the work exhibited by the artistic group known as the \"Fauves\" (Beasts) in 1905, he adopted a Fauvist style. The Fauves, a group that included Henri Matisse and André Derain among others, used brilliant colors to represent emotional response. Braque worked most closely with the artists Raoul Dufy and Othon Friesz, who shared Braque\'s hometown of Le Havre, to develop a somewhat more subdued Fauvist style. In 1906, Braque traveled with Friesz to L\'Estaque, to Antwerp, and home to Le Havre to paint.
In May 1907, he successfully exhibited works of the Fauve style in the Salon des Indépendants. The same year, Braque\'s style began a slow evolution as he became influenced by Paul Cézanne who had died in 1906 and whose works were exhibited in Paris for the first time in a large-scale, museum-like retrospective in September 1907. The 1907 Cézanne retrospective at the *italic=no* greatly affected the avant-garde artists of Paris, resulting in the advent of Cubism.
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# Georges Braque
## Cubism
Braque\'s paintings of 1908--1912 reflected his new interest in geometry and simultaneous perspective. He conducted an intense study of the effects of light and perspective and the technical means that painters use to represent these effects, seeming to question the most standard of artistic conventions. In his village scenes, for example, Braque frequently reduced an architectural structure to a geometric form approximating a cube, yet rendered its shading so that it looked both flat and three-dimensional by fragmenting the image. He showed this in the painting *Houses at l\'Estaque*.
Beginning in 1909, Braque began to work closely with Pablo Picasso who had been developing a similar proto-Cubist style of painting. At the time, Pablo Picasso was influenced by Gauguin, Cézanne, African masks and Iberian sculpture while Braque was interested mainly in developing Cézanne\'s ideas of multiple perspectives. \"A comparison of the works of Picasso and Braque during 1908 reveals that the effect of his encounter with Picasso was more to accelerate and intensify Braque's exploration of Cézanne's ideas, rather than to divert his thinking in any essential way.\" Braque\'s essential subject is the ordinary objects he has known practically forever. Picasso celebrates animation, while Braque celebrates contemplation. Thus, the invention of Cubism was a joint effort between Picasso and Braque, then residents of Montmartre, Paris. These artists were the style\'s main innovators. After meeting in October or November 1907, Braque and Picasso, in particular, began working on the development of Cubism in 1908. Both artists produced paintings of monochromatic color and complex patterns of faceted form, now termed Analytic Cubism.
A decisive time of its development occurred during the summer of 1911, when Georges Braque and Pablo Picasso painted side by side in Céret in the French Pyrenees, each artist producing paintings that are difficult---sometimes virtually impossible---to distinguish from those of the other. In 1912, they began to experiment with collage and Braque invented the *papier collé* technique.
On 14 November 1908, the French art critic Louis Vauxcelles, in his review of Georges Braque\'s exhibition at Kahnweiler\'s gallery called Braque a daring man who despises form, \"reducing everything, places and a figures and houses, to geometric schemas, to cubes\".
Vauxcelles, on 25 March 1909, used the terms \"bizarreries cubiques\" (cubic oddities) after seeing a painting by Braque at the Salon des Indépendants.
The term \'Cubism\', first pronounced in 1911 with reference to artists exhibiting at the Salon des Indépendants, quickly gained wide use but Picasso and Braque did not adopt it initially. Art historian Ernst Gombrich described Cubism as \"the most radical attempt to stamp out ambiguity and to enforce one reading of the picture---that of a man-made construction, a colored canvas.\" The Cubist style spread quickly throughout Paris and then Europe.
The two artists\' productive collaboration continued and they worked closely together until the beginning of World War I in 1914, when Braque enlisted with the French Army. In May 1915, Braque received a severe head injury in battle at Carency and suffered temporary blindness. He was trepanned, and required a long period of recuperation.
## Later work {#later_work}
Braque resumed painting in late 1916. Working alone, he began to moderate the harsh abstraction of cubism. He developed a more personal style characterized by brilliant color, textured surfaces, and---after his relocation to the Normandy seacoast---the reappearance of the human figure. He painted many still life subjects during this time, maintaining his emphasis on structure. One example of this is his 1943 work *Blue Guitar*, which hangs in the Allen Memorial Art Museum. During his recovery he became a close friend of the cubist artist Juan Gris.
He continued to work during the remainder of his life, producing a considerable number of paintings, graphics, and sculptures. Braque, along with Matisse, is credited for introducing Pablo Picasso to Fernand Mourlot, and most of the lithographs and book illustrations he himself created during the 1940s and \'50s were produced at the Mourlot Studios. In 1952--53 he also produced *The Birds*, a ceiling painting for a room in the Louvre. In 1962 Braque worked with master printmaker Aldo Crommelynck to create his series of etchings and aquatints titled *L'Ordre des Oiseaux* (*The Order of Birds*), which was accompanied by the poet Saint-John Perse\'s text.
Braque died on 31 August 1963 in Paris. He is buried in the cemetery of the Church of St. Valery in Varengeville-sur-Mer, Normandy whose windows he designed. Braque\'s work is in most major museums throughout the world.
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# Georges Braque
## Style
Braque believed that an artist experienced beauty \"... in terms of volume, of line, of mass, of weight, and through that beauty \[he\] interpret\[s\] \[his\] subjective impression\...\" He described \"objects shattered into fragments\... \[as\] a way of getting closest to the object\...Fragmentation helped me to establish space and movement in space\". He adopted a monochromatic and neutral color palette in the belief that such a palette would emphasize the subject matter.
Although Braque began his career painting landscapes, during 1908 he, alongside Picasso, discovered the advantages of painting still lifes instead. Braque explained that he \"\... began to concentrate on still lifes, because in the still-life you have a tactile, I might almost say a manual space\... This answered to the hankering I have always had to touch things and not merely see them\... In tactile space you measure the distance separating you from the object, whereas in visual space you measure the distance separating things from each other. This is what led me, long ago, from landscape to still-life\" A still life was also more accessible, in relation to perspective, than landscape, and permitted the artist to see the multiple perspectives of the object. Braque\'s early interest in still lifes revived during the 1930s.
During the period between the wars, Braque exhibited a freer, more relaxed style of Cubism, intensifying his color use and a looser rendering of objects. However, he still remained committed to the cubist method of simultaneous perspective and fragmentation. In contrast to Picasso, who continuously reinvented his style of painting, producing both representational and cubist images, and incorporating surrealist ideas into his work, Braque continued in the Cubist style, producing luminous, other-worldly still life and figure compositions. By the time of his death in 1963, he was regarded as one of the elder statesmen of the School of Paris, and of modern art.
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# Georges Braque
## 2010 theft
On 20 May 2010, the Musée d\'Art Moderne de la Ville de Paris reported the overnight theft of five paintings from its collection. The paintings taken were *Le pigeon aux petits pois* (*The Pigeon with the Peas*) by Pablo Picasso, *La Pastorale* by Henri Matisse, *L\'Olivier Près de l\'Estaque* (*Olive Tree near Estaque*) by Georges Braque, *`{{Interlanguage link|La Femme à l'Éventail|fr|3=La Femme à l'éventail (Modigliani)}}`{=mediawiki}* (*Woman with a Fan*) by Amedeo Modigliani and *Nature Morte aux Chandeliers* (*Still Life with Chandeliers*) by Fernand Léger and were valued at `{{Nowrap|€100 million}}`{=mediawiki} ( `{{Nowrap|$123 million USD}}`{=mediawiki}). A window had been smashed and CCTV footage showed a masked man taking the paintings. Authorities believe the thief acted alone. The man carefully removed the paintings from their frames, which he left behind.
## Gallery
<File:Georges> Braque, 1908, Plate and Fruit Dish, oil on canvas, 46 x 55 cm, private collection.jpg\|Georges Braque, 1908, *Plate and Fruit Dish*, oil on canvas, 46 × 55 cm, private collection <File:Georges> Braque, 1908, Cinq bananes et deux poires (Five Bananas and Two Pears), oil on canvas, 24 x 33 cm, Musée National d\'Art Moderne.jpg\|Georges Braque, 1908, *Cinq bananes et deux poires* (*Five Bananas and Two Pears*), oil on canvas, 24 × 33 cm, Musée National d\'Art Moderne <File:Georges> Braque, 1908, Maisons à l\'Estaque (Houses at L\'Estaque), oil on canvas, 73 x 59.5 cm, Kunst Museum Bern.jpg\|Georges Braque, 1908, *Maisons à l\'Estaque* (*Houses at l\'Estaque*), oil on canvas, 73 × 59.5 cm, Kunstmuseum Bern <File:Georges> Braque, 1908-09, Fruit Dish, oil on canvas, 54 x 65 cm.JPG\|Georges Braque, 1908--09, *Fruit Dish*, oil on canvas, 54 × 65 cm, Moderna Museet, Stockholm <File:Georges> Braque, 1909, Port en Normandie (Little Harbor in Normandy), 81.1 x, The Art Institute of Chicago.jpg\|Georges Braque, 1909, *Port en Normandie* (*Little Harbor in Normandy*), 81.1 × 80.5 cm, The Art Institute of Chicago <File:Georges> Braque, 1909, La Roche-Guyon, le château (The Castle at Roche-Guyon), oil on canvas, 80 x 59.5 cm, Moderna Museet, Stockholm.jpg\|Georges Braque, 1909, *La Roche-Guyon, le château* (*The Castle at Roche-Guyon*), oil on canvas, 80 × 59.5 cm, Moderna Museet, Stockholm <File:Georges> Braque, 1909 (September), Violin and Palette (Violon et palette, Dans l\'atelier), oil on canvas, 91.7 x 42.8 cm, Solomon R. Guggenheim Museum.jpg\|Georges Braque, 1909 (September), *Violin and Palette* (*Violon et palette, Dans l\'atelier*), oil on canvas, 91.7 × 42.8 cm, Solomon R. Guggenheim Museum <File:Georges> Braque, 1909-10, Pitcher and Violin, oil on canvas, 116.8 x 73.2 cm, Kunstmuseum Basel.jpg\|Georges Braque, 1909--10, *Pitcher and Violin*, oil on canvas, 116.8 × 73.2 cm, Kunstmuseum Basel <File:Georges> Braque, spring 1910, Femme tenant une Mandoline, 92 x 73 cm, Bayerische Staatsgemäldesammlungen, Munich\...jpg\|Georges Braque, 1910, *Femme tenant une Mandoline*, 92 × 73 cm, Bavarian State Painting Collections <File:Georges> Braque, 1910, Portrait of a Woman, Female Figure (Torso Ženy), oil on canvas, 91 x 61 cm, private collection.jpg\|Georges Braque, 1910, *Portrait of a Woman*, *Female Figure* (*Torso Ženy*), oil on canvas, 91 × 61 cm, private collection <File:Georges> Braque, 1911, Nature morte (Still Life), Reproduced in Du Cubisme, 1912.jpg\|Georges Braque, 1911, *Nature morte (Still Life)*, Reproduced in *Du \"Cubisme\"*, by Albert Gleizes and Jean Metzinger, 1912 <File:Georges> Braque, 1911, Nature Morte (The Pedestal Table), oil on canvas, 116.5 x 81.5 cm, Georges Pompidou Center, Paris.jpg\|Georges Braque, 1911, *Nature Morte (The Pedestal Table)*, oil on canvas, 116.5 × 81.5 cm, Georges Pompidou Center, Paris <File:Georges> Braque, 1911-12, Girl with a Cross, oil on canvas, 55 x 43 cm, Kimbell Art Museum, Fort Worth, Texas.jpg\|Georges Braque, 1911--12, *Girl with a Cross*, oil on canvas, 55 × 43 cm, Kimbell Art Museum, Fort Worth, Texas <File:Georges> Braque, 1911-12, Man with a Guitar (Figure, L'homme à la guitare), oil on canvas, 116.2 x, Museum of Modern Art, New York.jpg\|Georges Braque, 1911--12, *Man with a Guitar (Figure, L\'homme à la guitare)*, oil on canvas, 116.2 x, Museum of Modern Art, New York <File:Georges> Braque, 1912, Violin, Mozart Kubelick, oil on canvas, 45.7 x, Metropolitan Museum of Art.jpg\|Georges Braque, 1912, *Violin: \"Mozart Kubelick\"*, oil on canvas, 45.7 × 61 cm, Metropolitan Museum of Art <File:Georges> Braque, 1913, Nature morte (Fruit Dish, Ace of Clubs), oil, gouache and charcoal on canvas, 81 x, Musée National d\'Art Moderne, Centre Georges Pompidou, Paris.jpg\|Georges Braque, 1913, *Nature morte (Fruit Dish, Ace of Clubs)*, oil, gouache and charcoal on canvas, 81 x, Musée National d\'Art Moderne, Centre Georges Pompidou, Paris <File:Georges> Braque, 1913, Femme à la guitare (Woman with Guitar), oil and charcoal on canvas, 130 × 73 cm, Musée National d\'Art Moderne, Centre Pompidou.jpg\|Georges Braque, 1913, *Femme à la guitare* (*Woman with Guitar*), oil and charcoal on canvas, 130 × 73 cm, Musée National d\'Art Moderne, Centre Pompidou, Paris <File:Georges> Braque, 1913-14, Still Life on a Table (Duo pour Flute), oil on canvas, 45.7 × 55.2 cm, Lauder Cubist Collection, Metropolitan Museum of Art.jpg\|Georges Braque, 1913--14, *Still Life on a Table* (*Duo pour Flute*), oil on canvas, 45.7 × 55.2 cm, Lauder Cubist Collection, Metropolitan Museum of Art, New York <File:Georges> Braque, 1914, Violin and Glass, oil, charcoal and pasted paper on canvas, oval, 116 x 81 cm, Kunstmuseum Basel.jpg\|Georges Braque, 1914, *Violon et verre* (*Violin and Glass*), oil, charcoal and pasted paper on canvas, oval, 116 × 81 cm, Kunstmuseum Basel <File:Georges> Braque, 1914, Man With a Guitar, oil on canvas, 130 x 73 cm, Musée National d\'Art Moderne, Centre Georges Pompidou, Paris.jpg\|Georges Braque, 1914, *Man With a Guitar*, oil on canvas, 130 × 73 cm, Musée National d\'Art Moderne, Centre Georges Pompidou, Paris <File:Georges> Braque, 1918, Rhum et guitare, oil on canvas, 60 x 73 cm, Abelló Collection, Madrid.jpg\|Georges Braque, 1918, *Rhum et guitare* (*Rum and Guitar*), oil on canvas, 60 × 73 cm, Colección Abelló, Madrid <File:Still> Life with Grapes and Clarinet.jpeg\|Georges Braque, 1927, *Still Life with Grapes and Clarinet*, oil on canvas, The Phillips Collection, Washington, D.C
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# Gilbert Cesbron
**Gilbert Cesbron** (13 January 1913, Paris -- 12 August 1979, Paris) was a French novelist.
## Biography
**Gilbert Cesbron** (13 January 1913, Paris -- 12 August 1979, Paris) was a French novelist. Born in Paris, Cesbron attended what is now known as Lycée Condorcet. In 1944 he published his first novel, *Les innocents de Paris* (\"*The Innocent of Paris*\"), in Switzerland. He first achieved wide public acclaim with the publication of *Notre prison est un royaume* (\"*Our Prison is a Kingdom*\") in 1948 and *Il est minuit, docteur Schweitzer* (\"*It is midnight, Doctor Schweitzer*\") in 1950.
In his works Cesbron tended to illustrate and describe relevant social topics such as juvenile delinquency in *Chiens perdus sans collier* (\"*Lost Dogs Without Collars*\"), violence in *Entre chiens et loups* (\"*Between Dogs and Wolves*\"), euthanasia in *Il est plus tard que tu ne penses* (\"*It is Later than You Think*\") and working priests in *Les Saints vont en enfer* (\"*Saints in Hell*\").
In 1955, Cesbron\'s book *Chiens perdus sans collier*, the story of an orphan boy and a benevolent judge, was made into a movie starring Jean Gabin and Robert Dalban.
He died on 12 August 1979 at his home at 126 Boulevard Saint-Germain in the 6th arrondissement of Paris. He is buried in Bourré, Loir-et-Cher. His widow, Dominique, died in 2003.
## Works
### Novels
- *Les Innocents de Paris* , 1944.
- *On croit rêver* (1945).
- *La Tradition Fontquernie* (1947).
- *Notre prison est un royaume* (1948).
- *La Souveraine* (1949).
- *Bois mort où l\'oiseau chante* (1950).
- *Les saints vont en enfer* (1952).
- *Chiens perdus sans collier* (1954).
- *Vous verrez le ciel ouvert* (1956).
- *Il est plus tard que tu ne penses* (1958).
- *Avoir été* (1960).
- *Entre chiens et loups* (1962).
- *Une abeille contre la vitre* (1964).
- *C'est Mozart qu'on assassine* (1966).
- *Je suis mal dans ta peau* (1969).
- *Voici le temps des imposteurs* (1972).
- *Don Juan en automne* (1975).
- *Mais moi je vous aimais* (1977).
- *Compagnons de la nuit* (1938, published in 1995).
### Tales and short stories {#tales_and_short_stories}
- *D'Outremonde* (23 tales), (1949).
- *Traduit du vent* (1951).
- *Tout dort et je veille* (1959).
- *La Ville couronnée d'épines* (1964).
- *Des enfants aux cheveux gris* (1968).
- *Un vivier sans eau* (1979).
- *Leur pesant d'écume* (1980) ;
- *Tant d'amour perdu* (1981).
### Essays
- *Chasseur maudit* (1953).
