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[SOURCE: https://en.wikipedia.org/wiki/Fuath] | [TOKENS: 797] |
Contents Fuath A fuath (Scottish Gaelic: fuath; Scottish Gaelic pronunciation: [fuə]; lit. ‘hatred'; plural: fuathan; phonetic English: vough, vaugh) is a class of malevolent spirits in Scottish Highland folklore and Irish Folklore especially water spirits. In Sutherland was the so-called Moulin na Vaugha/Fouadh, ‘Mill of the Fuath', haunted by the fuath and her son, the amorphous brollachan. The mill was along a stream off Loch Migdale, and belonged to the Dempster family (Skibo Castle) estate. A fuath once seen at this mill was a nose-less banshee with yellow hair wearing a green silk dress; in the story of its capture[a] it was tormented into submission by use of steel (awl, and more effectively by a sewing needle), but it turned to a jellyfish-like mass when light was shone on it. A fuath on the estate farm, encountered on a different occasion, had webbed feet. They sometimes reputedly intermarry with human beings (typically the female), whose offspring develop a mane and tail. Nomenclature The term "fuath" has been explained to be a generic class of spirits inhabiting the sea, rivers, fresh water, or sea lochs, with several "subspecies" falling under it. The Scottish Gaelic term fuath has been explained to mean 'hatred' or 'aversion', derived from Old Irish fúath 'hate, likeness'. The term is also glossed to mean 'ghost' or 'spectre'. An alternative name for this class of monsters is the arrachd or fuath-arrachd. Generalization J. F. Campbell characterized the fuath of Sutherland as a water spirit, but it has been stressed by John Gregorson Campbell that the term designates a spectre or goblin more generally, not necessarily of aqueous nature or habitat. J. F. Campbell also conflated the traits of the fuath from different accounts in a generalized description of the fuath of Sutherland[b] and this has also fallen under criticism by Gregorson.[c] Furthermore, J. F. Campbell ascribed the mane and tail to the fuath, though these traits had evidently developed in the human progeny of the Munroe family, to which there was attached a floating rumour that their ancestor had interbred with a fuath several generations back.[d] While it has been generalized that the fuath of the locality wears green, "golden and silken gear" was worn by the weird woman seen plunging into the River Shin was seen by a (games)keeper of the Charlotte Dempster's family. Tales A fuath (in this instance spelled "fua") appears in the tale "The King of Ireland's Son". In it, the creature emerges from a body of water and attempts to steal the anvil of Goban Saor, a mythical craftsman. The King of Ireland's Son wrestles with the creature over the course of three nights in order to gain the favor of Goban Saor. The story of "The Brollachan" (and several of its variant tales) from Sutherland were collected by Charlotte Dempster in 1859, and supplied to J. F. Campbell who printed it. The stories are set in locales within the Dempster family estate (otherwise known as Skibo)[e] The writer Charlotte was a relative of the Dempsters of the estate (being the granddaughter of Harriet, the illegitimate daughter of the captain). Fuath tribe members Below are the supposed "subspecies" of the fuath class, according to certain commentators. Similarity or equivalence to the bean nighe or Northern Ireland's uisges have been noted.[citation needed] Explanatory notes References External links |
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[SOURCE: https://en.wikipedia.org/wiki/Applied_Mathematics] | [TOKENS: 2088] |
Contents Applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, social science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected with research in pure mathematics. History Historically, applied mathematics consisted principally of applied analysis, most notably differential equations; approximation theory (broadly construed, to include representations, asymptotic methods, variational methods, and numerical analysis); and applied probability. These areas of mathematics related directly to the development of Newtonian physics, and in fact, the distinction between mathematicians and physicists was not sharply drawn before the mid-19th century. This history left a pedagogical legacy in the United States: until the early 20th century, subjects such as classical mechanics were often taught in applied mathematics departments at American universities rather than in physics departments, and fluid mechanics may still be taught in applied mathematics departments. Engineering and computer science departments have traditionally made use of applied mathematics. Divisions Today, the term "applied mathematics" is used in a broader sense. It includes the classical areas noted above as well as other areas that have become increasingly important in applications. Even fields such as number theory that are part of pure mathematics are now important in applications (such as cryptography), though they are not generally considered to be part of the field of applied mathematics per se. There is no consensus as to what the various branches of applied mathematics are. Such categorizations are made difficult by the way mathematics and science change over time, and also by the way universities organize departments, courses, and degrees. Many mathematicians distinguish between "applied mathematics", which is concerned with mathematical methods, and the "applications of mathematics" within science and engineering. A biologist using a population model and applying known mathematics would not be doing applied mathematics, but rather using it; however, mathematical biologists have posed problems that have stimulated the growth of pure mathematics. Mathematicians such as Poincaré and Arnold deny the existence of "applied mathematics" and claim that there are only "applications of mathematics." Similarly, non-mathematicians blend applied mathematics and applications of mathematics. The use and development of mathematics to solve industrial problems is also called "industrial mathematics". The success of modern numerical mathematical methods and software has led to the emergence of computational mathematics, computational science, and computational engineering, which use high-performance computing for the simulation of phenomena and the solution of problems in the sciences and engineering. These are often considered interdisciplinary. Sometimes, the term applicable mathematics is used to distinguish between the traditional applied mathematics that developed alongside physics and the many areas of mathematics that are applicable to real-world problems today, although there is no consensus as to a precise definition. Mathematicians often distinguish between "applied mathematics" on the one hand, and the "applications of mathematics" or "applicable mathematics" both within and outside of science and engineering, on the other. Some mathematicians emphasize the term applicable mathematics to separate or delineate the traditional applied areas from new applications arising from fields that were previously seen as pure mathematics. For example, from this viewpoint, an ecologist or geographer using population models and applying known mathematics would not be doing applied, but rather applicable, mathematics. Even fields such as number theory that are part of pure mathematics are now important in applications (such as cryptography), though they are not generally considered to be part of the field of applied mathematics per se. Such descriptions can lead to applicable mathematics being seen as a collection of mathematical methods such as real analysis, linear algebra, mathematical modelling, optimisation, combinatorics, probability and statistics, which are useful in areas outside traditional mathematics and not specific to mathematical physics. Other authors prefer describing applicable mathematics as a union of "new" mathematical applications with the traditional fields of applied mathematics. With this outlook, the terms applied mathematics and applicable mathematics are thus interchangeable. Utility Historically, mathematics was most important in the natural sciences and engineering. However, since World War II, fields outside the physical sciences have spawned the creation of new areas of mathematics, such as game theory and social choice theory, which grew out of economic considerations. Further, the utilization and development of mathematical methods expanded into other areas leading to the creation of new fields such as mathematical finance and data science. The advent of the computer has enabled new applications: studying and using the new computer technology itself (computer science) to study problems arising in other areas of science (computational science) as well as the mathematics of computation (for example, theoretical computer science, computer algebra, numerical analysis). Statistics is probably the most widespread mathematical science used in the social sciences. Status in academic departments Academic institutions are not consistent in the way they group and label courses, programs, and degrees in applied mathematics. At some schools, there is a single mathematics department, whereas others have separate departments for Applied Mathematics and (Pure) Mathematics. It is very common for Statistics departments to be separated at schools with graduate programs, but many undergraduate-only institutions include statistics under the mathematics department. Many applied mathematics programs (as opposed to departments) consist primarily of cross-listed courses and jointly appointed faculty in departments representing applications. Some Ph.D. programs in applied mathematics require little or no coursework outside mathematics, while others require substantial coursework in a specific area of application. In some respects this difference reflects the distinction between "application of mathematics" and "applied mathematics". Some universities in the U.K. host departments of Applied Mathematics and Theoretical Physics, but it is now much less common to have separate departments of pure and applied mathematics. A notable exception to this is the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge, housing the Lucasian Professor of Mathematics whose past holders include Isaac Newton, Charles Babbage, James Lighthill, Paul Dirac, and Stephen Hawking. Schools with separate applied mathematics departments range from Brown University, which has a large Division of Applied Mathematics that offers degrees through the doctorate, to Santa Clara University, which offers only the M.S. in applied mathematics. Research universities dividing their mathematics department into pure and applied sections include MIT. Students in this program also learn another skill (computer science, engineering, physics, pure math, etc.) to supplement their applied math skills. Associated mathematical sciences Applied mathematics is associated with the following mathematical sciences: Mathematics is used in all branches of engineering and has subsequently developed as distinct specialties within the engineering profession. For example, continuum mechanics is foundational to civil, mechanical and aerospace engineering, with courses in solid mechanics and fluid mechanics being important components of the engineering curriculum. Continuum mechanics is also an important branch of mathematics in its own right. It has served as the inspiration for a vast range of difficult research questions for mathematicians involved in the analysis of partial differential equations, differential geometry and the calculus of variations. Perhaps the most well-known mathematical problem posed by a continuum mechanical system is the question of Navier-Stokes existence and smoothness. Prominent career mathematicians rather than engineers who have contributed to the mathematics of continuum mechanics are Clifford Truesdell, Walter Noll, Andrey Kolmogorov and George Batchelor. An essential discipline for many fields in engineering is that of control engineering. The associated mathematical theory of this specialism is control theory, a branch of applied mathematics that builds off the mathematics of dynamical systems. Control theory has played a significant enabling role in modern technology, serving a foundational role in electrical, mechanical and aerospace engineering. Like continuum mechanics, control theory has also become a field of mathematical research in its own right, with mathematicians such as Aleksandr Lyapunov, Norbert Wiener, Lev Pontryagin and Fields Medal recipient Pierre-Louis Lions contributing to its foundations. Scientific computing includes applied mathematics (especially numerical analysis), computing science (especially high-performance computing), and mathematical modelling in a scientific discipline. Computer science relies on logic, algebra, discrete mathematics such as graph theory, and combinatorics. Operations research and management science are often taught in faculties of engineering, business, and public policy. Applied mathematics has substantial overlap with the discipline of statistics. Statistical theorists study and improve statistical procedures with mathematics, and statistical research often raises mathematical questions. Statistical theory relies on probability and decision theory, and makes extensive use of scientific computing, analysis, and optimization; for the design of experiments, statisticians use algebra and combinatorial design. Applied mathematicians and statisticians often work in a department of mathematical sciences (particularly at colleges and small universities). Actuarial science applies probability, statistics, and economic theory to assess risk in insurance, finance and other industries and professions. Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. The applied methods usually refer to nontrivial mathematical techniques or approaches. Mathematical economics is based on statistics, probability, mathematical programming (as well as other computational methods), operations research, game theory, and some methods from mathematical analysis. In this regard, it resembles (but is distinct from) financial mathematics, another part of applied mathematics. According to the Mathematics Subject Classification (MSC), mathematical economics falls into the Applied mathematics/other classification of category 91: with MSC2010 classifications for 'Game theory' at codes 91Axx Archived 2015-04-02 at the Wayback Machine and for 'Mathematical economics' at codes 91Bxx Archived 2015-04-02 at the Wayback Machine. The line between applied mathematics and specific areas of application is often blurred. Many universities teach mathematical and statistical courses outside the respective departments, in departments and areas including business, engineering, physics, chemistry, psychology, biology, computer science, scientific computation, information theory, and mathematical physics. Applied Mathematics Societies The Society for Industrial and Applied Mathematics is an international applied mathematics organization. As of 2024, the society has 14,000 individual members. The American Mathematics Society has its Applied Mathematics Group. See also References Further reading External links |
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[SOURCE: https://en.wikipedia.org/wiki/Orion_(constellation)#cite_ref-kaler_43-0] | [TOKENS: 4993] |
Contents Orion (constellation) Orion is a prominent set of stars visible during winter in the northern celestial hemisphere. It is one of the 88 modern constellations; it was among the 48 constellations listed by the 2nd-century AD/CE astronomer Ptolemy. It is named after a hunter in Greek mythology. Orion is most prominent during winter evenings in the Northern Hemisphere, as are five other constellations that have stars in the Winter Hexagon asterism. Orion's two brightest stars, Rigel (β) and Betelgeuse (α), are both among the brightest stars in the night sky; both are supergiants and slightly variable. There are a further six stars brighter than magnitude 3.0, including three making the short straight line of the Orion's Belt asterism. Orion also hosts the radiant of the annual Orionids, the strongest meteor shower associated with Halley's Comet, and the Orion Nebula, one of the brightest nebulae in the sky. Characteristics Orion is bordered by Taurus to the northwest, Eridanus to the southwest, Lepus to the south, Monoceros to the east, and Gemini to the northeast. Covering 594 square degrees, Orion ranks 26th of the 88 constellations in size. The constellation boundaries, as set by Belgian astronomer Eugène Delporte in 1930, are defined by a polygon of 26 sides. In the equatorial coordinate system, the right ascension coordinates of these borders lie between 04h 43.3m and 06h 25.5m , while the declination coordinates are between 22.87° and −10.97°. The constellation's three-letter abbreviation, as adopted by the International Astronomical Union in 1922, is "Ori". Orion is most visible in the evening sky from January to April, winter in the Northern Hemisphere, and summer in the Southern Hemisphere. In the tropics (less than about 8° from the equator), the constellation transits at the zenith. From May to July (summer in the Northern Hemisphere, winter in the Southern Hemisphere), Orion is in the daytime sky and thus invisible at most latitudes. However, for much of Antarctica in the Southern Hemisphere's winter months, the Sun is below the horizon even at midday. Stars (and thus Orion, but only the brightest stars) are then visible at twilight for a few hours around local noon, just in the brightest section of the sky low in the North where the Sun is just below the horizon. At the same time of day at the South Pole itself (Amundsen–Scott South Pole Station), Rigel is only 8° above the horizon, and the Belt sweeps just along it. In the Southern Hemisphere's summer months, when Orion is normally visible in the night sky, the constellation is actually not visible in Antarctica because the Sun does not set at that time of year south of the Antarctic Circle. In countries close to the equator (e.g. Kenya, Indonesia, Colombia, Ecuador), Orion appears overhead in December around midnight and in the February evening sky. Navigational aid Orion is very useful as an aid to locating other stars. By extending the line of the Belt southeastward, Sirius (α CMa) can be found; northwestward, Aldebaran (α Tau). A line eastward across the two shoulders indicates the direction of Procyon (α CMi). A line from Rigel through Betelgeuse points to Castor and Pollux (α Gem and β Gem). Additionally, Rigel is part of the Winter Circle asterism. Sirius and Procyon, which may be located from Orion by following imaginary lines (see map), also are points in both the Winter Triangle and the Circle. Features Orion's seven brightest stars form a distinctive hourglass-shaped asterism, or pattern, in the night sky. Four stars—Rigel, Betelgeuse, Bellatrix, and Saiph—form a large roughly rectangular shape, at the center of which lie the three stars of Orion's Belt—Alnitak, Alnilam, and Mintaka. His head is marked by an additional eighth star called Meissa, which is fairly bright to the observer. Descending from the Belt is a smaller line of three stars, Orion's Sword (the middle of which is in fact not a star but the Orion Nebula), also known as the hunter's sword. Many of the stars are luminous hot blue supergiants, with the stars of the Belt and Sword forming the Orion OB1 association. Standing out by its red hue, Betelgeuse may nevertheless be a runaway member of the same group. Orion's Belt, or The Belt of Orion, is an asterism within the constellation. It consists of three bright stars: Alnitak (Zeta Orionis), Alnilam (Epsilon Orionis), and Mintaka (Delta Orionis). Alnitak is around 800 light-years away from Earth, 100,000 times more luminous than the Sun, and shines with a magnitude of 1.8; much of its radiation is in the ultraviolet range, which the human eye cannot see. Alnilam is approximately 2,000 light-years from Earth, shines with a magnitude of 1.70, and with an ultraviolet light that is 375,000 times more luminous than the Sun. Mintaka is 915 light-years away and shines with a magnitude of 2.21. It is 90,000 times more luminous than the Sun and is a double star: the two orbit each other every 5.73 days. In the Northern Hemisphere, Orion's Belt is best visible in the night sky during the month of January at around 9:00 pm, when it is approximately around the local meridian. Just southwest of Alnitak lies Sigma Orionis, a multiple star system composed of five stars that have a combined apparent magnitude of 3.7 and lying at a distance of 1150 light-years. Southwest of Mintaka lies the