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# Diogo Cão
**Diogo Cão** (`{{IPA|pt-PT|diˈoɣu ˈkɐ̃w}}`{=mediawiki}; c. 1452 -- 1486), also known as **Diogo Cam**, was a Portuguese mariner and one of the most notable explorers of the fifteenth century. He made two voyages along the west coast of Africa in the 1480s, exploring the Congo River and the coasts of present-day Angola and Namibia.
## Early life and family {#early_life_and_family}
Little is known about the early life of Diogo Cão. According to tradition, he was born in Vila Real, Portugal, around 1452. His grandfather, Gonçalo Cão, had fought for Portuguese independence at the Battle of Aljubarrota.
By 1480, Cão was sailing off the coast of Africa in the service of João II. There is a record that he returned to Portugal with captured Spanish ships.
## Exploration
When the Treaty of Alcáçovas (1480) confirmed Portugal\'s monopoly on trade and exploration along Africa\'s west coast, João II moved quickly to secure and expand his hold on the region. In 1481, a fleet of ten ships was dispatched to the Gold Coast to construct a fortress known as São Jorge da Mina. The fort would serve as a commercial center for trade (including in slaves) and an important point of resupply for Portuguese voyages. João II also re-instituted a program of exploration southward along the African coast, an initiative that had been held in abeyance during the war with Spain. Diogo Cão was selected to lead João\'s first voyage of exploration in 1482.
### First voyage {#first_voyage}
When João II restarted the work of Henry the Navigator, he sent out Cão, probably around midsummer 1482, to explore the African coast south of the equator. Diogo Cão filled his ship with stone pillars (*padrões*) surmounted by the cross of the Order of Christ and engraved with the Portuguese royal arms, planning to erect them at significant landmarks along his voyage of discovery. On the way, the expedition stopped at Sao Jorge da Mina to resupply.
In August 1482, Cão arrived at the Congo River mouth and marked it with a padrão erected on Shark Point, commemorating the Portuguese occupation. This padrão stood until 1642 when it was destroyed by the Dutch during their occupation of the Congo.
Cão sailed up the great river for a short distance and commenced modest commerce with the natives of the Bakongo kingdom. He was told that their king lived farther upriver, so he sent four Christian native messengers to search for the ruler and then proceeded south along the coast of present-day Angola where he erected a second *padrão*, probably marking the termination of this voyage, at Cabo de Santa Maria. When he returned to the Congo, Cão was annoyed to find that his messengers had not returned, so he abducted four local natives who were visiting his ship and returned with them to Portugal.
He reached Lisbon by 8 April 1484, where John II ennobled him, promoting him from esquire to a cavalier of his household, and granted him an annuity of eighteen thousand *reals* and a coat of arms on which two *padrões* are depicted.
The King also asked him to sail back to Kongo to repatriate the 4 men he left behind.
### Second voyage {#second_voyage}
That Cão, on his second voyage of 1484--1486, was accompanied by Martin Behaim (as alleged on the latter\'s Nuremberg globe of 1492) is very doubtful. But it is known that the explorer revisited the Congo and erected two more *padrões* on land beyond his previous voyage. The first was at Cabo Negro, Angola, the second at Cape Cross. The Cape Cross pillar probably marked the end of his progress southward, some 1,400 kilometers. Diogo Cão also embarked the four indigenous ambassadors, that he had promised not to keep for more than fifteen moons.
Cão sailed 170 kilometers up the Congo River to the Yellala Falls. On the cliffs above this site an inscription was engraved which records the passage of Cão and his men: \"Here arrived the ships of the illustrious monarch, Dom João the Second of Portugal -- Diogo Cão, Pedro Anes, Pedro da Costa, Alvaro Pires, Pero Escolar\".
### Death
Information regarding Cão\'s death is scanty and contradictory. A legend on the globe created by Martin Behaim reads \"*hic moritur*\" (here he dies), seeming to indicate that the explorer lost his life on the coast of Africa in 1486 during his second voyage. However, sixteenth-century historian João de Barros never mentions Cão\'s death but wrote instead of his return to the Congo, and subsequent taking of a native envoy back to Portugal.
A report by a board of astronomers and pilots presented at a 1525 conference in Badajo clearly stated that his death happened near Serra Parda. A coast map by Henricus Martellus Germanus published in 1489 indicated the location of a padrão erected by Diogo Cão in Ponta dos Farilhões nearby Serra Parda, with the legend \"et hic moritur\" (\"and here he died\").
## Padrões
The four pillars set up by Cão on his two voyages have all been discovered still on their original site, and the inscriptions on two of them from Cape Santa Maria and Cape Cross, dated 1482 and 1485 respectively, are still to be read and have been printed. The Cape Cross padrão was long in Berlin (replaced on the spot by a granite facsimile) but was recently returned to Namibia; those from the Kongo estuary and the more southerly Cape Santa Maria and Cabo Negro are in the Museum of the Lisbon Geographical Society.
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# Diogo Cão
## Tributes post-mortem {#tributes_post_mortem}
In 1951, botanists named a genus of plants from western central tropical Africa in his honour, *Diogoa*.
In Vila Real, the plaza Diogo Cão was named after him. In the center of the plaza, stands a bronze statue of him supported on a square granite pedestal base.
In 1999, André Roubertou from the French Hydrographic Office (SHOM) named an undersea hole located off the southern coast of Portugal (Gulf of Cádiz) the Diogo Cão Hole.
In 2018, a hopper dredger called the Diogo Cao and immatriculated in Luxembourg was launched afloat.
## In literature {#in_literature}
Diogo Cão is the subject of *Padrão*, one of the best-known poems in Fernando Pessoa\'s book *Mensagem*, the only one published during the author\'s lifetime. He also figures strongly in the 1996 novel *Lord of the Kongo* by Peter Forbath
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# Drinking game
\"Drinking Games\" (*Doctors*)\|Drinking Games (Slow Horses){{!}}\"Drinking Games\" (*Slow Horses*)}} **Drinking games** are games which involve the consumption of alcoholic beverages and often enduring the subsequent intoxication resulting from them. Evidence of the existence of drinking games dates back to antiquity. Drinking games have been banned at some institutions, particularly colleges and universities.
## History
### Ancient Greece {#ancient_greece}
Kottabos is one of the earliest known drinking games from ancient Greece, dated to the 5th to 4th centuries BC. Players would use dregs (remnants of what was left in their cup) to hit targets across the room with their wine. Often, there were special prizes and penalties for one\'s performance in the game.
### China
Drinking games were enjoyed in ancient China, usually incorporating the use of dice or verbal exchange of riddles. During the Tang dynasty (618--907), the Chinese used a silver canister where written lots could be drawn that designated which player had to drink and specifically how much; for example, from 1, 5, 7, or 10 measures of drink that the youngest player, or the last player to join the game, or the most talkative player, or the host, or the player with the greatest alcohol tolerance, etc. had to drink. There were even drinking game referee officials, including a \'registrar of the rules\' who knew all the rules to the game, a \'registrar of the horn\' who tossed a silver flag down on calling out second offenses, and a \'governor\' who decided one\'s third call of offense. These referees were used mainly for maintaining order (as drinking games often became rowdy) and for reviewing faults that could be punished with a player drinking a penalty cup. If a guest was considered a \'coward\' for dropping out of the game, he could be branded as a \'deserter\' and not invited back to further drinking bouts. There was another game where little puppets and dolls dressed as western foreigners with blue eyes (Iranian peoples) were set up and when one fell over, the person it pointed to had to empty his cup of wine.
Drinking games became popular among elites in the late Qing period as part of the privileged class\' urban leisure aesthetics. Novelists who invented literary-themed drinking games included Li Boyuan and Sun Yusheng. Drinking games also increasingly appeared as elements in novels of the period such as Yu Da\'s *The Dream in the Green Bower*.
### Germany
Drinking games in 19th century Germany included Bierskat, Elfern, Rammes and Quodlibet, as well as Schlauch and Laubober, probably the same game as Grasobern. But the \"crown of all drinking games\" was one with an ancient and distinctive name: Cerevis. One feature of the game was that everything went under a different name from normal. So the cards (*Karten*) were called \'spoons\' (*Löffel*), the Sevens were \'Septembers\' and the Aces were the \'Juveniles\' (*junge Leichtsinn*). A player who used the normal names was penalised. Every time a card was played, it was supposed to be accompanied by humorous words, so if a Jack or Unter was played, the player might say something like \"my merry *Unterkasser*\" (*Lustig mein Unterkasser*) or \"long live my *Unterkasser*\" (*Vivat mein Unterkasser*). If his opponent beat it, he might say \"hang the *Unterkasser*\" (*Hängt den Unterkasser*). The loser had to chalk up a figure such as a swallow, a wheel or a pair of scissors depending on the number of minus points gained and was only allowed to erase them once he had drunk the associated amount of beer.
Silver wager cups, also known as wedding cups, were used in Germany from the late 16th to mid 17th century. The smaller cup is on a pivot so both vessels can be face-up and filled with liquor. In wedding ceremonies, the man would drink from the larger vessel first, then turning the figure right side up, pass it to the woman, who would drink from the smaller cup; the challenge was for the two drinkers not to spill any liquor. They were also sometimes used during wine drinking boughts were a wager was placed if participant(s) could drink the contents of both sides without spilling a drop. In Germany they are known as *Jungfrauenbecher*, or maiden cups. Replicas of the cups were frequently manufactured during the 1880s to 1910s.
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# Drinking game
## Types
### Endurance
The simplest drinking games are endurance games in which players compete to out-drink one another. Players take turns taking shots, and the last person standing is the winner. Some games have rules involving the \"cascade\", \"fountain\", or \"waterfall\", which encourages each player to drink constantly from their cup so long as the player before him does not stop drinking. Such games can also favor speed over quantity, in which players race to drink a case of beer the fastest. Often drinking large amounts will be combined with a stylistic element or an abnormal method of drinking, as with the boot of beer, yard of ale, or a keg stand.
Tolerance games are simply about seeing which player can last the longest. It can be as simple as two people matching each other drink for drink until one of the participants \"passes out\". Power hour and its variant, centurion, fall under this category.
### Speed
Many pub or bar games involve competitive drinking for speed. Examples of such drinking games are Edward Fortyhands, boat races, beer bonging, shotgunning, flippy cup (a team-based speed game), and yard. Some say that the most important skill to improving speed is to relax and take fewer but larger gulps. There are a variety of individual tactics to accomplishing this, such as bending the knees in anticipation, or when drinking from a plastic cup, squeezing the sides of the cup to form a more perfect funnel.
Athletic races involving alcohol including the beer mile, which consists of a mile run with a can of beer consumed before each of the four laps. A variant is known in German speaking countries as *Bierkastenlauf* (beer crate running) where a team of two carries a crate of beer along a route of several kilometers and must consume all of the bottles prior to crossing the finish line.
### Skill
Some party and pub games focus on the performance of a particular act of skill, rather than on either the amount a participant drinks or the speed with which they do so. Examples include beer pong, quarters, chandeliers (also known as gauchoball, rage cage, stack cup), caps, polish horseshoes, pong, baseball, and beer darts.
Pub golf involves orienteering and pub crawling together.
A unique drinking game is made in the tavern Oepfelchammer in Zürich, Switzerland. It is called \"Balkenprobe\" and one has therefore to climb up a beam at the ceiling and move to another beam and then to drink a glass of wine with the head hanging down.
### Luck
Party games like the Korean *apateu* are mostly luck, as it has the players stack their hands, after which the leader shouts out a number, and whoever has their hand at that position in the stack will drink.
### Thinking
Thinking games rely on the players\' powers of observation, recollection, logic and articulation.
Numerous types of thinking games exist, including Think or Drink, 21, beer checkers, bizz buzz, buffalo, saved by the bell, bullshit, tourettes, matchboxes, never have I ever, roman numerals, fuzzy duck, pennying, wine games, and Zoom Schwartz Profigliano. Trivia games, such as Trivial Pursuit, are sometimes played as drinking games.
### Card and dice {#card_and_dice}
Drinking games involving cards include president, horserace, Kings, liar\'s poker, pyramid, ring of fire, toepen, ride the bus and black or red.
Dice games include beer die, dudo, kinito, liar\'s dice, Mexico, mia, ship, captain, and crew, three man, and Triple Snakes.
### Arts
Movie drinking games are played while watching a movie (sometimes a TV show or a sporting event) and have a set of rules for who drinks when and how much based on on-screen events and dialogue. The rules may be the same for all players, or alternatively players may each be assigned rules related to particular characters. The rules are designed so that rarer events require larger drinks. Rule sets for such games are usually arbitrary and local, although they are sometimes published by fan clubs.
In reference to film, a popular game among young adults consists of printing out a mustache and taping it on the television screen. Every time the mustache fits appropriately to a person on the screen, one must drink the designated amount.
Live drinking games such as Los Angeles--based \"A Drinking Game\" involve recreating films of the 80s in a \"Rocky Horror\" fashion, with gift bags, drinking cues, and costumed actors. A suggestion to \"do six shots for SEAL Team 6\" following every mention of Osama bin Laden at the 2012 Democratic National Convention necessitated a prominent disclaimer on the satire site that posted it, as the quantity of alcohol ingested would probably have been lethal.
\"Datsyuk Game\" involves a Datsyuk highlight reel being played and contestants drink every time the word *Datsyuk* is mentioned. The ceremonial playing of the Russian national anthem before the game is another tradition.
Music can also be used as a basis for drinking games. The song \"Thunderstruck\" by AC/DC is used in which a player begins drinking when the word thunder is sung and switches to the next player the next time it is sung.
Sport related drinking games involve the participants each selecting a scenario of the game resulting in their drink being downed. Examples of this include participants each picking a footballer in a game while other versions require multiple players to be selected. Should a player score or be sent off, a drink must be taken. Another version requires a drink for every touch a player takes of the ball.
### Hybrid games {#hybrid_games}
Some drinking games can fall into multiple categories such as a Power hour which is a primarily an endurance-based game, but can also incorporate the arts if players are prompted to drink by a playlist that changes songs every 60 seconds. Similarly, Flip cup combines the skill of flipping cups with the speed of drinking quickly prior to flipping.
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# Drinking game
## Types
### Russian roulette {#russian_roulette}
There is a drinking game based on Russian roulette. The game involves six shot glasses filled by a non-player: five are filled with water, but the sixth with vodka. Among some groups, low quality vodka is preferred, as it makes the glass representing the filled chamber less desirable. The glasses are arranged in a circle, and players take turns choosing a glass to take a shot from at random.
There is also a game called \"Beer Hunter\" (titled after the Russian roulette scenes in the film *The Deer Hunter*). In this game, six cans of beer are placed between the participants: one can is vigorously shaken, and the cans are scrambled. The participants take turns opening the cans of beer right under their noses; the person who opens the shaken can (and thus sprays beer up their nose) is deemed the loser.
Both are non-lethal compared to the game with the firearm which is almost always lethal.
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# Drinking game
## Health concerns {#health_concerns}
Drinking games are popular social activities, particularly among young adults and college students, but they come with significant health risks. These games often encourage rapid alcohol consumption, often leading to heavy drinking, which can result in severe consequences such as alcohol poisoning:
- Beer pong. Some writers have mentioned beer pong as contributing to \"out of control\" college drinking.
- Power hour. Players may have difficulty completing the specified number of drinks as the rate of consumption can raise their blood alcohol content to high levels.
- Keg stand is another drinking game known for its extreme consumption style.
- Neknominate. The original rules of the game require the participants to film themselves drinking a pint of an alcoholic beverage. Five people are believed to have died as a result of playing the game, including a Cardiff man thought to have downed a pint of vodka, and a London hostel worker who reportedly mixed an entire bottle of white wine with a quarter bottle of whisky, a small bottle of vodka and a can of lager. In the latter case, the victim\'s nominator was interviewed by police, but it was ruled an accidental death without coercion
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# Demographic statistics
**Demographic statistics** are measures of the characteristics of, or changes to, a population. Records of births, deaths, marriages, immigration and emigration and a regular census of population provide information that is key to making sound decisions about national policy.
A useful summary of such data is the population pyramid. It provides data about the sex and age distribution of the population in an accessible graphical format.
Another summary is called the life table. For a *cohort* of persons born in the same year, it traces and projects their life experiences from birth to death. For a given cohort, the proportion expected to survive each year (or decade in an *abridged life table*) is presented in tabular or graphical form.
The ratio of males to females by age indicates the consequences of differing mortality rates on the sexes. Thus, while values above one are common for newborns, the ratio dwindles until it is well below one for the older population.
## Collection
National population statistics are usually collected by conducting a census. However, because these are usually huge logistical exercises, countries normally conduct censuses only once every five to 10 years. Even when a census is conducted it may miss counting everyone (known as undercount). Also, some people counted in the census may be recorded in a different place than where they usually live, because they are travelling, for example (this may result in overcounting). Consequently, raw census numbers are often adjusted to produce *census estimates* that identify such statistics as *resident population*, *residents, tourists and other visitors*, *nationals and aliens (non-nationals)*. For privacy reasons, particularly when there are small counts, some census results may be rounded, often to the nearest ten, hundred, thousand and sometimes randomly up, down or to another small number such as within 3 of the actual count.
Between censuses, administrative data collected by various agencies about population events such as births, deaths, and cross-border migration may be used to produce intercensal estimates.
## Population estimates and projections {#population_estimates_and_projections}
**Population estimates** are usually derived from census and other administrative data. Population estimates are normally produced after the date the estimate is for.
Some estimates, such as the *Usually resident population* estimate who usually lives in a locality as at the census date, even though the census did not count them within that locality. Census questions usually include a questions about where a person usually lives, whether they are a resident or visitor, or also live somewhere else, to allow these estimates to be made.
Other estimates are concerned with estimating population on a particular date that is different from the census date, for example the middle or end of a calendar or financial year. These estimates often use birth and death records and migration data to adjust census counts for the changes that have happened since the census.
**Population projections** are produced in advance of the date they are for. They use time series analysis of existing census data and other sources of population information to forecast the size of future populations. Because there are unknown factors that may affect future population changes, population projections often incorporate high and low as well as expected values for future populations. Population projections are often recomputed after a census has been conducted. It depends on how the area is adjusted in a particular demarcation.
## History
While many censuses were conducted in antiquity, there are few population statistics that survive. One example though can be found in the Bible, in chapter 1 of the Book of Numbers. Not only are the statistics given, but the method used to compile those statistics is also described. In modern-day terms, this metadata about the census is probably of as much value as the statistics themselves as it allows researchers to determine not only what was being counted but how and why it was done.
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# Demographic statistics
## Metadata
Modern population statistics are normally accompanied by **metadata** that explains how the statistics have been compiled and adjusted to compensate for any collection issues
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# Democritus
**Democritus** (`{{IPAc-en|d|ɪ|ˈ|m|ɒ|k|r|ɪ|t|ə|s}}`{=mediawiki}, `{{respell|dim|OCK|rit|əs}}`{=mediawiki}; *Δημόκριτος*, *Dēmókritos*, meaning \"chosen of the people\"; c. 460 -- c. 370 BC) was an Ancient Greek pre-Socratic philosopher from Abdera, primarily remembered today for his formulation of an atomic theory of the universe. Democritus wrote extensively on a wide variety of topics.
None of Democritus\' original work has survived, except through second-hand references. Many of these references come from Aristotle, who viewed him as an important rival in the field of natural philosophy. He was known in antiquity as the 'laughing philosopher' because of his emphasis on the value of cheerfulness.
## Life
Although many anecdotes about Democritus\' life survive, their authenticity cannot be verified and modern scholars doubt their accuracy.
According to Aristotle, Democritus was born in Abdera, on the coast of Thrace. He was a polymath and prolific writer, producing nearly eighty treatises on subjects such as poetry, harmony, military tactics, and Babylonian theology. Some called him a Milesian, and the name of his father too is stated differently. His birth year was fixed by Apollodorus in the first year of the 80th Olympiad, or B. C. 460, while Thrasyllus had referred it to as the 3rd year of the 77th Olympiad. Democritus had called himself forty years younger than Anaxagoras. His father, Hegesistratus,\--or as others called him Damasippus or Athenocritus,\--was possessed of so large a property, that he was able to receive and treat Xerxes on his march through Abdera.
Democritus spent the inheritance, which his father left him, on travels into distant countries, which he undertook to satisfy his extraordinary thirst for knowledge. He travelled over a great part of Asia, and, as some state, he even reached India and Aethiopia. We know that he wrote on Babylon and Meroe; he must also have visited Egypt, and Diodorus Siculus even states, that he lived there for a period of five years. He himself declared, that among his contemporaries none had made greater journeys, seen more countries, and made the acquaintance of more men distinguished in every kind of science than himself. Among the last he mentions in particular the Egyptian mathematicians (ἀρπεδόναπ-ται ; comp. Sturz, de Dialect. Maced. p. 98), whose knowledge he praises, without, however, regarding himself inferior to them. Theophrastus, too, spoke of him as a man who had seen many countries. It was his desire to acquire an extensive knowledge of nature that led him into distant countries at a time when travelling was the principal means of acquiring an intellectual and scientific culture; and after returning to his native land he occupied himself only with philosophical investigations, especially such as related to natural history.
In Greece itself, too, he endeavored by means of traveling and residing in the principal cities to acquire a knowledge of Hellenic culture and civilization. He mentioned many Greek philosophers in his writings, and his wealth enabled him to purchase the works they had written. He thus succeeded in excelling, in the extent of his knowledge, all the earlier Greek philosophers, among whom Leucippus, the founder of the atomistic theory, is said to have exercised the greatest influence upon his philosophical studies. The opinion that he was a disciple of Anaxagoras or of the Pythagoreans, perhaps arose merely from the fact, that he mentioned them in his writings. The account of his hostility towards Anaxagoras, is contradicted by several passages in which he speaks of him in terms of high praise. It is further said, that he was on terms of friendship with Hippocrates, and some writers even speak of a correspondence between Democritus and Hippocrates; but this statement does not seem to be deserving of credit. As he was a contemporary of Plato, it may be that he was acquainted with Socrates, perhaps even with Plato, who, however, does not mention Democritus anywhere. Aristotle describes him and his views as belonging to the pre-Socratic period; but some scholars, such as Groen van Prinsterer, assert that there are symptoms in Plato which show a connection with Democritus, in Plato\'s language and style an imitation of Democritus.
The many anecdotes about Democritus which are preserved, especially in Diogenes Laertius, show that he was a man of a most sterling and honourable character. His diligence was incredible: he lived exclusively for his studies, and his disinterestedness, modesty, and simplicity are attested by many features which are related of him. Notwithstanding his great property, he seems to have died in poverty, though highly esteemed by his fellow-citizens, not so much on account of his philosophy, as \"because,\" as Diogenes says, \" he had foretold them some things which the event proved to be true.\" This had probably reference to his knowledge of natural phaenomena. His fellow-citizens honoured him with presents in money and bronze statues. Even the scoffer Timon, who in his *Silloi* spared no one, speaks of Democritus only in terms of praise. We cannot leave unnoticed the tradition that Democritus deprived himself of his sight, in order to be less disturbed in his pursuits. But this tradition is one of the inventions of a later age, which was fond of piquant anecdotes. It is more probable that he may have lost his sight by too severe application to study. This loss, however, did not disturb the cheerful disposition of his mind and his views of human life, which prompted him everywhere to look at the cheerful and comical side of things, which later writers took to mean, that he always laughed at the follies of men.
Ancient accounts of his life have claimed that he lived to a very old age, with some writers claiming that he was over a hundred years old at the time of his death, (some say that he was 109 years old), and even the manner in which he died is characteristic of his medical knowledge, which, combined as it was with his knowledge of nature, caused a report, which was believed by some persons, that he was a sorcerer and a magician. His death is placed in the 4th year of the 105th Olympiad, or 357 BC, in which year Hippocrates also is said to have died.
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# Democritus
## Philosophy
Democritus wrote on ethics as well as physics. Democritus was a student of Leucippus. Early sources such as Aristotle and Theophrastus credit Leucippus with creating atomism and sharing its ideas with Democritus, but later sources credit only Democritus, making it hard to distinguish their individual contributions.
### Atomism
It was Democritus who, in his numerous writings, carried out Leucippus\'s theory of atoms, and especially in his observations on nature. These atomists undertook the task of proving that the quantitative relations of matter were its original characteristics, and that its qualitative relations were something secondary and derivative, and of thus doing away with the distinction between matter and mind or power. In order to avoid the difficulties connected with the supposition of primitive matter with definite qualities, without admitting the coming into existence and annihilation as realities, and without giving up, as the Eleatic philosophers did, the reality of variety and its changes, the atomists derived all definiteness of phaenomena, both physical and mental, from elementary particles, the infinite number of which were homogeneous in quality, but heterogeneous in form. This made it necessary for them to establish the reality of a vacuum or space, and of motion. ) Motion, they said, is the eternal and necessary consequence of the original variety of atoms in the vacuum or space. All phaenomena arise from the infinite variety of the form, order, and position of the atoms in forming combinations. It is impossible, they add, to derive this supposition from any higher principle, for a beginning of the infinite is inconceivable. The atoms are impenetrable, and therefore offer resistance to one another. This creates a swinging, world-producing, and whirling motion. (This reminds us of the joke in the Clouds of Aristophanes about the god Δῖνος !) Now as similars attract one another, there arise in that motion real things and beings, that is, combinations of distinct atoms, which still continue to be separated from one another by the vacuum. The first cause of all existence is necessity, that is, the necessary predestination and necessary succession of cause and effect. This they called chance, in opposition to the νοῦς of Anaxagoras. But it does the highest honour to the mind of Democritus, that he made the discovery of causes the highest object of scientific investigations. He once said, that he preferred the discovery of a true cause to the possession of the kingdom of Persia. We must not, therefore, take the word chance (τυχή) in its vulgar acceptation. Aristotle understood Democritus rightly in this respect, as he generally valued him highly, and often says of him, that he had thought on all subjects, searched after the first causes of phenomena, and endeavored to find definitions. The only thing for which he censures him, is a disregard for teleological relations, and the want of a comprehensive system of induction. Democritus himself called the common notion of chance a cover of human ignorance (πρόφα-σιν ἰδίης ἀνοίης), and an invention of those who were too idle to think.
Democritus held that originally the universe was composed of nothing but tiny atoms churning in chaos, until they collided together to form larger units---including the earth and everything on it. He surmised that there are many worlds, some growing, some decaying; some with no sun or moon, some with several. He held that every world has a beginning and an end and that a world could be destroyed by collision with another world.He concluded that divisibility of matter comes to an end, and the smallest possible fragments must be bodies with sizes and shapes, although the exact argument for this conclusion of his is not known. The smallest and indivisible bodies he called \"atoms\".
Atoms, Democritus believed, are too small to be detected by the senses; they are infinite in numbers and come in infinitely many varieties, and they have existed forever and that these atoms are in constant motion in the void or vacuum. The middle-sized objects of everyday life are complexes of atoms that are brought together by random collisions, differing in kind based on the variations among their constituent atoms. For Democritus, the only true realities are atoms and the void. What we perceive as water, fire, plants, or humans are merely combinations of atoms in the void. The sensory qualities we experience are not real; they exist only by convention. Of the mass of atoms, Democritus said, \"The more any indivisible exceeds, the heavier it is.\" However, his exact position on atomic weight is disputed.
The atomistic void hypothesis was a response to the paradoxes of Parmenides and Zeno, the founders of metaphysical logic, who put forth difficult-to-answer arguments in favor of the idea that there can be no movement. They held that any movement would require a void---which is nothing---but a nothing cannot exist. The Parmenidean position was \"You say there *is* a void; therefore the void is not nothing; therefore there is not the void.\" The position of Parmenides appeared validated by the observation that where there seems to be nothing there is air, and indeed even where there is not matter there is *something*, for instance light waves. The atomists agreed that motion required a void, but simply rejected the argument of Parmenides on the grounds that motion was an observable fact. Therefore, they asserted, there must be a void.
His exact contributions are difficult to disentangle from those of his mentor Leucippus, as they are often mentioned together in texts. Their speculation on atoms, taken from Leucippus, bears a passing and partial resemblance to the 19th-century understanding of atomic structure that has led some to regard Democritus as more of a scientist than other Greek philosophers; however, their ideas rested on very different bases. Democritus, along with Leucippus and Epicurus, proposed the earliest views on the shapes and connectivity of atoms. They reasoned that the solidness of the material corresponded to the shape of the atoms involved. Using analogies from humans\' sense experiences, he gave a picture or an image of an atom that distinguished them from each other by their shape, their size, and the arrangement of their parts. Moreover, connections were explained by material links in which single atoms were supplied with attachments: some with hooks and eyes, others with balls and sockets.
Besides the infinite number of atoms existing in infinite space, Democritus also supposed the existence of an infinite number of worlds, some of which resembled one another, while others differed from one another, and each of these worlds was kept together as one thing by a sort of shell or skin. He derived the four elements from the form of the atoms predominating in each, from their quality, and their relations of magnitude. In deriving individual things from atoms, he mainly considered the qualities of warm and cold. The warm or firelike he took to be a combination of fine, spheric, and very movable atoms, as opposed to the cold and moist. His mode of proceeding, however, was, first carefully to observe and describe the phaenomena themselves, and then to attempt his atomistic explanation, whereby he essentially advanced the knowledge of nature. He derived the soul, the origin of life, consciousness, and thought, from the finest fire-atoms; and in connexion with this theory he made very profound physiological investigations. It was for this reason that, according to him, the soul while in the body acquires perceptions and knowledge by corporeal contact, and that it is affected by heat and cold. The sensuous perceptions themselves were to him affections of the organ or of the subject perceiving, dependent on the changes of bodily condition, on the difference of the organs and their quality, on air and light. Hence the differences, e. g., of taste, color, and temperature, are only conventional, the real cause of those differences being in the atoms.
### Epistemology
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# Democritus
## Philosophy
### Epistemology
It was very natural, given his theory or perception, that Democritus described even the knowledge obtained by sensuous perception as obscure (σκοτίην κρίσιν). A clear and pure knowledge is only that which has reference to the true principles or the true nature of things, that is, to the atoms and space. But knowledge derived from reason was, in his opinion, not specifically different from that acquired through the senses; for conception and reflection were to him only effects of impressions made upon the senses; and Aristotle, therefore, expressly states, that Democritus did not consider mind as something peculiar, or as a power distinct from the soul or sensuous perception, but that he considered knowledge derived from reason to be sensuous perceptions. A purer and higher knowledge which he opposed to the obscure knowledge obtained through the medium of the senses, must therefore have been to him a kind of sensation, that is, a direct perception of the atoms and of space. For this reason he assumed the three criteria (κριτήρια) : a. Phaenomena as criteria for discovering that which is hidden : b. Thought as a criterion of investigation : and c. Assertions as criteria of desires. Now as Democritus acknowledged the uncertainty of perceptions, and as he was unable to establish a higher and purely spiritual source of knowledge as distinct from perceptions, we often find him complaining that all human knowledge is uncertain, that in general either nothing is absolutely true, or at least not clear to us, that our senses grope about in the dark, and that all our views and opinions are subjective, and come to us only like something epidemic, as it were, with the air which we breathe.
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# Democritus
## Philosophy
### Mathematics
Democritus was also a pioneer of mathematics and geometry in particular. In *The Method of Mechanical Theorems*, Archimedes states that Eudoxus of Cnidus, whose rigorous proof using the method of exhaustion that the volume of a cone is one-third the volume of cylinder is preserved in Euclid\'s *Elements*, was aided by the fact that Democritus had already asserted it to be true on the argument that this is true for the same reason that the pyramid has one-third the rectangular prism of the same base. Plutarch also reports that Democritus argued that the circular cross-section of a cone would need step-like sides, rather than being shaped like a cylinder, which Thomas Heath suggests may be an early version of infinitesimal calculus.
### Anthropology
Democritus thought that the first humans lived an anarchic and animal sort of life, foraging individually and living off the most palatable herbs and the fruit which grew wild on the trees, until fear of wild animals drove them together into societies. He believed that these early people had no language, but that they gradually began to articulate their expressions, establishing symbols for every sort of object, and in this manner came to understand each other. He says that the earliest men lived laboriously, having none of the utilities of life; clothing, houses, fire, domestication, and farming were unknown to them. Democritus presents the early period of mankind as one of learning by trial and error, and says that each step slowly led to more discoveries; they took refuge in the caves in winter, stored fruits that could be preserved, and through reason and keenness of mind came to build upon each new idea.
### Ethics
In his ethical philosophy Democritus considered the acquisition of peace of mind (εὐθυμία) as the end and ultimate object of our actions. This peace, this tranquillity of the mind, and freedom from fear (φόβος and δεισδαιμονία) and passion, is the last and fairest fruit of philosophical inquiry. Many of his ethical writings referenced this idea and its establishment, and the fragments relating to this question are full of the most genuine practical wisdom. Abstinence from too many occupations, a steady consideration of one\'s own powers, which prevents our attempting that which we cannot accomplish, moderation in prosperity and misfortune, were to him the principal means of acquiring the εὐθυμία. The noblest and purest ethical tendency, lastly, is manifest in his views on virtue and on good. Truly pious and beloved by the gods, he says, are only those who hate that which is wrong (ὅσοις ἐχθρὸν τὸ αδικεῖν). The purest joy and the truest happiness are only the fruit of the higher mental activity exerted in the endeavour to understand the nature of things, of the peace of mind arising from good actions, and of a clear conscience.
Democritus was eloquent on ethical topics. Some sixty pages of his fragments, as recorded in Diels--Kranz, are devoted to moral counsel. The ethics and politics of Democritus come to us mostly in the form of maxims. In placing the quest for happiness at the center of moral philosophy, he was followed by almost every moralist of antiquity. The most common maxims associated with him are \"Accept favours only if you plan to do greater favours in return\", and he is also believed to impart some controversial advice such as \"It is better not to have any children, for to bring them up well takes great trouble and care, and seeing them grow up badly is the cruellest of all pains\". He also wrote a treatise on the purpose of life and the nature of happiness. He held that \"happiness was not to be found in riches but in the goods of the soul and one should not take pleasure in mortal things\". Another saying that is often attributed to him is \"The hopes of the educated were better than the riches of the ignorant\". He also stated that \"the cause of sin is ignorance of what is better\", which become a central notion later in the Socratic moral thought. Another idea he propounded which was later echoed in the Socratic moral thought was the maxim that \"you are better off being wronged than doing wrong\". His other moral notions went contrary to the then prevalent views such as his idea that \"A good person not only refrains from wrongdoing but does not even want to do wrong\", for the generally held notion back then was that virtue reaches it apex when it triumphs over conflicting human passions.
### Aesthetics
Later Greek historians consider Democritus to have established aesthetics as a subject of investigation and study, as he wrote theoretically on poetry and fine art long before authors such as Aristotle. Specifically, Thrasyllus identified six works in the philosopher\'s oeuvre which had belonged to aesthetics as a discipline, but only fragments of the relevant works are extant; hence of all Democritus writings on these matters, only a small percentage of his thoughts and ideas can be known.
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# Democritus
## Works
Of the extent of his knowledge, which embraced not only natural sciences, mathematics, mechanics (Brandis, in the Rhein. Mus. iii. p. 134, &c.), grammar, music, and philosophy, but various other useful arts, we may form some notion from the list of his numerous works which is given by Diogenes Laertius (9.46-49), and which, as Diogenes expressly states, contains only his genuine works. The grammarian Thrasyllus, a contemporary of the emperor Tiberius, arranged them, like the works of Plato, into tetralogies. Unfortunately, not one of his works has come down to us, and the treatise which we possess under his name is considered spurious. Callimachus wrote glosses upon his works and made a list of them; but they must have been lost at an early time, since even Simplicius, writing in the 6th century AD, does not appear to have read them, and since comparatively few fragments have come down to us, and these fragments refer more to ethics than to physical matters.
Diogenes Laertius attributes several works to Democritus, but none of them have survived in a complete form.
Ethics: *Pythagoras*, *On the Disposition of the Wise Man*, *On the Things in Hades*, *Tritogenia*, *On Manliness or On Virtue*, *The Horn of Amaltheia*, *On Contentment*, *Ethical Commentaries*\
Natural science: *The Great World-System*, *Cosmography*, *On the Planets*, *On Nature*, *On the Nature of Man or On Flesh* (two books), *On the Mind*, *On the Senses*, *On Flavours*, *On Colours*, *On Different Shapes*, *On Changing Shape*, *Buttresses*, *On Images*, *On Logic* (three books)\
Nature: *Heavenly Causes*, *Atmospheric Causes*, *Terrestrial Causes*, *Causes Concerned with Fire and Things in Fire*, *Causes Concerned with Sounds*, *Causes Concerned with Seeds and Plants and Fruits*, *Causes Concerned with Animals* (three books), *Miscellaneous Causes*, *On Magnets*\
Mathematics: *On Different Angles or On contact of Circles and Spheres*, *On Geometry*, *Geometry*, *Numbers*, *On Irrational Lines and Solids* (two books), *Planispheres*, *On the Great Year or Astronomy* (a calendar) *Contest of the Waterclock*, *Description of the Heavens*, *Geography*, *Description of the Poles*, *Description of Rays of Light*,\
Literature: *On the Rhythms and Harmony*, *On Poetry*, *On the Beauty of Verses*, *On Euphonious and Harsh-sounding Letters*, *On Homer*, *On Song*, *On Verbs*, *Names*\
Technical works: *Prognosis*, *On Diet*, *Medical Judgment*, *Causes Concerning Appropriate and Inappropriate Occasions*, *On Farming*, *On Painting*, *Tactics*, *Fighting in Armor*\
Commentaries: *On the Sacred Writings of Babylon*, *On Those in Meroe*, *Circumnavigation of the Ocean*, *On History*, *Chaldaean Account*, *Phrygian Account*, *On Fever and Coughing Sicknesses*, *Legal Causes*, *Problems*
A collections of sayings credited to Democritus have been preserved by Stobaeus, as well as a collection of sayings ascribed to Democrates which some scholars including Diels and Kranz have also ascribed to Democritus.