- *Ce siècle appelle au secours* (1955).
- *Libérez Barabbas* (1957).
- *Une sentinelle attend l'aurore* (1965).
- *Lettre ouverte à une jeune fille morte* (1968).
- *Ce que je crois* (1970).
- *Des leçons d'abîme* (1971).
- *Mourir étonné* (1976) ;
- *Huit paroles pour l'éternité* (1978).
- *Passé un certain âge* (1980).
- *La regarder en face* (1982).
### Plays
- *Il est minuit, docteur Schweitzer* (1952)
- *Briser la statue* (1952), raconte la vie de Sainte Thérèse de Lisieux.
- *L'Homme seul* (1961).
- *Phèdre à Colombes* (1961).
- *Dernier Acte* (1961).
- *Mort le premier* (1970).
- *Pauvre Philippe* (1970)
### Other
- *Torrent* (poèmes) (1934).
- *Les Petits des Hommes* (album de photos avec texte) (1954).
- *Il suffit d'aimer* (récit de la vie de Sainte Bernadette Soubirous (1960).
- *Journal sans date* (tome 1) (1963).
- *Journal sans date, (tome 2). Tant qu'il fait jour* (1967).
- *Journal sans date, (tome 3). Un miroir en miettes* (1973) ;
- *Merci l'oiseau !* (poèmes) (1976) ;
- *Ce qu'on appelle vivre* (interviewed by the journalist Maurice Chavardès)(1977).
- *Bonheur de rien* (1979).
- *Un désespoir allègre* (1983).
## Adaptations
### Films
- 1952 : *Il est minuit, Docteur Schweitzer*, director André Haguet, with Jean Debucourt, Pierre Fresnay, Jeanne Moreau, Jean Lanier.
- 1955 : *Chiens perdus sans collier*, director Jean Delannoy, with Jean Gabin, Robert Dalban, Jean-Jacques Delbo.
- 1960 : *Il suffit d\'aimer*, director Robert Darène, script and dialogue Gilbert Cesbron, with Madeleine Sologne, music Maurice Thiriet.
### Television
- 1959 : *Ruf ohne Echo*, director Rainer Wolffhardt, with Horst Tappert, Hans Christian Blech.
- 1962 : *Il est minuit, Docteur Schweitzer*, director Gilbert Pineau.
- 1977 : *C'est Mozart qu'on assassine*, director Pierre Goutas, with Cyril Brisse, Henri Garcin, Catherine Rich, Louis Seigner.
- 1979 : *Avoir été*, director Roland-Bernard
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# Demographics of Guadeloupe
**Guadeloupe** has a population of 375,693 (2021).
## Population
According to INSEE Guadeloupe had an estimated population of 403,977 on 1 January 2012. Life expectancy at birth is 77.0 years for males, and 83.5 for females (figures for 2011).
### Structure of the population {#structure_of_the_population}
Age Group Male Female Total \%
----------- --------- --------- --------- ---------
Total 186 946 214 838 401 784 100
0--4 13 809 12 996 26 805 6.67
5--9 15 175 14 109 29 284 7.29
10--14 16 306 15 377 31 683 7.89
15--19 15 755 15 037 30 792 7.66
20--24 10 649 10 440 21 089 5.25
25--29 7 826 10 264 18 090 4.50
30--34 8 654 12 726 21 380 5.32
35--39 12 372 17 029 29 401 7.32
40--44 13 848 18 229 32 077 7.98
45--49 15 179 17 619 32 798 8.16
50--54 13 007 14 572 27 579 6.86
55--59 10 979 13 036 24 015 5.98
60--64 9 991 11 635 21 626 5.38
65--69 7 342 9 028 16 370 4.07
70--74 5 914 7 384 13 298 3.31
75--79 4 505 6 073 10 578 2.63
80--84 2 931 4 424 7 355 1.83
85--89 1 844 2 913 4 757 1.18
90--94 605 1 335 1 940 0.48
95+ 255 612 867 0.22
Age group Male Female Total Percent
0--14 45 290 42 482 87 772 21.85
15--64 118 260 140 587 258 847 64.42
65+ 23 396 31 769 55 165 13.73
Age Group Male Female Total \%
----------- --------- --------- --------- ---------
Total 183 479 214 511 397 990 100
0--4 11 292 11 118 22 410 5.63
5--9 13 707 13 062 26 769 6.73
10--14 15 004 14 790 29 794 7.49
15--19 14 731 14 269 29 000 7.29
20--24 10 153 9 731 19 884 5.00
25--29 8 227 10 039 18 266 4.59
30--34 7 926 11 600 19 526 4.91
35--39 9 201 13 111 22 312 5.61
40--44 12 518 16 630 29 148 7.32
45--49 13 926 17 434 31 360 7.88
50--54 14 748 17 227 31 975 8.03
55--59 12 884 14 790 27 674 6.95
60--64 11 204 13 431 24 635 6.19
65--69 9 336 10 991 20 327 5.11
70--74 6 850 8 503 15 353 3.86
75--79 5 315 6 642 11 957 3.00
80--84 3 359 5 193 8 552 2.15
85--89 1 891 3 472 5 364 1.35
90--94 882 1 742 2 625 0.66
95--99 268 549 817 0.21
100+ 56 184 240 0.06
Age group Male Female Total Percent
0--14 40 003 38 970 78 973 19.84
15--64 115 519 138 265 253 784 63.77
65+ 27 957 37 276 65 233 16.39
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# Demographics of Guadeloupe
## Vital statistics {#vital_statistics}
The following vital statistics include Saint Martin and Saint Barthélemy.
Population(01.01) (x1000) Live births Deaths Natural change Crude birth rate (per 1000) Crude death rate (per 1000) Natural change (per 1000) Total fertility rate
------ --------------------------- ------------- -------- ---------------- ----------------------------- ----------------------------- --------------------------- ----------------------
1950 210 7 702 2 912 4 790 37.3 13.7 23.7
1951 213 8 319 2 893 5 426 38.8 14.2 24.6
1952 217 8 463 3 221 5 242 38.3 14.3 24.0
1953 223 8 720 2 879 5 841 39.6 11.6 27.9
1954 229 8 941 2 648 6 293 39.4 11.0 28.5
1955 236 9 506 2 769 6 737 39.8 11.2 28.6
1956 244 9 648 2 449 7 199 39.8 10.0 29.8
1957 252 9 401 2 852 6 549 39.1 10.6 28.5
1958 260 9 864 2 469 7 395 38.4 9.9 28.4
1959 268 9 815 2 359 7 456 37.5 8.7 28.8
1960 275 10 479 2 657 7 822 38.4 9.7 28.7
1961 281 10 047 2 367 7 680 36.5 8.2 28.3
1962 287 10 890 2 348 8 542 37.3 8.5 28.8
1963 291 10 712 2 400 8 312 35.4 8.3 27.1
1964 296 10 424 2 345 8 079 34.4 8.1 26.4
1965 300 10 605 2 558 8 047 34.8 8.1 26.8
1966 304 10 879 2 497 8 382 33.7 7.9 25.7
1967 309 10 116 2 581 7 535 31.7 7.9 23.8
1968 313 10 476 2 564 7 912 31.9 7.6 24.3
1969 316 9 724 2 442 7 282 29.0 7.7 21.3
1970 319 9 397 2 499 6 898 28.9 7.8 21.1
1971 322 10 060 2 337 7 723 29.7 7.0 22.6
1972 324 9 912 2 458 7 454 28.4 7.3 21.2
1973 326 9 578 2 548 7 030 26.3 7.4 18.9
1974 327 8 846 2 459 6 387 24.6 7.4 17.2
1975 328 8 257 2 351 5 906 22.9 7.1 15.8
1976 327 6 926 2 395 4 531 19.5 7.2 12.3
1977 326 6 321 2 297 4 024 17.9 6.8 11.1
1978 325 5 640 2 163 3 477 16.4 6.7 9.7
1979 324 5 818 2 154 3 664 17.2 6.5 10.7
1980 326 6 425 2 143 4 282 18.1 6.6 11.5
1981 329 6 486 2 141 4 345 18.2 6.4 11.8
1982 334 6 616 2 099 4 517 18.2 6.4 11.8
1983 340 6 722 2 206 4 516 18.5 6.6 11.9
1984 347 6 671 2 235 4 436 18.3 6.4 11.9
1985 354 6 750 2 309 4 441 18.2 6.5 11.7
1986 360 6 374 2 238 4 136 17.7 6.2 11.5
1987 367 6 855 2 244 4 611 18.6 6.2 12.4
1988 374 7 126 2 228 4 898 18.7 6.0 12.7
1989 380 7 645 2 315 5 330 19.3 6.1 13.2
1990 385 7 569 2 334 5 235 19.7 6.1 13.6
1991 389 7 547 2 242 5 305 19.4 5.8 13.6
1992 393 7 310 2 360 4 950 18.6 6.0 12.6
1993 396 7 056 2 406 4 650 17.8 6.1 11.7
1994 399 7 249 2 328 4 921 18.1 5.8 12.3
1995 403 7 086 2 470 4 616 17.6 6.1 11.5
1996 407 7 256 2 459 4 797 17.8 6.0 11.8
1997 412 7 554 2 441 5 113 18.3 5.9 12.4
1998 416 7 208 2 517 4 691 17.3 6.0 11.3 1.83
1999 385.609\* 7 452 2 664 4 788 17.7 6.3 11.4 2.10
2000 425 7 601 2 634 4 967 17.9 6.2 11.7 2.19
2001 430 7 658 2 608 5 050 17.8 6.1 11.8 2.23
2002 433 7 032 2 765 4 267 16.2 6.4 9.8 2.07
2003 437 7 047 2 662 4 385 16.1 6.1 10.0 2.11
2004 441 7 273 2 676 4 597 16.5 6.1 10.4 2.26
2005 444 7 551 2 904 4 647 17.0 6.5 10.5 2.37
2006 447 7 193 2 902 4 291 16.1 6.5 9.6 2.33
2007 400.584 6 862 2 769 4 093 15.2 6.2 9.1 2.27
2008 401.784 6 758 2 916 3 842 14.9 6.4 8.5 2.20
2009 401.554 6 387 2 987 3 400 14.0 6.6 7.5 2.13
2010 403.355 6 242 3 095 3 147 13.6 6.7 6.9 2.12
2011 404.635 6 284 2 965 3 319 13.6 6.4 7.2 2.19
2012 403.314 6 133 3 003 3 130 13.2 6.5 6.8 2.20
2013 402.119 5 069 2 951 2 118 12.6 7.3 5.3 2.17
2014 400.186 5 001 3 290 1 711 12.5 8.2 4.3 2.19
2015 397.990 4 714 2 906 1 808 11.9 7.3 4.6 2.10
2016 394.110 4 653 3 227 1 426 11.8 8.2 3.6 2.14
2017 390.253 4 126 3 121 1 005 10.6 8.0 2.6 1.94
2018 387.629 4 249 3 258 991 11.0 8.4 2.6 2.04
2019 384.239 4 601 3 469 1 132 12.0 9.0 3.0 2.23
2020 383.559 4 678 3 742 936 12.2 9.7 2.5 2.27
2021 384.315 4 344 4 589 -245 11.3 12.0 -0.7 2.11
2022 383.569 4 218 4 041 177 11.0 10.5 0.5 2.08
2023 382.733 4 061 3 866 195 10.6 10.1 0.5 2.01
2024 381.909 \| 9.2 10.5 -1.3 1.75
2025 380.387 \| \|
- Excluding data for Saint Barthélemy and Saint Martin
## Languages
French is the official language, taught in the school system. Antillean Creole French is spoken by a large part of the population, understood by nearly all, and taught in some schools. A 2007 document issued by the Organisation internationale de la Francophonie estimated the population to be 80.2% \"francophone\" and 14.9% \"partially francophone\".
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# Demographics of Guadeloupe
## Religion
Figures in 2020 state that 96% of the population is Christian (of these, approximately 86% are Roman Catholic, 8% Protestant and 6% other Christian); of the other 4%, most have no religion, although there is a small number of Hindus, Baháʼís and Muslims
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# Telecommunications in Guadeloupe
As an overseas department and region of France, Guadeloupe has a developed **telecommunication system**.
## Internet
In 2019, there were 170,000 active high speed internet broadband subscriptions in Guadeloupe. 3 Internet Service Providers (ISPs) service the region: Orange Caraïbes, Mediaserv, and Outremer Telecom.
In 2019, there were 623,000 active mobile phone lines in Guadeloupe, which represents a 145% equipment rate, higher than mainland France.
## Domain name {#domain_name}
Guadeloupe has its own domain name: .gp.
## Radio
There are 35 radio stations emitting in Guadeloupe. In 1997, there were 113,000 radio sets in the region.
## Television
There are [10 TV stations](https://www.csa.fr/Informer/PAF-le-paysage-audiovisuel-francais/Les-chaines-de-la-TNT/La-numerotation-des-chaines) emitting in Guadeloupe using digital terrestrial television, including 4 local stations.
In 1997, there were 118,000 television sets in Guadeloupe
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# Transport in Guadeloupe
As an archipelago, Guadeloupe depends on several systems of public transport. The two islands that make up Guadeloupe proper - Grande-Terre and Basse-Terre - have an extensive road network, while water and air transportation connects to the outer islands as well as international destinations.
## Road transport {#road_transport}
Guadeloupe uses right-hand traffic. Of the 2,082 km of roads in the region, the majority (1,742 km) are paved and are well-maintained. As Guadeloupe is a French-administered territory, road signs and directions are written in French. The two main islands of Grande-Terre and Basse-Terre are connected by the N1 and N11 highways. Winding roads are common, and in Basse-Terre, the mountain roads have especially sharp turns.
Karu\'lis operates several bus routes across Grande-Terre (including direct services to and around Basse-Terre), and a small route runs on the north-eastern island of La Désirade.
## Rail transport {#rail_transport}
There are no public railways in Guadeloupe. A public railway line between Pointe-à-Pitre and Le Moule (Grande-Terre) was proposed but was later scrapped. Some plantations operate private railways. There exists a tourist railway that is operational (as of 2014) from Beauport, Port Louis to de Poyen. The construction of a tramway was planned with two lines: one between the Abymes and the Memorial in Pointe-à-Pître; the other between Baie-Mahault and Gosier. This project was later abandoned due to High-service buses being preferred over the tramway.
## Water transport {#water_transport}
The container terminal Port de Jarry, in Pointe-à-Pitre, is Guadeloupe\'s primary port for cargo and cruise ship passengers. It handles more than 95% of Guadeloupe\'s trade. Basse-Terre city contains a smaller sea port which also handles passengers.
Ferries connect Guadeloupe proper to the outer islands of La Désirade, Marie-Galante, and Îles des Saintes, as well as other Caribbean ports.
## Air transport {#air_transport}
Pointe-à-Pitre International Airport is the primary gateway for international travel into and out of Guadeloupe. It offers direct and chartered/seasonal flights to South America, the Caribbean, North America and Europe. It is a hub airport for Air Caraïbes
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# Googolplex
A **googolplex** is the large number **10`{{sup|[[googol]]}}`{=mediawiki}**, or equivalently, **10`{{sup|10{{sup|100}}}}`{=mediawiki}** or **`{{not a typo|10<sup>10,000,000,000,​000,000,000,​000,000,000,​000,000,000,​000,000,000,​000,000,000,​000,000,000,​000,000,000,​000,000,000,​000,000,000,​000,000,000</sup>}}`{=mediawiki}**. Written out in ordinary decimal notation, it is 1 followed by 10^100^ zeroes; that is, a 1 followed by a googol of zeroes. Its prime factorization is 2`{{sup|googol}}`{=mediawiki} ×5`{{sup|googol}}`{=mediawiki}.
## History
In 1920, Edward Kasner\'s nine-year-old nephew, Milton Sirotta, coined the term *googol*, which is 10`{{sup|100}}`{=mediawiki}, and then proposed the further term *googolplex* to be \"one, followed by writing zeroes until you get tired\". Kasner decided to adopt a more formal definition because \"different people get tired at different times and it would never do to have Carnera \[be\] a better mathematician than Dr. Einstein, simply because he had more endurance and could write for longer\". It thus became standardized to 10^(10^100^)^ = 10^10^100^^, due to the right-associativity of exponentiation.
## Size
A typical book can be printed with 10`{{sup|6}}`{=mediawiki} zeros (around 400 pages with 50 lines per page and 50 zeros per line). Therefore, it requires 10`{{sup|94}}`{=mediawiki} such books to print all the zeros of a googolplex (that is, printing a googol zeros). If each book had a mass of 100 grams, all of them would have a total mass of 10`{{sup|93}}`{=mediawiki} kilograms. In comparison, Earth\'s mass is 5.97 × 10`{{sup|24}}`{=mediawiki} kilograms, the mass of the Milky Way galaxy is estimated at 1.8 × 10`{{sup|42}}`{=mediawiki} kilograms, and the total mass of all the stars in the observable universe is estimated at 2 × 10^52^ kg.
To put this in perspective, the mass of all such books required to write out a googolplex would be vastly greater than the mass of the observable universe by a factor of roughly 5 × 10^40^.
### In pure mathematics {#in_pure_mathematics}
In pure mathematics, there are several notational methods for representing large numbers by which the magnitude of a googolplex could be represented, such as tetration, hyperoperation, Knuth\'s up-arrow notation, Steinhaus--Moser notation, or Conway chained arrow notation.