quadruple star Eta Orionis. Orion's Sword contains the Orion Nebula, the Messier 43 nebula, Sh 2-279 (also known as the Running Man Nebula), and the stars Theta Orionis, Iota Orionis, and 42 Orionis. Three stars comprise a small triangle that marks the head. The apex is marked by Meissa (Lambda Orionis), a hot blue giant of spectral type O8 III and apparent magnitude 3.54, which lies some 1100 light-years distant. Phi-1 and Phi-2 Orionis make up the base. Also nearby is the young star FU Orionis. Stretching north from Betelgeuse are the stars that make up Orion's club. Mu Orionis marks the elbow, Nu and Xi mark the handle of the club, and Chi1 and Chi2 mark the end of the club. Just east of Chi1 is the Mira-type variable red giant star U Orionis. West from Bellatrix lie six stars all designated Pi Orionis (π1 Ori, π2 Ori, π3 Ori, π4 Ori, π5 Ori, and π6 Ori) which make up Orion's shield. Around 20 October each year, the Orionid meteor shower (Orionids) reaches its peak. Coming from the border with the constellation Gemini, as many as 20 meteors per hour can be seen. The shower's parent body is Halley's Comet. Hanging from Orion's Belt is his sword, consisting of the multiple stars θ1 and θ2 Orionis, called the Trapezium and the Orion Nebula (M42). This is a spectacular object that can be clearly identified with the naked eye as something other than a star. Using binoculars, its clouds of nascent stars, luminous gas, and dust can be observed. The Trapezium cluster has many newborn stars, including several brown dwarfs, all of which are at an approximate distance of 1,500 light-years. Named for the four bright stars that form a trapezoid, it is largely illuminated by the brightest stars, which are only a few hundred thousand years old. Observations by the Chandra X-ray Observatory show both the extreme temperatures of the main stars—up to 60,000 kelvins—and the star forming regions still extant in the surrounding nebula. M78 (NGC 2068) is a nebula in Orion. With an overall magnitude of 8.0, it is significantly dimmer than the Great Orion Nebula that lies to its south; however, it is at approximately the same distance, at 1600 light-years from Earth. It can easily be mistaken for a comet in the eyepiece of a telescope. M78 is associated with the variable star V351 Orionis, whose magnitude changes are visible in very short periods of time. Another fairly bright nebula in Orion is NGC 1999, also close to the Great Orion Nebula. It has an integrated magnitude of 10.5 and is 1500 light-years from Earth. The variable star V380 Orionis is embedded in NGC 1999. Another famous nebula is IC 434, the Horsehead Nebula, near Alnitak (Zeta Orionis). It contains a dark dust cloud whose shape gives the nebula its name. NGC 2174 is an emission nebula located 6400 light-years from Earth. Besides these nebulae, surveying Orion with a small telescope will reveal a wealth of interesting deep-sky objects, including M43, M78, and multiple stars including Iota Orionis and Sigma Orionis. A larger telescope may reveal objects such as the Flame Nebula (NGC 2024), as well as fainter and tighter multiple stars and nebulae. Barnard's Loop can be seen on very dark nights or using long-exposure photography. All of these nebulae are part of the larger Orion molecular cloud complex, which is located approximately 1,500 light-years away and is hundreds of light-years across. Due to its proximity, it is one of the most intense regions of stellar formation visible from Earth. The Orion molecular cloud complex forms the eastern part of an even larger structure, the Orion–Eridanus Superbubble, which is visible in X-rays and in hydrogen emissions. History and mythology The distinctive pattern of Orion is recognized in numerous cultures around the world, and many myths are associated with it. Orion is used as a symbol in the modern world. In Siberia, the Chukchi people see Orion as a hunter; an arrow he has shot is represented by Aldebaran (Alpha Tauri), with the same figure as other Western depictions. In Greek mythology, Orion was a gigantic, supernaturally strong hunter, born to Euryale, a Gorgon, and Poseidon (Neptune), god of the sea. One myth recounts Gaia's rage at Orion, who dared to say that he would kill every animal on Earth. The angry goddess tried to dispatch Orion with a scorpion. This is given as the reason that the constellations of Scorpius and Orion are never in the sky at the same time. However, Ophiuchus, the Serpent Bearer, revived Orion with an antidote. This is said to be the reason that the constellation of Ophiuchus stands midway between the Scorpion and the Hunter in the sky. The constellation is mentioned in Horace's Odes (Ode 3.27.18), Homer's Odyssey (Book 5, line 283) and Iliad, and Virgil's Aeneid (Book 1, line 535). In old Hungarian tradition, Orion is known as "Archer" (Íjász), or "Reaper" (Kaszás). In recently rediscovered myths, he is called Nimrod (Hungarian: Nimród), the greatest hunter, father of the twins Hunor and Magor. The π and o stars (on upper right) form together the reflex bow or the lifted scythe. In other Hungarian traditions, Orion's Belt is known as "Judge's stick" (Bírópálca). In Ireland and Scotland, Orion was called An Bodach, a figure from Irish folklore whose name literally means "the one with a penis [bod]" and was the husband of the Cailleach (hag). In Scandinavian tradition, Orion's Belt was known as "Frigg's Distaff" (friggerock) or "Freyja's distaff". The Finns call Orion's Belt and the stars below it "Väinämöinen's scythe" (Väinämöisen viikate). Another name for the asterism of Alnilam, Alnitak, and Mintaka is "Väinämöinen's Belt" (Väinämöisen vyö) and the stars "hanging" from the Belt as "Kaleva's sword" (Kalevanmiekka). There are claims in popular media that the Adorant from the Geißenklösterle cave, an ivory carving estimated to be 35,000 to 40,000 years old, is the first known depiction of the constellation. Scholars dismiss such interpretations, saying that perceived details such as a belt and sword derive from preexisting features in the grain structure of the ivory. The Babylonian star catalogues of the Late Bronze Age name Orion MULSIPA.ZI.AN.NA,[note 1] "The Heavenly Shepherd" or "True Shepherd of Anu" – Anu being the chief god of the heavenly realms. The Babylonian constellation is sacred to Papshukal and Ninshubur, both minor gods fulfilling the role of "messenger to the gods". Papshukal is closely associated with the figure of a walking bird on Babylonian boundary stones, and on the star map the figure of the Rooster is located below and behind the figure of the True Shepherd—both constellations represent the herald of the gods, in his bird and human forms respectively. In ancient Egypt, the stars of Orion were regarded as a god, called Sah. Because Orion rises before Sirius, the star whose heliacal rising was the basis for the Solar Egyptian calendar, Sah was closely linked with Sopdet, the goddess who personified Sirius. The god Sopdu is said to be the son of Sah and Sopdet. Sah is syncretized with Osiris, while Sopdet is syncretized with Osiris' mythological wife, Isis. In the Pyramid Texts, from the 24th and 23rd centuries BC, Sah is one of many gods whose form the dead pharaoh is said to take in the afterlife. The Armenians identified their legendary patriarch and founder Hayk with Orion. Hayk is also the name of the Orion constellation in the Armenian translation of the Bible. The Bible mentions Orion three times, naming it "Kesil" (כסיל, literally – fool). Though, this name perhaps is etymologically connected with "Kislev", the name for the ninth month of the Hebrew calendar (i.e. November–December), which, in turn, may derive from the Hebrew root K-S-L as in the words "kesel, kisla" (כֵּסֶל, כִּסְלָה, hope, positiveness), i.e. hope for winter rains.: Job 9:9 ("He is the maker of the Bear and Orion"), Job 38:31 ("Can you loosen Orion's belt?"), and Amos 5:8 ("He who made the Pleiades and Orion"). In ancient Aram, the constellation was known as Nephîlā′, the Nephilim are said to be Orion's descendants. In medieval Muslim astronomy, Orion was known as al-jabbar, "the giant". Orion's sixth brightest star, Saiph, is named from the Arabic, saif al-jabbar, meaning "sword of the giant". In China, Orion was one of the 28 lunar mansions Sieu (Xiù) (宿). It is known as Shen (參), literally meaning "three", for the stars of Orion's Belt. The Chinese character 參 (pinyin shēn) originally meant the constellation Orion (Chinese: 參宿; pinyin: shēnxiù); its Shang dynasty version, over three millennia old, contains at the top a representation of the three stars of Orion's Belt atop a man's head (the bottom portion representing the sound of the word was added later). The Rigveda refers to the constellation as Mriga (the Deer). Nataraja, "the cosmic dancer", is often interpreted as the representation of Orion. Rudra, the Rigvedic form of Shiva, is the presiding deity of Ardra nakshatra (Betelgeuse) of Hindu astrology. The Jain Symbol carved in the Udayagiri and Khandagiri Caves, India in 1st century BCE has a striking resemblance with Orion. Bugis sailors identified the three stars in Orion's Belt as tanra tellué, meaning "sign of three". The Seri people of northwestern Mexico call the three stars in Orion's Belt Hapj (a name denoting a hunter) which consists of three stars: Hap (mule deer), Haamoja (pronghorn), and Mojet (bighorn sheep). Hap is in the middle and has been shot by the hunter; its blood has dripped onto Tiburón Island. The same three stars are known in Spain and most of Latin America as "Las tres Marías" (Spanish for "The Three Marys"). In Puerto Rico, the three stars are known as the "Los Tres Reyes Magos" (Spanish for The Three Wise Men). The Ojibwa/Chippewa Native Americans call this constellation Mesabi for Big Man. To the Lakota Native Americans, Tayamnicankhu (Orion's Belt) is the spine of a bison. The great rectangle of Orion is the bison's ribs; the Pleiades star cluster in nearby Taurus is the bison's head; and Sirius in Canis Major, known as Tayamnisinte, is its tail. Another Lakota myth mentions that the bottom half of Orion, the Constellation of the Hand, represented the arm of a chief that was ripped off by the Thunder People as a punishment from the gods for his selfishness. His daughter offered to marry the person who can retrieve his arm from the sky, so the young warrior Fallen Star (whose father was a star and whose mother was human) returned his arm and married his daughter, symbolizing harmony between the gods and humanity with the help of the younger generation. The index finger is represented by Rigel; the Orion Nebula is the thumb; the Belt of Orion is the wrist; and the star Beta Eridani is the pinky finger. The seven primary stars of Orion make up the Polynesian constellation Heiheionakeiki which represents a child's string figure similar to a cat's cradle. Several precolonial Filipinos referred to the belt region in particular as "balatik" (ballista) as it resembles a trap of the same name which fires arrows by itself and is usually used for catching pigs from the bush. Spanish colonization later led to some ethnic groups referring to Orion's Belt as "Tres Marias" or "Tatlong Maria." In Māori tradition, the star Rigel (known as Puanga or Puaka) is closely connected with the celebration of Matariki. The rising of Matariki (the Pleiades) and Rigel before sunrise in midwinter marks the start of the Māori year. In Javanese culture, the constellation is often called Lintang Waluku or Bintang Bajak, referring to the shape of a paddy field plow. The imagery of the Belt and Sword has found its way into popular Western culture, for example in the form of the shoulder insignia of the 27th Infantry Division of the United States Army during both World Wars, probably owing to a pun on the name of the division's first commander, Major General John F. O'Ryan. The film distribution company Orion Pictures used the constellation as its logo. In artistic renderings, the surrounding constellations are sometimes related to Orion: he is depicted standing next to the river Eridanus with his two hunting dogs Canis Major and Canis Minor, fighting Taurus. He is sometimes depicted hunting Lepus the hare. He sometimes is depicted to have a lion's hide in his hand. There are alternative ways to visualise Orion. From the Southern Hemisphere, Orion is oriented south-upward, and the Belt and Sword are sometimes called the saucepan or pot in Australia and New Zealand. Orion's Belt is called Drie Konings (Three Kings) or the Drie Susters (Three Sisters) by Afrikaans speakers in South Africa and are referred to as les Trois Rois (the Three Kings) in Daudet's Lettres de Mon Moulin (1866). The appellation Driekoningen (the Three Kings) is also often found in 17th and 18th-century Dutch star charts and seaman's guides. The same three stars are known in Spain, Latin America, and the Philippines as "Las Tres Marías" (The Three Marys), and as "Los Tres Reyes Magos" (The Three Wise Men) in Puerto Rico. Even traditional depictions of Orion have varied greatly. Cicero drew Orion in a similar fashion to the modern depiction. The Hunter held an unidentified animal skin aloft in his right hand; his hand was represented by Omicron2 Orionis and the skin was represented by the five stars designated Pi Orionis. Saiph and Rigel represented his left and right knees, while Eta Orionis and Lambda Leporis were his left and right feet, respectively. As in the modern depiction, Mintaka, Alnilam, and Alnitak represented his Belt. His left shoulder was represented by Betelgeuse, and Mu Orionis made up his left arm. Meissa was his head, and Bellatrix his right shoulder. The depiction of Hyginus was similar to that of Cicero, though the two differed in a few important areas. Cicero's animal skin became Hyginus's shield (Omicron and Pi Orionis), and instead of an arm marked out by Mu Orionis, he holds a club (Chi Orionis). His right leg is represented by Theta Orionis and his left leg is represented by Lambda, Mu, and Epsilon Leporis. Further Western European and Arabic depictions have followed these two models. Future Orion is located on the celestial equator, but it will not always be so located due to the effects of precession of the Earth's axis. Orion lies well south of the ecliptic, and it only happens to lie on the celestial equator because the point on the ecliptic that corresponds to the June solstice is close to the border of Gemini and Taurus, to the north of Orion. Precession will eventually carry Orion further south, and by AD 14000, Orion will be far enough south that it will no longer be visible from the latitude of Great Britain. Further in the future, Orion's stars will gradually move away from the constellation due to proper motion. However, Orion's brightest stars all lie at a large distance from Earth on an astronomical scale—much farther away than Sirius, for example. Orion will still be recognizable long after most of the other constellations—composed of relatively nearby stars—have distorted into new configurations, with the exception of a few of its stars eventually exploding as supernovae, for example Betelgeuse, which is predicted to explode sometime in the next million years. See also References External links |
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Contents Red (programming language) Red is a programming language designed to overcome the limitations of the programming language Rebol. Red was introduced in 2011 by Nenad Rakočević, and is both an imperative and functional programming language. Its syntax and general usage overlaps that of the interpreted Rebol language. The implementation choices of Red intend to create a full stack programming language: Red can be used for extremely high-level programming (DSLs and GUIs) as well as low-level programming (operating systems and device drivers). Key to the approach is that the language has two parts: Red/System and Red. Red seeks to remain independent of any other toolchain; it does its own code generation. It is therefore possible to cross-compile Red programs from any platform it supports to any other, via a command-line switch. Both Red and Red/System are distributed as open-source software under the modified BSD license. The runtime library is distributed under the more permissive Boost Software License. As of version 0.6.4 Red includes a garbage collector "the Simple GC". Introduction Red was introduced in the Netherlands in February 2011 at the Rebol & Boron conference by its author Nenad Rakočević. In September 2011, the Red programming language was presented to a larger audience during the Software Freedom Day 2011. Rakočević is a long-time Rebol developer known as the creator of the Cheyenne HTTP server. Features Red's syntax and semantics are very close to those of Rebol. Like Rebol, it strongly supports metaprogramming and domain-specific languages (DSLs) and is therefore a highly efficient tool for dialecting (creating embedded DSLs). Red includes a dialect called Red/System, a C-level language which provides system programming facilities. Red is easy to integrate with other tools and languages as a DLL (libRed) and very lightweight (around 1 MB). It is also able to cross-compile to various platforms (see Cross Compilation section below) and create packages for platforms that require them (e.g., .APK on Android). Red also includes a fully reactive cross-platform GUI system based on an underlying reactive dataflow engine, a 2D drawing dialect comparable to SVG, compile-time and runtime macro support, and more than 40 standard datatypes. Goals The following is the list of Red's Goals as presented on the Software Freedom Day 2011: Commercial applications The following commercial applications are currently developed on Red: Development Red's development is planned to be done in two phases: Cross compilation Red currently supports the following cross-compilation targets: (Note: Presently, Red applications are 32-bit, but it is planned to switch to 64-bit in the future.) Hello World! The "Hello, World!" program in Red: Factorial example IMPORTANT: These are intended as syntax examples. Until Red has 64-bit support, the integer example will overflow a 32-bit integer very quickly. Changing that to `float!` will go farther, but these are merely to show the syntax of the language. The following is a factorial example in Red: The following is the same factorial example in Red/System (in this very simple case, the source code is very similar to Red's version): See also References Further reading External links |
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[SOURCE: https://en.wikipedia.org/wiki/Python_(programming_language)#cite_note-129] | [TOKENS: 4314] |
