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Avionics	Navigation	Navigation Air navigation is the determination of position and direction on or above the surface of the Earth. Avionics can use satellite navigation systems (such as GPS and WAAS), inertial navigation system (INS), ground-based radio navigation systems (such as VOR or LORAN), or any combination thereof. Some navigation systems such as GPS calculate the position automatically and display it to the flight crew on moving map displays. Older ground-based Navigation systems such as VOR or LORAN requires a pilot or navigator to plot the intersection of signals on a paper map to determine an aircraft's location; modern systems calculate the position automatically and display it to the flight crew on moving map displays.
Avionics	Monitoring	Monitoring thumb\|The Airbus A380 glass cockpit featuring pull-out keyboards and two wide computer screens on the sides for pilots The first hints of glass cockpits emerged in the 1970s when flight-worthy cathode-ray tube (CRT) screens began to replace electromechanical displays, gauges and instruments. A "glass" cockpit refers to the use of computer monitors instead of gauges and other analog displays. Aircraft were getting progressively more displays, dials and information dashboards that eventually competed for space and pilot attention. In the 1970s, the average aircraft had more than 100 cockpit instruments and controls.Avionics: Development and Implementation by Cary R. Spitzer (Hardcover – December 15, 2006) Glass cockpits started to come into being with the Gulfstream G‑IV private jet in 1985. One of the key challenges in glass cockpits is to balance how much control is automated and how much the pilot should do manually. Generally they try to automate flight operations while keeping the pilot constantly informed.
Avionics	Aircraft flight-control system	Aircraft flight-control system Aircraft have means of automatically controlling flight. Autopilot was first invented by Lawrence Sperry during World War I to fly bomber planes steady enough to hit accurate targets from 25,000 feet. When it was first adopted by the U.S. military, a Honeywell engineer sat in the back seat with bolt cutters to disconnect the autopilot in case of emergency. Nowadays most commercial planes are equipped with aircraft flight control systems in order to reduce pilot error and workload at landing or takeoff.By Jeffrey L. Rodengen. . Published by Write Stuff Syndicate, Inc. in 1995. "The Legend of Honeywell." The first simple commercial auto-pilots were used to control heading and altitude and had limited authority on things like thrust and flight control surfaces. In helicopters, auto-stabilization was used in a similar way. The first systems were electromechanical. The advent of fly-by-wire and electro-actuated flight surfaces (rather than the traditional hydraulic) has increased safety. As with displays and instruments, critical devices that were electro-mechanical had a finite life. With safety critical systems, the software is very strictly tested.
Avionics	Fuel Systems	Fuel Systems Fuel Quantity Indication System (FQIS) monitors the amount of fuel aboard. Using various sensors, such as capacitance tubes, temperature sensors, densitometers & level sensors, the FQIS computer calculates the mass of fuel remaining on board. Fuel Control and Monitoring System (FCMS) reports fuel remaining on board in a similar manner, but, by controlling pumps & valves, also manages fuel transfers around various tanks. Refuelling control to upload to a certain total mass of fuel and distribute it automatically. Transfers during flight to the tanks that feed the engines. E.G. from fuselage to wing tanks Centre of gravity control transfers from the tail (trim) tanks forward to the wings as fuel is expended Maintaining fuel in the wing tips (to alleviate wing bending due to lift in flight) & transferring to the main tanks after landing Controlling fuel jettison during an emergency to reduce the aircraft weight.
Avionics	Collision-avoidance systems	Collision-avoidance systems To supplement air traffic control, most large transport aircraft and many smaller ones use a traffic alert and collision avoidance system (TCAS), which can detect the location of nearby aircraft, and provide instructions for avoiding a midair collision. Smaller aircraft may use simpler traffic alerting systems such as TPAS, which are passive (they do not actively interrogate the transponders of other aircraft) and do not provide advisories for conflict resolution. To help avoid controlled flight into terrain (CFIT), aircraft use systems such as ground-proximity warning systems (GPWS), which use radar altimeters as a key element. One of the major weaknesses of GPWS is the lack of "look-ahead" information, because it only provides altitude above terrain "look-down". In order to overcome this weakness, modern aircraft use a terrain awareness warning system (TAWS).
Avionics	Flight recorders	Flight recorders Commercial aircraft cockpit data recorders, commonly known as "black boxes", store flight information and audio from the cockpit. They are often recovered from an aircraft after a crash to determine control settings and other parameters during the incident.
Avionics	Weather systems	Weather systems Weather systems such as weather radar (typically Arinc 708 on commercial aircraft) and lightning detectors are important for aircraft flying at night or in instrument meteorological conditions, where it is not possible for pilots to see the weather ahead. Heavy precipitation (as sensed by radar) or severe turbulence (as sensed by lightning activity) are both indications of strong convective activity and severe turbulence, and weather systems allow pilots to deviate around these areas. Lightning detectors like the Stormscope or Strikefinder have become inexpensive enough that they are practical for light aircraft. In addition to radar and lightning detection, observations and extended radar pictures (such as NEXRAD) are now available through satellite data connections, allowing pilots to see weather conditions far beyond the range of their own in-flight systems. Modern displays allow weather information to be integrated with moving maps, terrain, and traffic onto a single screen, greatly simplifying navigation. Modern weather systems also include wind shear and turbulence detection and terrain and traffic warning systems. In‑plane weather avionics are especially popular in Africa, India, and other countries where air-travel is a growing market, but ground support is not as well developed.
Avionics	Aircraft management systems	Aircraft management systems There has been a progression towards centralized control of the multiple complex systems fitted to aircraft, including engine monitoring and management. Health and usage monitoring systems (HUMS) are integrated with aircraft management computers to give maintainers early warnings of parts that will need replacement. The integrated modular avionics concept proposes an integrated architecture with application software portable across an assembly of common hardware modules. It has been used in fourth generation jet fighters and the latest generation of airliners.
Avionics	Mission or tactical avionics	Mission or tactical avionics Military aircraft have been designed either to deliver a weapon or to be the eyes and ears of other weapon systems. The vast array of sensors available to the military is used for whatever tactical means required. As with aircraft management, the bigger sensor platforms (like the E‑3D, JSTARS, ASTOR, Nimrod MRA4, Merlin HM Mk 1) have mission-management computers. Police and EMS aircraft also carry sophisticated tactical sensors.
Avionics	Military communications	Military communications While aircraft communications provide the backbone for safe flight, the tactical systems are designed to withstand the rigors of the battle field. UHF, VHF Tactical (30–88 MHz) and SatCom systems combined with ECCM methods, and cryptography secure the communications. Data links such as Link 11, 16, 22 and BOWMAN, JTRS and even TETRA provide the means of transmitting data (such as images, targeting information etc.).
Avionics	Radar	Radar Airborne radar was one of the first tactical sensors. The benefit of altitude providing range has meant a significant focus on airborne radar technologies. Radars include airborne early warning (AEW), anti-submarine warfare (ASW), and even weather radar (Arinc 708) and ground tracking/proximity radar. The military uses radar in fast jets to help pilots fly at low levels. While the civil market has had weather radar for a while, there are strict rules about using it to navigate the aircraft.
Avionics	Sonar	Sonar Dipping sonar fitted to a range of military helicopters allows the helicopter to protect shipping assets from submarines or surface threats. Maritime support aircraft can drop active and passive sonar devices (sonobuoys) and these are also used to determine the location of enemy submarines.
Avionics	Electro-optics	Electro-optics Electro-optic systems include devices such as the head-up display (HUD), forward looking infrared (FLIR), infrared search and track and other passive infrared devices (Passive infrared sensor). These are all used to provide imagery and information to the flight crew. This imagery is used for everything from search and rescue to navigational aids and target acquisition.
Avionics	ESM/DAS	ESM/DAS Electronic support measures and defensive aids systems are used extensively to gather information about threats or possible threats. They can be used to launch devices (in some cases automatically) to counter direct threats against the aircraft. They are also used to determine the state of a threat and identify it.
Avionics	Aircraft networks	Aircraft networks The avionics systems in military, commercial and advanced models of civilian aircraft are interconnected using an avionics databus. Common avionics databus protocols, with their primary application, include: Aircraft Data Network (ADN): Ethernet derivative for Commercial Aircraft Avionics Full-Duplex Switched Ethernet (AFDX): Specific implementation of ARINC 664 (ADN) for Commercial Aircraft ARINC 429: Generic Medium-Speed Data Sharing for Private and Commercial Aircraft ARINC 664: See ADN above ARINC 629: Commercial Aircraft (Boeing 777) ARINC 708: Weather Radar for Commercial Aircraft ARINC 717: Flight Data Recorder for Commercial Aircraft ARINC 825: CAN bus for commercial aircraft (for example Boeing 787 and Airbus A350) Commercial Standard Digital Bus IEEE 1394b: Military Aircraft MIL-STD-1553: Military Aircraft MIL-STD-1760: Military Aircraft TTP – Time-Triggered Protocol: Boeing 787, Airbus A380, Fly-By-Wire Actuation Platforms from Parker Aerospace
Avionics	See also	See also Astrionics, similar, for spacecraft Acronyms and abbreviations in avionics Avionics software Emergency locator beacon Emergency position-indicating radiobeacon station Integrated modular avionics
Avionics	Notes	Notes
Avionics	Further reading	Further reading Avionics: Development and Implementation by Cary R. Spitzer (Hardcover – December 15, 2006) Principles of Avionics, 4th Edition by Albert Helfrick, Len Buckwalter, and Avionics Communications Inc. (Paperback – July 1, 2007) Avionics Training: Systems, Installation, and Troubleshooting by Len Buckwalter (Paperback – June 30, 2005) Avionics Made Simple, by Mouhamed Abdulla, Ph.D.; Jaroslav V. Svoboda, Ph.D. and Luis Rodrigues, Ph.D. (Coursepack – Dec. 2005 - ).
Avionics	External links	External links Avionics in Commercial Aircraft Aircraft Electronics Association (AEA) Pilot's Guide to Avionics The Avionic Systems Standardisation Committee Space Shuttle Avionics Aviation Today Avionics magazine RAES Avionics homepage Category:Aircraft instruments Category:Spacecraft components Category:Electronic engineering
Avionics	Table of Content	Short description, History, Modern avionics, Market, Aircraft avionics, Avionics Installation, Installation Process, Regulatory Standards, Advancements in Avionics Technology, Communications, Navigation, Monitoring, Aircraft flight-control system, Fuel Systems, Collision-avoidance systems, Flight recorders, Weather systems, Aircraft management systems, Mission or tactical avionics, Military communications, Radar, Sonar, Electro-optics, ESM/DAS, Aircraft networks, See also, Notes, Further reading, External links
Ares	Short description	Ares (; , Árēs ) is the Greek god of war and courage. He is one of the Twelve Olympians, and the son of Zeus and Hera. The Greeks were ambivalent towards him. He embodies the physical valor necessary for success in war but can also personify sheer brutality and bloodlust, in contrast to his sister Athena, whose martial functions include military strategy and generalship. An association with Ares endows places, objects, and other deities with a savage, dangerous, or militarized quality. Although Ares' name shows his origins as Mycenaean, his reputation for savagery was thought by some to reflect his likely origins as a Thracian deity. Some cities in Greece and several in Asia Minor held annual festivals to bind and detain him as their protector. In parts of Asia Minor, he was an oracular deity. Still further away from Greece, the Scythians were said to ritually kill one in a hundred prisoners of war as an offering to their equivalent of Ares. The later belief that ancient Spartans had offered human sacrifice to Ares may owe more to mythical prehistory, misunderstandings, and reputation than to reality. Although there are many literary allusions to Ares' love affairs and children, he has a limited role in Greek mythology. When he does appear, he is often humiliated. In the Trojan War, Aphrodite, protector of Troy, persuades Ares to take the Trojans' side. The Trojans lose, while Ares' sister Athena helps the Greeks to victory. Most famously, when the craftsman-god Hephaestus discovers his wife Aphrodite is having an affair with Ares, he traps the lovers in a net and exposes them to the ridicule of the other gods. Ares' nearest counterpart in Roman religion is Mars, who was given a more important and dignified place in ancient Roman religion as ancestral protector of the Roman people and state. During the Hellenization of Latin literature, the myths of Ares were reinterpreted by Roman writers under the name of Mars, and in later Western art and literature, the mythology of the two figures became virtually indistinguishable.
Ares	Names	Names The etymology of the name Ares is traditionally connected with the Greek word (arē), the Ionic form of the Doric (ara), "bane, ruin, curse, imprecation".ἀρή, Georg Autenrieth, A Homeric Dictionary. . Walter Burkert notes that "Ares is apparently an ancient abstract noun meaning throng of battle, war."Burkert, p. 169. R. S. P. Beekes has suggested a Pre-Greek origin of the name.R. S. P. Beekes, Etymological Dictionary of Greek, Brill, 2009, pp. 129–130. The earliest attested form of the name is the Mycenaean Greek , a-re, written in the Linear B syllabic script. The adjectival epithet, Areios ("warlike") was frequently appended to the names of other gods when they took on a warrior aspect or became involved in warfare: Zeus Areios, Athena Areia, even Aphrodite Areia ("Aphrodite within Ares" or "feminine Ares"), who was warlike, fully armoured and armed, partnered with Athena in Sparta, and represented at Kythira's temple to Aphrodite Urania.Budin, Stephanie L. (2010). "Aphrodite Enoplion", In Smith, Amy C.; Pickup, Sadie (eds.). Brill's Companion to Aphrodite. Brill's Companions in Classical Studies. Boston, MA: Brill Publishers. pp. 79–116. . In the Iliad, the word ares is used as a common noun synonymous with "battle". In the Classical period, Ares is given the epithet Enyalios, which seems to appear on the Mycenaean KN V 52 tablet as , e-nu-wa-ri-jo. At Google Books. Enyalios was sometimes identified with Ares and sometimes differentiated from him as another war god with separate cult, even in the same town; Burkert describes them as "doubles almost".Burkert, p. 44
Ares	Epithets	Epithets Nilsson Vol I, p. 517-519 aatos or atos polemoio, insatiate at war. Liddel Scott alloprosallos,leaning first to one side, then to the other. andreifontēs, man slaying. apotimos,dishonoured by Sophocles. brotoloigos, plague of man. enyalios , warlike, Liddel Scott Thēritas,at Sparta. Laconic form of Thersites,audacious .Liddel Scott mainomenos,malignant. miaifonos, blood stained tykton kakon, complete evil.Liddell Scott
Ares	Cult	Cult thumb\|Ares, 2nd–3rd century AD, after a Greek bronze original by Alkamenes dated 420 BC,, excavated in 1925 in Rome's Largo di Torre Argentina In mainland Greece and the Peloponnese, only a few places are known to have had a formal temple and cult of Ares.Burkert, p. 170. Pausanias (2nd century AD) notes an altar to Ares at Olympia,Pausanias, 5.15.6. and the moving of a Temple of Ares to the Athenian agora during the reign of Augustus, essentially rededicating it (2 AD) as a Roman temple to the Augustan Mars Ultor. The Areopagus ("mount of Ares"), a natural rock outcrop in Athens, some distance from the Acropolis, was supposedly where Ares was tried and acquitted by the gods for his revenge-killing of Poseidon's son, Halirrhothius, who had raped Ares' daughter Alcippe. Its name was used for the court that met there, mostly to investigate and try potential cases of treason.Berens, E.M.: Myths and Legends of Ancient Greece and Rome, page 113. Project Gutenberg, 2007. Numismatist M. Jessop Price states that Ares "typified the traditional Spartan character", but had no important cult in Sparta;Cf. Pausanias, 3.19.7. and he never occurs on Spartan coins.Price, M. Jessop. "Greek Imperial Coins: Some Recent Acquisitions by the British Museum." The Numismatic Chronicle, vol. 11, 1971, p. 131. . Accessed 4 Aug. 2021. Pausanias gives two examples of his cult, both of them conjointly with or "within" a warlike Aphrodite, on the Spartan acropolis.Budin, 2010. "Aphrodite Enoplion", pp. 86-116. Gonzalez observes, in his 2005 survey of Ares' cults in Asia Minor, that cults to Ares on the Greek mainland may have been more common than some sources assert.Gonzales, Matthew, "The Oracle and Cult of Ares in Asia Minor", Greek, Roman, and Byzantine Studies, 45, 2005, p. 282; "...Ares was not so neglected by the cities of mainland Greece as many would have us believe" Wars between Greek states were endemic; war and warriors provided Ares's tribute, and fed his insatiable appetite for battle.Millington, Alexander T., War and the Warrior: Functions of Ares in Literature and Cult, University College, London, 2013, pp. 41-44, 230 ff Ares' attributes are instruments of war: a helmet, shield, and sword or spear. Libanius "makes the apple sacred to Ares", but "offers no further comment", nor connections to any aetiological myth. Apples are one of Aphrodites' sacred or symbolic fruits. Littlewood follows Artemidorus claim that to dream of sour apples presages conflict, and lists Ares alongside Eris and the mythological "Apples of Discord".Libanius, Progymnasmata, Model Exercises in Greek Prose Composition and Rhetoric, Translated and with an Introduction and Notes by Craig A. Gibson, 2008, p. 263, particularly note 270: and Littlewood, A. R. "The Symbolism of the Apple in Greek and Roman Literature." Harvard Studies in Classical Philology 72 (1968): pp. 161-162. https://doi.org/10.2307/311078.