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# Democritus
## Legacy
### Classical antiquity {#classical_antiquity}
Diogenes Laertius claims that Plato disliked Democritus so much that he wished to have all of his books burned. He was nevertheless well known to his fellow northern-born philosopher Aristotle, and was the teacher of Protagoras. The importance which was attached to the researches of Democritus is evident from the fact, that Aristotle is reported to have written a work in two books on the problems of Democritus. His works were composed in the Ionic dialect, though not without some admixture of the local peculiarities of Abdera. They are nevertheless much praised by Cicero on account of the poetical beauties and the liveliness of their style, and are in this respect compared even with the works of Plato. Pyrrho is said to have imitated his style, and even Timon praises it, and calls it περίφρονα καὶ ἀμφίνοον λέσχην.
### Renaissance and early Modern Period {#renaissance_and_early_modern_period}
Democritus is evoked by English writer Samuel Johnson in his poem, *The Vanity of Human Wishes* (1749), ll. 49--68, and summoned to \"arise on earth, /With chearful wisdom and instructive mirth, /See motley life in modern trappings dress\'d, /And feed with varied fools th\'eternal jest.\"
### Modern atomism {#modern_atomism}
The theory of the atomists appears to be more nearly aligned with that of modern science than any other theory of antiquity. However, the similarity with modern concepts of science can be confusing when trying to understand where the hypothesis came from. Classical atomists could not have had an empirical basis for modern concepts of atoms and molecules. The Democritean atom is an inert solid that excludes other bodies from its volume and interacts with other atoms mechanically. Quantum-mechanical atoms are similar in that their motion can be described by mechanics in addition to their electric, magnetic and quantum interactions. They are different in that they can be split into protons, neutrons, and electrons. The elementary particles are similar to Democritean atoms in that they are indivisible but their collisions are governed purely by quantum physics. Fermions observe the Pauli exclusion principle, which is similar to the Democritean principle that atoms exclude other bodies from their volume. However, bosons do not, with the prime example being the elementary particle photon
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# Dennis Ritchie
**Dennis MacAlistair Ritchie** (September 9, 1941 -- c. October 12, 2011) was an American computer scientist. He created the C programming language and the Unix operating system and B language with long-time colleague Ken Thompson. Ritchie and Thompson were awarded the Turing Award from the Association for Computing Machinery (ACM) in 1983, the IEEE Richard W. Hamming Medal from the Institute of Electrical and Electronics Engineers (IEEE) in 1990, and the National Medal of Technology from President Bill Clinton in 1999.
Ritchie was the head of Lucent Technologies System Software Research Department when he retired in 2007.
## Early life and education {#early_life_and_education}
Dennis Ritchie was born in Bronxville, New York. His father was Alistair E. Ritchie, a longtime Bell Labs scientist and co-author of *The Design of Switching Circuits* on switching circuit theory. As a child, Dennis moved with his family to Summit, New Jersey, where he graduated from Summit High School. He graduated from Harvard University with degrees in physics and applied mathematics in 1963.
## Career
In 1967, Ritchie began working at the Bell Labs Computing Science Research Center. In 1968, he completed a draft of his PhD thesis on \"Computational Complexity and Program Structure\" at Harvard under the supervision of Patrick C. Fischer. However, Ritchie never officially received his PhD degree. In 2020, the Computer History Museum worked with Ritchie\'s family and Fischer\'s family and found a copy of the lost dissertation.
During the 1960s, Ritchie and Ken Thompson worked on the Multics operating system at Bell Labs. Thompson then found an old PDP-7 machine and developed his own application programs and operating system from scratch, aided by Ritchie and others. In 1970, Brian Kernighan suggested the name \"Unix\", a pun on the name \"Multics\". To supplement assembly language with a system-level programming language, Thompson created B. Later, B was replaced by C, created by Ritchie, who continued to contribute to the development of Unix and C for many years.
During the 1970s, Ritchie collaborated with James Reeds and Robert Morris on a ciphertext-only attack on the M-209 US cipher machine that could solve messages of at least 2000--2500 letters. Ritchie relates that, after discussions with the National Security Agency, the authors decided not to publish it, as they were told that the principle applied to machines still in use by foreign governments.
Ritchie was also involved with the development of the operating systems Plan 9 and Inferno, and the programming language Limbo.
As part of an AT&T restructuring in the mid-1990s, Ritchie was transferred to Lucent Technologies, where he retired in 2007 as head of System Software Research Department.
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# Dennis Ritchie
## C and Unix {#c_and_unix}
Ritchie created the C programming language and was one of the developers of the Unix operating system. With Brian Kernighan, he co-wrote the book *The C Programming Language*, which is often referred to as *K&R* after their initials. Ritchie worked together with Ken Thompson, who is credited with writing the original version of Unix; one of Ritchie\'s contributions to Unix was its porting to different machines and platforms. They were so influential on Research Unix that Doug McIlroy later wrote, \"The names of Ritchie and Thompson may safely be assumed to be attached to almost everything not otherwise attributed.\"
Nowadays, the C language is widely used in application, operating system, and embedded system development, and its influence is seen in most modern programming languages. C is a low-level language with constructs closely translating to the hardware\'s instruction set. However, it is not tied to any given hardware, making it easy to write programs on any machine that supports C. Moreover, C is a high-level programming language with constructs mapping to data structures in application software.
C influenced several other languages and derivatives, such as C++, Objective-C used by Apple, C# used by Microsoft, and Java used in corporate environments extensively and by Android. Ritchie and Thompson used C to write Unix, which has been influential in establishing many computing concepts and principles that are adopted widely.
In an interview from 1999, Ritchie clarified that he saw Linux and Berkeley Software Distribution (BSD) operating systems as a continuation of the basis of the Unix operating system, and as derivatives of Unix:
In the same interview, he stated that he viewed Unix and Linux as \"the continuation of ideas that were started by Ken and me and many others, many years ago.\"
## Awards
In 1983, Ritchie and Thompson received the Turing Award \"for their development of generic operating systems theory and specifically for the implementation of the UNIX operating system\". Ritchie\'s Turing Award lecture was titled \"Reflections on Software Research\". In 1990, both Ritchie and Thompson received the IEEE Richard W. Hamming Medal from the Institute of Electrical and Electronics Engineers (IEEE), \"for the origination of the UNIX operating system and the C programming language\".
In 1997, both Ritchie and Thompson were made Fellows of the Computer History Museum, \"for co-creation of the UNIX operating system, and for development of the C programming language.\"
On April 21, 1999, Thompson and Ritchie jointly received the National Medal of Technology of 1998 from President Bill Clinton for co-inventing the UNIX operating system and the C programming language which, according to the citation for the medal, \"led to enormous advances in computer hardware, software, and networking systems and stimulated growth of an entire industry, thereby enhancing American leadership in the Information Age\".
In 2005, the Industrial Research Institute awarded Ritchie its Achievement Award in recognition of his contribution to science and technology, and to society generally, with his development of the Unix operating system.
In 2011, Ritchie, along with Thompson, was awarded the Japan Prize for Information and Communications for his work in the development of the Unix operating system.
## Death
Ritchie was found dead on October 12, 2011, at the age of 70 at his home in Berkeley Heights, New Jersey, where he lived alone. First news of his death came from his former colleague, Rob Pike. He had been in frail health for several years following treatment for prostate cancer and heart disease. News of Ritchie\'s death was largely overshadowed by the media coverage of the death of Apple co-founder Steve Jobs, which occurred the week before.
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# Dennis Ritchie
## Legacy
Following Ritchie\'s death, computer historian Paul E. Ceruzzi stated:
In an interview shortly after Ritchie\'s death, long-time colleague Brian Kernighan said Ritchie never expected C to be so significant. Kernighan told *The New York Times* \"The tools that Dennis built---and their direct descendants---run pretty much everything today.\" Kernighan reminded readers of how important a role C and Unix had played in the development of later high-profile projects, such as the iPhone. Other testimonials to his influence followed.
Reflecting upon his death, a commentator compared the relative importance of Steve Jobs and Ritchie, concluding that \"\[Ritchie\'s\] work played a key role in spawning the technological revolution of the last forty years---including technology on which Apple went on to build its fortune.\" Another commentator said, \"Ritchie, on the other hand, invented and co-invented two key software technologies which make up the DNA of effectively every single computer software product we use directly or even indirectly in the modern age. It sounds like a wild claim, but it really is true.\" Another said, \"many in computer science and related fields knew of Ritchie\'s importance to the growth and development of, well, everything to do with computing,\...\"
The Fedora 16 Linux distribution, which was released about a month after he died, was dedicated to his memory. FreeBSD 9.0, released January 12, 2012, was also dedicated in his memory.
Asteroid 294727 Dennisritchie, discovered by astronomers Tom Glinos and David H. Levy in 2008, was named in his memory. The official `{{MoMP|294727|naming citation}}`{=mediawiki} was published by the Minor Planet Center on 7 February 2012 (Minor Planet Circulars (M.P.C.) 78272).
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# Dennis Ritchie
## Notable works {#notable_works}
- B language
- C language on which many succeeding languages and technologies are based.
- Unix multiuser operating system. Several workalikes (commonly referred to as Unix-like systems) have been developed based on Unix\'s design. Some follow POSIX standards, again based on Unix.
- *Unix Programmer\'s Manual* (1971)
- *The C Programming Language* (sometimes referred to as *K&R*; 1978 with Brian Kernighan)
## Publications and academic papers {#publications_and_academic_papers}
Ritchie has been the author or contributor to about 50 academic papers, books and textbooks and which have had over 15,000 citations
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# Dumpster diving
**Dumpster diving** (also **totting**, **skipping**, **skip diving** or **skip salvage**) is salvaging from large commercial, residential, industrial and construction containers for unwanted items discarded by their owners but deemed useful to the picker. It is not confined to dumpsters and skips, and may cover standard household waste containers, curb sides, landfills or small dumps.
Different terms are used to refer to different forms of this activity. For picking materials from the curbside trash collection, expressions such as **curb shopping**, **trash picking** or **street scavenging** are sometimes used. In the UK, if someone is primarily seeking recyclable metal, they are **scrapping**, and if they are picking the leftover food from farming left in the fields, they are **gleaning**.
People dumpster dive for items such as clothing, furniture, food, and similar items in good working condition. Some people do this out of necessity due to poverty; others do it for ideological reasons or professionally and systematically for profit.
## Etymology
The term \"dumpster diving\" emerged in the 1980s, combining \"diving\" with \"dumpster\", a large commercial trash bin. The term \"Dumpster\" itself comes from the Dempster Dumpster, a brand of bins manufactured by Dempster Brothers beginning in 1937. \"Dumpster\" became genericized by the 1970s. According to the *Oxford English Dictionary*, the term \"dumpster diving\" is chiefly found in American English and first appeared in print in 1983, with the verb \"dumpster-dive\" appearing a few years later. In British English, the practice may be known as \"skipping\", from skip, another term for this type of container.
Alternative names for the practice include bin-diving, containering, D-mart, dumpstering, totting, and skipping. In Australia, garbage picking is called \"skip dipping.\"
## Participants
The term \"binner\" is often used to describe individuals who collect recyclable materials for their deposit value. For example, in Vancouver, British Columbia, binners, or bottle collectors, search garbage cans and dumpsters for recyclable materials that can be redeemed for their deposit value. On average, these binners earn about \$40 a day for several garbage bags full of discarded containers. Some are scammers seeking for receipts to use in committing return fraud.
Karung guni, Zabbaleen, the rag and bone man, waste picker, junk man or bin hoker are terms for people who make their living by sorting and trading trash. A similar process known as gleaning was practised in rural areas and some ancient agricultural societies, where the residue from farmers\' fields was collected.
Some dumpster divers, who self-identify as freegans, aim to reduce their ecological footprint by living from dumpster-dived-goods, sometimes exclusively.
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# Dumpster diving
## Overview
The activity is performed by people out of necessity in the developing world. Some scavengers perform in organized groups, and some organize on various internet forums and social networking websites. By reusing, or repurposing, resources destined for the landfill, dumpster diving is sometimes considered to be an environmentalist endeavor, and is thus practiced by many pro-green communities. The wastefulness of consumer society and throw-away culture compels some individuals to rescue usable items (for example, computers or smartphones, which are frequently discarded due to the extensive use of planned obsolescence in the technology industry) from destruction and divert them to those who can make use of the items.
A wide variety of things may be disposed while still repairable or in working condition, making salvage of them a source of potentially free items for personal use, or to sell for profit. Irregular, blemished or damaged items that are still otherwise functional are regularly thrown away. Discarded food that might have slight imperfections, near its expiration date, or that is simply being replaced by newer stock is often tossed out despite being still edible. Many retailers are reluctant to sell this stock at reduced prices because of the risks that people will buy it instead of the higher-priced newer stock, that extra handling time is required, and that there are liability risks. In the United Kingdom, cookery books have been written on the cooking and consumption of such foods, which has contributed to the popularity of skipping. Artists often use discarded materials retrieved from trash receptacles to create works of found objects or assemblage.
Students have been known to partake in dumpster diving to obtain high tech items for technical projects, or simply to indulge their curiosity for unusual items. Dumpster diving can additionally be used in support of academic research. Garbage picking serves as the main tool for garbologists, who study the sociology and archeology of trash in modern life. Private and government investigators may pick through garbage to obtain information for their inquiries. Illegal cigarette consumption may be deduced from discarded packages.
Dumpster diving can be hazardous, due to potential exposure to biohazardous matter, broken glass, and overall unsanitary conditions that may exist in dumpsters. In January 2012, in La Jolla, Swiss-American man Alfonso de Bourbon was killed by a truck while dumpster diving.
### Dumpster diving with criminal intentions (Garbage theft) {#dumpster_diving_with_criminal_intentions_garbage_theft}
The unauthorized taking of materials from a dumpster or other waste disposal container is commonly referred to as \"garbage theft\". Dumpster diving is a different idiom. Due to the typical low value of the stolen goods, garbage theft is not typically recognized as a serious crime, with laws against it frequently focusing on combating identity theft instead. Depending on the state or nation\'s rules surrounding low-level crime, garbage theft may be considered a form of petty theft and subject to a penalty that often entails a brief period of incarceration, a modest fine, or both. As a privacy violation, discarded medical records as trash led to a \$140,000 penalty against Massachusetts billing company Goldthwait Associates and a group of pathology offices in 2013 and a \$400,000 settlement between Midwest Women\'s Healthcare Specialists and 1,532 clients in Kansas City in 2014.
Identity theft has historically been carried out through garbage theft, with thieves utilizing bank and credit card statements discovered in trash to assume the identity of a victim or access their credit.
Criminals have been known to dumpster dive for cash receipts as part of a scheme to steal items and return them for cash, a form of return fraud known as \"shoplisting.\" Police investigating shoplifting in Bellingham, Washington, found dozens of receipts from retailers such as The Home Depot, Rite Aid and Fred Meyer, along with a list of items on the receipts. Suspects believed to have taken receipts from trash receptacles near Walmart locations were arrested for return fraud in 2016 in Madison, Wisconsin.
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# Dumpster diving
## Legal status {#legal_status}
Since dumpsters are usually located on private premises, divers may occasionally get in trouble for trespassing while dumpster diving, though the law is enforced with varying degrees of rigor. Some businesses may lock dumpsters to prevent pickers from congregating on their property, vandalism to their property, and to limit potential liability if a dumpster diver is injured while on their property.
Police searches of discarded waste as well as similar methods are also generally not considered violations of privacy rights; evidence seized in this manner has been permitted in many criminal trials. In the United States this has been affirmed by numerous courts including and up to the Supreme Court, in the decision *California v. Greenwood*. The doctrine is not as well established in regard to civil litigation.
Companies run by private investigators specializing in such techniques have emerged as a result of the need for discreet, undetected retrieval of documents and evidence for civil and criminal trials. Private investigators have also written books on \"P.I. technique\" in which dumpster diving or its equivalent \"wastebasket recovery\" figures prominently.
### By country {#by_country}
#### Belgium
In 2009, a Belgian dumpster diver and eco-activist nicknamed Ollie was detained for a month for removing food from a garbage can and was accused of theft and burglary. On February 25, 2009, he was arrested for removing food from a garbage can at an AD Delhaize supermarket in Bruges. Ollie\'s trial evoked protests in Belgium against restrictions from taking discarded food items.
#### Canada
In Ontario, Canada, the *Trespass to Property Act*---legislation dating back to the British North America Act 1867---grants property owners and security guards the power to ban anyone from their premises, for any reason, permanently. This is done by issuing a notice to the intruder, who will only be breaking the law upon return. Similar laws exist in Prince Edward Island and Saskatchewan. A recent case in Canada, which involved a police officer who retrieved a discarded weapon from a trash receptacle as evidence, created some controversy. The judge ruled the policeman\'s actions as legal although there was no warrant present, which led some to speculate the event as validation for any Canadian citizen to raid garbage disposals.
#### United Kingdom {#united_kingdom}
Skipping in England and Wales may qualify as theft within the Theft Act 1968`{{original research inline|date=October 2015}}`{=mediawiki} or as common-law theft in Scotland, though there is very little enforcement in practice.
#### Germany
In Germany, dumpster diving is referred to as \"containern\", and a waste container\'s contents are regarded as the property of the container\'s owner. Therefore, taking items from such a container is viewed as theft. However, the police will routinely disregard the illegality of garbage picking since the items found are generally of low value. There has only been one known instance where people were prosecuted. In 2009 individuals were arrested on assumed burglary as they had surmounted a supermarket\'s fence which was then followed by a theft complaint by the owner; the case was suspended.
#### United States {#united_states}
In the United States, the fourth amendment protects against certain searches by the government without a warrant. The 1988 *California v. Greenwood* case in the U.S. Supreme Court held that there is no common law expectation of privacy for discarded materials, and that therefore the police did not require a warrant to search through trash.
There are, however, limits to what can legally be taken from a company\'s refuse. In a 1983 Minnesota case involving the theft of customer lists from a garbage can, *Tennant Company v. Advance Machine Company* (355 N.W.2d 720), the owner of the discarded information was awarded \$500,000 in damages.
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# Dumpster diving
## Items
Dumpster diving is practiced differently in developed countries than in developing countries.
- **Food**. In many developing countries, food is rarely thrown away unless it is rotten as food is scarce in comparison to developed nations. In countries like the United States, where 40 to 50 percent of food is wasted, the trash contains a lot more food to gather. In many countries, charities collect excess food from supermarkets and restaurants and distribute it to impoverished neighbourhoods. Trash pickers, Karung guni, Zabaleen, and rag and bone men in these countries may concentrate on looking for usable items or scrap materials to sell rather than food items. In the United States, Canada, and Europe, some bakeries, grocery stores, or restaurants will routinely donate food according to a Good Samaritan Food Donation Act, but more often, because of health laws or company policy, they are required to discard food items by the expiration date, because of overstock, being overly ripened, spoiled, cosmetically imperfect, or blemished.
- **Books and periodicals**. As proof to publishing houses of unsold merchandise, booksellers will routinely remove the front covers of printed materials to render them destroyed prior to disposing of their remains in the garbage. Though readable, many damaged publications have disclaimers and legal notices against their existence or sale.
- **Irregular or damaged goods**. Offices, factories, department stores, and other commercial establishments may equally throw out non-perishable items that are irregular, were returned, have minor damages, or are replaced by newer inventory. Many items tend to be in such a state of disrepair or so cosmetically flawed that they will require some work to be made usable. For this reason, employees will at times intentionally destroy their items prior to being discarded to prevent them from being reused or resold.
- **Returned items**. Manufacturers often find it cheaper to routinely discard items returned as defective under warranty instead of repairing them, although a device is often repairable or usable as a source of spare parts to repair other, similar discarded devices.
- **School supplies**. At the end of each school year many perfectly useful supplies like pencils, pens, notebooks and art supplies are thrown away.
- **Electronic waste**. Some consumer electronics are dumped because of their rapid depreciation, obsolescence, cost to repair, or expense to upgrade. Owners of functional computers may find it easier to dump them rather than donate because many nonprofit organizations and schools are unable, or unwilling, to work with used equipment. Occasionally, vendors dispose of unsaleable, non-defective new merchandise as landfill. The Atari video game burial in Alamogordo, New Mexico, after the video game crash of 1983 is a well-known example; a 2014 excavation recovered about 1300 games for curation as museum exhibits or auction.
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- **Clothing**. While thrift stores routinely refuse used goods which they cannot cheaply and easily resell, the items which they do accept cost them nothing. There is therefore no shrinkage cost associated with discarding mendable garments, repairable appliances or even working donated items which are overstock or find no buyer after some arbitrary length of time.
- **Metal**. Sometimes waste may contain recyclable metals and materials that can be reused or sold to recycling plants and scrap yards. The most common recyclable metals found are steel and aluminum.
- **Wood**. Called **urban lumberjacking**, to salvage wood either for home heating, or home construction projects.
- **Empty cans and bottles**. Several countries, particularly in Northern Europe have enforced a system in which empty cans and bottles can be returned to stores for money. Usually the amount received per can/bottle is relatively low, so many simply discard them in dumpsters.
- **Personal Information**: cyber attackers may engage in dumpster diving to gather sensitive data, including IP addresses, bank account details, and Social Security numbers, by sifting through discarded mail or retrieving items disposed of in bins. Moreover, perpetrators may endeavor to broaden their contact databases by resorting to dumpster diving at corporate premises, aiming to obtain access to confidential and sensitive data, including phone lists or records.
### Other sources {#other_sources}
- **Residential buildings**. Clothing, furniture, appliances, and other housewares may be found at residential buildings.
- **College dormitories**. Items may be found at colleges with dormitories at the end of the semester when students throw away many items such as furniture, clothes and electronics.
## Notable instances {#notable_instances}
In the 1960s, Jerry Schneider, using recovered instruction manuals from The Pacific Telephone & Telegraph Company, used the company\'s own procedures to acquire hundreds of thousands of dollars\' worth of telephone equipment over several years until his arrest.
The *Castle Infinity* videogame, after its shutdown in 2005, was brought back from the dead by a fan rescuing its servers from the trash.
In October 2013, in North London, three men were arrested and charged under the 1824 Vagrancy Act when they were caught taking discarded food: tomatoes, mushrooms, cheese and cakes from bins behind an Iceland supermarket. The charges were dropped on 29 January 2014 after much public criticism as well as a request by Iceland\'s chief executive, Malcolm Walker.
In 1996, the source code for the Atari 7800 was discovered in the dumpster of the Atari office when the company closed.
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# Dumpster diving
## In popular culture {#in_popular_culture}
### Books
- Author John Hoffman wrote two books based on his own dumpster-diving exploits: *The Art and Science of Dumpster Diving* (1993; `{{ISBN|978-1-58160-550-1}}`{=mediawiki}) and *Dumpster Diving: The Advanced Course: How to Turn Other People\'s Trash into Money, Publicity, and Power* (2002; `{{ISBN|978-1-58160-369-9}}`{=mediawiki}), and was featured in the documentary DVD *The Ultimate Dive*, which was directed by Suzanne Girot and described by the Internet Movie Database as a \"Tongue-in-cheek how-to film on the art and science of dumpster diving.\"
- In 2001, dumpster diving was popularized in the book *Evasion,* published by CrimethInc.
- In Kim Stanley Robinson\'s science fiction novel *Fifty Degrees Below* (2005), the character Frank Vanderwal joins, for a time, a group of freegans (referred to as \"fregans\" in the novel) who frequently prepare feasts culled from dumpsters; kind-hearted restaurateurs aid them by setting aside foods which have not been touched by the public.
- Jeff Ferrell, Professor of Sociology at Texas Christian University, is the author of *Empire of Scrounge: Inside the Urban Underground of Dumpster Diving, Trash Picking, and Street Scavenging* (2005; `{{ISBN|978-0-81472-738-6}}`{=mediawiki}).
- Cory Doctorow integrated garbage picking characters into the plots of his novels *Someone Comes to Town, Someone Leaves Town* and *Pirate Cinema*.
- David Boarder Gilles\' *[A Mass Conspiracy to Feed People: Food Not Bombs and the World-class Waste of Global Cities](https://www.dukeupress.edu/a-mass-conspiracy-to-feed-people)* (2021) is an ethnography of this global movement of grassroots soup kitchens that recover wasted grocery surpluses and redistribute them to those in need.
### Television programs {#television_programs}
- British television shows have featured home renovations and decoration using salvaged materials. *Changing Rooms* (1996--2004) is one such show, broadcast on BBC One.
- TLC\'s *Extreme Cheapskates* and *Extreme Couponing* featured people who regularly dumpster dive to avoid spending money on different items---in the case of the latter, unwanted newspapers and newspaper inserts containing coupons were the subject of dumpster diving.
### Films
- *Surfing the Waste: A Musical Documentary About Dumpster Diving*, a film by Paul Aflalo, Sandra Lombardi and Tomoe Yoshihara, with music composed by Alden Penner and Nic Boshart.
- *Dumpster Wars: Reno\'s Trash Politics* (2008)
- *I Love Trash* (2007), a 30-minute documentary by David Brown and Greg Mann. OCLC\'s WorldCat provided a synopsis: \"*I Love Trash* is a documentary about the art of dumpster diving. Starting with an empty apartment, only the clothes they were wearing and a flashlight, David and Greg find everything they might otherwise buy, in trash cans and dumpsters. All their food, clothes, electronics, art materials and entertainment, all out of the trash.\" Accolades: Skyfest Film and Script Festival, (won 2nd place for Documentary Films); and Lake Michigan Film Competition, (won 3rd place for Documentary films).
- The 2010 documentary film *Dive!*, a short documentary written and directed by Jeremy Seifert, investigates dumpster diving in the Los Angeles area. *Dive!* premiered in October 2009 at the Gig Harbor Film Festival, where it won the Audience Choice Award. It has gone on to win awards at many other film festivals, including Best Documentary at the DC Independent Film Festival and Best Film at the Dutch Environmental Film Festival.
- *Spoils: Extraordinary Harvest*. A short film/mystery film and documentary by Alex Mallis. (2012) Accolades: Official Selection, New Orleans Film Festival. Official Selection, Independent Film Festival of Boston. Official Selection, DOC NYC.
- *The Leftovers: A Documentary about People Who Eat Trash* (2008), a 28-minute Swedish documentary by Michael Cavanagh and Kerstin Übelacker. Mykel Bently, Paul Hood, Krystal Trickey, Nick Gill, and Sofia Arborelius (the latter two were exchange students) joined for this dumpster diver adventure.
- *From Dumpster To Dinner Plate* (2011), an award-winning New Zealand short documentary directed by Vanessa Hudson. \"As the cost of food reaches record highs an underground movement of dumpster divers is rapidly gaining momentum fuelled by consumers who are forced to find creative ways to feed themselves
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# Digital synthesizer
A **digital synthesizer** is a synthesizer that uses digital signal processing (DSP) techniques to make musical sounds, in contrast to older analog synthesizers, which produce music using analog electronics, and samplers, which play back digital recordings of acoustic, electric, or electronic instruments. Some digital synthesizers emulate analog synthesizers, while others include sampling capability in addition to digital synthesis.
## History
The very earliest digital synthesis experiments were made with computers, as part of academic research into sound generation.
In 1957, the first programming language for computer music, MUSIC, was developed by Max Mathews on an IBM 704 at Bell Labs in 1957. It generates digital audio waveforms through direct synthesis.
, EMS MUSYS 3 system was developed by Peter Grogono (software), David Cockerell (hardware and interfacing) and Peter Zinovieff (system design and operation) at their London (Putney) Studio. The system ran on two mini-computers, Digital Equipment PDP-8\'s. These had a pair of fast D/A and A/D converters, 12,000 (12k) bytes of core memory (RAM), backed up by a hard drive of 32k and by tape storage (DecTape). The earliest digital sampling was done on that system during 1971--1972 for Harrison Birtwistle\'s \"*Chronometer*\" released in 1975.
In 1972--1974, Dartmouth Digital Synthesizer was developed by Dartmouth College Professors Jon Appleton and Frederick J. Hooven, in association with NED co-founders Sydney A. Alonso and Cameron W. Jones.
In 1977, Bell Labs Digital Synthesizer was developed by Hal Ales at Bell Labs.
In 1977, New England Digital (NED) released the Synclavier, the first commercial synthesizer to use purely digital sound generation and also the world\'s first commercial FM synthesizer.
Early commercial digital synthesizers used simple hard-wired digital circuitry to implement techniques such as additive synthesis and FM synthesis. `{{citation needed span|Other techniques, such as [[wavetable synthesis]] and [[physical modeling]], only became possible with the advent of high-speed microprocessor and digital signal processing technology.|date=April 2023|reason=wavetable synthesis was implemented in 1979 by PPG and it was regarded as a method to reduce the computational complexity of additive synthesis.}}`{=mediawiki} Two other early commercial digital synthesizers were the Fairlight CMI, introduced in 1979, and the New England Digital Synclavier II, introduced in 1979 as an upgrade to the original Synclavier. The Fairlight CMI was one of the earlier sampling synthesizers, while the Synclavier originally used FM synthesis technology licensed from Yamaha, before adding the world\'s first 16-bit, real-time hard drive streaming sampler later in 1982. The Fairlight CMI and the Synclavier were both expensive systems, retailing for more than \$20,000 in the early 1980s. The cost of digital synthesizers began falling rapidly in the early 1980s. E-mu Systems introduced the Emulator sampling synthesizer in 1982 at a retail price of \$7,900. Although not as flexible or powerful as either the Fairlight CMI or the Synclavier, its lower cost and portability made it popular.
With the addition of sophisticated sequencers on board, now added to built-in effects and other features, the \'workstation\' synthesizer had been born. These always include a multi-track sequencer, and can often record and play back samples, and in later years full audio tracks, to be used to record an entire song. These are usually also ROMplers, playing back samples, to give a wide variety of realistic instrument and other sounds such as drums, string instruments and wind instruments to sequence and compose songs, along with popular keyboard instrument sounds such as electric pianos and organs.
As there was still interest in analog synthesizers, and with the increase of computing power, over the 1990s another type of synthesizer arose: the analog modeling, or \"virtual analog\" synthesizer. These use computing power to simulate traditional analog waveforms and circuitry such as envelopes and filters, with the most popular examples of this type of instrument including the Nord Lead and Access Virus.
Digital synthesizers can now be completely emulated in software (\"softsynth\"), and run on conventional PC hardware. Such soft implementations require careful programming and a fast CPU to get the same latency response as their dedicated equivalents. To reduce latency, some professional sound card manufacturers have developed specialized Digital Signal Processing (\[DSP\]) hardware. Dedicated digital synthesizers have the advantage of a performance-friendly user interface (physical controls like buttons for selecting features and enabling functionality, and knobs for setting variable parameters). On the other hand, software synthesizers have the advantages afforded by a rich graphical display.
With focus on performance-oriented keyboards and digital computer technology, manufacturers of commercial electronic instruments created some of the earliest digital synthesizers for studio and experimental use with computers being able to handle built-in sound synthesis algorithms.
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# Digital synthesizer
## History
### In Japan {#in_japan}
In 1973, the Japanese company Yamaha licensed the patent for frequency modulation synthesis (FM synthesis) from John Chowning, who had experimented with it at Stanford University since 1971. Yamaha\'s engineers began adapting Chowning\'s algorithm for use in a commercial digital synthesizer, adding improvements such as the \"key scaling\" method to avoid the introduction of distortion that normally occurred in analog systems during frequency modulation, though it would take several years before Yamaha were to release their FM digital synthesizers. In the 1970s, Yamaha were granted a number of patents, under the company\'s former name \"Nippon Gakki Seizo Kabushiki Kaisha\", evolving Chowning\'s early work on FM synthesis technology. Yamaha built the first prototype digital synthesizer in 1974.`{{verification failed|date=April 2023|reason=}}`{=mediawiki}
Released in 1979, the Casio VL-1 was the first low budget digital synthesizer, selling for \$69.95. Yamaha eventually commercialized their FM synthesis technology and released the company\'s first FM digital synthesizer in 1980, the Yamaha GS-1, but at an expensive retail price of \$16,000.
Introduced in 1983, the Yamaha DX7 was the breakthrough digital synthesizer to have a major impact, both innovative and affordable, and thus spelling the decline of analog synthesizers. It used FM synthesis and, although it was incapable of the sampling synthesis of the Fairlight CMI, its price was around \$2,000, putting it within range of a much larger number of musicians. The DX-7 was also known for its \"key scaling\" method to avoid distortion and for its recognizably bright tonality that was partly due to its high sampling rate of 57 kHz. It became indispensable to many music artists of the 1980s, and would become one of the best-selling synthesizers of all time.
In 1987, Roland released its own influential synthesizer of the time, the D-50. This popular synth broke new ground in affordably combining short samples and digital oscillators, as well as the innovation of built-in digital effects (reverb., chorus, equalizer). Roland called this Linear Arithmetic (LA) synthesis. This instrument is responsible for some of the very recognisable preset synthesizer sounds of the late 1980s, such as the Pizzagogo sound used on Enya\'s \"Orinoco Flow.\"
It gradually became feasible to include high quality samples of existing instruments as opposed to synthesizing them. In 1988, Korg introduced the last of the hugely popular trio of digital synthesizers of the 1980s after the DX7 and D50, the M1. This heralded both the increasing popularisation of digital sample-based synthesis, and the rise of \'workstation\' synthesizers. After this time, many popular modern digital synthesizers have been described as not being full synthesizers in the most precise sense, as they play back samples stored in their memory. However, they still include options to shape the sounds through use of envelopes, LFOs, filters and effects such as reverb. The Yamaha Motif and Roland Fantom series of keyboards are typical examples of this type, described as \'ROMplers\'; at the same time, they are also examples of \"workstation\" synthesizers.
As the cost of processing power and memory fell, new types of synthesizers emerged, offering a variety of novel sound synthesis options. The Korg Oasys was one such example, packaging multiple digital synthesizers into a single unit.
## Analog vs. digital {#analog_vs._digital}
An analog synthesizer creates sound using electronic circuitry, such as voltage-controlled oscillators and voltage-controlled filters. In contrast, a digital synthesizer generates a stream of numbers, often using some form of digital signal processor, which are then converted to sound using a digital-to-analog converter (DAC).
A digital synthesizer is in essence a computer with (often) a piano or organ keyboard and an LCD as a user interface. Because computer technology is rapidly advancing, it is often possible to offer more features in a digital synthesizer than in an analog synthesizer at a given price. However, both technologies have their own merit. Some forms of synthesis, such as, for instance, sampling and additive synthesis are not feasible in analog synthesizers, while on the other hand, many musicians prefer the character of analog synthesizers over their digital equivalent.
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# Digital synthesizer
## Usage
The new wave era of the 1980s first brought the digital synthesizer to the public ear. Bands like Talking Heads and Duran Duran used the digitally made sounds on some of their most popular albums. Other more pop-inspired bands like Hall & Oates began incorporating the digital synthesizer into their sound in the 1980s. Through breakthroughs in technology in the 1990s many modern synthesizers use DSP.
## Digital synthesis {#digital_synthesis}
Working in more or less the same way, every digital synthesizer appears similar to a computer. At a steady sample rate, digital synthesis produces a stream of numbers. Sound from speakers is then produced by a conversion to analog form. Direct digital synthesis is the typical architecture for digital synthesizers. Through signal generation, voice and instrument-level processing, a signal flow is created and controlled either by MIDI capabilities or voice and instrument-level controls
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# Definition of music
*Organised Sound*}} `{{Use shortened footnotes|date=December 2022}}`{=mediawiki} A **definition of music** endeavors to give an accurate and concise explanation of music\'s basic attributes or essential nature and it involves a process of defining what is meant by the term *music*. Many authorities have suggested definitions, but defining music turns out to be more difficult than might first be imagined, and there is ongoing debate. A number of explanations start with the notion of music as *organized sound,* but they also highlight that this is perhaps too broad a definition and cite examples of organized sound that are not defined as music, such as human speech and sounds found in both natural and industrial environments . The problem of defining music is further complicated by the influence of culture in music cognition.
The *Concise Oxford Dictionary* defines music as \"the art of combining vocal or instrumental sounds (or both) to produce beauty of form, harmony, and expression of emotion\". However, some music genres, such as noise music and musique concrète, challenge these ideas by using sounds not widely considered as musical, beautiful or harmonious, like randomly produced electronic distortion, feedback, static, cacophony, and sounds produced using compositional processes which utilize indeterminacy.
An often-cited example of the dilemma in defining music is the work *4′33″* (1952) by the American composer John Cage (1912--1992). The written score has three movements and directs the performer(s) to appear on stage, indicate by gesture or other means when the piece begins, then make no sound throughout the duration of the piece, marking sections and the end by gesture. The audience hears only whatever ambient sounds may occur in the room. Some argue that *4′33″* is not music because, among other reasons, it contains no sounds that are conventionally considered \"musical\" and the composer and performer(s) exert no control over the organization of the sounds heard. Others argue it is music because the conventional definitions of musical sounds are unnecessarily and arbitrarily limited, and control over the organization of the sounds is achieved by the composer and performer(s) through their gestures that divide what is heard into specific sections and a comprehensible form.
## Concepts of music {#concepts_of_music}
Because of differing fundamental concepts of music, the languages of many cultures do not contain a word that can be accurately translated as \"music\" as that word is generally understood by Western cultures. Inuit and most North American Indian languages do not have a general term for music. Among the Aztecs, the ancient Mexican theory of rhetoric, poetry, dance, and instrumental music used the Nahuatl term *In xochitl-in kwikatl* to refer to a complex mix of music and other poetic verbal and non-verbal elements, and reserved the word *Kwikakayotl* (or cuicacayotl) only for the sung expressions. There is no term for music in Nigerian languages Tiv, Yoruba, Igbo, Efik, Birom, Hausa, Idoma, Eggon or Jarawa. Many other languages have terms which only partly cover what Western culture typically means by the term *music*. The Mapuche of Argentina do not have a word for *music*, but they do have words for instrumental versus improvised forms (*kantun*), European and non-Mapuche music (*kantun winka*), ceremonial songs (*öl*), and *tayil*.