### In the physical universe {#in_the_physical_universe}
In the PBS science program *Cosmos: A Personal Voyage*, Episode 9: \"The Lives of the Stars\", astronomer and television personality Carl Sagan estimated that writing a googolplex in full decimal form (i.e., \"10,000,000,000\...\") would be physically impossible, since doing so would require more space than is available in the known universe. Sagan gave an example that if the entire volume of the observable universe is filled with fine dust particles roughly 1.5 micrometers in size (0.0015 millimeters), then the number of different combinations in which the particles could be arranged and numbered would be about one googolplex.
is a high estimate of the elementary particles existing in the visible universe (not including dark matter), mostly photons and other massless force carriers.
## Mod *n* {#mod_n}
The residues (mod *n*) of a googolplex, starting with mod 1, are:
: 0, 0, 1, 0, 0, 4, 4, 0, 1, 0, 1, 4, 3, 4, 10, 0, 1, 10, 9, 0, 4, 12, 13, 16, 0, 16, 10, 4, 24, 10, 5, 0, 1, 18, 25, 28, 10, 28, 16, 0, 1, 4, 24, 12, 10, 36, 9, 16, 4, 0, \... `{{OEIS|id=A067007}}`{=mediawiki}
This sequence is the same as the sequence of residues (mod *n*) of a googol up until the 17th position
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# Gaia philosophy
**Gaia philosophy** (named after Gaia, Greek goddess of the Earth) is a broadly inclusive term for relating concepts about humanity as an effect of the life of this planet.
The Gaia hypothesis holds that all organisms on a life-giving planet regulate the biosphere in such a way as to promote its habitability. Gaia concepts draw a connection between the survivability of a species (hence its evolutionary course) and its usefulness to the survival of other species. While there were a number of precursors to Gaia hypothesis, the first scientific form of this idea was proposed as the Gaia hypothesis by James Lovelock, a UK chemist, in 1970. The Gaia hypothesis deals with the concept of biological homeostasis, and claims the resident life forms of a host planet coupled with their environment have acted and act like a single, self-regulating system. This system includes the near-surface rocks, the soil, and the atmosphere. These theories are, however, significant in green politics.
## Predecessors to the Gaia theory {#predecessors_to_the_gaia_theory}
There are some mystical, scientific and religious predecessors to the Gaia philosophy, which had a Gaia-like conceptual basis. Many religious mythologies had a view of Earth as being a whole that is greater than the sum of its parts (e.g. some Native American religions and various forms of shamanism).
Isaac Newton wrote of the earth, \"Thus this Earth resembles a great animal or rather inanimate vegetable, draws in æthereall breath for its dayly refreshment & vitall ferment & transpires again with gross exhalations, And according to the condition of all other things living ought to have its times of beginning youth old age & perishing.\"
Pierre Teilhard de Chardin, a paleontologist and geologist, believed that evolution fractally unfolded from cell to organism to planet to solar system and ultimately the whole universe, as we humans see it from our limited perspective. Teilhard later influenced Thomas Berry and many Catholic humanist thinkers of the 20th century.
Lewis Thomas believed that Earth should be viewed as a single cell; he derived this view from Johannes Kepler\'s view of Earth as a single round organism.
Buckminster Fuller is generally credited with making the idea respectable in Western scientific circles in the 20th century. Building to some degree on his observations and artifacts, e.g. the Dymaxion map of the Earth he created, others began to ask if there was a way to make the Gaia theory scientifically sound.
In 1931, L.G.M. Baas Becking delivered an inaugural lecture about Gaia in the sense of life and earth.
Oberon Zell-Ravenheart in 1970 in an article in *Green Egg* Magazine, independently articulated the Gaia Thesis.
Many believe that these ideas cannot be considered scientific hypotheses; by definition a scientific hypothesis must make testable predictions. As the above claims are not currently testable, they are outside the bounds of current science. This does not mean that these ideas are not theoretically testable. As one can postulate tests that could be applied, given enough time and space, then these ideas should be seen as scientific hypotheses.
These are conjectures and perhaps can only be considered as social and maybe political philosophy; they may have implications for theology, or *thealogy* as Zell-Ravenheart and Isaac Bonewits put it.
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# Gaia philosophy
## Range of views {#range_of_views}
According to James Kirchner there is a spectrum of Gaia hypotheses, ranging from the undeniable to radical. At one end is the undeniable statement that the organisms on the Earth have radically altered its composition. A stronger position is that the Earth\'s biosphere effectively acts as if it is a self-organizing system which works in such a way as to keep its systems in some kind of equilibrium that is conducive to life. Today many scientists consider that such a view (and any stronger views) are unlikely to be correct. An even stronger claim is that all lifeforms are part of a single planetary being, called Gaia. In this view, the atmosphere, the seas, the terrestrial crust would be the result of interventions carried out by Gaia, through the coevolving diversity of living organisms.
The most extreme form of Gaia theory is that the entire Earth is a single unified organism with a highly intelligent mind that arose as an emergent property of the whole biosphere. In this view, the Earth\'s biosphere is *consciously* manipulating the climate in order to make conditions more conducive to life. Scientists contend that there is no evidence at all to support this last point of view, and it has come about because many people do not understand the concept of homeostasis. Many non-scientists instinctively and incorrectly see homeostasis as a process that requires conscious control.`{{dubious|date=October 2014}}`{=mediawiki}
The more speculative versions of Gaia, including versions in which it is believed that the Earth is actually conscious, sentient, and highly intelligent, are usually considered outside the bounds of what is usually considered science.
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# Gaia philosophy
## Gaia in biology and science {#gaia_in_biology_and_science}
Buckminster Fuller has been credited as the first to incorporate scientific ideas into a Gaia theory, which he did with his Dymaxion map of the Earth.
The first scientifically rigorous theory was the Gaia hypothesis by James Lovelock, a UK chemist.
A variant of this hypothesis was developed by Lynn Margulis, a microbiologist, in 1979. Her version is sometimes called the \"Gaia Theory\" (note uppercase-T). Her model is more limited in scope than the one that Lovelock proposed.
Whether this sort of system is present on Earth is still open to debate. Some relatively simple homeostatic mechanisms are generally accepted. For example, when atmospheric carbon dioxide levels rise, plants are able to grow better and thus remove more carbon dioxide from the atmosphere. Other biological effects and feedbacks exist, but the extent to which these mechanisms have stabilized and modified the Earth\'s overall climate is largely not known.
The Gaia hypothesis is sometimes viewed from significantly different philosophical perspectives. Some environmentalists view it as an almost conscious process, in which the Earth\'s ecosystem is literally viewed as a single unified organism. Some evolutionary biologists, on the other hand, view it as an undirected emergent property of the ecosystem: as each individual species pursues its own self-interest, their combined actions tend to have counterbalancing effects on environmental change. Proponents of this view sometimes point to examples of life\'s actions in the past that have resulted in dramatic change rather than stable equilibrium, such as the conversion of the Earth\'s atmosphere from a reducing environment to an oxygen-rich one.
Depending on how strongly the case is stated, the hypothesis conflicts with mainstream neo-Darwinism. Most biologists would accept Daisyworld-style homeostasis as possible, but would certainly not accept the idea that this equates to the whole biosphere acting as one organism.
A very small number of scientists, and a much larger number of environmental activists, claim that Earth\'s biosphere is *consciously* manipulating the climate in order to make conditions more conducive to life. Scientists contend that there is no evidence to support this belief.
## Gaia in the social sciences and politics {#gaia_in_the_social_sciences_and_politics}
A social science view of Gaia theory is the role of humans as a keystone species who may be able to accomplish global homeostasis. Whilst a few social scientists who draw inspiration from \'organic\' views of society have embraced Gaia philosophy as a way to explain the human-nature interconnections, most professional social scientists are more involved in reflecting upon the way Gaia philosophy is used and engaged with within sub-sections of society. Alan Marshall, in the Department of Social Sciences at Mahidol University, for example, reflects upon the way Gaia philosophy has been used and advocated in various societal settings by environmentalists, spiritualists, managers, economists, and scientists and engineers. As Marshall explains, most social scientists had already given up on systems ideas of society in the 1960s before Gaia philosophy was born under James Lovelock\'s ideas since such ideas were interpreted as supporting conservatism and traditionalism. Gaia theory also influenced the dynamics of green politics.
## Gaia in religion {#gaia_in_religion}
Rosemary Radford Ruether, the American feminist scholar and theologian, wrote a book called *Gaia and God: An Ecofeminist Theology of Earth Healing*.
A book edited by Allan Hunt Badiner called Dharma Gaia explores the ground where Buddhism and ecology meet through writings by the Dalai Lama, Gary Snyder, Thich Nhat Hanh, Allen Ginsberg, David Abram, Joanna Macy, Robert Aitken, and 25 other Buddhists and ecologists.
Gaianism, an earth-centered philosophical, holistic, and spiritual belief that shares expressions with earth religions and paganism while not identifying exclusively with any specific religion, sprang from the gaia hypothesis.
## Criticism
One of the most problematic issues with referring to Gaia as an organism is its apparent failure to meet the biological criterion of being able to reproduce. Richard Dawkins has asserted that the planet is not the offspring of any parents and is unable to reproduce.
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# Gaia philosophy
## Books on Gaia {#books_on_gaia}
- Toby Tyrrell (2013), *On Gaia: A Critical Investigation of the Relationship between Life and Earth*
- Anne Primavesi (2008), *Gaia and Climate Change: A Theology of Gift Events*
- Mary Midgley (2007), *Earthy realism: the meaning of Gaia*
- Pepper Lewis (2005), *Gaia Speaks*
- Stephen Henry Schneider (2004), *Scientists debate gaia: the next century*
- Tyler Volk (2003), *Gaia\'s Body: Toward a Physiology of Earth*
- Anne Primavesi (2003), *Gaia\'s gift: earth, ourselves, and God after Copernicus*
- Alan Marshall (2002), *The Unity of Nature*, Imperial College Press.
- Francesca Ciancimino Howell (2002), *Making Magic with Gaia: Practices to Heal Ourselves and Our Planet*
- Mary Midgley (2001), *Gaia: the next big idea*
- Anne Primavesi (2000), *Sacred Gaia: holistic theology and earth system science*
- George Ronald Williams (1996), *The molecular biology of Gaia*
- Peter Bunyard (1996), *Gaia in Action: Science of the Living Earth*
- Norman Myers (1993), *Gaia An Atlas of Planet Management*
- Lawrence E
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# Group homomorphism
`{{Group theory sidebar |Basics}}`{=mediawiki}
In mathematics, given two groups, (*G*,∗) and (*H*, ·), a **group homomorphism** from (*G*,∗) to (*H*, ·) is a function *h* : *G* → *H* such that for all *u* and *v* in *G* it holds that
$$h(u*v) = h(u) \cdot h(v)$$
where the group operation on the left side of the equation is that of *G* and on the right side that of *H*.
From this property, one can deduce that *h* maps the identity element *e~G~* of *G* to the identity element *e~H~* of *H*,
$$h(e_G) = e_H$$
and it also maps inverses to inverses in the sense that
$$h\left(u^{-1}\right) = h(u)^{-1}. \,$$
Hence one can say that *h* \"is compatible with the group structure\".
In areas of mathematics where one considers groups endowed with additional structure, a *homomorphism* sometimes means a map which respects not only the group structure (as above) but also the extra structure. For example, a homomorphism of topological groups is often required to be continuous.
## Properties
Let $e_{H}$ be the identity element of the (*H*, ·) group and $u \in G$, then
$$h(u) \cdot e_{H} = h(u) = h(u*e_{G}) = h(u) \cdot h(e_{G})$$
Now by multiplying for the inverse of $h(u)$ (or applying the cancellation rule) we obtain
$$e_{H} = h(e_{G})$$
Similarly,
$$e_H = h(e_G) = h(u*u^{-1}) = h(u)\cdot h(u^{-1})$$
Therefore for the uniqueness of the inverse: $h(u^{-1}) = h(u)^{-1}$.
## Types
Monomorphism`{{anchor|monomorphism}}`{=mediawiki}: A group homomorphism that is injective (or, one-to-one); i.e., preserves distinctness.\
Epimorphism: A group homomorphism that is surjective (or, onto); i.e., reaches every point in the codomain.\
Isomorphism: A group homomorphism that is bijective; i.e., injective and surjective. Its inverse is also a group homomorphism. In this case, the groups *G* and *H* are called *isomorphic*; they differ only in the notation of their elements (except of identity element) and are identical for all practical purposes. I.e. we re-label all elements except identity.\
Endomorphism: A group homomorphism, *h*: *G* → *G*; the domain and codomain are the same. Also called an endomorphism of *G*.\
Automorphism: A group endomorphism that is bijective, and hence an isomorphism. The set of all automorphisms of a group *G*, with functional composition as operation, itself forms a group, the *automorphism group* of *G*. It is denoted by Aut(*G*). As an example, the automorphism group of (**Z**, +) contains only two elements, the identity transformation and multiplication with −1; it is isomorphic to (**Z**/2**Z**, +).
## Image and kernel {#image_and_kernel}
We define the *kernel of h* to be the set of elements in *G* which are mapped to the identity in *H*
: $\operatorname{ker}(h) := \left\{u \in G\colon h(u) = e_{H}\right\}.$
and the *image of h* to be
: $\operatorname{im}(h) := h(G) \equiv \left\{h(u)\colon u \in G\right\}.$
The kernel and image of a homomorphism can be interpreted as measuring how close it is to being an isomorphism. The first isomorphism theorem states that the image of a group homomorphism, *h*(*G*) is isomorphic to the quotient group *G*/ker *h*.
The kernel of h is a normal subgroup of *G*. Assume $u \in \operatorname{ker}(h)$ and show $g^{-1} \circ u \circ g \in \operatorname{ker}(h)$ for arbitrary $u, g$:
: \\begin{align}
` h\left(g^{-1} \circ u \circ g\right) &= h(g)^{-1} \cdot h(u) \cdot h(g) \\`\
` &= h(g)^{-1} \cdot e_H \cdot h(g) \\`\
` &= h(g)^{-1} \cdot h(g) = e_H,`
\\end{align} The image of h is a subgroup of *H*.
The homomorphism, *h*, is a *group monomorphism*; i.e., *h* is injective (one-to-one) if and only if `{{nowrap|ker(''h'') {{=}}`{=mediawiki} {*e*~*G*~}}}. Injection directly gives that there is a unique element in the kernel, and, conversely, a unique element in the kernel gives injection:
$$\begin{align}
&& h(g_1) &= h(g_2) \\
\Leftrightarrow && h(g_1) \cdot h(g_2)^{-1} &= e_H \\
\Leftrightarrow && h\left(g_1 \circ g_2^{-1}\right) &= e_H,\ \operatorname{ker}(h) = \{e_G\} \\
\Rightarrow && g_1 \circ g_2^{-1} &= e_G \\
\Leftrightarrow && g_1 &= g_2
\end{align}$$
## Examples
- Consider the cyclic group Z`{{sub|3}}`{=mediawiki} = (**Z**/3**Z**, +) = ({0, 1, 2}, +) and the group of integers (**Z**, +). The map *h* : **Z** → **Z**/3**Z** with *h*(*u*) = *u* mod 3 is a group homomorphism. It is surjective and its kernel consists of all integers which are divisible by 3.
```{=html}
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```
- The exponential map yields a group homomorphism from the group of real numbers **R** with addition to the group of non-zero real numbers **R**\* with multiplication. The kernel is {0} and the image consists of the positive real numbers.
- The exponential map also yields a group homomorphism from the group of complex numbers **C** with addition to the group of non-zero complex numbers **C**\* with multiplication. This map is surjective and has the kernel {2π*ki* : *k* ∈ **Z**}, as can be seen from Euler\'s formula. Fields like **R** and **C** that have homomorphisms from their additive group to their multiplicative group are thus called exponential fields.
- The function $\Phi: (\mathbb{Z}, +) \rightarrow (\mathbb{R}, +)$, defined by $\Phi(x) = \sqrt[]{2}x$ is a homomorphism.
- Consider the two groups $(\mathbb{R}^+, *)$ and $(\mathbb{R}, +)$, represented respectively by $G$ and $H$, where $\mathbb{R}^+$ is the positive real numbers. Then, the function $f: G \rightarrow H$ defined by the logarithm function is a homomorphism.
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# Group homomorphism
## Category of groups {#category_of_groups}
If `{{nowrap|''h'' : ''G'' → ''H''}}`{=mediawiki} and `{{nowrap|''k'' : ''H'' → ''K''}}`{=mediawiki} are group homomorphisms, then so is `{{nowrap|''k'' ∘ ''h'' : ''G'' → ''K''}}`{=mediawiki}. This shows that the class of all groups, together with group homomorphisms as morphisms, forms a category (specifically the category of groups).
## Homomorphisms of abelian groups {#homomorphisms_of_abelian_groups}
If *G* and *H* are abelian (i.e., commutative) groups, then the set `{{nowrap|Hom(''G'', ''H'')}}`{=mediawiki} of all group homomorphisms from *G* to *H* is itself an abelian group: the sum `{{nowrap|''h'' + ''k''}}`{=mediawiki} of two homomorphisms is defined by
: (*h* + *k*)(*u*) = *h*(*u*) + *k*(*u*) for all *u* in *G*.
The commutativity of *H* is needed to prove that `{{nowrap|''h'' + ''k''}}`{=mediawiki} is again a group homomorphism.
The addition of homomorphisms is compatible with the composition of homomorphisms in the following sense: if *f* is in `{{nowrap|Hom(''K'', ''G'')}}`{=mediawiki}, *h*, *k* are elements of `{{nowrap|Hom(''G'', ''H'')}}`{=mediawiki}, and *g* is in `{{nowrap|Hom(''H'', ''L'')}}`{=mediawiki}, then
: and `{{nowrap|1=''g'' ∘ (''h'' + ''k'') = (''g'' ∘ ''h'') + (''g'' ∘ ''k'')}}`{=mediawiki}.