Ares	Chained statues	Chained statues Gods were immortal but could be bound and restrained, both in mythic narrative and in cult practice. There was an archaic Spartan statue of Ares in chains in the temple of Enyalios (sometimes regarded as the son of Ares, sometimes as Ares himself), which Pausanias claimed meant that the spirit of war and victory was to be kept in the city. The Spartans are known to have ritually bound the images of other deities, including Aphrodite and Artemis (cf Ares and Aphrodite bound by Hephaestus), and in other places there were chained statues of Artemis and Dionysos.Gonzales, 2005, p. 282Burkert, p. 92. Statues of Ares in chains are described in the instructions given by an oracle of the late Hellenistic era to various cities of Pamphylia (in Anatolia) including Syedra, Lycia and Cilicia, places almost perpetually under threat from pirates. Each was told to set up a statue of "bloody, man-slaying Ares" and provide it with an annual festival in which it was ritually bound with iron fetters ("by Dike and Hermes") as if a supplicant for justice, put on trial and offered sacrifice. The oracle promises that "thus will he become a peaceful deity for you, once he has driven the enemy horde far from your country, and he will give rise to prosperity much prayed for". This Ares karpodotes ("giver of Fruits") is well attested in Lycia and Pisidia.Gonzalez, 2005, p. 282
Ares	Sacrifices	Sacrifices thumb\|upright=1.3\|Ares (right) with Demeter, Dionysus and Hermes on the frieze of the Parthenon, ca. 447–433 BC, British Museum. Like most Greek deities, Ares was given animal sacrifice; in Sparta, after battle, he was given an ox for a victory by stratagem, or a rooster for victory through onslaught.Hughes, Dennis D., Human Sacrifice in Ancient Greece, Routledge, 1991, Taylor & Francis e-Library, 2003, p. 128, The usual recipient of sacrifice before battle was Athena. Reports of historic human sacrifice to Ares in an obscure rite known as the Hekatomphonia represent a very long-standing error, repeated through several centuries and well into the modern era. The hekatomphonia was an animal sacrifice to Zeus; it could be offered by any warrior who had personally slain one hundred of the enemy.Hughes, "Human Sacrifice", 1991, pp.119-122 & notes 145, 146 for a clear account of the error, and how and why it might have been perpetuatedFaraone, Christopher A. "Binding and Burying the Forces of Evil: The Defensive Use of 'Voodoo Dolls' in Ancient Greece." Classical Antiquity, vol. 10, no. 2, 1991, pp. 165–220. . Accessed 18 Aug. 2021 Pausanias reports that in Sparta, each company of youths sacrificed a puppy to Enyalios before engaging in a hand-to-hand "fight without rules" at the Phoebaeum.Graf, F. "Women, War, and Warlike Divinities." Zeitschrift Für Papyrologie Und Epigraphik, vol. 55, 1984, p. 252. . Accessed 13 Aug. 2021. The chthonic night-time sacrifice of a dog to Enyalios became assimilated to the cult of Ares. Porphyry claims, without detail, that Apollodorus of Athens (circa second century BC) says the Spartans made human sacrifices to Ares, but this may be a reference to mythic pre-history.Hughes, Dennis D., Human Sacrifice in Ancient Greece, Routledge, 1991, Taylor & Francis e-Library, 2003, p. 128, . Hughes is citing Apollodorus of Athens, Die Fragmente der griechischen Historike, 244 F 125. English translation of Porphyry is in
Ares	Thrace and Scythia	Thrace and Scythia A Thracian god identified by Herodotus ( – ) as Ares, through interpretatio Graeca, was one of three otherwise unnamed deities that Thracian commoners were said to worship. Herodotus recognises and names the other two as "Dionysus" and "Artemis", and claims that the Thracian aristocracy exclusively worshiped "Hermes".Oppermann, Manfred, Dimittrova, Nora M., religion, Thracian, "Oxford Classical Dictionary, https://doi.org/10.1093/acrefore/9780199381135.013.5553 ..."Ares suggests the existence of a war-god, Dionysus probably stood for a deity of orgiastic character linked with fertility and vegetation, while Artemis was an embodiment of the major female deity, frequently interpreted as the Great Goddess"... In Herodotus' Histories, the Scythians worship an indigenous form of Greek Ares, who is otherwise unnamed, but ranked beneath Tabiti (whom Herodotus claims as a form of Hestia), Api and Papaios in Scythia's divine hierarchy. His cult object was an iron sword. The "Scythian Ares" was offered blood-sacrifices (or ritual killings) of cattle, horses and "one in every hundred human war-captives", whose blood was used to douse the sword. Statues, and complex platform-altars made of heaped brushwood were devoted to him. This sword-cult, or one very similar, is said to have persisted among the Alans.Sulimirski, T. (1985). "The Scyths" in: Fisher, W. B. (Ed.) The Cambridge History of Iran, Vol. 2: The Median and Achaemenian Periods. Cambridge: Cambridge University Press. . pp. 158–159. Sulimirski is citing Herodotus, Book IV, 71-73, for the account of sacrifice to Ares. Some have posited that the "Sword of Mars" in later European history alludes to the Huns having adopted Ares.Geary, Patrick J. (1994). "Chapter 3. Germanic Tradition and Royal Ideology in the Ninth Century: The Visio Karoli Magni". Living with the Dead in the Middle Ages. Cornell University Press. p. 63. .
Ares	Asia Minor	Asia Minor In some parts of Asia Minor, Ares was a prominent oracular deity, something not found in any Hellennic cult to Ares or Roman cult to Mars. Ares was linked in some regions or polities with a local god or cultic hero, and recognised as a higher, more prestigious deity than in mainland Greece. His cults in southern Asia Minor are attested from the 5th century BC and well into the later Roman Imperial era, at 29 different sites, and on over 70 local coin issues.Gonzales, 2005, pp.263, 271, 280-283. He is sometimes represented on coinage of the region by the "Helmet of Ares" or carrying a spear and a shield, or as a fully armed warrior, sometimes accompanied by a female deity. In what is now western Turkey, the Hellenistic city of Metropolis built a monumental temple to Ares as the city's protector, not before the 3rd century BC. It is now lost, but the names of some of its priests and priestesses survive, along with the temple's likely depictions on coins of the province.Millington, A.T. (2013) "Iyarri at the Interface: The Origins of Ares" in A. Mouton, I. Rutherford, & I. Yakubovich (eds.) Luwian Identities: Culture, Language and Religion Between Anatolia and the Aegean (Leiden) pp.555-557
Ares	Crete	Crete A sanctuary of Aphrodite was established at Sta Lenika, on Crete, between the cities of Lato and Olus, possibly during the Geometric period. It was rebuilt in the late 2nd century BC as a double-sanctuary to Ares and Aphrodite.Martha W. Baldwin Bowsky. "Portrait of a Polis: Lato Pros Kamara (Crete) in the Late Second Century B. C." Hesperia: The Journal of the American School of Classical Studies at Athens, vol. 58, no. 3, The American School of Classical Studies at Athens, 1989, pp. 331–47, https://doi.org/10.2307/148222 Inscriptions record disputes over the ownership of the sanctuary. The names of Ares and Aphrodite appear as witness to sworn oaths, and there is a Victory thanks-offering to Aphrodite, whom Millington believes had capacity as a "warrior-protector acting in the realm of Ares". There were cultic links between the Sta Lenika sanctuary, Knossos and other Cretan states, and perhaps with Argos on the mainland.This refers to a double-temple to Aphrodite and Ares reported by Pausanias. Its cult practises are unknown. See Fusco, U. (2017). The Sanctuary of Aphrodite and Ares (Paus. 2.25.1) in the Periurban Area of Argos and Temples with a Double Cella in Greece. Tekmeria, 13, 97-124. doi:https://doi.org/10.12681/tekmeria.1073. While the Greek literary and artistic record from both the Archaic and Classical eras connects Ares and Aphrodite as complementary companions and ideal though adulterous lovers, their cult pairing and Aphrodite as warrior-protector is localised to Crete.Millington, Alexander T., "Iyarri at the Interface: The Origins of Ares" in A. Mouton, I. Rutherford, & I. Yakubovich (eds.) Luwian Identities: Culture, Language and Religion Between Anatolia and the Aegean (Leiden) 2013, pp.555-557Millington, Alexander T., War and the Warrior: Functions of Ares in Literature and Cult, University College, London, 2013, pp. 101-105
Ares	Aksum	Aksum In Africa, Maḥrem, the principal god of the kings of Aksum prior to the 4th century AD, was invoked as Ares in Greek inscriptions. The anonymous king who commissioned the Monumentum Adulitanum in the late 2nd or early 3rd century refers to "my greatest god, Ares, who also begat me, through whom I brought under my sway [various peoples]". The monumental throne celebrating the king's conquests was itself dedicated to Ares.Glen Bowersock, The Throne of Adulis: Red Sea Wars on the Eve of Islam (Oxford University Press, 2013), pp. 45, 47–48. In the early 4th century, the last pagan king of Aksum, Ezana, referred to "the one who brought me forth, the invincible Ares".Bowersock, Throne of Adulis, p. 69.
Ares	Characterisation	Characterisation thumb\|250px\|The Ares Borghese Ares was one of the Twelve Olympians in the archaic tradition represented by the Iliad and Odyssey. In Greek literature, Ares often represents the physical or violent and untamed aspect of war and is the personification of sheer brutality and bloodlust ("overwhelming, insatiable in battle, destructive, and man-slaughtering", as Burkert puts it), in contrast to his sister, the armored Athena, whose functions as a goddess of intelligence include military strategy and generalship.Walter Burkert, Greek Religion (Blackwell, 1985, 2004 reprint, originally published 1977 in German), pp. 141; William Hansen, Classical Mythology: A Guide to the Mythical World of the Greeks and Romans (Oxford University Press, 2005), p. 113. An association with Ares endows places and objects with a savage, dangerous, or militarized quality;Hansen, Classical Mythology, pp. 114–115. but when Ares does appear in myths, he typically faces humiliation.Hansen, Classical Mythology, pp. 113–114. In the Iliad, Zeus expresses a recurring Greek revulsion toward the god when Ares returns wounded and complaining from the battlefield at Troy: This ambivalence is expressed also in the Greeks' association of Ares with the Thracians, whom they regarded as a barbarous and warlike people.Iliad 13.301; Ovid, Ars Amatoria, II.10. Thrace was considered to be Ares's birthplace and his refuge after the affair with Aphrodite was exposed to the general mockery of the other gods. A late-6th-century BC funerary inscription from Attica emphasizes the consequences of coming under Ares's sway:
Ares	Mythology	Mythology thumb\|The Ludovisi Ares, Roman version of a Greek original c. 320 BC, with 17th-century restorations by Bernini
Ares	Birth	Birth He is one of the Twelve Olympians, and the son of Zeus and Hera.Hesiod, Theogony 921 (Loeb Classical Library numbering); Iliad, 5.890–896. By contrast, Ares's Roman counterpart Mars was born from Juno alone, according to Ovid (Fasti 5.229–260).
Ares	Argonautica	Argonautica In the Argonautica, the Golden Fleece hangs in a grove sacred to Ares, until its theft by Jason. The Birds of Ares (Ornithes Areioi) drop feather darts in defense of the Amazons' shrine to Ares, as father of their queen, on a coastal island in the Black Sea.Argonautica (ii.382ff and 1031ff; Hyginus, Fabulae 30.
Ares	Founding of Thebes	Founding of Thebes Ares plays a central role in the founding myth of Thebes, as the progenitor of the water-dragon slain by Cadmus. The dragon's teeth were sown into the ground as if a crop and sprang up as the fully armored autochthonic Spartoi. Cadmus placed himself in the god's service for eight years to atone for killing the dragon.Roman, L., & Roman, M. (2010). To further propitiate Ares, Cadmus married Harmonia, a daughter of Ares's union with Aphrodite. In this way, Cadmus harmonized all strife and founded the city of Thebes. In reality, Thebes came to dominate Boeotia's great and fertile plain, which in both history and myth was a battleground for competing polities.Marchand, Fabienne, and Beck, Hans,The Dancing Floor of Ares: Local Conflict and Regional Violence in Central Greece, Ancient History Bulletin, Supplemental Volume 1 (2020) According to Plutarch, the plain was anciently described as "The dancing-floor of Ares".Plutarch, Marcellus, 21.2
Ares	Aphrodite	Aphrodite In Homer's Odyssey, in the tale sung by the bard in the hall of Alcinous,Odyssey 8.300 the Sun-god Helios once spied Ares and Aphrodite having sex secretly in the hall of Hephaestus, her husband.In the Iliad, the wife of Hephaestus is Charis, "Grace," as noted by Burkert, p. 168. Helios reported the incident to Hephaestus. Contriving to catch the illicit couple in the act, Hephaestus fashioned a finely-knitted and nearly invisible net with which to snare them. At the appropriate time, this net was sprung, and trapped Ares and Aphrodite locked in very private embrace. But Hephaestus was not satisfied with his revenge, so he invited the Olympian gods and goddesses to view the unfortunate pair. For the sake of modesty, the goddesses demurred, but the male gods went to witness the sight. Some commented on the beauty of Aphrodite, others remarked that they would eagerly trade places with Ares, but all who were present mocked the two. Once the couple was released, the embarrassed Ares returned to his homeland, Thrace, and Aphrodite went to Paphos. In a much later interpolated detail, Ares put the young soldier Alectryon, who was Ares companion in drinking and even love-making, by his door to warn them of Helios's arrival as Helios would tell Hephaestus of Aphrodite's infidelity if the two were discovered, but Alectryon fell asleep on guard duty. Helios discovered the two and alerted Hephaestus. The furious Ares turned the sleepy Alectryon into a rooster which now always announces the arrival of the sun in the morning, as a way of apologizing to Ares.Lucian, Gallus 3, see also scholiast on Aristophanes, Birds 835; Eustathius, Ad Odysseam 1.300; Ausonius, 26.2.27; Libanius, Progymnasmata 2.26. The Chorus of Aeschylus' Suppliants (written 463 BC) refers to Ares as Aphrodite's "mortal-destroying bedfellow". In the Illiad, Ares helps the Trojans because of his affection for their divine protector, Aphrodite; she thus redirects his innate destructive savagery to her own purposes.
Ares	Giants	Giants In one archaic myth, related only in the Iliad by the goddess Dione to her daughter Aphrodite, two chthonic giants, the Aloadae, named Otus and Ephialtes, bound Ares in chains and imprisoned him in a bronze urn, where he remained for thirteen months, a lunar year. "And that would have been the end of Ares and his appetite for war, if the beautiful Eriboea, the young giants' stepmother, had not told Hermes what they had done," she related.Iliad 5.385–391. In this, [Burkert] suspects "a festival of licence which is unleashed in the thirteenth month".Burkert, p. 169Faraone, "Binding and Burying", 1991, pp. 166–220 Ares was held screaming and howling in the urn until Hermes rescued him, and Artemis tricked the Aloadae into slaying each other. In Nonnus's Dionysiaca, in the war between Cronus and Zeus, Ares killed an unnamed giant son of Echidna who was allied with Cronus, and described as spitting "horrible poison" and having "snaky" feet.Nonnus, Dionysiaca 18.274–288 (II pp. 82, 83). In some versions of the Gigantomachy, Ares was the god who killed the giant Mimas.Apollonius of Rhodes, Argonautica 3.1225–7 (pp. 276–277); Claudian, Gigantomachia 85–91 (pp. 286–287). In the 2nd century AD Metamorphoses of Antoninus Liberalis, when the monstrous Typhon attacked Olympus the gods transformed into animals and fled to Egypt; Ares changed into a fish, the Lepidotus (sacred to the Egyptian war-god Anhur). Liberalis's koine Greek text is a "completely inartistic" epitome of Nicander's now lost Heteroeumena (2nd century BC).Myers, Sarah, University of Michigan, reviewing Celoria's translation in Bryn Mawr Classical Review, 1994 (on-line text).Francis Celoria points out that in Ovid's Metamorphoses, Venus [Aphrodite's Roman equivalent], hides herself as a fish. See Celoria, Francis, Antoninus Liberalis, The Metamorphoses of Antoninus Liberalis, A Translation with a Commentary, 1992, pp. 87, 186, eBook Published 24 October 2018, London, Routledge, DOI https://doi.org/10.4324/9781315812755
Ares	''Iliad''	Iliad In Homer's Iliad, Ares has no fixed allegiance. He promises Athena and Hera that he will fight for the Achaeans but Aphrodite persuades him to side with the Trojans. During the war, Diomedes fights Hector and sees Ares fighting on the Trojans' side. Diomedes calls for his soldiers to withdraw.Iliad 5.830–834, 5.590–605, 21.410–414. Zeus grants Athena permission to drive Ares from the battlefield. Encouraged by Hera and Athena, Diomedes thrusts with his spear at Ares. Athena drives the spear home, and all sides tremble at Ares's cries. Ares flees to Mount Olympus, forcing the Trojans to fall back.Iliad 5.711–769, 5.780–834, 5.855–864. Ares overhears that his son Ascalaphus has been killed and wants to change sides again, rejoining the Achaeans for vengeance, disregarding Zeus's order that no Olympian should join the battle. Athena stops him. Later, when Zeus allows the gods to fight in the war again, Ares attacks Athena to avenge his previous injury. Athena overpowers him by striking him with a boulder.Iliad 15.110–128, 20.20–29, 21.391–408.
Ares	Attendants	Attendants Deimos ("Terror" or "Dread") and Phobos ("Fear") are Ares' companions in war,Iliad 4.436f, and 13.299f Hesiod's Shield of Heracles 191, 460; Quintus Smyrnaeus, 10.51, etc. and according to Hesiod, are also his children by Aphrodite.Hesiod, Theogony 934f. Eris, the goddess of discord, or Enyo, the goddess of war, bloodshed, and violence, was considered the sister and companion of the violent Ares. In at least one tradition, Enyalius, rather than another name for Ares, was his son by Enyo.Eustathius on Homer, 944 Ares may also be accompanied by Kydoimos, the daemon of the din of battle; the Makhai ("Battles"); the "Hysminai" ("Acts of manslaughter"); Polemos, a minor spirit of war, or only an epithet of Ares, since it has no specific dominion; and Polemos's daughter, Alala, the goddess or personification of the Greek war-cry, whose name Ares uses as his own war-cry. Ares's sister Hebe ("Youth") also draws baths for him. According to Pausanias, local inhabitants of Therapne, Sparta, recognized Thero, "feral, savage", as a nurse of Ares.Pausanias, 3.19.7–8.