Contents Python (programming language) Python is a high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. Python is dynamically type-checked and garbage-collected. It supports multiple programming paradigms, including structured (particularly procedural), object-oriented and functional programming. Guido van Rossum began working on Python in the late 1980s as a successor to the ABC programming language. Python 3.0, released in 2008, was a major revision and not completely backward-compatible with earlier versions. Beginning with Python 3.5, capabilities and keywords for typing were added to the language, allowing optional static typing. As of 2026[update], the Python Software Foundation supports Python 3.10, 3.11, 3.12, 3.13, and 3.14, following the project's annual release cycle and five-year support policy. Python 3.15 is currently in the alpha development phase, and the stable release is expected to come out in October 2026. Earlier versions in the 3.x series have reached end-of-life and no longer receive security updates. Python has gained widespread use in the machine learning community. It is widely taught as an introductory programming language. Since 2003, Python has consistently ranked in the top ten of the most popular programming languages in the TIOBE Programming Community Index, which ranks based on searches in 24 platforms. History Python was conceived in the late 1980s by Guido van Rossum at Centrum Wiskunde & Informatica (CWI) in the Netherlands. It was designed as a successor to the ABC programming language, which was inspired by SETL, capable of exception handling and interfacing with the Amoeba operating system. Python implementation began in December 1989. Van Rossum first released it in 1991 as Python 0.9.0. Van Rossum assumed sole responsibility for the project, as the lead developer, until 12 July 2018, when he announced his "permanent vacation" from responsibilities as Python's "benevolent dictator for life" (BDFL); this title was bestowed on him by the Python community to reflect his long-term commitment as the project's chief decision-maker. (He has since come out of retirement and is self-titled "BDFL-emeritus".) In January 2019, active Python core developers elected a five-member Steering Council to lead the project. The name Python derives from the British comedy series Monty Python's Flying Circus. (See § Naming.) Python 2.0 was released on 16 October 2000, featuring many new features such as list comprehensions, cycle-detecting garbage collection, reference counting, and Unicode support. Python 2.7's end-of-life was initially set for 2015, and then postponed to 2020 out of concern that a large body of existing code could not easily be forward-ported to Python 3. It no longer receives security patches or updates. While Python 2.7 and older versions are officially unsupported, a different unofficial Python implementation, PyPy, continues to support Python 2, i.e., "2.7.18+" (plus 3.11), with the plus signifying (at least some) "backported security updates". Python 3.0 was released on 3 December 2008, and was a major revision and not completely backward-compatible with earlier versions, with some new semantics and changed syntax. Python 2.7.18, released in 2020, was the last release of Python 2. Several releases in the Python 3.x series have added new syntax to the language, and made a few (considered very minor) backward-incompatible changes. As of January 2026[update], Python 3.14.3 is the latest stable release. All older 3.x versions had a security update down to Python 3.9.24 then again with 3.9.25, the final version in 3.9 series. Python 3.10 is, since November 2025, the oldest supported branch. Python 3.15 has an alpha released, and Android has an official downloadable executable available for Python 3.14. Releases receive two years of full support followed by three years of security support. Design philosophy and features Python is a multi-paradigm programming language. Object-oriented programming and structured programming are fully supported, and many of their features support functional programming and aspect-oriented programming – including metaprogramming and metaobjects. Many other paradigms are supported via extensions, including design by contract and logic programming. Python is often referred to as a 'glue language' because it is purposely designed to be able to integrate components written in other languages. Python uses dynamic typing and a combination of reference counting and a cycle-detecting garbage collector for memory management. It uses dynamic name resolution (late binding), which binds method and variable names during program execution. Python's design offers some support for functional programming in the "Lisp tradition". It has filter, map, and reduce functions; list comprehensions, dictionaries, sets, and generator expressions. The standard library has two modules (itertools and functools) that implement functional tools borrowed from Haskell and Standard ML. Python's core philosophy is summarized in the Zen of Python (PEP 20) written by Tim Peters, which includes aphorisms such as these: However, Python has received criticism for violating these principles and adding unnecessary language bloat. Responses to these criticisms note that the Zen of Python is a guideline rather than a rule. The addition of some new features had been controversial: Guido van Rossum resigned as Benevolent Dictator for Life after conflict about adding the assignment expression operator in Python 3.8. Nevertheless, rather than building all functionality into its core, Python was designed to be highly extensible via modules. This compact modularity has made it particularly popular as a means of adding programmable interfaces to existing applications. Van Rossum's vision of a small core language with a large standard library and easily extensible interpreter stemmed from his frustrations with ABC, which represented the opposite approach. Python claims to strive for a simpler, less-cluttered syntax and grammar, while giving developers a choice in their coding methodology. Python lacks do .. while loops, which Rossum considered harmful. In contrast to Perl's motto "there is more than one way to do it", Python advocates an approach where "there should be one – and preferably only one – obvious way to do it". In practice, however, Python provides many ways to achieve a given goal. There are at least three ways to format a string literal, with no certainty as to which one a programmer should use. Alex Martelli is a Fellow at the Python Software Foundation and Python book author; he wrote that "To describe something as 'clever' is not considered a compliment in the Python culture." Python's developers typically prioritize readability over performance. For example, they reject patches to non-critical parts of the CPython reference implementation that would offer increases in speed that do not justify the cost of clarity and readability.[failed verification] Execution speed can be improved by moving speed-critical functions to extension modules written in languages such as C, or by using a just-in-time compiler like PyPy. Also, it is possible to transpile to other languages. However, this approach either fails to achieve the expected speed-up, since Python is a very dynamic language, or only a restricted subset of Python is compiled (with potential minor semantic changes). Python is meant to be a fun language to use. This goal is reflected in the name – a tribute to the British comedy group Monty Python – and in playful approaches to some tutorials and reference materials. For instance, some code examples use the terms "spam" and "eggs" (in reference to a Monty Python sketch), rather than the typical terms "foo" and "bar". A common neologism in the Python community is pythonic, which has a broad range of meanings related to program style: Pythonic code may use Python idioms well; be natural or show fluency in the language; or conform with Python's minimalist philosophy and emphasis on readability. Syntax and semantics Python is meant to be an easily readable language. Its formatting is visually uncluttered and often uses English keywords where other languages use punctuation. Unlike many other languages, it does not use curly brackets to delimit blocks, and semicolons after statements are allowed but rarely used. It has fewer syntactic exceptions and special cases than C or Pascal. Python uses whitespace indentation, rather than curly brackets or keywords, to delimit blocks. An increase in indentation comes after certain statements; a decrease in indentation signifies the end of the current block. Thus, the program's visual structure accurately represents its semantic structure. This feature is sometimes termed the off-side rule. Some other languages use indentation this way; but in most, indentation has no semantic meaning. The recommended indent size is four spaces. Python's statements include the following: The assignment statement (=) binds a name as a reference to a separate, dynamically allocated object. Variables may subsequently be rebound at any time to any object. In Python, a variable name is a generic reference holder without a fixed data type; however, it always refers to some object with a type. This is called dynamic typing—in contrast to statically-typed languages, where each variable may contain only a value of a certain type. Python does not support tail call optimization or first-class continuations; according to Van Rossum, the language never will. However, better support for coroutine-like functionality is provided by extending Python's generators. Before 2.5, generators were lazy iterators; data was passed unidirectionally out of the generator. From Python 2.5 on, it is possible to pass data back into a generator function; and from version 3.3, data can be passed through multiple stack levels. Python's expressions include the following: In Python, a distinction between expressions and statements is rigidly enforced, in contrast to languages such as Common Lisp, Scheme, or Ruby. This distinction leads to duplicating some functionality, for example: A statement cannot be part of an expression; because of this restriction, expressions such as list and dict comprehensions (and lambda expressions) cannot contain statements. As a particular case, an assignment statement such as a = 1 cannot be part of the conditional expression of a conditional statement. Python uses duck typing, and it has typed objects but untyped variable names. Type constraints are not checked at definition time; rather, operations on an object may fail at usage time, indicating that the object is not of an appropriate type. Despite being dynamically typed, Python is strongly typed, forbidding operations that are poorly defined (e.g., adding a number and a string) rather than quietly attempting to interpret them. Python allows programmers to define their own types using classes, most often for object-oriented programming. New instances of classes are constructed by calling the class, for example, SpamClass() or EggsClass()); the classes are instances of the metaclass type (which is an instance of itself), thereby allowing metaprogramming and reflection. Before version 3.0, Python had two kinds of classes, both using the same syntax: old-style and new-style. Current Python versions support the semantics of only the new style. Python supports optional type annotations. These annotations are not enforced by the language, but may be used by external tools such as mypy to catch errors. Python includes a module typing including several type names for type annotations. Also, mypy supports a Python compiler called mypyc, which leverages type annotations for optimization. 1.33333 frozenset() Python includes conventional symbols for arithmetic operators (+, -, *, /), the floor-division operator //, and the modulo operator %. (With the modulo operator, a remainder can be negative, e.g., 4 % -3 == -2.) Also, Python offers the ** symbol for exponentiation, e.g. 5**3 == 125 and 9**0.5 == 3.0. Also, it offers the matrix‑multiplication operator @ . These operators work as in traditional mathematics; with the same precedence rules, the infix operators + and - can also be unary, to represent positive and negative numbers respectively. Division between integers produces floating-point results. The behavior of division has changed significantly over time: In Python terms, the / operator represents true division (or simply division), while the // operator represents floor division. Before version 3.0, the / operator represents classic division. Rounding towards negative infinity, though a different method than in most languages, adds consistency to Python. For instance, this rounding implies that the equation (a + b)//b == a//b + 1 is always true. Also, the rounding implies that the equation b*(a//b) + a%b == a is valid for both positive and negative values of a. As expected, the result of a%b lies in the half-open interval [0, b), where b is a positive integer; however, maintaining the validity of the equation requires that the result must lie in the interval (b, 0] when b is negative. Python provides a round function for rounding a float to the nearest integer. For tie-breaking, Python 3 uses the round to even method: round(1.5) and round(2.5) both produce 2. Python versions before 3 used the round-away-from-zero method: round(0.5) is 1.0, and round(-0.5) is −1.0. Python allows Boolean expressions that contain multiple equality relations to be consistent with general usage in mathematics. For example, the expression a < b < c tests whether a is less than b and b is less than c. C-derived languages interpret this expression differently: in C, the expression would first evaluate a < b, resulting in 0 or 1, and that result would then be compared with c. Python uses arbitrary-precision arithmetic for all integer operations. The Decimal type/class in the decimal module provides decimal floating-point numbers to a pre-defined arbitrary precision with several rounding modes. The Fraction class in the fractions module provides arbitrary precision for rational numbers. Due to Python's extensive mathematics library and the third-party library NumPy, the language is frequently used for scientific scripting in tasks such as numerical data processing and manipulation. Functions are created in Python by using the def keyword. A function is defined similarly to how it is called, by first providing the function name and then the required parameters. Here is an example of a function that prints its inputs: To assign a default value to a function parameter in case no actual value is provided at run time, variable-definition syntax can be used inside the function header. Code examples "Hello, World!" program: Program to calculate the factorial of a non-negative integer: Libraries Python's large standard library is commonly cited as one of its greatest strengths. For Internet-facing applications, many standard formats and protocols such as MIME and HTTP are supported. The language includes modules for creating graphical user interfaces, connecting to relational databases, generating pseudorandom numbers, arithmetic with arbitrary-precision decimals, manipulating regular expressions, and unit testing. Some parts of the standard library are covered by specifications—for example, the Web Server Gateway Interface (WSGI) implementation wsgiref follows PEP 333—but most parts are specified by their code, internal documentation, and test suites. However, because most of the standard library is cross-platform Python code, only a few modules must be altered or rewritten for variant implementations. As of 13 March 2025,[update] the Python Package Index (PyPI), the official repository for third-party Python software, contains over 614,339 packages. Development environments Most[which?] Python implementations (including CPython) include a read–eval–print loop (REPL); this permits the environment to function as a command line interpreter, with which users enter statements sequentially and receive results immediately. Also, CPython is bundled with an integrated development environment (IDE) called IDLE, which is oriented toward beginners.[citation needed] Other shells, including IDLE and IPython, add additional capabilities such as improved auto-completion, session-state retention, and syntax highlighting. Standard desktop IDEs include PyCharm, Spyder, and Visual Studio Code; there are web browser-based IDEs, such as the following environments: Implementations CPython is the reference implementation of Python. This implementation is written in C, meeting the C11 standard since version 3.11. Older versions use the C89 standard with several select C99 features, but third-party extensions are not limited to older C versions—e.g., they can be implemented using C11 or C++. CPython compiles Python programs into an intermediate bytecode, which is then executed by a virtual machine. CPython is distributed with a large standard library written in a combination of C and native Python. CPython is available for many platforms, including Windows and most modern Unix-like systems, including macOS (and Apple M1 Macs, since Python 3.9.1, using an experimental installer). Starting with Python 3.9, the Python installer intentionally fails to install on Windows 7 and 8; Windows XP was supported until Python 3.5, with unofficial support for VMS. Platform portability was one of Python's earliest priorities. During development of Python 1 and 2, even OS/2 and Solaris were supported; since that time, support has been dropped for many platforms. All current Python versions (since 3.7) support only operating systems that feature multithreading, by now supporting not nearly as many operating systems (dropping many outdated) than in the past. All alternative implementations have at least slightly different semantics. For example, an alternative may include unordered dictionaries, in contrast to other current Python versions. As another example in the larger Python ecosystem, PyPy does not support the full C Python API. Creating an executable with Python often is done by bundling an entire Python interpreter into the executable, which causes binary sizes to be massive for small programs, yet there exist implementations that are capable of truly compiling Python. Alternative implementations include the following: Stackless Python is a significant fork of CPython that implements microthreads. This implementation uses the call stack differently, thus allowing massively concurrent programs. PyPy also offers a stackless version. Just-in-time Python compilers have been developed, but are now unsupported: There are several compilers/transpilers to high-level object languages; the source language is unrestricted Python, a subset of Python, or a language similar to Python: There are also specialized compilers: Some older projects existed, as well as compilers not designed for use with Python 3.x and related syntax: A performance comparison among various Python implementations, using a non-numerical (combinatorial) workload, was presented at EuroSciPy '13. In addition, Python's performance relative to other programming languages is benchmarked by The Computer Language Benchmarks Game. There are several approaches to optimizing Python performance, despite the inherent slowness of an interpreted language. These approaches include the following strategies or tools: Language Development Python's development is conducted mostly through the Python Enhancement Proposal (PEP) process; this process is the primary mechanism for proposing major new features, collecting community input on issues, and documenting Python design decisions. Python coding style is covered in PEP 8. Outstanding PEPs are reviewed and commented on by the Python community and the steering council. Enhancement of the language corresponds with development of the CPython reference implementation. The mailing list python-dev is the primary forum for the language's development. Specific issues were originally discussed in the Roundup bug tracker hosted by the foundation. In 2022, all issues and discussions were migrated to GitHub. Development originally took place on a self-hosted source-code repository running Mercurial, until Python moved to GitHub in January 2017. CPython's public releases have three types, distinguished by which part of the version number is incremented: Many alpha, beta, and release-candidates are also released as previews and for testing before final releases. Although there is a rough schedule for releases, they are often delayed if the code is not ready yet. Python's development team monitors the state of the code by running a large unit test suite during development. The major academic conference on Python is PyCon. Also, there are special Python mentoring programs, such as PyLadies. Naming Python's name is inspired by the British comedy group Monty Python, whom Python creator Guido van Rossum enjoyed while developing the language. Monty Python references appear frequently in Python code and culture; for example, the metasyntactic variables often used in Python literature are spam and eggs, rather than the traditional foo and bar. Also, the official Python documentation contains various references to Monty Python routines. Python users are sometimes referred to as "Pythonistas". Languages influenced by Python See also Notes References Further reading External links |
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[SOURCE: https://en.wikipedia.org/wiki/Python_(programming_language)#cite_note-130] | [TOKENS: 4314] |
