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Logo and uniforms. The Atlanta Falcons' colors are black, red, silver and white. When the team began play in 1966, the Falcons wore red helmets with a black falcon crest logo. In the center of the helmet was a center black stripe surrounded by two gold stripes and two white stripes. These colors represented the two college rival schools in the state of Georgia; rival schools Georgia Tech Yellow Jackets (white and gold) and the Georgia Bulldogs (red and black). Although the gold was removed after several seasons, the white remains to this day. They wore white pants and either black or white jerseys. At first, the falcon crest logo was also put on the jersey sleeves, but it was replaced by a red and white stripe pattern four years later. They switched from black to red jerseys in 1971, and the club began to wear silver pants in 1978. The facemasks on the helmets were initially gray, becoming white in 1978, and then black in 1984; the team wore black face masks until its 2020 redesign. A prototype white helmet was developed for the team prior to the 1974 season, but was never worn.
In 1990, the uniform design changed to black helmets, silver pants, and either black or white jerseys. The numbers on the white jerseys were black, but were changed to red in 1997. (The red numerals could be seen on the away jerseys briefly in 1990.) Both the logo and uniforms changed in 2003. The logo was redesigned with red and silver accents to depict a more powerful, aggressive falcon, which now more closely resembles the capital letter "F". Although the Falcons still wore black helmets, the new uniforms featured jerseys and pants with red trim down the sides. The uniform design consisted of either black or white jerseys, and either black or white pants. During that same year, a red alternate jersey with black trim was also introduced. The Falcons also started wearing black cleats with these uniforms. In 2004, the red jerseys became the primary jerseys, and the black ones became the alternate, both worn with white pants. In select road games, the Falcons wear black pants with white jerseys. The Falcons wore an all-black combination for home games against their archrivals, the New Orleans Saints, winning the first two contests (24–21 in and 36–17 in ), but losing 31–13 in . The Falcons wore the all-black combination against the New Orleans Saints for four straight seasons starting in 2004, With the last time being in 2007, losing 34–14. They wore the combination again in 2006, against the Tampa Bay Buccaneers in Week 2. The Falcons won that game, 14–3. The Falcons also wore their all-black uniform in 2007 against the New York Giants, and in 2008 against the Carolina Panthers and against the Tampa Bay Buccaneers (for the second time). After that, the black pants and uniforms were retired and the white pants were now used full-time with the regular uniforms.
In the 1980s, the Falcons wore their white uniforms at home most of the time because of the heat. When the Falcons started playing in a dome, the team switched to their dark uniforms for home games but have worn their white uniforms at home a few times since switching to the dome. It was announced at the 2009 state of the franchise meeting that the Falcons would wear 1966 throwback uniforms for a couple games during the 2009 season. The Atlanta Falcons wore 1966 throwback jerseys for two home games in 2009 – against the Carolina Panthers on September 20 and against the Tampa Bay Buccaneers on November 29. The Falcons won both of those games. They donned the throwbacks again for 2 games in 2010, against Baltimore and San Francisco, winning both of those games as well. The throwbacks were used twice in 2011 and 2012; both times were against the Panthers and Saints. However, the throwbacks were retired following a 2013 NFL rule requiring only one helmet shell per team. The Falcons unveiled an all-red Color Rush uniform on September 13, 2016; however, due to the fact that the Falcons and the Tampa Bay Buccaneers had similar all-red Color Rush uniforms, the Falcons were unable to wear their Color Rush uniform until the 2017 season.
Also in 2016, the Falcons unveiled a mixed throwback uniform set. The uniform tops, pants and socks closely resembled their 1960s kits. From 2016 to 2021, due to the NFL's one-shell rule, the Falcons wore the black helmets with the original logo decal similar to the design they wore in the 1990s. However, starting in 2022, with the NFL now reinstating the use of alternate helmets, the Falcons brought back the original red helmets to pair with their throwback uniforms. It was revealed in January 2020 that the Falcons will change uniforms for the 2020 NFL season. The ensuing design featured the return to black as the primary home uniform color for the first time since 2003. Both the primary home and road uniforms featured the "ATL" abbreviation in red above either white or black numbers with red drop shadows. The white and black tops are usually paired with either white or black pants. The alternate uniform featured a red/black gradient design and also featured the "ATL" abbreviation in white above white numbers with black drop shadows. Black pants are only used with this uniform. All three uniforms feature red side stripes. The current throwback uniform was also retained. In addition, the Falcons switched to matte helmets with the enlarged falcon logo and gray facemasks. The red/black gradient alternates only lasted three seasons before it was removed from the uniform rotation in 2023.
Rivalries. Divisional. New Orleans Saints. The Falcons have shared a heated divisional rivalry with the New Orleans Saints (first the NFC West, and now the NFC South). The two teams were often basement-dwellers in the division; but the rivalry grew as a means of pride between the two cities, as they were the only two NFL teams in the Deep South for multiple decades. The series is the oldest and most iconic rivalry in the NFC South as the two teams have long harbored bad blood against one another. The series is currently tied at 55–55, including the most recent loss to the Saints on January 7, 2024, when the Falcons lost 48–17. Carolina Panthers. In addition, the Falcons share a similar, rivalry with the Carolina Panthers, with both teams having been in the NFC West from the Panthers' founding in 1995 to the NFL realignment in 2002. Similar to their rivalry with the Saints, the Falcons have often endured several competitive divisional battles with the Panthers for lead of the NFC South, though the two have yet to meet in the postseason. The series is also known as the "I-85 Rivalry" due to Atlanta and Charlotte being only four hours apart on Interstate 85. The Falcons lead the series 36–22.
Tampa Bay Buccaneers. The Falcons share a less-intense divisional rivalry with the Tampa Bay Buccaneers since the NFL realignment in 2002. The two had been regional opponents but very little had linked any further animosity towards the two as the Buccaneers played in the former NFC Central before the realignment. The two teams would find themselves competing over staff and players alike, particularly during the 2000s after the Falcons had lured general manager Rich McKay after winning Super Bowl XXXVII the season prior. McKay's ties with Tampa extend into his family as his father John McKay was head coach of the Buccaneers for nine seasons. Conference. Philadelphia Eagles. The Eagles lead the Falcons 21–15–1, with a 3–1 lead in playoff games. The rivalry first emerged after the Falcons upset the Eagles 14–13 in the , and only intensified further in the 2000s thanks to the rivalry between prominent dual-threat quarterbacks Donovan McNabb, and Michael Vick. Recently, the Falcons lost to the Eagles in the . The Falcons managed a win against Philly in week 2 en route to Philly's eventual Super Bowl LIX victory.
Green Bay Packers. The Falcons have also shared a playoff rivalry with the Green Bay Packers as much of the connections between the two teams stems from Atlanta trading future hall-of-fame quarterback Brett Favre to the Green Bay on February 11, 1992, in exchange for a first-round pick. The two teams have met four times in the postseason, most recently during the 2016–17 NFC Championship as it would also be the final game played at the Georgia Dome. The Packers lead the all-time series 19–16, while both teams are tied in the postseason 2–2. Statistics. Record vs. opponents. Includes postseason records Source: ! Total \|\| 393\|\| 455 \|\| 6 \|\| \|\| \|\| \|\| \|\| 10–14 () Players. Pro Football Hall of Famers. Humphrey is the only person in the Hall of Fame who spent the majority of his career with the Falcons. Ring of Honor. Fourteen members are included in the Atlanta Falcons Ring of Honor. Draft history. In the team's history, the Falcons have had the number one overall pick four times. Coaching staff. Head coaches. In their history, the Atlanta Falcons have had 18 head coaches. Five coaches have served in interim roles
Radio and television. The Falcons' flagship radio station is WZGC 92.9 The Game. Wes Durham, son of longtime North Carolina Tar Heels voice Woody Durham, is the Falcons' play-by-play announcer, with former Atlanta Falcons quarterback and pro football veteran, Dave Archer serving as color commentator. In 2014, The CW affiliate WUPA became the official television station of the Falcons, gaining rights to its preseason games, which are produced by CBS Sports. In the regular season, the team's games are seen on Fox's O&O affiliate WAGA. When the Falcons challenge an AFC team, CBS affiliate WANF will air those games while Sunday night games are televised on WXIA, the local NBC affiliate. Radio affiliates. Source:
Heathenry in the United States Heathenry is a modern Pagan new religious movement that has been active in the United States since at least the early 1970s. Although the term "Heathenry" is often employed to cover the entire religious movement, different Heathen groups within the United States often prefer the term "Ásatrú" or "Odinism" as self-designations. Heathenry appeared in the United States during the 1960s, at the same time as the wider emergence of modern Paganism in the United States. Among the earliest American group was the Odinist Fellowship, founded by Danish migrant Else Christensen in 1969. History. Ásatrú grew steadily in the United States during the 1960s. In 1969, the Danish Odinist Else Christensen established the Odinist Fellowship from her home in Florida. Heavily influenced by Alexander Rud Mills' writings, she began publication of a magazine, "The Odinist", although this focused to a greater extent on right-wing and racialist ideas than theological ones. Stephen McNallen first founded the Viking Brotherhood in the early 1970s, before creating the Ásatrú Free Assembly (AFA) in 1976, which broke up in 1986 amid widespread political disagreements after McNallen's repudiation of neo-Nazis within the group. In the 1990s, McNallen founded the Ásatrú Folk Assembly (AFA), an ethnically oriented Heathen group headquartered in California.
Meanwhile, Valgard Murray and his kindred in Arizona founded the Ásatrú Alliance (AA) in the late 1980s, which shared the AFA's perspectives on race and which published the "Vor Tru" newsletter. In 1987, Edred Thorsson and James Chisholm founded The Troth, which was incorporated in Texas. Taking an inclusive, non-racialist view, it soon grew into an international organisation. Terminology. In English usage, the genitive "" "of Æsir faith" is often used on its own to denote adherents (both singular and plural). This term is favored by practitioners who focus on the deities of Scandinavia, although it is problematic as many Asatruar worship deities and entities other than the Æsir, such as the Vanir, Valkyries, Elves, and Dwarves. Other practitioners term their religion "Vanatrú", meaning "those who honour the Vanir" or "Dísitrú", meaning "those who honour the Goddesses", depending on their particular theological emphasis. Within the community it is sometimes stated that the term "Ásatrú" pertains to groups which are not racially focused, while "Odinism" is the term preferred by racially oriented groups. However, in practice, there is no such neat division in terminology.
There are notable differences of emphasis between "Ásatrú" as practiced in the US and in Scandinavia. According to , American Asatruar tend to prefer a more devotional form of worship and a more emotional conception of the Nordic gods than Scandinavian practitioners, reflecting the parallel tendency of highly emotional forms of Christianity prevalent in the United States. Demographics. Although deeming it impossible to calculate the exact size of the Heathen community in the US, sociologist Jeffrey Kaplan estimated that, in the mid-1990s, there were around 500 active practitioners in the country, with a further thousand individuals on the periphery of the movement. He noted that the overwhelming majority of individuals in the movement were white, male, and young. Most had at least an undergraduate degree, and worked in a mix of white collar and blue collar jobs. From her experience within the community, Snook concurred that the majority of American Heathens were male, adding also that most were also white and middle-aged, but believed that there had been a growth in the proportion of Heathen women in the US since the mid-1990s.
In 2003, the Pagan Census Project led by Helen A. Berger, Evan A. Leach, and Leigh S. Shaffer gained 60 responses from Heathens in the US, noting that 65% were male and 35% female, which they saw as the "opposite" of the rest of the country's Pagan community. The majority had a college education, but were generally less well educated than the wider Pagan community, with a lower median income than the wider Pagan community too. Politics and controversies. Ásatrú organizations have memberships which span the entire political and spiritual spectrum. There is a history of political controversy within organized US Ásatrú, mostly surrounding the question of how to deal with such adherents as place themselves in a context of the far right and white supremacy, notably resulting in the fragmentation of the "Asatru Free Assembly" in 1986. Externally, political activity on the part of Ásatrú organizations has surrounded campaigns against alleged religious discrimination, such as the call for the introduction of an Ásatrú "emblem of belief" by the United States Department of Veterans Affairs to parallel the Wiccan pentacle granted to the widow of Patrick Stewart in 2006. In May 2013, the "Hammer of Thor" was added to the list of United States Department of Veterans Affairs emblems for headstones and markers. It was reported in early 2019 that a Heathenry service was held on the U.S. Navy's USS John C. Stennis
Folkish Ásatrú, Universalism and racialism. Historically, the main dispute between the national organizations has generally centered on the interpretation of "Nordic heritage" as either something cultural, or as something genetic or racial. In the internal discourse within American Ásatrú, this cultural/racial divide has long been known as "universalist" vs. "folkish" Ásatrú. The Troth takes the "universalist" position, claiming "Ásatrú" as a synonym for "Northern European Heathenry" taken to comprise "many variations, names, and practices, including Theodism, Irminism, Odinism, and Anglo-Saxon Heathenry". The Asatru Folk Assembly takes the folkish position, claiming that Ásatrú and the Germanic beliefs are ancestral in nature, and as an indigenous religion of the European Folk should only be accessed by the descendants of Europe. In the UK, Germanic Neopaganism is more commonly known as Odinism or as "Heathenry". This is mostly a matter of terminology, and US Ásatrú may be equated with UK Odinism for practical purposes, as is evident in the short-lived International Asatru-Odinic Alliance of folkish Ásatrú/Odinist groups.