Ares	Offspring and affairs	Offspring and affairs thumb\|185x185px\|The Areopagus as viewed from the Acropolis. Though Ares plays a relatively limited role in Greek mythology as represented in literary narratives, his numerous love affairs and abundant offspring are often alluded to.Hansen, Classical Mythology, pp. 113–114; Burkert, p. 169. The union of Ares and Aphrodite created the gods Eros, Anteros, Phobos, Deimos, and Harmonia. Other versions include Alcippe as one of their daughters. Ares had a romantic liaison with Eos, the goddess of the dawn. Aphrodite discovered them, and in anger she cursed Eos with insatiable lust for men.Pseudo-Apollodorus, Bibliotheca 1.4.4 Cycnus (Κύκνος) of Macedonia was a mortal son of Ares who tried to build a temple to his father with the skulls and bones of guests and travellers. Heracles fought him and, in one account, killed him. In another account, Ares fought his son's killer but Zeus parted the combatants with a thunderbolt.Apollodorus, 2.5.11, 2.7.7. By a woman named Teirene he had a daughter named Thrassa, who in turn had a daughter named Polyphonte. Polyphonte was cursed by Aphrodite to love and mate with a bear, producing two sons, Agrius and Oreius, who were hubristic toward the gods and had a habit of eating their guests. Zeus sent Hermes to punish them, and he chose to chop off their hands and feet. Since Polyphonte was descended from him, Ares stopped Hermes, and the two brothers came into an agreement to turn Polyphonte's family into birds instead. Oreius became an eagle owl, Agrius a vulture, and Polyphonte a strix, possibly a small owl, certainly a portent of war; Polyphonte's servant prayed not to become a bird of evil omen and Ares and Hermes fulfilled her wish by choosing the woodpecker for her, a good omen for hunters.Antoninus Liberalis, 21.Liberalis credits the Greek writer Boios' Ornithogonia (now lost) as his source;
Ares	List of offspring and their mothers	List of offspring and their mothers Sometimes poets and dramatists recounted ancient traditions, which varied, and sometimes they invented new details; later scholiasts might draw on either or simply guess. Thus while Phobos and Deimos were regularly described as offspring of Ares, others listed here such as Meleager, Sinope and Solymus were sometimes said to be children of Ares and sometimes given other fathers. The following is a list of Ares' offspring, by various mothers. Beside each offspring, the earliest source to record the parentage is given, along with the century to which the source dates. Offspring Mother Source Date Phobos Aphrodite Hes. Theog. 8th cent. BC Hesiod, Theogony 934; Hard, p. 169. Deimos Hes. Theog. 8th cent. BC Harmonia Hes. Theog. 8th cent. BC Hesiod, Theogony 934–7; Hard, p. 169; Grimal, s.v. Ares, pp. 52–53; Scholia on Homer, Iliad 2.494, [= Hellanicus fr. 51a Fowler, pp. 179–181]; Gantz, p. 468. Eros Simonides Simonides, fr. 24 Diehls [= fr. PMG 575]; Gantz, p. 3; Hard, p. 196; Brill's New Pauly, s.v. Eros; Oxford Classical Dictionary, s.v. Ares, pp. 103–104. Anteros Cic. DND 1st cent. BC Cicero, De Natura Deorum 3.59; Brill's New Pauly, s.v. Anteros. Odomantus Calliope Mygdon Edonus Biston Terpsichore Etym. Mag. 12th cent. AD Etymologicum Magnum, 179.59 (p. 179). Callirrhoe Steph. Byz. 6th cent. AD Stephanus of Byzantium, s.v. Bistonia (pp. 352, 353). Enyalius Enyo Brill's New Pauly, s.v. Enyalius. Dragon of Thebes Erinys of Telphusa Nike No mother mentioned HH 8 Homeric Hymn to Ares (8), 4. Sinope (possibly) Aegina Schol. Ap. Rhod. Scholia on Apollonius Rhodius, Argonautica 2.946 Edonus Callirrhoe Steph. Byz. 6th cent. AD Odomantus Steph. Byz. 6th cent. AD Cycnus Cleobula Pelopia Apollod. 1st/2nd cent. AD Apollodorus, 2.7.7. Pyrene Apollod. 1st/2nd cent. AD Apollodorus, 2.5.11. Diomedes of Thrace Cyrene Apollod. 1st/2nd cent. AD Apollodorus, 2.5.8. Crestone Tzetzes 12th cent. AD Tzetzes on Lycophron, Alexandra 499: Thrace was said to have been called Crestone after her. The Amazons Harmonia Oenomaus Sterope Hyg. Fab. 1st cent. AD Hyginus, Fabulae 84; Hyginus, De Astronomica, 2.21.5; Brill's New Pauly, s.v. Oenomaus. Harpina Diod. Sic. 1st cent. BC Pausanias, 5.22.6; Diodorus Siculus, 4.73.1; Gantz, p. 232. Eurythoe the Danaid Tzetzes 12th cent. AD Tzetzes on Lycophron, Alexandra 157. Evenus Sterope Ps.-Plutarch Pseudo-Plutarch, Parallela minora 40. Demonice Apollod. 1st/2nd cent. AD Apollodorus, 1.7.7. Thrassa Tereine Ant. Lib. 2nd/3rd cent. AD Melanippus Triteia Paus. 2nd cent. AD Pausanias, 7.22.8; Smith, s.v. Melanippus (4). Aeropus Aerope Paus. 2nd cent. AD Pausanias, 8.44.8; Tripp, s.v. Ares; Smith, s.v. Aphneius. Alcippe Aglauros Apollod. 1st/2nd cent. AD Apollodorus, 3.14.2; Peck, s.v. Ares. Meleager Althaea Apollod. 1st/2nd cent. AD Gantz, p. 328; Apollodorus, 1.8.2; Hyginus, Fabulae 14.3. Calydon Astynome Brill's New Pauly, s.v. Calydon (2). Ascalaphus Astyoche Paus. 2nd cent. AD Brill's New Pauly, s.vv. Ascalaphus (2), Pausanias, 9.37.7. Ialmenus Paus. 2nd cent. AD Brill's New Pauly, Ialmenus; Grimal, s.v. Ialmenus, p. 224; Pausanias, 9.37.7. Parthenopaeus Atalanta Apollod. 1st/2nd cent. AD Gantz, p. 336; Apollodorus, 3.9.2. Solymus Caldene Etym. Mag. 12th cent. AD Etymologicum Magnum, 721.43–44 (p. 654); Grimal, s.v. Solymus, p. 424. Phlegyas Chryse Paus. 2nd cent. AD Pausanias, 9.36.1; Hard, p. 560; Grimal, s.v. Phlegyas, pp. 367–368. Dotis Apollod. 1st/2nd cent. AD Apollodorus, 3.5.5; Hard, p. 560; Grimal, s.v. Phlegyas, pp. 367–368. Pangaeus Critobule Ps.-Plutarch Pseudo-Plutarch, On Rivers, 3.2. Molus, Pylus Demonice Apollod. 1st/2nd cent. AD Apollodorus, 1.7.7; Brill's New Pauly, s.v. Thestius.Thestius Pisidice Ps.-Plutarch Pseudo-Plutarch, On Rivers, 22.1. Demonice Apollod. 1st/2nd cent. AD Apollodorus, 1.7.7; Hard, p. 413; Grimal, s.v. Thestius, p. 452; Brill's New Pauly, s.v. Thestius. Stymphelus Dormothea Ps.-Plutarch Pseudo-Plutarch, On Rivers 19.1. Antiope Otrera Hyg. Fab. 1st cent. AD Brill's New Pauly, s.v. Antiope (2); Hyginus, Fabulae 30. Hippolyta Hyg. Fab. 1st cent. AD Hyginus, Fabulae 30. Melanippe Penthesilea Apollod. 1st/2nd cent. AD Apollodorus, E.5.1; Hyginus, Fabulae 112. Sinope Parnassa Eumelus Scholia on Apollonius of Rhodes, 2.946–54c [= Eumelus, fr. 29 West, pp. 246, 247]. Lycaon Pyrene Grimal, s.v. Lycaon (3), p. 263. Lycastus Phylonome Ps.-Plutarch Pseudo-Plutarch, Parallela minora 36; Grimal, s.vv. Lycastus (2), Parrhasius. Parrhasius Ps.-Plutarch Oxylus Protogeneia Apollod. 1st/2nd cent. AD Apollodorus, 1.7.7; Grimal, s.v. Oxylus (1); Brill's New Pauly, s.v. Oxylus (1). Bithys Sete eponym of the Thracian tribe of Bithyae in Stephanus of Byzantium, Ethnica s.v. Bithyai Tmolus Theogone Ps.-Plutarch Pseudo-Plutarch, On Rivers, 7.5. Ismarus Thracia Alcon of Thrace No mother mentioned Hyg. Fab. 1st cent. AD Hyginus, Fabulae 173. Chalyps eponym of the Chalybes in Scholia on Apollonius Rhodius, Argonautica, 2. 373. Cheimarrhoos Schol. Hes., WD Scholia on Hesiod, Works and Days 1, p. 28. Dryas Apollod. 1st/2nd cent. AD Apollodorus, 1.8.2; Grimal, s.v. Dryas, p. 142. Hyperbius Pliny the Elder, Naturalis Historia 7.57. Lycus of Libya Pseudo-Plutarch, Greek and Roman Parallel Stories, 23. Nisos Hyg. Fab. 1st cent. AD Hyginus, Fabulae 198, 242; Tripp, s.v. Nisus. Oeagrus Nonnus 5th cent. AD Nonnus, Dionysiaca XIII.428. Paeon Etym. Mag. 12th cent. AD Portheus (Porthaon) Ant. Lib. 2nd/3rd cent. AD Antoninus Liberalis, 2. Tereus Apollod. 1st/2nd cent. AD Apollodorus, 3.14.8; Hard, p. 169.
Ares	Mars	Mars thumb\|Wall-painting in Pompeii, c. 20 BC – 50s AD, showing Mars and Venus. The Roman god of war is depicted as youthful and beardless, reflecting the influence of the Greek Ares. The nearest counterpart of Ares among the Roman gods is Mars, a son of Jupiter and Juno, pre-eminent among the Roman army's military gods but originally an agricultural deity.Beard, Mary, North, John A., Price, Simon R. F., Religions of Rome: A History (Cambridge University Press, 1998), pp. 47–48 As a father of Romulus, Rome's legendary founder, Mars was given an important and dignified place in ancient Roman religion, as a guardian deity of the entire Roman state and its people. Under the influence of Greek culture, Mars was identified with Ares,Larousse Desk Reference Encyclopedia, The Book People, Haydock, 1995, p. 215. but the character and dignity of the two deities differed fundamentally.Kurt A. Raaflaub, War and Peace in the Ancient World (Blackwell, 2007), p. 15.Paul Rehak and John G. Younger, Imperium and Cosmos: Augustus and the Northern Campus Martius (University of Wisconsin Press, 2006), pp. 11–12. Mars was represented as a means to secure peace, and he was a father (pater) of the Roman people.Isidore of Seville calls Mars Romanae gentis auctorem, the originator or founder of the Roman people as a gens (Etymologiae 5.33.5). In one tradition, he fathered Romulus and Remus through his rape of Rhea Silvia. In another, his lover, the goddess Venus, gave birth to Aeneas, the Trojan prince and refugee who "founded" Rome several generations before Romulus. In the Hellenization of Latin literature, the myths of Ares were reinterpreted by Roman writers under the name of Mars. Greek writers under Roman rule also recorded cult practices and beliefs pertaining to Mars under the name of Ares. Thus in the classical tradition of later Western art and literature, the mythology of the two figures later became virtually indistinguishable.The scene in which Ares and Aphrodite are entrapped by Hephaestus' net (Homer, Odyssey VIII: 166-365 is also in Ovid's Latin language Metamorphoses IV: 171-189
Ares	Renaissance and later depictions	Renaissance and later depictions In Renaissance and Neoclassical works of art, Ares's symbols are a spear and helmet, his animal is a dog, and his bird is the vulture. In literary works of these eras, Ares is replaced by the Roman Mars, a romantic emblem of manly valor rather than the cruel and blood-thirsty god of Greek mythology.
Ares	In popular culture	In popular culture
Ares	Genealogy	Genealogy
Ares	See also	See also Family tree of the Greek gods
Ares	Footnotes	Footnotes
Ares	Notes	Notes
Ares	References	References Antoninus Liberalis, The Metamorphoses of Antoninus Liberalis: A Translation with a Commentary, edited and translated by Francis Celoria, Routledge, 1992. . Online version at ToposText. Apollodorus, Apollodorus: The Library, with an English Translation by Sir James George Frazer, F.B.A., F.R.S. in 2 Volumes. Cambridge, Massachusetts: Harvard University Press; London: William Heinemann Ltd., 1921. . Online version at the Perseus Digital Library. Burkert, Walter, Greek Religion, Harvard University Press, 1985. . Internet Archive. Etymologicum Magnum, Friderici Sylburgii (ed.), Leipzig: J.A.G. Weigel, 1816. Internet Archive. Gantz, Timothy, Early Greek Myth: A Guide to Literary and Artistic Sources, Johns Hopkins University Press, 1996, Two volumes: (Vol. 1), (Vol. 2). Grimal, Pierre, The Dictionary of Classical Mythology, Wiley-Blackwell, 1996. . Internet Archive. Hansen, William, Handbook of Classical Mythology, ABC-CLIO, 2004. . Internet Archive. Hard, Robin, The Routledge Handbook of Greek Mythology: Based on H.J. Rose's "Handbook of Greek Mythology", Psychology Press, 2004. . Google Books. Hesiod, Theogony, in The Homeric Hymns and Homerica with an English Translation by Hugh G. Evelyn-White, Cambridge, Massachusetts, Harvard University Press; London, William Heinemann Ltd. 1914. Online version at the Perseus Digital Library. Internet Archive. Homer, The Iliad with an English Translation by A.T. Murray, Ph.D. in two volumes. Cambridge, Massachusetts, Harvard University Press; London, William Heinemann, Ltd. 1924. Online version at the Perseus Digital Library. Homer, The Odyssey with an English Translation by A.T. Murray, Ph.D. in two volumes. Cambridge, Massachusetts, Harvard University Press; London, William Heinemann, Ltd. 1919. Online version at the Perseus Digital Library. Homeric Hymn 8 to Ares, in The Homeric Hymns and Homerica with an English Translation by Hugh G. Evelyn-White, Cambridge, Massachusetts, Harvard University Press; London, William Heinemann Ltd. 1914. Online version at the Perseus Digital Library. Hyginus, Gaius Julius, De Astronomica, in The Myths of Hyginus, edited and translated by Mary A. Grant, Lawrence: University of Kansas Press, 1960. Online version at ToposText. Hyginus, Gaius Julius, Fabulae, in The Myths of Hyginus, edited and translated by Mary A. Grant, Lawrence: University of Kansas Press, 1960. Online version at ToposText. Nonnus, Dionysiaca, Volume II: Books 16–35, translated by W. H. D. Rouse, Loeb Classical Library No. 345, Cambridge, Massachusetts, Harvard University Press, 1940. Online version at Harvard University Press. . Internet Archive (1940). Oxford Classical Dictionary, revised third edition, Simon Hornblower and Antony Spawforth (editors), Oxford University Press, 2003. . Internet Archive. Pausanias, Pausanias Description of Greece with an English Translation by W.H.S. Jones, Litt.D., and H.A. Ormerod, M.A., in 4 Volumes. Cambridge, Massachusetts, Harvard University Press; London, William Heinemann Ltd. 1918. Online version at the Perseus Digital Library. Peck, Harry Thurston, Harpers Dictionary of Classical Antiquities, New York, Harper and Brothers, 1898. Online version at the Perseus Digital Library. Pseudo-Plutarch, De fluviis, in Plutarch's morals, Volume V, edited and translated by William Watson Goodwin, Boston: Little, Brown & Co., 1874. Online version at the Perseus Digital Library. Smith, William, Dictionary of Greek and Roman Biography and Mythology, London (1873). Online version at the Perseus Digital Library. Stephanus of Byzantium, Stephani Byzantii Ethnica: Volumen I Alpha - Gamma, edited by Margarethe Billerbeck, in collaboration with Jan Felix Gaertner, Beatrice Wyss and Christian Zubler, De Gruyter, 2006. . Online version at De Gruyter. Google Books. Tripp, Edward, Crowell's Handbook of Classical Mythology, Thomas Y. Crowell Co; First edition (June 1970). . Internet Archive. Category:Characters in the Odyssey Category:Children of Hera Category:Children of Zeus Category:Consorts of Aphrodite Category:Consorts of Eos Category:Deeds of Poseidon Category:Deities in the Iliad Category:Dog gods Category:Greek mythology of Thrace Category:Greek war deities Category:Martian deities Category:Planetary gods Category:Metamorphoses characters Category:Twelve Olympians Category:War gods
Ares	Table of Content	Short description, Names, Epithets, Cult, Chained statues, Sacrifices, Thrace and Scythia, Asia Minor, Crete, Aksum, Characterisation, Mythology, Birth, Argonautica, Founding of Thebes, Aphrodite, Giants, ''Iliad'', Attendants, Offspring and affairs, List of offspring and their mothers, Mars, Renaissance and later depictions, In popular culture, Genealogy, See also, Footnotes, Notes, References
Alexander Grothendieck	Short description	Alexander Grothendieck, later Alexandre Grothendieck in French (; ; ; 28 March 1928 – 13 November 2014), was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory, and category theory to its foundations, while his so-called "relative" perspective led to revolutionary advances in many areas of pure mathematics. He is considered by many to be the greatest mathematician of the twentieth century. Grothendieck began his productive and public career as a mathematician in 1949. In 1958, he was appointed a research professor at the Institut des hautes études scientifiques (IHÉS) and remained there until 1970, when, driven by personal and political convictions, he left following a dispute over military funding. He received the Fields Medal in 1966 for advances in algebraic geometry, homological algebra, and K-theory. He later became professor at the University of Montpellier and, while still producing relevant mathematical work, he withdrew from the mathematical community and devoted himself to political and religious pursuits (first Buddhism and later, a more Catholic Christian vision). In 1991, he moved to the French village of Lasserre in the Pyrenees, where he lived in seclusion, still working on mathematics and his philosophical and religious thoughts until his death in 2014.