While some languages in West Africa have no term for music, some West African languages accept the general concepts of music. *Musiqi* is the Persian word for the science and art of music, *muzik* being the sound and performance of music, though some things European-influenced listeners would include, such as Quran chanting, are excluded.
## Music vs. noise {#music_vs._noise}
Ben Watson points out that Ludwig van Beethoven\'s *Große Fuge* (1825) \"sounded like noise\" to his audience at the time. Indeed, Beethoven\'s publishers persuaded him to remove it from its original setting as the last movement of a string quartet. He did so, replacing it with a sparkling *Allegro*. They subsequently published it separately.`{{Clarify|date=October 2015|reason=Is this meant to differentiate "music" from "noise", or to assert that the two things may not be indistinguishable?}}`{=mediawiki} Musicologist Jean-Jacques Nattiez considers the difference between noise and music nebulous, explaining that \"The border between music and noise is always culturally defined---which implies that, even within a single society, this border does not always pass through the same place; in short, there is rarely a consensus \... By all accounts there is no *single* and *intercultural* universal concept defining what music might be\".
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# Definition of music
## Definitions
### Organized sound {#organized_sound}
An often-cited definition of music is that it is \"organized sound\", a term originally coined by modernist composer Edgard Varèse in reference to his own musical aesthetic. Varèse\'s concept of music as \"organized sound\" fits into his vision of \"sound as living matter\" and of \"musical space as open rather than bounded\". He conceived the elements of his music in terms of \"sound-masses\", likening their organization to the natural phenomenon of crystallization. Varèse thought that \"to stubbornly conditioned ears, anything new in music has always been called noise\", and he posed the question, \"what is music but organized noises?\"
The fifteenth edition of the *Encyclopædia Britannica* states that \"while there are no sounds that can be described as inherently unmusical, musicians in each culture have tended to restrict the range of sounds they will admit.\" A human organizing element is often felt to be implicit in music (sounds produced by non-human agents, such as waterfalls or birds, are often described as \"musical\", but perhaps less often as \"music\"). The composer R. Murray states that the sound of classical music \"has decays; it is granular; it has attacks; it fluctuates, swollen with impurities---and all this creates a musicality that comes before any \'cultural\' musicality.\" However, in the view of semiologist Jean-Jacques Nattiez, \"just as music is whatever people choose to recognize as such, noise is whatever is recognized as disturbing, unpleasant, or both\". (See \"music as social construct\" below.)
#### Language
Levi R. Bryant defines music not as a language, but as a marked-based, problem-solving method, comparable to mathematics.
### Musical universals {#musical_universals}
Most definitions of music include a reference to sound and a list of universals of music can be generated by stating the elements (or aspects) of sound: pitch, timbre, loudness, duration, spatial location and texture. However, in terms more specifically relating to music: following Wittgenstein, cognitive psychologist Eleanor Rosch proposes that categories are not clean cut but that something may be more or less a member of a category. As such the search for musical universals would fail and would not provide one with a valid definition. This is primarily because other cultures have different understandings in relation to the sounds that English-language writers refer to as music.
### Social construct {#social_construct}
Many people do, however, share a general idea of music. The Websters definition of music is a typical example: \"the science or art of ordering tones or sounds in succession, in combination, and in temporal relationships to produce a composition having unity and continuity\" (*Webster\'s Collegiate Dictionary*, online edition).
### Subjective experience {#subjective_experience}
This approach to the definition focuses not on the *construction* but on the *experience* of music. An extreme statement of the position has been articulated by the Italian composer Luciano Berio: \"Music is everything that one listens to with the intention of listening to music\". This approach permits the boundary between music and noise to change over time as the conventions of musical interpretation evolve within a culture, to be different in different cultures at any given moment, and to vary from person to person according to their experience and proclivities. It is further consistent with the subjective reality that even what would commonly be considered music is experienced as non-music if the mind is concentrating on other matters and thus not perceiving the sound\'s *essence* *as music*.
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# Definition of music
## Specific definitions {#specific_definitions}
### Clifton
In his 1983 book, *Music as Heard*, which sets out from the phenomenological position of Husserl, Merleau-Ponty, and Ricœur, Thomas Clifton defines music as \"an ordered arrangement of sounds and silences whose meaning is presentative rather than denotative \... This definition distinguishes music, as an end in itself, from compositional technique, and from sounds as purely physical objects.\" More precisely, \"music is the actualization of the possibility of any sound whatever to present to some human being a meaning which he experiences with his body---that is to say, with his mind, his feelings, his senses, his will, and his metabolism\". It is therefore \"a certain reciprocal relation established between a person, his behavior, and a sounding object\".
Clifton accordingly differentiates music from non-music on the basis of the human behavior involved, rather than on either the nature of compositional technique or of sounds as purely physical objects. Consequently, the distinction becomes a question of what is meant by musical behavior: \"a musically behaving person is one whose very being is absorbed in the significance of the sounds being experienced.\" However, \"It is not altogether accurate to say that this person is listening *to* the sounds. First, the person is doing more than listening: he is perceiving, interpreting, judging, and feeling. Second, the preposition \'to\' puts too much stress on the sounds as such. Thus, the musically behaving person experiences musical significance by means of, or through, the sounds\".
In this framework, Clifton finds that there are two things that separate music from non-music: (1) musical meaning is presentative, and (2) music and non-music are distinguished in the idea of personal involvement. \"It is the notion of personal involvement which lends significance to the word *ordered* in this definition of music\". This is not to be understood, however, as a sanctification of extreme relativism, since \"it is precisely the \'subjective\' aspect of experience which lured many writers earlier in this century down the path of sheer opinion-mongering. Later on this trend was reversed by a renewed interest in \'objective,\' scientific, or otherwise non-introspective musical analysis. But we have good reason to believe that a musical experience is not a purely private thing, like seeing pink elephants, and that reporting about such an experience need not be subjective in the sense of it being a mere matter of opinion\".
Clifton\'s task, then, is to describe musical experience and the objects of this experience which, together, are called \"phenomena\", and the activity of describing phenomena is called \"phenomenology\". It is important to stress that this definition of music says nothing about aesthetic standards.
> Music is not a fact or a thing in the world, but a meaning constituted by human beings. \... To talk about such experience in a meaningful way demands several things. First, we have to be willing to let the composition speak to us, to let it reveal its own order and significance. \... Second, we have to be willing to question our assumptions about the nature and role of musical materials. \... Last, and perhaps most important, we have to be ready to admit that describing a meaningful experience is itself meaningful.
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# Definition of music
## Specific definitions {#specific_definitions}
### Nattiez
\"Music, often an art/entertainment, is a total social fact whose definitions vary according to era and culture\", according to Jean Molino. It is often contrasted with noise. According to musicologist Jean-Jacques Nattiez: \"The border between music and noise is always culturally defined---which implies that, even within a single society, this border does not always pass through the same place; in short, there is rarely a consensus \... By all accounts there is no *single* and *intercultural* universal concept defining what music might be\". Given the above demonstration that \"there is no limit to the number or the genre of variables that might intervene in a definition of the musical\", an organization of definitions and elements is necessary.
Nattiez (1990, 17) describes definitions according to a tripartite semiological scheme similar to the following:
--------------------- ---
Poietic Process
Composer (Producer) →
--------------------- ---
There are three levels of description, the poietic, the neutral, and the esthesic:
- \" By \'poietic\' I understand describing the *link* among the composer\'s intentions, his creative procedures, his mental schemas, and the *result* of this collection of strategies; that is, the components that go into the work\'s material embodiment. Poietic description thus also deals with a quite special form of hearing (Varese called it \'the interior ear\'): what the composer hears while imagining the work\'s sonorous results, or while experimenting at the piano, or with tape.\"
- \"By \'esthesic\' I understand not merely the artificially attentive hearing of a musicologist, but the description of perceptive behaviors within a given population of listeners; that is how this or that aspect of sonorous reality is captured by their perceptive strategies\".
- The neutral level is that of the physical \"trace\", (Saussere\'s sound-image, a sonority, a score), created and interpreted by the esthesic level (which corresponds to a perceptive definition; the perceptive and/or \"social\" construction definitions below) and the poietic level (which corresponds to a creative, as in compositional, definition; the organizational and social construction definitions below).
Table describing types of definitions of music:
+-----------+--------------------------+-----------------------+-----------------------+
| | poietic level\ | neutral level\ | esthesic level\ |
| | (choice of the composer) | (physical definition) | (perceptive judgment) |
+===========+==========================+=======================+=======================+
| music | musical sound | sound of the\ | agreeable sound |
| | | harmonic\ | |
| | | spectrum | |
+-----------+--------------------------+-----------------------+-----------------------+
| non-music | noise\ | noise\ | disagreeable\ |
| | (nonmusical) | (complex sound) | noise |
+-----------+--------------------------+-----------------------+-----------------------+
Because of this range of definitions, the study of music comes in a wide variety of forms. There is the study of sound and vibration or acoustics, the cognitive study of music, the study of music theory and performance practice or music theory and ethnomusicology and the study of the reception and history of music, generally called musicology.
### Xenakis
Composer Iannis Xenakis in \"Towards a Metamusic\" (chapter 7 of *Formalized Music*) defined music in the following way:
1. It is a sort of comportment necessary for whoever thinks it and makes it.
2. It is an individual pleroma, a realization.
3. It is a fixing in sound of imagined virtualities (cosmological, philosophical, \..., arguments)
4. It is normative, that is, unconsciously it is a model for being or for doing by sympathetic drive.
5. It is catalytic: its mere presence permits internal psychic or mental transformations in the same way as the crystal ball of the hypnotist.
6. It is the gratuitous play of a child.
7. It is a mystical (but atheistic) asceticism. Consequently, expressions of sadness, joy, love and dramatic situations are only very limited particular instances
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# Dissociation constant
In chemistry, biochemistry, and pharmacology, a **dissociation constant** (*K*~D~) is a specific type of equilibrium constant that measures the propensity of a larger object to separate (dissociate) reversibly into smaller components, as when a complex falls apart into its component molecules, or when a salt splits up into its component ions. The dissociation constant is the inverse of the association constant. In the special case of salts, the dissociation constant can also be called an ionization constant. For a general reaction:
:
`A_\mathit{x} B_\mathit{y} <=> \mathit{x} A{} + \mathit{y} B`
in which a complex $\ce{A}_x \ce{B}_y$ breaks down into *x* A subunits and *y* B subunits, the dissociation constant is defined as
:
`K_\mathrm{D} = \frac{[\ce A]^x [\ce B]^y}{[\ce A_x \ce B_y]}`
where \[A\], \[B\], and \[A~*x*~ B~*y*~\] are the equilibrium concentrations of A, B, and the complex A~*x*~ B~*y*~, respectively.
One reason for the popularity of the dissociation constant in biochemistry and pharmacology is that in the frequently encountered case where *x* = *y* = 1, *K*~D~ has a simple physical interpretation: when \[A\] = *K*~D~, then \[B\] = \[AB\] or, equivalently, $\tfrac {[\ce{AB}]}{{[\ce B]} + [\ce{AB}]} = \tfrac{1}{2}$. That is, *K*~D~, which has the dimensions of concentration, equals the concentration of free A at which half of the total molecules of B are associated with A. This simple interpretation does not apply for higher values of *x* or *y*. It also presumes the absence of competing reactions, though the derivation can be extended to explicitly allow for and describe competitive binding. It is useful as a quick description of the binding of a substance, in the same way that EC~50~ and IC~50~ describe the biological activities of substances.
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# Dissociation constant
## Concentration of bound molecules {#concentration_of_bound_molecules}
### Molecules with one binding site {#molecules_with_one_binding_site}
Experimentally, the concentration of the molecule complex \[AB\] is obtained indirectly from the measurement of the concentration of a free molecules, either \[A\] or \[B\]. In principle, the total amounts of molecule \[A\]~0~ and \[B\]~0~ added to the reaction are known. They separate into free and bound components according to the mass conservation principle:
: \\begin{align}
` \ce{[A]_0} &= \ce{{[A]} + [AB]} \\`\
` \ce{[B]_0} &= \ce{{[B]} + [AB]}`
\\end{align}
To track the concentration of the complex \[AB\], one substitutes the concentration of the free molecules (\[A\] or \[B\]), of the respective conservation equations, by the definition of the dissociation constant,
:
`[\ce A]_0 = K_\mathrm{D} \frac{[\ce{AB}]}{[\ce B]} + [\ce{AB}]`
This yields the concentration of the complex related to the concentration of either one of the free molecules
:
`\ce{[AB]} = \frac\ce{[A]_0 [B]}{K_\mathrm{D} + [\ce B]} = \frac\ce{[B]_0 [A]}{K_\mathrm{D} + [\ce A]}`
### Macromolecules with identical independent binding sites {#macromolecules_with_identical_independent_binding_sites}
Many biological proteins and enzymes can possess more than one binding site. Usually, when a ligand `{{math|L}}`{=mediawiki} binds with a macromolecule `{{math|M}}`{=mediawiki}, it can influence binding kinetics of other ligands `{{math|L}}`{=mediawiki} binding to the macromolecule. A simplified mechanism can be formulated if the affinity of all binding sites can be considered independent of the number of ligands bound to the macromolecule. This is valid for macromolecules composed of more than one, mostly identical, subunits. It can be then assumed that each of these `{{mvar|n}}`{=mediawiki} subunits are identical, symmetric and that they possess only a single binding site. Then the concentration of bound ligands \[L\]\_{bound} becomes
:
`\ce{[L]}_\text{bound} = \frac{n\ce{[M]}_0 \ce{[L]}}{K_\mathrm{D} + \ce{[L]}}`
In this case, $\ce{[L]}_\text{bound} \neq \ce{[LM]}$, but comprises all partially saturated forms of the macromolecule:
:
`\ce{[L]}_\text{bound} = \ce{[LM]} + \ce{2[L_2 M]} + \ce{3[L_3 M]} + \ldots + n \ce{[L_\mathit{n} M]} `
where the saturation occurs stepwise
: \\begin{align}
` \ce{{[L]} + [M]} &\ce{{} <=> {[LM]}} & K'_1 &= \frac\ce{[L][M]}{[LM]} & \ce{[LM]} &= \frac\ce{[L][M]}{K'_1} \\`\
` \ce{{[L]} + [LM]} &\ce{{} <=> {[L2 M]}} & K'_2 &= \frac\ce{[L][LM]}{[L_2 M]} & \ce{[L_2 M]} &= \frac\ce{[L]^2[M]}{K'_1 K'_2} \\`\
` \ce{{[L]} + [L2 M]} &\ce{{} <=> {[L3 M]}} & K'_3 &= \frac\ce{[L][L_2 M]}{[L_3 M]} & \ce{[L_3 M]} &= \frac\ce{[L]^3[M]}{K'_1 K'_2 K'_3} \\`\
` & \vdots & & \vdots & & \vdots \\`\
`\ce{{[L]} + [L_\mathit{n - 1} M]} &\ce{{} <=> {[L_\mathit{n} M]}} & K'_n &= \frac\ce{[L][L_{n - 1} M]}{[L_n M]} & [\ce L_n \ce M] &= \frac{[\ce L]^n[\ce M]}{K'_1 K'_2 K'_3 \cdots K'_n}`
\\end{align}
For the derivation of the general binding equation a saturation function $r$ is defined as the quotient from the portion of bound ligand to the total amount of the macromolecule:
:
` r = \frac\ce{[L]_{bound}}\ce{[M]_0} `\
` = \frac\ce{{[LM]} + {2[L_2 M]} + {3[L_3 M]} + ... + \mathit n[L_\mathit{n} M]}\ce{{[M]} + {[LM]} + {[L_2 M]} + {[L_3 M]} + ... + [L_\mathit{n} M]}`\
` = \frac{\sum_{i=1}^n \left( \frac{i [\ce L]^i}{\prod_{j=1}^i K_j'} \right) }{1 + \sum_{i=1}^n \left( \frac{[\ce L]^i}{\prod_{j=1}^i K_j'} \right)}`
*K′~n~* are so-called macroscopic or apparent dissociation constants and can result from multiple individual reactions. For example, if a macromolecule *M* has three binding sites, *K′*~1~ describes a ligand being bound to any of the three binding sites. In this example, *K′*~2~ describes two molecules being bound and *K′~3~* three molecules being bound to the macromolecule. The microscopic or individual dissociation constant describes the equilibrium of ligands binding to specific binding sites. Because we assume identical binding sites with no cooperativity, the microscopic dissociation constant must be equal for every binding site and can be abbreviated simply as *K*~D~. In our example, *K′*~1~ is the amalgamation of a ligand binding to either of the three possible binding sites (I, II and III), hence three microscopic dissociation constants and three distinct states of the ligand--macromolecule complex. For *K′*~2~ there are six different microscopic dissociation constants (I--II, I--III, II--I, II--III, III--I, III--II) but only three distinct states (it does not matter whether you bind pocket I first and then II or II first and then I). For *K′*~3~ there are three different dissociation constants --- there are only three possibilities for which pocket is filled last (I, II or III) --- and one state (I--II--III).
Even when the microscopic dissociation constant is the same for each individual binding event, the macroscopic outcome (*K′*~1~, *K′*~2~ and *K′*~3~) is not equal. This can be understood intuitively for our example of three possible binding sites. *K′*~1~ describes the reaction from one state (no ligand bound) to three states (one ligand bound to either of the three binding sides). The apparent *K′*~1~ would therefore be three times smaller than the individual *K*~D~. *K′*~2~ describes the reaction from three states (one ligand bound) to three states (two ligands bound); therefore, *K′*~2~ would be equal to *K*~D~. *K′*~3~ describes the reaction from three states (two ligands bound) to one state (three ligands bound); hence, the apparent dissociation constant *K′*~3~ is three times bigger than the microscopic dissociation constant *K*~D~. The general relationship between both types of dissociation constants for *n* binding sites is
:
`K_i' = K_\mathrm{D} \frac{i}{n - i + 1}`
Hence, the ratio of bound ligand to macromolecules becomes
:
` r = \frac{\sum_{i=1}^n i \left( \prod_{j=1}^i \frac{n - j + 1}{j} \right) \left( \frac\ce{[L]}{K_\mathrm{D}} \right)^i }{1 + \sum_{i=1}^n \left( \prod_{j=1}^i \frac{n - j + 1}{j} \right) \left( \frac{[L]}{K_\mathrm{D}} \right)^i}`\
` = \frac{\sum_{i=1}^n i \binom{n}{i} \left( \frac{[L]}{K_\mathrm{D}} \right)^i }{1 + \sum_{i=1}^n \binom{n}{i} \left( \frac\ce{[L]}{K_\mathrm{D}} \right)^i}`
where $\binom{n}{i} = \frac{n!}{(n - i)!i!}$ is the binomial coefficient. Then the first equation is proved by applying the binomial rule
:
` r = \frac{n \left( \frac\ce{[L]}{K_\mathrm{D}} \right) \left(1 + \frac\ce{[L]}{K_\mathrm{D}} \right)^{n - 1} }{\left(1 + \frac\ce{[L]}{K_\mathrm{D}} \right)^n}`\
` = \frac{n \left( \frac\ce{[L]}{K_\mathrm{D}} \right) }{\left(1 + \frac\ce{[L]}{K_\mathrm{D}} \right)}`\
` = \frac{n [\ce L]}{K_\mathrm{D} + [\ce L]}`\
` = \frac\ce{[L]_{bound}}\ce{[M]_0}`
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# Dissociation constant
## Protein--ligand binding {#proteinligand_binding}
The dissociation constant is commonly used to describe the affinity between a ligand L (such as a drug) and a protein P; i.e., how tightly a ligand binds to a particular protein. Ligand--protein affinities are influenced by non-covalent intermolecular interactions between the two molecules such as hydrogen bonding, electrostatic interactions, hydrophobic and van der Waals forces. Affinities can also be affected by high concentrations of other macromolecules, which causes macromolecular crowding.
The formation of a ligand--protein complex LP can be described by a two-state process
:
`L + P <=> LP`
the corresponding dissociation constant is defined
:
`K_\mathrm{D} = \frac{\left[ \ce{L} \right] \left[ \ce{P} \right]}{\left[ \ce{LP} \right]}`
where \[P\], \[L\], and \[LP\] represent molar concentrations of the protein, ligand, and protein--ligand complex, respectively.
The dissociation constant has molar units (M) and corresponds to the ligand concentration \[L\] at which half of the proteins are occupied at equilibrium, i.e., the concentration of ligand at which the concentration of protein with ligand bound \[LP\] equals the concentration of protein with no ligand bound \[P\]. The smaller the dissociation constant, the more tightly bound the ligand is, or the higher the affinity between ligand and protein. For example, a ligand with a nanomolar (nM) dissociation constant binds more tightly to a particular protein than a ligand with a micromolar (μM) dissociation constant.
Sub-picomolar dissociation constants as a result of non-covalent binding interactions between two molecules are rare. Nevertheless, there are some important exceptions. Biotin and avidin bind with a dissociation constant of roughly 10^−15^ M = 1 fM = 0.000001 nM. Ribonuclease inhibitor proteins may also bind to ribonuclease with a similar 10^−15^ M affinity.
The dissociation constant for a particular ligand--protein interaction can change with solution conditions (e.g., temperature, pH and salt concentration). The effect of different solution conditions is to effectively modify the strength of any intermolecular interactions holding a particular ligand--protein complex together.
Drugs can produce harmful side effects through interactions with proteins for which they were not meant to or designed to interact. Therefore, much pharmaceutical research is aimed at designing drugs that bind to only their target proteins (negative design) with high affinity (typically 0.1--10 nM) or at improving the affinity between a particular drug and its *in vivo* protein target (positive design).
### Antibodies
In the specific case of antibodies (Ab) binding to antigen (Ag), usually the term **affinity constant** refers to the association constant.
:
`Ab + Ag <=> AbAg `
:
`K_\mathrm{A} = \frac{\left[ \ce{AbAg} \right]}{\left[ \ce{Ab} \right] \left[ \ce{Ag} \right]} = \frac{1}{K_\mathrm{D}} `
This chemical equilibrium is also the ratio of the on-rate (*k*~forward~ or *k*~a~) and off-rate (*k*~back~ or *k*~d~) constants. Two antibodies can have the same affinity, but one may have both a high on- and off-rate constant, while the other may have both a low on- and off-rate constant.
:
`K_A = \frac{k_\text{forward}}{k_\text{back}} = \frac{\mbox{on-rate}}{\mbox{off-rate}}`
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# Dissociation constant
## Acid--base reactions {#acidbase_reactions}
For the deprotonation of acids, *K* is known as *K*~a~, the acid dissociation constant. Strong acids, such as sulfuric or phosphoric acid, have large dissociation constants; weak acids, such as acetic acid, have small dissociation constants.
The symbol *K*~a~, used for the acid dissociation constant, can lead to confusion with the association constant, and it may be necessary to see the reaction or the equilibrium expression to know which is meant.
Acid dissociation constants are sometimes expressed by p*K*~a~, which is defined by
:
`\text{p}K_\text{a} = -\log_{10}{K_\mathrm{a}}`
This $\mathrm{p}K$ notation is seen in other contexts as well; it is mainly used for covalent dissociations (i.e., reactions in which chemical bonds are made or broken) since such dissociation constants can vary greatly.
A molecule can have several acid dissociation constants. In this regard, that is depending on the number of the protons they can give up, we define *monoprotic*, *diprotic* and *triprotic* acids. The first (e.g., acetic acid or ammonium) have only one dissociable group, the second (e.g., carbonic acid, bicarbonate, glycine) have two dissociable groups and the third (e.g., phosphoric acid) have three dissociable groups. In the case of multiple p*K* values they are designated by indices: p*K*~1~, p*K*~2~, p*K*~3~ and so on. For amino acids, the p*K*~1~ constant refers to its carboxyl (--COOH) group, p*K*~2~ refers to its amino (--NH~2~) group and the p*K*~3~ is the p*K* value of its side chain.
: \\begin{align}
` \ce{H3 B} &\ce{{} <=> {H+} + {H2 B^-}} & K_1 &= \ce{[H+] . [H2 B^-] \over [H3 B]} & \mathrm{p}K_1 &= -\log K_1 \\`\
` \ce{H2 B^-} &\ce{{} <=> {H+} + {H B^{2-}}} & K_2 &= \ce{[H+] . [H B ^{2-}] \over [H2 B^-]} & \mathrm{p}K_2 &= -\log K_2 \\`\
` \ce{H B^{-2}} &\ce{{} <=> {H+} + {B^{3-}}} & K_3 &= \ce{[H+] . [B^{3-}] \over [H B^{2-}]} & \mathrm{p}K_3 &= -\log K_3 `
\\end{align}
## Dissociation constant of water {#dissociation_constant_of_water}
The dissociation constant of water is denoted *K*~w~:
: $K_\mathrm{w} = [\ce{H}^+] [\ce{OH}^-]$
The concentration of water, \[H~2~O\], is omitted by convention, which means that the value of *K*~w~ differs from the value of *K*~eq~ that would be computed using that concentration.
The value of *K*~w~ varies with temperature, as shown in the table below. This variation must be taken into account when making precise measurements of quantities such as pH.
: {\| class=\"wikitable\" style=\"text-align:center;\"
\|- ! Water temperature ! *K*~w~ ! p*K*~w~ \|- \|`{{0|00}}`{=mediawiki}0 °C \|`{{0}}`{=mediawiki}0.112`{{e|-14}}`{=mediawiki} \|14.95 \|- \|`{{0}}`{=mediawiki}25 °C \|`{{0}}`{=mediawiki}1.023`{{e|-14}}`{=mediawiki} \|13.99 \|- \|`{{0}}`{=mediawiki}50 °C \|`{{0}}`{=mediawiki}5.495`{{e|-14}}`{=mediawiki} \|13.26 \|- \|`{{0}}`{=mediawiki}75 °C \|19.95`{{0}}`{=mediawiki}`{{e|-14}}`{=mediawiki} \|12.70 \|- \|100 °C \|56.23`{{0}}`{=mediawiki}`{{e|-14}}`{=mediawiki} \|12
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# Declaration of Arbroath
`thumb|upright=1.5|The '``Tyninghame``' copy of the Declaration from 1320, in the ``National Archives of Scotland`\
The **Declaration of Arbroath** (*Declaratio Arbroathis*; *Declaration o Aiberbrothock*; *Tiomnadh Bhruis*) is the name usually given to a letter, dated 6 April 1320 at Arbroath, written by Scottish barons and addressed to Pope John XXII. It constituted King Robert I\'s response to his excommunication for disobeying the pope\'s demand in 1317 for a truce in the First War of Scottish Independence. The letter asserted the antiquity of the independence of the Kingdom of Scotland, denouncing English attempts to subjugate it.
Generally believed to have been written in Arbroath Abbey by Bernard of Kilwinning (or of Linton), then Chancellor of Scotland and Abbot of Arbroath, and sealed by fifty-one magnates and nobles, the letter is the sole survivor of three created at the time. The others were a letter from the King of Scots, Robert I, and a letter from four Scottish bishops which all made similar points. The *Declaration* was intended to assert Scotland\'s status as an independent, sovereign state and defend Scotland\'s right to use military action when unjustly attacked.
Submitted in Latin, the *Declaration* was little known until the late 17th century, and is unmentioned by any of Scotland\'s major 16th-century historians. In the 1680s, the Latin text was printed for the first time and translated into English in the wake of the Glorious Revolution, after which time it was sometimes described as a declaration of independence.
## Overview
thumb\|upright=1.4\|right\|The Declaration of Arbroath included in the text of the *Scotichronicon* in the British Library. The *Declaration* was part of a broader diplomatic campaign, which sought to assert Scotland\'s position as an independent kingdom, rather than its being a feudal land controlled by England\'s Norman kings, as well as to lift the excommunication of Robert the Bruce. The pope had recognised Edward I of England\'s claim to overlordship of Scotland in 1305 and Bruce was excommunicated by the Pope for murdering John Comyn before the altar at Greyfriars Church in Dumfries in 1306. This excommunication was lifted in 1308; subsequently the pope threatened Robert with excommunication again if Avignon\'s demands in 1317 for peace with England were ignored. Warfare continued, and in 1320 John XXII again excommunicated Robert I. In reply, the *Declaration* was composed and signed and, in response, the papacy rescinded King Robert Bruce\'s excommunication and thereafter addressed him using his royal title.
The wars of Scottish independence began as a result of the deaths of King Alexander III of Scotland in 1286 and his heir the \"Maid of Norway\" in 1290, which left the throne of Scotland vacant and the subsequent succession crisis of 1290--1296 ignited a struggle among the Competitors for the Crown of Scotland, chiefly between the House of Comyn, the House of Balliol, and the House of Bruce who all claimed the crown. After July 1296\'s deposition of King John Balliol by Edward of England and then February 1306\'s killing of John Comyn III, Robert Bruce\'s rivals to the throne of Scotland were gone, and Robert was crowned king at Scone that year. Edward I, the \"Hammer of Scots\", died in 1307; his son and successor Edward II did not renew his father\'s campaigns in Scotland. In 1309 a parliament held at St Andrews acknowledged Robert\'s right to rule, received emissaries from the Kingdom of France recognising the Bruce\'s title, and proclaimed the independence of the kingdom from England.
By 1314 only Edinburgh, Berwick-upon-Tweed, Roxburgh, and Stirling remained in English hands. In June 1314 the Battle of Bannockburn had secured Robert Bruce\'s position as King of Scots; Stirling, the Central Belt, and much of Lothian came under Robert\'s control while the defeated Edward II\'s power on escaping to England via Berwick weakened under the sway of his cousin Henry, Earl of Lancaster. King Robert was thus able to consolidate his power, and sent his brother Edward Bruce to claim the Kingdom of Ireland in 1315 with an army landed in Ulster the previous year with the help of Gaelic lords from the Isles. Edward Bruce died in 1318 without achieving success, but the Scots campaigns in Ireland and in northern England were intended to press for the recognition of Robert\'s crown by King Edward. At the same time, it undermined the House of Plantagenet\'s claims to overlordship of the British Isles and halted the Plantagenets\' effort to absorb Scotland as had been done in Ireland and Wales. Thus were the Scots nobles confident in their letters to Pope John of the distinct and independent nature of Scotland\'s kingdom; the *Declaration of Arbroath* was one such. According to historian David Crouch, \"The two nations were mutually hostile kingdoms and peoples, and the ancient idea of Britain as an informal empire of peoples under the English king\'s presidency was entirely dead.\"
The text describes the ancient history of Scotland, in particular the *Scoti*, the Gaelic forebears of the Scots who the *Declaration* claims have origins in *Scythia Major* prior to migrating via Spain to Great Britain \"1,200 years from the Israelite people\'s crossing of the Red Sea\". The *Declaration* describes how the Scots had \"thrown out the Britons and completely destroyed the Picts\", resisted the invasions of \"the Norse, the Danes and the English\", and \"held itself ever since, free from all slavery\". It then claims that in the Kingdom of Scotland, \"one hundred and thirteen kings have reigned of their own Blood Royal, without interruption by foreigners\". The text compares Robert Bruce with the Biblical warriors Judah Maccabee and Joshua.
The *Declaration* made a number of points: that Edward I of England had unjustly attacked Scotland and perpetrated atrocities; that Robert the Bruce had delivered the Scottish nation from this peril; and, most controversially, that the independence of Scotland was the prerogative of the Scottish people, rather than the King of Scots.
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# Declaration of Arbroath
## Debates
Some have interpreted this last point as an early expression of popular sovereignty -- that government is contractual and that kings can be chosen by the community rather than by God alone. It has been considered to be the first statement of the contractual theory of monarchy underlying modern constitutionalism.
It has also been argued that the *Declaration* was not a statement of popular sovereignty (and that its signatories would have had no such concept) but a statement of royal propaganda supporting Bruce\'s faction. A justification had to be given for the rejection of King John Balliol in whose name William Wallace and Andrew de Moray had rebelled in 1297. The reason given in the *Declaration* is that Bruce was able to defend Scotland from English aggression whereas King John could not. `{{Blockquote|To this man, in as much as he saved our people, and for upholding our freedom, we are bound by right as much as by his merits, and choose to follow him in all that he does.}}`{=mediawiki} Whatever the true motive, the idea of a contract between King and people was advanced to the Pope as a justification for Bruce\'s coronation whilst John de Balliol, who had abdicated the Scottish throne, still lived as a Papal prisoner.
There is also recent scholarship that suggests that the Declaration was substantially derived from the 1317 Irish Remonstrance, also sent in protest of English actions. There are substantial similarities in content between the 1317 Irish Remonstrance and the Declaration of Arbroath, produced three years later. It is also clear that the drafters of the Declaration of Arbroath would have access to the 1317 Irish Remonstrance, it having been circulated to Scotland in addition to the Pope. It has been suggested therefore that the 1317 Remonstrance was a \"prototype\" for the Declaration of Arbroath, suggesting Irish-Scottish cooperation in attempts to protest against English interference.
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# Declaration of Arbroath
## Text
For the full text in Latin and a translation in English, See Declaration of Arbroath on WikiSource.
## Signatories
There are 39 names---eight earls and thirty-one barons---at the start of the document, all of whom may have had their seals appended, probably over the space of some time, possibly weeks, with nobles sending in their seals to be used. The folded foot of the document shows that at least eleven additional barons and freeholders (who were not noble) who were not listed on the head were associated with the letter. On the extant copy of the *Declaration* there are only 19 seals, and of those 19 people only 12 are named within the document. It is thought likely that at least 11 more seals than the original 39 might have been appended. The *Declaration* was then taken to the papal court at Avignon by Sir Adam Gordon, Sir Odard de Maubuisson, and Bishop Kininmund who was not yet a bishop and probably included for his scholarship. `{{multiple image|caption_align=center
| align = right
| direction = vertical
| width = 200
| image1 = Declaration of Arbroath translation 1.JPG
| caption1 =
| image2 = Declaration of Arbroath translation 2.JPG
| caption2 = The most-cited passages of the Declaration, translated from the Latin original as displayed on the walls of the [[National Museum of Scotland]].
}}`{=mediawiki}
The Pope heeded the arguments contained in the *Declaration*, influenced by the offer of support from the Scots for his long-desired crusade if they no longer had to fear English invasion. He exhorted Edward II in a letter to make peace with the Scots. However, it did not lead to his recognising Robert as King of Scots, and the following year was again persuaded by the English to take their side and issued six bulls to that effect.
Eight years later, on 1 March 1328, the new English king, Edward III, signed a peace treaty between Scotland and England, the Treaty of Edinburgh--Northampton. In this treaty, which was in effect until 1333, Edward renounced all English claims to Scotland. In October 1328, the interdict on Scotland, and the excommunication of its king, were removed by the Pope.
## Manuscript
The original copy of the *Declaration* that was sent to Avignon is lost. The only existing manuscript copy of the *Declaration* survives among Scotland\'s state papers, measuring 540mm wide by 675mm long (including the seals), it is held by the National Archives of Scotland in Edinburgh, a part of the National Records of Scotland.
The most widely known English language translation was made by Sir James Fergusson, formerly Keeper of the Records of Scotland, from text that he reconstructed using this extant copy and early copies of the original draft.
G. W. S. Barrow has shown that one passage in particular, often quoted from the Fergusson translation, was carefully written using different parts of *The Conspiracy of Catiline* by the Roman author, Sallust (86--35 BC) as the direct source:
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# Declaration of Arbroath
## List of signatories {#list_of_signatories}
Listed below are the signatories of the Declaration of Arbroath in 1320.
The letter itself is written in Latin. It uses the Latin versions of the signatories\' titles, and in some cases, the spelling of names has changed over the years. This list generally uses the titles of the signatories\' Wikipedia biographies.
- Duncan, Earl of Fife (changed sides in 1332)
- Thomas Randolph, Earl of Moray (nephew and supporter of King Robert although briefly fought for the English after being captured by them, Guardian of the Realm after Robert the Bruce\'s death)
- Patrick Dunbar, Earl of March (or Earl of Dunbar) (changed sides several times)
- Malise, Earl of Strathearn (King Robert loyalist)
- Malcolm, Earl of Lennox (King Robert loyalist)
- William, Earl of Ross (earlier betrayed King Robert\'s female relatives to the English)
- Magnús Jónsson, Earl of Orkney
- William de Moravia, Earl of Sutherland
- Walter, High Steward of Scotland (King Robert loyalist)
- William de Soules, Lord of Liddesdale and Butler of Scotland (later imprisoned for plotting against the King)
- Sir James Douglas, Lord of Douglas (one of King Robert\'s leading loyalists)
- Roger de Mowbray, Lord of Barnbougle and Dalmeny (later imprisoned for plotting against King Robert)
- David, Lord of Brechin (later executed for plotting against King Robert)
- David de Graham of Kincardine
- Ingram de Umfraville (fought on the English side at Bannockburn but then changed sides to support King Robert)
- John de Menteith, guardian of the earldom of Menteith (earlier betrayed William Wallace to the English)
- Alexander Fraser of Touchfraser and Cowie
- Gilbert de la Hay, Constable of Scotland (King Robert loyalist)
- Robert Keith, Marischal of Scotland (King Robert loyalist)
- Henry St Clair of Rosslyn
- John de Graham, Lord of Dalkeith, Abercorn & Eskdale
- David Lindsay of Crawford
- William Oliphant, Lord of Aberdalgie and Dupplin (briefly fought for the English)
- Patrick de Graham of Lovat
- John de Fenton, Lord of Baikie and Beaufort
- William de Abernethy of Saltoun
- David Wemyss of Wemyss
- William Mushet
- Fergus of Ardrossan
- Eustace Maxwell of Caerlaverock
- William Ramsay
- William de Monte Alto, Lord of Ferne
- Alan Murray
- Donald Campbell
- John Cameron
- Reginald le Chen, Lord of Inverugie and Duffus
- Alexander Seton
- Andrew de Leslie
- Alexander Straiton
In addition, the names of the following do not appear in the document\'s text, but their names are written on seal tags and their seals are present:
- Alexander de Lamberton (became a supporter of Edward Balliol after the Battle of Dupplin Moor, 1332)
- Edward Keith (subsequently Marischal of Scotland; d. 1346)
- Arthur Campbell (Bruce loyalist)
- Thomas de Menzies (Bruce loyalist)
- John de Inchmartin (became a supporter of Edward Balliol after the Battle of Dupplin Moor, 1332; d. after 1334)
- John Duraunt
- Thomas de Morham
## Legacy
In 1998 former majority leader Trent Lott succeeded in instituting an annual \"National Tartan Day\" on 6 April by resolution of the United States Senate. US Senate Resolution 155 of 10 November 1997 states that \"the Declaration of Arbroath, the Scottish Declaration of Independence, was signed on April 6, 1320 and the American Declaration of Independence was modeled \[sic\] on that inspirational document\". However this claim is generally unsupported by historians.