Some groups identifying as Ásatrú have been associated with national socialist and white nationalist movements. Wotansvolk, for example, is an explicitly racial form. More recently, however, many Ásatrú groups have been taking a harder stance against these elements of their community. Declaration 127, so named for the corresponding stanza of the Hávamál: "When you see misdeeds, speak out against them, and give your enemies no frið” is a collective statement denouncing and testifying disassociation with the Asatru Folk Assembly for alleged racial and sexually-discriminatory practices and beliefs signed by over 150 Ásatrú religious organizations from over 15 different nations mainly represented on Facebook. Discrimination charges. Inmates of the "Intensive Management Unit" at Washington State Penitentiary who are adherents of Ásatrú in 2001 were deprived of their Thor's Hammer medallions. In 2007, a federal judge confirmed that Ásatrú adherents in US prisons have the right to possess a Thor's Hammer pendant. An inmate sued the Virginia Department of Corrections after he was denied it while members of other religions were allowed their medallions. In the "Georgacarakos v. Watts" case Peter N. Georgacarakos filed a pro se civil-rights complaint in the United States District Court for the District of Colorado against 19 prison officials for "interference with the free exercise of his Ásatrú religion" and "discrimination on the basis of his being Ásatrú".
Ansible The term ansible refers to a category of fictional technological devices capable of superluminal or faster-than-light (FTL) communication. These devices can instantaneously transmit and receive communicative and informational data streams across vast distances and obstacles, including between star systems and even across galaxies. As a name for such a device, the term "ansible" first appeared in a 1966 novel by Ursula K. Le Guin. Since that time, the broad use of the term has continued in the works of numerous science-fiction authors, across a variety of settings and continuities. Related terms are ultraphone and ultrawave. Coinage by Ursula Le Guin. Ursula K. Le Guin first used the word "ansible" in her 1966 novel "Rocannon's World". Etymologically, the word was a contraction of "answerable", reflecting the device's ability to deliver responses to their messages in a reasonable amount of time, even over interstellar distances. The ansible was the basis for creating a specific kind of interstellar civilization, where communications between far-flung stars are instantaneous, but humans can only travel at relativistic speeds. Under these conditions, a full-fledged galactic empire is not possible, but there is a looser interstellar organization, in which several of Le Guin's protagonists are involved.
Although Le Guin invented the name "ansible" for this type of device (further developing its details in her fictional works), the broader concept of instantaneous superluminal or FTL communication had previously existed in science fiction. Similar communication functions were included in a device called an "interocitor" in the 1952 novel "This Island Earth" by Raymond F. Jones, and the 1955 film based on the novel. Similarly in 1954, another of these devices called the "Dirac Communicator" appeared in James Blish's short story "Beep", which was expanded into the 1974 novel "The Quincunx of Time". Additionally, Robert A. Heinlein, in his 1958 novel "Time for the Stars," employed instantaneous telepathic communication between identical twin pairs over interstellar distances, and like Le Guin, provided a technical explanation based on a non-Einsteinian principle of simultaneity. In Le Guin's works. In her subsequent works, Le Guin continued to develop the concept of the ansible: Any ansible may be used to communicate through any other, by setting its coordinates to those of the receiving ansible. They have a limited bandwidth, which only allows for at most a few hundred characters of text to be communicated in any transaction of a dialog session, and are attached to a keyboard and small display to perform text messaging.
Use by later authors. Since Le Guin's conception of the ansible, the name of the device has been borrowed by numerous authors. While Le Guin's ansible was said to communicate "instantaneously", the name has also been adopted for devices capable of communication at finite speeds that are faster than light. David Langford publishes the science fiction fanzine and newsletter Ansible. Orson Scott Card's works. Orson Scott Card used the term "ansible" as an unofficial name for the Philotic Parallax Instantaneous Communicator in his 1977 novelette, 1985 novel "Ender's Game", and its sequels. The Philotic Parallax Instantaneous Communicator is a machine capable of transmitting information across infinite distances with no time delay. In "Ender's Game", Colonel Graff states that "somebody dredged the name "ansible" out of an old book somewhere". In an answer on the question-and-answer website Quora, Card explained why he chose to appropriate the pre-existing term "ansible" for an FTL communication device instead of developing a new in-universe name for one: In a FTL universe, you have several levels. [If you] can travel hyperfast, but no radio signal can outstrip [outrun] your ship, [then] you have to carry the mail with you. It's like the way things were between Europe and America before the laying of the successful transatlantic cable. But once it was laid, messages could be sent long before a ship could make the passage. That is like the ansible universe in Ursula K. LeGuin's early Hainish novels. Since I needed to use exactly that rule set, why not use the word – an excellent word – which I apply in the same way we all say 'robot,' an invented word that has entered the language, [and thereby] pay tribute to the writer from whose works I learned the word.
In the universe of the "Ender's Game" series, the ansible's functions involved a fictional subatomic particle, the philote. The two quarks inside a pi meson can be separated by an arbitrary distance, while remaining connected by "philotic rays". This concept is similar to quantum teleportation due to entanglement; however, in reality, quark confinement prevents quarks from being separated by any observable distance. Card's version of the ansible was also featured in the video game "Advent Rising", for which Card helped write the story, and in the movie "Ender's Game", which was based on the book. Other writers. Numerous other writers have included ansibles and similar FTL communication devices in their fictional works. Notable examples include:
Adalbert of Prague Adalbert of Prague (, , , , ; 95623 April 997), known in the Czech Republic, Poland and Slovakia by his birth name Vojtěch (), was a Czech missionary and Christian saint. He was the Bishop of Prague and a missionary to the Hungarians, Poles, and Prussians, who was martyred in his efforts to convert the Baltic Prussians to Christianity. He is said to be the composer of the oldest Czech hymn "Hospodine, pomiluj ny" and "Bogurodzica", the oldest known Polish anthem but his authorship of them has not been confirmed. Adalbert was later declared the patron saint of the Czech Republic, Poland, and the Duchy of Prussia. He is also the patron saint of the Archdiocese of Esztergom in Hungary. Life. Early years. Born as "Vojtěch" in 952 or in gord Libice, he belonged to the Slavnik clan, one of the two most powerful families in Bohemia. Events from his life were later recorded by a Bohemian priest Cosmas of Prague (1045–1125). Vojtěch's father was Slavník (d. 978–981), a duke ruling a province centred at Libice. His mother was Střezislava (d. 985–987), and according to David Kalhous belonged to the Přemyslid dynasty. He had five brothers: Soběslav, Spytimír, Dobroslav, Pořej, and Čáslav. Cosmas also refers to Radim (later Gaudentius) as a brother; who is believed to have been a half-brother by his father's liaison with another woman. After he survived a grave illness in childhood, his parents decided to dedicate him to the service of God. Adalbert was well educated, having studied for approximately ten years (970–80) in Magdeburg under Adalbert of Magdeburg. The young Vojtěch took his tutor's name "Adalbert" at his Confirmation.
Episcopacy. In 981 Adalbert of Magdeburg died, and his young protege Adalbert returned to Bohemia. Later Bishop Dietmar of Prague ordained him a Catholic priest. In 982, Bishop Dietmar died, and Adalbert, despite being under canonical age, was chosen to succeed him as Bishop of Prague. Amiable and somewhat worldly, he was not expected to trouble the secular powers by making excessive claims for the Church. Although Adalbert was from a wealthy family, he avoided comfort and luxury, and was noted for his charity and austerity. After six years of preaching and prayer, he had made little headway in evangelising the Bohemians, who maintained deeply embedded pagan beliefs. Adalbert opposed the participation of Christians in the slave trade and complained of polygamy and idolatry, which were common among the people. Once he started to propose reforms he was met with opposition from both the secular powers and the clergy. His family refused to support Duke Boleslaus in an unsuccessful war against Poland. Adalbert was no longer welcome and eventually forced into exile. In 988 he went to Rome. He lived as a hermit at the Benedictine monastery of Saint Alexis. Five years later, Boleslaus requested that the Pope send Adalbert back to Prague, in hopes of securing his family's support. Pope John XV agreed, with the understanding that Adalbert was free to leave Prague if he continued to encounter entrenched resistance. Adalbert returned as bishop of Prague, where he was initially received with demonstrations of apparent joy. Together with a group of Italian Benedictine monks which brought with him, he founded in 14 January 993 a monastery in Břevnov (then situated westward from Prague, now part of the city), the second oldest monastery on Czech territory.
In 995, the Slavniks' former rivalry with the Přemyslids, who were allied with the powerful Bohemian clan of the Vršovids, resulted in the storming of the Slavnik town of Libice nad Cidlinou, which was led by the Přemyslid Boleslaus II the Pious. During the struggle four or five of Adalbert's brothers were killed. The Zlič Principality became part of the Přemyslids' estate. Adalbert unsuccessfully attempted to protect a noblewoman caught in adultery. She had fled to a convent, where she was killed. In upholding the right of sanctuary, Bishop Adalbert responded by excommunicating the murderers. Butler suggests that the incident was orchestrated by enemies of his family. After this, Adalbert could not safely stay in Bohemia and escaped from Prague. Strachkvas was eventually appointed to be his successor. However, Strachkvas suddenly died during the liturgy at which he was to accede to his episcopal office in Prague. The cause of his death is still ambiguous. The Pope directed Adalbert to resume his see, but believing that he would not be allowed back, Adalbert requested a brief as an itinerant missionary.
Adalbert then traveled to Hungary and probably baptized Géza of Hungary and his son Stephen in Esztergom. Then he went to Poland where he was cordially welcomed by then-Duke Boleslaus I and installed as Bishop of Gniezno. Mission and martyrdom in Prussia. Adalbert again relinquished his diocese, namely that of Gniezno, and set out as a missionary to preach to the inhabitants near Prussia. Bolesław I, Duke (and, later, King) of Poland, sent soldiers with Adalbert on his mission to the Prussians. The Bishop and his companions, entered Prussian territory and traveled along the coast of the Baltic Sea to Gdańsk. At the borders of the Polish realm, at the mouth of the Vistula River, his half-brother Radim (Gaudentius), Benedict-Bogusza (who was probably a Pole), and at least one interpreter, ventured out into Prussia alone, as Bolesław had only sent his soldiers to escort them to the border. Adalbert achieved some success upon his arrival, however his arrival mostly caused strain upon the local Prussian populations. Partially this was because of the imperious manner with which he preached, but potentially because he preached utilizing a book. The Prussians had an oral society where communication was face to face. To the locals Adalbert reading from a book may have come off as a manifestation of an evil action. He was forced to leave this first village after being struck in the back of the head by an oar by a local chieftain, causing the pages of his book to scatter upon the ground. He and his companions then fled across a river.
In the next place that Adalbert tried to preach, his message was met with the locals banging their sticks upon the ground, calling for the death of Adalbert and his companions. Retreating once again Adalbert and his companions went to a market place of Truso (near modern-day Elbląg). Here they were met with a similar response as at the previous place. On the 23 April 997, after mass, while Adalbert and his companions lay in the grass while eating a snack, they were set upon by a pagan mob. The mob was led by a man named Sicco, possibly a pagan priest, who delivered the first blow against Adalbert, before the others joined in. They removed Adalbert's head from his body after he was dead, and mounted on a pole while they returned home. This encounter may also have taken place in Tenkitten and Fischhausen (now Primorsk, Kaliningrad Oblast, Russia). It is recorded that his body was bought back for its weight in gold by King Boleslaus I of Poland. Veneration and relics. A few years after his martyrdom, Adalbert was canonized as Saint Adalbert of Prague. His life was written in "Vita Sancti Adalberti Pragensis" by various authors, the earliest being traced to imperial Aachen and the Bishop of Liège, Notger von Lüttich, although it was previously assumed that the Roman monk John Canaparius wrote the first "Vita" in 999. Another famous biographer of Adalbert was Bruno of Querfurt who wrote a hagiography of him in 1001–4.