Alexander Grothendieck	Life	Life
Alexander Grothendieck	Family and childhood	Family and childhood Grothendieck was born in Berlin to anarchist parents. His father, Alexander "Sascha" Schapiro (also known as Alexander Tanaroff), had Hasidic Jewish roots and had been imprisoned in Russia before moving to Germany in 1922, while his mother, Johanna "Hanka" Grothendieck, came from a Protestant German family in Hamburg and worked as a journalist. As teenagers, both of his parents had broken away from their early backgrounds. At the time of his birth, Grothendieck's mother was married to the journalist Johannes Raddatz and initially, his birth name was recorded as "Alexander Raddatz." That marriage was dissolved in 1929 and Schapiro acknowledged his paternity, but never married Hanka Grothendieck. Grothendieck had a maternal sibling, his half sister Maidi. Grothendieck lived with his parents in Berlin until the end of 1933, when his father moved to Paris to evade Nazism. His mother followed soon thereafter. Grothendieck was left in the care of Wilhelm Heydorn, a Lutheran pastor and teacher in Hamburg. According to Winfried Scharlau, during this time, his parents took part in the Spanish Civil War as non-combatant auxiliaries.: "Beide beteiligten sich am Spanischen Bürgerkrieg, nicht aktiv kämpfend, aber unterstützend." However, others state that Schapiro fought in the anarchist militia.
Alexander Grothendieck	World War II	World War II In May 1939, Grothendieck was put on a train in Hamburg for France. Shortly afterward his father was interned in Le Vernet. He and his mother were then interned in various camps from 1940 to 1942 as "undesirable dangerous foreigners."Piotr Pragacz, 'Notes on the Life and Work of Alexander Grothendieck,' in Piotr Pragacz (ed.), Topics in Cohomological Studies of Algebraic Varieties: Impanga Lecture Notes, Springer Science & Business Media, 2006 pp-xi-xxviii p.xii. The first camp was the Rieucros Camp, where his mother may have contracted the tuberculosis that would eventually cause her death in 1957. While there, Grothendieck managed to attend the local school, at Mende. Once, he managed to escape from the camp, intending to assassinate Hitler. Later, his mother Hanka was transferred to the Gurs internment camp for the remainder of World War II.Amir D. Aczel,The Artist and the Mathematician, Basic Books, 2009 pp.8ff.pp.8–15. Grothendieck was permitted to live separated from his mother.Luca Barbieri Viale, 'Alexander Grothendieck:entusiasmo e creatività,' in C. Bartocci, R. Betti, A. Guerraggio, R. Lucchetti (eds.,) Vite matematiche: Protagonisti del '900, da Hilbert a Wiles, Springer Science & Business Media, 2007 pp.237–249 p.237. In the village of Le Chambon-sur-Lignon, he was sheltered and hidden in local boarding houses or pensions, although he occasionally had to seek refuge in the woods during Nazi raids, surviving at times without food or water for several days. His father was arrested under the Vichy anti-Jewish legislation, and sent to the Drancy internment camp, and then handed over by the French Vichy government to the Germans to be sent to be murdered at the Auschwitz concentration camp in 1942. In Le Chambon, Grothendieck attended the Collège Cévenol (now known as the Le Collège-Lycée Cévenol International), a unique secondary school founded in 1938 by local Protestant pacifists and anti-war activists. Many of the refugee children hidden in Le Chambon attended Collège Cévenol, and it was at this school that Grothendieck apparently first became fascinated with mathematics. In 1990, for risking their lives to rescue Jews, the entire village was recognized as "Righteous Among the Nations".
Alexander Grothendieck	Studies and contact with research mathematics	Studies and contact with research mathematics After the war, the young Grothendieck studied mathematics in France, initially at the University of Montpellier where at first he did not perform well, failing such classes as astronomy. Working on his own, he rediscovered the Lebesgue measure. After three years of increasingly independent studies there, he went to continue his studies in Paris in 1948. Initially, Grothendieck attended Henri Cartan's Seminar at , but he lacked the necessary background to follow the high-powered seminar. On the advice of Cartan and André Weil, he moved to the University of Nancy where two leading experts were working on Grothendieck's area of interest, topological vector spaces: Jean Dieudonné and Laurent Schwartz. The latter had recently won a Fields Medal. Dieudonné and Schwartz showed the new student their latest paper La dualité dans les espaces () et (); it ended with a list of 14 open questions, relevant for locally convex spaces. Grothendieck introduced new mathematical methods that enabled him to solve all of these problems within a few months. In Nancy, he wrote his dissertation under those two professors on functional analysis, from 1950 to 1953. At this time he was a leading expert in the theory of topological vector spaces. In 1953 he moved to the University of São Paulo in Brazil, where he immigrated by means of a Nansen passport, given that he had refused to take French nationality (as that would have entailed military service against his convictions). He stayed in São Paulo (apart from a lengthy visit in France from October 1953 to March 1954) until the end of 1954. His published work from the time spent in Brazil is still in the theory of topological vector spaces; it is there that he completed his last major work on that topic (on "metric" theory of Banach spaces). Grothendieck moved to Lawrence, Kansas at the beginning of 1955, and there he set his old subject aside in order to work in algebraic topology and homological algebra, and increasingly in algebraic geometry. It was in Lawrence that Grothendieck developed his theory of abelian categories and the reformulation of sheaf cohomology based on them, leading to the very influential "Tôhoku paper". In 1957 he was invited to visit Harvard University by Oscar Zariski, but the offer fell through when he refused to sign a pledge promising not to work to overthrow the United States government—a refusal which, he was warned, threatened to land him in prison. The prospect of prison did not worry him, so long as he could have access to books. Comparing Grothendieck during his Nancy years to the -trained students at that time (Pierre Samuel, Roger Godement, René Thom, Jacques Dixmier, Jean Cerf, Yvonne Bruhat, Jean-Pierre Serre, and Bernard Malgrange), Leila Schneps said: His first works on topological vector spaces in 1953 have been successfully applied to physics and computer science, culminating in a relation between Grothendieck inequality and the Einstein–Podolsky–Rosen paradox in quantum physics.
Alexander Grothendieck	IHÉS years	IHÉS years In 1958, Grothendieck was installed at the Institut des hautes études scientifiques (IHÉS), a new privately funded research institute that, in effect, had been created for Jean Dieudonné and Grothendieck. Grothendieck attracted attention by an intense and highly productive activity of seminars there (de facto working groups drafting into foundational work some of the ablest French and other mathematicians of the younger generation). Grothendieck practically ceased publication of papers through the conventional, learned journal route. However, he was able to play a dominant role in mathematics for approximately a decade, gathering a strong school. Officially during this time, he had as students Michel Demazure (who worked on SGA3, on group schemes), (relative schemes and classifying topos), Luc Illusie (cotangent complex), Michel Raynaud, Michèle Raynaud, Jean-Louis Verdier (co-founder of the derived category theory), and Pierre Deligne. Collaborators on the SGA projects also included Michael Artin (étale cohomology), Nick Katz (monodromy theory, and Lefschetz pencils). Jean Giraud worked out torsor theory extensions of nonabelian cohomology there as well. Many others such as David Mumford, Robin Hartshorne, Barry Mazur and C.P. Ramanujam were also involved.
Alexander Grothendieck	"Golden Age"	"Golden Age" Alexander Grothendieck's work during what is described as the "Golden Age" period at the IHÉS established several unifying themes in algebraic geometry, number theory, topology, category theory, and complex analysis. His first (pre-IHÉS) discovery in algebraic geometry was the Grothendieck–Hirzebruch–Riemann–Roch theorem, a generalisation of the Hirzebruch–Riemann–Roch theorem proved algebraically; in this context he also introduced K-theory. Then, following the programme he outlined in his talk at the 1958 International Congress of Mathematicians, he introduced the theory of schemes, developing it in detail in his Éléments de géométrie algébrique (EGA) and providing the new more flexible and general foundations for algebraic geometry that has been adopted in the field since that time. He went on to introduce the étale cohomology theory of schemes, providing the key tools for proving the Weil conjectures, as well as crystalline cohomology and algebraic de Rham cohomology to complement it. Closely linked to these cohomology theories, he originated topos theory as a generalisation of topology (relevant also in categorical logic). He also provided, by means of a categorical Galois theory, an algebraic definition of fundamental groups of schemes giving birth to the now famous étale fundamental group and he then conjectured the existence of a further generalization of it, which is now known as the fundamental group scheme. As a framework for his coherent duality theory, he also introduced derived categories, which were further developed by Verdier. The results of his work on these and other topics were published in the EGA and in less polished form in the notes of the Séminaire de géométrie algébrique (SGA) that he directed at the IHÉS.
Alexander Grothendieck	Political activism	Political activism Grothendieck's political views were radical and pacifistic. He strongly opposed both United States intervention in Vietnam and Soviet military expansionism. To protest against the Vietnam War, he gave lectures on category theory in the forests surrounding Hanoi while the city was being bombed.The Life and Work of Alexander Grothendieck, American Mathematical Monthly, vol. 113, no. 9, footnote 6. In 1966, he had declined to attend the International Congress of Mathematicians (ICM) in Moscow, where he was to receive the Fields Medal. He retired from scientific life around 1970 after he had found out that IHÉS was partly funded by the military.SGA1, Springer Lecture Notes 224, He returned to academia a few years later as a professor at the University of Montpellier. While the issue of military funding was perhaps the most obvious explanation for Grothendieck's departure from the IHÉS, those who knew him say that the causes of the rupture ran more deeply. Pierre Cartier, a visiteur de longue durée ("long-term guest") at the IHÉS, wrote a piece about Grothendieck for a special volume published on the occasion of the IHÉS's fortieth anniversary. In that publication, Cartier notes that as the son of an antimilitary anarchist and one who grew up among the disenfranchised, Grothendieck always had a deep compassion for the poor and the downtrodden. As Cartier puts it, Grothendieck came to find Bures-sur-Yvette as "une cage dorée" ("a gilded cage"). While Grothendieck was at the IHÉS, opposition to the Vietnam War was heating up, and Cartier suggests that this also reinforced Grothendieck's distaste at having become a mandarin of the scientific world. In addition, after several years at the IHÉS, Grothendieck seemed to cast about for new intellectual interests. By the late 1960s, he had started to become interested in scientific areas outside mathematics. David Ruelle, a physicist who joined the IHÉS faculty in 1964, said that Grothendieck came to talk to him a few times about physics. Biology interested Grothendieck much more than physics, and he organized some seminars on biological topics. In 1970, Grothendieck, with two other mathematicians, Claude Chevalley and Pierre Samuel, created a political group entitled Survivre—the name later changed to Survivre et vivre. The group published a bulletin and was dedicated to antimilitary and ecological issues. It also developed strong criticism of the indiscriminate use of science and technology. Grothendieck devoted the next three years to this group and served as the main editor of its bulletin. Although Grothendieck continued with mathematical enquiries, his standard mathematical career mostly ended when he left the IHÉS. After leaving the IHÉS, Grothendieck became a temporary professor at Collège de France for two years. He then became a professor at the University of Montpellier, where he became increasingly estranged from the mathematical community. He formally retired in 1988, a few years after having accepted a research position at the CNRS.
Alexander Grothendieck	Manuscripts written in the 1980s	Manuscripts written in the 1980s While not publishing mathematical research in conventional ways during the 1980s, he produced several influential manuscripts with limited distribution, with both mathematical and biographical content. Produced during 1980 and 1981, La Longue Marche à travers la théorie de Galois (The Long March Through Galois Theory) is a 1600-page handwritten manuscript containing many of the ideas that led to the Esquisse d'un programme.Alexandre Grothendieck, Esquisse d'un Programme, English translation It also includes a study of Teichmüller theory. In 1983, stimulated by correspondence with Ronald Brown and Tim Porter at Bangor University, Grothendieck wrote a 600-page manuscript entitled Pursuing Stacks. It began with a letter addressed to Daniel Quillen. This letter and successive parts were distributed from Bangor (see External links below). Within these, in an informal, diary-like manner, Grothendieck explained and developed his ideas on the relationship between algebraic homotopy theory and algebraic geometry and prospects for a noncommutative theory of stacks. The manuscript, which is being edited for publication by G. Maltsiniotis, later led to another of his monumental works, Les Dérivateurs. Written in 1991, this latter opus of approximately 2000 pages, further developed the homotopical ideas begun in Pursuing Stacks. Much of this work anticipated the subsequent development during the mid-1990s of the motivic homotopy theory of Fabien Morel and Vladimir Voevodsky. In 1984, Grothendieck wrote the proposal Esquisse d'un Programme ("Sketch of a Programme") for a position at the Centre National de la Recherche Scientifique (CNRS). It describes new ideas for studying the moduli space of complex curves. Although Grothendieck never published his work in this area, the proposal inspired other mathematicians to work in the area by becoming the source of dessin d'enfant theory and anabelian geometry. Later, it was published in two-volumes and entitled Geometric Galois Actions (Cambridge University Press, 1997). During this period, Grothendieck also gave his consent to publishing some of his drafts for EGA on Bertini-type theorems (EGA V, published in Ulam Quarterly in 1992–1993 and later made available on the Grothendieck Circle web site in 2004). In the extensive autobiographical work, Récoltes et Semailles ('Harvests and Sowings', 1986), Grothendieck describes his approach to mathematics and his experiences in the mathematical community, a community that initially accepted him in an open and welcoming manner, but which he progressively perceived to be governed by competition and status. He complains about what he saw as the "burial" of his work and betrayal by his former students and colleagues after he had left the community. Récoltes et Semailles was finally published in 2022 by Gallimard and, thanks to French science historian Alain Herreman, is also available on the Internet. An English translation by Leila Schneps will be published by MIT Press in 2025. A partial English translation can be found on the Internet. A Japanese translation of the whole book in four volumes was completed by Tsuji Yuichi (1938–2002), a friend of Grothendieck from the Survivre period. The first three volumes (corresponding to Parts 0 to III of the book) were published between 1989 and 1993, while the fourth volume (Part IV) was completed and, although unpublished, copies of it as a typed manuscript are circulated. Grothendieck helped with the translation and wrote a preface for it, in which he called Tsuji his "first true collaborator". Parts of Récoltes et Semailles have been translated into Spanish, as well as into a Russian translation that was published in Moscow. In 1988, Grothendieck declined the Crafoord Prize with an open letter to the media. He wrote that he and other established mathematicians had no need for additional financial support and criticized what he saw as the declining ethics of the scientific community that was characterized by outright scientific theft that he believed had become commonplace and tolerated. The letter also expressed his belief that totally unforeseen events before the end of the century would lead to an unprecedented collapse of civilization. Grothendieck added however that his views were "in no way meant as a criticism of the Royal Academy's aims in the administration of its funds" and he added, "I regret the inconvenience that my refusal to accept the Crafoord prize may have caused you and the Royal Academy." La Clef des Songes, a 315-page manuscript written in 1987, is Grothendieck's account of how his consideration of the source of dreams led him to conclude that a deity exists. As part of the notes to this manuscript, Grothendieck described the life and the work of 18 "mutants", people whom he admired as visionaries far ahead of their time and heralding a new age. The only mathematician on his list was Bernhard Riemann. Influenced by the Catholic mystic Marthe Robin who was claimed to have survived on the Holy Eucharist alone, Grothendieck almost starved himself to death in 1988. His growing preoccupation with spiritual matters was also evident in a letter entitled Lettre de la Bonne Nouvelle sent to 250 friends in January 1990. In it, he described his encounters with a deity and announced that a "New Age" would commence on 14 October 1996. The Grothendieck Festschrift, published in 1990, was a three-volume collection of research papers to mark his sixtieth birthday in 1988. More than 20,000 pages of Grothendieck's mathematical and other writings are held at the University of Montpellier and remain unpublished.Le trésor oublié du génie des maths They have been digitized for preservation and are freely available in open access through the Institut Montpelliérain Alexander Grothendieck portal.Les «gribouillis» d'Alexandre Grothendieck enfin sauvegardés
Alexander Grothendieck	Retirement into reclusion and death	Retirement into reclusion and death In 1991, Grothendieck moved to a new address that he did not share with his previous contacts in the mathematical community. Very few people visited him afterward. Local villagers helped sustain him with a more varied diet after he tried to live on a staple of dandelion soup. At some point, Leila Schneps and Pierre Lochak located him, then carried on a brief correspondence. Thus they became among "the last members of the mathematical establishment to come into contact with him". After his death, it was revealed that he lived alone in a house in Lasserre, Ariège, a small village at the foot of the Pyrenees. In January 2010, Grothendieck wrote the letter entitled "Déclaration d'intention de non-publication" to Luc Illusie, claiming that all materials published in his absence had been published without his permission. He asked that none of his work be reproduced in whole or in part and that copies of this work be removed from libraries. He characterized a website devoted to his work as "an abomination". His dictate may have been reversed in 2010. In September 2014, almost totally deaf and blind, he asked a neighbour to buy him a revolver so he could kill himself. His neighbour refused to do so.Phil Hoad, ‘He was in mystic delirium’: was this hermit mathematician a forgotten genius whose ideas could transform AI – or a lonely madman?, The Guardian 31 August 2024 On 13 November 2014, aged 86, Grothendieck died in the hospital of Saint-Lizier or Saint-Girons, Ariège.
Alexander Grothendieck	Citizenship	Citizenship Grothendieck was born in Weimar Germany. In 1938, aged ten, he moved to France as a refugee. Records of his nationality were destroyed in the fall of Nazi Germany in 1945 and he did not apply for French citizenship after the war. Thus, he became a stateless person for at least the majority of his working life and he traveled on a Nansen passport. Part of his reluctance to hold French nationality is attributed to not wishing to serve in the French military, particularly due to the Algerian War (1954–62). He eventually applied for French citizenship in the early 1980s, after he was well past the age that would have required him to do military service.