Since the composition is associative, this shows that the set End(*G*) of all endomorphisms of an abelian group forms a ring, the *endomorphism ring* of *G*. For example, the endomorphism ring of the abelian group consisting of the direct sum of *m* copies of **Z**/*n***Z** is isomorphic to the ring of *m*-by-*m* matrices with entries in **Z**/*n***Z**. The above compatibility also shows that the category of all abelian groups with group homomorphisms forms a preadditive category; the existence of direct sums and well-behaved kernels makes this category the prototypical example of an abelian category
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# Group isomorphism
In abstract algebra, a **group isomorphism** is a function between two groups that sets up a bijection between the elements of the groups in a way that respects the given group operations. If there exists an isomorphism between two groups, then the groups are called **isomorphic**. From the standpoint of group theory, isomorphic groups have the same properties and need not be distinguished.
## Definition and notation {#definition_and_notation}
Given two groups $(G, *)$ and $(H, \odot),$ a *group isomorphism* from $(G, *)$ to $(H, \odot)$ is a bijective group homomorphism from $G$ to $H.$ Spelled out, this means that a group isomorphism is a bijective function $f : G \to H$ such that for all $u$ and $v$ in $G$ it holds that $f(u * v) = f(u) \odot f(v).$
The two groups $(G, *)$ and $(H, \odot)$ are isomorphic if there exists an isomorphism from one to the other. This is written $(G, *) \cong (H, \odot).$
Often shorter and simpler notations can be used. When the relevant group operations are understood, they are omitted and one writes $G \cong H.$
Sometimes one can even simply write $G = H.$ Whether such a notation is possible without confusion or ambiguity depends on context. For example, the equals sign is not very suitable when the groups are both subgroups of the same group. See also the examples.
Conversely, given a group $(G, *),$ a set $H,$ and a bijection $f : G \to H,$ we can make $H$ a group $(H, \odot)$ by defining $f(u) \odot f(v) = f(u * v).$
If $H = G$ and $\odot = *$ then the bijection is an automorphism (*q.v.*).
Intuitively, group theorists view two isomorphic groups as follows: For every element $g$ of a group $G,$ there exists an element $h$ of $H$ such that $h$ \"behaves in the same way\" as $g$ (operates with other elements of the group in the same way as $g$). For instance, if $g$ generates $G,$ then so does $h.$ This implies, in particular, that $G$ and $H$ are in bijective correspondence. Thus, the definition of an isomorphism is quite natural.
An isomorphism of groups may equivalently be defined as an invertible group homomorphism (the inverse function of a bijective group homomorphism is also a group homomorphism).
## Examples
In this section some notable examples of isomorphic groups are listed.
- The group of all real numbers under addition, $(\R, +)$, is isomorphic to the group of positive real numbers under multiplication $(\R^+, \times)$:
$$(\R, +) \cong (\R^+, \times)$$ via the isomorphism $f(x) = e^x$.
- The group $\Z$ of integers (with addition) is a subgroup of $\R,$ and the factor group $\R/\Z$ is isomorphic to the group $S^1$ of complex numbers of absolute value 1 (under multiplication):
$$\R/\Z \cong S^1$$
- The Klein four-group is isomorphic to the direct product of two copies of $\Z_2 = \Z/2\Z$, and can therefore be written $\Z_2 \times \Z_2.$ Another notation is $\operatorname{Dih}_2,$ because it is a dihedral group.
- Generalizing this, for all odd $n,$ $\operatorname{Dih}_{2 n}$ is isomorphic to the direct product of $\operatorname{Dih}_n$ and $\Z_2.$
- If $(G, *)$ is an infinite cyclic group, then $(G, *)$ is isomorphic to the integers (with the addition operation). From an algebraic point of view, this means that the set of all integers (with the addition operation) is the \"only\" infinite cyclic group.
Some groups can be proven to be isomorphic, relying on the axiom of choice, but the proof does not indicate how to construct a concrete isomorphism. Examples:
- The group $(\R, +)$ is isomorphic to the group $(\Complex, +)$ of all complex numbers under addition.
- The group $(\Complex^*, \cdot)$ of non-zero complex numbers with multiplication as the operation is isomorphic to the group $S^1$ mentioned above.
## Properties
The kernel of an isomorphism from $(G, *)$ to $(H, \odot)$ is always {e~G~}, where e~G~ is the identity of the group $(G, *)$
If $(G, *)$ and $(H, \odot)$ are isomorphic, then $G$ is abelian if and only if $H$ is abelian.
If $f$ is an isomorphism from $(G, *)$ to $(H, \odot),$ then for any $a \in G,$ the order of $a$ equals the order of $f(a).$
If $(G, *)$ and $(H, \odot)$ are isomorphic, then $(G, *)$ is a locally finite group if and only if $(H, \odot)$ is locally finite.
The number of distinct groups (up to isomorphism) of order $n$ is given by sequence A000001 in the OEIS. The first few numbers are 0, 1, 1, 1 and 2 meaning that 4 is the lowest order with more than one group.
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# Group isomorphism
## Cyclic groups {#cyclic_groups}
All cyclic groups of a given order are isomorphic to $(\Z_n, +_n),$ where $+_n$ denotes addition modulo $n.$
Let $G$ be a cyclic group and $n$ be the order of $G.$ Letting $x$ be a generator of $G$, $G$ is then equal to $\langle x \rangle = \left\{e, x, \ldots, x^{n-1}\right\}.$ We will show that $G \cong (\Z_n, +_n).$
Define $\varphi : G \to \Z_n = \{0, 1, \ldots, n - 1\},$ so that $\varphi(x^a) = a.$ Clearly, $\varphi$ is bijective. Then $\varphi(x^a \cdot x^b) = \varphi(x^{a+b}) = a + b = \varphi(x^a) +_n \varphi(x^b),$ which proves that $G \cong (\Z_n, +_n).$
## Consequences
From the definition, it follows that any isomorphism $f : G \to H$ will map the identity element of $G$ to the identity element of $H,$ $f(e_G) = e_H,$ that it will map inverses to inverses, $f(u^{-1}) = f(u)^{-1} \quad \text{ for all } u \in G,$ and more generally, $n$th powers to $n$th powers, $f(u^n)= f(u)^n \quad \text{ for all } u \in G,$ and that the inverse map $f^{-1} : H \to G$ is also a group isomorphism.
The relation \"being isomorphic\" is an equivalence relation. If $f$ is an isomorphism between two groups $G$ and $H,$ then everything that is true about $G$ that is only related to the group structure can be translated via $f$ into a true ditto statement about $H,$ and vice versa.
## Automorphisms
An isomorphism from a group $(G, *)$ to itself is called an automorphism of the group. Thus it is a bijection $f : G \to G$ such that $f(u) * f(v) = f(u * v).$
The image under an automorphism of a conjugacy class is always a conjugacy class (the same or another).
The composition of two automorphisms is again an automorphism, and with this operation the set of all automorphisms of a group $G,$ denoted by $\operatorname{Aut}(G),$ itself forms a group, the *automorphism group* of $G.$
For all abelian groups there is at least the automorphism that replaces the group elements by their inverses. However, in groups where all elements are equal to their inverses this is the trivial automorphism, e.g. in the Klein four-group. For that group all permutations of the three non-identity elements are automorphisms, so the automorphism group is isomorphic to $S_3$ (which itself is isomorphic to $\operatorname{Dih}_3$).
In $\Z_p$ for a prime number $p,$ one non-identity element can be replaced by any other, with corresponding changes in the other elements. The automorphism group is isomorphic to $\Z_{p-1}$ For example, for $n = 7,$ multiplying all elements of $\Z_7$ by 3, modulo 7, is an automorphism of order 6 in the automorphism group, because $3^6 \equiv 1 \pmod 7,$ while lower powers do not give 1. Thus this automorphism generates $\Z_6.$ There is one more automorphism with this property: multiplying all elements of $\Z_7$ by 5, modulo 7. Therefore, these two correspond to the elements 1 and 5 of $\Z_6,$ in that order or conversely.
The automorphism group of $\Z_6$ is isomorphic to $\Z_2,$ because only each of the two elements 1 and 5 generate $\Z_6,$ so apart from the identity we can only interchange these.
The automorphism group of $\Z_2 \oplus \Z_2 \oplus \Z_2 = \operatorname{Dih}_2 \oplus \Z_2$ has order 168, as can be found as follows. All 7 non-identity elements play the same role, so we can choose which plays the role of $(1,0,0).$ Any of the remaining 6 can be chosen to play the role of (0,1,0). This determines which element corresponds to $(1,1,0).$ For $(0,0,1)$ we can choose from 4, which determines the rest. Thus we have $7 \times 6 \times 4 = 168$ automorphisms. They correspond to those of the Fano plane, of which the 7 points correspond to the 7 `{{nowrap|non-identity}}`{=mediawiki} elements. The lines connecting three points correspond to the group operation: $a, b,$ and $c$ on one line means $a + b = c,$ $a + c = b,$ and $b + c = a.$ See also general linear group over finite fields.
For abelian groups, all non-trivial automorphisms are outer automorphisms.
Non-abelian groups have a non-trivial inner automorphism group, and possibly also outer automorphisms
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# Graph theory
thumb\|upright=0.8\|A graph with 6 vertices and 7 edges
In mathematics and computer science, **graph theory** is the study of *graphs*, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of *vertices* (also called *nodes* or *points*) which are connected by *edges* (also called *arcs*, *links* or *lines*). A distinction is made between **undirected graphs**, where edges link two vertices symmetrically, and **directed graphs**, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics.
## Definitions
Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures.
### Graph
In one restricted but very common sense of the term, a **graph** is an ordered pair $G=(V,E)$ comprising:
- $V$, a set of **vertices** (also called **nodes** or **points**);
- $E \subseteq \{ \{x, y\} \mid x, y \in V \;\textrm{ and }\; x \neq y \}$, a set of **edges** (also called **links** or **lines**), which are unordered pairs of vertices (that is, an edge is associated with two distinct vertices).
To avoid ambiguity, this type of object may be called an **undirected simple graph**.
In the edge $\{x, y\}$, the vertices $x$ and $y$ are called the **endpoints** of the edge. The edge is said to **join** $x$ and $y$ and to be **incident** on $x$ and on $y$. A vertex may exist in a graph and not belong to an edge. Under this definition, **multiple edges**, in which two or more edges connect the same vertices, are not allowed. `{{Multiple image
| image1 = Example of simple undirected graph 2.svg
| width1 = 75
| caption1 =For vertices A,B,C and D, the degrees are respectively 4,4,5,1
| image2 = Example of simple undirected graph 1.svg
| width2 = 75
| caption2 = For vertices U,V,W and X, the degrees are 2,2,3 and 1 respectively.
| footer = Examples of finding the degree of vertices.
}}`{=mediawiki} In one more general sense of the term allowing multiple edges, a **graph** is an ordered triple $G=(V,E,\phi)$ comprising:
- $V$, a set of **vertices** (also called **nodes** or **points**);
- $E$, a set of **edges** (also called **links** or **lines**);
- $\phi : E \to \{ \{x, y\} \mid x, y \in V \;\textrm{ and }\; x \neq y \}$, an **incidence function** mapping every edge to an unordered pair of vertices (that is, an edge is associated with two distinct vertices).
To avoid ambiguity, this type of object may be called an **undirected multigraph**.
A **loop** is an edge that joins a vertex to itself. Graphs as defined in the two definitions above cannot have loops, because a loop joining a vertex $x$ to itself is the edge (for an undirected simple graph) or is incident on (for an undirected multigraph) $\{x, x\} = \{x\}$ which is not in $\{ \{x, y\} \mid x, y \in V \;\textrm{ and }\; x \neq y \}$. To allow loops, the definitions must be expanded. For undirected simple graphs, the definition of $E$ should be modified to $E \subseteq \{ \{x, y\} \mid x, y \in V \}$. For undirected multigraphs, the definition of $\phi$ should be modified to $\phi : E \to \{ \{x, y\} \mid x, y \in V \}$. To avoid ambiguity, these types of objects may be called **undirected simple graph permitting loops** and **undirected multigraph permitting loops** (sometimes also **undirected pseudograph**), respectively.
$V$ and $E$ are usually taken to be finite, and many of the well-known results are not true (or are rather different) for infinite graphs because many of the arguments fail in the infinite case. Moreover, $V$ is often assumed to be non-empty, but $E$ is allowed to be the empty set. The **order** of a graph is $|V|$, its number of vertices. The **size** of a graph is $|E|$, its number of edges. The **degree** or **valency** of a vertex is the number of edges that are incident to it, where a loop is counted twice. The **degree** of a graph is the maximum of the degrees of its vertices.
In an undirected simple graph of order *n*, the maximum degree of each vertex is `{{nowrap|''n'' − 1}}`{=mediawiki} and the maximum size of the graph is `{{sfrac|''n''(''n'' − 1)|2}}`{=mediawiki}.
The edges of an undirected simple graph permitting loops $G$ induce a symmetric homogeneous relation $\sim$ on the vertices of $G$ that is called the **adjacency relation** of $G$. Specifically, for each edge $(x,y)$, its endpoints $x$ and $y$ are said to be **adjacent** to one another, which is denoted $x \sim y$.
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# Graph theory
## Definitions
### Directed graph {#directed_graph}
A **directed graph** or **digraph** is a graph in which edges have orientations.
In one restricted but very common sense of the term, a **directed graph** is an ordered pair $G=(V,E)$ comprising:
- $V$, a set of *vertices* (also called *nodes* or *points*);
- $E \subseteq \left\{(x,y) \mid (x, y) \in V^2 \;\textrm{ and }\; x \neq y \right\}$, a set of *edges* (also called *directed edges*, *directed links*, *directed lines*, *arrows* or *arcs*) which are ordered pairs of vertices (that is, an edge is associated with two distinct vertices).
To avoid ambiguity, this type of object may be called a **directed simple graph**. In set theory and graph theory, $V^n$ denotes the set of `{{mvar|n}}`{=mediawiki}-tuples of elements of $V,$ that is, ordered sequences of $n$ elements that are not necessarily distinct.
In the edge $(x, y)$ directed from $x$ to $y$, the vertices $x$ and $y$ are called the *endpoints* of the edge, $x$ the *tail* of the edge and $y$ the *head* of the edge. The edge is said to *join* $x$ and $y$ and to be *incident* on $x$ and on $y$. A vertex may exist in a graph and not belong to an edge. The edge $(y,x)$ is called the *inverted edge* of $(x, y)$. *Multiple edges*, not allowed under the definition above, are two or more edges with both the same tail and the same head.
In one more general sense of the term allowing multiple edges, a **directed graph** is an ordered triple $G=(V,E,\phi)$ comprising:
- $V$, a set of *vertices* (also called *nodes* or *points*);
- $E$, a set of *edges* (also called *directed edges*, *directed links*, *directed lines*, *arrows* or *arcs*);
- $\phi : E \to \left\{(x,y) \mid (x, y) \in V^2 \;\textrm{ and }\; x \neq y \right\}$, an *incidence function* mapping every edge to an ordered pair of vertices (that is, an edge is associated with two distinct vertices).
To avoid ambiguity, this type of object may be called a **directed multigraph**.
A *loop* is an edge that joins a vertex to itself. Directed graphs as defined in the two definitions above cannot have loops, because a loop joining a vertex $x$ to itself is the edge (for a directed simple graph) or is incident on (for a directed multigraph) $(x,x)$ which is not in $\left\{(x, y) \mid (x, y) \in V^2 \;\textrm{ and }\; x \neq y \right\}$. So to allow loops the definitions must be expanded. For directed simple graphs, the definition of $E$ should be modified to $E \subseteq \left\{(x, y) \mid (x, y) \in V^2\right\}$. For directed multigraphs, the definition of $\phi$ should be modified to $\phi : E \to \left\{(x, y) \mid (x, y) \in V^2\right\}$. To avoid ambiguity, these types of objects may be called precisely a **directed simple graph permitting loops** and a **directed multigraph permitting loops** (or a *quiver*) respectively.
The edges of a directed simple graph permitting loops $G$ is a homogeneous relation \~ on the vertices of $G$ that is called the *adjacency relation* of $G$. Specifically, for each edge $(x,y)$, its endpoints $x$ and $y$ are said to be *adjacent* to one another, which is denoted $x$ \~ $y$.
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# Graph theory
## Applications
Graphs can be used to model many types of relations and processes in physical, biological, social and information systems. Many practical problems can be represented by graphs. Emphasizing their application to real-world systems, the term *network* is sometimes defined to mean a graph in which attributes (e.g. names) are associated with the vertices and edges, and the subject that expresses and understands real-world systems as a network is called network science.
### Computer science {#computer_science}
Within computer science, \'causal\' and \'non-causal\' linked structures are graphs that are used to represent networks of communication, data organization, computational devices, the flow of computation, etc. For instance, the link structure of a website can be represented by a directed graph, in which the vertices represent web pages and directed edges represent links from one page to another. A similar approach can be taken to problems in social media, travel, biology, computer chip design, mapping the progression of neuro-degenerative diseases, and many other fields. The development of algorithms to handle graphs is therefore of major interest in computer science. The transformation of graphs is often formalized and represented by graph rewrite systems. Complementary to graph transformation systems focusing on rule-based in-memory manipulation of graphs are graph databases geared towards transaction-safe, persistent storing and querying of graph-structured data.