Notably, the Přemyslid rulers of Bohemia initially refused to ransom Adalbert's body from the Prussians who murdered him, and therefore it was purchased by Poles. This fact may be explained by Adalbert's belonging to the Slavniks family which was rival to the Přemyslids. Thus Adalbert's bones were preserved in Gniezno, which assisted Boleslaus I of Poland in increasing Polish political and diplomatic power in Europe. According to Bohemian accounts, in 1039 the Bohemian Duke Bretislav I looted the bones of Adalbert from Gniezno in a raid and translated them to Prague. According to Polish accounts, however, he stole the wrong relics, namely those of Gaudentius, while the Poles concealed Adalbert's relics which remain in Gniezno. In 1127 his severed head, which was not in the original purchase according to "Roczniki Polskie", was discovered and translated to Gniezno. In 1928, one of the arms of Adalbert, which Bolesław I had given to Holy Roman Emperor Otto III in 1000, was added to the bones preserved in Gniezno. Therefore, today Adalbert has two elaborate shrines in the Prague Cathedral and Royal Cathedral of Gniezno, each of which claims to possess his relics, but which of these bones are his authentic relics is unknown. For example, pursuant to both claims two skulls are attributed to Adalbert. The one in Gniezno was stolen in 1923.
The massive bronze doors of Gniezno Cathedral, dating from around 1175, are decorated with eighteen reliefs of scenes from Adalbert's life. They are the only Romanesque ecclesiastical doors in Europe depicting a cycle illustrating the life of a saint, and therefore are a precious relic documenting Adalbert's martyrdom. We can read that door literally and theologically. The one thousandth anniversary of Adalbert's martyrdom was on 23 April 1997. It was commemorated in Poland, the Czech Republic, Germany, Russia, and other nations. Representatives of Catholic, Eastern Orthodox, and Evangelical churches traveled on a pilgrimage to Adalbert's tomb located in Gniezno. Pope John Paul II visited the cathedral and celebrated a liturgy there in which heads of seven European nations and approximately one million faithful participated. A ten-meter cross was erected near the village of Beregovoe (formerly Tenkitten), Kaliningrad Oblast, where Adalbert is thought to have been martyred by the Prussians. Feast day. He is also commemorated on 23 April by Evangelical Church in Germany and Eastern Orthodox Church.
In popular culture and society. The Dagmar and Václav Havel VIZE 97 Foundation Prize, given annually to a distinguished thinker "whose work exceeds the traditional framework of scientific knowledge, contributes to the understanding of science as an integral part of general culture and is concerned with unconventional ways of asking fundamental questions about cognition, being and human existence" includes a massive replica of Adalbert's crozier by Czech artist Jiří Plieštík. St. Vojtech Fellowship was established in 1870 by Slovak Catholic priest Andrej Radlinský. It had facilitated Slovak Catholic thinkers and authors, continuing to publish religious original works and translations to this day. It is the official publishing body of Episcopal Conference of Slovakia.
Ælfheah of Canterbury Ælfheah ( – 19 April 1012), more commonly known today as Alphege, was an Anglo-Saxon Bishop of Winchester, later Archbishop of Canterbury. He became an anchorite before being elected abbot of Bath Abbey. His reputation for piety and sanctity led to his promotion to the episcopate and, eventually, to his becoming archbishop. Ælfheah furthered the cult of Dunstan and also encouraged learning. He was captured by Viking raiders in 1011 during the siege of Canterbury and killed by them the following year after refusing to allow himself to be ransomed. Ælfheah was canonised as a saint in 1078. Thomas Becket, a later Archbishop of Canterbury, prayed to Ælfheah just before his murder in Canterbury Cathedral in 1170. Life. Ælfheah was born around 953, supposedly in Weston on the outskirts of Bath, and became a monk early in life. He first entered the monastery of Deerhurst, but then moved to Bath, where he became an anchorite. He was noted for his piety and austerity and rose to become abbot of Bath Abbey. The 12th-century chronicler, William of Malmesbury recorded that Ælfheah was a monk and prior at Glastonbury Abbey, but this is not accepted by all historians. Indications are that Ælfheah became abbot at Bath by 982, perhaps as early as around 977. He perhaps shared authority with his predecessor Æscwig after 968.
Probably due to the influence of Dunstan, the Archbishop of Canterbury (959–988), Ælfheah was elected Bishop of Winchester in 984, and was consecrated on 19 October that year. While bishop he was largely responsible for the construction of a large organ in the cathedral, audible from over a mile (1600 m) away and said to require more than 24 men to operate. He also built and enlarged the city's churches, and promoted the cult of Swithun and his predecessor, Æthelwold of Winchester. One act promoting Æthelwold's cult was the translation of Æthelwold's body to a new tomb in the cathedral at Winchester, which Ælfheah presided over on 10 September 996. Following a Viking raid in 994, a peace treaty was agreed with one of the raiders, Olaf Tryggvason. Besides receiving danegeld, Olaf converted to Christianity and undertook never to raid or fight the English again. Ælfheah may have played a part in the treaty negotiations, and it is certain that he confirmed Olaf in his new faith. In 1006, Ælfheah succeeded Ælfric as Archbishop of Canterbury, taking Swithun's head with him as a relic for the new location. He went to Rome in 1007 to receive his pallium—symbol of his status as an archbishop—from Pope John XVIII, but was robbed during his journey. While at Canterbury, he promoted the cult of Dunstan, ordering the writing of the second "Life of Dunstan", which Adelard of Ghent composed between 1006 and 1011. He also introduced new practices into the liturgy, and was instrumental in the Witenagemot's recognition of Wulfsige of Sherborne as a saint in about 1012.
Ælfheah sent Ælfric of Eynsham to Cerne Abbey to take charge of its monastic school. He was present at the council of May 1008 at which Wulfstan II, Archbishop of York, preached his "Sermo Lupi ad Anglos" ("The Sermon of the Wolf to the English"), castigating the English for their moral failings and blaming the latter for the tribulations afflicting the country. In 1011, the Danes again raided England, and from 8–29 September they laid siege to Canterbury. Aided by the treachery of Ælfmaer, whose life Ælfheah had once saved, the raiders succeeded in sacking the city. Ælfheah was taken prisoner and held captive for seven months. Godwine (Bishop of Rochester), Leofrun (abbess of St Mildrith's), and the king's reeve, Ælfweard were captured also, but the abbot of St Augustine's Abbey, Ælfmær, managed to escape. Canterbury Cathedral was plundered and burned by the Danes following Ælfheah's capture. Death. Ælfheah refused to allow a ransom to be paid for his freedom, and as a result was killed on 19 April 1012 at Greenwich, reputedly on the site of St Alfege's Church. The account of Ælfheah's death appears in the E version of the "Anglo-Saxon Chronicle":
Ælfheah was the first Archbishop of Canterbury to die a violent death. A contemporary report tells that Thorkell the Tall attempted to save Ælfheah from the mob about to kill him by offering everything he owned except for his ship, in exchange for Ælfheah's life; Thorkell's presence is not mentioned in the "Anglo-Saxon Chronicle", however. Some sources record that the final blow, with the back of an axe, was delivered as an act of kindness by a Christian convert known as "Thrum". Ælfheah was buried in Old St Paul's Cathedral. In 1023, his body was moved by King Cnut to Canterbury, with great ceremony. Thorkell the Tall was appalled at the brutality of his fellow raiders, and switched sides to the English king Æthelred the Unready following Ælfheah's death. Veneration.
In the late medieval period, Ælfheah's feast day was celebrated in Scandinavia, perhaps because of the saint's connection with Cnut. Few church dedications to him are known, with most of them occurring in Kent and one each in London and Winchester; as well as St Alfege's Church in Greenwich, a nearby hospital (1931–1968) was named after him. In Kent, there are two 12th-century parish churches dedicated to St Alphege at Seasalter and Canterbury. Reputedly his body lay in these churches overnight on his way back to Canterbury Cathedral for burial. In the town of Solihull in the West Midlands, St Alphege Church is dedicated to Ælfheah dating back to approximately 1277. In 1929, a new Roman Catholic church in Bath, the Church of Our Lady & St Alphege, was designed by Giles Gilbert Scott in homage to the ancient Roman church of Santa Maria in Cosmedin, and dedicated to Ælfheah under the name of Alphege. St George the Martyr with St Alphege & St Jude stands in Borough in London. Artistic representations of Ælfheah often depict him holding a pile of stones in his chasuble, a reference to his martyrdom.
Associative algebra In mathematics, an associative algebra "A" over a commutative ring (often a field) "K" is a ring "A" together with a ring homomorphism from "K" into the center of "A". This is thus an algebraic structure with an addition, a multiplication, and a scalar multiplication (the multiplication by the image of the ring homomorphism of an element of "K"). The addition and multiplication operations together give "A" the structure of a ring; the addition and scalar multiplication operations together give "A" the structure of a module or vector space over "K". In this article we will also use the term "K"-algebra to mean an associative algebra over "K". A standard first example of a "K"-algebra is a ring of square matrices over a commutative ring "K", with the usual matrix multiplication. A commutative algebra is an associative algebra for which the multiplication is commutative, or, equivalently, an associative algebra that is also a commutative ring. In this article associative algebras are assumed to have a multiplicative identity, denoted 1; they are sometimes called unital associative algebras for clarification. In some areas of mathematics this assumption is not made, and we will call such structures non-unital associative algebras. We will also assume that all rings are unital, and all ring homomorphisms are unital.
Every ring is an associative algebra over its center and over the integers. Definition. Let "R" be a commutative ring (so "R" could be a field). An associative "R"-algebra "A (or more simply, an R"-algebra "A") is a ring "A" that is also an "R"-module in such a way that the two additions (the ring addition and the module addition) are the same operation, and scalar multiplication satisfies for all "r" in "R" and "x", "y" in the algebra. (This definition implies that the algebra, being a ring, is unital, since rings are supposed to have a multiplicative identity.) Equivalently, an associative algebra "A" is a ring together with a ring homomorphism from "R" to the center of "A". If "f" is such a homomorphism, the scalar multiplication is (here the multiplication is the ring multiplication); if the scalar multiplication is given, the ring homomorphism is given by . (See also "" below). Every ring is an associative Z-algebra, where Z denotes the ring of the integers. A is an associative algebra that is also a commutative ring.
As a monoid object in the category of modules. The definition is equivalent to saying that a unital associative "R"-algebra is a monoid object in "R"-Mod (the monoidal category of "R"-modules). By definition, a ring is a monoid object in the category of abelian groups; thus, the notion of an associative algebra is obtained by replacing the category of abelian groups with the category of modules. Pushing this idea further, some authors have introduced a "generalized ring" as a monoid object in some other category that behaves like the category of modules. Indeed, this reinterpretation allows one to avoid making an explicit reference to elements of an algebra "A". For example, the associativity can be expressed as follows. By the universal property of a tensor product of modules, the multiplication (the "R"-bilinear map) corresponds to a unique "R"-linear map The associativity then refers to the identity: From ring homomorphisms. An associative algebra amounts to a ring homomorphism whose image lies in the center. Indeed, starting with a ring "A" and a ring homomorphism whose image lies in the center of "A", we can make "A" an "R"-algebra by defining
for all and . If "A" is an "R"-algebra, taking , the same formula in turn defines a ring homomorphism whose image lies in the center. If a ring is commutative then it equals its center, so that a commutative "R"-algebra can be defined simply as a commutative ring "A" together with a commutative ring homomorphism . The ring homomorphism "η" appearing in the above is often called a structure map. In the commutative case, one can consider the category whose objects are ring homomorphisms for a fixed "R", i.e., commutative "R"-algebras, and whose morphisms are ring homomorphisms that are under "R"; i.e., is (i.e., the coslice category of the category of commutative rings under "R".) The prime spectrum functor Spec then determines an anti-equivalence of this category to the category of affine schemes over Spec "R". How to weaken the commutativity assumption is a subject matter of noncommutative algebraic geometry and, more recently, of derived algebraic geometry. See also: "Generic matrix ring". Algebra homomorphisms.
A homomorphism between two "R"-algebras is an "R"-linear ring homomorphism. Explicitly, is an associative algebra homomorphism if The class of all "R"-algebras together with algebra homomorphisms between them form a category, sometimes denoted "R"-Alg. The subcategory of commutative "R"-algebras can be characterized as the coslice category "R"/CRing where CRing is the category of commutative rings. Examples. The most basic example is a ring itself; it is an algebra over its center or any subring lying in the center. In particular, any commutative ring is an algebra over any of its subrings. Other examples abound both from algebra and other fields of mathematics. Dual of an associative algebra. Let "A" be an associative algebra over a commutative ring "R". Since "A" is in particular a module, we can take the dual module "A"* of "A". A priori, the dual "A"* need not have a structure of an associative algebra. However, "A" may come with an extra structure (namely, that of a Hopf algebra) so that the dual is also an associative algebra.
For example, take "A" to be the ring of continuous functions on a compact group "G". Then, not only "A" is an associative algebra, but it also comes with the co-multiplication and co-unit . The "co-" refers to the fact that they satisfy the dual of the usual multiplication and unit in the algebra axiom. Hence, the dual "A"* is an associative algebra. The co-multiplication and co-unit are also important in order to form a tensor product of representations of associative algebras (see "" below). Enveloping algebra. Given an associative algebra "A" over a commutative ring "R", the enveloping algebra "A"e of "A" is the algebra or , depending on authors. Note that a bimodule over "A" is exactly a left module over "A"e. Separable algebra. Let "A" be an algebra over a commutative ring "R". Then the algebra "A" is a right module over with the action . Then, by definition, "A" is said to separable if the multiplication map splits as an "A"e-linear map, where is an "A"e-module by . Equivalently, "A" is separable if it is a projective module over ; thus, the -projective dimension of "A", sometimes called the bidimension of "A", measures the failure of separability.