Alexander Grothendieck	Family	Family Grothendieck was very close to his mother, to whom he dedicated his dissertation. She died in 1957 from tuberculosis that she contracted in camps for displaced persons. He had five children: a son with his landlady during his time in Nancy; three children, Johanna (1959), Alexander (1961), and Mathieu (1965) with his wife Mireille Dufour; and one child with Justine Skalba, with whom he lived in a commune in the early 1970s.
Alexander Grothendieck	Mathematical work	Mathematical work Grothendieck's early mathematical work was in functional analysis. Between 1949 and 1953 he worked on his doctoral thesis in this subject at Nancy, supervised by Jean Dieudonné and Laurent Schwartz. His key contributions include topological tensor products of topological vector spaces, the theory of nuclear spaces as foundational for Schwartz distributions, and the application of Lp spaces in studying linear maps between topological vector spaces. In a few years, he had become a leading authority on this area of functional analysis—to the extent that Dieudonné compares his impact in this field to that of Banach. It is, however, in algebraic geometry and related fields where Grothendieck did his most important and influential work. From approximately 1955 he started to work on sheaf theory and homological algebra, producing the influential "Tôhoku paper" (Sur quelques points d'algèbre homologique, published in the Tohoku Mathematical Journal in 1957) where he introduced abelian categories and applied their theory to show that sheaf cohomology may be defined as certain derived functors in this context. Homological methods and sheaf theory had already been introduced in algebraic geometry by Jean-Pierre Serre and others, after sheaves had been defined by Jean Leray. Grothendieck took them to a higher level of abstraction and turned them into a key organising principle of his theory. He shifted attention from the study of individual varieties to his relative point of view (pairs of varieties related by a morphism), allowing a broad generalization of many classical theorems. The first major application was the relative version of Serre's theorem showing that the cohomology of a coherent sheaf on a complete variety is finite-dimensional; Grothendieck's theorem shows that the higher direct images of coherent sheaves under a proper map are coherent; this reduces to Serre's theorem over a one-point space. In 1956, he applied the same thinking to the Riemann–Roch theorem, which recently had been generalized to any dimension by Hirzebruch. The Grothendieck–Riemann–Roch theorem was announced by Grothendieck at the initial Mathematische Arbeitstagung in Bonn, in 1957. It appeared in print in a paper written by Armand Borel with Serre. This result was his first work in algebraic geometry. Grothendieck went on to plan and execute a programme for rebuilding the foundations of algebraic geometry, which at the time were in a state of flux and under discussion in Claude Chevalley's seminar. He outlined his programme in his talk at the 1958 International Congress of Mathematicians. His foundational work on algebraic geometry is at a higher level of abstraction than all prior versions. He adapted the use of non-closed generic points, which led to the theory of schemes. Grothendieck also pioneered the systematic use of nilpotents. As 'functions' these can take only the value 0, but they carry infinitesimal information, in purely algebraic settings. His theory of schemes has become established as the best universal foundation for this field, because of its expressiveness as well as its technical depth. In that setting one can use birational geometry, techniques from number theory, Galois theory, commutative algebra, and close analogues of the methods of algebraic topology, all in an integrated way. Grothendieck is noted for his mastery of abstract approaches to mathematics and his perfectionism in matters of formulation and presentation. Relatively little of his work after 1960 was published by the conventional route of the learned journal, circulating initially in duplicated volumes of seminar notes; his influence was to a considerable extent personal. His influence spilled over into many other branches of mathematics, for example the contemporary theory of D-modules. Although lauded as "the Einstein of mathematics", his work also provoked adverse reactions, with many mathematicians seeking out more concrete areas and problems.: "[A] mathematician of staggering accomplishment... a legendary figure in the mathematical world."
Alexander Grothendieck	''EGA'', ''SGA'', ''FGA''	EGA, SGA, FGA The bulk of Grothendieck's published work is collected in the monumental, yet incomplete, Éléments de géométrie algébrique (EGA) and Séminaire de géométrie algébrique (SGA). The collection Fondements de la Géometrie Algébrique (FGA), which gathers together talks given in the Séminaire Bourbaki, also contains important material. Grothendieck's work includes the invention of the étale and l-adic cohomology theories, which explain an observation made by André Weil that argued for a connection between the topological characteristics of a variety and its diophantine (number theoretic) properties. For example, the number of solutions of an equation over a finite field reflects the topological nature of its solutions over the complex numbers. Weil had realized that to prove such a connection, one needed a new cohomology theory, but neither he nor any other expert saw how to accomplish this until such a theory was expressed by Grothendieck. This program culminated in the proofs of the Weil conjectures, the last of which was settled by Grothendieck's student Pierre Deligne in the early 1970s after Grothendieck had largely withdrawn from mathematics.
Alexander Grothendieck	Major mathematical contributions	Major mathematical contributions In Grothendieck's retrospective Récoltes et Semailles, he identified twelve of his contributions that he believed qualified as "great ideas". In chronological order, they are: Topological tensor products and nuclear spaces "Continuous" and "discrete" duality (derived categories, "six operations") Yoga of the Grothendieck–Riemann–Roch theorem K-theory relation with intersection theory Schemes Topoi Étale cohomology and l-adic cohomology Motives and the motivic Galois group (Grothendieck ⊗-categories) Crystals and crystalline cohomology, yoga of "de Rham coefficients", "Hodge coefficients"... "Topological algebra": ∞-stacks, derivators; cohomological formalism of topoi as inspiration for a new homotopical algebra Tame topology Yoga of anabelian algebraic geometry, Galois–Teichmüller theory "Schematic" or "arithmetic" point of view for regular polyhedra and regular configurations of all kinds Here the term yoga denotes a kind of "meta-theory" that may be used heuristically; Michel Raynaud writes the other terms "Ariadne's thread" and "philosophy" as effective equivalents. Grothendieck wrote that, of these themes, the largest in scope was topoi, as they synthesized algebraic geometry, topology, and arithmetic. The theme that had been most extensively developed was schemes, which were the framework "par excellence" for eight of the other themes (all but 1, 5, and 12). Grothendieck wrote that the first and last themes, topological tensor products and regular configurations, were of more modest size than the others. Topological tensor products had played the role of a tool rather than of a source of inspiration for further developments; but he expected that regular configurations could not be exhausted within the lifetime of a mathematician who devoted oneself to it. He believed that the deepest themes were motives, anabelian geometry, and Galois–Teichmüller theory.
Alexander Grothendieck	Influence	Influence Grothendieck is considered by many to be the greatest mathematician of the twentieth century. In an obituary David Mumford and John Tate wrote: Although mathematics became more and more abstract and general throughout the 20th century, it was Alexander Grothendieck who was the greatest master of this trend. His unique skill was to eliminate all unnecessary hypotheses and burrow into an area so deeply that its inner patterns on the most abstract level revealed themselves–and then, like a magician, show how the solution of old problems fell out in straightforward ways now that their real nature had been revealed.Alexander Grothendieck obituary by David Mumford and John Tate David Mumford at Brown and Harvard Universities: Archive for Reprints: Can one explain schemes to biologists, 14 December 2014 By the 1970s, Grothendieck's work was seen as influential, not only in algebraic geometry and the allied fields of sheaf theory and homological algebra, but influenced logic, in the field of categorical logic. According to mathematician Ravi Vakil, "Whole fields of mathematics speak the language that he set up. We live in this big structure that he built. We take it for granted—the architect is gone". In the same article, Colin McLarty said, "Lots of people today live in Grothendieck's house, unaware that it's Grothendieck's house."
Alexander Grothendieck	Geometry	Geometry Grothendieck approached algebraic geometry by clarifying the foundations of the field, and by developing mathematical tools intended to prove a number of notable conjectures. Algebraic geometry has traditionally meant the understanding of geometric objects, such as algebraic curves and surfaces, through the study of the algebraic equations for those objects. Properties of algebraic equations are in turn studied using the techniques of ring theory. In this approach, the properties of a geometric object are related to the properties of an associated ring. The space (e.g., real, complex, or projective) in which the object is defined, is extrinsic to the object, while the ring is intrinsic. Grothendieck laid a new foundation for algebraic geometry by making intrinsic spaces ("spectra") and associated rings the primary objects of study. To that end, he developed the theory of schemes that informally can be thought of as topological spaces on which a commutative ring is associated to every open subset of the space. Schemes have become the basic objects of study for practitioners of modern algebraic geometry. Their use as a foundation allowed geometry to absorb technical advances from other fields. His generalization of the classical Riemann–Roch theorem related topological properties of complex algebraic curves to their algebraic structure and now bears his name, being called "the Grothendieck–Hirzebruch–Riemann–Roch theorem". The tools he developed to prove this theorem started the study of algebraic and topological K-theory, which explores the topological properties of objects by associating them with rings. After direct contact with Grothendieck's ideas at the Bonn Arbeitstagung, topological K-theory was founded by Michael Atiyah and Friedrich Hirzebruch.
Alexander Grothendieck	Cohomology theories	Cohomology theories Grothendieck's construction of new cohomology theories, which use algebraic techniques to study topological objects, has influenced the development of algebraic number theory, algebraic topology, and representation theory. As part of this project, his creation of topos theory, a category-theoretic generalization of point-set topology, has influenced the fields of set theory and mathematical logic. The Weil conjectures were formulated in the later 1940s as a set of mathematical problems in arithmetic geometry. They describe properties of analytic invariants, called local zeta functions, of the number of points on an algebraic curve or variety of higher dimension. Grothendieck's discovery of the ℓ-adic étale cohomology, the first example of a Weil cohomology theory, opened the way for a proof of the Weil conjectures, ultimately completed in the 1970s by his student Pierre Deligne. Grothendieck's large-scale approach has been called a "visionary program". The ℓ-adic cohomology then became a fundamental tool for number theorists, with applications to the Langlands program.R. P. Langlands, Modular forms and l-adic representations, Lecture Notes in Math. 349. (1973), 361—500 Grothendieck's conjectural theory of motives was intended to be the "ℓ-adic" theory but without the choice of "ℓ", a prime number. It did not provide the intended route to the Weil conjectures, but has been behind modern developments in algebraic K-theory, motivic homotopy theory, and motivic integration. This theory, Daniel Quillen's work, and Grothendieck's theory of Chern classes, are considered the background to the theory of algebraic cobordism, another algebraic analogue of topological ideas.
Alexander Grothendieck	Category theory	Category theory Grothendieck's emphasis on the role of universal properties across varied mathematical structures brought category theory into the mainstream as an organizing principle for mathematics in general. Among its uses, category theory creates a common language for describing similar structures and techniques seen in many different mathematical systems. His notion of abelian category is now the basic object of study in homological algebra. The emergence of a separate mathematical discipline of category theory has been attributed to Grothendieck's influence, although unintentional.
Alexander Grothendieck	In popular culture	In popular culture Colonel Lágrimas (Colonel Tears in English), a novel by Puerto Rican–Costa Rican writer Carlos Fonseca is about Grothendieck. The Benjamín Labatut book When We Cease to Understand the World dedicates one chapter to the work and life of Grothendieck, introducing his story by reference to the Japanese mathematician Shinichi Mochizuki. The book is a lightly fictionalized account of the world of scientific inquiry and was a finalist for the National Book Award. In Cormac McCarthy's The Passenger and its sequel Stella Maris, a main character is a student of Grothendieck's. The Istituto Grothendieck has been created in his honor.
Alexander Grothendieck	Publications	Publications
Alexander Grothendieck	See also	See also ∞-groupoid λ-ring AB5 category Abelian category Accessible category Algebraic geometry Algebraic stack Barsotti–Tate group Chern class Descent (mathematics) Dévissage Dunford–Pettis property Excellent ring Formally smooth map Fundamental group scheme K-theory Hilbert scheme Homotopy hypothesis List of things named after Alexander Grothendieck Nakai conjecture Nuclear operator Nuclear space Parafactorial local ring Projective tensor product Quasi-finite morphism Quot scheme Scheme (mathematics) Section conjecture Semistable abelian variety Sheaf cohomology Stack (mathematics) Standard conjectures on algebraic cycles Sketch of a program Tannakian formalism Theorem of absolute purity Theorem on formal functions Ultrabornological space Weil conjectures Vector bundles on algebraic curves Zariski's main theorem
Alexander Grothendieck	Notes	Notes
Alexander Grothendieck	References	References
Alexander Grothendieck	Sources and further reading	Sources and further reading English translation of . English translation: First part of planned four-volume biography. English version. A review of the German edition Third part of planned four-volume biography; crowd-financed translation into English. First 4 chapters from the incomplete second part of planned four-volume biography.