In 2016 the Declaration of Arbroath was placed on the UK Memory of the World Register, part of UNESCO\'s Memory of the World Programme.
2020 was the 700th anniversary of the Declaration of Arbroath\'s composition; an *Arbroath 2020* festival was arranged but postponed due to the COVID-19 pandemic. The National Museum of Scotland in Edinburgh planned to display the document to the public for the first time in fifteen years
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# Domino effect
A **domino effect** is the cumulative effect produced when one event sets off a series of similar or related events, a form of chain reaction. The term is an analogy to a falling row of dominoes. It typically refers to a linked sequence of events where the time between successive events is relatively short. The term can be used literally (about a series of actual collisions) or metaphorically (about causal linkages within systems such as global finance or politics).
The literal, mechanical domino effect is exploited in Rube Goldberg machines. In chemistry, the principle applies to a domino reaction, in which one chemical reaction sets up the conditions necessary for a subsequent one that soon follows. In the realm of process safety, a domino-effect accident is an initial undesirable event triggering additional ones in related equipment or facilities, leading to a total incident effect more severe than the primary accident alone.
The metaphorical usage implies that an outcome is inevitable or highly likely (as it has already started to happen) -- a form of slippery slope argument. When this outcome is actually unlikely (the argument is fallacious), it has also been called the *domino fallacy*
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# Diffusion pump
**Diffusion pumps** use a high speed jet of vapor to direct gas molecules in the pump throat down into the bottom of the pump and out the exhaust. They were the first type of high vacuum pumps operating in the regime of free molecular flow, where the movement of the gas molecules can be better understood as diffusion than by conventional fluid dynamics. Invented in 1915 by Wolfgang Gaede, he named it a *diffusion pump* since his design was based on the finding that gas cannot diffuse against the vapor stream, but will be carried with it to the exhaust. However, the principle of operation might be more precisely described as **gas-jet pump**, since diffusion also plays a role in other types of high vacuum pumps. In modern textbooks, the diffusion pump is categorized as a momentum transfer pump.
The diffusion pump is widely used in both industrial and research applications. Most modern diffusion pumps use silicone oil or polyphenyl ethers as the working fluid.
## History
In the late 19th century, most vacuums were created using a Sprengel pump, which had the advantage of being very simple to operate, and capable of achieving quite good vacuum given enough time. Compared to later pumps, however, the pumping speed was very slow and the vapor pressure of the liquid mercury limited the ultimate vacuum.
Following his invention of the molecular pump, Wolfgang Gaede invented the diffusion pump in 1915, and originally used elemental mercury as the working fluid. After its invention, the design was quickly commercialized by Leybold. It was then improved by Irving Langmuir and W. Crawford. Cecil Reginald Burch discovered the possibility of using silicone oil in 1928.
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# Diffusion pump
## Oil diffusion pumps {#oil_diffusion_pumps}
An oil diffusion pump is used to achieve higher vacuum (lower pressure) than is possible by use of positive displacement pumps alone. Although its use has been mainly associated within the high-vacuum range, down to 1e-9 mbar, diffusion pumps today can produce pressures approaching 1e-10 mbar when properly used with modern fluids and accessories. The features that make the diffusion pump attractive for high and ultra-high vacuum use are its high pumping speed for all gases and low cost per unit pumping speed when compared with other types of pump used in the same vacuum range. Diffusion pumps cannot discharge directly into the atmosphere, so a mechanical forepump is typically used to maintain an outlet pressure around 0.1 mbar.
The oil diffusion pump is operated with an oil of low vapor pressure. The high speed jet is generated by boiling the fluid and directing the vapor through a jet assembly. Note that the oil is gaseous when entering the nozzles. Within the nozzles, the flow changes from laminar to supersonic and molecular. Often, several jets are used in series to enhance the pumping action. The outside of the diffusion pump is cooled using either air flow, water lines or a water-filled jacket. As the vapor jet hits the outer cooled shell of the diffusion pump, the working fluid condenses and is recovered and directed back to the boiler. The pumped gases continue flowing to the base of the pump at increased pressure, flowing out through the diffusion pump outlet, where they are compressed to ambient pressure by the secondary mechanical forepump and exhausted.
Unlike turbomolecular pumps and cryopumps, diffusion pumps have no moving parts and as a result are quite durable and reliable. They can function over pressure ranges of 1e-10 to. They are driven only by convection and thus have a very low energy efficiency.
One major disadvantage of diffusion pumps is the tendency to backstream oil into the vacuum chamber. This oil can contaminate surfaces inside the chamber or upon contact with hot filaments or electrical discharges may result in carbonaceous or siliceous deposits. Due to backstreaming, oil diffusion pumps are not suitable for use with highly sensitive analytical equipment or other applications which require an extremely clean vacuum environment, but mercury diffusion pumps may be in the case of ultra high vacuum chambers used for metal deposition. Often cold traps and baffles are used to minimize backstreaming, although this results in some loss of pumping speed.
The oil of a diffusion pump cannot be exposed to the atmosphere when hot. If this occurs, the oil will oxidise and has to be replaced. If a fire occurs, the smoke and residue may contaminate other parts of the system.
### Oil types {#oil_types}
The least expensive diffusion pump oils are based on hydrocarbons which have been purified by double-distillation. Compared with the other fluids, they have higher vapor pressure, so are usually limited to a pressure of 1e-6 Torr. They are also the most likely to burn or explode if exposed to oxidizers.
The most common silicone oils used in diffusion pumps are trisiloxanes, which contain the chemical group Si-O-Si-O-Si, to which various phenyl groups or methyl groups are attached. These are available as the so-called 702 and 703 blends, which were formerly manufactured by Dow Corning. These can be further separated into 704 and 705 oils, which are made up of the isomers of tetraphenyl tetramethyl trisiloxane and pentaphenyl trimethyl trisiloxane respectively.
For pumping reactive species, usually a polyphenyl ether based oil is used. These oils are the most chemical and heat resistant type of diffusion pump oil.
## Steam ejectors {#steam_ejectors}
*Main article: Vacuum ejector*
The steam ejector is a popular form of pump for vacuum distillation and freeze-drying. A jet of steam entrains the vapour that must be removed from the vacuum chamber. Steam ejectors can have single or multiple stages, with and without condensers in between the stages. While both steam ejectors and diffusion pumps use jets of vapor to entrain gas, they work on fundamentally different principles - steam ejectors rely on viscous flow and mixing to pump gas, whereas diffusion pumps use molecular diffusion. This has several consequences. In diffusion pumps, the inlet pressure can be much lower than the static pressure of jet, whereas in steam ejectors the two pressures are about the same. Also, diffusion pumps are capable of much higher compression ratios, and cannot discharge directly to atmosphere
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# Domenico Alberti
**Domenico Alberti** (c. 1710 -- 14 October 1746 (according to other sources: 1740)) was an Italian singer, harpsichordist, and composer.
Alberti was born in Venice and studied music with Antonio Lotti. He wrote operas, songs, and sonatas for keyboard instruments, for which he is best known today. His sonatas frequently employ arpeggiated accompaniment in the left hand in one of several patterns that are now collectively known as *Alberti bass*. Alberti was one of the earliest composers to use those patterns, but was not the first or only one. The most well-known of these patterns consists of regular broken chords, with the lowest note sounding first, then the highest, then the middle and then the highest again, with the pattern repeated.
Today, Alberti is regarded as a minor composer, and his works are played or recorded only irregularly. However, the Alberti bass was used by many later composers, and it became an important element in much keyboard music of the classical music era.
An example of Alberti bass (Mozart\'s *Piano Sonata, K 545*):
In his own lifetime, Alberti was known as a singer, and often used to accompany himself on the harpsichord. In 1736, he served as a page for Pietro Andrea Cappello, the Venetian ambassador to Spain. While at the Spanish court, the famous castrato singer Farinelli heard him sing. Farinelli was said to have been impressed, although Alberti was an amateur.
Alberti\'s best known pieces are his keyboard sonatas, although even they are very rarely performed. It is thought he wrote around 36 sonatas, of which 14 have survived. They all have two movements, each in binary form.
It is probable that Mozart\'s first violin sonatas, written at the age of seven, were modeled on Alberti\'s work
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# Distillation
*Distill* (album)\|Distill (journal){{!}}*Distill* (journal)\|Distillate (motor fuel)}} `{{Use dmy dates|date=July 2019}}`{=mediawiki}
**Distillation**, also **classical distillation**, is the process of separating the component substances of a liquid mixture of two or more chemically discrete substances; the separation process is realized by way of the selective boiling of the mixture and the condensation of the vapors in a still.
Distillation can operate over a wide range of pressures from 0.14 bar (e.g., ethylbenzene/styrene) to nearly 21 bar (e.g.,propylene/propane) and is capable of separating feeds with high volumetric flowrates and various components that cover a range of relative volatilities from only 1.17 (o-xylene/m-xylene) to 81.2 (water/ethylene glycol). Distillation provides a convenient and time-tested solution to separate a diversity of chemicals in a continuous manner with high purity. However, distillation has an enormous environmental footprint, resulting in the consumption of approximately 25% of all industrial energy use. The key issue is that distillation operates based on phase changes, and this separation mechanism requires vast energy inputs.
Dry distillation (thermolysis and pyrolysis) is the heating of solid materials to produce gases that condense either into fluid products or into solid products. The term *dry distillation* includes the separation processes of destructive distillation and of chemical cracking, breaking down large hydrocarbon molecules into smaller hydrocarbon molecules. Moreover, a partial distillation results in partial separations of the mixture\'s components, which process yields nearly-pure components; partial distillation also realizes partial separations of the mixture to increase the concentrations of selected components. In either method, the separation process of distillation exploits the differences in the relative volatility of the component substances of the heated mixture.
In the industrial applications of classical distillation, the term *distillation* is used as a unit of operation that identifies and denotes a process of physical separation, not a chemical reaction; thus an industrial installation that produces distilled beverages, is a distillery of alcohol. These are some applications of the chemical separation process that is distillation:
- Distilling fermented products to yield alcoholic beverages with a high content by volume of ethyl alcohol.
- Desalination to produce potable water and for medico-industrial applications.
- Crude oil stabilisation, a partial distillation to reduce the vapor pressure of crude oil, which thus is safe to store and to transport, and thereby reduces the volume of atmospheric emissions of volatile hydrocarbons.
- Fractional distillation used in the midstream operations of an oil refinery for producing fuels and chemical raw materials for livestock feed.
- Cryogenic Air separation into the component gases --- oxygen, nitrogen, and argon --- for use as industrial gases.
- Chemical synthesis to separate impurities and unreacted materials.
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# Distillation
## History
### Iron Age {#iron_age}
Early evidence of distillation was found on Akkadian tablets dated c. 1200 \[\[BCE\]\] describing perfumery operations. The tablets provided textual evidence that an early, primitive form of distillation was known to the Babylonians of ancient Mesopotamia.
### Classical antiquity {#classical_antiquity}
#### Greek and Roman terminology {#greek_and_roman_terminology}
According to British chemist T. Fairley, neither the Greeks nor the Romans had any term for the modern concept of distillation. Words like \"distill\" would have referred to something else, in most cases a part of some process unrelated to what now is known as distillation. In the words of Fairley and German chemical engineer Norbert Kockmann respectively: `{{Blockquote|text=The Latin "distillo," from de-stillo, from stilla, a drop, referred to the dropping of a liquid by human or artificial means, and was applied to any process where a liquid was separated in drops. To distil in the modern sense could only be expressed in a roundabout manner.<ref>{{Cite journal |last=Fairley |first=T. |date=1907 |title=The Early History of Distillation |url=https://onlinelibrary.wiley.com/doi/10.1002/j.2050-0416.1907.tb02205.x |journal=Journal of the Institute of Brewing |language=en |volume=13 |issue=6 |pages=559–582 |doi=10.1002/j.2050-0416.1907.tb02205.x}}</ref>}}`{=mediawiki} `{{Blockquote|text=Distillation had a broader meaning in ancient and medieval times because nearly all purification and separation operations were subsumed under the term ''distillation'', such as filtration, crystallization, extraction, sublimation, or mechanical pressing of oil.<ref>{{Cite book |last=Kockmann |first=Norbert |url=https://www.academia.edu/43754849 |title=Distillation: Fundamentals and Principles |publisher=Academic Press |year=2014 |isbn=978-0-12-386547-2 |editor-last=Andrzej |editor-first=Górak |pages=1–43 |language=en |chapter=History of Distillation |doi=10.1016/B978-0-12-386547-2.00001-6 |editor-last2=Sorensen |editor-first2=Eva}}</ref>}}`{=mediawiki}According to Dutch chemical historian Robert J. Forbes, the word *distillare* (to drip off) when used by the Romans, e.g. Seneca and Pliny the Elder, was \"never used in our sense\".
#### Aristotle
Aristotle knew that water condensing from evaporating seawater is fresh: `{{Blockquote|text=I have proved by experiment that salt water evaporated forms fresh, and the vapour does not, when it condenses, condense into sea water again.}}`{=mediawiki} Letting seawater evaporate and condense into freshwater cannot be called \"distillation\" for distillation involves boiling, but the experiment may have been an important step towards distillation.
#### Alexandrian chemists {#alexandrian_chemists}
Early evidence of distillation has been found related to alchemists working in Alexandria in Roman Egypt in the 1st century CE.
Distilled water has been in use since at least c. 200 CE, when Alexander of Aphrodisias described the process. Work on distilling other liquids continued in early Byzantine Egypt under Zosimus of Panopolis in the 3rd century.
### Ancient India and China (1--500 CE) {#ancient_india_and_china_1500_ce}
Distillation was practiced in the ancient Indian subcontinent, which is evident from baked clay retorts and receivers found at Taxila, Shaikhan Dheri, and Charsadda in Pakistan and Rang Mahal in India dating to the early centuries of the Common Era. Frank Raymond Allchin says these terracotta distill tubes were \"made to imitate bamboo\". These \"Gandhara stills\" were only capable of producing very weak liquor, as there was no efficient means of collecting the vapors at low heat.
Distillation in China may have begun at the earliest during the Eastern Han dynasty (1st--2nd century CE).
### Islamic Golden Age {#islamic_golden_age}
Medieval Muslim chemists such as Jābir ibn Ḥayyān (Latin: Geber, ninth century) and Abū Bakr al-Rāzī (Latin: Rhazes, c. 865--925) experimented extensively with the distillation of various substances. The fractional distillation of organic substances plays an important role in the works attributed to Jābir, such as in the `{{transliteration|ar|Kitāb al-Sabʿīn}}`{=mediawiki} (\'The Book of Seventy\'), translated into Latin by Gerard of Cremona (c. 1114--1187) under the title *Liber de septuaginta*. The Jabirian experiments with fractional distillation of animal and vegetable substances, and to a lesser degree also of mineral substances, is the main topic of the *De anima in arte alkimiae*, an originally Arabic work falsely attributed to Avicenna that was translated into Latin and would go on to form the most important alchemical source for Roger Bacon (c. 1220--1292).
The distillation of wine is attested in Arabic works attributed to al-Kindī (c. 801--873 CE) and to al-Fārābī (c. 872--950), and in the 28th book of al-Zahrāwī\'s (Latin: Abulcasis, 936--1013) **Kitāb al-Taṣrīf\]\]** (later translated into Latin as **Liber servatoris**). In the twelfth century, recipes for the production of **aqua ardens** (\"burning water\", i.e., ethanol) by distilling wine with salt started to appear in a number of Latin works, and by the end of the thirteenth century it had become a widely known substance among Western European chemists. The works of Taddeo Alderotti (1223--1296) describe a method for concentrating alcohol involving repeated distillation through a water-cooled still, by which an alcohol purity of 90% could be obtained.
### Medieval China {#medieval_china}
The distillation of beverages began in the Southern Song (10th--13th century) and Jin (12th--13th century) dynasties, according to archaeological evidence. A still was found in an archaeological site in Qinglong, Hebei province, China, dating back to the 12th century. Distilled beverages were common during the Yuan dynasty (13th--14th century).
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# Distillation
## History
### Modern era {#modern_era}
In 1500, German alchemist Hieronymus Brunschwig published **\[\[Liber de arte distillandi de simplicibus\]\]** (*The Book of the Art of Distillation out of Simple Ingredients*), the first book solely dedicated to the subject of distillation, followed in 1512 by a much expanded version. Right after that, in 1518, the oldest surviving distillery in Europe, The Green Tree Distillery, was founded.
In 1651, John French published *The Art of Distillation*, the first major English compendium on the practice, but it has been claimed that much of it derives from Brunschwig\'s work. This includes diagrams with people in them showing the industrial rather than bench scale of the operation.
As alchemy evolved into the science of chemistry, vessels called retorts became used for distillations. Both alembics and retorts are forms of glassware with long necks pointing to the side at a downward angle to act as air-cooled condensers to condense the distillate and let it drip downward for collection. Later, copper alembics were invented. Riveted joints were often kept tight by using various mixtures, for instance a dough made of rye flour. These alembics often featured a cooling system around the beak, using cold water, for instance, which made the condensation of alcohol more efficient. These were called pot stills. Today, the retorts and pot stills have been largely supplanted by more efficient distillation methods in most industrial processes. However, the pot still is still widely used for the elaboration of some fine alcohols, such as cognac, Scotch whisky, Irish whiskey, tequila, rum, cachaça, and some vodkas. Pot stills made of various materials (wood, clay, stainless steel) are also used by bootleggers in various countries. Small pot stills are also sold for use in the domestic production of flower water or essential oils.
Early forms of distillation involved batch processes using one vaporization and one condensation. Purity was improved by further distillation of the condensate. Greater volumes were processed by simply repeating the distillation. Chemists reportedly carried out as many as 500 to 600 distillations in order to obtain a pure compound.
In the early 19th century, the basics of modern techniques, including pre-heating and reflux, were developed. In 1822, Anthony Perrier developed one of the first continuous stills, and then, in 1826, Robert Stein improved that design to make his patent still. In 1830, Aeneas Coffey got a patent for improving the design even further. Coffey\'s continuous still may be regarded as the archetype of modern petrochemical units. The French engineer Armand Savalle developed his steam regulator around 1846. In 1877, Ernest Solvay was granted a U.S. Patent for a tray column for ammonia distillation, and the same and subsequent years saw developments in this theme for oils and spirits.
With the emergence of chemical engineering as a discipline at the end of the 19th century, scientific rather than empirical methods could be applied. The developing petroleum industry in the early 20th century provided the impetus for the development of accurate design methods, such as the McCabe--Thiele method by Ernest Thiele and the Fenske equation. The first industrial plant in the United States to use distillation as a means of ocean desalination opened in Freeport, Texas in 1961 with the hope of bringing water security to the region. The availability of powerful computers has allowed direct computer simulations of distillation columns.
## Applications
The application of distillation can roughly be divided into four groups: laboratory scale, industrial distillation, distillation of herbs for perfumery and medicinals (herbal distillate), and food processing. The latter two are distinctively different from the former two in that distillation is not used as a true purification method but more to transfer all volatiles from the source materials to the distillate in the processing of beverages and herbs.
The main difference between laboratory scale distillation and industrial distillation are that laboratory scale distillation is often performed on a batch basis, whereas industrial distillation often occurs continuously. In batch distillation, the composition of the source material, the vapors of the distilling compounds, and the distillate change during the distillation. In batch distillation, a still is charged (supplied) with a batch of feed mixture, which is then separated into its component fractions, which are collected sequentially from most volatile to less volatile, with the bottoms -- remaining least or non-volatile fraction -- removed at the end. The still can then be recharged and the process repeated.
In continuous distillation, the source materials, vapors, and distillate are kept at a constant composition by carefully replenishing the source material and removing fractions from both vapor and liquid in the system. This results in a more detailed control of the separation process.
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# Distillation
## Idealized model {#idealized_model}
The boiling point of a liquid is the temperature at which the vapor pressure of the liquid equals the pressure around the liquid, enabling bubbles to form without being crushed. A special case is the normal boiling point, where the vapor pressure of the liquid equals the ambient atmospheric pressure.
It is a misconception that in a liquid mixture at a given pressure, each component boils at the boiling point corresponding to the given pressure, allowing the vapors of each component to collect separately and purely. However, this does not occur, even in an idealized system. Idealized models of distillation are essentially governed by Raoult\'s law and Dalton\'s law and assume that vapor--liquid equilibria are attained.
Raoult\'s law states that the vapor pressure of a solution is dependent on 1) the vapor pressure of each chemical component in the solution and 2) the fraction of solution each component makes up, a.k.a. the mole fraction. This law applies to ideal solutions, or solutions that have different components but whose molecular interactions are the same as or very similar to pure solutions.
Dalton\'s law states that the total pressure is the sum of the partial pressures of each individual component in the mixture. When a multi-component liquid is heated, the vapor pressure of each component will rise, thus causing the total vapor pressure to rise. When the total vapor pressure reaches the pressure surrounding the liquid, boiling occurs and liquid turns to gas throughout the bulk of the liquid. A mixture with a given composition has one boiling point at a given pressure when the components are mutually soluble. A mixture of constant composition does not have multiple boiling points.
An implication of one boiling point is that lighter components never cleanly \"boil first\". At boiling point, all volatile components boil, but for a component, its percentage in the vapor is the same as its percentage of the total vapor pressure. Lighter components have a higher partial pressure and, thus, are concentrated in the vapor, but heavier volatile components also have a (smaller) partial pressure and necessarily vaporize also, albeit at a lower concentration in the vapor. Indeed, batch distillation and fractionation succeed by varying the composition of the mixture. In batch distillation, the batch vaporizes, which changes its composition; in fractionation, liquid higher in the fractionation column contains more lights and boils at lower temperatures. Therefore, starting from a given mixture, it appears to have a boiling range instead of a boiling point, although this is because its composition changes: each intermediate mixture has its own, singular boiling point.
The idealized model is accurate in the case of chemically similar liquids, such as benzene and toluene. In other cases, severe deviations from Raoult\'s law and Dalton\'s law are observed, most famously in the mixture of ethanol and water. These compounds, when heated together, form an azeotrope, which is when the vapor phase and liquid phase contain the same composition. Although there are computational methods that can be used to estimate the behavior of a mixture of arbitrary components, the only way to obtain accurate vapor--liquid equilibrium data is by measurement.
It is not possible to completely purify a mixture of components by distillation, as this would require each component in the mixture to have a zero partial pressure. If ultra-pure products are the goal, then further chemical separation must be applied. When a binary mixture is vaporized and the other component, e.g., a salt, has zero partial pressure for practical purposes, the process is simpler.
### Batch or differential distillation {#batch_or_differential_distillation}
Heating an ideal mixture of two volatile substances, A and B, with A having the higher volatility, or lower boiling point, in a batch distillation setup (such as in an apparatus depicted in the opening figure) until the mixture is boiling results in a vapor above the liquid that contains a mixture of A and B. The ratio between A and B in the vapor will be different from the ratio in the liquid. The ratio in the liquid will be determined by how the original mixture was prepared, while the ratio in the vapor will be enriched in the more volatile compound, A (due to Raoult\'s Law, see above). The vapor goes through the condenser and is removed from the system. This, in turn, means that the ratio of compounds in the remaining liquid is now different from the initial ratio (i.e., more enriched in B than in the starting liquid).
The result is that the ratio in the liquid mixture is changing, becoming richer in component B. This causes the boiling point of the mixture to rise, which results in a rise in the temperature in the vapor, which results in a changing ratio of A : B in the gas phase (as distillation continues, there is an increasing proportion of B in the gas phase). This results in a slowly changing ratio of A : B in the distillate.
If the difference in vapour pressure between the two components A and B is large -- generally expressed as the difference in boiling points -- the mixture in the beginning of the distillation is highly enriched in component A, and when component A has distilled off, the boiling liquid is enriched in component B.
### Continuous distillation {#continuous_distillation}
Continuous distillation is an ongoing distillation in which a liquid mixture is continuously (without interruption) fed into the process and separated fractions are removed continuously as output streams occur over time during the operation. Continuous distillation produces a minimum of two output fractions, including at least one volatile distillate fraction, which has boiled and been separately captured as a vapor and then condensed to a liquid. There is always a bottoms (or residue) fraction, which is the least volatile residue that has not been separately captured as a condensed vapor.
Continuous distillation differs from batch distillation in the respect that concentrations should not change over time. Continuous distillation can be run at a steady state for an arbitrary amount of time. For any source material of specific composition, the main variables that affect the purity of products in continuous distillation are the reflux ratio and the number of theoretical equilibrium stages, in practice determined by the number of trays or the height of packing. Reflux is a flow from the condenser back to the column, which generates a recycle that allows a better separation with a given number of trays. Equilibrium stages are ideal steps where compositions achieve vapor--liquid equilibrium, repeating the separation process and allowing better separation given a reflux ratio. A column with a high reflux ratio may have fewer stages, but it refluxes a large amount of liquid, giving a wide column with a large holdup. Conversely, a column with a low reflux ratio must have a large number of stages, thus requiring a taller column.
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# Distillation
## Idealized model {#idealized_model}
### General improvements {#general_improvements}
Both batch and continuous distillations can be improved by making use of a fractionating column on top of the distillation flask. The column improves separation by providing a larger surface area for the vapor and condensate to come into contact. This helps it remain at equilibrium for as long as possible. The column can even consist of small subsystems (\'trays\' or \'dishes\') which all contain an enriched, boiling liquid mixture, all with their own vapor--liquid equilibrium.
There are differences between laboratory-scale and industrial-scale fractionating columns, but the principles are the same. Examples of laboratory-scale fractionating columns (in increasing efficiency) include:
- Air condenser
- Vigreux column (usually laboratory scale only)
- Packed column (packed with glass beads, metal pieces, or other chemically inert material)
- Spinning band distillation system.
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# Distillation
## Laboratory procedures {#laboratory_procedures}
Laboratory scale distillations are almost exclusively run as batch distillations. The device used in distillation, sometimes referred to as a *still*, consists at a minimum of a reboiler or *pot* in which the source material is heated, a condenser in which the heated vapor is cooled back to the liquid state, and a receiver in which the concentrated or purified liquid, called the distillate, is collected. Several laboratory scale techniques for distillation exist (see also distillation types).
A completely sealed distillation apparatus could experience extreme and rapidly varying internal pressure, which could cause it to burst open at the joints. Therefore, some path is usually left open (for instance, at the receiving flask) to allow the internal pressure to equalize with atmospheric pressure. Alternatively, a vacuum pump may be used to keep the apparatus at a lower than atmospheric pressure. If the substances involved are air- or moisture-sensitive, the connection to the atmosphere can be made through one or more drying tubes packed with materials that scavenge the undesired air components, or through bubblers that provide a movable liquid barrier. Finally, the entry of undesired air components can be prevented by pumping a low but steady flow of suitable inert gas, like nitrogen, into the apparatus.
### Simple distillation {#simple_distillation}
In simple distillation, the vapor is immediately channeled into a condenser. Consequently, the distillate is not pure but rather its composition is identical to the composition of the vapors at the given temperature and pressure. That concentration follows Raoult\'s law.
As a result, simple distillation is effective only when the liquid boiling points differ greatly (rule of thumb is 25 °C) or when separating liquids from non-volatile solids or oils. For these cases, the vapor pressures of the components are usually different enough that the distillate may be sufficiently pure for its intended purpose.
A cutaway schematic of a simple distillation operation is shown at right. The starting liquid 15 in the boiling flask 2 is heated by a combined hotplate and magnetic stirrer 13 via a silicone oil bath (orange, 14). The vapor flows through a short Vigreux column 3, then through a Liebig condenser 5, is cooled by water (blue) that circulates through ports 6 and 7. The condensed liquid drips into the receiving flask 8, sitting in a cooling bath (blue, 16). The adapter 10 has a connection 9 that may be fitted to a vacuum pump. The components are connected by ground glass joints.
### Fractional distillation {#fractional_distillation}
For many cases, the boiling points of the components in the mixture will be sufficiently close that Raoult\'s law must be taken into consideration. Therefore, fractional distillation must be used to separate the components by repeated vaporization-condensation cycles within a packed fractionating column. This separation, by successive distillations, is also referred to as rectification.
As the solution to be purified is heated, its vapors rise to the fractionating column. As it rises, it cools, condensing on the condenser walls and the surfaces of the packing material. Here, the condensate continues to be heated by the rising hot vapors; it vaporizes once more. However, the composition of the fresh vapors is determined once again by Raoult\'s law. Each vaporization-condensation cycle (called a *theoretical plate*) will yield a purer solution of the more volatile component. In reality, each cycle at a given temperature does not occur at exactly the same position in the fractionating column; *theoretical plate* is thus a concept rather than an accurate description.
More theoretical plates lead to better separations. A spinning band distillation system uses a spinning band of PTFE or metal to force the rising vapors into close contact with the descending condensate, increasing the number of theoretical plates.
### Steam distillation {#steam_distillation}
Like vacuum distillation, steam distillation is a method for distilling compounds which are heat-sensitive. The temperature of the steam is easier to control than the surface of a heating element and allows a high rate of heat transfer without heating at a very high temperature. This process involves bubbling steam through a heated mixture of the raw material. By Raoult\'s law, some of the target compound will vaporize (in accordance with its partial pressure). The vapor mixture is cooled and condensed, usually yielding a layer of oil and a layer of water.
Steam distillation of various aromatic herbs and flowers can result in two products: an essential oil as well as a watery herbal distillate. The essential oils are often used in perfumery and aromatherapy while the watery distillates have many applications in aromatherapy, food processing and skin care.
\[\[<File:perkin> triangle distillation apparatus.svg\|thumb\|Perkin triangle distillation setup {{#invoke:list\|horizontal_ordered
`| Stirrer bar/anti-bumping granules`\
`| Still pot`\
`| Fractionating column`\
`| Thermometer/Boiling point temperature`\
`| Teflon tap 1`\
`| Cold finger`\
`| Cooling water out`\
`| Cooling water in`\
`| Teflon tap 2`\
`| Vacuum/gas inlet`\
`| Teflon tap 3`\
`| Still receiver`
}}\]\]
### Vacuum distillation {#vacuum_distillation}
Some compounds have very high boiling points. To boil such compounds, it is often better to lower the pressure at which such compounds are boiled instead of increasing the temperature. Once the pressure is lowered to the vapor pressure of the compound (at the given temperature), boiling and the rest of the distillation process can commence. This technique is referred to as vacuum distillation and it is commonly found in the laboratory in the form of the rotary evaporator.
This technique is also very useful for compounds which boil beyond their decomposition temperature at atmospheric pressure and which would therefore be decomposed by any attempt to boil them under atmospheric pressure.
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# Distillation
## Laboratory procedures {#laboratory_procedures}
### Molecular distillation {#molecular_distillation}
Molecular distillation is vacuum distillation below the pressure of 0.01 torr. 0.01 torr is one order of magnitude above high vacuum, where fluids are in the free molecular flow regime, i.e., the mean free path of molecules is comparable to the size of the equipment. The gaseous phase no longer exerts significant pressure on the substance to be evaporated, and consequently, rate of evaporation no longer depends on pressure. That is, because the continuum assumptions of fluid dynamics no longer apply, mass transport is governed by molecular dynamics rather than fluid dynamics. Thus, a short path between the hot surface and the cold surface is necessary, typically by suspending a hot plate covered with a film of feed next to a cold plate with a line of sight in between. Molecular distillation is used industrially for purification of oils.
### Short path distillation {#short_path_distillation}
\[\[<File:short> path distillation apparatus.svg\|thumb\|right\|Short path vacuum distillation apparatus with vertical condenser (cold finger), to minimize the distillation path; {{#invoke:list\|horizontal_ordered
`| style=display:inline;`\
`| list_style=display:inline;`\
`| Still pot with stirrer bar/anti-bumping granules`\
`| Cold finger – bent to direct condensate`\
`| Cooling water out`\
`| cooling water in`\
`| Vacuum/gas inlet`\
`| Distillate flask/distillate.`
}}\]\] Short path distillation is a distillation technique that involves the distillate travelling a short distance, often only a few centimeters, and is normally done at reduced pressure. A classic example would be a distillation involving the distillate travelling from one glass bulb to another, without the need for a condenser separating the two chambers. This technique is often used for compounds which are unstable at high temperatures or to purify small amounts of compound. The advantage is that the heating temperature can be considerably lower (at reduced pressure) than the boiling point of the liquid at standard pressure, and the distillate only has to travel a short distance before condensing. A short path ensures that little compound is lost on the sides of the apparatus.
### Air-sensitive vacuum distillation {#air_sensitive_vacuum_distillation}
Some compounds have high boiling points as well as being air sensitive. A simple vacuum distillation system as exemplified above can be used, whereby the vacuum is replaced with an inert gas after the distillation is complete. However, this is a less satisfactory system if one desires to collect fractions under a reduced pressure. To do this a \"cow\" or \"pig\" adaptor can be added to the end of the condenser, or for better results or for very air sensitive compounds a Perkin triangle apparatus can be used.
The Perkin triangle has means via a series of glass or Teflon taps to allows fractions to be isolated from the rest of the still, without the main body of the distillation being removed from either the vacuum or heat source, and thus can remain in a state of reflux. To do this, the sample is first isolated from the vacuum by means of the taps, the vacuum over the sample is then replaced with an inert gas (such as nitrogen or argon) and can then be stoppered and removed. A fresh collection vessel can then be added to the system, evacuated and linked back into the distillation system via the taps to collect a second fraction, and so on, until all fractions have been collected.
### Zone distillation {#zone_distillation}
Zone distillation is a distillation process in a long container with partial melting of refined matter in moving liquid zone and condensation of vapor in the solid phase at condensate pulling in cold area. The process is worked in theory. When zone heater is moving from the top to the bottom of the container then solid condensate with irregular impurity distribution is forming. Then most pure part of the condensate may be extracted as product. The process may be iterated many times by moving (without turnover) the received condensate to the bottom part of the container on the place of refined matter. The irregular impurity distribution in the condensate (that is efficiency of purification) increases with the number of iterations. Zone distillation is the distillation analog of zone recrystallization. Impurity distribution in the condensate is described by known equations of zone recrystallization -- with the replacement of the distribution co-efficient k of crystallization - for the separation factor α of distillation.
### Closed-system vacuum distillation (cryovap) {#closed_system_vacuum_distillation_cryovap}
Non-condensable gas can be expelled from the apparatus by the vapor of relatively volatile co-solvent, which spontaneously evaporates during initial pumping, and this can be achieved with regular oil or diaphragm pump.
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# Distillation
## Laboratory procedures {#laboratory_procedures}
### Other types {#other_types}
- The process of reactive distillation involves using the reaction vessel as the still. In this process, the product is usually significantly lower boiling than its reactants. As the product is formed from the reactants, it is vaporized and removed from the reaction mixture. This technique is an example of a continuous vs. a batch process; advantages include less downtime to charge the reaction vessel with starting material, and less workup. Distillation \"over a reactant\" could be classified as a reactive distillation. It is typically used to remove volatile impurity from the distillation feed. For example, a little lime may be added to remove carbon dioxide from water followed by a second distillation with a little sulfuric acid added to remove traces of ammonia.
- Catalytic distillation is the process by which the reactants are catalyzed while being distilled to continuously separate the products from the reactants. This method is used to assist equilibrium reactions in reaching completion.
- Pervaporation is a method for the separation of mixtures of liquids by partial vaporization through a non-porous membrane.
- Extractive distillation is defined as distillation in the presence of a miscible, high boiling, relatively non-volatile component, the solvent, that forms no azeotrope with the other components in the mixture.
- Flash evaporation (or partial evaporation) is the partial vaporization that occurs when a saturated liquid stream undergoes a reduction in pressure by passing through a throttling valve or other throttling device. This process is one of the simplest unit operations, being equivalent to a distillation with only one equilibrium stage.
- Codistillation is distillation which is performed on mixtures in which the two compounds are not miscible. In the laboratory, the Dean-Stark apparatus is used for this purpose to remove water from synthesis products. The Bleidner apparatus is another example with two refluxing solvents.
- Membrane distillation is a type of distillation in which vapors of a mixture to be separated are passed through a membrane, which selectively permeates one component of mixture. Vapor pressure difference is the driving force. It has potential applications in seawater desalination and in removal of organic and inorganic components.
The unit process of evaporation may also be called \"distillation\":
- In rotary evaporation a vacuum distillation apparatus is used to remove bulk solvents from a sample. Typically the vacuum is generated by a water aspirator or a membrane pump.
- In a Kugelrohr apparatus a short path distillation apparatus is typically used (generally in combination with a (high) vacuum) to distill high boiling (\> 300 °C) compounds. The apparatus consists of an oven in which the compound to be distilled is placed, a receiving portion which is outside of the oven, and a means of rotating the sample. The vacuum is normally generated by using a high vacuum pump.