Finite-dimensional algebra. Let "A" be a finite-dimensional algebra over a field "k". Then "A" is an Artinian ring. Commutative case. As "A" is Artinian, if it is commutative, then it is a finite product of Artinian local rings whose residue fields are algebras over the base field "k". Now, a reduced Artinian local ring is a field and thus the following are equivalent Let formula_24, the profinite group of finite Galois extensions of "k". Then formula_25 is an anti-equivalence of the category of finite-dimensional separable "k"-algebras to the category of finite sets with continuous formula_26-actions. Noncommutative case. Since a simple Artinian ring is a (full) matrix ring over a division ring, if "A" is a simple algebra, then "A" is a (full) matrix algebra over a division algebra "D" over "k"; i.e., . More generally, if "A" is a semisimple algebra, then it is a finite product of matrix algebras (over various division "k"-algebras), the fact known as the Artin–Wedderburn theorem. The fact that "A" is Artinian simplifies the notion of a Jacobson radical; for an Artinian ring, the Jacobson radical of "A" is the intersection of all (two-sided) maximal ideals (in contrast, in general, a Jacobson radical is the intersection of all left maximal ideals or the intersection of all right maximal ideals.)
The Wedderburn principal theorem states: for a finite-dimensional algebra "A" with a nilpotent ideal "I", if the projective dimension of as a module over the enveloping algebra is at most one, then the natural surjection splits; i.e., "A" contains a subalgebra "B" such that is an isomorphism. Taking "I" to be the Jacobson radical, the theorem says in particular that the Jacobson radical is complemented by a semisimple algebra. The theorem is an analog of Levi's theorem for Lie algebras. Lattices and orders. Let "R" be a Noetherian integral domain with field of fractions "K" (for example, they can be Z, Q). A "lattice" "L" in a finite-dimensional "K"-vector space "V" is a finitely generated "R"-submodule of "V" that spans "V"; in other words, . Let "A""K" be a finite-dimensional "K"-algebra. An "order" in "A""K" is an "R"-subalgebra that is a lattice. In general, there are a lot fewer orders than lattices; e.g., Z is a lattice in Q but not an order (since it is not an algebra). A "maximal order" is an order that is maximal among all the orders.
Related concepts. Coalgebras. An associative algebra over "K" is given by a "K"-vector space "A" endowed with a bilinear map having two inputs (multiplicator and multiplicand) and one output (product), as well as a morphism identifying the scalar multiples of the multiplicative identity. If the bilinear map is reinterpreted as a linear map (i.e., morphism in the category of "K"-vector spaces) (by the universal property of the tensor product), then we can view an associative algebra over "K" as a "K"-vector space "A" endowed with two morphisms (one of the form and one of the form ) satisfying certain conditions that boil down to the algebra axioms. These two morphisms can be dualized using categorial duality by reversing all arrows in the commutative diagrams that describe the algebra axioms; this defines the structure of a coalgebra. There is also an abstract notion of "F"-coalgebra, where "F" is a functor. This is vaguely related to the notion of coalgebra discussed above. Representations. A representation of an algebra "A" is an algebra homomorphism from "A" to the endomorphism algebra of some vector space (or module) "V". The property of "ρ" being an algebra homomorphism means that "ρ" preserves the multiplicative operation (that is, for all "x" and "y" in "A"), and that "ρ" sends the unit of "A" to the unit of End("V") (that is, to the identity endomorphism of "V").
If "A" and "B" are two algebras, and and are two representations, then there is a (canonical) representation of the tensor product algebra on the vector space . However, there is no natural way of defining a tensor product of two representations of a single associative algebra in such a way that the result is still a representation of that same algebra (not of its tensor product with itself), without somehow imposing additional conditions. Here, by "tensor product of representations", the usual meaning is intended: the result should be a linear representation of the same algebra on the product vector space. Imposing such additional structure typically leads to the idea of a Hopf algebra or a Lie algebra, as demonstrated below. Motivation for a Hopf algebra. Consider, for example, two representations and . One might try to form a tensor product representation according to how it acts on the product vector space, so that However, such a map would not be linear, since one would have for . One can rescue this attempt and restore linearity by imposing additional structure, by defining an algebra homomorphism , and defining the tensor product representation as
Such a homomorphism Δ is called a comultiplication if it satisfies certain axioms. The resulting structure is called a bialgebra. To be consistent with the definitions of the associative algebra, the coalgebra must be co-associative, and, if the algebra is unital, then the co-algebra must be co-unital as well. A Hopf algebra is a bialgebra with an additional piece of structure (the so-called antipode), which allows not only to define the tensor product of two representations, but also the Hom module of two representations (again, similarly to how it is done in the representation theory of groups). Motivation for a Lie algebra. One can try to be more clever in defining a tensor product. Consider, for example, so that the action on the tensor product space is given by This map is clearly linear in "x", and so it does not have the problem of the earlier definition. However, it fails to preserve multiplication: But, in general, this does not equal This shows that this definition of a tensor product is too naive; the obvious fix is to define it such that it is antisymmetric, so that the middle two terms cancel. This leads to the concept of a Lie algebra.
Non-unital algebras. Some authors use the term "associative algebra" to refer to structures which do not necessarily have a multiplicative identity, and hence consider homomorphisms which are not necessarily unital. One example of a non-unital associative algebra is given by the set of all functions whose limit as "x" nears infinity is zero. Another example is the vector space of continuous periodic functions, together with the convolution product.
Axiom of regularity In mathematics, the axiom of regularity (also known as the axiom of foundation) is an axiom of Zermelo–Fraenkel set theory that states that every non-empty set "A" contains an element that is disjoint from "A". In first-order logic, the axiom reads: formula_1 The axiom of regularity together with the axiom of pairing implies that no set is an element of itself, and that there is no infinite sequence ("an") such that "ai+1" is an element of "ai" for all "i". With the axiom of dependent choice (which is a weakened form of the axiom of choice), this result can be reversed: if there are no such infinite sequences, then the axiom of regularity is true. Hence, in this context the axiom of regularity is equivalent to the sentence that there are no downward infinite membership chains. The axiom was originally formulated by von Neumann; it was adopted in a formulation closer to the one found in contemporary textbooks by Zermelo. Virtually all results in the branches of mathematics based on set theory hold even in the absence of regularity. However, regularity makes some properties of ordinals easier to prove; and it not only allows induction to be done on well-ordered sets but also on proper classes that are well-founded relational structures such as the lexicographical ordering on formula_2
Given the other axioms of Zermelo–Fraenkel set theory, the axiom of regularity is equivalent to the axiom of induction. The axiom of induction tends to be used in place of the axiom of regularity in intuitionistic theories (ones that do not accept the law of the excluded middle), where the two axioms are not equivalent. In addition to omitting the axiom of regularity, non-standard set theories have indeed postulated the existence of sets that are elements of themselves. Elementary implications of regularity. No set is an element of itself. Let "A" be a set, and apply the axiom of regularity to {"A"}, which is a set by the axiom of pairing. We see that there must be an element of {"A"} which is disjoint from {"A"}. Since the only element of {"A"} is "A", it must be that "A" is disjoint from {"A"}. So, since formula_3, we cannot have "A" an element of "A" (by the definition of disjoint). No infinite descending sequence of sets exists. Suppose, to the contrary, that there is a function, "f", on the natural numbers with "f"("n"+1) an element of "f"("n") for each "n". Define "S" = {"f"("n"): "n" a natural number}, the range of "f", which can be seen to be a set from the axiom schema of replacement. Applying the axiom of regularity to "S", let "B" be an element of "S" which is disjoint from "S". By the definition of "S", "B" must be "f"("k") for some natural number "k". However, we are given that "f"("k") contains "f"("k"+1) which is also an element of "S". So "f"("k"+1) is in the intersection of "f"("k") and "S". This contradicts the fact that they are disjoint sets. Since our supposition led to a contradiction, there must not be any such function, "f".
The nonexistence of a set containing itself can be seen as a special case where the sequence is infinite and constant. Notice that this argument only applies to functions "f" that can be represented as sets as opposed to undefinable classes. The hereditarily finite sets, "V"ω, satisfy the axiom of regularity (and all other axioms of ZFC except the axiom of infinity). So if one forms a non-trivial ultrapower of Vω, then it will also satisfy the axiom of regularity. The resulting model will contain elements, called non-standard natural numbers, that satisfy the definition of natural numbers in that model but are not really natural numbers. They are "fake" natural numbers which are "larger" than any actual natural number. This model will contain infinite descending sequences of elements. For example, suppose "n" is a non-standard natural number, then formula_4 and formula_5, and so on. For any actual natural number "k", formula_6. This is an unending descending sequence of elements. But this sequence is not definable in the model and thus not a set. So no contradiction to regularity can be proved.
Simpler set-theoretic definition of the ordered pair. The axiom of regularity enables defining the ordered pair ("a","b") as {"a",{"a","b"}}; see ordered pair for specifics. This definition eliminates one pair of braces from the canonical Kuratowski definition ("a","b") = . Every set has an ordinal rank. This was actually the original form of the axiom in von Neumann's axiomatization. Suppose "x" is any set. Let "t" be the transitive closure of {"x"}. Let "u" be the subset of "t" consisting of unranked sets. If "u" is empty, then "x" is ranked and we are done. Otherwise, apply the axiom of regularity to "u" to get an element "w" of "u" which is disjoint from "u". Since "w" is in "u", "w" is unranked. "w" is a subset of "t" by the definition of transitive closure. Since "w" is disjoint from "u", every element of "w" is ranked. Applying the axioms of replacement and union to combine the ranks of the elements of "w", we get an ordinal rank for "w", to wit formula_7. This contradicts the conclusion that "w" is unranked. So the assumption that "u" was non-empty must be false and "x" must have rank.
For every two sets, only one can be an element of the other. Let "X" and "Y" be sets. Then apply the axiom of regularity to the set {"X","Y"} (which exists by the axiom of pairing). We see there must be an element of {"X","Y"} which is also disjoint from it. It must be either "X" or "Y". By the definition of disjoint then, we must have either "Y" is not an element of "X" or vice versa. The axiom of dependent choice and no infinite descending sequence of sets implies regularity. Let the non-empty set "S" be a counter-example to the axiom of regularity; that is, every element of "S" has a non-empty intersection with "S". We define a binary relation "R" on "S" by formula_8, which is entire by assumption. Thus, by the axiom of dependent choice, there is some sequence ("an") in "S" satisfying "anRan+1" for all "n" in N. As this is an infinite descending chain, we arrive at a contradiction and so, no such "S" exists. Regularity and the rest of ZF(C) axioms. Regularity was shown to be relatively consistent with the rest of ZF by Skolem and von Neumann, meaning that if ZF without regularity is consistent, then ZF (with regularity) is also consistent.
The axiom of regularity was also shown to be independent from the other axioms of ZFC, assuming they are consistent. The result was announced by Paul Bernays in 1941, although he did not publish a proof until 1954. The proof involves (and led to the study of) Rieger-Bernays permutation models (or method), which were used for other proofs of independence for non-well-founded systems. Regularity and Russell's paradox. Naive set theory (the axiom schema of unrestricted comprehension and the axiom of extensionality) is inconsistent due to Russell's paradox. In early formalizations of sets, mathematicians and logicians have avoided that contradiction by replacing the axiom schema of comprehension with the much weaker axiom schema of separation. However, this step alone takes one to theories of sets which are considered too weak. So some of the power of comprehension was added back via the other existence axioms of ZF set theory (pairing, union, powerset, replacement, and infinity) which may be regarded as special cases of comprehension. So far, these axioms do not seem to lead to any contradiction. Subsequently, the axiom of choice and the axiom of regularity were added to exclude models with some undesirable properties. These two axioms are known to be relatively consistent.
In the presence of the axiom schema of separation, Russell's paradox becomes a proof that there is no set of all sets. The axiom of regularity together with the axiom of pairing also prohibit such a universal set. However, Russell's paradox yields a proof that there is no "set of all sets" using the axiom schema of separation alone, without any additional axioms. In particular, ZF without the axiom of regularity already prohibits such a universal set. If a theory is extended by adding an axiom or axioms, then any (possibly undesirable) consequences of the original theory remain consequences of the extended theory. In particular, if ZF without regularity is extended by adding regularity to get ZF, then any contradiction (such as Russell's paradox) which followed from the original theory would still follow in the extended theory. The existence of Quine atoms (sets that satisfy the formula equation "x" = {"x"}, i.e. have themselves as their only elements) is consistent with the theory obtained by removing the axiom of regularity from ZFC. Various non-wellfounded set theories allow "safe" circular sets, such as Quine atoms, without becoming inconsistent by means of Russell's paradox.