Contents Python (programming language) Python is a high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. Python is dynamically type-checked and garbage-collected. It supports multiple programming paradigms, including structured (particularly procedural), object-oriented and functional programming. Guido van Rossum began working on Python in the late 1980s as a successor to the ABC programming language. Python 3.0, released in 2008, was a major revision and not completely backward-compatible with earlier versions. Beginning with Python 3.5, capabilities and keywords for typing were added to the language, allowing optional static typing. As of 2026[update], the Python Software Foundation supports Python 3.10, 3.11, 3.12, 3.13, and 3.14, following the project's annual release cycle and five-year support policy. Python 3.15 is currently in the alpha development phase, and the stable release is expected to come out in October 2026. Earlier versions in the 3.x series have reached end-of-life and no longer receive security updates. Python has gained widespread use in the machine learning community. It is widely taught as an introductory programming language. Since 2003, Python has consistently ranked in the top ten of the most popular programming languages in the TIOBE Programming Community Index, which ranks based on searches in 24 platforms. History Python was conceived in the late 1980s by Guido van Rossum at Centrum Wiskunde & Informatica (CWI) in the Netherlands. It was designed as a successor to the ABC programming language, which was inspired by SETL, capable of exception handling and interfacing with the Amoeba operating system. Python implementation began in December 1989. Van Rossum first released it in 1991 as Python 0.9.0. Van Rossum assumed sole responsibility for the project, as the lead developer, until 12 July 2018, when he announced his "permanent vacation" from responsibilities as Python's "benevolent dictator for life" (BDFL); this title was bestowed on him by the Python community to reflect his long-term commitment as the project's chief decision-maker. (He has since come out of retirement and is self-titled "BDFL-emeritus".) In January 2019, active Python core developers elected a five-member Steering Council to lead the project. The name Python derives from the British comedy series Monty Python's Flying Circus. (See § Naming.) Python 2.0 was released on 16 October 2000, featuring many new features such as list comprehensions, cycle-detecting garbage collection, reference counting, and Unicode support. Python 2.7's end-of-life was initially set for 2015, and then postponed to 2020 out of concern that a large body of existing code could not easily be forward-ported to Python 3. It no longer receives security patches or updates. While Python 2.7 and older versions are officially unsupported, a different unofficial Python implementation, PyPy, continues to support Python 2, i.e., "2.7.18+" (plus 3.11), with the plus signifying (at least some) "backported security updates". Python 3.0 was released on 3 December 2008, and was a major revision and not completely backward-compatible with earlier versions, with some new semantics and changed syntax. Python 2.7.18, released in 2020, was the last release of Python 2. Several releases in the Python 3.x series have added new syntax to the language, and made a few (considered very minor) backward-incompatible changes. As of January 2026[update], Python 3.14.3 is the latest stable release. All older 3.x versions had a security update down to Python 3.9.24 then again with 3.9.25, the final version in 3.9 series. Python 3.10 is, since November 2025, the oldest supported branch. Python 3.15 has an alpha released, and Android has an official downloadable executable available for Python 3.14. Releases receive two years of full support followed by three years of security support. Design philosophy and features Python is a multi-paradigm programming language. Object-oriented programming and structured programming are fully supported, and many of their features support functional programming and aspect-oriented programming – including metaprogramming and metaobjects. Many other paradigms are supported via extensions, including design by contract and logic programming. Python is often referred to as a 'glue language' because it is purposely designed to be able to integrate components written in other languages. Python uses dynamic typing and a combination of reference counting and a cycle-detecting garbage collector for memory management. It uses dynamic name resolution (late binding), which binds method and variable names during program execution. Python's design offers some support for functional programming in the "Lisp tradition". It has filter, map, and reduce functions; list comprehensions, dictionaries, sets, and generator expressions. The standard library has two modules (itertools and functools) that implement functional tools borrowed from Haskell and Standard ML. Python's core philosophy is summarized in the Zen of Python (PEP 20) written by Tim Peters, which includes aphorisms such as these: However, Python has received criticism for violating these principles and adding unnecessary language bloat. Responses to these criticisms note that the Zen of Python is a guideline rather than a rule. The addition of some new features had been controversial: Guido van Rossum resigned as Benevolent Dictator for Life after conflict about adding the assignment expression operator in Python 3.8. Nevertheless, rather than building all functionality into its core, Python was designed to be highly extensible via modules. This compact modularity has made it particularly popular as a means of adding programmable interfaces to existing applications. Van Rossum's vision of a small core language with a large standard library and easily extensible interpreter stemmed from his frustrations with ABC, which represented the opposite approach. Python claims to strive for a simpler, less-cluttered syntax and grammar, while giving developers a choice in their coding methodology. Python lacks do .. while loops, which Rossum considered harmful. In contrast to Perl's motto "there is more than one way to do it", Python advocates an approach where "there should be one – and preferably only one – obvious way to do it". In practice, however, Python provides many ways to achieve a given goal. There are at least three ways to format a string literal, with no certainty as to which one a programmer should use. Alex Martelli is a Fellow at the Python Software Foundation and Python book author; he wrote that "To describe something as 'clever' is not considered a compliment in the Python culture." Python's developers typically prioritize readability over performance. For example, they reject patches to non-critical parts of the CPython reference implementation that would offer increases in speed that do not justify the cost of clarity and readability.[failed verification] Execution speed can be improved by moving speed-critical functions to extension modules written in languages such as C, or by using a just-in-time compiler like PyPy. Also, it is possible to transpile to other languages. However, this approach either fails to achieve the expected speed-up, since Python is a very dynamic language, or only a restricted subset of Python is compiled (with potential minor semantic changes). Python is meant to be a fun language to use. This goal is reflected in the name – a tribute to the British comedy group Monty Python – and in playful approaches to some tutorials and reference materials. For instance, some code examples use the terms "spam" and "eggs" (in reference to a Monty Python sketch), rather than the typical terms "foo" and "bar". A common neologism in the Python community is pythonic, which has a broad range of meanings related to program style: Pythonic code may use Python idioms well; be natural or show fluency in the language; or conform with Python's minimalist philosophy and emphasis on readability. Syntax and semantics Python is meant to be an easily readable language. Its formatting is visually uncluttered and often uses English keywords where other languages use punctuation. Unlike many other languages, it does not use curly brackets to delimit blocks, and semicolons after statements are allowed but rarely used. It has fewer syntactic exceptions and special cases than C or Pascal. Python uses whitespace indentation, rather than curly brackets or keywords, to delimit blocks. An increase in indentation comes after certain statements; a decrease in indentation signifies the end of the current block. Thus, the program's visual structure accurately represents its semantic structure. This feature is sometimes termed the off-side rule. Some other languages use indentation this way; but in most, indentation has no semantic meaning. The recommended indent size is four spaces. Python's statements include the following: The assignment statement (=) binds a name as a reference to a separate, dynamically allocated object. Variables may subsequently be rebound at any time to any object. In Python, a variable name is a generic reference holder without a fixed data type; however, it always refers to some object with a type. This is called dynamic typing—in contrast to statically-typed languages, where each variable may contain only a value of a certain type. Python does not support tail call optimization or first-class continuations; according to Van Rossum, the language never will. However, better support for coroutine-like functionality is provided by extending Python's generators. Before 2.5, generators were lazy iterators; data was passed unidirectionally out of the generator. From Python 2.5 on, it is possible to pass data back into a generator function; and from version 3.3, data can be passed through multiple stack levels. Python's expressions include the following: In Python, a distinction between expressions and statements is rigidly enforced, in contrast to languages such as Common Lisp, Scheme, or Ruby. This distinction leads to duplicating some functionality, for example: A statement cannot be part of an expression; because of this restriction, expressions such as list and dict comprehensions (and lambda expressions) cannot contain statements. As a particular case, an assignment statement such as a = 1 cannot be part of the conditional expression of a conditional statement. Python uses duck typing, and it has typed objects but untyped variable names. Type constraints are not checked at definition time; rather, operations on an object may fail at usage time, indicating that the object is not of an appropriate type. Despite being dynamically typed, Python is strongly typed, forbidding operations that are poorly defined (e.g., adding a number and a string) rather than quietly attempting to interpret them. Python allows programmers to define their own types using classes, most often for object-oriented programming. New instances of classes are constructed by calling the class, for example, SpamClass() or EggsClass()); the classes are instances of the metaclass type (which is an instance of itself), thereby allowing metaprogramming and reflection. Before version 3.0, Python had two kinds of classes, both using the same syntax: old-style and new-style. Current Python versions support the semantics of only the new style. Python supports optional type annotations. These annotations are not enforced by the language, but may be used by external tools such as mypy to catch errors. Python includes a module typing including several type names for type annotations. Also, mypy supports a Python compiler called mypyc, which leverages type annotations for optimization. 1.33333 frozenset() Python includes conventional symbols for arithmetic operators (+, -, *, /), the floor-division operator //, and the modulo operator %. (With the modulo operator, a remainder can be negative, e.g., 4 % -3 == -2.) Also, Python offers the ** symbol for exponentiation, e.g. 5**3 == 125 and 9**0.5 == 3.0. Also, it offers the matrix‑multiplication operator @ . These operators work as in traditional mathematics; with the same precedence rules, the infix operators + and - can also be unary, to represent positive and negative numbers respectively. Division between integers produces floating-point results. The behavior of division has changed significantly over time: In Python terms, the / operator represents true division (or simply division), while the // operator represents floor division. Before version 3.0, the / operator represents classic division. Rounding towards negative infinity, though a different method than in most languages, adds consistency to Python. For instance, this rounding implies that the equation (a + b)//b == a//b + 1 is always true. Also, the rounding implies that the equation b*(a//b) + a%b == a is valid for both positive and negative values of a. As expected, the result of a%b lies in the half-open interval [0, b), where b is a positive integer; however, maintaining the validity of the equation requires that the result must lie in the interval (b, 0] when b is negative. Python provides a round function for rounding a float to the nearest integer. For tie-breaking, Python 3 uses the round to even method: round(1.5) and round(2.5) both produce 2. Python versions before 3 used the round-away-from-zero method: round(0.5) is 1.0, and round(-0.5) is −1.0. Python allows Boolean expressions that contain multiple equality relations to be consistent with general usage in mathematics. For example, the expression a < b < c tests whether a is less than b and b is less than c. C-derived languages interpret this expression differently: in C, the expression would first evaluate a < b, resulting in 0 or 1, and that result would then be compared with c. Python uses arbitrary-precision arithmetic for all integer operations. The Decimal type/class in the decimal module provides decimal floating-point numbers to a pre-defined arbitrary precision with several rounding modes. The Fraction class in the fractions module provides arbitrary precision for rational numbers. Due to Python's extensive mathematics library and the third-party library NumPy, the language is frequently used for scientific scripting in tasks such as numerical data processing and manipulation. Functions are created in Python by using the def keyword. A function is defined similarly to how it is called, by first providing the function name and then the required parameters. Here is an example of a function that prints its inputs: To assign a default value to a function parameter in case no actual value is provided at run time, variable-definition syntax can be used inside the function header. Code examples "Hello, World!" program: Program to calculate the factorial of a non-negative integer: Libraries Python's large standard library is commonly cited as one of its greatest strengths. For Internet-facing applications, many standard formats and protocols such as MIME and HTTP are supported. The language includes modules for creating graphical user interfaces, connecting to relational databases, generating pseudorandom numbers, arithmetic with arbitrary-precision decimals, manipulating regular expressions, and unit testing. Some parts of the standard library are covered by specifications—for example, the Web Server Gateway Interface (WSGI) implementation wsgiref follows PEP 333—but most parts are specified by their code, internal documentation, and test suites. However, because most of the standard library is cross-platform Python code, only a few modules must be altered or rewritten for variant implementations. As of 13 March 2025,[update] the Python Package Index (PyPI), the official repository for third-party Python software, contains over 614,339 packages. Development environments Most[which?] Python implementations (including CPython) include a read–eval–print loop (REPL); this permits the environment to function as a command line interpreter, with which users enter statements sequentially and receive results immediately. Also, CPython is bundled with an integrated development environment (IDE) called IDLE, which is oriented toward beginners.[citation needed] Other shells, including IDLE and IPython, add additional capabilities such as improved auto-completion, session-state retention, and syntax highlighting. Standard desktop IDEs include PyCharm, Spyder, and Visual Studio Code; there are web browser-based IDEs, such as the following environments: Implementations CPython is the reference implementation of Python. This implementation is written in C, meeting the C11 standard since version 3.11. Older versions use the C89 standard with several select C99 features, but third-party extensions are not limited to older C versions—e.g., they can be implemented using C11 or C++. CPython compiles Python programs into an intermediate bytecode, which is then executed by a virtual machine. CPython is distributed with a large standard library written in a combination of C and native Python. CPython is available for many platforms, including Windows and most modern Unix-like systems, including macOS (and Apple M1 Macs, since Python 3.9.1, using an experimental installer). Starting with Python 3.9, the Python installer intentionally fails to install on Windows 7 and 8; Windows XP was supported until Python 3.5, with unofficial support for VMS. Platform portability was one of Python's earliest priorities. During development of Python 1 and 2, even OS/2 and Solaris were supported; since that time, support has been dropped for many platforms. All current Python versions (since 3.7) support only operating systems that feature multithreading, by now supporting not nearly as many operating systems (dropping many outdated) than in the past. All alternative implementations have at least slightly different semantics. For example, an alternative may include unordered dictionaries, in contrast to other current Python versions. As another example in the larger Python ecosystem, PyPy does not support the full C Python API. Creating an executable with Python often is done by bundling an entire Python interpreter into the executable, which causes binary sizes to be massive for small programs, yet there exist implementations that are capable of truly compiling Python. Alternative implementations include the following: Stackless Python is a significant fork of CPython that implements microthreads. This implementation uses the call stack differently, thus allowing massively concurrent programs. PyPy also offers a stackless version. Just-in-time Python compilers have been developed, but are now unsupported: There are several compilers/transpilers to high-level object languages; the source language is unrestricted Python, a subset of Python, or a language similar to Python: There are also specialized compilers: Some older projects existed, as well as compilers not designed for use with Python 3.x and related syntax: A performance comparison among various Python implementations, using a non-numerical (combinatorial) workload, was presented at EuroSciPy '13. In addition, Python's performance relative to other programming languages is benchmarked by The Computer Language Benchmarks Game. There are several approaches to optimizing Python performance, despite the inherent slowness of an interpreted language. These approaches include the following strategies or tools: Language Development Python's development is conducted mostly through the Python Enhancement Proposal (PEP) process; this process is the primary mechanism for proposing major new features, collecting community input on issues, and documenting Python design decisions. Python coding style is covered in PEP 8. Outstanding PEPs are reviewed and commented on by the Python community and the steering council. Enhancement of the language corresponds with development of the CPython reference implementation. The mailing list python-dev is the primary forum for the language's development. Specific issues were originally discussed in the Roundup bug tracker hosted by the foundation. In 2022, all issues and discussions were migrated to GitHub. Development originally took place on a self-hosted source-code repository running Mercurial, until Python moved to GitHub in January 2017. CPython's public releases have three types, distinguished by which part of the version number is incremented: Many alpha, beta, and release-candidates are also released as previews and for testing before final releases. Although there is a rough schedule for releases, they are often delayed if the code is not ready yet. Python's development team monitors the state of the code by running a large unit test suite during development. The major academic conference on Python is PyCon. Also, there are special Python mentoring programs, such as PyLadies. Naming Python's name is inspired by the British comedy group Monty Python, whom Python creator Guido van Rossum enjoyed while developing the language. Monty Python references appear frequently in Python code and culture; for example, the metasyntactic variables often used in Python literature are spam and eggs, rather than the traditional foo and bar. Also, the official Python documentation contains various references to Monty Python routines. Python users are sometimes referred to as "Pythonistas". Languages influenced by Python See also Notes References Further reading External links |