Other uses:
- Dry distillation or destructive distillation, despite the name, is not truly distillation, but rather a chemical reaction known as pyrolysis in which solid substances are heated in an inert or reducing atmosphere and any volatile fractions, containing high-boiling liquids and products of pyrolysis, are collected. The destructive distillation of wood to give methanol is the root of its common name -- *wood alcohol*.
- Freeze distillation is an analogous method of purification using freezing instead of evaporation. It is not truly distillation, but a recrystallization where the product is the mother liquor, and does not produce products equivalent to distillation. This process is used in the production of ice beer and ice wine to increase ethanol and sugar content, respectively. It is also used to produce applejack. Unlike distillation, freeze distillation concentrates poisonous congeners rather than removing them; As a result, many countries prohibit such applejack as a health measure. Also, distillation by evaporation can separate these since they have different boiling points.
- Distillation by filtration: In early alchemy and chemistry, otherwise known as natural philosophy, a form of \"distillation\" by capillary filtration was known as a form of distillation at the time. In this, a series of cups or bowls were set upon a stepped support with a \"wick\" of cotton or felt-like material, which had been wetted with water or a clear liquid with each step dripping down through the wetted cloth through capillary action in succeeding steps, creating a \"purification\" of the liquid, leaving solid materials behind in the upper bowls and purifying the succeeding product through capillary action through the moistened cloth. This was called \"distillatio\" by filtration by those using the method.
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# Distillation
## Azeotropic process {#azeotropic_process}
Interactions between the components of the solution create properties unique to the solution, as most processes entail non-ideal mixtures, where Raoult\'s law does not hold. Such interactions can result in a constant-boiling **azeotrope** which behaves as if it were a pure compound (i.e., boils at a single temperature instead of a range). At an azeotrope, the solution contains the given component in the same proportion as the vapor, so that evaporation does not change the purity, and distillation does not result in separation. For example, 95.6% ethanol (by mass) in water forms an azeotrope at 78.1 °C.
If the azeotrope is not considered sufficiently pure for use, there exist some techniques to break the azeotrope to give a more pure distillate. These techniques are known as **azeotropic distillation**. Some techniques achieve this by \"jumping\" over the azeotropic composition (by adding another component to create a new azeotrope, or by varying the pressure). Others work by chemically or physically removing or sequestering the impurity. For example, to purify ethanol beyond 95%, a drying agent (or desiccant, such as potassium carbonate) can be added to convert the soluble water into insoluble water of crystallization. Molecular sieves are often used for this purpose as well.
Immiscible liquids, such as water and toluene, easily form azeotropes. Commonly, these azeotropes are referred to as a low boiling azeotrope because the boiling point of the azeotrope is lower than the boiling point of either pure component. The temperature and composition of the azeotrope is easily predicted from the vapor pressure of the pure components, without use of Raoult\'s law. The azeotrope is easily broken in a distillation set-up by using a liquid--liquid separator (a decanter) to separate the two liquid layers that are condensed overhead. Only one of the two liquid layers is refluxed to the distillation set-up.
High boiling azeotropes, such as a 20 percent by weight mixture of hydrochloric acid in water, also exist. As implied by the name, the boiling point of the azeotrope is greater than the boiling point of either pure component.
### Breaking an azeotrope with unidirectional pressure manipulation {#breaking_an_azeotrope_with_unidirectional_pressure_manipulation}
The boiling points of components in an azeotrope overlap to form a band. By exposing an azeotrope to a vacuum or positive pressure, it is possible to bias the boiling point of one component away from the other by exploiting the differing vapor pressure curves of each; the curves may overlap at the azeotropic point, but are unlikely to remain identical further along the pressure axis to either side of the azeotropic point. When the bias is great enough, the two boiling points no longer overlap and so the azeotropic band disappears.
This method can remove the need to add other chemicals to a distillation, but it has two potential drawbacks.
Under negative pressure, power for a vacuum source is needed and the reduced boiling points of the distillates requires that the condenser be run cooler to prevent distillate vapors being lost to the vacuum source. Increased cooling demands will often require additional energy and possibly new equipment or a change of coolant.
Alternatively, if positive pressures are required, standard glassware can not be used, energy must be used for pressurization and there is a higher chance of side reactions occurring in the distillation, such as decomposition, due to the higher temperatures required to effect boiling.
A unidirectional distillation will rely on a pressure change in one direction, either positive or negative.
### Pressure-swing distillation {#pressure_swing_distillation}
Pressure-swing distillation is essentially the same as the unidirectional distillation used to break azeotropic mixtures, but here both positive and negative pressures may be employed.
This improves the selectivity of the distillation and allows a chemist to optimize distillation by avoiding extremes of pressure and temperature that waste energy. This is particularly important in commercial applications.
One example of the application of pressure-swing distillation is during the industrial purification of ethyl acetate after its catalytic synthesis from ethanol.
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# Distillation
## Industrial process {#industrial_process}
*Main article: Continuous distillation* Large scale industrial distillation applications include both batch and continuous fractional, vacuum, azeotropic, extractive, and steam distillation. The most widely used industrial applications of continuous, steady-state fractional distillation are in petroleum refineries, petrochemical and chemical plants and natural gas processing plants.
To control and optimize such industrial distillation, a standardized laboratory method, ASTM D86, is established. This test method extends to the atmospheric distillation of petroleum products using a laboratory batch distillation unit to quantitatively determine the boiling range characteristics of petroleum products.
Industrial distillation is typically performed in large, vertical cylindrical columns known as distillation towers or distillation columns with diameters ranging from about 0.65 to and heights ranging from about 6 to or more. When the process feed has a diverse composition, as in distilling crude oil, liquid outlets at intervals up the column allow for the withdrawal of different *fractions* or products having different boiling points or boiling ranges. The \"lightest\" products (those with the lowest boiling point) exit from the top of the columns and the \"heaviest\" products (those with the highest boiling point) exit from the bottom of the column and are often called the bottoms.
Industrial towers use reflux to achieve a more complete separation of products. Reflux refers to the portion of the condensed overhead liquid product from a distillation or fractionation tower that is returned to the upper part of the tower as shown in the schematic diagram of a typical, large-scale industrial distillation tower. Inside the tower, the downflowing reflux liquid provides cooling and condensation of the upflowing vapors thereby increasing the efficiency of the distillation tower. The more reflux that is provided for a given number of theoretical plates, the better the tower\'s separation of lower boiling materials from higher boiling materials. Alternatively, the more reflux that is provided for a given desired separation, the fewer the number of theoretical plates required. Chemical engineers must choose what combination of reflux rate and number of plates is both economically and physically feasible for the products purified in the distillation column.
Such industrial fractionating towers are also used in cryogenic air separation, producing liquid oxygen, liquid nitrogen, and high purity argon. Distillation of chlorosilanes also enables the production of high-purity silicon for use as a semiconductor.
Design and operation of a distillation tower depends on the feed and desired products. Given a simple, binary component feed, analytical methods such as the McCabe--Thiele method or the Fenske equation can be used. For a multi-component feed, simulation models are used both for design and operation. Moreover, the efficiencies of the vapor--liquid contact devices (referred to as \"plates\" or \"trays\") used in distillation towers are typically lower than that of a theoretical 100% efficient equilibrium stage. Hence, a distillation tower needs more trays than the number of theoretical vapor--liquid equilibrium stages. A variety of models have been postulated to estimate tray efficiencies.
In modern industrial uses, a packing material is used in the column instead of trays when low pressure drops across the column are required. Other factors that favor packing are: vacuum systems, smaller diameter columns, corrosive systems, systems prone to foaming, systems requiring low liquid holdup, and batch distillation. Conversely, factors that favor plate columns are: presence of solids in feed, high liquid rates, large column diameters, complex columns, columns with wide feed composition variation, columns with a chemical reaction, absorption columns, columns limited by foundation weight tolerance, low liquid rate, large turn-down ratio and those processes subject to process surges. This packing material can either be random or dumped packing (1 - wide) such as Raschig rings or structured sheet metal. Liquids tend to wet the surface of the packing and the vapors pass across this wetted surface, where mass transfer takes place. Unlike conventional tray distillation in which every tray represents a separate point of vapor--liquid equilibrium, the vapor--liquid equilibrium curve in a packed column is continuous. However, when modeling packed columns, it is useful to compute a number of \"theoretical stages\" to denote the separation efficiency of the packed column with respect to more traditional trays. Differently shaped packings have different surface areas and void space between packings. Both these factors affect packing performance.
Another factor in addition to the packing shape and surface area that affects the performance of random or structured packing is the liquid and vapor distribution entering the packed bed. The number of theoretical stages required to make a given separation is calculated using a specific vapor to liquid ratio. If the liquid and vapor are not evenly distributed across the superficial tower area as it enters the packed bed, the liquid to vapor ratio will not be correct in the packed bed and the required separation will not be achieved. The packing will appear to not be working properly. The height equivalent to a theoretical plate (HETP) will be greater than expected. The problem is not the packing itself but the mal-distribution of the fluids entering the packed bed. Liquid mal-distribution is more frequently the problem than vapor. The design of the liquid distributors used to introduce the feed and reflux to a packed bed is critical to making the packing perform to it maximum efficiency. Methods of evaluating the effectiveness of a liquid distributor to evenly distribute the liquid entering a packed bed can be found in references. Considerable work has been done on this topic by Fractionation Research, Inc. (commonly known as FRI).
### Multi-effect distillation {#multi_effect_distillation}
The goal of multi-effect distillation is to increase the energy efficiency of the process, for use in desalination, or in some cases one stage in the production of ultrapure water. The number of effects is inversely proportional to the kW·h/m^3^ of water recovered figure and refers to the volume of water recovered per unit of energy compared with single-effect distillation. One effect is roughly 636 kW·h/m^3^:
- Multi-stage flash distillation can achieve more than 20 effects with thermal energy input, as mentioned in the article.
- Vapor compression evaporation -- Commercial large-scale units can achieve around 72 effects with electrical energy input, according to manufacturers.
There are many other types of multi-effect distillation processes, including one referred to as simply multi-effect distillation (MED), in which multiple chambers, with intervening heat exchangers, are employed.
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# Distillation
## In food processing {#in_food_processing}
### Beverages
Carbohydrate-containing plant materials are allowed to ferment, producing a dilute solution of ethanol in the process. Spirits such as whiskey and rum are prepared by distilling these dilute solutions of ethanol. Components other than ethanol, including water, esters, and other alcohols, are collected in the condensate, which account for the flavor of the beverage. Some of these beverages are then stored in barrels or other containers to acquire more flavor compounds and characteristic flavors.
## Gallery
<File:Retort-in-operation-early-chemistry.png%7CChemistry> in its beginnings used retorts as laboratory equipment exclusively for distillation processes. <File:Distillation> of dry and oxygen-free toluene.jpg\| A simple set-up to distill dry and oxygen-free toluene. <File:Vacuum> Column.png\|Diagram of an industrial-scale vacuum distillation column as commonly used in oil refineries <File:Rotavapor.jpg%7CA> rotary evaporator is able to distill solvents more quickly at lower temperatures through the use of a vacuum. <File:Semi-microscale> distillation.jpg\|Distillation using semi-microscale apparatus. The jointless design eliminates the need to fit pieces together. The pear-shaped flask allows the last drop of residue to be removed, compared with a similarly sized round-bottom flask. The small holdup volume prevents losses. A \"pig\" is used to channel the various distillates into three receiving flasks. If necessary the distillation can be carried out under vacuum using the vacuum adapter at the pig
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# Duesberg hypothesis
The **Duesberg hypothesis** is the claim that AIDS is not caused by HIV, but instead that AIDS is caused by noninfectious factors such as recreational and pharmaceutical drug use and that HIV is merely a harmless passenger virus. The hypothesis was popularized by Peter Duesberg, a professor of biology at University of California, Berkeley, from whom the hypothesis gets its name. The scientific consensus is that the Duesberg hypothesis is incorrect and that HIV is the cause of AIDS. The most prominent supporters of the hypothesis are Duesberg himself, biochemist and vitamin proponent David Rasnick, and journalist Celia Farber. The scientific community generally contends that Duesberg\'s arguments in favor of the hypothesis are the result of cherry-picking predominantly outdated scientific data and selectively ignoring evidence that demonstrates HIV\'s role in causing AIDS.
## Role of legal and illegal drug use {#role_of_legal_and_illegal_drug_use}
Duesberg argues that there is a statistical correlation between trends in recreational drug use and trends in AIDS cases. He argues that the epidemic of AIDS cases in the 1980s corresponds to a supposed epidemic of recreational drug use in the United States and Europe during the same time frame.
These claims are not supported by epidemiologic data. The average yearly increase in opioid-related deaths from 1990 to 2002 was nearly three times the yearly increase from 1979 to 1990, with the greatest increase in 2000--2002, yet AIDS cases and deaths fell dramatically during the mid-to-late-1990s. Duesberg\'s claim that recreational drug use, rather than HIV, was the cause of AIDS has been specifically examined and found to be false. Cohort studies have found that only HIV-positive drug users develop opportunistic infections; HIV-negative drug users do not develop such infections, indicating that HIV rather than drug use is the cause of AIDS.
Duesberg has also argued that nitrite inhalants were the cause of the epidemic of Kaposi sarcoma (KS) in gay men. However, this argument has been described as an example of the fallacy of a statistical confounding effect; it is now known that a herpesvirus, potentiated by HIV, is responsible for AIDS-associated KS.
Moreover, in addition to recreational drugs, Duesberg argues that anti-HIV drugs such as zidovudine (AZT) can cause AIDS. Duesberg\'s claim that antiviral medication causes AIDS is regarded as disproven within the scientific community. Placebo-controlled studies have found that AZT as a single agent produces modest and short-lived improvements in survival and delays the development of opportunistic infections; it certainly did not cause AIDS, which develops in both treated and untreated study patients. With the subsequent development of protease inhibitors and highly active antiretroviral therapy, numerous studies have documented the fact that anti-HIV drugs prevent the development of AIDS and substantially prolong survival, further disproving the claim that these drugs \"cause\" AIDS.
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# Duesberg hypothesis
## Role of legal and illegal drug use {#role_of_legal_and_illegal_drug_use}
### Scientific study and rejection of Duesberg\'s risk-AIDS hypothesis {#scientific_study_and_rejection_of_duesbergs_risk_aids_hypothesis}
Several studies have specifically addressed Duesberg\'s claim that recreational drug abuse or sexual promiscuity were responsible for the manifestations of AIDS. An early study of his claims, published in *Nature* in 1993, found Duesberg\'s drug abuse-AIDS hypothesis to have \"no basis in fact.\"
A large prospective study followed a group of 715 homosexual men in the Vancouver, Canada, area; approximately half were HIV-seropositive or became so during the follow-up period, and the remainder were HIV-seronegative. After more than eight years of follow-up, despite similar rates of drug use, sexual contact, and other supposed risk factors in both groups, only the HIV-positive group suffered from opportunistic infections. Similarly, CD4 counts dropped in the patients who were HIV-infected, but remained stable in the HIV-negative patients, despite similar rates of risk behavior. The authors concluded that \"the risk-AIDS hypothesis \... is clearly rejected by our data,\" and that \"the evidence supports the hypothesis that HIV-1 has an integral role in the CD4 depletion and progressive immune dysfunction that characterise AIDS.\"
Similarly, the Multicenter AIDS Cohort Study (MACS) and the Women\'s Interagency HIV Study (WIHS)---which between them observed more than 8,000 Americans---demonstrated that \"the presence of HIV infection is the only factor that is strongly and consistently associated with the conditions that define AIDS.\" A 2008 study found that recreational drug use (including cannabis, cocaine, poppers, and amphetamines) had no effect on CD4 or CD8 T-cell counts, providing further evidence against a role of recreational drugs as a cause of AIDS.
## Current AIDS definitions {#current_aids_definitions}
Duesberg argued in 1989 that a significant number of AIDS victims had died without proof of HIV infection. However, with the use of modern culture techniques and polymerase chain reaction testing, HIV can be demonstrated in virtually all patients with AIDS. Since AIDS is now defined partially by the presence of HIV, Duesberg claims it is impossible by definition to offer evidence that AIDS does not require HIV. However, the first definitions of AIDS mentioned no cause and the first AIDS diagnoses were made before HIV was discovered. The addition of HIV positivity to surveillance criteria as an absolutely necessary condition for case reporting occurred only in 1993, after a scientific consensus was established that HIV caused AIDS.
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# Duesberg hypothesis
## AIDS in Africa {#aids_in_africa}
According to the Duesberg hypothesis, AIDS is not found in Africa. What Duesberg calls \"the myth of an African AIDS epidemic,\" among people\" exists for several reasons, including:
- The need, according to Duesberg, of the CDC, the WHO, and other health organizations to justify their existences, resulting in their \"manufacturing contagious plagues out of noninfectious medical conditions.\"
- Media sensationalism, with stories that \"helped shape the Western impression of an AIDS problem out of control,\" resulting in high levels of funding.
- Willing participation in deception by local doctors who wish to take advantage of this aid money: \"African doctors themselves participate in building the myth of the AIDS pandemic.\"
- Confusion or incompetence on the part of African doctors: \"Many common Third World diseases are confused with AIDS even if they are not part of its official definition.\"
Duesberg states that African AIDS cases are \"a collection of long-established, indigenous diseases, such as chronic fevers, weight loss, alias \"slim disease,\" diarrhea, and tuberculosis\" that result from malnutrition and poor sanitation. African AIDS cases, though, have increased in the last three decades as HIV\'s prevalence has increased but as malnutrition percentages and poor sanitation have declined in many African regions. In addition, while HIV and AIDS are more prevalent in urban than in rural settings in Africa, malnutrition and poor sanitation are found more commonly in rural than in urban settings.
According to Duesberg, common diseases are easily misdiagnosed as AIDS in Africa because \"the diagnosis of African AIDS is arbitrary\" and does not include HIV testing. A definition of AIDS agreed upon in 1985 by the World Health Organization in Bangui did not require a positive HIV test, but since 1985, many African countries have added positive HIV tests to the Bangui criteria for AIDS or changed their definitions to match those of the U.S. Centers for Disease Control. One of the reasons for using more HIV tests despite their expense is that, rather than overestimating AIDS as Duesberg suggests, the Bangui definition alone excluded nearly half of African AIDS patients.\"
Duesberg notes that diseases associated with AIDS differ between African and Western populations, concluding that the causes of immunodeficiency must be different. Tuberculosis is much more commonly diagnosed among AIDS patients in Africa than in Western countries, while PCP conforms to the opposite pattern. Tuberculosis, though, had higher prevalence in Africa than in the West before the spread of HIV. In Africa and the United States, HIV has spurred a similar percentage increase in tuberculosis cases. PCP may be underestimated in Africa: since machinery \"required for accurate testing is relatively rare in many resource-poor areas, including large parts of Africa, PCP is likely to be underdiagnosed in Africa. Consistent with this hypothesis, studies that report the highest rates of PCP in Africa are those that use the most advanced diagnostic methods\" Duesberg also claims that Kaposi\'s sarcoma is \"exclusively diagnosed in male homosexual risk groups using nitrite inhalants and other psychoactive drugs as aphrodisiacs\", but the cancer is fairly common among heterosexuals in some parts of Africa, and is found in heterosexuals in the United States as well.
Because reported AIDS cases in Africa and other parts of the developing world include a larger proportion of people who do not belong to Duesberg\'s preferred risk groups of drug addicts and male homosexuals, Duesberg writes on his website that \"There are no risk groups in Africa, like drug addicts and homosexuals.\" However, many studies have addressed the issue of risk groups in Africa and concluded that the risk of AIDS is not equally distributed. In addition, AIDS in Africa largely kills sexually active working-age adults.
South African president Thabo Mbeki accepted Duesberg\'s hypothesis and, through the mid-2000s, rejected offers of medical assistance to fight HIV infection, a policy of inaction that cost over 300,000 lives.
## Duesberg claims that retroviruses like HIV must be harmless to survive {#duesberg_claims_that_retroviruses_like_hiv_must_be_harmless_to_survive}
Duesberg argues that retroviruses like HIV must be harmless to survive: they do not kill cells and they do not cause cancer, he maintains. Duesberg writes, \"retroviruses do not kill cells because they depend on viable cells for the replication of their RNA from viral DNA integrated into cellular DNA.\" Duesberg elsewhere states that \"the typical virus reproduces by entering a living cell and commandeering the cell\'s resources in order to make new virus particles, a process that ends with the disintegration of the dead cell.\"
Duesberg also rejects the involvement of retroviruses and other viruses in cancer. To him, virus-associated cancers are \"freak accidents of nature\" that do not warrant research programs such as the war on cancer. Duesberg rejects a role in cancer for numerous viruses, including leukemia viruses, Epstein--Barr virus, human papilloma virus, hepatitis B, feline leukemia virus, and human T-lymphotropic virus.
Duesberg claims that the supposedly innocuous nature of all retroviruses is supported by what he considers to be their normal mode of proliferation: infection from mother to child *in utero*. Duesberg does not suggest that HIV is an endogenous retrovirus, a virus integrated into the germline and genetically heritable:
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# Duesberg hypothesis
## Scientific response to the Duesberg hypothesis {#scientific_response_to_the_duesberg_hypothesis}
The consensus in the scientific community is that the Duesberg hypothesis has been refuted by a large and growing mass of evidence showing that HIV causes AIDS, that the amount of virus in the blood correlates with disease progression, that a plausible mechanism for HIV\'s action has been proposed, and that anti-HIV medication decreases mortality and opportunistic infection in people with AIDS.
In `{{nat|the 9 December 1994}}`{=mediawiki} issue of *Science* (Vol. 266, No. 5191), Duesberg\'s methods and claims were evaluated in a group of articles. The authors concluded that
- It is abundantly evident that HIV causes disease and death in hemophiliacs, a group generally lacking Duesberg\'s proposed risk factors.
- HIV fulfills Koch\'s postulates, which are one set of criteria for demonstrating a causal relationship between a microbe and a disease. (Subsequently, additional data further demonstrated the fulfillment of Koch\'s postulates.)
- the AIDS epidemic in Thailand cited by Duesberg as confirmation of his hypothesis is in fact evidence of the role of HIV in AIDS.
- According to researchers who conducted large-scale studies of AZT, the drug does not cause AIDS. Furthermore, researchers acknowledged that recreational drugs do cause immune abnormalities, though not the type of immunodeficiency seen in AIDS.
### Effectiveness of antiretroviral medication {#effectiveness_of_antiretroviral_medication}
The vast majority of people with AIDS have never received antiretroviral drugs, including those in developed countries prior to the licensure of AZT (zidovudine) in 1987, and people in developing countries today where very few individuals have access to these medications.
The NIAID reports that `{{Blockquote|in the mid-1980s, clinical trials enrolling patients with AIDS found that AZT given as single-drug therapy conferred a modest survival advantage compared [with] placebo. Among HIV-infected patients who had not yet developed AIDS, placebo-controlled trials found that AZT given as single-drug therapy delayed, for a year or two, the onset of AIDS-related illnesses. Significantly, long-term follow-up of these trials did not show a prolonged benefit of AZT, but also did not indicate that the drug increased disease progression or mortality. The lack of excess AIDS cases and death in the AZT arms of these placebo-controlled trials in effect counters the argument that AZT causes AIDS. Subsequent clinical trials found that patients receiving two-drug combinations had up to 50 percent improvements in time to progression to AIDS and in survival when compared with people receiving single-drug therapy. In more recent years, three-drug combination therapies have produced another 50 to 80 percent improvement in progression to AIDS and in survival when compared with two-drug regimens in clinical trials.<ref>{{Cite web |url=http://www.hivatis.org/guidelines/adult/AA_040705.pdf |title=HHS, 2005 |access-date=24 August 2005 |archive-url=https://web.archive.org/web/20171004135919/http://www.hivatis.org/guidelines/adult/AA_040705.pdf |archive-date=4 October 2017 |url-status=dead }}</ref>}}`{=mediawiki}`{{Blockquote|Use of potent anti-HIV combination therapies has contributed to dramatic reductions in the incidence of AIDS and AIDS-related deaths in populations where these drugs are widely available, an effect which clearly would not be seen if antiretroviral drugs caused AIDS.<ref name="niaid"/>}}`{=mediawiki}
### Opponents claim that nearly all HIV-positive people will develop AIDS {#opponents_claim_that_nearly_all_hiv_positive_people_will_develop_aids}
Duesberg claims as support for his idea that many drug-free HIV-positive people have not yet developed AIDS; HIV/AIDS scientists note that many drug-free HIV-positive people have developed AIDS, and that, in the absence of medical treatment or rare genetic factors postulated to delay disease progression, it is very likely that nearly all HIV-positive people will eventually develop AIDS. Scientists also note that HIV-negative drug users do not suffer from immune system collapse
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# Diamagnetism
`{{Condensed matter physics}}`{=mediawiki}
**Diamagnetism** is the property of materials that are repelled by a magnetic field; an applied magnetic field creates an induced magnetic field in them in the opposite direction, causing a repulsive force. In contrast, paramagnetic and ferromagnetic materials are attracted by a magnetic field. Diamagnetism is a quantum mechanical effect that occurs in all materials; when it is the only contribution to the magnetism, the material is called diamagnetic. In paramagnetic and ferromagnetic substances, the weak diamagnetic force is overcome by the attractive force of magnetic dipoles in the material. The magnetic permeability of diamagnetic materials is less than the permeability of vacuum, *μ*~0~. In most materials, diamagnetism is a weak effect which can be detected only by sensitive laboratory instruments, but a superconductor acts as a strong diamagnet because it entirely expels any magnetic field from its interior (the Meissner effect).
Diamagnetism was first discovered when Anton Brugmans observed in 1778 that bismuth was repelled by magnetic fields. In 1845, Michael Faraday demonstrated that it was a property of matter and concluded that every material responded (in either a diamagnetic or paramagnetic way) to an applied magnetic field. On a suggestion by William Whewell, Faraday first referred to the phenomenon as *diamagnetic* (the prefix *dia-* meaning *through* or *across*), then later changed it to *diamagnetism*.
A simple rule of thumb is used in chemistry to determine whether a particle (atom, ion, or molecule) is paramagnetic or diamagnetic: If all electrons in the particle are paired, then the substance made of this particle is diamagnetic; If it has unpaired electrons, then the substance is paramagnetic.
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# Diamagnetism
## Materials
thumb\|left\|upright=1.4\|Diamagnetic material interaction in magnetic field. On keeping diamagnetic materials in a magnetic field, the electron orbital motion changes in such a way that magnetic dipole moments are induced on the atoms / molecules in the direction opposite to the external magnetic field
Diamagnetism is a property of all materials, and always makes a weak contribution to the material\'s response to a magnetic field. However, other forms of magnetism (such as ferromagnetism or paramagnetism) are so much stronger such that, when different forms of magnetism are present in a material, the diamagnetic contribution is usually negligible. Substances where the diamagnetic behaviour is the strongest effect are termed diamagnetic materials, or diamagnets. Diamagnetic materials are those that some people generally think of as *non-magnetic*, and include water, wood, most organic compounds such as petroleum and some plastics, and many metals including copper, particularly the heavy ones with many core electrons, such as mercury, gold and bismuth. The magnetic susceptibility values of various molecular fragments are called Pascal\'s constants (named after Paul Pascal (physicist)).
Diamagnetic materials, like water, or water-based materials, have a relative magnetic permeability that is less than or equal to 1, and therefore a magnetic susceptibility less than or equal to 0, since susceptibility is defined as `{{nowrap|''χ''<sub>v</sub> {{=}}`{=mediawiki} *μ*~v~ − 1}}. This means that diamagnetic materials are repelled by magnetic fields. However, since diamagnetism is such a weak property, its effects are not observable in everyday life. For example, the magnetic susceptibility of diamagnets such as water is `{{nowrap|''χ''<sub>v</sub> {{=}}`{=mediawiki} `{{val|-9.05|e=-6}}`{=mediawiki}}}. The most strongly diamagnetic material is bismuth, `{{nowrap|''χ''<sub>v</sub> {{=}}`{=mediawiki} `{{val|-1.66|e=-4}}`{=mediawiki}}}, although pyrolytic carbon may have a susceptibility of `{{nowrap|''χ''<sub>v</sub> {{=}}`{=mediawiki} `{{val|-4.00|e=-4}}`{=mediawiki}}} in one plane. Nevertheless, these values are orders of magnitude smaller than the magnetism exhibited by paramagnets and ferromagnets. Because *χ*~v~ is derived from the ratio of the internal magnetic field to the applied field, it is a dimensionless value.
In rare cases, the diamagnetic contribution can be stronger than paramagnetic contribution. This is the case for gold, which has a magnetic susceptibility less than 0 (and is thus by definition a diamagnetic material), but when measured carefully with X-ray magnetic circular dichroism, has an extremely weak paramagnetic contribution that is overcome by a stronger diamagnetic contribution.
Material *χ*~v~ \[× 10^−5^ (SI units)\]
------------------- --------------------------------
Superconductor −10^5^
Pyrolytic carbon −40.9
Bismuth −16.6
Neon −6.74
Mercury −2.9
Gold −2.8
Silver −2.6
Carbon (diamond) −2.1
Lead −1.8
Carbon (graphite) −1.6
Copper −1.0
Water −0.91
: Notable diamagnetic materials
### Superconductors
Superconductors may be considered perfect diamagnets (`{{nowrap|''χ''<sub>v</sub> {{=}}`{=mediawiki} −1}}), because they expel all magnetic fields (except in a thin surface layer) due to the Meissner effect.
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# Diamagnetism
## Demonstrations
### Curving water surfaces {#curving_water_surfaces}
If a powerful magnet (such as a supermagnet) is covered with a layer of water (that is thin compared to the diameter of the magnet) then the field of the magnet significantly repels the water. This causes a slight dimple in the water\'s surface that may be seen by a reflection in its surface.
### Levitation
Diamagnets may be levitated in stable equilibrium in a magnetic field, with no power consumption. Earnshaw\'s theorem seems to preclude the possibility of static magnetic levitation. However, Earnshaw\'s theorem applies only to objects with positive susceptibilities, such as ferromagnets (which have a permanent positive moment) and paramagnets (which induce a positive moment). These are attracted to field maxima, which do not exist in free space. Diamagnets (which induce a negative moment) are attracted to field minima, and there can be a field minimum in free space.
A thin slice of pyrolytic graphite, which is an unusually strongly diamagnetic material, can be stably floated in a magnetic field, such as that from rare earth permanent magnets. This can be done with all components at room temperature, making a visually effective and relatively convenient demonstration of diamagnetism.
The Radboud University Nijmegen, the Netherlands, has conducted experiments where water and other substances were successfully levitated. Most spectacularly, a live frog (see figure) was levitated.
In September 2009, NASA\'s Jet Propulsion Laboratory (JPL) in Pasadena, California announced it had successfully levitated mice using a superconducting magnet, an important step forward since mice are closer biologically to humans than frogs. JPL said it hopes to perform experiments regarding the effects of microgravity on bone and muscle mass.
Recent experiments studying the growth of protein crystals have led to a technique using powerful magnets to allow growth in ways that counteract Earth\'s gravity.
A simple homemade device for demonstration can be constructed out of bismuth plates and a few permanent magnets that levitate a permanent magnet.
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# Diamagnetism
## Theory
The electrons in a material generally settle in orbitals, with effectively zero resistance and act like current loops. Thus it might be imagined that diamagnetism effects in general would be common, since any applied magnetic field would generate currents in these loops that would oppose the change, in a similar way to superconductors, which are essentially perfect diamagnets. However, since the electrons are rigidly held in orbitals by the charge of the protons and are further constrained by the Pauli exclusion principle, many materials exhibit diamagnetism, but typically respond very little to the applied field.
The Bohr--Van Leeuwen theorem proves that there cannot be any diamagnetism or paramagnetism in a purely classical system. However, the classical theory of Langevin for diamagnetism gives the same prediction as the quantum theory. The classical theory is given below.
### Langevin diamagnetism {#langevin_diamagnetism}
Paul Langevin\'s theory of diamagnetism (1905) applies to materials containing atoms with closed shells (see dielectrics). A field with intensity `{{math|<var>B</var>}}`{=mediawiki}, applied to an electron with charge `{{math|<var>e</var>}}`{=mediawiki} and mass `{{math|<var>m</var>}}`{=mediawiki}, gives rise to Larmor precession with frequency `{{math|<var>ω</var> {{=}}`{=mediawiki} eB / 2m}}. The number of revolutions per unit time is`{{math|<var> ω</var> / 2{{pi}}}}`{=mediawiki}, so the current for an atom with `{{math|<var>Z</var>}}`{=mediawiki} electrons is (in SI units)
$$I = -\frac{Ze^2B}{4 \pi m}.$$
The magnetic moment of a current loop is equal to the current times the area of the loop. Suppose the field is aligned with the `{{math|<var>z</var>}}`{=mediawiki} axis. The average loop area can be given as $\scriptstyle \pi\left\langle\rho^2\right\rangle$, where $\scriptstyle \left\langle\rho^2\right\rangle$ is the mean square distance of the electrons perpendicular to the `{{math|<var>z</var>}}`{=mediawiki} axis. The magnetic moment is therefore
$$\mu = -\frac{Ze^2B}{4 m}\langle\rho^2\rangle.$$
If the distribution of charge is spherically symmetric, we can suppose that the distribution of `{{math|<var>x,y,z</var>}}`{=mediawiki} coordinates are independent and identically distributed. Then $\scriptstyle \left\langle x^2 \right\rangle \;=\; \left\langle y^2 \right\rangle \;=\; \left\langle z^2 \right\rangle \;=\; \frac{1}{3}\left\langle r^2 \right\rangle$, where $\scriptstyle \left\langle r^2 \right\rangle$ is the mean square distance of the electrons from the nucleus. Therefore, $\scriptstyle \left\langle \rho^2 \right\rangle \;=\; \left\langle x^2\right\rangle \;+\; \left\langle y^2 \right\rangle \;=\; \frac{2}{3}\left\langle r^2 \right\rangle$. If $n$ is the number of atoms per unit volume, the volume diamagnetic susceptibility in SI units is
$$\chi = \frac{\mu_0 n \mu}{B} = -\frac{\mu_0e^2 Zn }{6 m}\langle r^2\rangle.$$ In atoms, Langevin susceptibility is of the same order of magnitude as Van Vleck paramagnetic susceptibility.
### In metals {#in_metals}
The Langevin theory is not the full picture for metals because there are also non-localized electrons. The theory that describes diamagnetism in a free electron gas is called **Landau diamagnetism**, named after Lev Landau, and instead considers the weak counteracting field that forms when the electrons\' trajectories are curved due to the Lorentz force. Landau diamagnetism, however, should be contrasted with Pauli paramagnetism, an effect associated with the polarization of delocalized electrons\' spins. For the bulk case of a 3D system and low magnetic fields, the (volume) diamagnetic susceptibility can be calculated using Landau quantization, which in SI units is
$$\chi = -\mu_0\frac{e^2}{12\pi^2 m\hbar}\sqrt{2mE_{\rm F}},$$
where $E_{\rm F}$ is the Fermi energy. This is equivalent to $-\mu_0\mu_{\rm B}^2 g(E_{\rm F})/3$, exactly $-1/3$ times Pauli paramagnetic susceptibility, where $\mu_{\rm B}=e\hbar/2m$ is the Bohr magneton and $g(E)$ is the density of states (number of states per energy per volume). This formula takes into account the spin degeneracy of the carriers (spin-1/2 electrons).
In doped semiconductors the ratio between Landau and Pauli susceptibilities may change due to the effective mass of the charge carriers differing from the electron mass in vacuum, increasing the diamagnetic contribution. The formula presented here only applies for the bulk; in confined systems like quantum dots, the description is altered due to quantum confinement. Additionally, for strong magnetic fields, the susceptibility of delocalized electrons oscillates as a function of the field strength, a phenomenon known as the De Haas--Van Alphen effect, also first described theoretically by Landau
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# Difference engine
A **difference engine** is an automatic mechanical calculator designed to tabulate polynomial functions. It was designed in the 1820s, and was created by Charles Babbage. The name *difference engine* is derived from the method of finite differences, a way to interpolate or tabulate functions by using a small set of polynomial co-efficients. Some of the most common mathematical functions used in engineering, science and navigation are built from logarithmic and trigonometric functions, which can be approximated by polynomials, so a difference engine can compute many useful tables.
## History
The notion of a mechanical calculator for mathematical functions can be traced back to the Antikythera mechanism of the 2nd century BC, while early modern examples are attributed to Pascal and Leibniz in the 17th century.
In 1784 J. H. Müller, an engineer in the Hessian army, devised and built an adding machine and described the basic principles of a difference machine in a book published in 1786 (the first written reference to a difference machine is dated to 1784), but he was unable to obtain funding to progress with the idea.
### Charles Babbage\'s difference engines {#charles_babbages_difference_engines}
Charles Babbage began to construct a small difference engine in c. 1819 and had completed it by 1822 (Difference Engine 0). He announced his invention on 14 June 1822, in a paper to the Royal Astronomical Society, entitled \"Note on the application of machinery to the computation of astronomical and mathematical tables\". This machine used the decimal number system and was powered by cranking a handle. The British government was interested, since producing tables was time-consuming and expensive and they hoped the difference engine would make the task more economical.