Regularity, the cumulative hierarchy, and types. In ZF it can be proven that the class formula_9, called the von Neumann universe, is equal to the class of all sets. This statement is even equivalent to the axiom of regularity (if we work in ZF with this axiom omitted). From any model which does not satisfy the axiom of regularity, a model which satisfies it can be constructed by taking only sets in formula_9. Herbert Enderton wrote that "The idea of rank is a descendant of Russell's concept of "type"". Comparing ZF with type theory, Alasdair Urquhart wrote that "Zermelo's system has the notational advantage of not containing any explicitly typed variables, although in fact it can be seen as having an implicit type structure built into it, at least if the axiom of regularity is included. Dana Scott went further and claimed that: In the same paper, Scott shows that an axiomatic system based on the inherent properties of the cumulative hierarchy turns out to be equivalent to ZF, including regularity. History. The concept of well-foundedness and rank of a set were both introduced by Dmitry Mirimanoff. Mirimanoff called a set "x" "regular" () if every descending chain "x" ∋ "x"1 ∋ "x"2 ∋ ... is finite. Mirimanoff however did not consider his notion of regularity (and well-foundedness) as an axiom to be observed by all sets; in later papers Mirimanoff also explored what are now called non-well-founded sets ( in Mirimanoff's terminology).
Skolem and von Neumann pointed out that non-well-founded sets are superfluous and in the same publication von Neumann gives an axiom which excludes some, but not all, non-well-founded sets. In a subsequent publication, von Neumann gave an equivalent but more complex version of the axiom of class foundation: formula_11 The contemporary and final form of the axiom is due to Zermelo. Regularity in the presence of urelements. Urelements are objects that are not sets, but which can be elements of sets. In ZF set theory, there are no urelements, but in some other set theories such as ZFA, there are. In these theories, the axiom of regularity must be modified. The statement "formula_12" needs to be replaced with a statement that formula_13 is not empty and is not an urelement. One suitable replacement is formula_14, which states that "x" is inhabited.
IBM AIX AIX (pronounced ) is a series of proprietary Unix operating systems developed and sold by IBM since 1986. The name stands for "Advanced Interactive eXecutive". Current versions are designed to work with Power ISA based server and workstation computers such as IBM's Power line. Background. Originally released for the IBM RT PC RISC workstation in 1986, AIX has supported a wide range of hardware platforms, including the IBM RS/6000 series and later Power and PowerPC-based systems, IBM System i, System/370 mainframes, PS/2 personal computers, and the Apple Network Server. Currently, it is supported on IBM Power Systems alongside IBM i and Linux. AIX is based on UNIX System V with 4.3BSD-compatible extensions. It is certified to the UNIX 03 and UNIX V7 specifications of the Single UNIX Specification, beginning with AIX versions 5.3 and 7.2 TL5, respectively. Older versions were certified to the UNIX 95 and UNIX 98 specifications. AIX was the first operating system to implement a journaling file system. IBM has continuously enhanced the software with features such as processor, disk, and network virtualization, dynamic hardware resource allocation (including fractional processor units), and reliability engineering concepts derived from its mainframe designs.
History. Unix began in the early 1970s at AT&T's Bell Labs research center, running on DEC minicomputers. By 1976, the operating system was used in various academic institutions, including Princeton, where Tom Lyon and others ported it to the S/370 to run as a guest OS under VM/370. This port later grew into UTS, a mainframe Unix offering from IBM's competitor Amdahl Corporation. IBM's involvement with Unix began in 1979 when it assisted Bell Labs in porting Unix to the S/370 platform to be used as a build host for the 5ESS switch's software. During this process, IBM made modifications to the TSS/370 Resident Supervisor to better support Unix. In 1984, IBM introduced its own Unix variant for the S/370 platform called VM/IX, developed by Interactive Systems Corporation using Unix System III. However, VM/IX was only available as a PRPQ (Programming Request for Price Quotation) and was not a General Availability product. It was replaced in 1985 by IBM IX/370, a fully supported product based on AT&T's Unix/360 6th Edition, later updated to Unix System V.
In 1986, IBM introduced AIX Version 1 for the IBM RT PC workstation. It was based on UNIX System V Releases 1 and 2, incorporating source code from 4.2 and 4.3 BSD UNIX. AIX Version 2 followed in 1987 for the RT PC. In 1990, AIX Version 3 was released for the POWER-based RS/6000 platform. It became the primary operating system for the RS/6000 series, which was later renamed "IBM eServer pSeries", "IBM System p", and finally "IBM Power Systems". AIX Version 4, introduced in 1994, added symmetric multiprocessing and evolved through the 1990s, culminating with AIX 4.3.3 in 1999. A modified version of Version 4.1 was also used as the standard OS for the Apple Network Server line by Apple Computer. In the late 1990s, under Project Monterey, IBM and the Santa Cruz Operation attempted to integrate AIX and UnixWare into a multiplatform Unix for Intel IA-64 architecture. The project was discontinued in 2002 after limited commercial success. In 2003, the SCO Group filed a lawsuit against IBM, alleging misappropriation of UNIX System V source code in AIX. The case was resolved in 2010 when a jury ruled that Novell owned the rights to Unix, not SCO.
AIX 6 was announced in May 2007 and became generally available on November 9, 2007. Key features included role-based access control, workload partitions, and Live Partition Mobility. AIX 7.1 was released in September 2010 with enhancements such as Cluster Aware AIX and support for large-scale memory and real-time application requirements. Supported hardware platforms. IBM RT PC. The original AIX (sometimes called AIX/RT) was developed for the IBM RT PC workstation by IBM in conjunction with Interactive Systems Corporation, who had previously ported UNIX System III to the IBM PC for IBM as PC/IX. According to its developers, the AIX source (for this initial version) consisted of one million lines of code. Installation media consisted of eight 1.2M floppy disks. The RT was based on the IBM ROMP microprocessor, the first commercial RISC chip. This was based on a design pioneered at IBM Research (the IBM 801). One of the novel aspects of the RT design was the use of a microkernel, called Virtual Resource Manager (VRM). The keyboard, mouse, display, disk drives and network were all controlled by a microkernel. One could "hotkey" from one operating system to the next using the Alt-Tab key combination. Each OS in turn would get possession of the keyboard, mouse and display. Besides AIX v2, the PICK OS also included this microkernel.
Much of the AIX v2 kernel was written in the PL.8 programming language, which proved troublesome during the migration to AIX v3. AIX v2 included full TCP/IP networking, as well as SNA and two networking file systems: NFS, licensed from Sun Microsystems, and Distributed Services (DS). DS had the distinction of being built on top of SNA, and thereby being fully compatible with DS on and on midrange systems running OS/400 through IBM i. For the graphical user interfaces, AIX v2 came with the X10R3 and later the X10R4 and X11 versions of the X Window System from MIT, together with the Athena widget set. Compilers for Fortran and C were available. IBM PS/2 series. AIX PS/2 (also known as AIX/386) was developed by Locus Computing Corporation under contract to IBM. AIX PS/2, first released in October 1988, ran on IBM PS/2 personal computers with Intel 386 and compatible processors. The product was announced in September 1988 with a baseline tag price of $595, although some utilities, such as UUCP, were included in a separate Extension package priced at $250. nroff and troff for AIX were also sold separately in a Text Formatting System package priced at $200. The TCP/IP stack for AIX PS/2 retailed for another $300. The X Window System package was priced at $195, and featured a graphical environment called the AIXwindows Desktop, based on IXI's X.desktop. The C and FORTRAN compilers each had a price tag of $275. Locus also made available their DOS Merge virtual machine environment for AIX, which could run MS DOS 3.3 applications inside AIX; DOS Merge was sold separately for another $250. IBM also offered a $150 AIX PS/2 DOS Server Program, which provided file server and print server services for client computers running PC DOS 3.3.
The last version of PS/2 AIX is 1.3. It was released in 1992 and announced to add support for non-IBM (non-microchannel) computers as well. Support for PS/2 AIX ended in March 1995. IBM mainframes. In 1988, IBM announced AIX/370, also developed by Locus Computing. AIX/370 was IBM's fourth attempt to offer Unix-like functionality for their mainframe line, specifically the System/370 (the prior versions were a TSS/370-based Unix system developed jointly with AT&T c.1980, a VM/370-based system named VM/IX developed jointly with Interactive Systems Corporation c.1984, and a VM/370-based version of TSS/370 named IX/370 which was upgraded to be compatible with UNIX System V). AIX/370 was released in 1990 with functional equivalence to System V Release 2 and 4.3BSD as well as IBM enhancements. With the introduction of the ESA/390 architecture, AIX/370 was replaced by AIX/ESA in 1991, which was based on OSF/1, and also ran on the System/390 platform. This development effort was made partly to allow IBM to compete with Amdahl UTS. Unlike AIX/370, AIX/ESA ran both natively as the host operating system, and as a guest under VM. AIX/ESA, while technically advanced, had little commercial success, partially because UNIX functionality was added as an option to the existing mainframe operating system, MVS, as MVS/ESA SP Version 4 Release 3 OpenEdition in 1994, and continued as an integral part of MVS/ESA SP Version 5, OS/390 and z/OS, with the name eventually changing from "OpenEdition" to "Unix System Services". IBM also provided OpenEdition in VM/ESA Version 2 through z/VM.
IA-64 systems. As part of Project Monterey, IBM released a beta test version of AIX 5L for the IA-64 (Itanium) architecture in 2001, but this never became an official product due to lack of interest. Apple Network Servers. The Apple Network Server (ANS) systems were PowerPC-based systems designed by Apple Computer to have numerous high-end features that standard Apple hardware did not have, including swappable hard drives, redundant power supplies, and external monitoring capability. These systems were more or less based on the Power Macintosh hardware available at the time but were designed to use AIX (versions 4.1.4 or 4.1.5) as their native operating system in a specialized version specific to the ANS called AIX for Apple Network Servers. AIX was only compatible with the Network Servers and was not ported to standard Power Macintosh hardware. It should not be confused with A/UX, Apple's earlier version of Unix for 68k-based Macintoshes. POWER ISA/PowerPC/Power ISA-based systems. The release of AIX version 3 (sometimes called AIX/6000) coincided with the announcement of the first POWER1-based IBM RS/6000 models in 1990.
AIX v3 innovated in several ways on the software side. It was the first operating system to introduce the idea of a journaling file system, JFS, which allowed for fast boot times by avoiding the need to ensure the consistency of the file systems on disks (see fsck) on every reboot. Another innovation was shared libraries which avoid the need for static linking from an application to the libraries it used. The resulting smaller binaries used less of the hardware RAM to run, and used less disk space to install. Besides improving performance, it was a boon to developers: executable binaries could be in the tens of kilobytes instead of a megabyte for an executable statically linked to the C library. AIX v3 also scrapped the microkernel of AIX v2, a contentious move that resulted in v3 containing no PL.8 code and being somewhat more "pure" than v2. Other notable subsystems included: In addition, AIX applications can run in the PASE subsystem under IBM i. Source code. IBM formerly made the AIX for RS/6000 source code available to customers for a fee; in 1991, IBM customers could order the AIX 3.0 source code for a one-time charge of US$60,000; subsequently, IBM released the AIX 3.1 source code in 1992, and AIX 3.2 in 1993. These source code distributions excluded certain files (authored by third-parties) which IBM did not have rights to redistribute, and also excluded layered products such as the MS-DOS emulator and the C compiler. Furthermore, in order to be able to license the AIX source code, the customer first had to procure source code license agreements with AT&T and the University of California, Berkeley.