### Linguistics
Graph-theoretic methods, in various forms, have proven particularly useful in linguistics, since natural language often lends itself well to discrete structure. Traditionally, syntax and compositional semantics follow tree-based structures, whose expressive power lies in the principle of compositionality, modeled in a hierarchical graph. More contemporary approaches such as head-driven phrase structure grammar model the syntax of natural language using typed feature structures, which are directed acyclic graphs. Within lexical semantics, especially as applied to computers, modeling word meaning is easier when a given word is understood in terms of related words; semantic networks are therefore important in computational linguistics. Still, other methods in phonology (e.g. optimality theory, which uses lattice graphs) and morphology (e.g. finite-state morphology, using finite-state transducers) are common in the analysis of language as a graph. Indeed, the usefulness of this area of mathematics to linguistics has borne organizations such as [TextGraphs](http://www.textgraphs.org/), as well as various \'Net\' projects, such as WordNet, VerbNet, and others.
### Physics and chemistry {#physics_and_chemistry}
Graph theory is also used to study molecules in chemistry and physics. In condensed matter physics, the three-dimensional structure of complicated simulated atomic structures can be studied quantitatively by gathering statistics on graph-theoretic properties related to the topology of the atoms. Also, \"the Feynman graphs and rules of calculation summarize quantum field theory in a form in close contact with the experimental numbers one wants to understand.\" In chemistry a graph makes a natural model for a molecule, where vertices represent atoms and edges bonds. This approach is especially used in computer processing of molecular structures, ranging from chemical editors to database searching. In statistical physics, graphs can represent local connections between interacting parts of a system, as well as the dynamics of a physical process on such systems. Similarly, in computational neuroscience graphs can be used to represent functional connections between brain areas that interact to give rise to various cognitive processes, where the vertices represent different areas of the brain and the edges represent the connections between those areas. Graph theory plays an important role in electrical modeling of electrical networks, here, weights are associated with resistance of the wire segments to obtain electrical properties of network structures. Graphs are also used to represent the micro-scale channels of porous media, in which the vertices represent the pores and the edges represent the smaller channels connecting the pores. Chemical graph theory uses the molecular graph as a means to model molecules. Graphs and networks are excellent models to study and understand phase transitions and critical phenomena. Removal of nodes or edges leads to a critical transition where the network breaks into small clusters which is studied as a phase transition. This breakdown is studied via percolation theory.
### Social sciences {#social_sciences}
Graph theory is also widely used in sociology as a way, for example, to measure actors\' prestige or to explore rumor spreading, notably through the use of social network analysis software. Under the umbrella of social networks are many different types of graphs. Acquaintanceship and friendship graphs describe whether people know each other. Influence graphs model whether certain people can influence the behavior of others. Finally, collaboration graphs model whether two people work together in a particular way, such as acting in a movie together.
### Biology
Likewise, graph theory is useful in biology and conservation efforts where a vertex can represent regions where certain species exist (or inhabit) and the edges represent migration paths or movement between the regions. This information is important when looking at breeding patterns or tracking the spread of disease, parasites or how changes to the movement can affect other species.
Graphs are also commonly used in molecular biology and genomics to model and analyse datasets with complex relationships. For example, graph-based methods are often used to \'cluster\' cells together into cell-types in single-cell transcriptome analysis. Another use is to model genes or proteins in a pathway and study the relationships between them, such as metabolic pathways and gene regulatory networks. Evolutionary trees, ecological networks, and hierarchical clustering of gene expression patterns are also represented as graph structures.
Graph theory is also used in connectomics; nervous systems can be seen as a graph, where the nodes are neurons and the edges are the connections between them.
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# Graph theory
## Applications
### Mathematics
In mathematics, graphs are useful in geometry and certain parts of topology such as knot theory. Algebraic graph theory has close links with group theory. Algebraic graph theory has been applied to many areas including dynamic systems and complexity.
### Other topics {#other_topics}
A graph structure can be extended by assigning a weight to each edge of the graph. Graphs with weights, or weighted graphs, are used to represent structures in which pairwise connections have some numerical values. For example, if a graph represents a road network, the weights could represent the length of each road. There may be several weights associated with each edge, including distance (as in the previous example), travel time, or monetary cost. Such weighted graphs are commonly used to program GPS\'s, and travel-planning search engines that compare flight times and costs.
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# Graph theory
## History
The paper written by Leonhard Euler on the Seven Bridges of Königsberg and published in 1736 is regarded as the first paper in the history of graph theory. This paper, as well as the one written by Vandermonde on the *knight problem,* carried on with the *analysis situs* initiated by Leibniz. Euler\'s formula relating the number of edges, vertices, and faces of a convex polyhedron was studied and generalized by Cauchy and L\'Huilier, and represents the beginning of the branch of mathematics known as topology.
More than one century after Euler\'s paper on the bridges of Königsberg and while Listing was introducing the concept of topology, Cayley was led by an interest in particular analytical forms arising from differential calculus to study a particular class of graphs, the *trees*. This study had many implications for theoretical chemistry. The techniques he used mainly concern the enumeration of graphs with particular properties. Enumerative graph theory then arose from the results of Cayley and the fundamental results published by Pólya between 1935 and 1937. These were generalized by De Bruijn in 1959. Cayley linked his results on trees with contemporary studies of chemical composition. The fusion of ideas from mathematics with those from chemistry began what has become part of the standard terminology of graph theory.
In particular, the term \"graph\" was introduced by Sylvester in a paper published in 1878 in *Nature*, where he draws an analogy between \"quantic invariants\" and \"co-variants\" of algebra and molecular diagrams:
: \"\[...\] Every invariant and co-variant thus becomes expressible by a *graph* precisely identical with a Kekuléan diagram or chemicograph. \[...\] I give a rule for the geometrical multiplication of graphs, *i.e.* for constructing a *graph* to the product of in- or co-variants whose separate graphs are given. \[...\]\" (italics as in the original).
The first textbook on graph theory was written by Dénes Kőnig, and published in 1936. Another book by Frank Harary, published in 1969, was \"considered the world over to be the definitive textbook on the subject\", and enabled mathematicians, chemists, electrical engineers and social scientists to talk to each other. Harary donated all of the royalties to fund the Pólya Prize.
One of the most famous and stimulating problems in graph theory is the four color problem: \"Is it true that any map drawn in the plane may have its regions colored with four colors, in such a way that any two regions having a common border have different colors?\" This problem was first posed by Francis Guthrie in 1852 and its first written record is in a letter of De Morgan addressed to Hamilton the same year. Many incorrect proofs have been proposed, including those by Cayley, Kempe, and others. The study and the generalization of this problem by Tait, Heawood, Ramsey and Hadwiger led to the study of the colorings of the graphs embedded on surfaces with arbitrary genus. Tait\'s reformulation generated a new class of problems, the *factorization problems*, particularly studied by Petersen and Kőnig. The works of Ramsey on colorations and more specially the results obtained by Turán in 1941 was at the origin of another branch of graph theory, *extremal graph theory*.
The four color problem remained unsolved for more than a century. In 1969 Heinrich Heesch published a method for solving the problem using computers. A computer-aided proof produced in 1976 by Kenneth Appel and Wolfgang Haken makes fundamental use of the notion of \"discharging\" developed by Heesch. The proof involved checking the properties of 1,936 configurations by computer, and was not fully accepted at the time due to its complexity. A simpler proof considering only 633 configurations was given twenty years later by Robertson, Seymour, Sanders and Thomas.
The autonomous development of topology from 1860 and 1930 fertilized graph theory back through the works of Jordan, Kuratowski and Whitney. Another important factor of common development of graph theory and topology came from the use of the techniques of modern algebra. The first example of such a use comes from the work of the physicist Gustav Kirchhoff, who published in 1845 his Kirchhoff\'s circuit laws for calculating the voltage and current in electric circuits.
The introduction of probabilistic methods in graph theory, especially in the study of Erdős and Rényi of the asymptotic probability of graph connectivity, gave rise to yet another branch, known as *random graph theory*, which has been a fruitful source of graph-theoretic results.
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# Graph theory
## Representation
A graph is an abstraction of relationships that emerge in nature; hence, it cannot be coupled to a certain representation. The way it is represented depends on the degree of convenience such representation provides for a certain application. The most common representations are the visual, in which, usually, vertices are drawn and connected by edges, and the tabular, in which rows of a table provide information about the relationships between the vertices within the graph.
### Visual: Graph drawing {#visual_graph_drawing}
Graphs are usually represented visually by drawing a point or circle for every vertex, and drawing a line between two vertices if they are connected by an edge. If the graph is directed, the direction is indicated by drawing an arrow. If the graph is weighted, the weight is added on the arrow.
A graph drawing should not be confused with the graph itself (the abstract, non-visual structure) as there are several ways to structure the graph drawing. All that matters is which vertices are connected to which others by how many edges and not the exact layout. In practice, it is often difficult to decide if two drawings represent the same graph. Depending on the problem domain some layouts may be better suited and easier to understand than others.
The pioneering work of W. T. Tutte was very influential on the subject of graph drawing. Among other achievements, he introduced the use of linear algebraic methods to obtain graph drawings.
Graph drawing also can be said to encompass problems that deal with the crossing number and its various generalizations. The crossing number of a graph is the minimum number of intersections between edges that a drawing of the graph in the plane must contain. For a planar graph, the crossing number is zero by definition. Drawings on surfaces other than the plane are also studied.
There are other techniques to visualize a graph away from vertices and edges, including circle packings, intersection graph, and other visualizations of the adjacency matrix.
### Tabular: Graph data structures {#tabular_graph_data_structures}
The tabular representation lends itself well to computational applications. There are different ways to store graphs in a computer system. The data structure used depends on both the graph structure and the algorithm used for manipulating the graph. Theoretically one can distinguish between list and matrix structures but in concrete applications the best structure is often a combination of both. List structures are often preferred for sparse graphs as they have smaller memory requirements. Matrix structures on the other hand provide faster access for some applications but can consume huge amounts of memory. Implementations of sparse matrix structures that are efficient on modern parallel computer architectures are an object of current investigation.
List structures include the edge list, an array of pairs of vertices, and the adjacency list, which separately lists the neighbors of each vertex: Much like the edge list, each vertex has a list of which vertices it is adjacent to.
Matrix structures include the incidence matrix, a matrix of 0\'s and 1\'s whose rows represent vertices and whose columns represent edges, and the adjacency matrix, in which both the rows and columns are indexed by vertices. In both cases a 1 indicates two adjacent objects and a 0 indicates two non-adjacent objects. The degree matrix indicates the degree of vertices. The Laplacian matrix is a modified form of the adjacency matrix that incorporates information about the degrees of the vertices, and is useful in some calculations such as Kirchhoff\'s theorem on the number of spanning trees of a graph. The distance matrix, like the adjacency matrix, has both its rows and columns indexed by vertices, but rather than containing a 0 or a 1 in each cell it contains the length of a shortest path between two vertices.
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# Graph theory
## Problems
### Enumeration
There is a large literature on graphical enumeration: the problem of counting graphs meeting specified conditions. Some of this work is found in Harary and Palmer (1973).
### Subgraphs, induced subgraphs, and minors {#subgraphs_induced_subgraphs_and_minors}
A common problem, called the subgraph isomorphism problem, is finding a fixed graph as a subgraph in a given graph. One reason to be interested in such a question is that many graph properties are *hereditary* for subgraphs, which means that a graph has the property if and only if all subgraphs have it too. Finding maximal subgraphs of a certain kind is often an NP-complete problem. For example:
- Finding the largest complete subgraph is called the clique problem (NP-complete).
One special case of subgraph isomorphism is the graph isomorphism problem. It asks whether two graphs are isomorphic. It is not known whether this problem is NP-complete, nor whether it can be solved in polynomial time.
A similar problem is finding induced subgraphs in a given graph. Again, some important graph properties are hereditary with respect to induced subgraphs, which means that a graph has a property if and only if all induced subgraphs also have it. Finding maximal induced subgraphs of a certain kind is also often NP-complete. For example:
- Finding the largest edgeless induced subgraph or independent set is called the independent set problem (NP-complete).
Still another such problem, the minor containment problem, is to find a fixed graph as a minor of a given graph. A minor or subcontraction of a graph is any graph obtained by taking a subgraph and contracting some (or no) edges. Many graph properties are hereditary for minors, which means that a graph has a property if and only if all minors have it too. For example, Wagner\'s Theorem states:
- A graph is planar if it contains as a minor neither the complete bipartite graph *K*~3,3~ (see the Three-cottage problem) nor the complete graph *K*~5~.
A similar problem, the subdivision containment problem, is to find a fixed graph as a subdivision of a given graph. A subdivision or homeomorphism of a graph is any graph obtained by subdividing some (or no) edges. Subdivision containment is related to graph properties such as planarity. For example, Kuratowski\'s Theorem states:
- A graph is planar if it contains as a subdivision neither the complete bipartite graph *K*~3,3~ nor the complete graph *K*~5~.
Another problem in subdivision containment is the Kelmans--Seymour conjecture:
- Every 5-vertex-connected graph that is not planar contains a subdivision of the 5-vertex complete graph *K*~5~.
Another class of problems has to do with the extent to which various species and generalizations of graphs are determined by their *point-deleted subgraphs*. For example:
- The reconstruction conjecture
### Graph coloring {#graph_coloring}
Many problems and theorems in graph theory have to do with various ways of coloring graphs. Typically, one is interested in coloring a graph so that no two adjacent vertices have the same color, or with other similar restrictions. One may also consider coloring edges (possibly so that no two coincident edges are the same color), or other variations. Among the famous results and conjectures concerning graph coloring are the following:
- Four-color theorem
- Strong perfect graph theorem
- Erdős--Faber--Lovász conjecture
- Total coloring conjecture, also called Behzad\'s conjecture (unsolved)
- List coloring conjecture (unsolved)
- Hadwiger conjecture (graph theory) (unsolved)
### Subsumption and unification {#subsumption_and_unification}
Constraint modeling theories concern families of directed graphs related by a partial order. In these applications, graphs are ordered by specificity, meaning that more constrained graphs---which are more specific and thus contain a greater amount of information---are subsumed by those that are more general. Operations between graphs include evaluating the direction of a subsumption relationship between two graphs, if any, and computing graph unification. The unification of two argument graphs is defined as the most general graph (or the computation thereof) that is consistent with (i.e. contains all of the information in) the inputs, if such a graph exists; efficient unification algorithms are known.
For constraint frameworks which are strictly compositional, graph unification is the sufficient satisfiability and combination function. Well-known applications include automatic theorem proving and modeling the elaboration of linguistic structure.
### Route problems {#route_problems}
- Hamiltonian path problem
- Minimum spanning tree
- Route inspection problem (also called the \"Chinese postman problem\")
- Seven bridges of Königsberg
- Shortest path problem
- Steiner tree
- Three-cottage problem
- Traveling salesman problem (NP-hard)
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# Graph theory
## Problems
### Network flow {#network_flow}
There are numerous problems arising especially from applications that have to do with various notions of flows in networks, for example:
- Max flow min cut theorem
### Visibility problems {#visibility_problems}
- Museum guard problem
### Covering problems {#covering_problems}
Covering problems in graphs may refer to various set cover problems on subsets of vertices/subgraphs.
- Dominating set problem is the special case of set cover problem where sets are the closed neighborhoods.
- Vertex cover problem is the special case of set cover problem where sets to cover are every edges.
- The original set cover problem, also called hitting set, can be described as a vertex cover in a hypergraph.
### Decomposition problems {#decomposition_problems}
Decomposition, defined as partitioning the edge set of a graph (with as many vertices as necessary accompanying the edges of each part of the partition), has a wide variety of questions. Often, the problem is to decompose a graph into subgraphs isomorphic to a fixed graph; for instance, decomposing a complete graph into Hamiltonian cycles. Other problems specify a family of graphs into which a given graph should be decomposed, for instance, a family of cycles, or decomposing a complete graph *K*~*n*~ into `{{nobreak|''n'' − 1}}`{=mediawiki} specified trees having, respectively, 1, 2, 3, \..., `{{nobreak|''n'' − 1}}`{=mediawiki} edges.
Some specific decomposition problems and similar problems that have been studied include:
- Arboricity, a decomposition into as few forests as possible
- Cycle double cover, a collection of cycles covering each edge exactly twice
- Edge coloring, a decomposition into as few matchings as possible
- Graph factorization, a decomposition of a regular graph into regular subgraphs of given degrees
### Graph classes {#graph_classes}
Many problems involve characterizing the members of various classes of graphs. Some examples of such questions are below:
- Enumerating the members of a class
- Characterizing a class in terms of forbidden substructures
- Ascertaining relationships among classes (e.g
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# Guanosine
**Guanosine** (symbol **G** or **Guo**) is a purine nucleoside comprising guanine attached to a ribose (ribofuranose) ring via a β-N~9~-glycosidic bond. Guanosine can be phosphorylated to become guanosine monophosphate (GMP), cyclic guanosine monophosphate (cGMP), guanosine diphosphate (GDP), and guanosine triphosphate (GTP). These forms play important roles in various biochemical processes such as synthesis of nucleic acids and proteins, photosynthesis, muscle contraction, and intracellular signal transduction (cGMP). When guanine is attached by its N9 nitrogen to the C1 carbon of a deoxyribose ring it is known as deoxyguanosine.
## Physical and chemical properties {#physical_and_chemical_properties}
Guanosine is a white, crystalline powder with no odor and mild saline taste. It is very soluble in acetic acid, slightly soluble in water, insoluble in ethanol, diethyl ether, benzene and chloroform.