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Contents PlayStation (console) The PlayStation[a] (codenamed PSX, abbreviated as PS, and retroactively PS1 or PS one) is a home video game console developed and marketed by Sony Computer Entertainment. It was released in Japan on 3 December 1994, followed by North America on 9 September 1995, Europe on 29 September 1995, and other regions following thereafter. As a fifth-generation console, the PlayStation primarily competed with the Nintendo 64 and the Sega Saturn. Sony began developing the PlayStation after a failed venture with Nintendo to create a CD-ROM peripheral for the Super Nintendo Entertainment System in the early 1990s. The console was primarily designed by Ken Kutaragi and Sony Computer Entertainment in Japan, while additional development was outsourced in the United Kingdom. An emphasis on 3D polygon graphics was placed at the forefront of the console's design. PlayStation game production was designed to be streamlined and inclusive, enticing the support of many third party developers. The console proved popular for its extensive game library, popular franchises, low retail price, and aggressive youth marketing which advertised it as the preferable console for adolescents and adults. Critically acclaimed games that defined the console include Gran Turismo, Crash Bandicoot, Spyro the Dragon, Tomb Raider, Resident Evil, Metal Gear Solid, Tekken 3, and Final Fantasy VII. Sony ceased production of the PlayStation on 23 March 2006—over eleven years after it had been released, and in the same year the PlayStation 3 debuted. More than 4,000 PlayStation games were released, with cumulative sales of 962 million units. The PlayStation signaled Sony's rise to power in the video game industry. It received acclaim and sold strongly; in less than a decade, it became the first computer entertainment platform to ship over 100 million units. Its use of compact discs heralded the game industry's transition from cartridges. The PlayStation's success led to a line of successors, beginning with the PlayStation 2 in 2000. In the same year, Sony released a smaller and cheaper model, the PS one. History The PlayStation was conceived by Ken Kutaragi, a Sony executive who managed a hardware engineering division and was later dubbed "the Father of the PlayStation". Kutaragi's interest in working with video games stemmed from seeing his daughter play games on Nintendo's Famicom. Kutaragi convinced Nintendo to use his SPC-700 sound processor in the Super Nintendo Entertainment System (SNES) through a demonstration of the processor's capabilities. His willingness to work with Nintendo was derived from both his admiration of the Famicom and conviction in video game consoles becoming the main home-use entertainment systems. Although Kutaragi was nearly fired because he worked with Nintendo without Sony's knowledge, president Norio Ohga recognised the potential in Kutaragi's chip and decided to keep him as a protégé. The inception of the PlayStation dates back to a 1988 joint venture between Nintendo and Sony. Nintendo had produced floppy disk technology to complement cartridges in the form of the Family Computer Disk System, and wanted to continue this complementary storage strategy for the SNES. Since Sony was already contracted to produce the SPC-700 sound processor for the SNES, Nintendo contracted Sony to develop a CD-ROM add-on, tentatively titled the "Play Station" or "SNES-CD". The PlayStation name had already been trademarked by Yamaha, but Nobuyuki Idei liked it so much that he agreed to acquire it for an undisclosed sum rather than search for an alternative. Sony was keen to obtain a foothold in the rapidly expanding video game market. Having been the primary manufacturer of the MSX home computer format, Sony had wanted to use their experience in consumer electronics to produce their own video game hardware. Although the initial agreement between Nintendo and Sony was about producing a CD-ROM drive add-on, Sony had also planned to develop a SNES-compatible Sony-branded console. This iteration was intended to be more of a home entertainment system, playing both SNES cartridges and a new CD format named the "Super Disc", which Sony would design. Under the agreement, Sony would retain sole international rights to every Super Disc game, giving them a large degree of control despite Nintendo's leading position in the video game market. Furthermore, Sony would also be the sole benefactor of licensing related to music and film software that it had been aggressively pursuing as a secondary application. The Play Station was to be announced at the 1991 Consumer Electronics Show (CES) in Las Vegas. However, Nintendo president Hiroshi Yamauchi was wary of Sony's increasing leverage at this point and deemed the original 1988 contract unacceptable upon realising it essentially handed Sony control over all games written on the SNES CD-ROM format. Although Nintendo was dominant in the video game market, Sony possessed a superior research and development department. Wanting to protect Nintendo's existing licensing structure, Yamauchi cancelled all plans for the joint Nintendo–Sony SNES CD attachment without telling Sony. He sent Nintendo of America president Minoru Arakawa (his son-in-law) and chairman Howard Lincoln to Amsterdam to form a more favourable contract with Dutch conglomerate Philips, Sony's rival. This contract would give Nintendo total control over their licences on all Philips-produced machines. Kutaragi and Nobuyuki Idei, Sony's director of public relations at the time, learned of Nintendo's actions two days before the CES was due to begin. Kutaragi telephoned numerous contacts, including Philips, to no avail. On the first day of the CES, Sony announced their partnership with Nintendo and their new console, the Play Station. At 9 am on the next day, in what has been called "the greatest ever betrayal" in the industry, Howard Lincoln stepped onto the stage and revealed that Nintendo was now allied with Philips and would abandon their work with Sony. Incensed by Nintendo's renouncement, Ohga and Kutaragi decided that Sony would develop their own console. Nintendo's contract-breaking was met with consternation in the Japanese business community, as they had broken an "unwritten law" of native companies not turning against each other in favour of foreign ones. Sony's American branch considered allying with Sega to produce a CD-ROM-based machine called the Sega Multimedia Entertainment System, but the Sega board of directors in Tokyo vetoed the idea when Sega of America CEO Tom Kalinske presented them the proposal. Kalinske recalled them saying: "That's a stupid idea, Sony doesn't know how to make hardware. They don't know how to make software either. Why would we want to do this?" Sony halted their research, but decided to develop what it had developed with Nintendo and Sega into a console based on the SNES. Despite the tumultuous events at the 1991 CES, negotiations between Nintendo and Sony were still ongoing. A deal was proposed: the Play Station would still have a port for SNES games, on the condition that it would still use Kutaragi's audio chip and that Nintendo would own the rights and receive the bulk of the profits. Roughly two hundred prototype machines were created, and some software entered development. Many within Sony were still opposed to their involvement in the video game industry, with some resenting Kutaragi for jeopardising the company. Kutaragi remained adamant that Sony not retreat from the growing industry and that a deal with Nintendo would never work. Knowing that they had to take decisive action, Sony severed all ties with Nintendo on 4 May 1992. To determine the fate of the PlayStation project, Ohga chaired a meeting in June 1992, consisting of Kutaragi and several senior Sony board members. Kutaragi unveiled a proprietary CD-ROM-based system he had been secretly working on which played games with immersive 3D graphics. Kutaragi was confident that his LSI chip could accommodate one million logic gates, which exceeded the capabilities of Sony's semiconductor division at the time. Despite gaining Ohga's enthusiasm, there remained opposition from a majority present at the meeting. Older Sony executives also opposed it, who saw Nintendo and Sega as "toy" manufacturers. The opposers felt the game industry was too culturally offbeat and asserted that Sony should remain a central player in the audiovisual industry, where companies were familiar with one another and could conduct "civili[s]ed" business negotiations. After Kutaragi reminded him of the humiliation he suffered from Nintendo, Ohga retained the project and became one of Kutaragi's most staunch supporters. Ohga shifted Kutaragi and nine of his team from Sony's main headquarters to Sony Music Entertainment Japan (SMEJ), a subsidiary of the main Sony group, so as to retain the project and maintain relationships with Philips for the MMCD development project. The involvement of SMEJ proved crucial to the PlayStation's early development as the process of manufacturing games on CD-ROM format was similar to that used for audio CDs, with which Sony's music division had considerable experience. While at SMEJ, Kutaragi worked with Epic/Sony Records founder Shigeo Maruyama and Akira Sato; both later became vice-presidents of the division that ran the PlayStation business. Sony Computer Entertainment (SCE) was jointly established by Sony and SMEJ to handle the company's ventures into the video game industry. On 27 October 1993, Sony publicly announced that it was entering the game console market with the PlayStation. According to Maruyama, there was uncertainty over whether the console should primarily focus on 2D, sprite-based graphics or 3D polygon graphics. After Sony witnessed the success of Sega's Virtua Fighter (1993) in Japanese arcades, the direction of the PlayStation became "instantly clear" and 3D polygon graphics became the console's primary focus. SCE president Teruhisa Tokunaka expressed gratitude for Sega's timely release of Virtua Fighter as it proved "just at the right time" that making games with 3D imagery was possible. Maruyama claimed that Sony further wanted to emphasise the new console's ability to utilise redbook audio from the CD-ROM format in its games alongside high quality visuals and gameplay. Wishing to distance the project from the failed enterprise with Nintendo, Sony initially branded the PlayStation the "PlayStation X" (PSX). Sony formed their European division and North American division, known as Sony Computer Entertainment Europe (SCEE) and Sony Computer Entertainment America (SCEA), in January and May 1995. The divisions planned to market the new console under the alternative branding "PSX" following the negative feedback regarding "PlayStation" in focus group studies. Early advertising prior to the console's launch in North America referenced PSX, but the term was scrapped before launch. The console was not marketed with Sony's name in contrast to Nintendo's consoles. According to Phil Harrison, much of Sony's upper management feared that the Sony brand would be tarnished if associated with the console, which they considered a "toy". Since Sony had no experience in game development, it had to rely on the support of third-party game developers. This was in contrast to Sega and Nintendo, which had versatile and well-equipped in-house software divisions for their arcade games and could easily port successful games to their home consoles. Recent consoles like the Atari Jaguar and 3DO suffered low sales due to a lack of developer support, prompting Sony to redouble their efforts in gaining the endorsement of arcade-savvy developers. A team from Epic Sony visited more than a hundred companies throughout Japan in May 1993 in hopes of attracting game creators with the PlayStation's technological appeal. Sony found that many disliked Nintendo's practices, such as favouring their own games over others. Through a series of negotiations, Sony acquired initial support from Namco, Konami, and Williams Entertainment, as well as 250 other development teams in Japan alone. Namco in particular was interested in developing for PlayStation since Namco rivalled Sega in the arcade market. Attaining these companies secured influential games such as Ridge Racer (1993) and Mortal Kombat 3 (1995), Ridge Racer being one of the most popular arcade games at the time, and it was already confirmed behind closed doors that it would be the PlayStation's first game by December 1993, despite Namco being a longstanding Nintendo developer. Namco's research managing director Shegeichi Nakamura met with Kutaragi in 1993 to discuss the preliminary PlayStation specifications, with Namco subsequently basing the Namco System 11 arcade board on PlayStation hardware and developing Tekken to compete with Virtua Fighter. The System 11 launched in arcades several months before the PlayStation's release, with the arcade release of Tekken in September 1994. Despite securing the support of various Japanese studios, Sony had no developers of their own by the time the PlayStation was in development. This changed in 1993 when Sony acquired the Liverpudlian company Psygnosis (later renamed SCE Liverpool) for US$48 million, securing their first in-house development team. The acquisition meant that Sony could have more launch games ready for the PlayStation's release in Europe and North America. Ian Hetherington, Psygnosis' co-founder, was disappointed after receiving early builds of the PlayStation and recalled that the console "was not fit for purpose" until his team got involved with it. Hetherington frequently clashed with Sony executives over broader ideas; at one point it was suggested that a television with a built-in PlayStation be produced. In the months leading up to the PlayStation's launch, Psygnosis had around 500 full-time staff working on games and assisting with software development. The purchase of Psygnosis marked another turning point for the PlayStation as it played a vital role in creating the console's development kits. While Sony had provided MIPS R4000-based Sony NEWS workstations for PlayStation development, Psygnosis employees disliked the thought of developing on these expensive workstations and asked Bristol-based SN Systems to create an alternative PC-based development system. Andy Beveridge and Martin Day, owners of SN Systems, had previously supplied development hardware for other consoles such as the Mega Drive, Atari ST, and the SNES. When Psygnosis arranged an audience for SN Systems with Sony's Japanese executives at the January 1994 CES in Las Vegas, Beveridge and Day presented their prototype of the condensed development kit, which could run on an ordinary personal computer with two extension boards. Impressed, Sony decided to abandon their plans for a workstation-based development system in favour of SN Systems's, thus securing a cheaper and more efficient method for designing software. An order of over 600 systems followed, and SN Systems supplied Sony with additional software such as an assembler, linker, and a debugger. SN Systems produced development kits for future PlayStation systems, including the PlayStation 2 and was bought out by Sony in 2005. Sony strived to make game production as streamlined and inclusive as possible, in contrast to the relatively isolated approach of Sega and Nintendo. Phil Harrison, representative director of SCEE, believed that Sony's emphasis on developer assistance reduced most time-consuming aspects of development. As well as providing programming libraries, SCE headquarters in London, California, and Tokyo housed technical support teams that could work closely with third-party developers if needed. Sony did not favour their own over non-Sony products, unlike Nintendo; Peter Molyneux of Bullfrog Productions admired Sony's open-handed approach to software developers and lauded their decision to use PCs as a development platform, remarking that "[it was] like being released from jail in terms of the freedom you have". Another strategy that helped attract software developers was the PlayStation's use of the CD-ROM format instead of traditional cartridges. Nintendo cartridges were expensive to manufacture, and the company controlled all production, prioritising their own games, while inexpensive compact disc manufacturing occurred at dozens of locations around the world. The PlayStation's architecture and interconnectability with PCs was beneficial to many software developers. The use of the programming language C proved useful, as it safeguarded future compatibility of the machine should developers decide to make further hardware revisions. Despite the inherent flexibility, some developers found themselves restricted due to the console's lack of RAM. While working on beta builds of the PlayStation, Molyneux observed that its MIPS processor was not "quite as bullish" compared to that of a fast PC and said that it took his team two weeks to port their PC code to the PlayStation development kits and another fortnight to achieve a four-fold speed increase. An engineer from Ocean Software, one of Europe's largest game developers at the time, thought that allocating RAM was a challenging aspect given the 3.5 megabyte restriction. Kutaragi said that while it would have been easy to double the amount of RAM for the PlayStation, the development team refrained from doing so to keep the retail cost down. Kutaragi saw the biggest challenge in developing the system to be balancing the conflicting goals of high performance, low cost, and being easy to program for, and felt he and his team were successful in this regard. Its technical specifications were finalised in 1993 and its design during 1994. The PlayStation name and its final design were confirmed during a press conference on May 10, 1994, although the price and release dates had not been disclosed yet. Sony released the PlayStation in Japan on 3 December 1994, a week after the release of the Sega Saturn, at a price of ¥39,800. Sales in Japan began with a "stunning" success with long queues in shops. Ohga later recalled that he realised how important PlayStation had become for Sony when friends and relatives begged for consoles for their children. PlayStation sold 100,000 units on the first day and two million units within six months, although the Saturn outsold the PlayStation in the first few weeks due to the success of Virtua Fighter. By the end of 1994, 300,000 PlayStation units were sold in Japan compared to 500,000 Saturn units. A grey market emerged for PlayStations shipped from Japan to North America and Europe, with buyers of such consoles paying up to £700. "When September 1995 arrived and Sony's Playstation roared out of the gate, things immediately felt different than [sic] they did with the Saturn launch earlier that year. Sega dropped the Saturn $100 to match the Playstation's $299 debut price, but sales weren't even close—Playstations flew out the door as fast as we could get them in stock. Before the release in North America, Sega and Sony presented their consoles at the first Electronic Entertainment Expo (E3) in Los Angeles on 11 May 1995. At their keynote presentation, Sega of America CEO Tom Kalinske revealed that their Saturn console would be released immediately to select retailers at a price of $399. Next came Sony's turn: Olaf Olafsson, the head of SCEA, summoned Steve Race, the head of development, to the conference stage, who said "$299" and left the audience with a round of applause. The attention to the Sony conference was further bolstered by the surprise appearance of Michael Jackson and the showcase of highly anticipated games, including Wipeout (1995), Ridge Racer and Tekken (1994). In addition, Sony announced that no games would be bundled with the console. Although the Saturn had released early in the United States to gain an advantage over the PlayStation, the surprise launch upset many retailers who were not informed in time, harming sales. Some retailers such as KB Toys responded by dropping the Saturn entirely. The PlayStation went on sale in North America on 9 September 1995. It sold more units within two days than the Saturn had in five months, with almost all of the initial shipment of 100,000 units sold in advance and shops across the country running out of consoles and accessories. The well-received Ridge Racer contributed to the PlayStation's early success, — with some critics considering it superior to Sega's arcade counterpart Daytona USA (1994) — as did Battle Arena Toshinden (1995). There were over 100,000 pre-orders placed and 17 games available on the market by the time of the PlayStation's American launch, in comparison to the Saturn's six launch games. The PlayStation released in Europe on 29 September 1995 and in Australia on 15 November 1995. By November it had already outsold the Saturn by three to one in the United Kingdom, where Sony had allocated a £20 million marketing budget during the Christmas season compared to Sega's £4 million. Sony found early success in the United Kingdom by securing listings with independent shop owners as well as prominent High Street chains such as Comet and Argos. Within its first year, the PlayStation secured over 20% of the entire American video game market. From September to the end of 1995, sales in the United States amounted to 800,000 units, giving the PlayStation a commanding lead over the other fifth-generation consoles,[b] though the SNES and Mega