User interfaces. The default shell was Bourne shell up to AIX version 3, but was changed to KornShell (ksh88) in version 4 for XPG4 and POSIX compliance. Graphical. The Common Desktop Environment (CDE) is AIX's default graphical user interface. As part of Linux Affinity and the free AIX Toolbox for Linux Applications (ATLA), open-source KDE and GNOME desktops are also available. System Management Interface Tool. SMIT is the System Management Interface Tool for AIX. It allows a user to navigate a menu hierarchy of commands, rather than using the command line. Invocation is typically achieved with the command codice_1. Experienced system administrators make use of the codice_2 function key which generates the command line that SMIT will invoke to complete it. SMIT also generates a log of commands that are performed in the codice_3 file. The codice_3 file automatically records the commands with the command flags and parameters used. The codice_3 file can be used as an executable shell script to rerun system configuration tasks. SMIT also creates the codice_6 file, which contains additional detailed information that can be used by programmers in extending the SMIT system.
codice_1 and codice_8 refer to the same program, though codice_8 invokes the text-based version, while codice_1 will invoke an X Window System based interface if possible; however, if codice_1 determines that X Window System capabilities are not present, it will present the text-based version instead of failing. Determination of X Window System capabilities is typically performed by checking for the existence of the codice_12 variable. Database. Object Data Manager (ODM) is a database of system information integrated into AIX, analogous to the registry in Microsoft Windows. A good understanding of the ODM is essential for managing AIX systems. Data managed in ODM is stored and maintained as objects with associated attributes. Interaction with ODM is possible via application programming interface (API) library for programs, and command-line utilities such as "odmshow", "odmget", "odmadd", "odmchange" and "odmdelete" for shell scripts and users. SMIT and its associated AIX commands can also be used to query and modify information in the ODM. ODM is stored on disk using Berkeley DB files. Example of information stored in the ODM database are:
AppleTalk AppleTalk is a discontinued proprietary suite of networking protocols developed by Apple Computer for their Macintosh computers. AppleTalk includes a number of features that allow local area networks to be connected with no prior setup or the need for a centralized router or server of any sort. Connected AppleTalk-equipped systems automatically assign addresses, update the distributed namespace, and configure any required inter-networking routing. AppleTalk was released in 1985 and was the primary protocol used by Apple devices through the 1980s and 1990s. Versions were also released for the IBM PC and compatibles and the Apple IIGS. AppleTalk support was also available in most networked printers (especially laser printers), some file servers, and a number of routers. The rise of TCP/IP during the 1990s led to a reimplementation of most of these types of support on that protocol, and AppleTalk became unsupported as of the release of Mac OS X v10.6 in 2009. Many of AppleTalk's more advanced autoconfiguration features have since been introduced in Bonjour, while Universal Plug and Play serves similar needs.
History. AppleNet. After the release of the Apple Lisa computer in January 1983, Apple invested considerable effort in the development of a local area networking (LAN) system for the machines. Known as AppleNet, it was based on the seminal Xerox XNS protocol stack but running on a custom 1 Mbit/s coaxial cable system rather than Xerox's 2.94 Mbit/s Ethernet. AppleNet was announced early in 1983 with a full introduction at the target price of $500 for plug-in AppleNet cards for the Lisa and the Apple II. At that time, early LAN systems were just coming to market, including Ethernet, Token Ring, Econet, and ARCNET. This was a topic of major commercial effort at the time, dominating shows like the National Computer Conference (NCC) in Anaheim in May 1983. All of the systems were jockeying for position in the market, but even at this time, Ethernet's widespread acceptance suggested it was to become a "de facto" standard. It was at this show that Steve Jobs asked Gursharan Sidhu a seemingly innocuous question: "Why has networking not caught on?"
Four months later, in October, AppleNet was cancelled. At the time, they announced that "Apple realized that it's not in the business to create a networking system. We built and used AppleNet in-house, but we realized that if we had shipped it, we would have seen new standards coming up." In January, Jobs announced that they would instead be supporting IBM's Token Ring, which he expected to come out in a "few months". AppleBus. Through this period, Apple was deep in development of the Macintosh computer. During development, engineers had made the decision to use the Zilog 8530 serial controller chip (SCC) instead of the lower-cost and more common UART to provide serial port connections. The SCC cost about $5 more than a UART, but offered much higher speeds of up to 250 kilobits per second (or higher with additional hardware) and internally supported a number of basic networking-like protocols like IBM's Bisync. The SCC was chosen because it would allow multiple devices to be attached to the port. Peripherals equipped with similar SCCs could communicate using the built-in protocols, interleaving their data with other peripherals on the same bus. This would eliminate the need for more ports on the back of the machine, and allowed for the elimination of expansion slots for supporting more complex devices. The initial concept was known as AppleBus, envisioning a system controlled by the host Macintosh polling "dumb" devices in a fashion similar to the modern Universal Serial Bus.
AppleBus networking. The Macintosh team had already begun work on what would become the LaserWriter and had considered a number of other options to answer the question of how to share these expensive machines and other resources. A series of memos from Bob Belleville clarified these concepts, outlining the Mac, LaserWriter, and a file server system which would become the Macintosh Office. By late 1983 it was clear that IBM's Token Ring would not be ready in time for the launch of the Mac, and might miss the launch of these other products as well. In the end, Token Ring would not ship until October 1985. Jobs' earlier question to Sidhu had already sparked a number of ideas. When AppleNet was cancelled in October, Sidhu led an effort to develop a new networking system based on the AppleBus hardware. This new system would not have to conform to any existing preconceptions, and was designed to be worthy of the Mac – a system that was user-installable and required no configuration or fixed network addresses – in short, a true plug-and-play network. Considerable effort was needed, but by the time the Mac was released, the basic concepts had been outlined, and some of the low-level protocols were on their way to completion. Sidhu mentioned the work to Belleville only two hours after the Mac was announced.
The "new" AppleBus was announced in early 1984, allowing direct connection from the Mac or Lisa through a small box that is plugged into the serial port and connected via cables to the next computer upstream and downstream. Adaptors for Apple II and Apple III were also announced. Apple also announced that an AppleBus network could be attached to, and would appear to be a single node within, a Token Ring system. Details of how this would work were sketchy. AppleTalk Personal Network. Just prior to its release in early 1985, AppleBus was renamed AppleTalk. Initially marketed as AppleTalk Personal Network, it comprised a family of network protocols and a physical layer. The physical layer had a number of limitations, including a speed of only 230.4 kbit/s, a maximum distance of from end to end, and only 32 nodes per LAN. But as the basic hardware was built into the Mac, adding nodes only cost about $50 for the adaptor box. In comparison, Ethernet or Token Ring cards cost hundreds or thousands of dollars. Additionally, the entire networking stack required only about 6 kB of RAM, allowing it to run on any Mac.
The relatively slow speed of AppleTalk allowed further reductions in cost. Instead of using RS-422's balanced transmit and receive circuits, the AppleTalk cabling used a single common electrical ground, which limited speeds to about 500 kbit/s, but allowed one conductor to be removed. This meant that common three-conductor cables could be used for wiring. Additionally, the adaptors were designed to be "self-terminating", meaning that nodes at the end of the network could simply leave their last connector unconnected. There was no need for the wires to be connected back together into a loop, nor the need for hubs or other devices. The system was designed for future expansion; the addressing system allowed for expansion to 255 nodes in a LAN (although only 32 could be used at that time), and by using "bridges" (which came to be known as "routers", although technically not the same) one could interconnect LANs into larger collections. "Zones" allowed devices to be addressed within a bridge-connected internet. Additionally, AppleTalk was designed from the start to allow use with any potential underlying physical link, and within a few years, the physical layer would be renamed LocalTalk, so as to differentiate it from the AppleTalk protocols.
The main advantage of AppleTalk was that it was completely maintenance-free. To join a device to a network, a user simply plugged the adaptor into the machine, then connected a cable from it to any free port on any other adaptor. The AppleTalk network stack negotiated a network address, assigned the computer a human-readable name, and compiled a list of the names and types of other machines on the network so the user could browse the devices through the Chooser. AppleTalk was so easy to use that ad hoc networks tended to appear whenever multiple Macs were in the same room. Apple would later use this in an advertisement showing a network being created between two seats in an airplane. PhoneNet and other adaptors. A thriving third-party market for AppleTalk devices developed over the next few years. One particularly notable example was an alternate adaptor designed by BMUG and commercialised by Farallon as PhoneNET in 1987. This was essentially a replacement for Apple's connector that had conventional phone jacks instead of Apple's round connectors. PhoneNet allowed AppleTalk networks to be connected together using normal telephone wires, and with very little extra work, could run analog phones and AppleTalk on a single four-conductor phone cable.
Other companies took advantage of the SCC's ability to read external clocks in order to support higher transmission speeds, up to 1 Mbit/s. In these systems, the external adaptor also included its own clock, and used that to signal the SCC's clock input pins. The best-known such system was Centram's FlashTalk, which ran at 768 kbit/s, and was intended to be used with their TOPS networking system. A similar solution was the 850 kbit/s DaynaTalk, which used a separate box that plugged in between the computer and a normal LocalTalk/PhoneNet box. Dayna also offered a PC expansion card that ran up to 1.7 Mbit/s when talking to other Dayna PC cards. Several other systems also existed with even higher performance, but these often required special cabling that was incompatible with LocalTalk/PhoneNet, and also required patches to the networking stack that often caused problems. AppleTalk over Ethernet. As Apple expanded into more commercial and education markets, they needed to integrate AppleTalk into existing network installations. Many of these organisations had already invested in a very expensive Ethernet infrastructure and there was no direct way to connect a Macintosh to Ethernet. AppleTalk included a protocol structure for interconnecting AppleTalk subnets and so as a solution, EtherTalk was initially created to use the Ethernet as a backbone between LocalTalk subnets. To accomplish this, organizations would need to purchase a LocalTalk-to-Ethernet bridge and Apple left it to third parties to produce these products. A number of companies responded, including Hayes and a few newly formed companies like Kinetics.
LocalTalk, EtherTalk, TokenTalk, and AppleShare. By 1987, Ethernet was clearly winning the standards battle over Token Ring, and in the middle of that year, Apple introduced EtherTalk 1.0, an implementation of the AppleTalk protocol over the Ethernet physical layer. Introduced for the newly released Macintosh II computer, one of Apple's first two Macintoshes with expansion slots (the Macintosh SE had one slot of a different type), the operating system included a new Network control panel that allowed the user to select which physical connection to use for networking (from "Built-in" or "EtherTalk"). At introduction, Ethernet interface cards were available from 3Com and Kinetics that plugged into a Nubus slot in the machine. The new networking stack also expanded the system to allow a full 255 nodes per LAN. With EtherTalk's release, AppleTalk Personal Network was renamed LocalTalk, the name it would be known under for the bulk of its life. Token Ring would later be supported with a similar TokenTalk product, which used the same Network control panel and underlying software. Over time, many third-party companies would introduce compatible Ethernet and Token Ring cards that used these same drivers.
The appearance of a Macintosh with a direct Ethernet connection also magnified the Ethernet and LocalTalk compatibility problem: Networks with new and old Macs needed some way to communicate with each other. This could be as simple as a network of Ethernet Mac II's trying to talk to a LaserWriter that only connected to LocalTalk. Apple initially relied on the aforementioned LocalTalk-to-Ethernet bridge products, but contrary to Apple's belief that these would be low-volume products, by the end of 1987, 130,000 such networks were in use. AppleTalk was at that time the most used networking system in the world, with over three times the installations of any other vendor. 1987 also marked the introduction of the AppleShare product, a dedicated file server that ran on any Mac with 512 kB of RAM or more. A common AppleShare machine was the Mac Plus with an external SCSI hard drive. AppleShare was the #3 network operating system in the late 1980s, behind Novell NetWare and Microsoft's MS-Net. AppleShare was effectively the replacement for the failed Macintosh Office efforts, which had been based on a dedicated file server device.
AppleTalk Phase II and other developments. A significant re-design was released in 1989 as AppleTalk Phase II. In many ways, Phase II can be considered an effort to make the earlier version (never called Phase I) more generic. LANs could now support more than 255 nodes, and zones were no longer associated with physical networks but were entirely virtual constructs used simply to organize nodes. For instance, one could now make a "Printers" zone that would list all the printers in an organization, or one might want to place that same device in the "2nd Floor" zone to indicate its physical location. Phase II also included changes to the underlying inter-networking protocols to make them less "chatty", which had previously been a serious problem on networks that bridged over wide-area networks. By this point, Apple had a wide variety of communications products under development, and many of these were announced along with AppleTalk Phase II. These included updates to EtherTalk and TokenTalk, AppleTalk software and LocalTalk hardware for the IBM PC, EtherTalk for Apple's A/UX operating system allowing it to use LaserWriters and other network resources, and the Mac X.25 and MacX products.
Ethernet had become almost universal by 1990, and it was time to build Ethernet into Macs direct from the factory. However, the physical wiring used by these networks was not yet completely standardized. Apple solved this problem using a single port on the back of the computer into which the user could plug an adaptor for any given cabling system. This FriendlyNet system was based on the industry-standard Attachment Unit Interface or AUI, but deliberately chose a non-standard connector that was smaller and easier to use, which they called "Apple AUI", or AAUI. FriendlyNet was first introduced on the Quadra 700 and Quadra 900 computers, and used across much of the Mac line for some time. As with LocalTalk, a number of third-party FriendlyNet adaptors quickly appeared. As 10BASE-T became the de facto cabling system for Ethernet, second-generation Power Macintosh machines added a 10BASE-T port in addition to AAUI. The PowerBook 3400c and lower-end Power Macs also added 10BASE-T. The Power Macintosh 7300/8600/9600 were the final Macs to include AAUI, and 10BASE-T became universal starting with the Power Macintosh G3 and PowerBook G3.