## Functions
Guanosine is required for an RNA splicing reaction in mRNA, when a \"self-splicing\" intron removes itself from the mRNA message by cutting at both ends, re-ligating, and leaving just the exons on either side to be translated into protein.
## Uses
The antiviral drug acyclovir, often used in herpes treatment, and the anti-HIV drug abacavir, are structurally similar to guanosine. Guanosine was also used to make regadenoson
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# Lists of gymnasts
**Gymnasts** are people who participate in the sport of gymnastics. This sport contains disciplines that include, but are not limited to: `{{columns-list|colwidth=22em|
* [[acrobatic gymnastics]]<ref name="FIGacrobatic">{{cite web|url=http://www.fig-gymnastics.com/vsite/vnavsite/page/directory/0,10853,5187-188459-205681-nav-list,00.html|title=Fédération Internationale de Gymnastique : About Acrobatic|publisher=[[Fédération Internationale de Gymnastique]]|access-date=18 November 2012|quote=Practised by both men and women, Acrobatic Gymnastics (ACRO) is among the oldest known disciplines since already practiced at the ancient Egyptian period, as evidenced by certain frescos. But its name comes from the Greek acrobateo, meaning to rise or go forth.|archive-url=https://web.archive.org/web/20121102010802/http://www.fig-gymnastics.com/vsite/vnavsite/page/directory/0,10853,5187-188459-205681-nav-list,00.html|archive-date=2012-11-02|url-status=dead}}</ref>
* [[aerobic gymnastics]]<ref name="FIGAerobics">{{cite web|url=http://www.fig-gymnastics.com/vsite/vnavsite/page/directory/0,10853,5187-188475-205697-nav-list,00.html|title=Fédération Internationale de Gymnastique : About Aerobic|publisher=[[Fédération Internationale de Gymnastique]]|access-date=18 November 2012|quote=Aerobic has not only been a great form of physical training for the general public since the end of the 1980's, but also a top-level competitive sport. Aerobic Gymnastics presents dynamic moves, strength, flexibility, co-ordination and musicality in a routine, lasting up to 1 minute 50 seconds (1'30" for all categories from 2013).|archive-url=https://web.archive.org/web/20090323030420/http://www.fig-gymnastics.com/vsite/vnavsite/page/directory/0,10853,5187-188475-205697-nav-list,00.html|archive-date=2009-03-23|url-status=dead}}</ref>
* [[artistic gymnastics]]<ref name="FIGartisticM">{{cite web|url=http://www.fig-gymnastics.com/vsite/vnavsite/page/directory/0,10853,5187-188060-205282-nav-list,00.html|title=Fédération Internationale de Gymnastique : About MAG|publisher=[[Fédération Internationale de Gymnastique]]|access-date=18 November 2012|archive-url=https://web.archive.org/web/20121111040308/http://www.fig-gymnastics.com/vsite/vnavsite/page/directory/0,10853,5187-188060-205282-nav-list,00.html|archive-date=11 November 2012|url-status=dead|df=dmy-all}}</ref><ref name="FIGartisticW">{{cite web|url=http://www.fig-gymnastics.com/vsite/vnavsite/page/directory/0,10853,5187-188433-205655-nav-list,00.html |title=Fédération Internationale de Gymnastique : About WAG |publisher=[[Fédération Internationale de Gymnastique]] |access-date=18 November 2012 |quote=The competition program of women's artistic gymnastics includes the vaulting table, the uneven bars, the beam, and the floor. |url-status=dead |archive-url=https://web.archive.org/web/20121111033313/http://www.fig-gymnastics.com/vsite/vnavsite/page/directory/0%2C10853%2C5187-188433-205655-nav-list%2C00.html |archive-date=11 November 2012 }}</ref>
* [[rhythmic gymnastics]]<ref name="FIGRhythmic">{{cite web|url=http://www.fig-gymnastics.com/vsite/vnavsite/page/directory/0,10853,5187-188467-205689-nav-list,00.html|title=Fédération Internationale de Gymnastique : About Rhythmic|access-date=18 November 2012|quote=Women only compete in Rhythmic Gymnastics, although in Japan and some other countries, men also practice the sport.|archive-url=https://web.archive.org/web/20121118022550/http://www.fig-gymnastics.com/vsite/vnavsite/page/directory/0,10853,5187-188467-205689-nav-list,00.html|archive-date=18 November 2012|url-status=dead|df=dmy-all}}</ref>
* [[trampolining|trampoline gymnastics]]<ref name="FIGTrampoline">{{cite web|url=http://www.fig-gymnastics.com/vsite/vnavsite/page/directory/0,10853,5187-188484-205706-nav-list,00.html|title=Fédération Internationale de Gymnastique : About Trampoline|publisher=[[Fédération Internationale de Gymnastique]]|access-date=18 November 2012|quote=Trampoline, an Olympic discipline, symbolizes freedom, flying and space. Multiple somersaults and twists are performed at a height of 8 meters and require precise technique and perfect body control. The Trampoline is also used as a basic training device for all sports that contain acrobatic elements|archive-url=https://web.archive.org/web/20121111040820/http://www.fig-gymnastics.com/vsite/vnavsite/page/directory/0,10853,5187-188484-205706-nav-list,00.html|archive-date=2012-11-11|url-status=dead}}</ref>
* [[Tumbling (gymnastics)|tumbling]]}}`{=mediawiki} This list is of those who are considered to be notable in their chosen discipline.
See gymnasium (ancient Greece) for the origin of the word *gymnast* from **gymnastikos**
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# Genetic programming
**Genetic programming** (**GP**) is an evolutionary algorithm, an artificial intelligence technique mimicking natural evolution, which operates on a population of programs. It applies the genetic operators selection according to a predefined fitness measure, mutation and crossover.
The crossover operation involves swapping specified parts of selected pairs (parents) to produce new and different offspring that become part of the new generation of programs. Some programs not selected for reproduction are copied from the current generation to the new generation. Mutation involves substitution of some random part of a program with some other random part of a program. Then the selection and other operations are recursively applied to the new generation of programs.
Typically, members of each new generation are on average more fit than the members of the previous generation, and the best-of-generation program is often better than the best-of-generation programs from previous generations. Termination of the evolution usually occurs when some individual program reaches a predefined proficiency or fitness level.
It may and often does happen that a particular run of the algorithm results in premature convergence to some local maximum which is not a globally optimal or even good solution. Multiple runs (dozens to hundreds) are usually necessary to produce a very good result. It may also be necessary to have a large starting population size and variability of the individuals to avoid pathologies.
## History
The first record of the proposal to evolve programs is probably that of Alan Turing in 1950 in \"Computing Machinery and Intelligence\". There was a gap of 25 years before the publication of John Holland\'s \'Adaptation in Natural and Artificial Systems\' laid out the theoretical and empirical foundations of the science. In 1981, Richard Forsyth demonstrated the successful evolution of small programs, represented as trees, to perform classification of crime scene evidence for the UK Home Office.
Although the idea of evolving programs, initially in the computer language Lisp, was current amongst John Holland\'s students, it was not until they organised the first Genetic Algorithms (GA) conference in Pittsburgh that Nichael Cramer published evolved programs in two specially designed languages, which included the first statement of modern \"tree-based\" Genetic Programming (that is, procedural languages organized in tree-based structures and operated on by suitably defined GA-operators). In 1988, John Koza (also a PhD student of John Holland) patented his invention of a GA for program evolution. This was followed by publication in the International Joint Conference on Artificial Intelligence IJCAI-89.
Koza followed this with 205 publications on "Genetic Programming" (GP), name coined by David Goldberg, also a PhD student of John Holland. However, it is the series of 4 books by Koza, starting in 1992 with accompanying videos, that really established GP. Subsequently, there was an enormous expansion of the number of publications with the Genetic Programming Bibliography, surpassing 10,000 entries. In 2010, Koza listed 77 results where Genetic Programming was human competitive.
The departure of GP from the rigid, fixed-length representations typical of early GA models was not entirely without precedent. Early work on variable-length representations laid the groundwork. One notable example is Messy Genetic Algorithms, which introduced irregular, variable-length chromosomes to address building block disruption and positional bias in standard GAs.
Another precursor was robot trajectory programming, where genome representations encoded program instructions for robotic movements---structures inherently variable in length.
Even earlier, unfixed-length representations were proposed in a doctoral dissertation by Cavicchio, who explored adaptive search using simulated evolution. His work provided foundational ideas for flexible program structures.
In 1996, Koza started the annual Genetic Programming conference which was followed in 1998 by the annual EuroGP conference, and the first book in a GP series edited by Koza. 1998 also saw the first GP textbook. GP continued to flourish, leading to the first specialist GP journal and three years later (2003) the annual Genetic Programming Theory and Practice (GPTP) workshop was established by Rick Riolo. Genetic Programming papers continue to be published at a diversity of conferences and associated journals. Today there are nineteen GP books including several for students.
Year Description Reference
------ -------------------------------------------------------------------------------------------------- -----------
1992 Introduction of GP as genetically bred populations of computer programs
2000 Cartesian genetic programming
2000 Grammar-guided GP - Dynamic grammar pruning is applied in initialization
2001 Gene expression programming
2012 Multi-gene GP - Combination of classical method for parameter estimation and structure selection
2012 Geometric semantic GP - Direct search in the space of the underlying semantics of the programs
2015 Surrogate GP
2015 Memetic semantic GP
2017 Statistical GP - statistical information used to generate well-structured subtrees
2018 Multi-dimensional GP - novel program representation for multi-dimensional features
: Timeline of EP - selected algorithms
### Foundational work in GP {#foundational_work_in_gp}
Early work that set the stage for current genetic programming research topics and applications is diverse, and includes software synthesis and repair, predictive modeling, data mining, financial modeling, soft sensors, design, and image processing. Applications in some areas, such as design, often make use of intermediate representations, such as Fred Gruau\'s cellular encoding. Industrial uptake has been significant in several areas including finance, the chemical industry, bioinformatics and the steel industry.
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# Genetic programming
## Methods
### Program representation {#program_representation}
*Main article: genetic representation*
GP evolves computer programs, traditionally represented in memory as tree structures. Trees can be easily evaluated in a recursive manner. Every internal node has an operator function and every terminal node has an operand, making mathematical expressions easy to evolve and evaluate. Thus traditionally GP favors the use of programming languages that naturally embody tree structures (for example, Lisp; other functional programming languages are also suitable).
Non-tree representations have been suggested and successfully implemented, such as linear genetic programming which perhaps suits the more traditional imperative languages. The commercial GP software *Discipulus* uses automatic induction of binary machine code (\"AIM\") to achieve better performance. *μGP* uses directed multigraphs to generate programs that fully exploit the syntax of a given assembly language. Multi expression programming uses Three-address code for encoding solutions. Other program representations on which significant research and development have been conducted include programs for stack-based virtual machines, and sequences of integers that are mapped to arbitrary programming languages via grammars. Cartesian genetic programming is another form of GP, which uses a graph representation instead of the usual tree based representation to encode computer programs.
Most representations have structurally noneffective code (introns). Such non-coding genes may seem to be useless because they have no effect on the performance of any one individual. However, they alter the probabilities of generating different offspring under the variation operators, and thus alter the individual\'s variational properties. Experiments seem to show faster convergence when using program representations that allow such non-coding genes, compared to program representations that do not have any non-coding genes. Instantiations may have both trees with introns and those without; the latter are called canonical trees. Special canonical crossover operators are introduced that maintain the canonical structure of parents in their children.
### Initialisation
The methods for creation of the initial population include:
- **Grow** creates the individuals sequentially. Every GP tree is created starting from the root, creating functional nodes with children as well as terminal nodes up to a certain depth.
- **Full** is similar to the *Grow*. The difference is that all brunches in a tree are of same predetermined depth.
- **Ramped half-and-half** creates a populations consisting of $md-1$ parts and a maximum depth of $md$ for its trees. The first part has a maximum depth of 2, second of 3 and so on up to the $md-1$-th part with maximum depth $md$. Half of every part is created by *Grow*, while the other part is created by *Full*.
### Selection
Selection is a process whereby certain individuals are selected from the current generation that would serve as parents for the next generation. The individuals are selected probabilistically such that the better performing individuals have a higher chance of getting selected. The most commonly used selection method in GP is tournament selection, although other methods such as fitness proportionate selection, lexicase selection, and others have been demonstrated to perform better for many GP problems.
Elitism, which involves seeding the next generation with the best individual (or best *n* individuals) from the current generation, is a technique sometimes employed to avoid regression.
### Crossover
In Genetic Programming two fit individuals are chosen from the population to be parents for one or two children. In tree genetic programming, these parents are represented as inverted lisp like trees, with their root nodes at the top. In subtree crossover in each parent a subtree is randomly chosen. (Highlighted with yellow in the animation.) In the root donating parent (in the animation on the left) the chosen subtree is removed and replaced with a copy of the randomly chosen subtree from the other parent, to give a new child tree.
Sometimes two child crossover is used, in which case the removed subtree (in the animation on the left) is not simply deleted but is copied to a copy of the second parent (here on the right) replacing (in the copy) its randomly chosen subtree. Thus this type of subtree crossover takes two fit trees and generates two child trees.
The tree-based approach in Genetic Programming also shares structural and procedural similarities with earlier knowledge-based and topology-oriented crossover methods. Specifically, analogous crossover and homologous crossover, both implemented in robot trajectory planning, exhibit a resemblance to subtree operations in tree GP. These crossover mechanisms were described in the context of heuristic optimisation strategies in robotics.
### Replication
Some individuals selected according to fitness criteria do not participate in crossover, but are copied into the next generation, akin to asexual reproduction in the natural world. They may be further subject to mutation.
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# Genetic programming
## Methods
### Mutation
There are many types of mutation in genetic programming. They start from a fit syntactically correct parent and aim to randomly create a syntactically correct child. In the animation a subtree is randomly chosen (highlighted by yellow). It is removed and replaced by a randomly generated subtree.
Other mutation operators select a leaf (external node) of the tree and replace it with a randomly chosen leaf. Another mutation is to select at random a function (internal node) and replace it with another function with the same arity (number of inputs). Hoist mutation randomly chooses a subtree and replaces it with a subtree within itself. Thus hoist mutation is guaranteed to make the child smaller. Leaf and same arity function replacement ensure the child is the same size as the parent. Whereas subtree mutation (in the animation) may, depending upon the function and terminal sets, have a bias to either increase or decrease the tree size. Other subtree based mutations try to carefully control the size of the replacement subtree and thus the size of the child tree.
Similarly there are many types of linear genetic programming mutation, each of which tries to ensure the mutated child is still syntactically correct.
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# Genetic programming
## Applications
GP has been successfully used as an automatic programming tool, a machine learning tool and an automatic problem-solving engine. GP is especially useful in the domains where the exact form of the solution is not known in advance or an approximate solution is acceptable (possibly because finding the exact solution is very difficult). Some of the applications of GP are curve fitting, data modeling, symbolic regression, feature selection, classification, etc. John R. Koza mentions 76 instances where Genetic Programming has been able to produce results that are competitive with human-produced results (called Human-competitive results). Since 2004, the annual Genetic and Evolutionary Computation Conference (GECCO) holds Human Competitive Awards (called Humies) competition, where cash awards are presented to human-competitive results produced by any form of genetic and evolutionary computation. GP has won many awards in this competition over the years.
## Meta-genetic programming {#meta_genetic_programming}
Meta-genetic programming is the proposed meta-learning technique of evolving a genetic programming system using genetic programming itself. It suggests that chromosomes, crossover, and mutation were themselves evolved, therefore like their real life counterparts should be allowed to change on their own rather than being determined by a human programmer. Meta-GP was formally proposed by Jürgen Schmidhuber in 1987. Doug Lenat\'s Eurisko is an earlier effort that may be the same technique. It is a recursive but terminating algorithm, allowing it to avoid infinite recursion. In the \"autoconstructive evolution\" approach to meta-genetic programming, the methods for the production and variation of offspring are encoded within the evolving programs themselves, and programs are executed to produce new programs to be added to the population.
Critics of this idea often say this approach is overly broad in scope. However, it might be possible to constrain the fitness criterion onto a general class of results, and so obtain an evolved GP that would more efficiently produce results for sub-classes. This might take the form of a meta evolved GP for producing human walking algorithms which is then used to evolve human running, jumping, etc. The fitness criterion applied to the meta GP would simply be one of efficiency
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# Guanine
**Guanine** (`{{IPAc-en|audio=En-us-guanine.ogg|ˈ|g|w|ɑː|n|iː|n}}`{=mediawiki}) (symbol **G** or **Gua**) is one of the four main nucleotide bases found in the nucleic acids DNA and RNA, the others being adenine, cytosine, and thymine (uracil in RNA). In DNA, guanine is paired with cytosine. The guanine nucleoside is called guanosine.
With the formula C~5~H~5~N~5~O, guanine is a derivative of purine, consisting of a fused pyrimidine-imidazole ring system with conjugated double bonds. This unsaturated arrangement means the bicyclic molecule is planar.
## Properties
Guanine, along with adenine and cytosine, is present in both DNA and RNA, whereas thymine is usually seen only in DNA, and uracil only in RNA. Guanine has multiple tautomeric forms. For the imidazole ring, the proton can reside on either nitrogen. For the pyrimidine ring, the ring N-H can center can reside on either of the ring nitrogens. The latter tautomer does not apply to nucleoside or nucleotide versions of guanine.
It binds to cytosine through three hydrogen bonds. In cytosine, the amino group acts as the hydrogen bond donor and the C-2 carbonyl and the N-3 amine as the hydrogen-bond acceptors. Guanine has the C-6 carbonyl group that acts as the hydrogen bond acceptor, while a group at N-1 and the amino group at C-2 act as the hydrogen bond donors.