In 1823, the British government gave Babbage £1700 to start work on the project. Although Babbage\'s design was feasible, the metalworking techniques of the era could not economically make parts in the precision and quantity required. Thus the implementation proved to be much more expensive and doubtful of success than the government\'s initial estimate. According to the 1830 design for Difference Engine No. 1, it would have about 25,000 parts, weigh 4 tons, and operate on 20-digit numbers by sixth-order differences. In 1832, Babbage and Joseph Clement produced a small working model (one-seventh of the plan), which operated on 6-digit numbers by second-order differences. Lady Byron described seeing the working prototype in 1833: \"We both went to see the thinking machine (or so it seems) last Monday. It raised several Nos. to the 2nd and 3rd powers, and extracted the root of a Quadratic equation.\" Lady Byron\'s daughter Ada Lovelace would later become fascinated with and work on creating the first computer program intended to solve Bernoulli\'s equation utilizing the difference engine. Work on the larger engine was suspended in 1833.
By the time the government abandoned the project in 1842, Babbage had received and spent over £17,000 on development, which still fell short of achieving a working engine. The government valued only the machine\'s output (economically produced tables), not the development (at unpredictable cost) of the machine itself. Babbage refused to recognize that predicament. Meanwhile, Babbage\'s attention had moved on to developing an analytical engine, further undermining the government\'s confidence in the eventual success of the difference engine. By improving the concept as an analytical engine, Babbage had made the difference engine concept obsolete, and the project to implement it an utter failure in the view of the government.
The incomplete Difference Engine No. 1 was put on display to the public at the 1862 International Exhibition in South Kensington, London.
Babbage went on to design his much more general analytical engine, but later designed an improved \"Difference Engine No. 2\" design (31-digit numbers and seventh-order differences), between 1846 and 1849. Babbage was able to take advantage of ideas developed for the analytical engine to make the new difference engine calculate more quickly while using fewer parts.
### Scheutzian calculation engine {#scheutzian_calculation_engine}
thumb\|upright=1.8\|Per Georg Scheutz\'s third difference engine, in the Science Museum, London
Inspired by Babbage\'s difference engine in 1834, the Swedish inventor Per Georg Scheutz built several experimental models. In 1837 his son Edward proposed to construct a working model in metal, and in 1840 finished the calculating part, capable of calculating series with 5-digit numbers and first-order differences, which was later extended to third-order (1842). In 1843, after adding the printing part, the model was completed.
In 1851, funded by the government, construction of the larger and improved (15-digit numbers and fourth-order differences) machine began, and finished in 1853. The machine was demonstrated at the World\'s Fair in Paris, 1855 and then sold in 1856 to the Dudley Observatory in Albany, New York. Delivered in 1857, it was the first printing calculator sold. In 1857 the British government ordered the next Scheutz\'s difference machine, which was built in 1859. It had the same basic construction as the previous one, weighing about 10 -Lcwt.
### Others
Martin Wiberg improved Scheutz\'s construction (c. 1859, his machine has the same capacity as Scheutz\'s: 30-digit and sixth-order) but used his device only for producing and publishing printed tables (interest tables in 1860, and logarithmic tables in 1875).
Alfred Deacon of London in c. 1862 produced a small difference engine (20-digit numbers and third-order differences).
American George B. Grant started working on his calculating machine in 1869, unaware of the works of Babbage and Scheutz (Schentz). One year later (1870) he learned about difference engines and proceeded to design one himself, describing his construction in 1871. In 1874 the Boston Thursday Club raised a subscription for the construction of a large-scale model, which was built in 1876. It could be expanded to enhance precision and weighed about 2000 lb.
Christel Hamann built one machine (16-digit numbers and second-order differences) in 1909 for the \"Tables of Bauschinger and Peters\" (\"Logarithmic-Trigonometrical Tables with eight decimal places\"), which was first published in Leipzig in 1910. It weighed about 40 kg.
Burroughs Corporation in about 1912 built a machine for the Nautical Almanac Office which was used as a difference engine of second-order. It was later replaced in 1929 by a Burroughs Class 11 (13-digit numbers and second-order differences, or 11-digit numbers and \[at least up to\] fifth-order differences).
Alexander John Thompson about 1927 built *integrating and differencing machine* (13-digit numbers and fifth-order differences) for his table of logarithms \"Logarithmetica britannica\". This machine was composed of four modified Triumphator calculators.
Leslie Comrie in 1928 described how to use the Brunsviga-Dupla calculating machine as a difference engine of second-order (15-digit numbers). He also noted in 1931 that National Accounting Machine Class 3000 could be used as a difference engine of sixth-order.
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# Difference engine
## History
### Construction of two working No. 2 difference engines {#construction_of_two_working_no._2_difference_engines}
During the 1980s, Allan G. Bromley, an associate professor at the University of Sydney, Australia, studied Babbage\'s original drawings for the Difference and Analytical Engines at the Science Museum library in London. This work led the Science Museum to construct a working calculating section of difference engine No. 2 from 1985 to 1991, under Doron Swade, the then Curator of Computing. This was to celebrate the 200th anniversary of Babbage\'s birth in 1991. In 2002, the printer which Babbage originally designed for the difference engine was also completed. The conversion of the original design drawings into drawings suitable for engineering manufacturers\' use revealed some minor errors in Babbage\'s design (possibly introduced as a protection in case the plans were stolen), which had to be corrected. The difference engine and printer were constructed to tolerances achievable with 19th-century technology, resolving a long-standing debate as to whether Babbage\'s design could have worked using Georgian-era engineering methods. The machine contains 8,000 parts and weighs about 5 tons.Press Releases {{!}} Computer History
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The printer\'s primary purpose is to produce stereotype plates for use in printing presses, which it does by pressing type into soft plaster to create a flong. Babbage intended that the Engine\'s results be conveyed directly to mass printing, having recognized that many errors in previous tables were not the result of human calculating mistakes but from slips in the manual typesetting process. The printer\'s paper output is mainly a means of checking the engine\'s performance.
In addition to funding the construction of the output mechanism for the Science Museum\'s difference engine, Nathan Myhrvold commissioned the construction of a second complete Difference Engine No. 2, which was on exhibit at the Computer History Museum in Mountain View, California, from May 2008 to January 2016. It has since been transferred to Intellectual Ventures in Seattle where it is on display just outside the main lobby.
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# Difference engine
## Operation
The difference engine consists of a number of columns, numbered from **1** to ***N***. The machine is able to store one decimal number in each column. The machine can only add the value of a column *n* + 1 to column *n* to produce the new value of *n*. Column *N* can only store a constant, column 1 displays (and possibly prints) the value of the calculation on the current iteration.
The engine is programmed by setting initial values to the columns. Column 1 is set to the value of the polynomial at the start of computation. Column 2 is set to a value derived from the first and higher derivatives of the polynomial at the same value of ***X***. Each of the columns from 3 to *N* is set to a value derived from the $(n-1)$ first and higher derivatives of the polynomial.
### Timing
In the Babbage design, one iteration (i.e. one full set of addition and carry operations) happens for each rotation of the main shaft. Odd and even columns alternately perform an addition in one cycle. The sequence of operations for column $n$ is thus:
1. Count up, receiving the value from column $n+1$ (Addition step)
2. Perform carry propagation on the counted up value
3. Count down to zero, adding to column $n-1$
4. Reset the counted-down value to its original value
Steps 1,2,3,4 occur for every odd column, while steps 3,4,1,2 occur for every even column.
While Babbage\'s original design placed the crank directly on the main shaft, it was later realized that the force required to crank the machine would have been too great for a human to handle comfortably. Therefore, the two models that were built incorporate a 4:1 reduction gear at the crank, and four revolutions of the crank are required to perform one full cycle.
### Steps
Each iteration creates a new result, and is accomplished in four steps corresponding to four complete turns of the handle shown at the far right in the picture below. The four steps are:
1. All even numbered columns (2,4,6,8) are added to all odd numbered columns (1,3,5,7) simultaneously. An interior sweep arm turns each even column to cause whatever number is on each wheel to count down to zero. As a wheel turns to zero, it transfers its value to a sector gear located between the odd/even columns. These values are transferred to the odd column causing them to count up. Any odd column value that passes from \"9\" to \"0\" activates a carry lever.
2. This is like Step 1, except it is odd columns (3,5,7) added to even columns (2,4,6), and column one has its values transferred by a sector gear to the print mechanism on the left end of the engine. Any even column value that passes from \"9\" to \"0\" activates a carry lever. The column 1 value, the result for the polynomial, is sent to the attached printer mechanism.
3. This is like Step 2, but for doing carries on even columns, and returning odd columns to their original values.
### Subtraction
The engine represents negative numbers as ten\'s complements. Subtraction amounts to addition of a negative number. This works in the same manner that modern computers perform subtraction, known as two\'s complement.
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# Difference engine
## Method of differences {#method_of_differences}
The principle of a difference engine is Newton\'s method of divided differences. If the initial value of a polynomial (and of its finite differences) is calculated by some means for some value of ***X***, the difference engine can calculate any number of nearby values, using the method generally known as the **method of finite differences**. For example, consider the quadratic polynomial
: $p(x) = 2x^2 - 3x + 2 \,$
with the goal of tabulating the values *p*(0), *p*(1), *p*(2), *p*(3), *p*(4), and so forth. The table below is constructed as follows: the second column contains the values of the polynomial, the third column contains the differences of the two left neighbors in the second column, and the fourth column contains the differences of the two neighbors in the third column:
x *p*(*x*) = 2*x*^2^ − 3*x* + 2 diff1(*x*) = ( *p*(*x* + 1) − p(*x*) ) diff2(*x*) = ( diff1(*x* + 1) − diff1(*x*) )
--- ------------------------------- ---------------------------------------- ----------------------------------------------
0 2 −1 4
1 1 3 4
2 4 7 4
3 11 11
4 22
The numbers in the third values-column are constant. In fact, by starting with any polynomial of degree *n*, the column number *n* + 1 will always be constant. This is the crucial fact behind the success of the method.
This table was built from left to right, but it is possible to continue building it from right to left down a diagonal in order to compute more values. To calculate *p*(5) use the values from the lowest diagonal. Start with the fourth column constant value of 4 and copy it down the column. Then continue the third column by adding 4 to 11 to get 15. Next continue the second column by taking its previous value, 22 and adding the 15 from the third column. Thus *p*(5) is 22 + 15 = 37. In order to compute *p*(6), we iterate the same algorithm on the *p*(5) values: take 4 from the fourth column, add that to the third column\'s value 15 to get 19, then add that to the second column\'s value 37 to get 56, which is *p*(6). This process may be continued *ad infinitum*. The values of the polynomial are produced without ever having to multiply. A difference engine only needs to be able to add. From one loop to the next, it needs to store 2 numbers---in this example (the last elements in the first and second columns). To tabulate polynomials of degree *n*, one needs sufficient storage to hold *n* numbers.
Babbage\'s difference engine No. 2, finally built in 1991, can hold 8 numbers of 31 decimal digits each and can thus tabulate 7th degree polynomials to that precision. The best machines from Scheutz could store 4 numbers with 15 digits each.
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# Difference engine
## Initial values {#initial_values}
The initial values of columns can be calculated by first manually calculating N consecutive values of the function and by backtracking (i.e. calculating the required differences).
Col $1_0$ gets the value of the function at the start of computation $f(0)$. Col $2_0$ is the difference between $f(1)$ and $f(0)$\...
If the function to be calculated is a polynomial function, expressed as
: $f(x) = a_n x^n + a_{n-1} x^{n-1} + \cdots + a_2 x^2 + a_1 x + a_0 \,$
the initial values can be calculated directly from the constant coefficients *a*~0~, *a*~1~,*a*~2~, \..., *a~n~* without calculating any data points. The initial values are thus:
- Col $1_0$ = *a*~0~
- Col $2_0$ = *a*~1~ + *a*~2~ + *a*~3~ + *a*~4~ + \... + *a~n~*
- Col $3_0$ = 2*a*~2~ + 6*a*~3~ + 14*a*~4~ + 30*a*~5~ + \...
- Col $4_0$ = 6*a*~3~ + 36*a*~4~ + 150*a*~5~ + \...
- Col $5_0$ = 24*a*~4~ + 240*a*~5~ + \...
- Col $6_0$ = 120*a*~5~ + \...
- $...$
### Use of derivatives {#use_of_derivatives}
Many commonly used functions are analytic functions, which can be expressed as power series, for example as a Taylor series. The initial values can be calculated to any degree of accuracy; if done correctly the engine will give exact results for first N steps. After that, the engine will only give an approximation of the function.
The Taylor series expresses the function as a sum obtained from its derivatives at one point. For many functions the higher derivatives are trivial to obtain; for instance, the sine function at 0 has values of 0 or $\pm1$ for all derivatives. Setting 0 as the start of computation we get the simplified Maclaurin series
$$\sum_{n=0}^{\infin} \frac{f^{(n)}(0)}{n!}\ x^{n}$$
The same method of calculating the initial values from the coefficients can be used as for polynomial functions. The polynomial constant coefficients will now have the value
$$a_n \equiv \frac{f^{(n)}(0)}{n!}$$
### Curve fitting {#curve_fitting}
The problem with the methods described above is that errors will accumulate and the series will tend to diverge from the true function. A solution which guarantees a constant maximum error is to use curve fitting. A minimum of *N* values are calculated evenly spaced along the range of the desired calculations. Using a curve fitting technique like Gaussian reduction an *N*−1th degree polynomial interpolation of the function is found. With the optimized polynomial, the initial values can be calculated as above
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# Draupnir
In Norse mythology, **Draupnir** (Old Norse: `{{IPA|non|ˈdrɔupnez̠|}}`{=mediawiki}, \"the dripper\") is a gold ring possessed by the god Odin with the ability to multiply itself: Every ninth night, eight new rings \'drip\' from Draupnir, each one of the same size and weight as the original.
Draupnir was forged by the dwarven brothers Brokkr and Eitri (or Sindri). Brokkr and Eitri made this ring as one of a set of three gifts which included Mjöllnir and Gullinbursti. They made these gifts in accordance with a bet Loki made saying that Brokkr and Eitri could not make better gifts than the three made by the Sons of Ivaldi. In the end, Mjöllnir, Thor\'s hammer, won the contest for Brokkr and Eitri. Loki used a loophole to get out of the wager for his head (the wager was for Loki\'s head only, but he argued that, to remove his head, they would have to injure his neck, which was not in the bargain) and Brokkr punished him by sealing his lips shut with wire.
The ring was placed by Odin on the funeral pyre of his son Baldr:
The ring was subsequently retrieved by Hermóðr. It was offered as a gift by Freyr\'s servant Skírnir in the wooing of Gerðr, which is described in the poem *Skírnismál*
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# Dromi
**Dromi** (*דרומי*) is a Hebrew surname
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# Decision problem
In computability theory and computational complexity theory, a **decision problem** is a computational problem that can be posed as a yes--no question on a set of input values. An example of a decision problem is deciding whether a given natural number is prime. Another example is the problem, \"given two numbers *x* and *y*, does *x* evenly divide *y*?\"
A **decision procedure** for a decision problem is an algorithmic method that answers the yes-no question on all inputs, and a decision problem is called **decidable** if there is a decision procedure for it. For example, the decision problem \"given two numbers *x* and *y*, does *x* evenly divide *y*?\" is decidable since there is a decision procedure called long division that gives the steps for determining whether *x* evenly divides *y* and the correct answer, *YES* or *NO*, accordingly. Some of the most important problems in mathematics are **undecidable**, e.g. the halting problem.
The field of computational complexity theory categorizes *decidable* decision problems by how difficult they are to solve. \"Difficult\", in this sense, is described in terms of the computational resources needed by the most efficient algorithm for a certain problem. On the other hand, the field of recursion theory categorizes *undecidable* decision problems by Turing degree, which is a measure of the noncomputability inherent in any solution.
## Definition
A *decision problem* is the formal language of all inputs for which the output (the answer to the yes-no question on a given input) is *YES*.
- These inputs can be natural numbers, but can also be values of some other kind, like binary strings or strings over some other alphabet.
```{=html}
<!-- -->
```
- For example, if every input can be encoded by the alphabet $\{0,1\}$, then a decision problem is a subset $L\subseteq\{0,1\}^*$.
```{=html}
<!-- -->
```
- For another example, using an encoding such as Gödel numbering, any string can be encoded as a natural number, via which a decision problem can be defined as a subset of the natural numbers. Therefore, the decision procedure of a decision problem is to compute the characteristic function of a subset of the natural numbers.
## Examples
A classic example of a decidable decision problem is the set of prime numbers. It is possible to effectively decide whether a given natural number is prime by testing every possible nontrivial factor. Although much more efficient procedures of primality testing are known, the existence of any effective procedure is enough to establish decidability.
## Decidability
- A decision problem is *decidable* or *effectively solvable* if the set of inputs for which the answer is *YES* is a recursive set.
- A decision problem is *partially decidable*, *semidecidable*, *solvable*, or *provable* if the set of inputs for which the answer is *YES* is a recursively enumerable set.
Problems that are not decidable are *undecidable*, which means it is not possible to create an algorithm (efficient or not) that solves them. The halting problem is an important undecidable decision problem; for more examples, see list of undecidable problems.
## Complete problems {#complete_problems}
Decision problems can be ordered according to many-one reducibility and related to feasible reductions such as polynomial-time reductions. A decision problem *P* is said to be *complete* for a set of decision problems *S* if *P* is a member of *S* and every problem in *S* can be reduced to *P*. Complete decision problems are used in computational complexity theory to characterize complexity classes of decision problems. For example, the Boolean satisfiability problem is complete for the class NP of decision problems under polynomial-time reducibility.
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# Decision problem
## Function problems {#function_problems}
Decision problems are closely related to function problems, which can have answers that are more complex than a simple *YES* or *NO*. A corresponding function problem is \"given two numbers *x* and *y*, what is *x* divided by *y*?\".
A function problem consists of a partial function *f*; the informal \"problem\" is to compute the values of *f* on the inputs for which it is defined.
Every function problem can be turned into a decision problem; the decision problem is just the graph of the associated function. (The graph of a function *f* is the set of pairs (*x*,*y*) such that *f*(*x*) = *y*.) If this decision problem were effectively solvable then the function problem would be as well. This reduction does not respect computational complexity, however. For example, it is possible for the graph of a function to be decidable in polynomial time (in which case running time is computed as a function of the pair (*x*,*y*)) when the function is not computable in polynomial time (in which case running time is computed as a function of *x* alone). The function *f*(*x*) = 2^*x*^ has this property.
Every decision problem can be converted into the function problem of computing the characteristic function of the set associated to the decision problem. If this function is computable then the associated decision problem is decidable. However, this reduction is more liberal than the standard reduction used in computational complexity (sometimes called polynomial-time many-one reduction); for example, the complexity of the characteristic functions of an NP-complete problem and its co-NP-complete complement is exactly the same even though the underlying decision problems may not be considered equivalent in some typical models of computation.
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# Decision problem
## Optimization problems {#optimization_problems}
Unlike decision problems, for which there is only one correct answer for each input, optimization problems are concerned with finding the *best* answer to a particular input. Optimization problems arise naturally in many applications, such as the traveling salesman problem and many questions in linear programming.
Function and optimization problems are often transformed into decision problems by considering the question of whether the output is *equal to* or *less than or equal to* a given value. This allows the complexity of the corresponding decision problem to be studied; and in many cases the original function or optimization problem can be solved by solving its corresponding decision problem. For example, in the traveling salesman problem, the optimization problem is to produce a tour with minimal weight. The associated decision problem is: for each *N*, to decide whether the graph has any tour with weight less than *N*. By repeatedly answering the decision problem, it is possible to find the minimal weight of a tour.
Because the theory of decision problems is very well developed, research in complexity theory has typically focused on decision problems. Optimization problems themselves are still of interest in computability theory, as well as in fields such as operations research
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# David Janssen
**David Janssen** (born **David Harold Meyer**; March 27, 1931 -- February 13, 1980) was an American film and television actor who is best known for his starring role as Richard Kimble in the television series *The Fugitive* (1963--1967). Janssen also had the title roles in three other series: *Richard Diamond, Private Detective*; *O\'Hara, U.S. Treasury*; and *Harry O*.
In 1996, *TV Guide* ranked him number 36 on its *50 Greatest TV Stars of All Time* list.
## Early life {#early_life}
David Janssen was born on March 27, 1931, in Naponee, a village in Franklin County in southern Nebraska. His father was Harold Edward Meyer, a banker, and his mother, Berniece Graf, was formerly Miss Nebraska and a Ziegfeld girl. Following his parents\' divorce in 1935, his mother moved with David to Los Angeles and married Eugene Janssen in 1940. David used his stepfather\'s name after he entered the show business as a child.
He attended Fairfax High School, where he excelled on the basketball court, setting a school scoring record that lasted over 20 years. His first film part was at the age of thirteen, and by the age of twenty-five, he had appeared in twenty films and served two years as an enlisted man in the United States Army. During his Army days, Janssen became a friend of fellow enlistees Martin Milner and Clint Eastwood while posted at Fort Ord, California.
## Acting career {#acting_career}
Janssen starred in four television series of his own:
- *Richard Diamond, Private Detective* (1957--1960)
- *The Fugitive* (1963--1967)
- *O\'Hara, U.S. Treasury* (1971--1972)
- *Harry O* (1974--1976)
At the time of its airing in August 1967, the final episode of *The Fugitive* held the record for the greatest number of American homes to watch a series finale -- 72 percent. In 1996 *TV Guide* ranked *The Fugitive* number 36 on its *50 Greatest Shows of All Time* list.
His films include: *To Hell and Back*, the biography of Audie Murphy, who was the most decorated American soldier of World War II; *Hell to Eternity*, a 1960 American World War II biopic starring Jeffrey Hunter as a Hispanic boy who fought in the Battle of Saipan and who was raised by Japanese-American foster parents; John Wayne\'s Vietnam war film *The Green Berets*; opposite Gregory Peck, in the space story *Marooned*, in which Janssen played an astronaut sent to rescue three stranded men in space; and *The Shoes of the Fisherman*, as a television journalist in Rome reporting on the election of a new Pope (Anthony Quinn).
He also played pilot Harry Walker in the 1973 action movie *Birds of Prey*. He starred as a Los Angeles police detective trying to clear himself in the killing of an apparently innocent doctor in the 1967 film *Warning Shot*, which was shot during a break in the spring and summer of 1966 between the third and fourth seasons of *The Fugitive.*
Janssen played an alcoholic in the 1977 TV movie *A Sensitive, Passionate Man*, which co-starred Angie Dickinson, and played an engineer who devises an unbeatable system for blackjack in the 1978 made-for-TV movie *Nowhere to Run*, co-starring Stefanie Powers and Linda Evans. Janssen\'s impressively husky voice was used to good effect as the narrator for the TV mini-series *Centennial* (1978--79); he also appeared in the final episode. And in 1979 he starred in the made-for-TV mini series *S.O.S. Titanic* as John Jacob Astor, playing opposite Beverly Ross as his wife, Madeleine.
Though Janssen\'s scenes were cut from the final release, he also appeared as a journalist in the film *Inchon*, which he accepted to work with Laurence Olivier, who played General Douglas MacArthur. At the time of his death, Janssen had just begun filming a television movie playing the part of Father Damien, the priest who dedicated himself to the leper colony on the island of Molokai, Hawaii. The part was eventually reassigned to actor Ken Howard of the CBS series *The White Shadow*.
<File:David> Janssen Richard Diamond 1957.JPG\|`{{center|David Janssen in 1957}}`{=mediawiki} <File:David> Janssen Richard Diamond 1959.JPG\|`{{center|Janssen as Richard Diamond (1959)}}`{=mediawiki} <File:David> Janssen Fugitive 1967.JPG\|David Janssen as Dr. Richard Kimble in the TV series *The Fugitive*, 1967 (final episode)
## Personal life {#personal_life}
Janssen was married twice, first to interior decorator Ellie Graham from 1958 until their divorce in 1968. In 1964, amid marital problems with Ellie, Janssen had a three-month affair with Suzanne Pleshette. In 1975, he married actress-turned-socialite Dani Crayne, and they remained married until Janssen\'s death in 1980.
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# David Janssen
## Death
Janssen was a heavy drinker, and a chain smoker who smoked up to four packs of cigarettes a day. He died from a sudden heart attack in the early morning of February 13, 1980, at his beachfront home in Malibu, California, at the age of 48. At the time of his death, Janssen was filming the television movie *Father Damien*. Janssen was buried at the Hillside Memorial Park Cemetery in Culver City, California. A non-denominational funeral was held at the Jewish chapel of the cemetery on February 17. Suzanne Pleshette delivered the eulogy at the request of Janssen\'s widow. Milton Berle, Johnny Carson, Tommy Gallagher, Richard Harris, Stan Herman, Rod Stewart, and Gregory Peck were among Janssen\'s pallbearers. Honorary pallbearers included Jack Lemmon, George Peppard, James Stewart, and Danny Thomas.
For his contribution to the television industry, David Janssen has a star on the Hollywood Walk of Fame located on the 7700 block of Hollywood Boulevard.
## Selected filmography {#selected_filmography}
- *It\'s a Pleasure* (1945) as Davey / Boy Referee (uncredited)
- *Swamp Fire* (1946) as Emile\'s Eldest Son (uncredited)
- *No Room for the Groom* (1952) as Soldier (scenes deleted)
- *Francis Goes to West Point* (1952) as Corporal Thomas
- *Untamed Frontier* (1952) as Lottie\'s Dance Partner (uncredited)
- *Bonzo Goes to College* (1952) as Jack (uncredited)
- *Yankee Buccaneer* (1952) as Beckett
- *Back at the Front* (1952) as Soldier (uncredited)
- *Leave It to Harry* (1954) as Quiz Show Host (short subject)
- *Chief Crazy Horse* (1955) as Lieutenant Colin Cartwright
- *Cult of the Cobra* (1955) as Rico Nardi
- *Francis in the Navy* (1955) as Lieutenant Anders
- *The Private War of Major Benson* (1955) as Young Lieutenant
- *To Hell and Back* (1955) as Lieutenant Lee
- *All That Heaven Allows* (1955) as Freddie Norton (uncredited)
- *The Square Jungle* (1955) as Jack Lindsay
- *Never Say Goodbye* (1956) as Dave Heller
- *The Toy Tiger* (1956) as Larry Tripps
- *Francis in the Haunted House* (1956) as Police Lieutenant Hopkins
- *Away All Boats* (1956) as Talker (uncredited)
- *Mr. Black Magic* (1956) as Master of Ceremonies (short subject)
- *Showdown at Abilene* (1956) as Verne Ward
- *The Girl He Left Behind* (1956) as Captain Genaro
- *Lafayette Escadrille* (1958) as Duke Sinclair
- *Hell to Eternity* (1960) as Sergeant Bill Hazen
- *Dondi* (1961) as Dealey
- *King of the Roaring 20s -- The Story of Arnold Rothstein* (1961) as Arnold Rothstein
- *Ring of Fire* (1961) as Sergeant Steve Walsh
- *Twenty Plus Two* (1961) as Tom Alder
- *Man-Trap* (1961) as Vince Biskay
- *My Six Loves* (1963) as Marty Bliss
- *Warning Shot* (1967) as Sergeant Tom Valens
- *The Green Berets* (1968) as George Beckworth
- *The Shoes of the Fisherman* (1968) as George Faber
- *Where It\'s At* (1969) as A.C.
- *Marooned* (1969) as Ted Dougherty
- *Generation* (1969) as Jim Bolton
- *Macho Callahan* (1970) as Diego Callahan
- *Once Is Not Enough* (1975) as Tom Colt
- *The Swiss Conspiracy* (1976) as David Christopher
- *Two-Minute Warning* (1976) as Steve
- *Warhead* (1977) as Tony Stevens
- *Golden Rendezvous* (1977) as Charles Conway
- *Covert Action* (1978) as Lester Horton
- *Inchon* (1981) as David Feld (scenes deleted after premiere; final film role; filmed in 1979; released posthumously)
### Television films {#television_films}
- *Belle Sommers* (1962) as Danny Castle
- *Night Chase* (1970) as Adrian Vico
- *The Longest Night* (1972) as Alan Chambers
- *Moon of the Wolf* (1972) as Sheriff Aaron Whitaker
- *Hijack* (1973) as Jake Wilkenson
- *Birds of Prey* (1973) as Harry Walker
- *Harry O -- Such Dust As Dreams Are Made On* (1973) as Harry Orwell
- *Pioneer Woman* (1973) as Robert Douglas
- *Harry O -- Smile Jenny, You\'re Dead* (1974) as Harry Orwell
- *Don\'t Call the Police* (1974) as Harry Orwell
- *Fer-de-Lance* (1974) as Russ Bogan
- *Stalk the Wild Child* (1976) as Dr. James Hazard
- *Mayday at 40,000 Feet!* (1976) as Captain Pete Douglass
- *A Sensitive, Passionate Man* (1977) as Michael Delaney
- *Superdome* (1978) as Mike Shelley
- *Nowhere to Run* (1978) as Harry Adams
- *S.O.S. Titanic* (1979) as John Jacob Astor
- *The Golden Gate Murders* (1979) as Detective Sergeant Paul Silver
- *High Ice* (1980) as Glencoe MacDonald
- *City in Fear* (1980) as Vince Perrino (released posthumously)
- *Father Damien: The Leper Priest* (1980) (Incomplete -- Replaced by Ken Howard)
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# David Janssen
## Selected filmography {#selected_filmography}
### Television series {#television_series}
- *Boston Blackie* (1951) (Season 1 Episode 2: \"Cop Killer\") as Armored Car Driver (uncredited)
- *Lux Video Theatre* (1955--1956) (3 episodes)
- (Season 5 Episode 30: \"It Grows on Trees\") (1955) as Ralph
- (Season 5 Episode 51: \"Perilous Deception\") (1955) as Joe Davies
- (Season 6 Episode 27: \"It Started With Eve\") (1956) as Johnny Reynolds Jr.
- *Matinee Theatre* (1956) (Episode 193: \"Belong to Me\") as Paul Merrick
- *Conflict* (1957) (Season 1 Episode 12: \"The Money\") as Sid Lukes
- *You Are There* (1957) (Season 5 Episode 8: \"The End of the Dalton Gang (October 5, 1892)\" as Grat Dalton
- *U.S. Marshal* (1 episode )
- *Alcoa Theatre* (1957--1958) (2 episodes)
- (Season 1 Episode 6: \"Cupid Wore a Badge\") (1957) as Mike Harper
- (Season 1 Episode 20: \"Decoy Duck\") (1958) as Jim McCandless
- *The Millionaire* (1957--1958) (2 episodes)
- (Season 4 Episode 14: \"The Regina Wainwright Story\") (1957) as Peter Miller
- (Season 5 Episode 5: \"The David Barrett Story\") (1958) as David Barrett
- *Dick Powell\'s Zane Grey Theatre* (1957--1959) (4 episodes)
- (Season 1 Episode 23: \"There Were Four\") (1957) as Danny Ensign
- (Season 2 Episode 14: \"Trial by Fear\") (1958) as Tod Owen
- (Season 3 Episode 1: \"Trail to Nowhere\") (1958) as Seth Larker
- (Season 3 Episode 15: \"Hang the Heart High\") (1959) as Dix Porter
- *Richard Diamond, Private Detective* (1957--1960) (77 episodes) as Richard Diamond / Chuck Garrett
- *Sheriff of Cochise* (1958) (Season 3 Episode 9: \"The Turkey Farmers\") as Arnie Hix
- *Westinghouse Desilu Playhouse* (1959) (Season 1 Episode 25: \"Two Counts of Murder\") as Ross Ingraham
- *Death Valley Days* (1961) (Season 9 Episode 18: \"Deadline at Austin\") as Dr. Bill Breckenridge
- *Adventures in Paradise* (1961) (Season 3 Episode 6: \"Show Me a Hero\") as Scotty Bell
- *Naked City* (1961--1963) (2 episodes)
- (Season 3 Episode 5: \"A Wednesday Night Story\") (1961) as Blair Cameron
- (Season 4 Episode 26: \"On the Battle Front: Every Minute is Important\") (1963) as Carl Ashland
- *Thriller* (1962)
- *Target: The Corruptors* (1962) (Season 1 Episode 19: \"The Middle Man\") as Robbie Wilson
- *General Electric Theater* (1962) (Season 10 Episode 20: \"Shadow of a Hero\") as Pat Howard
- *Follow the Sun* (1962) (Season 1 Episode 24: \"A Choice of Weapons\") as Johnny Sadowsky
- *Checkmate* (1962) (Season 2 Episode 25: \"Ride a Wild Horse\") as Len Kobalsky
- *Cain\'s Hundred* (1962) (Season 1 Episode 26: \"Inside Track\") as Dan Mullin
- *Kraft Mystery Theatre* (1962)
- *Route 66* (1962) (Season 3 Episode 1: \"One Tiger to a Hill\") as Karno Starling
- *The Eleventh Hour* (1962) (Season 1 Episode 3: \"Make Me a Place\") as Hal Kincaid
- *The Dick Powell Show* (1963) (Season 2 Episode 23: \"Thunder in a Forgotten Town\") as Kenneth \'Ken\' Morgan
- *The Fugitive* (1963--1967) (120 episodes) as Dr. Richard Kimble / varied aliases
- *The Hollywood Palace* (1965)
- *O\'Hara, U.S
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# Denarius
The ***denarius*** (`{{IPA|la|deːˈnaːriʊs|lang}}`{=mediawiki}; `{{plural form}}`{=mediawiki}: ***dēnāriī***, `{{IPA|la|deːˈnaːriiː|lang}}`{=mediawiki}) was the standard Roman silver coin from its introduction in the Second Punic War c. 211 BC to the reign of Gordian III (AD 238--244), when it was gradually replaced by the *antoninianus*. It continued to be minted in very small quantities, likely for ceremonial purposes, until and through the Tetrarchy (293--313).
The word *dēnārius* is derived from the Latin *dēnī* \"containing ten\", as its value was originally of 10 *assēs*. The word for \"money\" descends from it in Italian (*denaro*), Slovene (*denar*), Portuguese (*dinheiro*), and Spanish (*dinero*). Its name also survives in the dinar currency.
Its symbol is represented in Unicode as 𐆖 (U+10196), a numeral monogram that appeared on the obverse in the Republican period, denoting the 10 *asses* (\"X\") to 1 *denarius* (\"I\") conversion rate. However it can also be represented as X̶ (capital letter X with combining long stroke overlay).
## History
A predecessor of the *denarius* was first struck in 269 or 268 BC, five years before the First Punic War, with an average weight of 6.81 grams, or `{{frac|1|48}}`{=mediawiki} of a Roman pound. Contact with the Greeks had prompted a need for silver coinage in addition to the bronze currency that the Romans were using at that time. This predecessor of the *denarius* was a Greek-styled silver coin of *didrachm* weight, which was struck in Neapolis and other Greek cities in southern Italy. These coins were inscribed with a legend that indicated that they were struck for Rome, but in style they closely resembled their Greek counterparts. They were rarely seen at Rome, to judge from finds and hoards, and were probably used either to buy supplies or to pay soldiers.
The first distinctively Roman silver coin appeared around 226 BC. Classical historians have sometimes called these coins \"heavy *denarii*\", but they are classified by modern numismatists as *quadrigati*, a term which survives in one or two ancient texts and is derived from the *quadriga*, or four-horse chariot, on the reverse. This, with a two-horse chariot or *biga* which was used as a reverse type for some early *denarii*, was the prototype for the most common designs used on Roman silver coins for a number of years.
Rome overhauled its coinage shortly before 211 BC, and introduced the *denarius* alongside a short-lived denomination called the *victoriatus*. The *denarius* contained an average 4.5 grams, or `{{frac|1|72}}`{=mediawiki} of a Roman pound, of silver, and was at first tariffed at ten *asses*, hence its name, which means \'tenner\'. It formed the backbone of Roman currency throughout the Roman Republic and the early Empire.
The *denarius* began to undergo slow debasement toward the end of the republican period. Under the rule of Augustus (27 BC -- 14 AD) its weight fell to 3.9 grams (a theoretical weight of `{{frac|1|84}}`{=mediawiki} of a Roman pound). It remained at nearly this weight until the time of Nero (AD 37--68), when it was reduced to `{{frac|1|96}}`{=mediawiki} of a pound, or 3.4 grams. Debasement of the coin\'s silver content continued after Nero. Later Roman emperors also reduced its weight to 3 grams around the late 3rd century.
The value at its introduction was 10 *asses*, giving the *denarius* its name, which translates as \"containing ten\". In about 141 BC, it was re-tariffed at 16 *asses*, to reflect the decrease in weight of the *as*. The *denarius* continued to be the main coin of the Roman Empire until it was replaced by the antoninianus in the early 3rd century AD. The coin was last issued, in bronze, under Aurelian between 270 and 275 AD, and in the first years of the reign of Diocletian.