Drive from the fourth generation still outsold it. Sony reported that the attach rate of sold games and consoles was four to one. To meet increasing demand, Sony chartered jumbo jets and ramped up production in Europe and North America. By early 1996, the PlayStation had grossed $2 billion (equivalent to $4.106 billion 2025) from worldwide hardware and software sales. By late 1996, sales in Europe totalled 2.2 million units, including 700,000 in the UK. Approximately 400 PlayStation games were in development, compared to around 200 games being developed for the Saturn and 60 for the Nintendo 64. In India, the PlayStation was launched in test market during 1999–2000 across Sony showrooms, selling 100 units. Sony finally launched the console (PS One model) countrywide on 24 January 2002 with the price of Rs 7,990 and 26 games available from start. PlayStation was also doing well in markets where it was never officially released. For example, in Brazil, due to the registration of the trademark by a third company, the console could not be released, which was why the market was taken over by the officially distributed Sega Saturn during the first period, but as the Sega console withdraws, PlayStation imports and large piracy increased. In another market, China, the most popular 32-bit console was Sega Saturn, but after leaving the market, PlayStation grown with a base of 300,000 users until January 2000, although Sony China did not have plans to release it. The PlayStation was backed by a successful marketing campaign, allowing Sony to gain an early foothold in Europe and North America. Initially, PlayStation demographics were skewed towards adults, but the audience broadened after the first price drop. While the Saturn was positioned towards 18- to 34-year-olds, the PlayStation was initially marketed exclusively towards teenagers. Executives from both Sony and Sega reasoned that because younger players typically looked up to older, more experienced players, advertising targeted at teens and adults would draw them in too. Additionally, Sony found that adults reacted best to advertising aimed at teenagers; Lee Clow surmised that people who started to grow into adulthood regressed and became "17 again" when they played video games. The console was marketed with advertising slogans stylised as "LIVE IN YUR WRLD. PLY IN URS" (Live in Your World. Play in Ours.) and "U R NOT E" (red E). The four geometric shapes were derived from the symbols for the four buttons on the controller. Clow thought that by invoking such provocative statements, gamers would respond to the contrary and say "'Bullshit. Let me show you how ready I am.'" As the console's appeal enlarged, Sony's marketing efforts broadened from their earlier focus on mature players to specifically target younger children as well. Shortly after the PlayStation's release in Europe, Sony tasked marketing manager Geoff Glendenning with assessing the desires of a new target audience. Sceptical over Nintendo and Sega's reliance on television campaigns, Glendenning theorised that young adults transitioning from fourth-generation consoles would feel neglected by marketing directed at children and teenagers. Recognising the influence early 1990s underground clubbing and rave culture had on young people, especially in the United Kingdom, Glendenning felt that the culture had become mainstream enough to help cultivate PlayStation's emerging identity. Sony partnered with prominent nightclub owners such as Ministry of Sound and festival promoters to organise dedicated PlayStation areas where demonstrations of select games could be tested. Sheffield-based graphic design studio The Designers Republic was contracted by Sony to produce promotional materials aimed at a fashionable, club-going audience. Psygnosis' Wipeout in particular became associated with nightclub culture as it was widely featured in venues. By 1997, there were 52 nightclubs in the United Kingdom with dedicated PlayStation rooms. Glendenning recalled that he had discreetly used at least £100,000 a year in slush fund money to invest in impromptu marketing. In 1996, Sony expanded their CD production facilities in the United States due to the high demand for PlayStation games, increasing their monthly output from 4 million discs to 6.5 million discs. This was necessary because PlayStation sales were running at twice the rate of Saturn sales, and its lead dramatically increased when both consoles dropped in price to $199 that year. The PlayStation also outsold the Saturn at a similar ratio in Europe during 1996, with 2.2 million consoles sold in the region by the end of the year. Sales figures for PlayStation hardware and software only increased following the launch of the Nintendo 64. Tokunaka speculated that the Nintendo 64 launch had actually helped PlayStation sales by raising public awareness of the gaming market through Nintendo's added marketing efforts. Despite this, the PlayStation took longer to achieve dominance in Japan. Tokunaka said that, even after the PlayStation and Saturn had been on the market for nearly two years, the competition between them was still "very close", and neither console had led in sales for any meaningful length of time. By 1998, Sega, encouraged by their declining market share and significant financial losses, launched the Dreamcast as a last-ditch attempt to stay in the industry. Although its launch was successful, the technically superior 128-bit console was unable to subdue Sony's dominance in the industry. Sony still held 60% of the overall video game market share in North America at the end of 1999. Sega's initial confidence in their new console was undermined when Japanese sales were lower than expected, with disgruntled Japanese consumers reportedly returning their Dreamcasts in exchange for PlayStation software. On 2 March 1999, Sony officially revealed details of the PlayStation 2, which Kutaragi announced would feature a graphics processor designed to push more raw polygons than any console in history, effectively rivalling most supercomputers. The PlayStation continued to sell strongly at the turn of the new millennium: in June 2000, Sony released the PSOne, a smaller, redesigned variant which went on to outsell all other consoles in that year, including the PlayStation 2. In 2005, PlayStation became the first console to ship 100 million units with the PlayStation 2 later achieving this faster than its predecessor. The combined successes of both PlayStation consoles led to Sega retiring the Dreamcast in 2001, and abandoning the console business entirely. The PlayStation was eventually discontinued on 23 March 2006—over eleven years after its release, and less than a year before the debut of the PlayStation 3. Hardware The main microprocessor is a R3000 CPU made by LSI Logic operating at a clock rate of 33.8688 MHz and 30 MIPS. This 32-bit CPU relies heavily on the "cop2" 3D and matrix math coprocessor on the same die to provide the necessary speed to render complex 3D graphics. The role of the separate GPU chip is to draw 2D polygons and apply shading and textures to them: the rasterisation stage of the graphics pipeline. Sony's custom 16-bit sound chip supports ADPCM sources with up to 24 sound channels and offers a sampling rate of up to 44.1 kHz and music sequencing. It features 2 MB of main RAM, with an additional 1 MB of video RAM. The PlayStation has a maximum colour depth of 16.7 million true colours with 32 levels of transparency and unlimited colour look-up tables. The PlayStation can output composite, S-Video or RGB video signals through its AV Multi connector (with older models also having RCA connectors for composite), displaying resolutions from 256×224 to 640×480 pixels. Different games can use different resolutions. Earlier models also had proprietary parallel and serial ports that could be used to connect accessories or multiple consoles together; these were later removed due to a lack of usage. The PlayStation uses a proprietary video compression unit, MDEC, which is integrated into the CPU and allows for the presentation of full motion video at a higher quality than other consoles of its generation. Unusual for the time, the PlayStation lacks a dedicated 2D graphics processor; 2D elements are instead calculated as polygons by the Geometry Transfer Engine (GTE) so that they can be processed and displayed on screen by the GPU. While running, the GPU can also generate a total of 4,000 sprites and 180,000 polygons per second, in addition to 360,000 per second flat-shaded. The PlayStation went through a number of variants during its production run. Externally, the most notable change was the gradual reduction in the number of external connectors from the rear of the unit. This started with the original Japanese launch units; the SCPH-1000, released on 3 December 1994, was the only model that had an S-Video port, as it was removed from the next model. Subsequent models saw a reduction in number of parallel ports, with the final version only retaining one serial port. Sony marketed a development kit for amateur developers known as the Net Yaroze (meaning "Let's do it together" in Japanese). It was launched in June 1996 in Japan, and following public interest, was released the next year in other countries. The Net Yaroze allowed hobbyists to create their own games and upload them via an online forum run by Sony. The console was only available to buy through an ordering service and with the necessary documentation and software to program PlayStation games and applications through C programming compilers. On 7 July 2000, Sony released the PS One (stylised as "PS one" or "PSone"), a smaller, redesigned version of the original PlayStation. It was the highest-selling console through the end of the year, outselling all other consoles—including the PlayStation 2. In 2002, Sony released a 5-inch (130 mm) LCD screen add-on for the PS One, referred to as the "Combo pack". It also included a car cigarette lighter adaptor adding an extra layer of portability. Production of the LCD "Combo Pack" ceased in 2004, when the popularity of the PlayStation began to wane in markets outside Japan. A total of 28.15 million PS One units had been sold by the time it was discontinued in March 2006. Three iterations of the PlayStation's controller were released over the console's lifespan. The first controller, the PlayStation controller, was released alongside the PlayStation in December 1994. It features four individual directional buttons (as opposed to a conventional D-pad), a pair of shoulder buttons on both sides, Start and Select buttons in the centre, and four face buttons consisting of simple geometric shapes: a green triangle, red circle, blue cross, and a pink square (, , , ). Rather than depicting traditionally used letters or numbers onto its buttons, the PlayStation controller established a trademark which would be incorporated heavily into the PlayStation brand. Teiyu Goto, the designer of the original PlayStation controller, said that the circle and cross represent "yes" and "no", respectively (though this layout is reversed in Western versions); the triangle symbolises a point of view and the square is equated to a sheet of paper to be used to access menus. The European and North American models of the original PlayStation controllers are roughly 10% larger than its Japanese variant, to account for the fact the average person in those regions has larger hands than the average Japanese person. Sony's first analogue gamepad, the PlayStation Analog Joystick (often erroneously referred to as the "Sony Flightstick"), was first released in Japan in April 1996. Featuring two parallel joysticks, it uses potentiometer technology previously used on consoles such as the Vectrex; instead of relying on binary eight-way switches, the controller detects minute angular changes through the entire range of motion. The stick also features a thumb-operated digital hat switch on the right joystick, corresponding to the traditional D-pad, and used for instances when simple digital movements were necessary. The Analog Joystick sold poorly in Japan due to its high cost and cumbersome size. The increasing popularity of 3D games prompted Sony to add analogue sticks to its controller design to give users more freedom over their movements in virtual 3D environments. The first official analogue controller, the Dual Analog Controller, was revealed to the public in a small glass booth at the 1996 PlayStation Expo in Japan, and released in April 1997 to coincide with the Japanese releases of analogue-capable games Tobal 2 and Bushido Blade. In addition to the two analogue sticks (which also introduced two new buttons mapped to clicking in the analogue sticks), the Dual Analog controller features an "Analog" button and LED beneath the "Start" and "Select" buttons which toggles analogue functionality on or off. The controller also features rumble support, though Sony decided that haptic feedback would be removed from all overseas iterations before the United States release. A Sony spokesman stated that the feature was removed for "manufacturing reasons", although rumours circulated that Nintendo had attempted to legally block the release of the controller outside Japan due to similarities with the Nintendo 64 controller's Rumble Pak. However, a Nintendo spokesman denied that Nintendo took legal action. Next Generation's Chris Charla theorised that Sony dropped vibration feedback to keep the price of the controller down. In November 1997, Sony introduced the DualShock controller. Its name derives from its use of two (dual) vibration motors (shock). Unlike its predecessor, its analogue sticks feature textured rubber grips, longer handles, slightly different shoulder buttons and has rumble feedback included as standard on all versions. The DualShock later replaced its predecessors as the default controller. Sony released a series of peripherals to add extra layers of functionality to the PlayStation. Such peripherals include memory cards, the PlayStation Mouse, the PlayStation Link Cable, the Multiplayer Adapter (a four-player multitap), the Memory Drive (a disk drive for 3.5-inch floppy disks), the GunCon (a light gun), and the Glasstron (a monoscopic head-mounted display). Released exclusively in Japan, the PocketStation is a memory card peripheral which acts as a miniature personal digital assistant. The device features a monochrome liquid crystal display (LCD), infrared communication capability, a real-time clock, built-in flash memory, and sound capability. Sharing similarities with the Dreamcast's VMU peripheral, the PocketStation was typically distributed with certain PlayStation games, enhancing them with added features. The PocketStation proved popular in Japan, selling over five million units. Sony planned to release the peripheral outside Japan but the release was cancelled, despite receiving promotion in Europe and North America. In addition to playing games, most PlayStation models are equipped to play CD-Audio. The Asian model SCPH-5903 can also play Video CDs. Like most CD players, the PlayStation can play songs in a programmed order, shuffle the playback order of the disc and repeat one song or the entire disc. Later PlayStation models use a music visualisation function called SoundScope. This function, as well as a memory card manager, is accessed by starting the console without either inserting a game or closing the CD tray, thereby accessing a graphical user interface (GUI) for the PlayStation BIOS. The GUI for the PS One and PlayStation differ depending on the firmware version: the original PlayStation GUI had a dark blue background with rainbow graffiti used as buttons, while the early PAL PlayStation and PS One GUI had a grey blocked background with two icons in the middle. PlayStation emulation is versatile and can be run on numerous modern devices. Bleem! was a commercial emulator which was released for IBM-compatible PCs and the Dreamcast in 1999. It was notable for being aggressively marketed during the PlayStation's lifetime, and was the centre of multiple controversial lawsuits filed by Sony. Bleem! was programmed in assembly language, which allowed it to emulate PlayStation games with improved visual fidelity, enhanced resolutions, and filtered textures that was not possible on original hardware. Sony sued Bleem! two days after its release, citing copyright infringement and accusing the company of engaging in unfair competition and patent infringement by allowing use of PlayStation BIOSs on a Sega console. Bleem! were subsequently forced to shut down in November 2001. Sony was aware that using CDs for game distribution could have left games vulnerable to piracy, due to the growing popularity of CD-R and optical disc drives with burning capability. To preclude illegal copying, a proprietary process for PlayStation disc manufacturing was developed that, in conjunction with an augmented optical drive in Tiger H/E assembly, prevented burned copies of games from booting on an unmodified console. Specifically, all genuine PlayStation discs were printed with a small section of deliberate irregular data, which the PlayStation's optical pick-up was capable of detecting and decoding. Consoles would not boot game discs without a specific wobble frequency contained in the data of the disc pregap sector (the same system was also used to encode discs' regional lockouts). This signal was within Red Book CD tolerances, so PlayStation discs' actual content could still be read by a conventional disc drive; however, the disc drive could not detect the wobble frequency (therefore duplicating the discs omitting it), since the laser pick-up system of any optical disc drive would interpret this wobble as an oscillation of the disc surface and compensate for it in the reading process. Early PlayStations, particularly early 1000 models, experience skipping full-motion video or physical "ticking" noises from the unit. The problems stem from poorly placed vents leading to overheating in some environments, causing the plastic mouldings inside the console to warp slightly and create knock-on effects with the laser assembly. The solution is to sit the console on a surface which dissipates heat efficiently in a well vented area or raise the unit up slightly from its resting surface. Sony representatives also recommended unplugging the PlayStation when it is not in use, as the system draws in a small amount of power (and therefore heat) even when turned off. The first batch of PlayStations use a KSM-440AAM laser unit, whose case and movable parts are all built out of plastic. Over time, the plastic lens sled rail wears out—usually unevenly—due to friction. The placement of the laser unit close to the power supply accelerates wear, due to the additional heat, which makes the plastic more vulnerable to friction. Eventually, one side of the lens sled will become so worn that the laser can tilt, no longer pointing directly at the CD; after this, games will no longer load due to data read errors. Sony fixed the problem by making the sled out of die-cast metal and placing the laser unit further away from the power supply on later PlayStation models. Due to an engineering oversight, the PlayStation does not produce a proper signal on several older models of televisions, causing the display to flicker or bounce around the screen. Sony decided not to change the console design, since only a small percentage of PlayStation owners used such televisions, and instead gave consumers the option of sending their PlayStation unit to a Sony service centre to have an official modchip installed, allowing play on older televisions. Game library The PlayStation featured a diverse game library which grew to appeal to all types of players. Critically acclaimed PlayStation games included Final Fantasy VII (1997), Crash Bandicoot (1996), Spyro the Dragon (1998), Metal Gear Solid (1998), all of which became established franchises. Final Fantasy VII is credited with allowing role-playing games to gain mass-market appeal outside Japan, and is considered one of the most influential and greatest video games ever made. The PlayStation's bestselling game is Gran Turismo (1997), which sold 10.85 million units. After the PlayStation's discontinuation in 2006, the cumulative software shipment was 962 million units. Following its 1994 launch in Japan, early games included Ridge Racer, Crime Crackers, King's Field, Motor Toon Grand Prix, Toh Shin Den (i.e. Battle Arena Toshinden), and Kileak: The Blood. The first two games available at its later North American launch were Jumping Flash! (1995) and Ridge Racer, with Jumping Flash! heralded as an ancestor for 3D graphics in console gaming. Wipeout, Air Combat, Twisted Metal, Warhawk and Destruction Derby were among the popular first-year games, and the first to be reissued as part of Sony's Greatest Hits or Platinum range. At the time of the PlayStation's first Christmas season, Psygnosis had produced around 70% of its launch catalogue; their breakthrough racing game Wipeout was acclaimed for its techno soundtrack and helped raise awareness of Britain's underground music community. Eidos Interactive's action-adventure game Tomb Raider contributed substantially to the success of the console in 1996, with its main protagonist Lara Croft becoming an early gaming icon and garnering unprecedented media promotion. Licensed tie-in video games of popular films were also prevalent; Argonaut Games' 2001 adaptation of Harry Potter and the Philosopher's Stone went on to sell over eight million copies late in the console's lifespan. Third-party developers committed largely to the console's wide-ranging game catalogue even after the launch of the PlayStation 2; some of the notable exclusives in this era include Harry Potter and the Philosopher's Stone, Fear Effect 2: Retro Helix, Syphon Filter 3, C-12: Final Resistance, Dance Dance Revolution Konamix and Digimon World 3.