The capital-I Internet. From the beginning of AppleTalk, users wanted to connect the Macintosh to TCP/IP network environments. In 1984, Bill Croft at Stanford University pioneered the development of IP packets encapsulated in DDP as part of the SEAGATE (Stanford Ethernet–AppleTalk Gateway) project. SEAGATE was commercialized by Kinetics in their LocalTalk-to-Ethernet bridge as an additional routing option. A few years later, MacIP was separated from the SEAGATE code and became the de facto method for IP packets to be routed over LocalTalk networks. By 1986, Columbia University released the first version of the Columbia AppleTalk Package (CAP) that allowed higher integration of Unix, TCP/IP, and AppleTalk environments. In 1988, Apple released MacTCP, a system that allowed the Mac to support TCP/IP on machines with suitable Ethernet hardware. However, this left many universities with the problem of supporting IP on their many LocalTalk-equipped Macs. It was soon common to include MacIP support in LocalTalk-to-Ethernet bridges. MacTCP would not become a standard part of the Classic Mac OS until 1994, by which time it also supported SNMP and PPP.
For some time in the early 1990s, the Mac was a primary client on the rapidly expanding Internet. Among the better-known programs in wide use were Fetch, Eudora, eXodus, NewsWatcher, and the NCSA packages, especially NCSA Mosaic and its offspring, Netscape Navigator. Additionally, a number of server products appeared that allowed the Mac to host Internet content. Through this period, Macs had about 2 to 3 times as many clients connected to the Internet as any other platform, despite the relatively small overall microcomputer market share. As the world quickly moved to IP for both LAN and WAN uses, Apple was faced with maintaining two increasingly outdated code bases on an ever-wider group of machines as well as the introduction of the PowerPC-based machines. This led to the Open Transport efforts, which re-implemented both MacTCP and AppleTalk on an entirely new code base adapted from the Unix standard STREAMS. Early versions had problems and did not become stable for some time. By that point, Apple was deep in their ultimately doomed Copland efforts.
Legacy and abandonment. With the purchase of NeXT and subsequent development of Mac OS X, AppleTalk was strictly a legacy system. Support was added to Mac OS X in order to provide support for a large number of existing AppleTalk devices, notably laser printers and file shares, but alternate connection solutions common in this era, notably USB for printers, limited their demand. As Apple abandoned many of these product categories, and all new systems were based on IP, AppleTalk became less and less common. AppleTalk support was finally removed from the macOS line in Mac OS X v10.6 in 2009. However, the loss of AppleTalk did not reduce the desire for networking solutions that combined its ease of use with IP routing. Apple has led the development of many such efforts, from the introduction of the AirPort router to the development of the zero-configuration networking system and their implementation of it, Rendezvous, later renamed "Bonjour". As of 2020, AppleTalk support has been completely removed from legacy support with macOS 11 Big Sur.
Design. The AppleTalk design rigorously followed the OSI model of protocol layering. Unlike most of the early LAN systems, AppleTalk was not built using the archetypal Xerox XNS system. The intended target was not Ethernet, and it did not have 48-bit addresses to route. Nevertheless, many portions of the AppleTalk system have direct analogs in XNS. One key differentiation for AppleTalk was it contained two protocols aimed at making the system completely self-configuring. The "AppleTalk address resolution protocol" ("AARP") allowed AppleTalk hosts to automatically generate their own network addresses, and the "Name Binding Protocol" ("NBP") was a dynamic system for mapping network addresses to user-readable names. Although systems similar to AARP existed in other systems, Banyan VINES for instance. Beginning about 2002 Rendezvous (the combination of DNS-based service discovery, Multicast DNS, and link-local addressing) provided capabilities and usability using IP that were similar to those of AppleTalk. Both AARP and NBP had defined ways to allow "controller" devices to override the default mechanisms. The concept was to allow routers to provide the information or "hardwire" the system to known addresses and names. On larger networks where AARP could cause problems as new nodes searched for free addresses, the addition of a router could reduce "chattiness." Together AARP and NBP made AppleTalk an easy-to-use networking system. New machines were added to the network by plugging them in and optionally giving them a name. The NBP lists were examined and displayed by a program known as the "Chooser" which would display a list of machines on the local network, divided into classes such as file-servers and printers.
Addressing. An AppleTalk address was a four-byte quantity. This consisted of a two-byte network number, a one-byte node number, and a one-byte socket number. Of these, only the network number required any configuration, being obtained from a router. Each node dynamically chose its own node number, according to a protocol (originally the LocalTalk Link Access Protocol LLAP and later, for Ethernet/EtherTalk, the AppleTalk Address Resolution Protocol, AARP) which handled contention between different nodes accidentally choosing the same number. For socket numbers, a few well-known numbers were reserved for special purposes specific to the AppleTalk protocol itself. Apart from these, all application-level protocols were expected to use dynamically assigned socket numbers at both the client and server end. Because of this dynamism, users could not be expected to access services by specifying their address. Instead, all services had "names" which, being chosen by humans, could be expected to be meaningful to users, and also could be sufficiently long to minimize the chance of conflicts.
As NBP names translated to an address, which included a socket number as well as a node number, a name in AppleTalk mapped directly to a "service" being provided by a machine, which was entirely separate from the name of the machine itself. Thus, services could be moved to a different machine and, so long as they kept the same service name, there was no need for users to do anything different in order to continue accessing the service. And the same machine could host any number of instances of services of the same type, without any network connection conflicts. Contrast this with "A records" in the DNS, in which a name translates to a machine's address, not including the port number that might be providing a service. Thus, if people are accustomed to using a particular machine name to access a particular service, their access will break when the service is moved to a different machine. This can be mitigated somewhat by insistence on using "CNAME records" indicating service rather than actual machine names to refer to the service, but there is no way of guaranteeing that users will follow such a convention. Some newer protocols, such as Kerberos and Active Directory use DNS SRV records to identify services by name, which is much closer to the AppleTalk model.
Protocols. AppleTalk Address Resolution Protocol. The AppleTalk Address Resolution Protocol (AARP) resolves AppleTalk addresses to link layer addresses. It is functionally equivalent to ARP and obtains address resolution by a method very similar to ARP. AARP is a fairly simple system. When powered on, an AppleTalk machine broadcasts an "AARP probe packet" asking for a network address, intending to hear back from controllers such as routers. If no address is provided, one is picked at random from the "base subnet", 0. It then broadcasts another packet saying "I am selecting this address", and then waits to see if anyone else on the network complains. If another machine has that address, the newly connecting machine will pick another address, and keep trying until it finds a free one. On a network with many machines it may take several tries before a free address is found, so for performance purposes the successful address is recorded in NVRAM and used as the default address in the future. This means that in most real-world setups where machines are added a few at a time, only one or two tries are needed before the address effectively becomes constant.
AppleTalk Data Stream Protocol. The AppleTalk Data Stream Protocol (ADSP) was a comparatively late addition to the AppleTalk protocol suite, done when it became clear that a TCP-style reliable connection-oriented transport was needed. Significant differences from TCP were that: Apple Filing Protocol. The Apple Filing Protocol (AFP), formerly AppleTalk Filing Protocol, is the protocol for communicating with AppleShare file servers. Built on top of AppleTalk Session Protocol (for legacy AFP over DDP) or the Data Stream Interface (for AFP over TCP), it provides services for authenticating users (extensible to different authentication methods including two-way random-number exchange) and for performing operations specific to the Macintosh HFS filesystem. AFP is still in use in macOS, even though most other AppleTalk protocols have been deprecated. AppleTalk Session Protocol. The AppleTalk Session Protocol (ASP) was an intermediate protocol, built on top of AppleTalk Transaction Protocol (ATP), which in turn was the foundation of AFP. It provided basic services for requesting responses to arbitrary "commands" and performing out-of-band status queries. It also allowed the server to send asynchronous "attention" messages to the client.
AppleTalk Transaction Protocol. The AppleTalk Transaction Protocol (ATP) was the original reliable transport-level protocol for AppleTalk, built on top of DDP. At the time it was being developed, a full, reliable connection-oriented protocol like TCP was considered to be too expensive to implement for most of the intended uses of AppleTalk. Thus, ATP was a simple request/response exchange, with no need to set up or tear down connections. An ATP "request" packet could be answered by up to eight "response" packets. The requestor then sent an "acknowledgement" packet containing a bit mask indicating which of the response packets it received, so the responder could retransmit the remainder. ATP could operate in either "at-least-once" mode or "exactly-once" mode. Exactly-once mode was essential for operations which were not idempotent; in this mode, the responder kept a copy of the response buffers in memory until successful receipt of a "release" packet from the requestor, or until a timeout elapsed. This way, it could respond to duplicate requests with the same transaction ID by resending the same response data, without performing the actual operation again.
Datagram Delivery Protocol. The Datagram Delivery Protocol (DDP) was the lowest-level data-link-independent transport protocol. It provided a datagram service with no guarantees of delivery. All application-level protocols, including the infrastructure protocols NBP, RTMP and ZIP, were built on top of DDP. AppleTalk's DDP corresponds closely to the Network layer of the Open Systems Interconnection (OSI) communication model. Name Binding Protocol. The Name Binding Protocol (NBP) was a dynamic, distributed system for managing AppleTalk names. When a service started up on a machine, it registered a name for itself as chosen by a human administrator. At this point, NBP provided a system for checking that no other machine had already registered the same name. Later, when a client wanted to access that service, it used NBP to query machines to find that service. NBP provided browsability ("what are the names of all the services available?") as well as the ability to find a service with a particular name. Names were human-readable, containing spaces and upper- and lower-case letters, and including support for searching.
AppleTalk Echo Protocol. The AppleTalk Echo Protocol (AEP) was a transport layer protocol designed to test the reachability of network nodes. AEP generates packets to be sent to the network node and is identified in the Type field of a packet as an AEP packet. The packet is first passed to the source DDP. After it is identified as an AEP packet, it is forwarded to the node where the packet is examined by the DDP at the destination. After the packet is identified as an AEP packet, the packet is then copied and a field in the packet is altered to create an AEP reply packet, and is then returned to the source node. Printer Access Protocol. The Printer Access Protocol (PAP) was the standard way of communicating with PostScript printers. It was built on top of ATP. When a PAP connection was opened, each end sent the other an ATP request which basically meant "send me more data". The client's response to the server was to send a block of PostScript code, while the server could respond with any diagnostic messages that might be generated as a result, after which another "send-more-data" request was sent. This use of ATP provided automatic flow control; each end could only send data to the other end if there was an outstanding ATP request to respond to.
PAP also provided for out-of-band status queries, handled by separate ATP transactions. Even while it was busy servicing a print job from one client, a PAP server could continue to respond to status requests from any number of other clients. This allowed other Macintoshes on the LAN that were waiting to print to display status messages indicating that the printer was busy, and what the job was that it was busy with. Routing Table Maintenance Protocol. The Routing Table Maintenance Protocol (RTMP) was the protocol by which routers kept each other informed about the topology of the network. This was the only part of AppleTalk that required periodic unsolicited broadcasts: every 10 seconds, each router had to send out a list of all the network numbers it knew about and how far away it thought they were. Zone Information Protocol. The Zone Information Protocol (ZIP) was the protocol by which AppleTalk network numbers were associated with zone names. A "zone" was a subdivision of the network that made sense to humans (for example, "Accounting Department"); but while a network number had to be assigned to a topologically contiguous section of the network, a zone could include several different discontiguous portions of the network.
Physical implementation. The initial default hardware implementation for AppleTalk was a high-speed serial protocol known as "LocalTalk" that used the Macintosh's built-in RS-422 ports at 230.4 kbit/s. LocalTalk used a splitter box in the RS-422 port to provide an upstream and downstream cable from a single port. The topology was a bus: cables were daisy-chained from each connected machine to the next, up to the maximum of 32 permitted on any LocalTalk segment. The system was slow by today's standards, but at the time the additional cost and complexity of networking on PC machines was such that it was common that Macs were the only networked personal computers in an office. Other larger computers, such as UNIX or VAX workstations, would commonly be networked via Ethernet. Other physical implementations were also available. A very popular replacement for LocalTalk was "PhoneNET", a third-party solution from Farallon Computing, Inc. (renamed Netopia, acquired by Motorola in 2007) that also used the RS-422 port and was indistinguishable from LocalTalk as far as Apple's LocalTalk port drivers were concerned, but ran over very inexpensive standard phone cabling with four-wire, six-position modular connectors, the same cables used to connect landline telephones. Since it used the second pair of wires, network devices could even be connected through existing telephone jacks if a second line was not present. Foreshadowing today's network hubs and switches, Farallon provided solutions for PhoneNet to be used in "star" as well as "bus" configurations, with both "passive" star connections (with the phone wires simply bridged to each other at a central point), and "active" star with "PhoneNet Star Controller" hub hardware. In a star configuration, any wiring issue only affected one device, and problems were easy to pinpoint. PhoneNet's low cost, flexibility, and easy troubleshooting resulted in it being the dominant choice for Mac networks into the early 1990s.