Guanine can be hydrolyzed with strong acid to glycine, ammonia, carbon dioxide, and carbon monoxide. First, guanine gets deaminated to become xanthine. Guanine oxidizes more readily than adenine, the other purine-derivative base in DNA. Its high melting point of 350 °C reflects the intermolecular hydrogen bonding between the oxo and amino groups in the molecules in the crystal. Because of this intermolecular bonding, guanine is relatively insoluble in water, but it is soluble in dilute acids and bases.
## History
The first isolation of guanine was reported in 1844 by the German chemist Julius Bodo Unger (1819--1885), who obtained it as a mineral formed from the excreta of sea birds, which is known as guano and which was used as a source of fertilizer; guanine was named in 1846.Guanine was first isolated in 1844 by Julius Bodo Unger (1819--1885), a student of Heinrich Gustav Magnus. See:
- Paul O. P. Ts\'o, *Basic Principles in Nucleic Acid Chemistry*, vol. 1 (New York, New York: Academic Press, 1974), [page 7.](https://books.google.com/books?id=oAKAbV7FHfgC&pg=PA7)
- Magnus (1844) [\"Ueber das Vorkommen von Xanthicoxyd im Guano\"](https://books.google.com/books?id=nT49AAAAcAAJ&pg=PA395) (On the occurrence of xanthic oxide in guano), *Annalen der Chemie und Pharmacie*, **51** : 395-397.
- B. Unger (1846) [\"Bemerkungen zu obiger Notiz\"](https://books.google.com/books?id=7TU9AAAAcAAJ&pg=PA18) (Comments on the above notice), *Annalen der Chemie und Pharmacie*, **58** : 18-20. From page 20: *\" \... desshalb möchte ich den Namen*Guanin*vorschlagen, welcher an seine Herkunft erinnert.\"* ( \... therefore I would like to suggest the name *guanine*, which is reminiscent of its origin.)
- B. Unger (1846) [\"Das Guanin und seine Verbindungen\"](https://books.google.com/books?id=AjY9AAAAcAAJ&pg=PA58) (Guanine and its compounds), *Annalen der Chemie und Pharmacie*, **59** : 58-68.
Between 1882 and 1906, Emil Fischer determined the structure and also showed that uric acid can be converted to guanine.
## Synthesis
A Fischer--Tropsch synthesis can be used to form guanine, along with adenine, uracil, and thymine. Heating an equimolar gas mixture of CO, H~2~, and NH~3~ to 700 °C for 15 to 24 minutes, followed by quick cooling and then sustained reheating to 100 to 200 °C for 16 to 44 hours with an alumina catalyst, yielded guanine and uracil:
: 10CO + H~2~ + 10NH~3~ → 2C~5~H~8~N~5~O (guanine) + 8H~2~O
Trace amounts of guanine form by the polymerization of ammonium cyanide (`{{chem|NH|4|CN}}`{=mediawiki}). Two experiments conducted by Levy et al. showed that heating 10 mol·L^−1^ `{{chem|NH|4|CN}}`{=mediawiki} at 80 °C for 24 hours gave a yield of 0.0007%, while using 0.1 mol·L^−1^ `{{chem|NH|4|CN}}`{=mediawiki} frozen at −20 °C for 25 years gave a 0.0035% yield. These results indicate guanine could arise in frozen regions of the primitive earth. In 1984, Yuasa reported a 0.00017% yield of guanine after the electrical discharge of `{{chem|NH|3}}`{=mediawiki}, `{{chem|CH|4}}`{=mediawiki}, `{{chem|C|2|H|6}}`{=mediawiki}, and 50 mL of water, followed by a subsequent acid hydrolysis. However, it is unknown whether the presence of guanine was not simply a resultant contaminant of the reaction.
: 10NH~3~ + 2CH~4~ + 4C~2~H~6~ + 2H~2~O → 2C~5~H~8~N~5~O (guanine) + 25H~2~
Another possible abiotic route was explored by quenching a 90% N~2~--10%CO--H~2~O gas mixture high-temperature plasma.
Traube\'s synthesis involves heating 4-hydroxy-2,4,5-triaminopyrimidine with formic acid for several hours.
## Biosynthesis
Guanine is not primarily synthesized de novo.`{{clarification needed|date=March 2022}}`{=mediawiki} Instead, it is split from the more complex molecule guanosine by the enzyme guanosine phosphorylase:
: guanosine + phosphate $\rightleftharpoons$ guanine + alpha-D-ribose 1-phosphate
Guanine can be synthesized de novo, with the rate-limiting enzyme of inosine monophosphate dehydrogenase.
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# Guanine
## Other occurrences and biological uses {#other_occurrences_and_biological_uses}
The word guanine derives from the Spanish loanword *guano* (\'bird/bat droppings\'), which itself is from the Quechua word *wanu*, meaning \'dung\'. As the Oxford English Dictionary notes, guanine is \"A white amorphous substance obtained abundantly from guano, forming a constituent of the excrement of birds\".
In 1656 in Paris, a Mr. Jaquin extracted from the scales of the fish *Alburnus alburnus* so-called \"pearl essence\", which is crystalline guanine. In the cosmetics industry, crystalline guanine is used as an additive to various products (e.g., shampoos), where it provides a pearly iridescent effect. It is also used in metallic paints and simulated pearls and plastics. It provides shimmering luster to eye shadow and nail polish. Facial treatments using the droppings, or guano, from Japanese nightingales have been used in Japan and elsewhere, because the guanine in the droppings makes the skin look paler. Guanine crystals are rhombic platelets composed of multiple transparent layers, but they have a high index of refraction that partially reflects and transmits light from layer to layer, thus producing a pearly luster. It can be applied by spray, painting, or dipping. It may irritate the eyes. Its alternatives are mica, faux pearl (from ground shells), and aluminium and bronze particles.
Guanine has a very wide variety of biological uses that include a range of functions ranging in both complexity and versatility. These include camouflage, display, and vision among other purposes.
Spiders, scorpions, and some amphibians convert ammonia, as a product of protein metabolism in the cells, to guanine, as it can be excreted with minimal water loss.
Guanine is also found in specialized skin cells of fish called iridocytes (e.g., the sturgeon), as well as being present in the reflective deposits of the eyes of deep-sea fish and some reptiles, such as crocodiles and chameleons.
On 8 August 2011, a report, based on NASA studies with meteorites found on Earth, was published suggesting building blocks of DNA and RNA (guanine, adenine and related organic molecules) may have been formed extra-terrestrially in outer space
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# Gödel's completeness theorem
thumb\|upright=1.8\|The formula (∀*x*. *R*(*x*,*x*)) → (∀*x*∃*y*. *R*(*x*,*y*)) holds in all structures (only the simplest 8 are shown left). By Gödel\'s completeness result, it must hence have a natural deduction proof (shown right). **Gödel\'s completeness theorem** is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic.
The completeness theorem applies to any first-order theory: If *T* is such a theory, and φ is a sentence (in the same language) and every model of *T* is a model of φ, then there is a (first-order) proof of φ using the statements of *T* as axioms. One sometimes says this as \"anything true in all models is provable\". (This does not contradict Gödel\'s \<!\-\--first\-\--\> incompleteness theorem, which is about a formula φ~u~ that is unprovable in a certain theory *T* but true in the \"standard\" model of the natural numbers: φ~u~ is false in some other, \"non-standard\" models of *T*.)
The completeness theorem makes a close link between model theory, which deals with what is true in different models, and proof theory, which studies what can be formally proven in particular formal systems.
It was first proved by Kurt Gödel in 1929. It was then simplified when Leon Henkin observed in his Ph.D. thesis that the hard part of the proof can be presented as the Model Existence Theorem (published in 1949). Henkin\'s proof was simplified by Gisbert Hasenjaeger in 1953.
## Preliminaries
There are numerous deductive systems for first-order logic, including systems of natural deduction and Hilbert-style systems. Common to all deductive systems is the notion of a *formal deduction*. This is a sequence (or, in some cases, a finite tree) of formulae with a specially designated *conclusion*. The definition of a deduction is such that it is finite and that it is possible to verify algorithmically (by a computer, for example, or by hand) that a given sequence (or tree) of formulae is indeed a deduction.
A first-order formula is called *logically valid* if it is true in every structure for the language of the formula (i.e. for any assignment of values to the variables of the formula). To formally state, and then prove, the completeness theorem, it is necessary to also define a deductive system. A deductive system is called *complete* if every logically valid formula is the conclusion of some formal deduction, and the completeness theorem for a particular deductive system is the theorem that it is complete in this sense. Thus, in a sense, there is a different completeness theorem for each deductive system. A converse to completeness is *soundness*, the fact that only logically valid formulas are provable in the deductive system.
If some specific deductive system of first-order logic is sound and complete, then it is \"perfect\" (a formula is provable if and only if it is logically valid), thus equivalent to any other deductive system with the same quality (any proof in one system can be converted into the other).
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# Gödel's completeness theorem
## Statement
We first fix a deductive system of first-order predicate calculus, choosing any of the well-known equivalent systems. Gödel\'s original proof assumed the Hilbert-Ackermann proof system.
### Gödel\'s original formulation {#gödels_original_formulation}
The completeness theorem says that if a formula is logically valid then there is a finite deduction (a formal proof) of the formula.
Thus, the deductive system is \"complete\" in the sense that no additional inference rules are required to prove all the logically valid formulae. A converse to completeness is *soundness*, the fact that only logically valid formulae are provable in the deductive system. Together with soundness (whose verification is easy), this theorem implies that a formula is logically valid if and only if it is the conclusion of a formal deduction.
### More general form {#more_general_form}
The theorem can be expressed more generally in terms of logical consequence. We say that a sentence *s* is a *syntactic consequence* of a theory *T*, denoted $T\vdash s$, if *s* is provable from *T* in our deductive system. We say that *s* is a *semantic consequence* of *T*, denoted $T\models s$, if *s* holds in every model of *T*. The completeness theorem then says that for any first-order theory *T* with a well-orderable language, and any sentence *s* in the language of *T*,
Since the converse (soundness) also holds, it follows that $T\models s$ if and only if $T\vdash s$, and thus that syntactic and semantic consequence are equivalent for first-order logic.
This more general theorem is used implicitly, for example, when a sentence is shown to be provable from the axioms of group theory by considering an arbitrary group and showing that the sentence is satisfied by that group.
Gödel\'s original formulation is deduced by taking the particular case of a theory without any axiom.
### Model existence theorem {#model_existence_theorem}
The completeness theorem can also be understood in terms of consistency, as a consequence of Henkin\'s model existence theorem. We say that a theory *T* is *syntactically consistent* if there is no sentence *s* such that both *s* and its negation ¬*s* are provable from *T* in our deductive system. The model existence theorem says that for any first-order theory *T* with a well-orderable language,
Another version, with connections to the Löwenheim--Skolem theorem, says:
Given Henkin\'s theorem, the completeness theorem can be proved as follows: If $T \models s$, then $T\cup\lnot s$ does not have models. By the contrapositive of Henkin\'s theorem, then $T\cup\lnot s$ is syntactically inconsistent. So a contradiction ($\bot$) is provable from $T\cup\lnot s$ in the deductive system. Hence $(T\cup\lnot s) \vdash \bot$, and then by the properties of the deductive system, $T\vdash s$.
### As a theorem of arithmetic {#as_a_theorem_of_arithmetic}
The model existence theorem and its proof can be formalized in the framework of Peano arithmetic. Precisely, we can systematically define a model of any consistent effective first-order theory *T* in Peano arithmetic by interpreting each symbol of *T* by an arithmetical formula whose free variables are the arguments of the symbol. (In many cases, we will need to assume, as a hypothesis of the construction, that *T* is consistent, since Peano arithmetic may not prove that fact.) However, the definition expressed by this formula is not recursive (but is, in general, Δ~2~).
## Consequences
An important consequence of the completeness theorem is that it is possible to recursively enumerate the semantic consequences of any effective first-order theory, by enumerating all the possible formal deductions from the axioms of the theory, and use this to produce an enumeration of their conclusions.
This comes in contrast with the direct meaning of the notion of semantic consequence, that quantifies over all structures in a particular language, which is clearly not a recursive definition.
Also, it makes the concept of \"provability\", and thus of \"theorem\", a clear concept that only depends on the chosen system of axioms of the theory, and not on the choice of a proof system.
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# Gödel's completeness theorem
## Relationship to the incompleteness theorems {#relationship_to_the_incompleteness_theorems}
Gödel\'s incompleteness theorems show that there are inherent limitations to what can be proven within any given first-order theory in mathematics. The \"incompleteness\" in their name refers to another meaning of *complete* (see model theory -- Using the compactness and completeness theorems): A theory $T$ is complete (or decidable) if every sentence $S$ in the language of $T$ is either provable ($T\vdash S$) or disprovable ($T\vdash \neg S$).
The first incompleteness theorem states that any $T$ which is consistent, effective and contains Robinson arithmetic (\"*Q*\") must be incomplete in this sense, by explicitly constructing a sentence $S_T$ which is demonstrably neither provable nor disprovable within $T$. The second incompleteness theorem extends this result by showing that $S_T$ can be chosen so that it expresses the consistency of $T$ itself.
Since $S_T$ cannot be proven in $T$, the completeness theorem implies the existence of a model of $T$ in which $S_T$ is false. In fact, $S_T$ is a Π~1~ sentence, i.e. it states that some finitistic property is true of all natural numbers; so if it is false, then some natural number is a counterexample. If this counterexample existed within the standard natural numbers, its existence would disprove $S_T$ within $T$; but the incompleteness theorem showed this to be impossible, so the counterexample must not be a standard number, and thus any model of $T$ in which $S_T$ is false must include non-standard numbers.
In fact, the model of *any* theory containing *Q* obtained by the systematic construction of the arithmetical model existence theorem, is *always* non-standard with a non-equivalent provability predicate and a non-equivalent way to interpret its own construction, so that this construction is non-recursive (as recursive definitions would be unambiguous).
Also, if $T$ is at least slightly stronger than *Q* (e.g. if it includes induction for bounded existential formulas), then Tennenbaum\'s theorem shows that it has no recursive non-standard models.
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# Gödel's completeness theorem
## Relationship to the compactness theorem {#relationship_to_the_compactness_theorem}
The completeness theorem and the compactness theorem are two cornerstones of first-order logic. While neither of these theorems can be proven in a completely effective manner, each one can be effectively obtained from the other.
The compactness theorem says that if a formula φ is a logical consequence of a (possibly infinite) set of formulas Γ then it is a logical consequence of a finite subset of Γ. This is an immediate consequence of the completeness theorem, because only a finite number of axioms from Γ can be mentioned in a formal deduction of φ, and the soundness of the deductive system then implies φ is a logical consequence of this finite set. This proof of the compactness theorem is originally due to Gödel.
Conversely, for many deductive systems, it is possible to prove the completeness theorem as an effective consequence of the compactness theorem.
The ineffectiveness of the completeness theorem can be measured along the lines of reverse mathematics. When considered over a countable language, the completeness and compactness theorems are equivalent to each other and equivalent to a weak form of choice known as weak Kőnig\'s lemma, with the equivalence provable in RCA~0~ (a second-order variant of Peano arithmetic restricted to induction over Σ^0^~1~ formulas). Weak Kőnig\'s lemma is provable in ZF, the system of Zermelo--Fraenkel set theory without axiom of choice, and thus the completeness and compactness theorems for countable languages are provable in ZF. However the situation is different when the language is of arbitrary large cardinality since then, though the completeness and compactness theorems remain provably equivalent to each other in ZF, they are also provably equivalent to a weak form of the axiom of choice known as the ultrafilter lemma. In particular, no theory extending ZF can prove either the completeness or compactness theorems over arbitrary (possibly uncountable) languages without also proving the ultrafilter lemma on a set of the same cardinality.
## Completeness in other logics {#completeness_in_other_logics}
The completeness theorem is a central property of first-order logic that does not hold for all logics. Second-order logic, for example, does not have a completeness theorem for its standard semantics (though does have the completeness property for Henkin semantics), and the set of logically valid formulas in second-order logic is not recursively enumerable. The same is true of all higher-order logics. It is possible to produce sound deductive systems for higher-order logics, but no such system can be complete.
Lindström\'s theorem states that first-order logic is the strongest (subject to certain constraints) logic satisfying both compactness and completeness.
A completeness theorem can be proved for modal logic or intuitionistic logic with respect to Kripke semantics.
## Proofs
Gödel\'s original proof of the theorem proceeded by reducing the problem to a special case for formulas in a certain syntactic form, and then handling this form with an *ad hoc* argument.
In modern logic texts, Gödel\'s completeness theorem is usually proved with Henkin\'s proof, rather than with Gödel\'s original proof. Henkin\'s proof directly constructs a term model for any consistent first-order theory. James Margetson (2004) developed a computerized formal proof using the Isabelle theorem prover. Other proofs are also known
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# Geri and Freki
In Norse mythology, **Geri** and **Freki** are two wolves which are said to accompany the god Odin. They are attested in the *Poetic Edda*, a collection of epic poetry compiled in the 13th century from earlier traditional sources, in the *Prose Edda*, written in the 13th century by Snorri Sturluson, and in the poetry of skalds. The pair has been compared to similar figures found in Greek, Roman and Vedic mythology, and may also be connected to beliefs surrounding the Germanic \"wolf-warrior bands\", the Úlfhéðnar.