[c] Sony assisted with game reprints as late as 2008 with Metal Gear Solid: The Essential Collection, this being the last PlayStation game officially released and licensed by Sony. Initially, in the United States, PlayStation games were packaged in long cardboard boxes, similar to non-Japanese 3DO and Saturn games. Sony later switched to the jewel case format typically used for audio CDs and Japanese video games, as this format took up less retailer shelf space (which was at a premium due to the large number of PlayStation games being released), and focus testing showed that most consumers preferred this format. Reception The PlayStation was mostly well received upon release. Critics in the west generally welcomed the new console; the staff of Next Generation reviewed the PlayStation a few weeks after its North American launch, where they commented that, while the CPU is "fairly average", the supplementary custom hardware, such as the GPU and sound processor, is stunningly powerful. They praised the PlayStation's focus on 3D, and complemented the comfort of its controller and the convenience of its memory cards. Giving the system 41⁄2 out of 5 stars, they concluded, "To succeed in this extremely cut-throat market, you need a combination of great hardware, great games, and great marketing. Whether by skill, luck, or just deep pockets, Sony has scored three out of three in the first salvo of this war." Albert Kim from Entertainment Weekly praised the PlayStation as a technological marvel, rivalling that of Sega and Nintendo. Famicom Tsūshin scored the console a 19 out of 40, lower than the Saturn's 24 out of 40, in May 1995. In a 1997 year-end review, a team of five Electronic Gaming Monthly editors gave the PlayStation scores of 9.5, 8.5, 9.0, 9.0, and 9.5—for all five editors, the highest score they gave to any of the five consoles reviewed in the issue. They lauded the breadth and quality of the games library, saying it had vastly improved over previous years due to developers mastering the system's capabilities in addition to Sony revising their stance on 2D and role playing games. They also complimented the low price point of the games compared to the Nintendo 64's, and noted that it was the only console on the market that could be relied upon to deliver a solid stream of games for the coming year, primarily due to third party developers almost unanimously favouring it over its competitors. Legacy SCE was an upstart in the video game industry in late 1994, as the video game market in the early 1990s was dominated by Nintendo and Sega. Nintendo had been the clear leader in the industry since the introduction of the Nintendo Entertainment System in 1985 and the Nintendo 64 was initially expected to maintain this position. The PlayStation's target audience included the generation which was the first to grow up with mainstream video games, along with 18- to 29-year-olds who were not the primary focus of Nintendo. By the late 1990s, Sony became a highly regarded console brand due to the PlayStation, with a significant lead over second-place Nintendo, while Sega was relegated to a distant third. The PlayStation became the first "computer entertainment platform" to ship over 100 million units worldwide, with many critics attributing the console's success to third-party developers. It remains the sixth best-selling console of all time as of 2025[update], with a total of 102.49 million units sold. Around 7,900 individual games were published for the console during its 11-year life span, the second-most games ever produced for a console. Its success resulted in a significant financial boon for Sony as profits from their video game division contributed to 23%. Sony's next-generation PlayStation 2, which is backward compatible with the PlayStation's DualShock controller and games, was announced in 1999 and launched in 2000. The PlayStation's lead in installed base and developer support paved the way for the success of its successor, which overcame the earlier launch of the Sega's Dreamcast and then fended off competition from Microsoft's newcomer Xbox and Nintendo's GameCube. The PlayStation 2's immense success and failure of the Dreamcast were among the main factors which led to Sega abandoning the console market. To date, five PlayStation home consoles have been released, which have continued the same numbering scheme, as well as two portable systems. The PlayStation 3 also maintained backward compatibility with original PlayStation discs. Hundreds of PlayStation games have been digitally re-released on the PlayStation Portable, PlayStation 3, PlayStation Vita, PlayStation 4, and PlayStation 5. The PlayStation has often ranked among the best video game consoles. In 2018, Retro Gamer named it the third best console, crediting its sophisticated 3D capabilities as one of its key factors in gaining mass success, and lauding it as a "game-changer in every sense possible". In 2009, IGN ranked the PlayStation the seventh best console in their list, noting its appeal towards older audiences to be a crucial factor in propelling the video game industry, as well as its assistance in transitioning game industry to use the CD-ROM format. Keith Stuart from The Guardian likewise named it as the seventh best console in 2020, declaring that its success was so profound it "ruled the 1990s". In January 2025, Lorentio Brodesco announced the nsOne project, attempting to reverse engineer PlayStation's motherboard. Brodesco stated that "detailed documentation on the original motherboard was either incomplete or entirely unavailable". The project was successfully crowdfunded via Kickstarter. In June, Brodesco manufactured the first working motherboard, promising to bring a fully rooted version with multilayer routing as well as documentation and design files in the near future. The success of the PlayStation contributed to the demise of cartridge-based home consoles. While not the first system to use an optical disc format, it was the first highly successful one, and ended up going head-to-head with the proprietary cartridge-relying Nintendo 64,[d] which the industry had expected to use CDs like PlayStation. After the demise of the Sega Saturn, Nintendo was left as Sony's main competitor in Western markets. Nintendo chose not to use CDs for the Nintendo 64; they were likely concerned with the proprietary cartridge format's ability to help enforce copy protection, given their substantial reliance on licensing and exclusive games for their revenue. Besides their larger capacity, CD-ROMs could be produced in bulk quantities at a much faster rate than ROM cartridges, a week compared to two to three months. Further, the cost of production per unit was far cheaper, allowing Sony to offer games about 40% lower cost to the user compared to ROM cartridges while still making the same amount of net revenue. In Japan, Sony published fewer copies of a wide variety of games for the PlayStation as a risk-limiting step, a model that had been used by Sony Music for CD audio discs. The production flexibility of CD-ROMs meant that Sony could produce larger volumes of popular games to get onto the market quickly, something that could not be done with cartridges due to their manufacturing lead time. The lower production costs of CD-ROMs also allowed publishers an additional source of profit: budget-priced reissues of games which had already recouped their development costs. Tokunaka remarked in 1996: Choosing CD-ROM is one of the most important decisions that we made. As I'm sure you understand, PlayStation could just as easily have worked with masked ROM [cartridges]. The 3D engine and everything—the whole PlayStation format—is independent of the media. But for various reasons (including the economies for the consumer, the ease of the manufacturing, inventory control for the trade, and also the software publishers) we deduced that CD-ROM would be the best media for PlayStation. The increasing complexity of developing games pushed cartridges to their storage limits and gradually discouraged some third-party developers. Part of the CD format's appeal to publishers was that they could be produced at a significantly lower cost and offered more production flexibility to meet demand. As a result, some third-party developers switched to the PlayStation, including Square and Enix, whose Final Fantasy VII and Dragon Quest VII respectively had been planned for the Nintendo 64 (both companies later merged to form Square Enix). Other developers released fewer games for the Nintendo 64 (Konami, releasing only thirteen N64 games but over fifty on the PlayStation). Nintendo 64 game releases were less frequent than the PlayStation's, with many being developed by either Nintendo themselves or second-parties such as Rare. The PlayStation Classic is a dedicated video game console made by Sony Interactive Entertainment that emulates PlayStation games. It was announced in September 2018 at the Tokyo Game Show, and released on 3 December 2018, the 24th anniversary of the release of the original console. As a dedicated console, the PlayStation Classic features 20 pre-installed games; the games run off the open source emulator PCSX. The console is bundled with two replica wired PlayStation controllers (those without analogue sticks), an HDMI cable, and a USB-Type A cable. Internally, the console uses a MediaTek MT8167a Quad A35 system on a chip with four central processing cores clocked at @ 1.5 GHz and a Power VR GE8300 graphics processing unit. It includes 16 GB of eMMC flash storage and 1 Gigabyte of DDR3 SDRAM. The PlayStation Classic is 45% smaller than the original console. The PlayStation Classic received negative reviews from critics and was compared unfavorably to Nintendo's rival Nintendo Entertainment System Classic Edition and Super Nintendo Entertainment System Classic Edition. Criticism was directed at its meagre game library, user interface, emulation quality, use of PAL versions for certain games, use of the original controller, and high retail price, though the console's design received praise. The console sold poorly. See also Notes References |
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[SOURCE: https://en.wikipedia.org/wiki/Minkowski_space] | [TOKENS: 19597] |
Contents Minkowski space In physics, Minkowski space (or Minkowski spacetime) (/mɪŋˈkɔːfski, -ˈkɒf-/) is the main mathematical description of spacetime in the absence of gravitation. It combines inertial space and time manifolds into a four-dimensional model. The model helps show how a spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded. Mathematician Hermann Minkowski developed it from the work of Hendrik Lorentz, Henri Poincaré, and others, and said it "was grown on experimental physical grounds". Minkowski space is closely associated with Einstein's theories of special relativity and general relativity and is the most common mathematical structure by which special relativity is formalized. While the individual components in Euclidean space and time might differ due to length contraction and time dilation, in Minkowski spacetime, all frames of reference will agree on the total interval in spacetime between events.[nb 1] Minkowski space differs from four-dimensional Euclidean space insofar as it treats time differently from the three spatial dimensions. In 3-dimensional Euclidean space, the isometry group (maps preserving the regular Euclidean distance) is the Euclidean group. It is generated by rotations, reflections and translations. When time is appended as a fourth dimension, the further transformations of translations in time and Lorentz boosts are added, and the group of all these transformations is called the Poincaré group. Minkowski's model follows special relativity, where motion causes time dilation changing the scale applied to the frame in motion and shifts the phase of light. Minkowski space is a pseudo-Euclidean space equipped with an isotropic quadratic form called the spacetime interval or the Minkowski norm squared. An event in Minkowski space for which the spacetime interval is zero is on the null cone of the origin, called the light cone in Minkowski space. Using the polarization identity the quadratic form is converted to a symmetric bilinear form called the Minkowski inner product, though it is not a geometric inner product. Another misnomer is Minkowski metric,[further explanation needed] but Minkowski space is not a metric space. The group of transformations for Minkowski space that preserves the spacetime interval (as opposed to the spatial Euclidean distance) is the Lorentz group (as opposed to the Galilean group). History In his second relativity paper in 1905, Henri Poincaré showed how, by taking time to be an imaginary fourth spacetime coordinate ict, where c is the speed of light and i is the imaginary unit, Lorentz transformations can be visualized as ordinary rotations of the four-dimensional Euclidean sphere. The four-dimensional spacetime can be visualized as a four-dimensional space, with each point representing an event in spacetime. The Lorentz transformations can then be thought of as rotations in this four-dimensional space, where the rotation axis corresponds to the direction of relative motion between the two observers and the rotation angle is related to their relative velocity. To understand this concept, one should consider the coordinates of an event in spacetime represented as a four-vector (t, x, y, z). A Lorentz transformation is represented by a matrix that acts on the four-vector, changing its components. This matrix can be thought of as a rotation matrix in four-dimensional space, which rotates the four-vector around a particular axis. x 2 + y 2 + z 2 + ( i c t ) 2 = constant . {\displaystyle x^{2}+y^{2}+z^{2}+(ict)^{2}={\text{constant}}.} Rotations in planes spanned by two space unit vectors appear in coordinate space as well as in physical spacetime as Euclidean rotations and are interpreted in the ordinary sense. The "rotation" in a plane spanned by a space unit vector and a time unit vector, while formally still a rotation in coordinate space, is a Lorentz boost in physical spacetime with real inertial coordinates. The analogy with Euclidean rotations is only partial since the radius of the sphere is actually imaginary, which turns rotations into rotations in hyperbolic space (see hyperbolic rotation). This idea, which was mentioned only briefly by Poincaré, was elaborated by Minkowski in a paper in German published in 1908 called "The Fundamental Equations for Electromagnetic Processes in Moving Bodies". He reformulated Maxwell equations as a symmetrical set of equations in the four variables (x, y, z, ict) combined with redefined vector variables for electromagnetic quantities, and he was able to show directly and very simply their invariance under Lorentz transformation. He also made other important contributions and used matrix notation for the first time in this context. From his reformulation, he concluded that time and space should be treated equally, and so arose his concept of events taking place in a unified four-dimensional spacetime continuum. In a further development in his 1908 "Space and Time" lecture, Minkowski gave an alternative formulation of this idea that used a real time coordinate instead of an imaginary one, representing the four variables (x, y, z, t) of space and time in the coordinate form in a four-dimensional real vector space. Points in this space correspond to events in spacetime. In this space, there is a defined light-cone associated with each point, and events not on the light cone are classified by their relation to the apex as spacelike or timelike. It is principally this view of spacetime that is current nowadays, although the older view involving imaginary time has also influenced special relativity. In the English translation of Minkowski's paper, the Minkowski metric, as defined below, is referred to as the line element. The Minkowski inner product below appears unnamed when referring to orthogonality (which he calls normality) of certain vectors, and the Minkowski norm squared is referred to as "sum" (a word choice that might be attributable to language translation). Minkowski's principal tool is the Minkowski diagram, and he uses it to define concepts and demonstrate properties of Lorentz transformations (e.g., proper time and length contraction) and to provide geometrical interpretation to the generalization of Newtonian mechanics to relativistic mechanics. For these special topics, see the referenced articles, as the presentation below will be principally confined to the mathematical structure (Minkowski metric and from it derived quantities and the Poincaré group as symmetry group of spacetime) following from the invariance of the spacetime interval on the spacetime manifold as consequences of the postulates of special relativity, not to specific application or derivation of the invariance of the spacetime interval. This structure provides the background setting of all present relativistic theories, barring general relativity for which flat Minkowski spacetime still provides a springboard as curved spacetime is locally Lorentzian. Minkowski, aware of the fundamental restatement of the theory which he had made, said The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth, space by itself and time by itself are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality. — Hermann Minkowski, 1908, 1909 Though Minkowski took an important step for physics, Albert Einstein saw its limitation: At a time when Minkowski was giving the geometrical interpretation of special relativity by extending the Euclidean three-space to a quasi-Euclidean four-space that included time, Einstein was already aware that this is not valid, because it excludes the phenomenon of gravitation. He was still far from the study of curvilinear coordinates and Riemannian geometry, and the heavy mathematical apparatus entailed. For further historical information see references Galison (1979), Corry (1997) and Walter (1999). Causal structure Where v is velocity, x, y, and z are Cartesian coordinates in 3-dimensional space, c is the constant representing the universal speed limit, and t is time, the four-dimensional vector v = (ct, x, y, z) = (ct, r) is classified according to the sign of c2t2 − r2. A vector is timelike if c2t2 > r2, spacelike if c2t2 < r2, and null or lightlike if c2t2 = r2. This can be expressed in terms of the sign of η(v, v), also called scalar product, as well, which depends on the signature. The classification of any vector will be the same in all frames of reference that are related by a Lorentz transformation (but not by a general Poincaré transformation because the origin may then be displaced) because of the invariance of the spacetime interval under Lorentz transformation. The set of all null vectors at an event[nb 2] of Minkowski space constitutes the light cone of that event. Given a timelike vector v, there is a worldline of constant velocity associated with it, represented by a straight line in a Minkowski diagram. Once a direction of time is chosen,[nb 3] timelike and null vectors can be further decomposed into various classes. For timelike vectors, one has Null vectors fall into three classes: Together with spacelike vectors, there are 6 classes in all. An orthonormal basis for Minkowski space necessarily consists of one timelike and three spacelike unit vectors. If one wishes to work with non-orthonormal bases, it is possible to have other combinations of vectors. For example, one can easily construct a (non-orthonormal) basis consisting entirely of null vectors, called a null basis. Vector fields are called timelike, spacelike, or null if the associated vectors are timelike, spacelike, or null at each point where the field is defined. Properties of time-like vectors Time-like vectors have special importance in the theory of relativity as they correspond to events that are accessible to the observer at (0, 0, 0, 0) with a speed less than that of light. Of most interest are time-like vectors that are similarly directed, i.e. all either in the forward or in the backward cones. Such vectors have several properties not shared by space-like vectors. These arise because both forward and backward cones are convex, whereas the space-like region is not convex. The scalar product of two time-like vectors u1 = (t1, x1, y1, z1) and u2 = (t2, x2, y2, z2) is η ( u 1 , u 2 ) = u 1 ⋅ u 2 = c 2 t 1 t 2 − x 1 x 2 − y 1 y 2 − z 1 z 2 . {\displaystyle \eta (u_{1},u_{2})=u_{1}\cdot u_{2}=c^{2}t_{1}t_{2}-x_{1}x_{2}-y_{1}y_{2}-z_{1}z_{2}.