AppleTalk protocols also came to run over Ethernet (first coaxial and then twisted pair) and Token Ring physical layers, labeled by Apple as "EtherTalk" and "TokenTalk", respectively. EtherTalk gradually became the dominant implementation method for AppleTalk as Ethernet became generally popular in the PC industry throughout the 1990s. Besides AppleTalk and TCP/IP, any Ethernet network could also simultaneously carry other protocols such as DECnet and IPX. Cross-platform solutions. When AppleTalk was first introduced, the dominant office computing platform was the PC compatible running MS-DOS. Apple introduced the AppleTalk PC Card in early 1987, allowing PCs to join AppleTalk networks and print to LaserWriter printers. A year later AppleShare PC was released, allowing PCs to access AppleShare file servers. The "TOPS Teleconnector" MS-DOS networking system over AppleTalk system enabled MS-DOS PCs to communicate over AppleTalk network hardware; it comprised an AppleTalk interface card for the PC and a suite of networking software allowing such functions as file, drive and printer sharing. As well as allowing the construction of a PC-only AppleTalk network, it allowed communication between PCs and Macs with TOPS software installed. (Macs without TOPS installed could use the same network but only to communicate with other Apple machines.) The Mac TOPS software did not match the quality of Apple's own either in ease of use or in robustness and freedom from crashes, but the DOS software was relatively simple to use in DOS terms, and was robust.
The BSD and Linux operating systems support AppleTalk through an open source project called Netatalk, which implements the complete protocol suite and allows them to both act as native file or print servers for Macintosh computers, and print to LocalTalk printers over the network. The Windows Server operating systems supported AppleTalk starting with Windows NT and ending after Windows Server 2003. Miramar included AppleTalk in its PC MacLAN product which was discontinued by CA in 2007. GroupLogic continues to bundle its AppleTalk protocol with its ExtremeZ-IP server software for Macintosh-Windows integration which supports Windows Server 2008 and Windows Vista as well prior versions. HELIOS Software GmbH offers a proprietary implementation of the AppleTalk protocol stack, as part of their HELIOS UB2 server. This is essentially a File and Print Server suite that runs on a whole range of different platforms. In addition, Columbia University released the Columbia AppleTalk Package (CAP) which implemented the protocol suite for various Unix flavours including Ultrix, SunOS, BSD and IRIX. This package is no longer actively maintained.
Apple II Apple II ("apple two", stylized as "Apple ][") is a series of microcomputers manufactured by Apple Computer, Inc. from 1977 to 1993. The original Apple II model, which gave the series its name, was designed by Steve Wozniak and was first sold on June 10, 1977. Its success led to it being followed by the Apple II Plus, Apple IIe, Apple IIc, and Apple IIc Plus, with the 1983 IIe being the most popular. The name is trademarked with square brackets as Apple ][, then, beginning with the IIe, as Apple //. The Apple II was a major advancement over its predecessor, the Apple I, in terms of ease of use, features, and expandability. It became one of several recognizable and successful computers throughout the 1980s, although this was mainly limited to the US. It was aggressively marketed through volume discounts and manufacturing arrangements to educational institutions, which made it the first computer in widespread use in American secondary schools, displacing the early leader Commodore PET. The effort to develop educational and business software for the Apple II, including the 1979 release of the popular VisiCalc spreadsheet, made the computer especially popular with business users and families.
The Apple II computers are based on the 6502 8-bit processor and can display text and two resolutions of color graphics. A software-controlled speaker provides one channel of low-fidelity audio. A model with more advanced graphics and sound and a 16-bit processor, the Apple II, was added in 1986. It remained compatible with earlier Apple II models, but the II has more in common with mid-1980s systems like the Atari ST, Amiga, and Acorn Archimedes. Despite the introduction of the Motorola 68000-based Macintosh in 1984, the Apple II series still reportedly accounted for 85% of the company's hardware sales in the first quarter of fiscal 1985. Apple continued to sell Apple II systems alongside the Macintosh until terminating the II in December 1992 and the IIe in November 1993. The last II-series Apple in production, the IIe card for Macintoshes, was discontinued on October 15, 1993; having been one of the longest running mass-produced home computer series, the total Apple II sales of all of its models during its 16-year production run were about 6 million units (including about 1.25 million Apple II models) with the peak occurring in 1983 when 1 million were sold.
Hardware. Unlike preceding home microcomputers, the Apple II was sold as a finished consumer appliance rather than as a kit (unassembled or preassembled). Apple marketed the Apple II as a durable product, including a 1981 ad in which an Apple II survived a fire started when a cat belonging to one early user knocked over a lamp. All the machines in the series, except the IIc, share similar overall design elements. The plastic case was designed to look more like a home appliance than a piece of electronic equipment, and the case can be opened without the use of tools. All models in the Apple II series have a built-in keyboard, with the exception of the II which has a separate keyboard. Apple IIs have color and high-resolution graphics modes, sound capabilities and a built-in BASIC programming language. The motherboard holds eight expansion slots and an array of random access memory (RAM) sockets that can hold up to 48 kilobytes. Over the course of the Apple II series' life, an enormous amount of first- and third-party hardware was made available to extend the capabilities of the machine. The IIc was designed as a compact, portable unit, not intended to be disassembled, and cannot use most of the expansion hardware sold for the other machines in the series.
Software. The original Apple II has the operating system in ROM along with a BASIC variant called Integer BASIC. Apple eventually released Applesoft BASIC, a more advanced variant of the language which users can run instead of Integer BASIC. The Apple II series eventually supported over 1,500 software programs. When the Disk II floppy disk drive was released in 1978, a new operating system, Apple DOS, was commissioned from Shepardson Microsystems and developed by Paul Laughton, adding support for the disk drive. The final and most popular version of this software was Apple DOS 3.3. Apple DOS was superseded by ProDOS, which supported a hierarchical file system and larger storage devices. With an optional third-party Z80-based expansion card, the Apple II could boot into the CP/M operating system and run WordStar, dBase II, and other CP/M software. With the release of MousePaint in 1984 and the Apple II in 1986, the platform took on the look of the Macintosh user interface, including a mouse. Much commercial Apple II software shipped on self-booting disks and does not use standard DOS disk formats. This discouraged the copying or modifying of the software on the disks, and improved loading speed.
Models. Apple II. The first Apple II computers went on sale on June 10, 1977 with a MOS Technology 6502 (later Synertek) microprocessor running at 1.023 MHz, 4 KB of RAM, an audio cassette interface for loading programs and storing data, and the Integer BASIC programming language built into the ROMs. The video controller displayed 40 columns by 24 lines of monochrome, upper-case-only (the original character set matches ASCII characters 0x20 to 0x5F) text on the screen, with NTSC composite video output suitable for display on a TV monitor, or on a regular TV set by way of a separate RF modulator. The original retail price of the computer was (with 4 KB of RAM) and (with the maximum 48 KB of RAM). To reflect the computer's color graphics capability, the Apple logo on the casing was represented using rainbow stripes, which remained a part of Apple's corporate logo until early 1998. The earliest Apple IIs were assembled in Silicon Valley, and later in Texas; printed circuit boards were manufactured in Ireland and Singapore.
An external -inch floppy disk drive, the Disk II, attached via a controller card that plugged into one of the computer's expansion slots (usually slot 6), was used for data storage and retrieval to replace cassettes. The Disk II interface, created by Steve Wozniak, was regarded as an engineering masterpiece for its economy of electronic components. Rather than having a dedicated sound-synthesis chip, the Apple II had a toggle circuit that could only emit a click through a built-in speaker; all other sounds (including two, three and, eventually, four-voice music and playback of audio samples and speech synthesis) were generated entirely by software that clicked the speaker at just the right times. The Apple II's multiple expansion slots permitted a wide variety of third-party devices, including Apple II peripheral cards such as serial controllers, display controllers, memory boards, hard disks, networking components, and real-time clocks. There were plug-in expansion cards – such as the Z-80 SoftCard – that permitted the Apple to use the Z80 processor and run a multitude of programs developed under the CP/M operating system, including the dBase II database and the WordStar word processor. There was also a third-party 6809 card that would allow OS-9 Level One to be run. Third-party sound cards greatly improved audio capabilities, allowing simple music synthesis and text-to-speech functions. Eventually, Apple II accelerator cards were created to double or quadruple the computer's speed.
Rod Holt designed the Apple II's power supply. He employed a switched-mode power supply design, which was far smaller and generated less unwanted heat than the linear power supply some other home computers used. The original Apple II was discontinued at the start of 1981; it was superseded by the Apple II+. Apple II Plus. The Apple II Plus, introduced in June 1979, included the Applesoft BASIC programming language in ROM. This Microsoft-authored dialect of BASIC, which was previously available as an upgrade, supported floating-point arithmetic, and became the standard BASIC dialect on the Apple II series (though it ran at a noticeably slower speed than Steve Wozniak's Integer BASIC). Except for improved graphics and disk-booting support in the ROM, and the removal of the 2k 6502 assembler to make room for the floating point BASIC, the II+ was otherwise identical to the original II in terms of electronic functionality. There were small differences in the physical appearance and keyboard. RAM prices fell during 1980–81 and all II+ machines came from the factory with a full 48 KB of memory already installed.
Apple II Europlus and J-Plus. After the success of the first Apple II in the United States, Apple expanded its market to include Europe, the Middle East, Australia and the Far East in 1979, with the Apple II Europlus (Europe, Australia) and the Apple II J-Plus (Japan). In these models, Apple made the necessary hardware, software and firmware changes in order to comply to standards outside of the US. Apple IIe. The Apple II Plus was followed in 1983 by the Apple IIe, a cost-reduced yet more powerful machine that used newer chips to reduce the component count and add new features, such as the display of upper and lowercase letters and a standard 64 KB of RAM. The IIe RAM was configured as if it were a 48 KB Apple II Plus with a language card. The machine had no slot 0, but instead had an auxiliary slot that could accept a 1 KB memory card to enable the 80-column display. This card contained only RAM; the hardware and firmware for the 80-column display was built into the Apple IIe. An "extended 80-column card" with more memory increased the machine's RAM to 128 KB.
The Apple IIe was the most popular machine in the Apple II series. It has the distinction of being the longest-lived Apple computer of all time—it was manufactured and sold with only minor changes for nearly 11 years. The IIe was the last Apple II model to be sold, and was discontinued in November 1993. During its lifespan two variations were introduced: the Apple IIe Enhanced (four replacement chips to give it some of the features of the later model Apple IIc) and the Apple IIe Platinum (a modernized case color to match other Apple products of the era, along with the addition of a numeric keypad). Some of the feature of the IIe were carried over from the less successful "Apple III", among them the ProDOS operating system. Apple IIc. The Apple IIc was released in April 1984, billed as a portable Apple II because it could be easily carried due to its size and carrying handle, which could be flipped down to prop the machine up into a typing position. Unlike modern portables, it lacked a built-in display and battery. It was the first of three Apple II models to be made in the Snow White design language, and the only one that used its unique creamy off-white color.
The Apple IIc was the first Apple II to use the 65C02 low-power variant of the 6502 processor, and featured a built-in 5.25-inch floppy drive and 128 KB RAM, with a built-in disk controller that could control external drives, composite video (NTSC or PAL), serial interfaces for modem and printer, and a port usable by either a joystick or mouse. Unlike previous Apple II models, the IIc had no internal expansion slots at all. Two different monochrome LC displays were sold for use with the IIc's video expansion port, although both were short-lived due to high cost and poor legibility. The IIc had an external power supply that converted AC power to 15 V DC, though the IIc itself will accept between 12 V and 17 V DC, allowing third parties to offer battery packs and automobile power adapters that connected in place of the supplied AC adapter. Apple II. The Apple II, released on September 15, 1986, is the penultimate and most advanced model in the Apple II series, and a radical departure from prior models. It uses a 16-bit microprocessor, the 65C816 operating at 2.8 MHz with 24-bit addressing, allowing expansion up to 8 MB of RAM. The graphics are significantly improved, with 4096 colors and new modes with resolutions of 320×200 and 640×400. The audio capabilities are vastly improved, with a built-in music synthesizer that far exceeded any other home computer.
The Apple II evolved the platform while still maintaining near-complete backward compatibility. Its Mega II chip contains the functional equivalent of an entire Apple IIe computer (sans processor). This, combined with the 65816's ability to execute 65C02 code directly, provides full support for legacy software, while also supporting 16-bit software running under a new OS. The OS eventually included a Macintosh-like graphical Finder for managing disks and files and opening documents and applications, along with desk accessories. Later, the II gained the ability to read and write Macintosh disks and, through third-party software, a multitasking Unix-like shell and TrueType font support. The GS includes a 32-voice Ensoniq 5503 DOC sample-based sound synthesizer chip with 64 KB dedicated RAM, 256 KB (or later 1.125 MB) of standard RAM, built-in peripheral ports (switchable between IIe-style card slots and IIc-style onboard controllers for disk drives, mouse, RGB video, and serial devices), and built-in AppleTalk networking.

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