Alexander Grothendieck	External links	External links Centre for Grothendieckian Studies (CSG) is a research centre of the Grothendieck Institute, with a dedicated mission to honour the memory of Alexander Grothendieck. Séminaire Grothendieck is a peripatetic seminar on Grothendieck view not just on mathematics Grothendieck Circle, collection of mathematical and biographical information, photos, links to his writings The origins of 'Pursuing Stacks': This is an account of how 'Pursuing Stacks' was written in response to a correspondence in English with Ronnie Brown and Tim Porter at Bangor, which continued until 1991. See also Alexander Grothendieck: some recollections. Récoltes et Semailles "Récoltes et Semailles", Spanish translation "La Clef des Songes", French originals and Spanish translations English summary of "La Clef des Songes" Video of a lecture with photos from Grothendieck's life, given by Winfried Scharlau at IHES in 2009 Can one explain schemes to biologists —biographical sketch of Grothendieck by David Mumford & John Tate Archives Grothendieck "Who Is Alexander Grothendieck?, Winfried Scharlau, Notices of the AMS 55(8), 2008. "Alexander Grothendieck: A Country Known Only by Name, Pierre Cartier, Notices of the AMS 62(4), 2015. Alexandre Grothendieck 1928–2014, Part 1, Notices of the AMS 63(3), 2016. Les-archives-insaisissables-d-alexandre-grothendieck Kutateladze S.S. Rebellious Genius: In Memory of Alexander Grothendieck Alexandre-Grothendieck-une-mathematique-en-cathedrale-gothique Les-archives-insaisissables-d-alexandre-grothendieck Category:1928 births Category:2014 deaths Category:20th-century French mathematicians Category:Algebraic geometers Category:Algebraists Category:Emigrants from Nazi Germany to France Category:Fields Medalists Category:French pacifists Category:Functional analysts Category:German people of Russian-Jewish descent Category:Nancy-Université alumni Category:Nicolas Bourbaki Category:Operator theorists Category:Scientists from Berlin Category:Stateless people
Alexander Grothendieck	Table of Content	Short description, Life, Family and childhood, World War II, Studies and contact with research mathematics, IHÉS years, "Golden Age", Political activism, Manuscripts written in the 1980s, Retirement into reclusion and death, Citizenship, Family, Mathematical work, ''EGA'', ''SGA'', ''FGA'', Major mathematical contributions, Influence, Geometry, Cohomology theories, Category theory, In popular culture, Publications, See also, Notes, References, Sources and further reading, External links
Alcoholics Anonymous	short description	Alcoholics Anonymous (AA) is a global, peer-led mutual-aid fellowship focused on an abstinence-based recovery model from alcoholism through its spiritually inclined twelve-step program. AA's Twelve Traditions, besides emphasizing anonymity, stress lack of hierarchy, staying non-promotional, and non-professional, while also unaffiliated, non-denominational, apolitical and free to all. , AA estimated it is active in 180 countries with an estimated membership of nearly two million—73% in the United States and Canada. AA traces its origins to a 1935 meeting between Bill Wilson (commonly referred to as Bill W.) and Dr. Bob Smith (Dr. Bob), two individuals seeking to address their shared struggles with alcoholism. Their collaboration, influenced by the Christian revivalist Oxford Group, evolved into a mutual support group that eventually became AA. In 1939, the fellowship published Alcoholics Anonymous: The Story of How More than One Hundred Men Have Recovered from Alcoholism, colloquially known as the "Big Book". This publication introduced the twelve-step program and provided the basis for the organization's name. Later editions of the book expanded its subtitle to reflect the inclusion of "Thousands of Men and Women". The Twelve Steps outline a suggested program of ongoing drug rehabilitation and self-improvement. A key component involves seeking alignment or divining with a personally defined concept of "God as we understood Him". The steps begin with an acknowledgment of powerlessness over alcohol and the unmanageability of life due to alcoholism. Subsequent steps emphasize rigorous honesty, including the completion of a "searching and fearless moral inventory", acknowledgment of "character defects", sharing the inventory with a trusted person, making amends to individuals harmed, and engaging in regular prayer or meditation to seek "conscious contact with God" and guidance in following divine will. The final step, the 12th, focuses on maintaining the principles of recovery, sharing the message with other alcoholics, and participating in "12th Step work," such as peer sponsorship, organizing meetings, and outreach to institutions like hospitals and prisons. AA meetings differ in format, with variations including personal storytelling, readings from the Big Book, and open discussions. While certain meetings may cater to specific demographic groups, attendance is generally open to anyone with a desire to stop drinking alcohol. The organization is self-supporting through member donations and literature sales. Its operations follow an "inverted pyramid" structure, allowing local groups significant autonomy. AA does not accept external funding or contributions. Empirical evidence supports AA's efficacy. A 2020 Cochrane review found that manualized AA and Twelve-Step Facilitation (TSF) therapy demonstrated higher rates of continuous abstinence compared to alternative treatments, such as cognitive-behavioral therapy, with added healthcare cost savings over time.{{efn\|name=manualized\|Regarding "manualized AA and Twelve-Step Facilitation (TSF) therapy", manualized' 'means "the treatment is based on standardized content delivered in a linear or modular fashion to ensure that the same treatment is delivered across time and different sites where the intervention may be implemented. This ensures that the treatment can be replicated – a key factor in confirming the findings across different studies using the same treatment." (2020 Cochrane review article, p. 5, PDF version).}} Criticism of AA has addressed various aspects of its program and operations. Concerns have been raised about its overall success rate, the perceived religious nature of its approach, and allegations of cult-like elements. Additional critiques include reports of "thirteenth-stepping," where senior members engage romantically with newer members, and legal challenges related to safety and the religious content of court-mandated participation in AA programs. History Hazard's search for treatment, spiritual conversion, & involvement with the Oxford Group Rowland Hazard’s journey from Carl Jung’s psychiatric treatment to spiritual conversion through the Oxford Group played a pivotal role in shaping the foundations of Alcoholics Anonymous, influencing its principles of recovery. In 1926, Hazard went to Zurich, Switzerland, to seek treatment for alcoholism with psychiatrist Carl Jung. When Hazard ended treatment with Jung after about a year, and came back to the US, he soon resumed drinking, and returned to Jung in Zurich for further treatment. Jung told Hazard that his case was nearly hopeless (as with other alcoholics) and that his only hope might be a "spiritual conversion" with a "religious group".Pass It On, p. 1141961 letter from Carl Jung to Bill Wilson concerning Rowland Hazard III – photographic imageJung, C.G., Retrospective 1961 letter from C.G. Jung to Bill Wilson about Rowland Hazard III with commentary by the Big Book Bunch. Back in America, Hazard went to the Oxford Group, whose teachings were eventually the source of such AA concepts as "meetings" and "sharing" (public confession), making "restitution", "rigorous honesty" and "surrendering one's will and life to God's care". He became converted to a lifetime of sobriety while on a train ride from New York to Detroit after reading For Sinners Only, by Oxford Group member AJ Russell.Pass It On, pp. 113–114 Hazard underwent a spiritual conversion" with the help of the Group and began to experience the liberation from drink that he was seeking. Members of the group introduced Hazard to Ebby Thacher, whom Hazard brought to the Calvary Rescue Mission, directed by Oxford Group leader Sam Shoemaker.Pass It On, p. 127. Bill Wilson & his spiritual awakening In keeping with the Oxford Group teaching that a new convert must win other converts to preserve his own conversion experience, Thacher contacted his old friend Bill Wilson, whom he knew had a drinking problem.Pass It On, p. 117.Walter HA, Soul Surgery p. 44 Oxford: The Oxford Group Thacher approached Wilson, saying that he had "got religion", was sober, and that Wilson could do the same if he set aside objections and instead formed a personal idea of God, "another power" or "higher power".Pass It On, 1984, p 117.thumb\|upright=1.15\|right\|Sobriety token or "chip", given for specified lengths of sobriety. On the back is the Serenity Prayer. Here green is for six months of sobriety; purple is for nine months.Feeling a "kinship of common suffering", Wilson attended his first group gathering, although he was drunk. Within days, Wilson admitted himself to the Charles B. Towns Hospital after drinking four beers on the way—the last alcohol he ever drank. Under the care of Dr. William Duncan Silkworth, an early benefactor of AA, Wilson's detox included the deliriant belladonna.Pittman, Bill "AA the Way it Began" 1988, Glenn Abbey Books At the hospital, a despairing Wilson experienced a bright flash of light, which he felt to be God revealing himself. Founding of AA Wilson's early efforts and influence of the Oxford Group Following his hospital discharge, Wilson joined the Oxford Group and tried to recruit other alcoholics to the group. These early efforts to help others kept him sober, but were ineffective in getting anyone else to join the group. Dr. Silkworth suggested that Wilson place less stress on religion (as required by The Oxford Group) and more on the science of treating alcoholism. Bill W. would later write: "The early AA got its ideas of self-examination, acknowledgment of character defects, restitution for harm done, and working with others straight from the Oxford Group and directly from Sam Shoemaker, their former leader in America, and from nowhere else".Pittman, Bill AA the Way it Began Glen Abbey Books, 1988 According to Mercadante, however, the AA concept of powerlessness over alcohol departs significantly from Oxford Group belief. According to AA, alcoholism cannot be cured, whereas the Oxford Group stressed the possibility of complete victory over sin.Mercadante, Linda A, Victims and Sinners: p. 55. Westminster John Knox Press: 1996 Beginnings of AA right\|thumb\|250x250px\|Robert Smith's House in Akron In 1935, AA began in Akron, Ohio, as the outcome of a meeting between Wilson—who became known as "Bill W." in AA circles—and Dr. Robert Smith, an Akron surgeon, who would become Wilson's first recruitment success. On a business trip by Bill W. to Akron, he was introduced to the surgeon, who despite connections with the Oxford Group, was unable to stay sober. Bill W. explained that alcoholism affects the mind, emotions, and body, a concept he had learned from Dr. Silkworth at Towns Hospital in New York, where he had been a patient multiple times. Convinced by these insights, Dr. Bob took his last alcoholic drink on 10 June 1935 and never drank again, soon achieving sobriety. This date is regarded by AA as its inception. Bill W. and Dr. Bob started working with alcoholics at Akron's City Hospital. One patient, who soon achieved sobriety, joined them and together, the three men formed the foundation of what would later become known as Alcoholics Anonymous. In late 1935, a new group of alcoholics began forming in New York, followed by another in Cleveland in 1939. Over the course of four years, these three initial groups helped around 100 people achieve sobriety. In early 1939, the fellowship published its foundational text, Alcoholics Anonymous, which outlined AA's philosophy; introduced the Twelve Steps; and included the case histories of 30 individuals who had achieved recovery. The Twelve Steps were influenced by the Oxford Group's six steps and various readings, including William James's The Varieties of Religious Experience. This publication marked a significant milestone in AA's development. The first meeting outside the Oxford Group was held at Dr. Bob's house with 80 members in attendance. Dr. Bob began the meeting in his dining room by identifying himself as an alcoholic, and placing his foot on the dining room table, read the Sermon on the Mount from the Gospel of Matthew.Dr. Bob and the Good Oldtimers A Biography, with Recollections of Early A.A. in the Midwest pg. 218 The first female member, Florence Rankin, joined AA in March 1937, and the first non-Protestant member, a Roman Catholic, joined in 1939. The first Black AA group commenced in 1945 in Washington, D.C., founded by Jim S., an African-American physician from Virginia. The Alcoholic Foundation thumb\|250x250px\|Alcoholics Anonymous material on walls at The Wilson House, 378 Village Street in downtown East Dorset, Vermont. In 1938, Dr. Bob and Bill created The Alcoholic Foundation in New York, bringing in friends of John D. Rockefeller Jr. as board members. Although they sought to raise significant funds, Rockefeller advised that large contributions might jeopardize the Fellowship. The foundation opened a small office in New York, funded primarily by AA members, to handle inquiries and distribute the Alcoholics Anonymous book. The next year, Rockefeller organized a dinner to promote AA, which further increased the number of inquiries. The office became effective. Each request received a personal reply and a pamphlet, enhancing interest in the book. Consequently, many new AA groups were established, and by the end of 1940, membership had grown to 2,000. Media coverage leads to expansion In 1939, media coverage, particularly from The Cleveland Plain Dealer, generated a surge of interest and requests for help. The Cleveland group, although small, successfully assisted many alcoholics, quickly growing from 20 to around 500 members. A subsequent article in Liberty magazine resulted in a flood of requests for assistance, further expanding AA's reach. In 1941, The Saturday Evening Post published an article about AA, sparking a surge in inquires, and AA membership tripled over the next year.Jack Alexander (1 March 1941). "Alcoholics Anonymous." Saturday Evening Post, 22 December 2015, Post Perspective. Retrieved 10 December 2022 AA-related interviews on American radio and favorable articles in US magazines led to increased book sales and membership. As the growing fellowship faced disputes over structure, purpose, authority, and publicity, Bill W. began promoting the Twelve Traditions. He first introduced his ideas on these in an April 1946 article for The Grapevine, titled "Twelve Suggested Points for AA Tradition", aiming to preserve the organization's unity and purpose as AA expanded. He described the input he received as a "welter of exciting and fearsome experience" which greatly influenced the development of the Traditions. From December 1947 to November 1948, The Grapevine published the Traditions individually, and in 1950, the First International Convention in Cleveland officially adopted them. Creation of the General Service Conference (GSC) In 1951, AA's headquarters in New York expanded its activities, including public relations, support for new groups, services to hospitals and prisons, and cooperation with agencies in the field of alcoholism. It also published standard AA literature and oversaw translations, while the AA Grapevine gained substantial circulation. Despite these essential services, they were managed by a disconnected board of trustees, primarily linked to Bill and Dr. Bob. Recognizing the need for accountability, delegates from across the US and Canada were convened, leading to the first meeting of the AA General Service Conference in 1951. This successful gathering established direct oversight of AA's trusteeship by the fellowship itself, ensuring the organization's future governance. At the 1955 conference in St. Louis, Missouri, Bill W. relinquished stewardship of AA to the General Service Conference,Pass It On, 1984, p. 359 as AA had grown to millions of members internationally. International expansion thumb\|250x250px\|An AA meeting The World Service Meeting (WSM), established in 1969, is a biennial international forum at which AA delegates from around the world exchange ideas and experiences about carrying the message of recovery. Held in various cities around the world, the WSM focuses on sharing strategies to help alcoholics in different countries and languages. Today, AA is present in approximately 180 nations worldwide. By 2018, AA had 2,087,840 members and 120,300 AA groups worldwide. There are AA meetings in Beijing, China. In July 2024, AA launched its first UK-wide advertising campaign with a unique approach—no logos, phone numbers, or links—focusing on subtle messaging like "You Are Not Alone" and "Alcohol Isn't the Answer". The campaign, created by The Raised Eyebrow Society, aims to attract people struggling with alcohol without violating AA's principles of anonymity and non-promotion. AA will celebrate its 100th anniversary meeting in Indianapolis, Indiana, in 2035. The international convention is anticipated to attract tens of thousands of attendees to the Indiana Convention Center and Lucas Oil Stadium. AA literature Alcoholics Anonymous publishes several books, reports, pamphlets, and other media, including a periodical known as the AA Grapevine.A WorldCat search for materials authored by Alcoholics Anonymous and more specific divisions of the organization (AA Grapevine, World Services, General Service Conference, World Service Meeting) yields well over 500 results. Two books are used primarily: Alcoholics Anonymous (the "Big Book") and, expounding on the big book in regard to its subject, Twelve Steps and Twelve Traditions. As with all AA literature, the texts are freely available on AA.org. The Big Book thumb\|250x250px\|Plaque at site of Calumet Building in Newark where much of the text for the "Big Book" of Alcoholics Anonymous was written In 1939, Bill W. and other members wrote the book initially titled Alcoholics Anonymous: The Story of How More than One Hundred Men Have Recovered from Alcoholism, from which AA drew its name, informally known as the "Big Book". The second edition of the Big Book was released in 1955, the third in 1976, and the fourth in 2001. The first part of the book, which details the program, has remained largely intact since the 1939 edition, with minor statistical updates and edits. The second part contains personal stories that are updated with every edition to reflect current AA membership, resulting in earlier stories being removed—these were published separately in 2003 in the book Experience, Strength, and Hope.Experience, Strength and Hope: Stories from the First Three Editions of Alcoholics Anonymous, New York: Alcoholics Anonymous, 2003, . The Big Book suggests a twelve-step program in which members admit that they are powerless over alcohol and need help from a "higher power". It offers guidance and strength through prayer and meditation from God or a higher power of their own understanding; take a moral inventory with care to include resentments; list and become ready to remove character defects; list and make amends to those harmed; continue to take a moral inventory, pray, meditate, and try to help other alcoholics recover. The second half of the book, "Personal Stories" (subject to additions, removal, and retitling in subsequent editions), is made of AA members' redemptive autobiographical sketches. Illness and allergy terminology AA's Big Book calls alcoholism "an illness which only a spiritual experience will conquer". Ernest Kurtz says this is "The closest the book Alcoholics Anonymous comes to a definition of alcoholism". Somewhat divergently in his introduction to The Big Book, non-member and early benefactor William Silkworth said those unable to moderate their drinking suffer from an allergy. In presenting the doctor's postulate, AA said "The doctor's theory that we have an allergy to alcohol interests us. As laymen, our opinion as to its soundness may, of course, mean little. But as ex-problem drinkers, we can say that his explanation makes good sense. It explains many things for which we cannot otherwise account".Alcoholics Anonymous page xxx AA later acknowledged that "alcoholism is not a true allergy, the experts now inform us". Twelve Steps and Twelve Traditions The "Twelve Steps and Twelve Traditions" is a book published in 1953 that serves as a key text for AA. Written by AA co-founder Bill W., it provides detailed explanations of the Twelve Steps and the Twelve Traditions. The book is commonly used in AA meetings and individual study, offering a framework for understanding the organization's approach to recovery and community. The story of Eddie Rickenbacker "and his courageous company" appears in the book. It pertains to when his plane crashed in the Pacific and is used in the closing remarks of Tradition One: "Our common welfare should come first; personal recovery depends upon AA unity".Alcoholics Anonymous (2002-02-10). Twelve Steps and Twelve Traditions. Hazelden. . . Grapevine The Grapevine, established in June 1944 by six AA members in New York, became AA's national journal by 1945 and later its international journal. Supported by Bill W., the magazine featured first-person stories, AA news, and discussions on key topics like women in AA and veterans returning from war. Initially intended as a resource for alcoholics worldwide, the Grapevine evolved into a unifying publication for the AA community, chronicling the Fellowship's growth, including the creation of the General Service Structure and publication of later editions of the Big Book. The Twelve Traditions were introduced to AA by Bill W. in April 1946 through an article titled "Twelve Suggested Points for AA Tradition". The AA Preamble, inspired by the foreword of the book Alcoholics Anonymous, was written by one of the Grapevine's early editors Tom. Y. and first appeared in the June 1947 issue. In 1986, the Grapevine was reaffirmed as AA's international journal by the General Service Conference. The AA program Twelve steps thumb\|333x333px\|Alcoholics Anonymous Twelve Steps exhibit at AA Intergroup in Akron, Ohio. AA's program extends beyond abstaining from alcohol. Its goal is to effect enough change in the alcoholic's thinking "to bring about recovery from alcoholism" through "an entire psychic change," or spiritual awakening. A spiritual awakening is meant to be achieved by taking the Twelve Steps, and sobriety is furthered by volunteering for AAQuestions & Answers on Sponsorship and regular AA meeting attendance or contact with AA members. Taking AA's 12 steps are a "suggested", but not required, "program of recovery"—also called a "spiritual solution". They start with members admitting to being "powerless over alcohol" (which the Big Book calls an "Illness" or "malady", but never a "disease’’), and out of control—for which on going divining and following the will an unspecified 'higher power' ("God, as we understood Him") could restore them to "sanity". In the steps members acknowledge and make amends and seek to correct personal character defects aided by their higher power for guidance. Those "having achieved a spiritual awakening as a result of these steps" are suggested to carry AA's message to other alcoholics. This is often done through meetings of AA groups as well as with members taking on sponsees, although the Big Book makes no mention of the latter term. While taking care to avoid becoming affiliated, some AA members perform outreach to hospitals, treatment centers and correctional facilities. Sponsorship Members are encouraged to find an experienced fellow alcoholic, called a sponsor, to help them understand and follow the AA program. The sponsor should preferably have experienced all twelve of the steps, be the same sex as the sponsored person, and refrain from imposing personal views on the sponsored person. Following the helper therapy principle, sponsors in AA may benefit from their relationship with their charges, as "helping behaviors" correlate with increased abstinence and lower probabilities of binge drinking. Twelve Traditions The Twelve Traditions provide essential guidelines—not rules—that help AA groups navigate their relationships both internally and with the outside world. These traditions ensure that membership is open to anyone seeking to stop drinking, with no dues or fees required. These Traditions foster an altruistic, unaffiliated, non-coercive, and non-hierarchical organization, limiting AA's mission to helping alcoholics at a non-professional level while avoiding publicity. To prioritize recovery, the traditions discourage hierarchies, dogma, public controversies, property acquisition, and outside contributions. Members are advised against using AA for personal gain or public prestige, and anonymity is emphasized, particularly in media, with no prescribed consequences for breaches. Meetings Overview AA meetings serve as a space where individuals discuss recovery from alcoholism, with flexibility in how meetings are conducted. While AA offers pamphlets suggesting formats, groups have the autonomy to organize their meetings according to their preferences, as long as their decisions do not impact other groups or AA as a whole. Despite cultural differences influencing certain rituals, many elements of AA meetings remain consistent worldwide. Types AA meetings encompass a variety of formats, each designed to serve different needs. Open meetings are accessible to anyone, including non-alcoholics who can attend as observers. In contrast, closed meetings are reserved for individuals who identify as having a desire to stop drinking, a declaration that cannot be questioned by other members. Speaker meetings feature one or more members who share their personal stories of recovery, fostering connection and understanding among participants. Big Book meetings focus on reading and discussing passages from AA's foundational text, while sharing meetings provide an open platform for members to speak freely and share their experiences, with or without a predetermined topic. AA meetings are gatherings where recovery from alcoholism is discussed. One perspective sees them as "quasi-ritualized therapeutic sessions run by and for, alcoholics". In recent years, online meetings have become popular, allowing members to connect virtually through platforms