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# Denarius
## Debasement and evolution {#debasement_and_evolution}
+-----------+------------------------------+--------+-----------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Year | Event | Weight | Purity | Notes |
+===========+==============================+========+===========+=========================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================+
| 267 BC | Predecessor | 6.81 g | ? | pound. Equals 10 *assēs*, giving the *denarius* its name, which translates as \"containing ten\". The original copper coinage was weight-based, and was related to the Roman pound, the *libra*, which was about 325 g. The basic copper coin, the *as*, was to weigh 1 Roman pound. This was a large cast coin, and subdivisions of the *as* were used. The \"pound\" (*libra*, etc.) continued to be used as a currency unit, and survives e.g. in the British monetary system, which still uses the pound, abbreviated as £. |
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| 211 BC | Introduction | 4.55 g | 95--98% | pound. *Denarius* first struck. According to Pliny, it was established that the *denarius* should be given in exchange for ten pounds of bronze, the *quinarius* for five pounds, and the *sestertius* for two-and-a-half. But when the *as* was reduced in weight to one ounce, the *denarius* became equivalent to 16 *assēs*, the *quinarius* to eight, and the *sestertius* to four; although they retained their original names. It also appears, from Pliny and other writers, that the ancient *libra* was equivalent to 84 *denarii*. |
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| 200 BC | Debasement | 3.9 g | 95--98% | pound. |
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| 141 BC | Debasement | 3.9 g | 95--98% | pound. Retariffed to equal 16 *assēs* due to the decrease in weight of the *as*. |
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| 44 BC | Debasement | 3.9 g | 95--98% | Death of Julius Caesar, who set the *denarius* at 3.9 g. Legionary (professional soldier) pay was doubled to 225 *denarii* per year. |
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| 14--37 AD | | 3.9 g | 97.5--98% | Tiberius slightly improved the fineness as he gathered his infamous hoard of 675 million *denarii*. |
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| 64--68 | Debasement | 3.41 g | 93.5% | pound. This more closely matched the Greek *drachma*. In 64 AD, Nero reduced the standard of the *aureus* to 45 to the Roman pound (7.2 g) and of the *denarius* to 96 to the Roman pound (3.30 g). He also lowered the *denarius* to 94.5% fine. Successive emperors lowered the fineness of the *denarius*; in 180 Commodus reduced its weight by one-eighth to 108 to the pound. |
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| 85--107 | Debasement | 3.41 g | 93.5% | Reduction in silver content under Domitian |
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| 148--161 | Debasement | 3.41 g | 83.5% | |
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| 193--235 | Debasement | 3.41 g | 83.5% | Several emperors (193--235) steadily debased the *denarius* from a standard of 78.5% to 50% fine. In 212 Caracalla reduced the weight of the *aureus* from 45 to 50 to the Roman pound. They also coined the *aes* from a bronze alloy with a heavy lead admixture, and discontinued fractional denominations below the *as*. In 215 Caracalla introduced the *antoninianus* (5.1 g; 52% fine), a double *denarius*, containing 80% of the silver of two *denarii*. The coin invariably carried the radiate imperial portrait. Elagabalus demonetized the coin in 219, but the senatorial emperors Pupienus and Balbinus in 238 revived the *antoninianus* as the principal silver denomination which successive emperors reduced to a less intrinsically valuable billon coin (2.60 g; 2% fine). |
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| 241 | Debasement | 3.41 g | 48% | |
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| 274 | Double *Denarius* | 3.41 g | 5% | In 274, the emperor Aurelian reformed the currency and his denominations remained in use until the great recoinage of Diocletian in 293. Aurelian struck a radiate *aurelianianus* of increased weight (84 to the Roman pound) and fineness (5% fine) that was tariffed at five notational`{{clarify|date=July 2018}}`{=mediawiki} *denarii* (sometimes called \"common *denarii*\" or \"*denarii communes*\" by modern writers, although this phrase does not appear in any ancient text). The coin carried on the reverse the numerals XXI, or in Greek κα (both meaning 21 or 20:1). Some scholars believe that this shows that the coin was equal to 20 *sestertii*`{{clarify|date=July 2018}}`{=mediawiki} (or 5 *denarii*), but it is more likely that it was intended to guarantee that it contained `{{frac|1|20}}`{=mediawiki} or 5% of silver, and was thus slightly better than many of the coins in circulation. The *aureus* (minted at 50 or 60 to the Roman pound) was exchanged at rates of 600 to 1,000 *denarii*, equivalent to 120 to 200 *aurelianiani*. Rare fractions of billion`{{clarify|date=July 2018}}`{=mediawiki} *denarii*, and of bronze *sestertii* and *assēs*, were also coined. At the same time, Aurelian reorganized the provincial mint at Alexandria, and he minted an improved Alexandrine *tetradrachmon* that might`{{clarify|date=July 2018}}`{=mediawiki} have been tariffed at par with the *aurelianianus*. |
| | | | | |
| | | | | The emperor Tacitus in 276 briefly doubled the silver content of the *aurelianianus* and halved its tariffing`{{clarify|date=July 2018}}`{=mediawiki} to 2.5 d.c. (hence`{{clarify|date=July 2018}}`{=mediawiki} coins of Antioch and Tripolis (in Phoenicia) carry the value marks X.I), but Probus (276--282) immediately returned the *aurelianianus* to the standard and tariffing`{{clarify|date=July 2018}}`{=mediawiki} of Aurelian, and was the official tariffing until the reform of Diocletian in 293. |
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| 755 | *Novus denarius* (new penny) | | | Pepin the Short (`{{reign|751|768}}`{=mediawiki}), the first king of the Carolingian dynasty and father of Charlemagne, minted the *novus denarius* (\"new penny\"): 240 pennies minted from one Carolingian pound. So a single coin contained 21 grains of silver. Around 755, Pepin\'s Carolingian Reform established the European monetary system, which can be expressed as: 1 pound = 20 shillings = 240 pennies. Originally the pound was a weight of silver rather than a coin, and from a pound of pure silver 240 pennies were struck. The Carolingian Reform restored the silver content of the penny that was already in circulation and was the direct descendant of the Roman *denarius*. The shilling was equivalent to the *solidus*, the money of account that prevailed in Europe before the Carolingian Reform; it originated from the Byzantine gold coin that was the foundation of the international monetary system for more than 500 years. Debts contracted before the Carolingian Reform were defined in *solidi*. For three centuries following the Carolingian Reform, the only coin minted in Europe was the silver penny. Shillings and pounds were units of account used for convenience to express large numbers of pence, not actual coins. The Carolingian Reform also reduced the number of mints, strengthened royal authority over the mints, and provided for uniform design of coins. All coins bore the ruler\'s name, initial, or title, signifying royal sanction of the quality of the coins. Charlemagne spread the Carolingian system throughout Western Europe. The Italian *lira* and the French *livre* were derived from the Latin word for pound. Until the French Revolution, the unit of account in France was the *livre*, which equalled 20 *sols* or *sous*, each of which in turn equalled 12 *deniers*. During the Revolution the *franc* replaced the *livre*, and Napoleon\'s conquest spread the *franc* to Switzerland and Belgium. The Italian unit of account remained the *lira*, and in Britain the pound-shilling-penny relationship survived until 1971. Even in England the pennies were eventually debased, leaving 240 pennies representing substantially less than a pound of silver, and the pound as a monetary unit became divorced from a pound weight of silver. After the breakup of the Carolingian Empire pennies debased much faster, particularly in Mediterranean Europe, and in 1172 Genoa began minting a silver coin equal to four pennies. Rome, Florence, and Venice followed with coins of denominations greater than a penny, and late in the 12th century Venice minted a silver coin equal to 24 pennies. By the mid-13th century Florence and Genoa were minting gold coins, effectively ending the reign of the silver penny (*denier*, *denarius*) as the only circulating coin in Europe. |
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| 785 | Penny | | | Offa, king of Mercia, minted and introduced to England a penny of 22.5 grains of silver. The coin\'s designated value, however, was that of 24 troy grains of silver (one pennyweight, or `{{frac|1|240}}`{=mediawiki} of a troy pound, or about 1.56 grams), with the difference being a premium attached by virtue of the minting into coins (seigniorage). The penny led to the term \"penny weight\". 240 actual pennies (22.5 grains; minus the 1.5 grain for the seigniorage) weighed only 5,400 troy grains, known as a Saxon pound and later known as the tower pound, a unit used only by mints. The tower pound was abolished in the 16th century. However, 240 pennyweights (24 grains) made one troy pound of silver in weight, and the monetary value of 240 pennies also became known as a \"pound\". The silver penny remained the primary unit of coinage for about 500 years. |
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| 790 | Penny | 1.76 g | 95--96% | Charlemagne new penny with smaller diameter but greater weight. Average weight of 1.7 g, but ideal theoretical`{{clarify|date=July 2018}}`{=mediawiki} mass of 1.76 g. Purity is from 95% to 96%. |
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| | Penny | 1.58 g | 99% | Tower pound of 5400 grains abolished and replaced by the Troy pound of 5760 grains. |
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| 1158 | Penny | | 92.5% | The purity of 92.5% silver (i.e. sterling silver) was instituted by Henry II in 1158 with the \"Tealby Penny\" --- a hammered coin. |
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| 1500s | Penny | | | By the 16th century it contained about a third the silver content of a Troy pennyweight of 24 grains. |
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| 1915 | Penny | | | The penny, now struck in bronze, was worth around one-sixth of its value during the Middle Ages. British government sources suggest that there has been an 8700% price inflation since 1914, or an average of 4.2% annually. |
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| 1,641 |
Denarius
| 1 |
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# Denarius
## Value, comparisons and silver content {#value_comparisons_and_silver_content}
1 gold *aureus* = 2 gold *quinarii* = 25 silver *denarii* = 50 silver *quinarii* = 100 bronze *sestertii* = 200 bronze dupondii = 400 copper *asses* = 800 copper *semisses* = 1,600 copper *quadrantes*`{{When|date=July 2019}}`{=mediawiki}
It is difficult to give even rough comparative values for money from before the 20th century, as the range of products and services available for purchase was so different. During the republic (509 BC -- 27 BC), a legionary earned 112.5 *denarii* per year (0.3 *denarii* per day). Under Julius Caesar, this was doubled to 225 *denarii*/yr, with soldiers having to pay for their own food and arms, while in the reign of Augustus a Centurion received at least 3,750 *denarii* per year, and for the highest rank, 15,000 *denarii*.
By the late Roman Republic and early Roman Empire (c. 27 BC), a common soldier or unskilled laborer would be paid 1 *denarius*/day (with no tax deductions), around 300% inflation compared to the early period. Using the cost of bread as a baseline, this pay equates to around US\$20 in 2013 terms. Expressed in terms of the price of silver, and assuming 0.999 purity, a `{{frac|1|10}}`{=mediawiki} troy ounce *denarius* had a precious metal value of around US\$2.60 in 2021.
At the height of the Roman Empire a *sextarius* (546 ml or about 2`{{frac|1|4}}`{=mediawiki} American cups) of ordinary wine cost roughly one *dupondius* (`{{frac|8}}`{=mediawiki} of a *denarius*); after Diocletian\'s Edict on Maximum Prices was issued in 301 AD, the same item cost 8 debased common *denarii* -- 6300% inflation.
Silver content plummeted across the lifespan of the *denarius*. Under the Roman Empire (after Nero) the *denarius* contained approximately 50 grains, 3.24 grams, or 0.105 ozt (about `{{frac|1|10}}`{=mediawiki} troy ounce). The fineness of the silver content varied with political and economic circumstances. From a purity of greater than 90% silver in the 1st century AD, the *denarius* fell to under 60% purity by 200 AD, and plummeted to 5% purity by 300 AD. By the reign of Gallienus, the *antoninianus* was a copper coin with a thin silver wash.
| 352 |
Denarius
| 2 |
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# Denarius
## Influence
In the final years of the 1st century BC Tincomarus, a local ruler in southern Britain, started issuing coins that appear to have been made from melted down *denarii*. The coins of Eppillus, issued around Calleva Atrebatum around the same time, appear to have derived design elements from various *denarii*, such as those of Augustus and M. Volteius.
Even after the *denarius* was no longer regularly issued, it continued to be used as a unit of account, and the name was applied to later Roman coins in a way that is not understood. The Arabs who conquered large parts of the land that once belonged to the Eastern Roman Empire issued their own gold dinar. The lasting legacy of the *denarius* can be seen in the use of \"d\" as the abbreviation for the British penny until 1971. It also survived in France as the name of a coin, the denier. The *denarius* also survives in the common Arabic name for a currency unit, the *dinar* used from pre-Islamic times, and still used in several modern Arab nations. The major currency unit in former Principality of Serbia, Kingdom of Serbia and former Yugoslavia was *dinar*, and it is still used in present-day Serbia. The Macedonian currency *denar* is also derived from the Roman *denarius*. The Italian word *denaro*, the Spanish word *dinero*, the Portuguese word *dinheiro*, and the Slovene word **denar**, all meaning money, are also derived from Latin *denarius*. The pre-decimal currency of the United Kingdom until 1970 of pounds, shillings and pence was abbreviated as £sd, with \"d\" referring to *denarius* and standing for penny.
## Use in the Bible {#use_in_the_bible}
In the New Testament, the gospels refer to the *denarius* as a day\'s wage for a common laborer (Matthew 20:2, John 12:5). In the Book of Revelation, during the Third Seal: Black Horse, a choinix (\"quart\") of wheat and three quarts of barley were each valued at one *denarius*. Bible scholar Robert H. Mounce says the price of the wheat and barley as described in the vision appears to be ten to twelve times their normal cost in ancient times. Revelation thus describes a condition where basic goods are sold at greatly inflated prices. Thus, the black horse rider depicts times of deep scarcity or famine, but not of starvation. Apparently, a choinix of wheat was the daily ration of one adult. Thus, in the conditions pictured by Revelation 6, the normal income for a working-class family would buy enough food for only one person. The less costly barley would feed three people for one day\'s wages.
The *denarius* is also mentioned in the Parable of the Unforgiving Servant & in Parable of the Good Samaritan (Luke 10:25--37). The Render unto Caesar passage in Matthew 22:15--22 and Mark 12:13--17 uses the word (δηνάριον) to describe the coin held up by Jesus, translated in the King James Bible as \"tribute penny\". It is commonly thought to be a *denarius* with the head of Tiberius
| 500 |
Denarius
| 3 |
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# Della Rovere
The **House of Della Rovere** (`{{IPA|it|della ˈroːvere|pron}}`{=mediawiki}; literally \"of the oak tree\") was a powerful Italian noble family. It had humble origins in Savona, in Liguria, and acquired power and influence through nepotism and ambitious marriages arranged by two Della Rovere popes: Francesco Della Rovere, who ruled as Sixtus IV from 1471 to 1484 and his nephew Giuliano, who became Julius II in 1503.`{{r|trecc}}`{=mediawiki} Sixtus IV built the Sistine Chapel, which was named after him. Julius II was patron to Michelangelo, Raphael and many other Renaissance artists and started the modern rebuilt of St. Peter\'s Basilica. Also the Basilica of San Pietro in Vincoli in Rome was the family church of the Della Rovere. Members of the family were influential in the Church of Rome, and as dukes of Urbino, dukes of Sora and lords of Senigallia; the title of Urbino was extinguished with the death of Francesco Maria II in 1631, and the family died out with the death of his granddaughter Vittoria, Grand Duchess of Tuscany.`{{r|trecc}}`{=mediawiki}
## History
Francesco Della Rovere was born into a poor family in Liguria in north-west Italy in 1414, the son of Leonardo della Rovere of Savona.`{{r|trecc}}`{=mediawiki} A Franciscan who became Minister General of his order, then cardinal, he had a reputation for unworldliness until he was elected pope in 1471. As Sixtus IV he was both wealthy and powerful, and at once set about giving power and wealth to his nephews of the Della Rovere and Riario families. Within months of his election, he had made Giuliano della Rovere (the future pope Julius II) and Pietro Riario both cardinals and bishops; four other nephews were also made cardinals.`{{r|cronin|hibbert|page1=252|page2=128}}`{=mediawiki} He made Giovanni Della Rovere, who was not a priest, prefect of Rome, and arranged for him to marry into the da Montefeltro family, dukes of Urbino. Sixtus claimed descent from a noble Della Rovere family, the counts of Vinovo in Piemonte, and adopted their coat-of-arms.`{{r|trecc2}}`{=mediawiki}
Guidobaldo da Montefeltro adopted Francesco Maria I della Rovere, his sister\'s child and nephew of Pope Julius II. Guidobaldo I, who was heirless, called Francesco Maria at his court, and named him as heir of the Duchy of Urbino in 1504, this through the intercession of Julius II. In 1508, Francesco Maria inherited the duchy thereby starting the line of Rovere Dukes of Urbino. That dynasty ended in 1626 when Pope Urban VIII incorporated Urbino into the papal dominions. As compensation to the last sovereign duke, the title only could be continued by Francesco Maria II, and after his death by his heir, Federico Ubaldo.
Vittoria, last descendant of the della Rovere family (she was the only child of Federico Ubaldo), married Ferdinando II de\' Medici, Grand Duke of Tuscany. They had two children: Cosimo III, Tuscany\'s longest reigning monarch, and Francesco Maria de\' Medici, a prince of the Church.
## Della Rovere Dukes of Urbino (1508) {#della_rovere_dukes_of_urbino_1508}
1. Francesco Maria I della Rovere (1490--1538)
2. Guidobaldo II della Rovere (1514--1574)
3. Francesco Maria II della Rovere (1549--1631) - duchy abolished, title continued
4. Federico Ubaldo della Rovere (1605--1623) - title became extinct with his death.
## Other people with the same surname {#other_people_with_the_same_surname}
Among the many people who did not belong to this family, but bore the same name, are:
- the Della Rovere family, counts of Vinovo, among them:
- Domenico della Rovere of Vinovo, cardinal, who built the Castello Della Rovere (Vinovo) there
- his brother Cristoforo della Rovere of Vinovo`{{r|trecc3}}`{=mediawiki}
and various artists, including:
- the brothers Giovan Battista Della Rovere and Giovan Mauro Della Rovere, both known as \"il Fiamminghino\"
- an unrelated Lombard family of painters and illuminators active in the seventeenth century.`{{r|trecc4}}`{=mediawiki}
## Gallery
<File:Tizian> Portrait Papst Sixtus IV ca. 1545-46 Uffizien Florenz-01 (cropped).jpg\|Francesco della Rovere, later Sixtus IV <File:Pope> Julius II.jpg\|Giuliano della Rovere, later Julius II <File:Titian> - Portrait of Francesco Maria della Rovere, Duke of Urbino - WGA22982.jpg\|Francesco Maria I della Rovere <File:Titian> (Tiziano Vecellio) - Portrait of Guidobaldo II della Rovere, Duke of Urbino - 1956.7.1 - Yale University Art Gallery.jpg\|Guidobaldo II della Rovere <File:Francesco> II della Rovere.jpg\|Francesco Maria II della Rovere <File:Sustermans>, Justus - Vittoria della Rovere con una rosa.jpg\|Vittoria della Rovere
<File:Urbino>, palazzo ducale visto dal mercatale 02.JPG\|Palazzo Ducale, Urbino <File:Panoramica> P.za Duca Rocca.jpg\|Rocca Della Rovere in Senigallia <File:Rocca> Roveresca2 - Mondavio, Italia.JPG\|Rocca Roveresca in Mondavio <File:Palazzo> Della Rovere di San Lorenzo in Campo.JPG\|Palazzo Della Rovere in San Lorenzo in Campo <File:Borgo> - palazzo dei Penitenzieri 1150682
| 744 |
Della Rovere
| 0 |
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# Definable real number
Informally, a **definable real number** is a real number that can be uniquely specified by its description. The description may be expressed as a construction or as a formula of a formal language. For example, the positive square root of 2, $\sqrt{2}$, can be defined as the unique positive solution to the equation $x^2 = 2$, and it can be constructed with a compass and straightedge.
Different choices of a formal language or its interpretation give rise to different notions of definability. Specific varieties of definable numbers include the constructible numbers of geometry, the algebraic numbers, and the computable numbers. Because formal languages can have only countably many formulas, every notion of definable numbers has at most countably many definable real numbers. However, by Cantor\'s diagonal argument, there are uncountably many real numbers, so almost every real number is undefinable.
## Constructible numbers {#constructible_numbers}
One way of specifying a real number uses geometric techniques. A real number $r$ is a constructible number if there is a method to construct a line segment of length $r$ using a compass and straightedge, beginning with a fixed line segment of length 1.
Each positive integer, and each positive rational number, is constructible. The positive square root of 2 is constructible. However, the cube root of 2 is not constructible; this is related to the impossibility of doubling the cube.
## Real algebraic numbers {#real_algebraic_numbers}
A real number $r$ is called a real algebraic number if there is a polynomial $p(x)$, with only integer coefficients, so that $r$ is a root of $p$, that is, $p(r)=0$. Each real algebraic number can be defined individually using the order relation on the reals. For example, if a polynomial $q(x)$ has 5 real roots, the third one can be defined as the unique $r$ such that $q(r)=0$ and such that there are two distinct numbers less than $r$ at which $q$ is zero.
All rational numbers are constructible, and all constructible numbers are algebraic. There are numbers such as the cube root of 2 which are algebraic but not constructible.
The real algebraic numbers form a subfield of the real numbers. This means that 0 and 1 are algebraic numbers and, moreover, if $a$ and $b$ are algebraic numbers, then so are $a+b$, $a-b$, $ab$ and, if $b$ is nonzero, $a/b$.
The real algebraic numbers also have the property, which goes beyond being a subfield of the reals, that for each positive integer $n$ and each real algebraic number $a$, all of the $n$th roots of $a$ that are real numbers are also algebraic.
There are only countably many algebraic numbers, but there are uncountably many real numbers, so in the sense of cardinality most real numbers are not algebraic. This nonconstructive proof that not all real numbers are algebraic was first published by Georg Cantor in his 1874 paper \"On a Property of the Collection of All Real Algebraic Numbers\".
Non-algebraic numbers are called transcendental numbers. The best known transcendental numbers are `{{pi}}`{=mediawiki} and `{{mvar|[[e (mathematical constant)|e]]}}`{=mediawiki}.
## Computable real numbers {#computable_real_numbers}
A real number is a computable number if there is an algorithm that, given a natural number $n$, produces a decimal expansion for the number accurate to $n$ decimal places. This notion was introduced by Alan Turing in 1936.`{{r|turing}}`{=mediawiki}
The computable numbers include the algebraic numbers along with many transcendental numbers including $\pi$ `{{nowrap|and <math>e</math>.}}`{=mediawiki} Like the algebraic numbers, the computable numbers also form a subfield of the real numbers, and the positive computable numbers are closed under taking $n$th roots for each `{{nowrap|positive <math>n</math>.}}`{=mediawiki}
Not all real numbers are computable. Specific examples of noncomputable real numbers include the limits of Specker sequences, and algorithmically random real numbers such as Chaitin\'s Ω numbers.
| 623 |
Definable real number
| 0 |
8,361 |
# Definable real number
## Definability in arithmetic {#definability_in_arithmetic}
Another notion of definability comes from the formal theories of arithmetic, such as Peano arithmetic. The language of arithmetic has symbols for 0, 1, the successor operation, addition, and multiplication, intended to be interpreted in the usual way over the natural numbers. Because no variables of this language range over the real numbers, a different sort of definability is needed to refer to real numbers. A real number $a$ is *definable in the language of arithmetic* (or *arithmetical*) if its Dedekind cut can be defined as a predicate in that language; that is, if there is a first-order formula $\varphi$ in the language of arithmetic, with three free variables, such that $\forall m \, \forall n \, \forall p \left (\varphi(n,m,p)\iff\frac{(-1)^p\cdot n}{m+1}<a \right ).$ Here *m*, *n*, and *p* range over nonnegative integers.
The second-order language of arithmetic is the same as the first-order language, except that variables and quantifiers are allowed to range over sets of naturals. A real that is second-order definable in the language of arithmetic is called *analytical*.
Every computable real number is arithmetical, and the arithmetical numbers form a subfield of the reals, as do the analytical numbers. Every arithmetical number is analytical, but not every analytical number is arithmetical. Because there are only countably many analytical numbers, most real numbers are not analytical, and thus also not arithmetical.
Every computable number is arithmetical, but not every arithmetical number is computable. For example, the limit of a Specker sequence is an arithmetical number that is not computable.
The definitions of arithmetical and analytical reals can be stratified into the arithmetical hierarchy and analytical hierarchy. In general, a real is computable if and only if its Dedekind cut is at level $\Delta^0_1$ of the arithmetical hierarchy, one of the lowest levels. Similarly, the reals with arithmetical Dedekind cuts form the lowest level of the analytical hierarchy.
| 319 |
Definable real number
| 1 |
8,361 |
# Definable real number
## Definability in models of ZFC {#definability_in_models_of_zfc}
A real number $a$ is **first-order definable in the language of set theory, without parameters**, if there is a formula $\varphi$ in the language of set theory, with one free variable, such that $a$ is the unique real number such that $\varphi(a)$ holds.`{{r|kunen}}`{=mediawiki} This notion cannot be expressed as a formula in the language of set theory.
All analytical numbers, and in particular all computable numbers, are definable in the language of set theory. Thus the real numbers definable in the language of set theory include all familiar real numbers such as 0, 1, $\pi$, $e$, et cetera, along with all algebraic numbers. Assuming that they form a set in the model, the real numbers definable in the language of set theory over a particular model of ZFC form a field.
Each set model $M$ of ZFC set theory that contains uncountably many real numbers must contain real numbers that are not definable within $M$ (without parameters). This follows from the fact that there are only countably many formulas, and so only countably many elements of $M$ can be definable over $M$. Thus, if $M$ has uncountably many real numbers, one can prove from \"outside\" $M$ that not every real number of $M$ is definable over $M$.
This argument becomes more problematic if it is applied to class models of ZFC, such as the von Neumann universe. The assertion \"the real number $x$ is definable over the *class* model $N$\" cannot be expressed as a formula of ZFC.`{{r|hlr|tsirelson}}`{=mediawiki} Similarly, the question of whether the von Neumann universe contains real numbers that it cannot define cannot be expressed as a sentence in the language of ZFC. Moreover, there are countable models of ZFC in which all real numbers, all sets of real numbers, functions on the reals, etc. are definable
| 310 |
Definable real number
| 2 |
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# Dumnonii
The **Dumnonii** or **Dumnones** were a British tribe who inhabited Dumnonia, the area now known as Cornwall and Devon (and some areas of present-day Dorset and Somerset) in the further parts of the South West peninsula of Britain, from at least the Iron Age up to the early Saxon period. They were bordered to the east by the Durotriges tribe.
## Etymology
William Camden, in his 1607 edition of *Britannia*, describes Cornwall and Devon as being two parts of the same \'country\' which:`{{Blockquote|was in ancient time inhabited by those Britains whom [[Gaius Julius Solinus|Solinus]] called Dunmonii, [[Ptolemy|Ptolomee]] Damnonii, or (as we find in some other copies) more truly Danmonii. ... . But... the Country of this nation is at this day divided into two parts, known by later names of Cornwall and Denshire [Devonshire] ... The near or hithermore region of the Danmonians that I spake of is now commonly called Denshire, [or] by the Cornish-Britains 'Dewnan', and by the Welsh Britains 'Duffneint' [sic], that is, 'low valleys', for that the people dwell for the most part beneath in Vales; by the English Saxons [it is known as] 'Deven-schire', whereof grew the Latin name 'Devonia', and by that contraction which the vulgar people useth, 'Denshire'.<ref>{{cite web |last1=Southhall |first1=Humphrey |last2=Camden |first2=William |title=Home/Travel Writing/William Camden/Selection 8 |url=https://www.visionofbritain.org.uk/text/chap_page.jsp?t_id=Camden&c_id=8&cpub_id=0 |website=A vision of Britain through time |access-date=1 June 2024}}</ref>}}`{=mediawiki}
Camden had learnt some Welsh during the course of his studies and it would appear that he is the origin of the interpretation of Dumnonii as \"deep valley dwellers\" from his understanding of the Welsh of his time. The modern Welsh term is *Dyfnaint*. John Rhŷs later theorized that the tribal name was derived from the name of a goddess, *Domnu*, probably meaning \"the goddess of the deep\". The proto-Celtic root \*dubno- or \*dumno- meaning \"the deep\" or \"the earth\" (or alternatively meaning \"dark\" or \"gloomy\") appears in personal names such as Dumnorix and Dubnovellaunus. Another group with a similar name but with no known links were the Fir Domnann of Connacht.
The Roman name of the town of Exeter, *Isca Dumnoniorum* (\"Isca of the Dumnonii\"), contains the root *\*iska-* \"water\" for \"Water of the Dumnonii\". The Latin name suggests that the city was already an *oppidum*, or walled town, on the banks on the River Exe before the foundation of the Roman city, in about AD 50. The Dumnonii gave their name to the English county of Devon, and their name is represented in Britain\'s two extant Brythonic languages as *Dewnens* in Cornish and *Dyfnaint* in Welsh. Amédée Thierry (*Histoire des Gaulois*, 1828), one of the inventors of the historic race of Gauls, could confidently equate them with the Cornish (\"les Cornouailles\").
Victorian historians often referred to the tribe as the Damnonii, which is also the name of another people from lowland Scotland, although there are no known links between the two populations.
## Language
The people of Dumnonia spoke a Southwestern Brythonic dialect of Celtic similar to the forerunner of more recent Cornish and Breton. Irish immigrants, the Déisi, are evidenced by the Ogham-inscribed stones they have left behind, confirmed and supplemented by toponymical studies. The stones are sometimes inscribed in Latin, sometimes in both scripts. Tristram Risdon suggested the continuance of a Brythonic dialect in the South Hams, Devon, as late as the 14th century, in addition to its use in Cornwall.
## Territory
Ptolemy\'s 2nd century *Geography* places the Dumnonii to the west of the Durotriges. The name *purocoronavium* that appears in the Ravenna Cosmography implies the existence of a sub-tribe called the Cornavii or Cornovii, perhaps the ancestors of the Cornish people.
Gaius Iulius Solinus, probably in the 3rd century, remarks: \"This turbid strait also divides the island Silura from the shore which is held by the Dumnonii, a British tribe. The men of this island even now preserve an old custom: they do not use coins. They give and accept, obtaining the necessities of life by exchange rather than by money. They reverence gods, and the men and women equally declare knowledge of the future.\"
In the sub-Roman period a Brythonic kingdom called Dumnonia emerged, covering the entire peninsula, although it is believed by some to have effectively been a collection of sub-kingdoms.
A kingdom of Domnonée (and of Cornouaille alongside) was established in the province of Armorica directly across the English Channel, and has apparent links with the British population, suggesting an ancient connection of peoples along the western Atlantic seaboard which is also borne out by the modern genetics of Devonian and Cornish populations.
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# Dumnonii
## Settlements
### Isca Dumnoniorum {#isca_dumnoniorum}
The Latin name for Exeter is Isca Dumnoniorum (\"Water of the Dumnonii\"). This oppidum (a Latin term meaning an important town) on the banks of River Exe certainly existed prior to the foundation of the Roman city in about AD 50. *Isca* is derived from the Brythonic word for flowing water, which was given to the River Exe. The Gaelic term for water is *uisce/uisge*. This is reflected in the Welsh name for Exeter: *Caerwysg* meaning \"fortified settlement on the river Uisc\".
Isca Dumnoniorum originated with a settlement that developed around the Roman fortress of the Legio II Augusta and is one of the four *poleis* (cities) attributed to the tribe by Ptolemy. It is also listed in two routes of the late 2nd century Antonine Itinerary.
A legionary bath-house was built inside the fortress sometime between 55 and 60 and underwent renovation shortly afterwards (c. 60-65) but by c. 68 (perhaps even 66) the legion had transferred to a newer fortress at Gloucester. This saw the dismantling of the Isca fortress, and the site was then abandoned. Around AD 75, work on the *civitas forum* and *basilica* had commenced on the site of the former *principia* and by the late 2nd century the *civitas* walls had been completed. They were 3 metres thick and 6 metres high and enclosed exactly the same area as the earlier fortress. However, by the late 4th century the *civitas* was in decline.
### Other settlements {#other_settlements}
As well as Isca Dumnoniorum, Ptolemy\'s 2nd century *Geography* names three other towns:
- Voliba, which remains unidentified,
- Uxella, possibly on the River Axe, or at Launceston, and
- Tamara, generally considered to be somewhere on the River Tamar.
The Ravenna Cosmography includes the last two names (in slightly different forms, as \"Tamaris\" and \"Uxelis\"), and adds several more names which may be settlements in the territory. These include:
- Nemetostatio, a name relating to *nemeton*, signifying \"sanctuary\' or \"sacred grove\". Probably to be identified with North Tawton in Devon where there is a Roman earthwork that may be military, or possibly a tax collection station.
- Purocoronavis, which may refer to an important native hill fort, such as Carn Brea or Tintagel. The name has led to speculation about the Cornish Cornovii.
Other Romano-British sites in Dumnonia include:
- Topsham, Devon - a settlement and harbour that served Isca Dumnoniorum to which it was connected by road and river.
- Nanstallon (Cornwall) - a square military enclosure, seemingly associated with tin workings at nearby Boscarne.
- Mount Batten (Devon) - an Iron Age tin port that continued into Roman times.
- Plymouth (Devon) - evidence of a Roman settlement has been found on the north side of the harbour.
- Ictis - an ancient port trading in tin.
New settlements continued to be built throughout the Roman period, including sites at Chysauster and Trevelgue Head. The style is native in form with no Romanised features. Near Padstow, a site of some importance that was inhabited from the late Bronze/early Iron Age to the mid 6th century now lies buried under the sands on the opposite side of the Camel estuary near St. Enodoc\'s Church, and may have been a western coastal equivalent of a Saxon Shore Fort. Byzantine and African pottery has been discovered at the site. At Magor Farm in Illogan, near Camborne, an archaeological site has been identified as being a villa.
## Archaeology
The Dumnonii are thought to have occupied relatively isolated territory in Cornwall, Devon, Somerset and possibly part of Dorset. Their cultural connections, as expressed in their ceramics, were with the peninsula of Armorica across the Channel, rather than with the southeast of Britain. They do not seem to have been politically centralised: coins are relatively rare, none of them locally minted, and the structure, distribution and construction of Bronze Age and Iron Age hill forts, *Cornish rounds*, and defensible farmsteads in the south west point to a number of smaller tribal groups living alongside each other.
Dumnonia is noteworthy for its many settlements that have survived from the Romano-British period, but also for its lack of a villa system. Local archaeology has revealed instead the isolated enclosed farmsteads known locally as *rounds*. These seem to have survived the Roman abandonment of Britain, but were subsequently replaced, in the 6th and 7th centuries, by the unenclosed farms taking the Brythonic toponymic *tre-*.
As in most other Brythonic areas, Iron Age hill forts, such as Hembury Castle, were refortified for the use of chieftains or kings. Other high-status settlements such as Tintagel seem to have been reconstructed during this period. Post-Roman imported pottery has been excavated from many sites across the region, and the apparent surge in late 5th century Mediterranean and/or Byzantine imports is yet to be explained satisfactorily.
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# Dumnonii
## Industries
Apart from fishing and agriculture, the main economic resource of the Dumnonii was tin mining. The area of Dumnonia had been mined since ancient times, and the tin was exported from the ancient trading port of Ictis (St Michael\'s Mount). Tin extraction (mainly by streaming) had existed here from the early Bronze Age around the 22nd century BC. West Cornwall, around Mount\'s Bay, was traditionally thought to have been visited by metal traders from the eastern Mediterranean
During the first millennium BC trade became more organised, first with the Phoenicians, who settled Gades (Cadiz) around 1100 BC, and later with the Greeks, who had settled Massilia (Marseille) and Narbo (Narbonne) around 600 BC. Smelted Cornish tin was collected at Ictis whence it was conveyed across the Bay of Biscay to the mouth of the Loire and then to Gades via the Loire and Rhone valleys. It went then through the Mediterranean Sea in ships to Gades.
During the period c. 500-450 BC, the tin deposits seem to have become more important, and fortified settlements appear such as at Chun Castle and Kenidjack Castle, to protect both the tin smelters and mines.
The earliest account of Cornish tin mining was written by Pytheas of Massilia late in the 4th century BC after his circumnavigation of the British Isles. Underground mining was described in this account, although it cannot be determined when it had started. Pytheas\'s account was noted later by other writers including Pliny the Elder and Diodorus Siculus.
It is likely that tin trade with the Mediterranean was later on under the control of the Veneti. Britain was one of the places proposed for the *Cassiterides*, that is Tin Islands. Tin working continued throughout Roman occupation although it appears that output declined because of new supplies brought in from the deposits discovered in Iberia (Spain and Portugal). However, when these supplies diminished, production in Dumnonia increased and appears to have reached a peak during the 3rd century AD.
## Sub-Roman and post-Roman Dumnonia {#sub_roman_and_post_roman_dumnonia}
The Sub-Roman or Post-Roman history of Dumnonia comes from a variety of sources and is considered exceedingly difficult to interpret given that historical fact, legend and confused pseudo-history are compounded by a variety of sources in Middle Welsh and Latin. The main sources available for discussion of this period include Gildas\'s *De Excidio Britanniae* and Nennius\'s *Historia Brittonum*, the *Annales Cambriae*, *Anglo-Saxon Chronicle*, William of Malmesbury\'s *Gesta Regum Anglorum* and *De Antiquitate Glastoniensis Ecclesiae*, along with texts from the *Black Book of Carmarthen* and the *Red Book of Hergest*, and Bede\'s *Historia ecclesiastica gentis Anglorum* as well as \"The Descent of the Men of the North\" (*Bonedd Gwŷr y Gogledd*, in Peniarth MS 45 and elsewhere) and the *Book of Baglan*
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# Draught beer
thumb\|upright=1.3\|Draught beer fonts at the Delirium Café in Brussels
**Draught beer**, also spelt **draft**, is beer served from a cask or keg rather than from a bottle or can. Draught beer served from a pressurised keg is also known as `{{nowrap|'''keg beer'''.}}`{=mediawiki}
## Name
Until Joseph Bramah patented the beer engine in 1785, beer was served directly from the barrel and carried to the customer. The Old English **dragan}}** (\"carry; pull\") developed into a series of related words including *drag*, *draw*, and *draught*. By the time Bramah\'s beer pumps became popular, the use of the term *draught* to refer to the acts of serving or drinking beer was well established and transferred easily to beer served via the hand pumps. In time, the word came to be restricted to only such beer. The usual spelling is now \"draught\" in the United Kingdom, Ireland, Australia, and New Zealand and more commonly \"draft\" in North America, although it can be spe lt either way. Regardless of spelling, the word is pronounced `{{IPAc-en|d|r|ɑː|f|t}}`{=mediawiki} or `{{IPAc-en|d|r|æ|f|t}}`{=mediawiki} depending on the region the speaker is from.
**Canned draught** is beer served from a pressurised container featuring a widget. **Smooth flow** (also known as **cream flow**, **nitrokeg**, or **smooth**) is the name brewers give to draught beers pressurised with a partial nitrogen gas blend.