## Etymology
The name *Geri* has been interpreted as meaning either \"the greedy one\" or \"the ravenous one\". The name *Geri* can be traced back to the Proto-Germanic adjective *geraz\]\]*, attested in Burgundian *girs*, Old Norse *gerr*, Old Swedish *giri*, Old High German *ger* or `{{wikt-lang|goh|giri}}`{=mediawiki} and Old Dutch *gir*, all of which mean \"greedy\". Compare modern *gerrig*, *girig*, *girug*, *girig*, all meaning greedy.
The name *Freki* can be traced back to the Proto-Germanic adjective *frekaz\]\]*, attested in Gothic `{{wikt-lang|got|𐍆𐌰𐌹𐌷𐌿𐍆𐍂𐌹𐌺𐍃}}`{=mediawiki} (*faihufriks*) \"covetous, avaricious\", Old English `{{wikt-lang|ang|frec}}`{=mediawiki} \"desirous, greedy, gluttonous, audacious\" and Old High German `{{wikt-lang|goh|freh}}`{=mediawiki} \"greedy, covetous, desirous\", The Old Norse form `{{wikt-lang|non|frekr}}`{=mediawiki} is fairly broad (compare modern *fræk*, *frek*, *fräck*, *fräk*), meaning \"brazen, enterprising, covetous, greedy and insatiable\", including having a voracious appetite ("gluttonous").
John Lindow interprets both Old Norse names as nominalized adjectives. Bruce Lincoln further traces *Geri* back to a Proto-Indo-European stem \**`{{PIE|gher-}}`{=mediawiki}*, which is the same as that found in *\[\[Garmr\]\]*, a name referring to the hound closely associated with the events of *italic=no*.
## Attestations
In the *Poetic Edda* poem *Grímnismál*, the god Odin (disguised as *Grímnir*) provides the young Agnarr with information about Odin\'s companions. Agnarr is told that Odin feeds Geri and Freki while the god himself consumes only wine:
> +-----------------------------------------+---------------------------------------------------+---+
> | : Benjamin Thorpe translation: | : Henry Adams Bellows translation: | |
> | : Geri and Freki the war-wont sates, | : Freki and Geri does Heerfather feed, | |
> | : the triumphant sire of hosts; | : The far-famed fighter of old: | |
> | : but on wine only the famed in arms, | : But on wine alone does the weapon-decked god, | |
> | : Odin, ever lives. | : Othin, forever live. | |
> +-----------------------------------------+---------------------------------------------------+---+
The pair is also alluded to via the kenning \"Viðrir\'s (Odin\'s) hounds\" in *Helgakviða Hundingsbana I*, verse 13, where it is related that they roam the field \"greedy for the corpses of those who have fallen in battle\".
> +-----------------------------------------------------------+-------------------------------------------------------+---+
> | : Benjamin Thorpe translation: | : Henry Adams Bellows translation: | |
> | : The warriors went to the trysting place of swords, | : The warriors forth to the battle went, | |
> | : which they had appointed at Logafiöll. | : The field they chose at Logafjoll; | |
> | : Broken was Frodi\'s peace between the foes: | : Frothi\'s peace midst foes they broke, | |
> | : Vidrir's hounds went about the isle slaughter-greedy. | : Through the isle went hungrily Vithrir\'s hounds. | |
> +-----------------------------------------------------------+-------------------------------------------------------+---+
In the *Prose Edda* book *Gylfaginning* (chapter 38), the enthroned figure of High explains that Odin gives all of the food on his table to his wolves Geri and Freki and that Odin requires no food, for wine is to him both meat and drink. High then quotes the above-mentioned stanza from the poem *Grímnismál* in support. In chapter 75 of the *Prose Edda* book *Skáldskaparmál* a list of names for wargs and wolves is provided that includes both Geri and Freki.
In skaldic poetry *Geri* and *Freki* are used as common nouns for \"wolf\" in chapter 58 of *Skáldskaparmál* (quoted in works by the skalds Þjóðólfr of Hvinir and Egill Skallagrímsson) and *Geri* is again used as a common noun for \"wolf\" in chapter 64 of the *Prose Edda* book *Háttatal*. Geri is referenced in kennings for \"blood\" in chapter 58 of *Skáldskaparmál* (\"Geri\'s ales\" in a work by the skald Þórðr Sjáreksson) and in for \"carrion\" in chapter 60 (\"Geri\'s morsel\" in a work by the skald Einarr Skúlason). *Freki* is also used in a kenning for \"carrion\" (\"Freki\'s meal\") in a work by Þórðr Sjáreksson in chapter 58 of *Skáldskaparmál*.
## Archaeological record {#archaeological_record}
If the rider on horseback on the image on the Böksta Runestone has been correctly identified as Odin, then Geri and Freki are shown taking part in hunting an elk.
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# Geri and Freki
## Theories
*Freki* is also a name applied to the monstrous wolf Fenrir in the *Poetic Edda* poem *Völuspá*. Folklorist John Lindow sees irony in the fact that Odin feeds one Freki at his dinner table and another---Fenrir---with his flesh during the events of Ragnarök.
Historian Michael Spiedel connects Geri and Freki with archaeological finds depicting figures wearing wolf-pelts and frequently found wolf-related names among the Germanic peoples, including Wulfhroc (\"Wolf-Frock\"), Wolfhetan (\"Wolf-Hide\"), Isangrim (\"Grey-Mask\"), Scrutolf (\"Garb-Wolf\"), Wolfram (\"Wolf (and) Raven\"), Wolfgang (\"Wolf-Gait\"), Wolfdregil (\"Wolf-Runner\"), and Vulfolaic (\"Wolf-Dancer\") and myths regarding wolf warriors from Norse mythology (such as the Úlfhéðnar). Michael Speidel believes this to point to the pan-Germanic wolf-warrior band cult centered on Odin that waned away after Christianization.
Scholars have also noted Indo-European parallels to the wolves Geri and Freki as companions of a divinity. 19th century scholar Jacob Grimm observed a connection between this aspect of Odin\'s character and the Greek Apollo, to whom both the wolf and the raven are sacred. Philologist Maurice Bloomfield further connected the pair with the two dogs of Yama in Vedic mythology, and saw them as a Germanic counterpart to a more general and widespread Indo-European \"Cerberus\"-theme. Speidel finds similar parallels in the Vedic Rudra and the Roman Mars. Elaborating on the connection between wolves and figures of great power, he writes: \"This is why Geri and Freki, the wolves at Woden\'s side, also glowered on the throne of the Anglo-Saxon kings. Wolf-warriors, like Geri and Freki, were not mere animals but mythical beings: as Woden\'s followers they bodied forth his might, and so did wolf-warriors.\"
Bernd Heinrich theorizes that Geri and Freki, along with Odin and his ravens Huginn and Muninn, reflect a symbiosis observed in the natural world among ravens, wolves, and humans on the hunt:
> : In a biological symbiosis one organism typically shores up some weakness or deficiency of the other(s). As in such a symbiosis, Odin the father of all humans and gods, though in human form was imperfect by himself. As a separate entity he lacked depth perception (being one-eyed) and he was apparently also uninformed and forgetful. But his weaknesses were compensated by his ravens, Hugin (mind) and Munin (memory) who were part of him. They perched on his shoulders and reconnoitered to the ends of the earth each day to return in the evening and tell him the news. He also had two wolves at his side, and the man/god-raven-wolf association was like one single organism in which the ravens were the eyes, mind, and memory, and the wolves the providers of meat and nourishment. As god, Odin was the ethereal part---he only drank wine and spoke only in poetry. I wondered if the Odin myth was a metaphor that playfully and poetically encapsulates ancient knowledge of our prehistoric past as hunters in association with two allies to produce a powerful hunting alliance. It would reflect a past that we have long forgotten and whose meaning has been obscured and badly frayed as we abandoned our hunting cultures to become herders and agriculturists, to whom ravens act as competitors
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# Ginnungagap
In Norse mythology, **Ginnungagap** (old Norse: `{{IPA|non|ˈɡinːoŋɡɑˌɡɑp|}}`{=mediawiki}; \"gaping abyss\", \"yawning void\") is the primordial, magical void mentioned in three poems from the *Poetic Edda* and the *Gylfaginning*, the Eddaic text recording Norse cosmogony.
## Etymology
*Ginnunga-* is usually interpreted as deriving from a verb meaning \"gape\" or \"yawn\", but no such word occurs in Old Norse except in verse 3 of the Eddic poem \"Vǫluspá\", \"*gap var ginnunga*\", which may be a play on the term.
In her edition of the poem, Ursula Dronke suggested it was borrowed from Old High German *ginunga*, as the term Múspell is believed to have been borrowed from Old High German. An alternative etymology links the *ginn-* prefix with that found in terms with a sacral meaning, such as *ginn-heilagr*, *ginn-regin* (both referring to the gods) and *ginn-runa* (referring to the runes), thus interpreting *Ginnungagap* as signifying a \"magical (and creative) power-filled space\".
## Creation
Ginnungagap appears as the primordial void in the Norse creation account. The *Gylfaginning* states:
In the *Völuspá*, a supernaturally long-lived völva who was raised by jötnar tells the story of how Odin and his two brothers created the world from Ginnungagap.
## Geographic rationalization {#geographic_rationalization}
Scandinavian cartographers from the early 15th century attempted to localize or identify Ginnungagap as a real geographic location from which the creation myth derived. A fragment from a 15th-century (pre-Columbus) Old Norse encyclopedic text entitled *Gripla* (Little Compendium) places Ginnungagap between Greenland and Vinland:
A scholion in a 15th-century manuscript of Adam of Bremen\'s *Gesta Hammaburgensis Ecclesiae Pontificum* similarly refers to *Ghimmendegop* as the Norse word for the abyss in the far north.
Later, the 17th-century Icelandic bishop Guðbrandur Thorlaksson also used the name *Ginnung**e**gap* to refer to a narrow body of water, possibly the Davis Strait, separating the southern tip of Greenland from *Estotelandia, pars America extrema*, probably Baffin Island.
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# Ginnungagap
## In popular culture {#in_popular_culture}
- *Ginnungagap* is song taken from the Jethro Tull album, RökFlöte, and released as a single on January 20, 2023.
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- Ginnungagap is featured in the Marvel Universe, as a void that existed before the formation of the world. In this place were formed entities such as the Elder Gods, Xian, Ennead, Frost Giants, Fire Demons, Nyx and Amatsu-Mikaboshi.
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- In the Netflix series *Ragnarok*, Ginnungagap is visited as camping site for a classroom field trip during Season 1, Episode 4; it also happens to be the name of this particular episode. In Season 2, Episode 2, Ginnungagap is visited by the characters Laurits and Vidar, and is depicted as a scenic vantage point overlooking a fjord and two adjoining mountains.
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- Alastair Reynolds\' space opera novel *Absolution Gap* features a chasm named Ginnungagap Rift.
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- Swedish death metal band, Amon Amarth and their 2001 album The Crusher features a track titled, \"Fall Through Ginnungagap\".
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- Swedish symphonic metal band, Therion, features a track titled \"Ginnungagap\" on their *Secret of the Runes* album from 2001.
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- EVE Online has a black hole whose accretion disk shows up in the skybox named Ginnungagap.
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- \"Ginungagap\" (sic) is the title of a science fiction short story by Michael Swanwick.
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- French neofolk group SKÁLD included a song titled \"Ginnunga\" in their 2018 album *Vikings Chant*.
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- Ginnungagap (ギンヌンガガプ, *Ginnungagapu*) is a weaponized grimoire introduced in *Fire Emblem Fates*, part of a video-game franchise published by Nintendo. It is a high-level item that hits the hardest of all tomes and scrolls in the game.
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- Ginungagap is the hub world of the video game *Jøtun*.
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- In PlatinumGames\'s *Bayonetta 3*, the main characters travel through the multiverse, and the Ginnungagap is used as a gateway. In the game, it is referred to as \"Ginnungagap, the Chaotic Rift\".
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- A variation of Ginnungagap called \"The Spark of the World\" appears in the 2022 action-adventure video game *God of War Ragnarök*. This location becomes accessible during the main quest while in Muspelheim, appearing as a cosmic tapestry of orange sparks merged with blue-tinged essence, presumably from Niflheim
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# Gauss (unit)
\| units2 = Gaussian base units \| inunits2 = 1 cm^−1/2^⋅g^1/2^⋅s^−1^ \| units3 = esu-cgs \| inunits3 = 1/`{{math|''c''}}`{=mediawiki}`{{sub|cgs}}`{=mediawiki} esu `{{val|2.99792458e10}}`{=mediawiki} is the numeric part of the speed of light when expressed in cgs units.}} }} The **gauss** (symbol: **`{{val|u=G}}`{=mediawiki}**, sometimes **Gs**) is a unit of measurement of magnetic induction, also known as magnetic flux density. The unit is part of the Gaussian system of units, which inherited it from the older centimetre--gram--second electromagnetic units (CGS-EMU) system. It was named after the German mathematician and physicist Carl Friedrich Gauss in 1936. One gauss is defined as one maxwell per square centimetre.
As the centimetre--gram--second system of units (cgs system) has been superseded by the International System of Units (SI), the use of the gauss has been deprecated by the standards bodies, but is still regularly used in various subfields of science. The SI unit for magnetic flux density is the tesla (symbol T), which corresponds to `{{gaps|10,000|gauss}}`{=mediawiki}.
## Name, symbol, and metric prefixes {#name_symbol_and_metric_prefixes}
Although not a component of the International System of Units, the usage of the gauss generally follows the rules for SI units. Since the name is derived from a person\'s name, its symbol is the uppercase letter \"G\". When the unit is spelled out, it is written in lowercase (\"gauss\"), unless it begins a sentence. The gauss may be combined with metric prefixes, such as in milligauss, mG (or mGs), or kilogauss, kG (or kGs).
## Unit conversions {#unit_conversions}
$\begin{align}
1\,{\rm G} &= {\rm Mx}{\cdot}{\rm cm}^{-2} = \frac{\rm g}{{\rm Bi}{\cdot}{\rm s}^2}\\
&\text{ ≘ } 10^{-4}\,{\rm T} = 10^{-4}\frac{\rm kg}{{\rm A}{\cdot}{\rm s^2}}
\end{align}$
The gauss is the unit of magnetic flux density **B** in the system of Gaussian units and is equal to Mx/cm^2^ or g/Bi/s^2^, while the oersted is the unit of `{{math|'''H'''}}`{=mediawiki}-field. One tesla (T) corresponds to 10^4^ gauss, and one ampere (A) per metre corresponds to 4π × 10^−3^ oersted.
The units for magnetic flux Φ, which is the integral of magnetic `{{math|'''B'''}}`{=mediawiki}-field over an area, are the weber (Wb) in the SI and the maxwell (Mx) in the CGS-Gaussian system. The conversion factor is `{{val|e=8|u=maxwell per weber}}`{=mediawiki}, since flux is the integral of field over an area, area having the units of the square of distance, thus `{{val|e=4|u=G/T}}`{=mediawiki} (magnetic field conversion factor) times the square of `{{val|e=2|u=cm/m}}`{=mediawiki} (linear distance conversion factor). 10^8^ Mx/Wb = 10^4^ G/T × (10^2^ cm/m)^2^.
## Typical values {#typical_values}
- 10^−9^--10^−8^ G -- the magnetic field of the human brain
- 10^−6^--10^−3^ G -- the magnetic field of Galactic molecular clouds. Typical magnetic field strengths within the interstellar medium of the Milky Way are \~5 μG.
- 0.25--0.60 G -- the Earth\'s magnetic field at its surface
- 4 G -- near Jupiter\'s equator
- 25 G -- the Earth\'s magnetic field in its core
- 50 G -- a typical refrigerator magnet
- 100 G -- an iron magnet
- 1500 G -- within a sun spot
- 10000 to 13000 G -- remanence of a neodymium-iron-boron (NIB) magnet
- 16000 to 22000 G -- saturation of high permeability iron alloys used in transformers
- 3000--70000 G -- a medical magnetic resonance imaging machine
- 10^12^--10^13^ G -- the surface of a neutron star
- 4 × 10^13^ G -- the Schwinger limit
- 10^14^ G -- the magnetic field of SGR J1745-2900, orbiting the supermassive black hole Sgr A\* in the center of the Milky Way
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# Great Lakes Colleges Association
The **Great Lakes Colleges Association** (**GLCA**) is a consortium of 13 liberal arts colleges located in the states around the Great Lakes. The GLCA\'s offices are located in Ann Arbor, Michigan and its 13 schools are located in Michigan, Ohio, Pennsylvania and Indiana. It was chartered in the state of Michigan and incorporated as a 501(c)(3) non-profit organization in 1962. Its stated mission is to take actions that will help strengthen and preserve its colleges, being a leading force on behalf of education in the tradition of the liberal arts and sciences.
The organization is the founder and administrator of the Global Liberal Arts Alliance.
## Operations
GLCA operates a Tuition Remission Exchange involving its 13 colleges plus Beloit College, Grinnell College, Willamette University, and Wittenberg University, by which students eligible for tuition remission because of parental employment at one of the colleges will receive tuition remission at any one of the other colleges in the Exchange.
GLCA awards three literary prizes annually to a poet, a fiction writer, and a creative nonfiction writer to honor their first books. Winning authors receive all-expense-paid trips to several of GLCA\'s member colleges, at which they will be paid an honorarium of at least \$500 to meet with students, give readings, and lead discussions.
The Philadelphia Center, which offers an off-campus study program with the opportunity to gain college credit while living and learning independently in Philadelphia, Pennsylvania, is managed and operated by Albion College in partnership with the GLCA.
The consortium extended its first offer of membership in 46 years to Allegheny College in 2008
| 268 |
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