like Zoom and What's App. Offline or in-person meetings, often referred to as "brick and mortar" meetings, take place in physical locations, and some groups host hybrid meetings, enabling participants to attend either in person or virtually. Inclusivity & language accessibility Inclusivity is a core principle of AA meetings, which welcome all alcoholics, though some are tailored to specific demographics such as gender, age, profession, or cultural background. Since the mid-1970s, several 'agnostic' or 'no-prayer' AA groups have begun across the US, Canada, and other parts of the world, which hold meetings that adhere to a tradition allowing alcoholics to freely express their doubts or disbelief that spirituality will help their recovery, and these meetings forgo the use of opening or closing prayers. Meetings in the United States are held in a variety of languages including Armenian, English, Farsi, Finnish, French, Japanese, Korean, Russian, and Spanish.thumb\|Headquarters of Alcohólicos Anónimos in Montevideo, Uruguay Donations and contributions At some point during the meeting, a basket is passed around for voluntary contributions. AA's 7th tradition requires that groups be "self-supporting, declining outside contributions". Serenity prayer The Serenity Prayer is commonly used in AA meetings as a tool for reflection and guidance. It was called the AA prayer in the 1940s. Often recited at meetings, it emphasizes the concepts of acceptance, courage, and wisdom, which align with the principles of the AA program. The prayer encourages individuals to accept things they cannot change, to find the courage to make changes where possible, and to seek the wisdom to distinguish between the two. thumb\|right\|Building for Spanish-speaking AA group in Westlake neighborhood, Los Angeles Sobriety anniversaries and coins Sobriety coins, also known as sobriety chips, are tokens given to members of AA to signify the duration of their sobriety. While the chip system is common, it is not universally adopted across all AA groups. The tradition began with Sister Ignatia in Akron, Ohio, who distributed medallions to newly released patients as reminders to avoid drinking. The actual sobriety chip as known today is believed to have originated in 1942 in Indianapolis, gaining popularity as various AA groups adopted the practice. Typically, different colored chips represent milestones of sobriety within the first year, with tokens awarded for 24 hours, 30 days, 60 days, 90 days, and beyond, culminating in a bronze chip for one year of sobriety. AA members celebrate Founders Day on the weekend closest to 10 June, marking the anniversary of the organization with thousands of attendees engaging in tours of historical sites, sharing recovery stories, and participating in related activities in Akron, Ohio. Organization and finances thumb\|left\|A regional service center for Alcoholics Anonymous Structure and governance AA describes itself as "not organized in the formal or political sense" and has been referred to as a "benign anarchy," borrowing a phrase from anarchy theorist Peter Kropotkin. The Twelve Traditions guide the functioning of individual AA groups, while the Twelve Concepts for World Service outline how the organization operates on a global scale. Each AA group is self-governing, with AA World Services acting only in an advisory capacity. This "inverted pyramid" style of governance has been key to the organization's resilience and adaptability. In Ireland, Shane Butler noted that AA's lack of top-level leadership might make it seem unsustainable, but its structure has proven extremely robust since its establishment there in 1946. AA's 21-member Board of Trustees includes seven "nonalcoholic friends of the fellowship," though the organization is primarily served and run by alcoholics. Members who accept service positions, termed "trusted servants," hold these roles for limited terms, typically ranging from three months to two years, depending on the position and group vote. This approach ensures regular rotation and participation from a broad spectrum of members, maintaining AA's commitment to shared responsibility and leadership. Financial structure AA is entirely self-supporting, relying on voluntary contributions from its members to cover expenses. Contributions to the General Service Office (GSO) are limited to $5,000 per member per year. In addition to these contributions, more than 50% of AA's income comes from the sale of AA literature, such as books and pamphlets. This practice aligns with AA's Seventh Tradition, which emphasizes financial independence by not accepting donations from outside individuals or organizations. The Central Office is also fully self-supporting through the sale of literature and member contributions. Employment and service roles The Eighth Tradition permits AA to employ "special workers" for roles that require specific expertise or full-time responsibilities, such as administrative tasks. However, these paid roles do not involve working directly with alcoholics in need of help, a function known as the "Twelfth Step". Calls from alcoholics seeking assistance are always passed on to sober AA members who have volunteered to handle them, ensuring the program remains grounded in its peer-to-peer support model. Organizational operations The AA Central Office coordinates activities such as printing literature, responding to public inquiries, and organizing conferences. It operates independently but ensures alignment with the core principles of the organization. Other International General Service Offices—such as those in Australia, Costa Rica, and Russia—function independently of AA World Services in New York, reflecting AA's decentralized and autonomous structure. Hospitals & institutions Many AA meetings take place in treatment facilities. Carrying the message of AA into hospitals was how the co-founders of AA first remained sober. They discovered great value in working with alcoholics who are still suffering, and that even if the alcoholic they were working with did not stay sober, they did. Bill W. wrote, "Practical experience shows that nothing will so much insure immunity from drinking as intensive work with other alcoholics". Bill Wilson visited Towns Hospital in New York City in an attempt to help the alcoholics who were patients there in 1934. At St. Thomas Hospital in Akron, Ohio, Smith worked with still more alcoholics. In 1939, a New York mental institution, Rockland State Hospital, was one of the first institutions to allow AA hospital groups. Service to corrections and treatment facilities used to be combined until the General Service Conference, in 1977, voted to dissolve its Institutions Committee and form two separate committees, one for treatment facilities, and one for correctional facilities. In the United States and Canada, AA meetings are held in hundreds of correctional facilities. The AA General Service Office has published a workbook with detailed recommendations for methods of approaching correctional-facility officials with the intent of developing an in-prison AA program. In addition, AA publishes a variety of pamphlets specifically for the incarcerated alcoholic. Additionally, the AA General Service Office provides a pamphlet with guidelines for members working with incarcerated alcoholics. Demographics thumb\|AA group in Pátzcuaro, Michoacán, Mexico 2014 membership survey AA's New York General Service Office survey of over 6,000 members in Canada and the United States concluded that, in North America, AA members who responded to the survey were 62% male and 38% female. The survey found that 89% of AA members were white. Average member sobriety is slightly under 10 years with 36% sober more than ten years, 13% sober from five to ten years, 24% sober from one to five years, and 27% sober less than one year. Before coming to AA, 63% of members received some type of treatment or counseling, such as medical, psychological, or spiritual. After coming to AA, 59% received outside treatment or counseling. Of those members, 84% said that outside help played an important part in their recovery. The same survey showed that AA received 32% of its membership from other members, another 32% from treatment facilities, 30% were self-motivated to attend AA, 12% of its membership from court-ordered attendance, and only 1% of AA members decided to join based on information obtained from the Internet. People taking the survey were allowed to select multiple answers for what motivated them to join AA. Diversity A 2024 study found that Black, Hispanic, and younger adults are less likely to attend AA meetings compared to white and older adults, with these disparities remaining consistent over time. Effectiveness Measuring Several metrics are used to evaluate the success of AA including abstinence, reduced drinking intensity, reduced alcohol-related consequences, addiction severity, and healthcare costs. Because of the anonymous and voluntary nature of AA meetings, it has been difficult to perform random trials with them. However, environmental and quasi-experiment studies suggest that AA can help alcoholics make positive changes. Until recently, ethical and operational issues had prevented robust randomized controlled trials from being conducted comparing 12-step programs directly to other approaches. Reviews and studies Long-term recovery effectiveness There have been numerous studies on the effectiveness of AA. A 2006 study by Rudolf H. Moos and Bernice S. Moos saw a 67% success rate 16 years later for the 24.9% of alcoholics who ended up, on their own, undergoing a lot of AA treatment. However, this may be influenced by self-selection bias. Project MATCH, a 1990s multi-site study, found AA to be more effective than no treatment. Other studies link increased AA attendance with higher spirituality and reduced alcohol consumption. Brandsma 1980 is paywalled, but is summarized in the Wikipedia A 2020 Cochrane review concluded that AA is more effective than other treatments, such as MET and CBT, in terms of abstinence rates. It also noted similar success in reducing drinking and alcohol-related problems, though this conclusion was based on moderate-certainty evidence. The review found that AA participation via AA twelve step facilitation (AA/TSF) had sustained remission rates 20-60% above other well-established treatments. Additionally, 4 of the 5 economic studies in the review found that AA/TSF lowered healthcare costs considerably. Nick Heather, an addiction researcher, critiqued the review, arguing it may have a sample bias and that it failed to measure outcomes like quality of life or alcohol dependence, which are important for evaluating recovery. The authors responded, stating their review showed AA is at least as effective as other treatments and more cost-effective.Kelly, John F.; Humphreys, Keith; Ferri, Marica (2020). "Alcoholics Anonymous and other 12-step programs for alcohol use disorder". Cochrane Database of Systematic Reviews. 3 (CD012880): 35. doi:10.1002/14651858.CD012880.pub2. PMC 7065341. PMID 32159228. The authors also noted the lack of quality-of-life measures was due to the limitations of the reviewed studies. Comparative effectiveness and cost effectiveness A 2020 systematic review indicated that manualized AA and Twelve-Step Facilitation (TSF) therapy yields more healthcare cost savings and leads to higher continuous abstinence rates. A longitudinal study suggests that LifeRing and SMART Recovery fared worse than AA across several outcomes, however, the effects are insignificant when controlling for the baseline alcohol goal of total abstinence. More recent studies employing randomized and blinded trials have shown 12-step programs provide similar benefit compared to motivational enhancement therapy (MET) and cognitive behavioral therapy (CBT), and were more effective in producing continuous abstinence and remission compared to these approaches. Patterns of engagement and disengagement The 2001–2002 National Epidemiological Survey on Alcoholism and Related Conditions (NESARC) found that 3.4% of respondents had attended a 12-step meeting. Of those, 988 had ceased attending, 348 continued attending, and 105 were newcomers. These figures help to understand engagement and disengagement patterns within AA. Mechanisms of recovery Although AA claims that spirituality is the primary mechanism for achieving change and recovery, there is growing evidence that suggests this is only true for a minority of AA attendees with a high addiction severity. Instead, AA's beneficial effects are carried predominantly by social, cognitive and affective mechanisms. However, atheist and agnostic people are less likely to initiate and sustain AA attendance in comparison to spiritual and religious people. Criticism The effectiveness of AA, compared to other methods and treatments, has been challenged over the years. Lance Dodes, in The Sober Truth, claims only five to eight percent of the people who go to one or more AA meetings achieve sobriety. Dodes opposes the idea that a social network is needed to overcome substance abuse. Dodes' assertion that AA is ineffective has been criticized. Some other experts claim that the book's conclusion that "[12-step] approaches are almost completely ineffective and even harmful in treating substance use disorders" is wrong. In a 2015 article for The Atlantic, Gabrielle Glaser criticized the dominance of AA in the treatment of addiction in the United States, citing Dodes's figures and a 2006 Cochrane report, to claim AA had a low success rate. In the past, others have criticized 12-step programs as pseudoscientific Her figures and assertions, however were criticized by other experts. Philosophical and sociological dimensions AA shares the view that acceptance of one's inherent limitations is critical to finding one's proper place among other humans and God. Such ideas are described as "Counter-Enlightenment" because they are contrary to the Enlightenment's ideal that humans have the capacity to make their lives and societies a heaven on Earth using their own power and reason. After evaluating AA's literature and observing AA meetings for sixteen months, sociologists David R. Rudy and Arthur L. Greil found that for an AA member to remain sober, a high level of commitment is necessary. This commitment is facilitated by a change in the member's worldview. They argue that to help members stay sober, AA must provide an all-encompassing worldview while creating and sustaining an atmosphere of transcendence in the organization. To be all-encompassing, AA's ideology emphasizes tolerance rather than a narrow religious worldview that may make the organization unpalatable to potential members and thereby limit its effectiveness. AA's emphasis on the spiritual nature of its program, however, is necessary to institutionalize a feeling of transcendence. A tension results from the risk that the necessity of transcendence, if taken too literally, would compromise AA's efforts to maintain a broad appeal. As this tension is an integral part of AA, Rudy and Greil argue that AA is best described as a quasi-religious organization. Criticism and controversy Zoombombing Zoombombing emerged as a significant challenge for AA meetings during the COVID-19 pandemic, when many groups moved online. Disruptive individuals often infiltrated these virtual meetings, harassing participants and sharing inappropriate content. Some AA members experienced racial hatred. This intrusion undermined the safe, supportive environment essential for recovery, raising concerns about privacy and security. In response, AA groups and Zoom implemented stricter access controls and guidelines to protect participants and maintain a welcoming atmosphere for those seeking help. Disease model Though AA usually avoids the term disease, 1973 conference-approved literature said "we had the disease of alcoholism", while Living Sober, published in 1975, contains several references to alcoholism as a disease, including a chapter urging the reader to "Remember that alcoholism is an incurable, progressive, fatal disease". Regardless of official positions, since AA's inception, most members have believed alcoholism to be a disease. Its association with AA, as well as a good deal of its broader acceptance, stems from many members propagating it. Bill Wilson explained in 1960 why AA had refrained from using the term disease: 13th-step and sexual advances "Thirteenth-stepping" is a term used to describe a predatory behavior in AA where some individuals exploit vulnerable members for sexual relationships. This can involve unwanted advances and harassment, often targeting newer members who may be more susceptible due to their recovery status. In 2003, a study in the Journal of Addiction Nursing sampled 55 women in AA and found that 35% of these women had experienced a "pass" and 29% had felt seduced at least once in AA settings. This has also happened with new male members who received guidance from older female AA members pursuing sexual company. The authors suggest that both men and women must be prepared for this behavior or find male or female-only groups. Response As of 2010, women-only meetings are a very prevalent part of AA culture, and AA has become more welcoming for women. AA's pamphlet on sponsorship suggests that men be sponsored by men and women be sponsored by women.Questions and Answers on Sponsorship, page 10. 2005. AA also has a safety flier which states that "Unwanted sexual advances and predatory behaviors are in conflict with carrying the AA message of recovery". Criticism of culture Stanton Peele argued that some AA groups apply the disease model to all problem drinkers, whether or not they are "full-blown" alcoholics. Along with Nancy Shute, Peele has advocated that besides AA, other options should be readily available to those problem drinkers who can manage their drinking with the right treatment. The Big Book says "moderate drinkers" and "a certain type of hard drinker" can stop or moderate their drinking. The Big Book suggests no program for these drinkers, but instead seeks to help drinkers without "power of choice in drink".Alcoholics Anonymous page 20-1,24 In 1983, a review stated that the AA program's focus on admission of having a problem increases deviant stigma and strips members of their previous cultural identity, replacing it with the deviant identity. A 1985 study based on observations of AA meetings warned of detrimental iatrogenic effects of the twelve-step philosophy and concluded that AA uses many methods that are also used by cults. A later review disagreed, stating that AA's program bore little resemblance to religious cult practices. In 2014, George Eman Vaillant published a paper making the case that Alcoholics Anonymous is not a cult. Spirituality Some have criticized 12-step programs as "a cult that relies on God as the mechanism of action" and as "overly theistic and outdated". Others have cited the necessity of a "higher power" (an "HP") in formal AA as creating dependence on outside factors rather than internal efficacy. Gabrielle Glaser criticized 12-step programs for being "faith-based", but 12-step programs allow for a very wide diversity of spiritual beliefs, and there are a growing number of secular 12-step meetings. Secular meetings in Toronto controversy Reception to secular 12 step meetings from within AA has been mixed. In 2011, secular meetings in Toronto, where the 12 steps were altered to remove references to God and prayer, were delisted from the Toronto AA online and print directories, effectively removing them from the network of meetings. They appealed this decision, but were rejected, leading to a complaint to the Human Rights Tribunal of Ontario. The Toronto co-ordinating body, the Greater Toronto Area Intergroup of Alcoholics Anonymous, argued both that as a special interest group they have the right to restrict its membership, and that a belief in God is a requirement for groups in Toronto. Mediation between the two groups resulted in the delisted groups being listed again, however the secular groups would be required to not alter the 12 steps. Lawsuits and court rulings Privileged communication In the Fifth Step, AA members typically reveal their own past misconduct to their sponsors. US courts have not extended the status of privileged communication, such as physician-patient privilege or clergy–penitent privilege, to communications between an AA member and their sponsor. Court rulings on mandatory attendance United States courts have ruled that inmates, parolees, and probationers cannot be ordered to attend AA. Though AA itself was not deemed a religion, it was ruled that it contained enough religious components (variously described in Griffin v. Coughlin below as, inter alia, "religion", "religious activity", "religious exercise") to make coerced attendance at AA meetings a violation of the Establishment Clause of the First Amendment of the constitution. In 2007, the Ninth Circuit of the US Court of Appeals stated that a parolee who was ordered to attend AA had standing to sue his parole office. Family lawsuit The family of Karla Mendez, who was murdered in 2011 by a man she met at an AA meeting, filed a civil lawsuit in 2012 against AA asserting AA had a "reckless disregard for, and deliberate indifference...to the safety and security of victims attending AA meetings who are repeatedly preyed upon at those meetings by financial, violent, and sexual predators...". The lawsuit against AA was dismissed in 2016. Big Book manuscript case In May 2017, Alcoholics Anonymous World Services Inc. filed a lawsuit in the Supreme Court of the State of New York seeking the return of the original manuscript of the Big Book from its then-owner. AAWS claimed that the manuscript had been given to them as a gift in 1979. This action was criticized by many members of Alcoholics Anonymous since they didn't want their parent organization engaged in lawsuits.Michael Levin "Alcoholics Anonymous goes to court (and its members are livid)" Fox News Opinion, 7 June 2017 Alcoholics Anonymous World Services Inc. asked the court to voluntarily discontinue the action in November 2017."PLAINTIFF’S MEMORANDUM OF LAW IN SUPPORT OF ITS MOTION TO VOLUNTARILY DISCONTINUE THIS ACTION PURSUANT TO CPLR 3217(b)" filed 27 November 2017 Notable people who have attended AA While AA emphasizes personal anonymity, many notable individuals have publicly acknowledged their participation in the program for various lengths of time. Roger Ebert stated he was a member of AA according to a 2009 blog entry he wrote. Eminem has posted pictures of AA Sobriety coins. Anthony Hopkins has credited AA with saving him and marked 48 years of sobriety in 2023. Others who have spoken publicly about their AA attendance include James K. Baxter, Art Carney,Wilkins, Barbara. Art Carney Wins in a Film—and Over Alcoholism. People magazine, Vol. 2, Issue 17 via Internet Archive. Published 21 October 1974. Retrieved 18 June 2020. Bonnie Raitt, Mychal Judge, Moby, Hank Azaria, Matthew Perry, Jim Irsay, Demi Lovato, Elton John, Tom Waits, Capers Williamson, among others. Some have received pushback, including Brad Pitt recently and criticism from some people in AA regarding its anonymity guidelines. AA in media and arts Film My Name Is Bill W. – dramatized biography of co-founder Bill Wilson. When Love Is Not Enough: The Lois Wilson Story – a 2010 film about the wife of founder Bill Wilson, and the beginnings of Alcoholics Anonymous and Al-Anon. Bill W. – a 2011 biographical documentary film that tells the story of Bill Wilson using interviews, recreations, and rare archival material. A Walk Among the Tombstones (2015), a mystery/suspense film based on Lawrence Block's books featuring Matthew Scudder, a recovering alcoholic detective whose AA membership is a central element of the plot. When a Man Loves a Woman – a school counselor attends AA meetings in a residential treatment facility. Clean and Sober – an addict (alcohol, cocaine) visits an AA meeting to get a sponsor. Days of Wine and Roses – a 1962 film about a married couple struggling with alcoholism. Jack Lemmon's character attends an AA meeting in the film. Drunks – a 1995 film starring Richard Lewis as an alcoholic who leaves an AA meeting and relapses. The film cuts back and forth between his eventual relapse and the other meeting attendees. Come Back, Little Sheba – A 1952 film based on a play of the same title about a loveless marriage where the husband played by Burt Lancaster is an alcoholic who gets help from two members of the local AA chapter. A 1977 TV drama was also based on the play. I'll Cry Tomorrow – A 1955 film about singer Lillian Roth played by Susan Hayward who goes to AA to help her stop drinking. The film was based on Roth's autobiography of the same name detailing her alcoholism and sobriety through AA. You Kill Me – a 2007 crime-comedy film starring Ben Kingsley as a mob hit man with a drinking problem who is forced to accept a job at a mortuary and go to AA meetings. Smashed – a 2012 drama film starring Mary Elizabeth Winstead. An elementary school teacher's drinking begins to interfere with her job, so she attempts to get sober in AA. Don't Worry, He Won't Get Far on Foot – a 2018 biography/comedy/drama by Gus Van Sant, based on the life of cartoonist John Callahan. Doctor Sleep – Released in 2019, Doctor Sleep is a sequel to The Shining, directed by Mike Flanagan and based on Stephen King's work. Ewan McGregor stars as a man who, after overcoming his own demons through AA, helps others do the same. Television In "Days of Wine and D'oh'ses" (The Simpsons) after watching a video of his drunken antics at his birthday party, Barney resolves to get sober. He attends Alcoholics Anonymous meetings, cleans up his appearance, and attends helicopter-flying lessons. He remains sober by the episode's end, though his alcoholism is replaced by an unhealthy dependence on coffee. Bloody Mary - A 2005 episode of the animated TV series South Park where Randy Marsh must attend AA meetings after getting a DUI. In CBS' Elementary, Jonny Lee Miller plays an adaptation of Sherlock Holmes who is a recovering drug addict. Several episodes are centered around AA meetings and the process of recovery. Music Faithful (Macklemore song) released in October 2022 AA (song) by American country music singer Walker Hayes In 2024, Jelly Roll revealed that an Alcoholics Anonymous meeting served as the inspiration for his new album track, "Winning Streak". Theater Bill W. and Dr. Bob'' is a play by Stephen Bergman and Janet Surrey that chronicles the lives of AA founders Bill Wilson and Dr. Robert Smith, and their wives, and has been produced Off-Broadway and in multiple countries since its debut in 2007.