## History
In 1691, an article in the *London Gazette* mentioned John Lofting, who held a patent for a fire engine: \"The said patentee has also projected a very useful engine for starting of beer, and other liquors which will draw from 20 to 30 barrels an hour, which are completely fixed with brass joints and screws at reasonable rates\".
In the early 20th century, draught beer started to be served from pressurised containers. Artificial carbonation was introduced in the United Kingdom in 1936, with Watney\'s experimental pasteurised beer Red Barrel. Though this method of serving beer did not take hold in the UK until the late 1950s, it did become the favoured method in the rest of Europe, where it is known by such terms as *en pression*. The carbonation method of serving beer subsequently spread to the rest of the world; by the early 1970s the term \"draught beer\" almost exclusively referred to beer served under pressure as opposed to the traditional cask or barrel beer.
In Britain, the Campaign for Real Ale (CAMRA) was founded in 1971 to protect traditional---unpressurised---beer and brewing methods. The group devised the term *real ale* to differentiate between beer served from the cask and beer served under pressure. The term *real ale* has since been expanded to include bottle-conditioned beer.
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# Draught beer
## Keg beer {#keg_beer}
Keg beer is often filtered and/or pasteurised, both of which are processes that render the yeast inactive.
In brewing parlance, a keg is different from a cask. A cask has a tap hole near the edge of the top, and a spile hole on the side used for conditioning the unfiltered and unpasteurised beer. A keg has a single opening in the centre of the top to which a flow pipe is attached. Kegs are artificially pressurised after fermentation with carbon dioxide or a mixture of carbon dioxide and nitrogen gas or especially in Czech Republic solely compressed air.
*Keg* has become a term of contempt used by some, particularly in the UK, since the 1960s when pasteurised draught beers started replacing traditional cask beers.
Keg beer was replacing traditional cask ale in all parts of the UK, primarily because it requires less care to handle. Since 1971, CAMRA has conducted a consumer campaign on behalf of those who prefer traditional cask beer. CAMRA has lobbied the British Parliament to ensure support for cask ale and microbreweries have sprung up to serve those consumers who prefer traditional cask beer.
Pressurised CO~2~ in the keg\'s headspace maintains carbonation in the beer. The CO~2~ pressure varies depending on the amount of CO~2~ already in the beer and the keg storage temperature. Occasionally the CO~2~ gas is blended with nitrogen gas. CO~2~ / nitrogen blends are used to allow a higher operating pressure in complex dispensing systems.
Nitrogen is used under high pressure when dispensing dry stouts (such as Guinness) and other creamy beers because it displaces CO~2~ to (artificially) form a rich tight head and a less carbonated taste. This makes the beer feel smooth on the palate and gives a foamy appearance. Premixed bottled gas for creamy beers is usually 75% nitrogen and 25% CO~2~. This premixed gas, which only works well with creamy beers, is often referred to as Guinness Gas, Beer Gas, or Aligal (an Air Liquide brand name). Using \"Beer Gas\" with other beer styles can cause the last 5% to 10% of the beer in each keg to taste very flat and lifeless. In the UK, the term *keg beer* would imply the beer is pasteurised, in contrast to unpasteurised cask ale. Some of the newer microbreweries may offer a nitro keg stout which is filtered but not pasteurised.
## Storage and serving temperature {#storage_and_serving_temperature}
Cask beer should be stored and served at a cellar temperature of 12 C. Once a cask is opened, it should be consumed within three days. Keg beer is given additional cooling just prior to being served either by flash coolers or a remote cooler in the cellar. This chills the beer to temperatures between 3 and.
## Canned and bottled \"draught\" {#canned_and_bottled_draught}
The words \"draft\" and \"draught\" have been used as marketing terms to describe canned or bottled beers, implying that they taste and appear like beers from a cask or keg. Commercial brewers use this as a marketing tool although it is incorrect to call any beer not drawn from a cask or keg \"draught\". Two examples are Miller Genuine Draft, a pale lager which is produced using a cold filtering system, and Guinness stout in patented \"Draught-flow\" cans and bottles. Guinness is an example of beers that use a nitrogen widget to create a smooth beer with a dense head. Guinness has recently replaced the widget system from their bottled \"draught\" beer with a coating of cellulose fibres on the inside of the bottle. Statements indicate a new development in bottling technology that enables the mixture of nitrogen and carbon dioxide to be present in the beer without using a widget, making it according to Guinness \"more drinkable\" from the bottle.
In East Asian countries, such as China and Japan, the term \"draft beer\" (`{{cjkv|c=生啤酒|j=生ビール}}`{=mediawiki}) applied to canned or bottled beer indicates that the beer is not pasteurised (though it may be filtered), giving it a fresher taste but shorter shelf-life than conventional packaged beers
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# Darwinism
***Darwinism*** is a term used to describe a theory of biological evolution developed by the English naturalist Charles Darwin (1809--1882) and others. The theory states that all species of organisms arise and develop through the natural selection of small, inherited variations that increase the individual\'s ability to compete, survive, and reproduce. Also called ***Darwinian theory***, it originally included the broad concepts of transmutation of species or of evolution which gained general scientific acceptance after Darwin published *On the Origin of Species* in 1859, including concepts which predated Darwin\'s theories. English biologist Thomas Henry Huxley coined the term *Darwinism* in April 1860.
## Terminology
*Darwinism* subsequently referred to the specific concepts of natural selection, the Weismann barrier, or the central dogma of molecular biology. Though the term usually refers strictly to biological evolution, creationists have appropriated it to refer to the origin of life or to cosmic evolution, that are distinct to biological evolution, and therefore consider it to be the belief and acceptance of Darwin\'s and of his predecessors\' work, in place of other concepts, including divine design and extraterrestrial origins.
English biologist Thomas Henry Huxley coined the term *Darwinism* in April 1860. It was used to describe evolutionary concepts in general, including earlier concepts published by English philosopher Herbert Spencer. Many of the proponents of Darwinism at that time, including Huxley, had reservations about the significance of natural selection, and Darwin himself gave credence to what was later called Lamarckism. The strict neo-Darwinism of German evolutionary biologist August Weismann gained few supporters in the late 19th century. During the approximate period of the 1880s to about 1920, sometimes called \"the eclipse of Darwinism\", scientists proposed various alternative evolutionary mechanisms which eventually proved untenable. The development of the modern synthesis in the early 20th century, incorporating natural selection with population genetics and Mendelian genetics, revived Darwinism in an updated form.
While the term *Darwinism* has remained in use amongst the public when referring to modern evolutionary theory, it has increasingly been argued by science writers such as Olivia Judson, Eugenie Scott, and Carl Safina that it is an inappropriate term for modern evolutionary theory. For example, Darwin was unfamiliar with the work of the Moravian scientist and Augustinian friar Gregor Mendel, and as a result had only a vague and inaccurate understanding of heredity. He naturally had no inkling of later theoretical developments and, like Mendel himself, knew nothing of genetic drift, for example.
In the United States and to some extent in the United Kingdom, creationists often use the term \"Darwinism\" as a pejorative term in reference to beliefs such as scientific materialism.
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# Darwinism
## Huxley
thumb\|upright=1.15\|As evolution became widely accepted in the 1870s, caricatures of Charles Darwin with the body of an ape or monkey symbolised evolution.
Huxley, upon first reading Darwin\'s theory in 1858, responded, \"How extremely stupid not to have thought of that!\"
While the term *Darwinism* had been used previously to refer to the work of Erasmus Darwin in the late 18th century, the term as understood today was introduced when Charles Darwin\'s 1859 book *On the Origin of Species* was reviewed by Thomas Henry Huxley in the April 1860 issue of *The Westminster Review*. Having hailed the book as \"a veritable Whitworth gun in the armoury of liberalism\" promoting scientific naturalism over theology, and praising the usefulness of Darwin\'s ideas while expressing professional reservations about Darwin\'s gradualism and doubting if it could be proved that natural selection could form new species, Huxley compared Darwin\'s achievement to that of Nicolaus Copernicus in explaining planetary motion: `{{quotation|What if the orbit of Darwinism should be a little too circular? What if species should offer residual phenomena, here and there, not explicable by natural selection? Twenty years hence naturalists may be in a position to say whether this is, or is not, the case; but in either event they will owe the author of "The Origin of Species" an immense debt of gratitude.... And viewed as a whole, we do not believe that, since the publication of Von Baer's "Researches on Development," thirty years ago, any work has appeared calculated to exert so large an influence, not only on the future of Biology, but in extending the domination of Science over regions of thought into which she has, as yet, hardly penetrated.<ref name="westminster" />}}`{=mediawiki}
These are the basic tenets of evolution by natural selection as defined by Darwin:
1. More individuals are produced each generation than can survive.
2. Phenotypic variation exists among individuals and the variation is heritable.
3. Those individuals with heritable traits better suited to the environment will survive.
4. When reproductive isolation occurs new species will form.
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# Darwinism
## Other 19th-century usage {#other_19th_century_usage}
\"Darwinism\" soon came to stand for an entire range of evolutionary (and often revolutionary) philosophies about both biology and society. One of the more prominent approaches, summed in the 1864 phrase \"survival of the fittest\" by Herbert Spencer, later became emblematic of Darwinism even though Spencer\'s own understanding of evolution (as expressed in 1857) was more similar to that of Jean-Baptiste Lamarck than to that of Darwin, and predated the publication of Darwin\'s theory in 1859. What is now called \"Social Darwinism\" was, in its day, synonymous with \"Darwinism\"---the application of Darwinian principles of \"struggle\" to society, usually in support of anti-philanthropic political agenda. Another interpretation, one notably favoured by Darwin\'s half-cousin Francis Galton, was that \"Darwinism\" implied that because natural selection was apparently no longer working on \"civilized\" people, it was possible for \"inferior\" strains of people (who would normally be filtered out of the gene pool) to overwhelm the \"superior\" strains, and voluntary corrective measures would be desirable---the foundation of eugenics.
In Darwin\'s day there was no rigid definition of the term \"Darwinism\", and it was used by opponents and proponents of Darwin\'s biological theory alike to mean whatever they wanted it to in a larger context. The ideas had international influence, and Ernst Haeckel developed what was known as *Darwinismus* in Germany, although, like Spencer\'s \"evolution\", Haeckel\'s \"Darwinism\" had only a rough resemblance to the theory of Charles Darwin, and was not centred on natural selection. In 1886, Alfred Russel Wallace went on a lecture tour across the United States, starting in New York and going via Boston, Washington, Kansas, Iowa and Nebraska to California, lecturing on what he called \"Darwinism\" without any problems.
In his book *Darwinism* (1889), Wallace had used the term *pure-Darwinism* which proposed a \"greater efficacy\" for natural selection. George Romanes dubbed this view as \"Wallaceism\", noting that in contrast to Darwin, this position was advocating a \"pure theory of natural selection to the exclusion of any supplementary theory.\" Taking influence from Darwin, Romanes was a proponent of both natural selection and the inheritance of acquired characteristics. The latter was denied by Wallace who was a strict selectionist. Romanes\' definition of Darwinism conformed directly with Darwin\'s views and was contrasted with Wallace\'s definition of the term.
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# Darwinism
## Contemporary usage {#contemporary_usage}
The term *Darwinism* is often used in the United States by promoters of creationism, notably by leading members of the intelligent design movement, as an epithet to attack evolution as though it were an ideology (an \"-ism\") based on philosophical naturalism, atheism, or both. For example, in 1993, UC Berkeley law professor and author Phillip E. Johnson made this accusation of atheism with reference to Charles Hodge\'s 1874 book *What Is Darwinism?* However, unlike Johnson, Hodge confined the term to exclude those like American botanist Asa Gray who combined Christian faith with support for Darwin\'s natural selection theory, before answering the question posed in the book\'s title by concluding: \"It is Atheism.\"
Creationists use pejoratively the term *Darwinism* to imply that the theory has been held as true only by Darwin and a core group of his followers, whom they cast as dogmatic and inflexible in their belief. In the 2008 documentary film *Expelled: No Intelligence Allowed*, which promotes intelligent design (ID), American writer and actor Ben Stein refers to scientists as Darwinists. Reviewing the film for *Scientific American*, John Rennie says \"The term is a curious throwback, because in modern biology almost no one relies solely on Darwin\'s original ideas \... Yet the choice of terminology isn\'t random: Ben Stein wants you to stop thinking of evolution as an actual science supported by verifiable facts and logical arguments and to start thinking of it as a dogmatic, atheistic ideology akin to Marxism.\"
However, *Darwinism* is also used neutrally within the scientific community to distinguish the modern evolutionary synthesis, which is sometimes called \"neo-Darwinism\", from those first proposed by Darwin. *Darwinism* also is used neutrally by historians to differentiate his theory from other evolutionary theories current around the same period. For example, *Darwinism* may refer to Darwin\'s proposed mechanism of natural selection, in comparison to more recent mechanisms such as genetic drift and gene flow. It may also refer specifically to the role of Charles Darwin as opposed to others in the history of evolutionary thought---particularly contrasting Darwin\'s results with those of earlier theories such as Lamarckism or later ones such as the modern evolutionary synthesis.
In political discussions in the United States, the term is mostly used by its enemies. Biologist E. O. Wilson at Harvard University described the term as being \"a rhetorical device to make evolution seem like a kind of faith, like \'Maoism \[\...\] Scientists don\'t call it \'Darwinism\'.\" In the United Kingdom, the term often retains its positive sense as a reference to natural selection, and for example British ethologist and evolutionary biologist Richard Dawkins wrote in his collection of essays *A Devil\'s Chaplain*, published in 2003, that as a scientist he is a Darwinist.
In his 1995 book *Darwinian Fairytales*, Australian philosopher David Stove used the term \"Darwinism\" in a different sense from the above examples. Describing himself as non-religious and as accepting the concept of natural selection as a well-established fact, Stove nonetheless attacked what he described as flawed concepts proposed by some \"Ultra-Darwinists\". Stove alleged that by using weak or false *ad hoc* reasoning, these Ultra-Darwinists used evolutionary concepts to offer explanations that were not valid: for example, Stove suggested that the sociobiological explanation of altruism as an evolutionary feature was presented in such a way that the argument was effectively immune to any criticism. English philosopher Simon Blackburn wrote a rejoinder to Stove, though a subsequent essay by Stove\'s protégé James Franklin suggested that Blackburn\'s response actually \"confirms Stove\'s central thesis that Darwinism can \'explain\' anything.\"
In more recent times, the Australian moral philosopher and professor Peter Singer, who serves as the Ira W. DeCamp Professor of Bioethics at Princeton University, has proposed the development of a \"Darwinian left\" based on the contemporary scientific understanding of biological anthropology, human evolution, and applied ethics in order to achieve the establishment of a more equal and cooperative human society in accordance with the sociobiological explanation of altruism.
## Esoteric usage {#esoteric_usage}
In evolutionary aesthetics theory, there is evidence that perceptions of beauty are determined by natural selection and therefore Darwinian; that things, aspects of people and landscapes considered beautiful are typically found in situations likely to give enhanced survival of the perceiving human\'s genes
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# Sideroxylon grandiflorum
***Sideroxylon grandiflorum***, also known as the **tambalacoque** or **dodo tree**, is a long-lived species of tree in the sapote family Sapotaceae. It is endemic to Mauritius.
## Description
The fruit of *Sideroxylon grandiflorum* is analogous to a peach. Each is termed a drupe because each has a hard endocarp, or pit, surrounding the seed. The plant itself superficially resembles the unrelated *Plumeria*, but the dodo tree\'s flowers and fruit are cauliflorous.
## Ecology
In 1973, it was argued that the species was becoming extinct. There were supposedly only 13 specimens left, all estimated to be about 300 years old; the true age could not be determined because tambalacoque has no growth rings. Stanley Temple hypothesized that the dodo, which became extinct in the 17th century, ate tambalacoque fruits, and that only after passing through the digestive tract of the dodo could the seeds germinate. Temple force-fed seventeen tambalacoque fruits to wild turkeys in 1977. Seven of the fruits were crushed by the bird\'s gizzard, while the remaining ten were either regurgitated or passed with the bird\'s feces. Temple planted the remaining ten fruits, three of which germinated. Temple did not try to germinate any seeds from control fruits that had not been fed to turkeys so the effect on germination of feeding fruits to turkeys was unknown. Studies on tambalacoque seed germination by Hill (1941) and King (1946) found that the seeds germinated without abrading.
Temple\'s hypothesis that the tree required the dodo was contested. Others have suggested that the decline of the tree was exaggerated or that other extinct animals, such as giant tortoises, fruit bats, or the broad-billed parrot, may also have been distributing the seeds. The decline of the tree may be due to introduction of domestic pigs and crab-eating macaques, and competition from introduced plants. Alternatively, the difference in reported tree numbers may arise from the fact that young trees are not distinct in appearance and may easily be confused with similar species. Catling (2001) in a summary cites Owadally and Temple (1979) and Witmer (1991), while Hershey (2004) reviewed the flaws in Temple\'s dodo-tambalacoque hypothesis.
In 2004, the Botanical Society of America\'s Plant Science Bulletin disputed Temple\'s research as flawed. The Bulletin published evidence as to why the dodo\'s extinction did not directly cause the increasing disappearance of young trees, including suggestions that the *Cylindraspis* giant tortoises would have been more likely to disperse the seeds than dodos, casting doubt on Temple\'s view as to the dodo and the tree\'s sole survival relationship. More recently, the tree's decline within native forests was shown to be in fact driven by invasive introduced species: The tree's first germination in its native habitat were observed in 2001 (26 seedlings) exclusively where invasive alien weeds had been cleared and further observations and controlled experiments showed that invasive introduced macaques (Macaca fascicularis Rafles 1821) pick most of the tree's fruits when still unripe, killing the seeds, and reducing natural germination rates by up to about 40 times.
## Uses
The dodo tree is highly valued for its wood in Mauritius, which has led some foresters to scrape the pits by hand to make them sprout and grow
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# Diedrich Hermann Westermann
**Diedrich Hermann Westermann** (24 June 1875 -- 31 May 1956) was a German missionary, Africanist, and linguist. He substantially extended and revised the work of Carl Meinhof, his teacher, although he rejected some of Meinhof\'s theories only implicitly. Westermann is seen as one of the founders of modern African linguistics.
He carried out extensive linguistic and anthropological research in the area ranging from Senegal eastwards to the Upper Nile. His linguistic publications cover a wide range of African languages, including the Gbe languages, Nuer, Kpelle, Shilluk, Hausa, and Guang.
Westermann\'s comparative work, begun in 1911, initially brought together much of today\'s Niger--Congo and Nilo-Saharan language phyla under the name Sudanic languages. His most important later publication *Die westlichen Sudansprachen* 1927a divided these into East and West Sudanic languages and laid the basis for what would become Niger--Congo. In this book and a series of associated articles between 1925 and 1928, Westermann both identified a large number of roots that form the basis of our understanding of Niger--Congo and set out the evidence for the coherence of many of the families that constitute it. Much of the classification of African languages associated with Joseph Greenberg actually derives from the work of Westermann.
In 1927 Westermann published a *Practical Orthography of African Languages*, which became later known as the *Westermann script*. Subsequently, he published the influential and oft-reprinted *Practical Phonetics for Students of African Languages* in collaboration with Ida C. Ward (1933).
He was born in Baden near Bremen and also died there
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# Double planet
In astronomy, a **double planet** (also **binary planet**) is a binary satellite system where both objects are planets, or planetary-mass objects, and whose barycenter is external to both planetary bodies.
Although up to a third of the star systems in the Milky Way are binary, double planets are expected to be much rarer given the typical planet to satellite mass ratio is around 1:10,000, they are influenced heavily by the gravitational pull of the parent star and according to the giant-impact hypothesis are gravitationally stable only under particular circumstances.
The Solar System does not have an official double planet, however the Earth--Moon system is sometimes considered to be one. In promotional materials advertising the SMART-1 mission, the European Space Agency referred to the Earth--Moon system as a double planet.
Several dwarf planet candidates can be described as binary planets. At its 2006 General Assembly, the International Astronomical Union considered a proposal that Pluto and Charon be reclassified as a double planet, but the proposal was abandoned in favor of the current IAU definition of planet. Other trans-Neptunian systems with proportionally large planetary-mass satellites include Eris--Dysnomia, Orcus--Vanth and Varda--Ilmarë.
Binary asteroids with components of roughly equal mass are sometimes referred to as double minor planets. These include binary asteroids 69230 Hermes and 90 Antiope and binary Kuiper belt objects (KBOs) 79360 Sila--Nunam and `{{mpl|1998 WW|31}}`{=mediawiki}.
## Definition of \"double planet\" {#definition_of_double_planet}
There is debate as to what criteria should be used to distinguish a \"double planet\" from a \"planet--moon system\". The following are considerations.
### Both bodies satisfy planet criterion {#both_bodies_satisfy_planet_criterion}
A definition proposed in the *Astronomical Journal* calls for both bodies to individually satisfy an orbit-clearing criterion in order to be called a double planet.
### Mass ratios closer to 1 {#mass_ratios_closer_to_1}
One important consideration for defining \"double planets\" is the ratio of the masses of the two bodies. A mass ratio of 1 would indicate bodies of equal mass, and bodies with mass ratios closer to 1 are more attractive to label as \"doubles\". Using this definition, the satellites of Mars, Jupiter, Saturn, Uranus, and Neptune can all easily be excluded; they all have masses less than 0.00025 (`{{frac|4000}}`{=mediawiki}) of the planets around which they revolve. Some dwarf planets, too, have satellites substantially less massive than the dwarf planets themselves.
The most notable exception is the Pluto--Charon system. The Charon-to-Pluto mass ratio of 0.122 (≈ `{{frac|1|8}}`{=mediawiki}) is close enough to 1 that Pluto and Charon have frequently been described by many scientists as \"double dwarf planets\" (\"double planets\" prior to the 2006 definition of \"planet\"). The International Astronomical Union (IAU) earlier classified Charon as a satellite of Pluto, but had also explicitly expressed the willingness to reconsider the bodies as double dwarf planets in the future. However, a 2006 IAU report classified Charon--Pluto as a double planet. The Moon-to-Earth mass ratio of 0.01230 (≈ `{{frac|81}}`{=mediawiki}) is also notably close to 1 when compared to all other satellite-to-planet ratios. Consequently, some scientists view the Earth--Moon system as a double planet as well, though this is a minority view. Eris\'s lone satellite, Dysnomia, has a radius somewhere around `{{frac|1|4}}`{=mediawiki} that of Eris; assuming similar densities (Dysnomia\'s compositional make-up may or may not differ substantially from Eris\'s), the mass ratio would be near `{{frac|40}}`{=mediawiki}, a value intermediate to the Moon--Earth and Charon--Pluto ratios.
### Center-of-mass position {#center_of_mass_position}
Currently, the most commonly proposed definition for a double-planet system is one in which the barycenter, around which both bodies orbit, lies outside both bodies. Under this definition, Pluto and Charon are double dwarf planets, since they orbit a point clearly outside of Pluto, as visible in animations created from images of the *New Horizons* space probe in June 2015.
Under this definition, the Earth--Moon system is not currently a double planet; although the Moon is massive enough to cause the Earth to make a noticeable revolution around this center of mass, this point nevertheless lies well within Earth. However, the Moon currently migrates outward from Earth at a rate of approximately 1.5 in per year; in a few billion years, the Earth--Moon system\'s center of mass will lie outside Earth, which would make it a double-planet system.
The center of mass of the Jupiter--Sun system lies outside the surface of the Sun, though arguing that Jupiter and the Sun are a double star is not analogous to arguing Pluto--Charon is a double dwarf planet. Jupiter is too light to be a fusor; were it thirteen times heavier, it would achieve deuterium fusion and become a brown dwarf.
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# Double planet
## Definition of \"double planet\" {#definition_of_double_planet}
### Tug-of-war value {#tug_of_war_value}
Isaac Asimov suggested a distinction between planet--moon and double-planet structures based in part on what he called a \"tug-of-war\" value, which does not consider their relative sizes. This quantity is simply the ratio of the force exerted on the smaller body by the larger (primary) body to the force exerted on the smaller body by the Sun. This can be shown to equal
$\text{tug-of-war value} = \frac{m_\mathrm{p}}{m_\mathrm{s}} \cdot \left( \frac{d_\mathrm{s}}{d_\mathrm{p}} \right)^2$
where `{{math|''m''<sub>p</sub>}}`{=mediawiki} is the mass of the primary (the larger body), `{{math|''m''<sub>s</sub>}}`{=mediawiki} is the mass of the Sun, `{{math|''d''<sub>s</sub>}}`{=mediawiki} is the distance between the smaller body and the Sun, and `{{math|''d''<sub>p</sub>}}`{=mediawiki} is the distance between the smaller body and the primary. The tug-of-war value does not rely on the mass of the satellite (the smaller body).
This formula actually reflects the relation of the gravitational effects on the smaller body from the larger body and from the Sun. The tug-of-war figure for Saturn\'s moon Titan is 380, which means that Saturn\'s hold on Titan is 380 times as strong as the Sun\'s hold on Titan. Titan\'s tug-of-war value may be compared with that of Saturn\'s moon Phoebe, which has a tug-of-war value of just 3.5; that is, Saturn\'s hold on Phoebe is only 3.5 times as strong as the Sun\'s hold on Phoebe.
Asimov calculated tug-of-war values for several satellites of the planets. He showed that even the largest gas giant, Jupiter, had only a slightly better hold than the Sun on its outer captured satellites, some with tug-of-war values not much higher than one. In nearly every one of Asimov\'s calculations the tug-of-war value was found to be greater than one, so in those cases the Sun loses the tug-of-war with the planets. The one exception was Earth\'s Moon, where the Sun wins the tug-of-war with a value of 0.46, which means that Earth\'s hold on the Moon is less than half as strong as the Sun\'s. Asimov included this with his other arguments that Earth and the Moon should be considered a binary planet.
See the Path of Earth and Moon around Sun section in the \"Orbit of the Moon\" article for a more detailed explanation.
This definition of double planet depends on the pair\'s distance from the Sun. If the Earth--Moon system happened to orbit farther away from the Sun than it does now, then Earth would win the tug of war. For example, at the orbit of Mars, the Moon\'s tug-of-war value would be 1.05. Also, several tiny moons discovered since Asimov\'s proposal would qualify as double planets by this argument. Neptune\'s small outer moons Neso and Psamathe, for example, have tug-of-war values of 0.42 and 0.44, less than that of Earth\'s Moon. Yet their masses are tiny compared to Neptune\'s, with an estimated ratio of 1.5`{{e|-9}}`{=mediawiki} (`{{frac|700,000,000}}`{=mediawiki}) and 0.4`{{e|-9}}`{=mediawiki} (`{{frac|2,500,000,000}}`{=mediawiki}).
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# Double planet
## Definition of \"double planet\" {#definition_of_double_planet}
### Formation of the system {#formation_of_the_system}
A final consideration is the way in which the two bodies came to form a system. Both the Earth--Moon and Pluto--Charon systems are thought to have been formed as a result of giant impacts: one body was impacted by a second body, resulting in a debris disk, and through accretion, either two new bodies formed or one new body formed, with the larger body remaining (but changed). However, a giant impact is not a sufficient condition for two bodies being \"double planets\" because such impacts can also produce tiny satellites, such as the four small outer satellites of Pluto.
A now-abandoned hypothesis for the origin of the Moon was actually called the \"double-planet hypothesis\"; the idea was that the Earth and the Moon formed in the same region of the Solar System\'s proto-planetary disk, forming a system under gravitational interaction. This idea, too, is a problematic condition for defining two bodies as \"double planets\" because planets can \"capture\" moons through gravitational interaction. For example, the moons of Mars (Phobos and Deimos) are thought to be asteroids captured long ago by Mars. Such a definition would also deem Neptune--Triton a double planet, since Triton was a Kuiper belt body the same size and of similar composition to Pluto, later captured by Neptune
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# Dwight L. Moody
**Dwight Lyman Moody** (February 5, 1837 -- December 22, 1899), also known as **D. L. Moody**, was an American evangelist and publisher connected with Keswickianism, who founded the Moody Church, Northfield School and Mount Hermon School in Massachusetts (now Northfield Mount Hermon School), Moody Bible Institute, and Moody Publishers. One of his most famous quotes was \"Faith makes all things possible\... Love makes all things easy.\" Moody gave up his lucrative boot and shoe business to devote his life to revivalism, working first in the Civil War with Union troops through YMCA in the United States Christian Commission. In Chicago, he built one of the major evangelical centers in the nation, which is still active. Working with singer Ira Sankey, he toured the country and the British Isles, drawing large crowds with a dynamic speaking style.
## Early life {#early_life}
Dwight Moody was born in Northfield, Massachusetts, as the seventh child of a large family. His father, Edwin J. Moody (1800--1841), was a small farmer and stonemason. His mother was Betsey Moody (née Holton; 1805--1896). They had five sons and a daughter before Dwight\'s birth. His father died when Dwight was age four; fraternal twins, a boy, and a girl were born one month after the father\'s death. Their mother struggled to support the nine children, but she still found it necessary to send some off to work for their room and board. Dwight too was sent off, where he received cornmeal porridge, and milk three times a day. He complained to his mother, but when she learned that he was getting all he wanted to eat, she sent him back. During this time, she continued to send the children to church. Together with his eight siblings, Dwight was raised in the Unitarian church. His oldest brother ran away and was not heard from by the family until many years later.
When Moody turned 17, he moved to Boston to work (after receiving many job rejections locally) in an uncle\'s shoe store. One of the uncle\'s requirements was that Moody attend the Congregational Church of Mount Vernon, where Dr. Edward Norris Kirk served as the pastor. In April 1855 Moody was converted to evangelical Christianity when his Sunday school teacher, Edward Kimball, talked to him about how much God loved him. His conversion sparked the start of his career as an evangelist. Moody first applied to the church in May 1855, but he was not received as a church member until May 4, 1856.
According to Moody\'s memoir, his teacher, Edward Kimball, said:
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# Dwight L. Moody
## Civil War {#civil_war}
`{{Blockquote|The first meeting I ever saw him at was in a little old shanty that had been abandoned by a saloon-keeper. Mr. Moody had got the place to hold the meetings at night. I went there a little late; and the first thing I saw was a man standing up with a few tallow candles around him, holding a negro boy, and trying to read to him the story of the Prodigal Son and a great many words he could not readout, and had to skip. I thought, 'If the Lord can ever use such an instrument as that for His honor and glory, it will astonish me.' As a result of his tireless labor, within a year the average attendance at his school<!-- What school? --> was 650, while 60 volunteers from various churches served as teachers. It became so well known that the just-elected [[Abraham Lincoln|President Lincoln]] visited and spoke at a Sunday School meeting on November 25, 1860.<ref>{{cite book |url=https://books.google.com/books?id=JmuuMa2uVTYC&q=It+became+so+well+known+that+the+just-elected+President+Lincoln+visited+and+spoke+at+a+Sunday+School+meeting+on+November+25,+1860&pg=PA114 |title=What Will A Man Give In Exchange For His Soul? |first=George D. |last=Johnson |date=26 October 2011 |publisher=Xlibris |isbn=9781465380982}}</ref>}}`{=mediawiki}
D. L. Moody \"could not conscientiously enlist\" in the Union Army during the Civil War, later describing himself as \"a Quaker\" in this respect. After the Civil War started, he became involved with the United States Christian Commission of YMCA. He paid nine visits to the battlefront, being present among the Union soldiers after the Battle of Shiloh (a.k.a. Pittsburg Landing) and the Battle of Stones River; he also entered Richmond, Virginia, with the troops of General Grant.
On August 28, 1862, Moody married Emma C. Revell, with whom he had a daughter, Emma Reynolds Moody, and two sons, William Revell Moody and Paul Dwight Moody.
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# Dwight L. Moody
## Chicago and the postwar years {#chicago_and_the_postwar_years}
In 1858, he started a Sunday school.
The growing Sunday School congregation needed a permanent home, so Moody started a church in Chicago, the Illinois Street Church in 1864.
In June 1871 at an International Sunday School Convention in Indianapolis, Indiana, Dwight Moody met Ira D. Sankey. He was a gospel singer, with whom Moody soon began to cooperate and collaborate. Four months later, in October 1871, the Great Chicago Fire destroyed Moody\'s church building, as well as his house and those of most of his congregation. Many had to flee the flames, saving only their lives, and ending up completely destitute. Moody, reporting on the disaster, said about his own situation that: \"\... he saved nothing but his reputation and his Bible.\"
In the years after the fire, Moody\'s wealthy Chicago patron John V. Farwell tried to persuade him to make his permanent home in the city, offering to build a new house for Moody and his family. But the newly famous Moody, also sought by supporters in New York, Philadelphia, and elsewhere, chose a tranquil farm he had purchased near his birthplace in Northfield, Massachusetts. He felt he could better recover from his lengthy preaching trips in a rural setting.
Northfield became an important location in evangelical Christian history in the late 19th century as Moody organized summer conferences. These were led and attended by prominent Christian preachers and evangelists from around the world. Western Massachusetts has had a rich evangelical tradition including Jonathan Edwards preaching in colonial Northampton and C.I. Scofield preaching in Northfield. A protégé of Moody founded Moores Corner Church, in Leverett, Massachusetts.
Moody founded two schools here: Northfield School for Girls, founded in 1879, and the Mount Hermon School for Boys, founded in 1881. In the late 20th century, these merged, forming today\'s co-educational, nondenominational Northfield Mount Hermon School.
### Evangelistic travels {#evangelistic_travels}
During a trip to the United Kingdom in the spring of 1872, Moody became well known as an evangelist. Literary works published by the Moody Bible Institute claim that he was the greatest evangelist of the 19th century. He preached almost a hundred times and came into communion with the Plymouth Brethren. On several occasions, he filled stadia of a capacity of 2,000 to 4,000. According to his memoir, in the Botanic Gardens Palace, he attracted an audience estimated at between 15,000 and 30,000.
That turnout continued throughout 1874 and 1875, with crowds of thousands at all of his meetings. During his visit to Scotland, Moody was helped and encouraged by Andrew A. Bonar. The famous London Baptist preacher Charles Spurgeon invited him to speak, and he promoted the American as well. When Moody returned to the US, he was said to frequently attract crowds of 12,000 to 20,000, such crowds being as common as they had been in England. President Grant and some of his cabinet officials attended a Moody meeting on January 19, 1876. Moody held evangelistic meetings from Boston to New York, throughout New England, and as far west as San Francisco, also visiting other West Coast towns from Vancouver, British Columbia, Canada to San Diego.
Moody aided the work of cross-cultural evangelism by promoting \"The Wordless Book\", a teaching tool Charles Spurgeon had developed in 1866. In 1875, Moody added a fourth color to the design of the three-color evangelistic device: gold --- to \"represent heaven.\" This \"book\" has been and is still used to teach uncounted thousands of illiterate people, young and old, around the globe about the gospel message.
Moody visited Britain with Ira D. Sankey, with Moody preaching and Sankey singing at meetings. Together they published books of Christian hymns. In 1883, they visited Edinburgh and raised £10,000 for the building of a new home for the Carrubbers Close Mission. Moody later preached at the laying of the foundation stone for what is now called the Carrubbers Christian Centre, one of the few buildings on the Royal Mile which continues to be used for its original purpose.
Moody greatly influenced the cause of cross-cultural Christian missions after he met Hudson Taylor, a pioneer missionary to China. He actively supported the China Inland Mission and encouraged many of his congregation to volunteer for service overseas.
### International acclaim {#international_acclaim}
His influence was felt among Swedes. Being of English heritage, never visiting Sweden or any other Scandinavian country, and never speaking a word of Swedish, nonetheless, he became a hero revivalist among Swedish Mission Friends (*Missionsvänner*) in Sweden and America.
News of Moody\'s large revival campaigns in Great Britain from 1873 through 1875 traveled quickly to Sweden, making \"Mr. Moody\" a household name in homes of many Mission Friends. Moody\'s sermons published in Sweden were distributed in books, newspapers, and colporteur tracts, and they led to the spread of Sweden\'s \"Moody fever\" from 1875 through 1880.
He preached his last sermon on November 16, 1899, in Kansas City, Missouri. Becoming ill, he returned home by train to Northfield. During the preceding several months, friends had observed he had added some 30 lb to his already ample frame. Although his illness was never diagnosed, it has been speculated that he suffered from congestive heart failure. He died on December 22, 1899, surrounded by his family. Already installed as the leader of the Chicago Bible Institute, R. A. Torrey succeeded Moody as its pastor.
## Legacy
Religious historian James Findlay says that:
: Speaking before thousands in the dark business suit, bearded, rotund Dwight L. Moody seemed the epitome of the \"businessman in clerical garb\" who typified popular religion in late 19th-century America\... Earthy, unlettered, a dynamo of energy, the revivalist was very much a man of his times\... Moody adapted revivalism, one of the major institutions of evangelical Protestantism, to the urban context. \... His organizational ability, demonstrated in the great revivals he conducted in England, combined to fashion his spectacular career as the creator of modern mass revivalism.
Ten years after Moody\'s death the Chicago Avenue Church was renamed the Moody Church in his honor, and the Chicago Bible Institute was likewise renamed the Moody Bible Institute.
Dwight D. Eisenhower, who was born in 1890, was named after him. During World War II, the Liberty ship `{{SS|Dwight L. Moody}}`{=mediawiki} was built in Panama City, Florida, and named in his honor.
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# Dwight L. Moody
## Works
- *Heaven* Diggory Press `{{ISBN|978-1-84685-812-3}}`{=mediawiki}
- *Prevailing Prayer---What Hinders it?* Diggory Press `{{ISBN|978-1-84685-803-1}}`{=mediawiki}
- *Secret Power* (1881) Diggory Press `{{ISBN|978-1-84685-802-4}}`{=mediawiki}
- *The Ten Commandments*
- Also, A Life for Christ---What a Normal Christian Life Looks Like
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