Alcoholics Anonymous	See also	See also Adult Children of Alcoholics Al-Anon/Alateen Calix Society Community reinforcement approach and family training (CRAFT) Drug addiction recovery groups Drug rehabilitation Group psychotherapy Health benefits of quitting alcohol List of twelve-step groups Long-term effects of alcohol Recovery approach Short-term effects of alcohol consumption Stepping Stones (house), home of Bill W. Washingtonian movement
Alcoholics Anonymous	Notes	Notes
Alcoholics Anonymous	References	References
Alcoholics Anonymous	Bibliography	Bibliography
Alcoholics Anonymous	External links	External links A History of Agnostic Groups in AA Reproduction of the 1938 Original Manuscript of Alcoholics Anonymous Category:Addiction and substance abuse organizations Category:Non-profit organizations based in New York City Category:Organizations established in 1935 Category:Therapeutic community Category:Twelve-step programs
Alcoholics Anonymous	Table of Content	short description, See also, Notes, References, Bibliography, External links
Alpha compositing	short description	thumb\|A color spectrum image with an alpha channel that falls off to zero at its base, where it is blended with the background color. In computer graphics, alpha compositing or alpha blending is the process of combining one image with a background to create the appearance of partial or full transparency. It is often useful to render picture elements (pixels) in separate passes or layers and then combine the resulting 2D images into a single, final image called the composite. Compositing is used extensively in film when combining computer-rendered image elements with live footage. Alpha blending is also used in 2D computer graphics to put rasterized foreground elements over a background. In order to combine the picture elements of the images correctly, it is necessary to keep an associated matte for each element in addition to its color. This matte layer contains the coverage information—the shape of the geometry being drawn—making it possible to distinguish between parts of the image where something was drawn and parts that are empty. Although the most basic operation of combining two images is to put one over the other, there are many operations, or blend modes, that are used.
Alpha compositing	History	History The concept of an alpha channel was introduced by Alvy Ray Smith and Ed Catmull in the late 1970s at the New York Institute of Technology Computer Graphics Lab. Bruce A. Wallace derived the same straight over operator based on a physical reflectance/transmittance model in 1981. A 1984 paper by Thomas Porter and Tom Duff introduced premultiplied alpha using a geometrical approach. The use of the term alpha is explained by Smith as follows: "We called it that because of the classic linear interpolation formula that uses the Greek letter (alpha) to control the amount of interpolation between, in this case, two images A and B". That is, when compositing image A atop image B, the value of in the formula is taken directly from A's alpha channel.
Alpha compositing	Description	Description In a 2D image a color combination is stored for each picture element (pixel), often a combination of red, green and blue (RGB). When alpha compositing is in use, each pixel has an additional numeric value stored in its alpha channel, with a value ranging from 0 to 1. A value of 0 means that the pixel is fully transparent and the color in the pixel beneath will show through. A value of 1 means that the pixel is fully opaque. With the existence of an alpha channel, it is possible to express compositing image operations using a compositing algebra. For example, given two images A and B, the most common compositing operation is to combine the images so that A appears in the foreground and B appears in the background. This can be expressed as A over B. In addition to over, Porter and Duff defined the compositing operators in, held out by (the phrase refers to holdout matting and is usually abbreviated out), atop, and xor (and the reverse operators rover, rin, rout, and ratop) from a consideration of choices in blending the colors of two pixels when their coverage is, conceptually, overlaid orthogonally: Image:Alpha compositing.svg As an example, the over operator can be accomplished by applying the following formula to each pixel: Here , and stand for the color components of the pixels in the result of the "over", image A, and image B respectively, applied to each color channel (red/green/blue) individually, whereas , and are the alpha values of the respective pixels. The over operator is, in effect, the normal painting operation (see Painter's algorithm). The in and out operators are the alpha compositing equivalent of clipping. The two use only the alpha channel of the second image and ignore the color components. In addition, plus defines additive blending.
Alpha compositing	Straight versus premultiplied	Straight versus premultiplied If an alpha channel is used in an image, there are two common representations that are available: straight (unassociated) alpha and premultiplied (associated) alpha. With straight alpha, the RGB components represent the color of the object or pixel, disregarding its opacity. This is the method implied by the over operator in the previous section. With premultiplied alpha, the RGB components represent the emission of the object or pixel, and the alpha represents the occlusion. The over operator then becomes:
Alpha compositing	Comparison	Comparison The most significant advantage of premultiplied alpha is that it allows for correct blending, interpolation, and filtering. Ordinary interpolation without premultiplied alpha leads to RGB information leaking out of fully transparent (A=0) regions, even though this RGB information is ideally invisible. When interpolating or filtering images with abrupt borders between transparent and opaque regions, this can result in borders of colors that were not visible in the original image. Errors also occur in areas of semitransparency because the RGB components are not correctly weighted, giving incorrectly high weighting to the color of the more transparent (lower alpha) pixels. Premultiplied alpha may also be used to allow regions of regular alpha blending (e.g. smoke) and regions with additive blending mode (e.g. flame and glitter effects) to be encoded within the same image. This is represented by an RGBA triplet that express emission with no occlusion, such as (0.4, 0.3, 0.2, 0.0). Another advantage of premultiplied alpha is performance; in certain situations, it can reduce the number of multiplication operations (e.g. if the image is used many times during later compositing). The Porter–Duff operations have a simple form only in premultiplied alpha. Some rendering pipelines expose a "straight alpha" API surface, but converts them into premultiplied alpha for performance. One disadvantage of premultiplied alpha is that it can reduce the available relative precision in the RGB values when using integer or fixed-point representation for the color components. This may cause a noticeable loss of quality if the color information is later brightened or if the alpha channel is removed. In practice, this is not usually noticeable because during typical composition operations, such as OVER, the influence of the low-precision color information in low-alpha areas on the final output image (after composition) is correspondingly reduced. This loss of precision also makes premultiplied images easier to compress using certain compression schemes, as they do not record the color variations hidden inside transparent regions, and can allocate fewer bits to encode low-alpha areas. The same “limitations” of lower quantisation bit depths such as 8 bit per channel are also present in imagery without alpha, and this argument is problematic as a result.
Alpha compositing	Examples	Examples Assuming that the pixel color is expressed using straight (non-premultiplied) RGBA tuples, a pixel value of (0, 0.7, 0, 0.5) implies a pixel that has 70% of the maximum green intensity and 50% opacity. If the color were fully green, its RGBA would be (0, 1, 0, 0.5). However, if this pixel uses premultiplied alpha, all of the RGB values (0, 0.7, 0) are multiplied, or scaled for occlusion, by the alpha value 0.5, which is appended to yield (0, 0.35, 0, 0.5). In this case, the 0.35 value for the G channel actually indicates 70% green emission intensity (with 50% occlusion). A pure green emission would be encoded as (0, 0.5, 0, 0.5). Knowing whether a file uses straight or premultiplied alpha is essential to correctly process or composite it, as a different calculation is required. Emission with no occlusion cannot be represented in straight alpha. No conversion is available in this case.
Alpha compositing	Image formats supporting alpha channels	Image formats supporting alpha channels The most popular image formats that support the alpha channel are PNG and TIFF. GIF supports alpha channels, but is considered to be inefficient when it comes to file size. Support for alpha channels is present in some video codecs, such as Animation and Apple ProRes 4444 of the QuickTime format, or in the Techsmith multi-format codec. The file format BMP generally does not support this channel; however, in different formats such as 32-bit (888–8) or 16-bit (444–4) it is possible to save the alpha channel, although not all systems or programs are able to read it: it is exploited mainly in some video games or particular applications; specific programs have also been created for the creation of these BMPs. File/Codec format Maximum Depth Type Browser support Media type Notes Apple ProRes 4444 16-bit None Video (.mov) ProRes is the successor of the Apple Intermediate CodecHEVC / h.265 10-bit Limited to Safari Video (.hevc) Intended successor to H.264WebM (codec video VP8, VP9, or AV1) 12-bit All modern browsers Video (.webm) While VP8/VP9 is widely supported with modern browsers, AV1 still has limited support. Only Chromium-based browsers will display alpha layers.OpenEXR 32-bit None Image (.exr) Has largest HDR spread. PNG 16-bit straight All modern browsers Image (.png) APNG 24-bit straight Moderate support Image (.apng) Supports animation. TIFF 32-bit both None Image (.tiff) GIF 8-bit All modern browsers Image (.gif) Browsers generally do not support GIF alpha layers.SVG 32-bit straight All modern browsers Image (.svg) Based on CSS color.JPEG XL32-bitbothModerate supportImage (.jxl)Allows lossy and HDR.
Alpha compositing	Gamma correction	Gamma correction thumb\|Alpha blending, not taking into account gamma correction thumb\|Alpha blending, taking into account gamma correction The RGB values of typical digital images do not directly correspond to the physical light intensities, but are rather compressed by a gamma correction function: This transformation better utilizes the limited number of bits in the encoded image by choosing that better matches the non-linear human perception of luminance. Accordingly, computer programs that deal with such images must decode the RGB values into a linear space (by undoing the gamma-compression), blend the linear light intensities, and re-apply the gamma compression to the result: When combined with premultiplied alpha, pre-multiplication is done in linear space, prior to gamma compression. This results in the following formula: Note that the alpha channel may or may not undergo gamma-correction, even when the color channels do.
Alpha compositing	Other transparency methods	Other transparency methods Although used for similar purposes, transparent colors and image masks do not permit the smooth blending of the superimposed image pixels with those of the background (only whole image pixels or whole background pixels allowed). A similar effect can be achieved with a 1-bit alpha channel, as found in the 16-bit RGBA high color mode of the Truevision TGA image file format and related TARGA and AT-Vista/NU-Vista display adapters' high color graphic mode. This mode devotes 5 bits for every primary RGB color (15-bit RGB) plus a remaining bit as the "alpha channel". Dithering can be used to simulate partial occlusion where only 1-bit alpha is available. For some applications, a single alpha channel is not sufficient: a stained-glass window, for instance, requires a separate transparency channel for each RGB channel to model the red, green and blue transparency separately. More alpha channels can be added for accurate spectral color filtration applications. Some order-independent transparency methods replace the over operator with a commutative approximation.
Alpha compositing	See also	See also
Alpha compositing	References	References
Alpha compositing	External links	External links Compositing Digital Images - Thomas Porter and Tom Duff (Original Paper) Image Compositing Fundamentals Understand Compositing and Color extensions in SVG 1.2 in 30 minutes! Alpha Matting and Premultiplication Category:Computer graphics algorithms
Alpha compositing	Table of Content	short description, History, Description, Straight versus premultiplied, Comparison, Examples, Image formats supporting alpha channels, Gamma correction, Other transparency methods, See also, References, External links
Array (data structure)	short description	In computer science, an array is a data structure consisting of a collection of elements (values or variables), of same memory size, each identified by at least one array index or key, a collection of which may be a tuple, known as an index tuple. An array is stored such that the position (memory address) of each element can be computed from its index tuple by a mathematical formula. The simplest type of data structure is a linear array, also called a one-dimensional array. For example, an array of ten 32-bit (4-byte) integer variables, with indices 0 through 9, may be stored as ten words at memory addresses 2000, 2004, 2008, ..., 2036, (in hexadecimal: 0x7D0, 0x7D4, 0x7D8, ..., 0x7F4) so that the element with index i has the address 2000 + (i × 4).David R. Richardson (2002), The Book on Data Structures. iUniverse, 112 pages. , . The memory address of the first element of an array is called first address, foundation address, or base address. Because the mathematical concept of a matrix can be represented as a two-dimensional grid, two-dimensional arrays are also sometimes called "matrices". In some cases the term "vector" is used in computing to refer to an array, although tuples rather than vectors are the more mathematically correct equivalent. Tables are often implemented in the form of arrays, especially lookup tables; the word "table" is sometimes used as a synonym of array. Arrays are among the oldest and most important data structures, and are used by almost every program. They are also used to implement many other data structures, such as lists and strings. They effectively exploit the addressing logic of computers. In most modern computers and many external storage devices, the memory is a one-dimensional array of words, whose indices are their addresses. Processors, especially vector processors, are often optimized for array operations. Arrays are useful mostly because the element indices can be computed at run time. Among other things, this feature allows a single iterative statement to process arbitrarily many elements of an array. For that reason, the elements of an array data structure are required to have the same size and should use the same data representation. The set of valid index tuples and the addresses of the elements (and hence the element addressing formula) are usually, but not always, fixed while the array is in use. The term "array" may also refer to an array data type, a kind of data type provided by most high-level programming languages that consists of a collection of values or variables that can be selected by one or more indices computed at run-time. Array types are often implemented by array structures; however, in some languages they may be implemented by hash tables, linked lists, search trees, or other data structures. The term is also used, especially in the description of algorithms, to mean associative array or "abstract array", a theoretical computer science model (an abstract data type or ADT) intended to capture the essential properties of arrays.
Array (data structure)	History	History The first digital computers used machine-language programming to set up and access array structures for data tables, vector and matrix computations, and for many other purposes. John von Neumann wrote the first array-sorting program (merge sort) in 1945, during the building of the first stored-program computer. Array indexing was originally done by self-modifying code, and later using index registers and indirect addressing. Some mainframes designed in the 1960s, such as the Burroughs B5000 and its successors, used memory segmentation to perform index-bounds checking in hardware.. Assembly languages generally have no special support for arrays, other than what the machine itself provides. The earliest high-level programming languages, including FORTRAN (1957), Lisp (1958), COBOL (1960), and ALGOL 60 (1960), had support for multi-dimensional arrays, and so has C (1972). In C++ (1983), class templates exist for multi-dimensional arrays whose dimension is fixed at runtime as well as for runtime-flexible arrays.
Array (data structure)	Applications	Applications Arrays are used to implement mathematical vectors and matrices, as well as other kinds of rectangular tables. Many databases, small and large, consist of (or include) one-dimensional arrays whose elements are records. Arrays are used to implement other data structures, such as lists, heaps, hash tables, deques, queues, stacks, strings, and VLists. Array-based implementations of other data structures are frequently simple and space-efficient (implicit data structures), requiring little space overhead, but may have poor space complexity, particularly when modified, compared to tree-based data structures (compare a sorted array to a search tree). One or more large arrays are sometimes used to emulate in-program dynamic memory allocation, particularly memory pool allocation. Historically, this has sometimes been the only way to allocate "dynamic memory" portably. Arrays can be used to determine partial or complete control flow in programs, as a compact alternative to (otherwise repetitive) multiple IF statements. They are known in this context as control tables and are used in conjunction with a purpose-built interpreter whose control flow is altered according to values contained in the array. The array may contain subroutine pointers (or relative subroutine numbers that can be acted upon by SWITCH statements) that direct the path of the execution.

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