} Positivity of scalar product: An important property is that the scalar product of two similarly directed time-like vectors is always positive. This can be seen from the reversed Cauchy–Schwarz inequality below. It follows that if the scalar product of two vectors is zero, then one of these, at least, must be space-like. The scalar product of two space-like vectors can be positive or negative as can be seen by considering the product of two space-like vectors having orthogonal spatial components and times either of different or the same signs. Using the positivity property of time-like vectors, it is easy to verify that a linear sum with positive coefficients of similarly directed time-like vectors is also similarly directed time-like (the sum remains within the light cone because of convexity). The norm of a time-like vector u = (ct, x, y, z) is defined as ‖ u ‖ = η ( u , u ) = c 2 t 2 − x 2 − y 2 − z 2 {\displaystyle \left\|u\right\|={\sqrt {\eta (u,u)}}={\sqrt {c^{2}t^{2}-x^{2}-y^{2}-z^{2}}}} The reversed Cauchy inequality is another consequence of the convexity of either light cone. For two distinct similarly directed time-like vectors u1 and u2 this inequality is η ( u 1 , u 2 ) > ‖ u 1 ‖ ‖ u 2 ‖ {\displaystyle \eta (u_{1},u_{2})>\left\|u_{1}\right\|\left\|u_{2}\right\|} or algebraically, c 2 t 1 t 2 − x 1 x 2 − y 1 y 2 − z 1 z 2 > ( c 2 t 1 2 − x 1 2 − y 1 2 − z 1 2 ) ( c 2 t 2 2 − x 2 2 − y 2 2 − z 2 2 ) {\displaystyle c^{2}t_{1}t_{2}-x_{1}x_{2}-y_{1}y_{2}-z_{1}z_{2}>{\sqrt {\left(c^{2}t_{1}^{2}-x_{1}^{2}-y_{1}^{2}-z_{1}^{2}\right)\left(c^{2}t_{2}^{2}-x_{2}^{2}-y_{2}^{2}-z_{2}^{2}\right)}}} From this, the positive property of the scalar product can be seen. For two similarly directed time-like vectors u and w, the inequality is ‖ u + w ‖ ≥ ‖ u ‖ + ‖ w ‖ , {\displaystyle \left\|u+w\right\|\geq \left\|u\right\|+\left\|w\right\|,} where the equality holds when the vectors are linearly dependent. The proof uses the algebraic definition with the reversed Cauchy inequality: ‖ u + w ‖ 2 = ‖ u ‖ 2 + 2 ( u , w ) + ‖ w ‖ 2 ≥ ‖ u ‖ 2 + 2 ‖ u ‖ ‖ w ‖ + ‖ w ‖ 2 = ( ‖ u ‖ + ‖ w ‖ ) 2 . {\displaystyle {\begin{aligned}\left\|u+w\right\|^{2}&=\left\|u\right\|^{2}+2\left(u,w\right)+\left\|w\right\|^{2}\\[5mu]&\geq \left\|u\right\|^{2}+2\left\|u\right\|\left\|w\right\|+\left\|w\right\|^{2}=\left(\left\|u\right\|+\left\|w\right\|\right)^{2}.\end{aligned}}} The result now follows by taking the square root on both sides. Mathematical structure It is assumed below that spacetime is endowed with a coordinate system corresponding to an inertial frame. This provides an origin, which is necessary for spacetime to be modeled as a vector space. This addition is not required, and more complex treatments analogous to an affine space can remove the extra structure. However, this is not the introductory convention and is not covered here. For an overview, Minkowski space is a 4-dimensional real vector space equipped with a non-degenerate, symmetric bilinear form on the tangent space at each point in spacetime, here simply called the Minkowski inner product, with metric signature either (+ − − −) or (− + + +). The tangent space at each event is a vector space of the same dimension as spacetime, 4. In practice, one need not be concerned with the tangent spaces. The vector space structure of Minkowski space allows for the canonical identification of vectors in tangent spaces at points (events) with vectors (points, events) in Minkowski space itself. See e.g. Lee (2003, Proposition 3.8.) or Lee (2012, Proposition 3.13.) These identifications are routinely done in mathematics. They can be expressed formally in Cartesian coordinates as ( x 0 , x 1 , x 2 , x 3 ) ↔ x 0 e 0 | p + x 1 e 1 | p + x 2 e 2 | p + x 3 e 3 | p ↔ x 0 e 0 | q + x 1 e 1 | q + x 2 e 2 | q + x 3 e 3 | q {\displaystyle {\begin{aligned}\left(x^{0},\,x^{1},\,x^{2},\,x^{3}\right)\ &\leftrightarrow \ \left.x^{0}\mathbf {e} _{0}\right|_{p}+\left.x^{1}\mathbf {e} _{1}\right|_{p}+\left.x^{2}\mathbf {e} _{2}\right|_{p}+\left.x^{3}\mathbf {e} _{3}\right|_{p}\\&\leftrightarrow \ \left.x^{0}\mathbf {e} _{0}\right|_{q}+\left.x^{1}\mathbf {e} _{1}\right|_{q}+\left.x^{2}\mathbf {e} _{2}\right|_{q}+\left.x^{3}\mathbf {e} _{3}\right|_{q}\end{aligned}}} with basis vectors in the tangent spaces defined by e μ | p = ∂ ∂ x μ | p or e 0 | p = ( 1 0 0 0 ) , etc . {\displaystyle \left.\mathbf {e} _{\mu }\right|_{p}=\left.{\frac {\partial }{\partial x^{\mu }}}\right|_{p}{\text{ or }}\mathbf {e} _{0}|_{p}=\left({\begin{matrix}1\\0\\0\\0\end{matrix}}\right){\text{, etc}}.} Here, p and q are any two events, and the second basis vector identification is referred to as parallel transport. The first identification is the canonical identification of vectors in the tangent space at any point with vectors in the space itself. The appearance of basis vectors in tangent spaces as first-order differential operators is due to this identification. It is motivated by the observation that a geometrical tangent vector can be associated in a one-to-one manner with a directional derivative operator on the set of smooth functions. This is promoted to a definition of tangent vectors in manifolds not necessarily being embedded in Rn. This definition of tangent vectors is not the only possible one, as ordinary n-tuples can be used as well. A tangent vector at a point p may be defined, here specialized to Cartesian coordinates in Lorentz frames, as 4 × 1 column vectors v associated to each Lorentz frame related by Lorentz transformation Λ such that the vector v in a frame related to some frame by Λ transforms according to v → Λv. This is the same way in which the coordinates xμ transform. Explicitly, x ′ μ = Λ μ ν x ν , v ′ μ = Λ μ ν v ν . {\displaystyle {\begin{aligned}x'^{\mu }&={\Lambda ^{\mu }}_{\nu }x^{\nu },\\v'^{\mu }&={\Lambda ^{\mu }}_{\nu }v^{\nu }.\end{aligned}}} This definition is equivalent to the definition given above under a canonical isomorphism. For some purposes, it is desirable to identify tangent vectors at a point p with displacement vectors at p, which is, of course, admissible by essentially the same canonical identification. The identifications of vectors referred to above in the mathematical setting can correspondingly be found in a more physical and explicitly geometrical setting in Misner, Thorne & Wheeler (1973). They offer various degrees of sophistication (and rigor) depending on which part of the material one chooses to read. The metric signature refers to which sign the Minkowski inner product yields when given space (spacelike to be specific, defined further down) and time basis vectors (timelike) as arguments. Further discussion about this theoretically inconsequential but practically necessary choice for purposes of internal consistency and convenience is deferred to the hide box below. See also the page treating sign convention in Relativity. In general, but with several exceptions, mathematicians and general relativists prefer spacelike vectors to yield a positive sign, (− + + +), while particle physicists tend to prefer timelike vectors to yield a positive sign, (+ − − −). Authors covering several areas of physics, e.g. Steven Weinberg and Landau and Lifshitz ((− + + +) and (+ − − −), respectively) stick to one choice regardless of topic. Arguments for the former convention include "continuity" from the Euclidean case corresponding to the non-relativistic limit c → ∞. Arguments for the latter include that minus signs, otherwise ubiquitous in particle physics, go away. Yet other authors, especially of introductory texts, e.g. Kleppner & Kolenkow (1978), do not choose a signature at all, but instead, opt to coordinatize spacetime such that the time coordinate (but not time itself!) is imaginary. This removes the need for the explicit introduction of a metric tensor (which may seem like an extra burden in an introductory course), and one need not be concerned with covariant vectors and contravariant vectors (or raising and lowering indices) to be described below. The inner product is instead effected by a straightforward extension of the dot product from R 3 {\displaystyle \mathbb {R} ^{3}} over to C × R 3 . {\displaystyle \mathbb {C} \times \mathbb {R} ^{3}.} This works in the flat spacetime of special relativity, but not in the curved spacetime of general relativity, see Misner, Thorne & Wheeler (1973, Box 2.1, "Farewell to i c t ") (who, by the way use (− + + +) ). MTW also argues that it hides the true indefinite nature of the metric and the true nature of Lorentz boosts, which are not rotations. It also needlessly complicates the use of tools of differential geometry that are otherwise immediately available and useful for geometrical description and calculation – even in the flat spacetime of special relativity, e.g. of the electromagnetic field. Mathematically associated with the bilinear form is a tensor of type (0,2) at each point in spacetime, called the Minkowski metric.[nb 4] The Minkowski metric, the bilinear form, and the Minkowski inner product are all the same object; it is a bilinear function that accepts two (contravariant) vectors and returns a real number. In coordinates, this is the 4×4 matrix representing the bilinear form. For comparison, in general relativity, a Lorentzian manifold L is likewise equipped with a metric tensor g, which is a nondegenerate symmetric bilinear form on the tangent space TpL at each point p of L. In coordinates, it may be represented by a 4×4 matrix depending on spacetime position. Minkowski space is thus a comparatively simple special case of a Lorentzian manifold. Its metric tensor is in coordinates with the same symmetric matrix at every point of M, and its arguments can, per above, be taken as vectors in spacetime itself. Introducing more terminology (but not more structure), Minkowski space is thus a pseudo-Euclidean space with total dimension n = 4 and signature (1, 3) or (3, 1). Elements of Minkowski space are called events. Minkowski space is often denoted R1,3 or R3,1 to emphasize the chosen signature, or just M. It is an example of a pseudo-Riemannian manifold. Then mathematically, the metric is a bilinear form on an abstract four-dimensional real vector space V, that is, η : V × V → R {\displaystyle \eta :V\times V\rightarrow \mathbf {R} } where η has signature (+, -, -, -), and signature is a coordinate-invariant property of η. The space of bilinear maps forms a vector space which can be identified with M ∗ ⊗ M ∗ {\displaystyle M^{*}\otimes M^{*}} , and η may be equivalently viewed as an element of this space. By making a choice of orthonormal basis { e μ } {\displaystyle \{e_{\mu }\}} , M := ( V , η ) {\displaystyle M:=(V,\eta )} can be identified with the space R 1 , 3 := ( R 4 , η μ ν ) {\displaystyle \mathbf {R} ^{1,3}:=(\mathbf {R} ^{4},\eta _{\mu \nu })} . The notation is meant to emphasize the fact that M and R 1 , 3 {\displaystyle \mathbf {R} ^{1,3}} are not just vector spaces but have added structure. η μ ν = diag ( + 1 , − 1 , − 1 , − 1 ) {\displaystyle \eta _{\mu \nu }={\text{diag}}(+1,-1,-1,-1)} . An interesting example of non-inertial coordinates for (part of) Minkowski spacetime is the Born coordinates. Another useful set of coordinates is the light-cone coordinates. The Minkowski inner product is not an inner product, since it has non-zero null vectors. Since it is not a definite bilinear form it is called indefinite. The Minkowski metric η is the metric tensor of Minkowski space. It is a pseudo-Euclidean metric, or more generally, a constant pseudo-Riemannian metric in Cartesian coordinates. As such, it is a nondegenerate symmetric bilinear form, a type (0, 2) tensor. It accepts two arguments up, vp, vectors in TpM, p ∈ M, the tangent space at p in M. Due to the above-mentioned canonical identification of TpM with M itself, it accepts arguments u, v with both u and v in M. As a notational convention, vectors v in M, called 4-vectors, are denoted in italics, and not, as is common in the Euclidean setting, with boldface v. The latter is generally reserved for the 3-vector part (to be introduced below) of a 4-vector. The definition u ⋅ v = η ( u , v ) {\displaystyle u\cdot v=\eta (u,\,v)} yields an inner product-like structure on M, previously and also henceforth, called the Minkowski inner product, similar to the Euclidean inner product, but it describes a different geometry. It is also called the relativistic dot product. If the two arguments are the same, u ⋅ u = η ( u , u ) ≡ ‖ u ‖ 2 ≡ u 2 , {\displaystyle u\cdot u=\eta (u,u)\equiv \|u\|^{2}\equiv u^{2},} the resulting quantity will be called the Minkowski norm squared. The Minkowski inner product satisfies the following properties. The first two conditions imply bilinearity. The most important feature of the inner product and norm squared is that these are quantities unaffected by Lorentz transformations. In fact, it can be taken as the defining property of a Lorentz transformation in that it preserves the inner product (i.e. the value of the corresponding bilinear form on two vectors). This approach is taken more generally for all classical groups definable this way in classical group. There, the matrix Φ is identical in the case O(3, 1) (the Lorentz group) to the matrix η to be displayed below. Minkowski space is constructed so that the speed of light will be the same constant regardless of the reference frame in which it is measured. This property results from the relation of the time axis to a space axis. Two events u and v are orthogonal when the bilinear form is zero for them: η(v, w) = 0. When both u and v are both space-like, then they are perpendicular, but if one is time-like and the other space-like, then the relation is hyperbolic orthogonality. The relation is preserved in a change of reference frames and consequently the computation of light speed yields a constant result. The change of reference frame is called a Lorentz boost and in mathematics it is a hyperbolic rotation. Each reference frame is associated with a hyperbolic angle, which is zero for the rest frame in Minkowski space. Such a hyperbolic angle has been labelled rapidity since it is associated with the speed of the frame. From the second postulate of special relativity, together with homogeneity of spacetime and isotropy of space, it follows that the spacetime interval between two arbitrary events called 1 and 2 is: c 2 ( t 1 − t 2 ) 2 − ( x 1 − x 2 ) 2 − ( y 1 − y 2 ) 2 − ( z 1 − z 2 ) 2 . {\displaystyle c^{2}\left(t_{1}-t_{2}\right)^{2}-\left(x_{1}-x_{2}\right)^{2}-\left(y_{1}-y_{2}\right)^{2}-\left(z_{1}-z_{2}\right)^{2}.} This quantity is not consistently named in the literature. The interval is sometimes referred to as the square root of the interval as defined here. The invariance of the interval under coordinate transformations between inertial frames follows from the invariance of c 2 t 2 − x 2 − y 2 − z 2 {\displaystyle c^{2}t^{2}-x^{2}-y^{2}-z^{2}} provided the transformations are linear. This quadratic form can be used to define a bilinear form u ⋅ v = c 2 t 1 t 2 − x 1 x 2 − y 1 y 2 − z 1 z 2 {\displaystyle u\cdot v=c^{2}t_{1}t_{2}-x_{1}x_{2}-y_{1}y_{2}-z_{1}z_{2}} via the polarization identity. This bilinear form can in turn be written as u ⋅ v = u T [ η ] v , {\displaystyle u\cdot v=u^{\textsf {T}}\,[\eta ]\,v,} where [η] is a 4 × 4 {\displaystyle 4\times 4} matrix associated with η. While possibly confusing, it is common practice to denote [η] with just η. The matrix is read off from the explicit bilinear form as η = ( 1 0 0 0 0 − 1 0 0 0 0 − 1 0 0 0 0 − 1 ) , {\displaystyle \eta =\left({\begin{array}{r}1&0&0&0\\0&-1&0&0\\0&0&-1&0\\0&0&0&-1\end{array}}\right)\!,} and the bilinear form u ⋅ v = η ( u , v ) , {\displaystyle u\cdot v=\eta (u,v),} with which this section started by assuming its existence, is now identified. For definiteness and shorter presentation, the signature (− + + +) is adopted below. This choice (or the other possible choice) has no (known) physical implications. The symmetry group preserving the bilinear form with one choice of signature is isomorphic (under the map given here) with the symmetry group preserving the other choice of signature. This means that both choices are in accord with the two postulates of relativity. Switching between the two conventions is straightforward. If the metric tensor η has been used in a derivation, go back to the earliest point where it was used, substitute η for −η, and retrace forward to the desired formula with the desired metric signature. A standard or orthonormal basis for Minkowski space is a set of four mutually orthogonal vectors {e0, e1, e2, e3} such that η ( e 0 , e 0 ) = − η ( e 1 , e 1 ) = − η ( e 2 , e 2 ) = − η ( e 3 , e 3 ) = 1 {\displaystyle \eta (e_{0},e_{0})=-\eta (e_{1},e_{1})=-\eta (e_{2},e_{2})=-\eta (e_{3},e_{3})=1} and for which η ( e μ , e ν ) = 0 {\displaystyle \eta (e_{\mu },e_{\nu })=0} when μ ≠ ν . {\textstyle \mu \neq \nu \,.} These conditions can be written compactly in the form η ( e μ , e ν ) = η μ ν . {\displaystyle \eta (e_{\mu },e_{\nu })=\eta _{\mu \nu }.} Relative to a standard basis, the components of a vector v are written (v0, v1, v2, v3) where the Einstein notation is used to write v = vμ eμ. The component v0 is called the timelike component of v while the other three components are called the spatial components. The spatial components of a 4-vector v may be identified with a 3-vector v = (v1, v2, v3). In terms of components, the Minkowski inner product between two vectors v and w is given by η ( v , w ) = η μ ν v μ w ν = v 0 w 0 + v 1 w 1 + v 2 w 2 + v 3 w 3 = v μ w μ = v μ w μ , {\displaystyle \eta (v,w)=\eta _{\mu \nu }v^{\mu }w^{\nu }=v^{0}w_{0}+v^{1}w_{1}+v^{2}w_{2}+v^{3}w_{3}=v^{\mu }w_{\mu }=v_{\mu }w^{\mu },} and η ( v , v ) = η μ ν v μ v ν = v 0 v 0 + v 1 v 1 + v 2 v 2 + v 3 v 3 = v μ v μ . {\displaystyle \eta (v,v)=\eta _{\mu \nu }v^{\mu }v^{\nu }=v^{0}v_{0}+v^{1}v_{1}+v^{2}v_{2}+v^{3}v_{3}=v^{\mu }v_{\mu }.} Here lowering of an index with the metric was used. There are many possible choices of standard basis obeying the condition η ( e μ , e ν ) = η μ ν . {\displaystyle \eta (e_{\mu },e_{\nu })=\eta _{\mu \nu }.} Any two such bases are related in some sense by a Lorentz transformation, either by a change-of-basis matrix Λ ν μ {\displaystyle \Lambda _{\nu }^{\mu }} , a real 4 × 4 matrix satisfying Λ ρ μ η μ ν Λ σ ν = η ρ σ . {\displaystyle \Lambda _{\rho }^{\mu }\eta _{\mu \nu }\Lambda _{\sigma }^{\nu }=\eta _{\rho \sigma }.} or Λ, a linear map on the abstract vector space satisfying, for any pair of vectors u, v, η ( Λ u , Λ v ) = η ( u , v ) . {\displaystyle \eta (\Lambda u,\Lambda v)=\eta (u,v).} Then if two different bases exist, {e0, e1, e2, e3} and {e′0, e′1, e′2, e′3}, e μ ′ = e ν Λ μ ν {\displaystyle e_{\mu }'=e_{\nu }\Lambda _{\mu }^{\nu }} can be represented as e μ ′ = e ν Λ μ ν {\displaystyle e_{\mu }'=e_{\nu }\Lambda _{\mu }^{\nu }} or e μ ′ = Λ e μ {\displaystyle e_{\mu }'=\Lambda e_{\mu }} . While it might be tempting to think of Λ ν μ {\displaystyle \Lambda _{\nu }^{\mu }} and Λ as the same thing, mathematically, they are elements of different spaces, and act on the space of standard bases from different sides. Technically, a non-degenerate bilinear form provides a map between a vector space and its dual; in this context, the map is between the tangent spaces of M and the cotangent spaces of M. At a point in M, the tangent and cotangent spaces are dual vector spaces (so the dimension of the cotangent space at an event is also 4). Just as an authentic inner product on a vector space with one argument fixed, by Riesz representation theorem, may be expressed as the action of a linear functional on the vector space, the same holds for the Minkowski inner product of Minkowski space. Thus if vμ are the components of a vector in tangent space, then ημν vμ = vν are the components of a vector in the cotangent space (a linear functional). Due to the identification of vectors in tangent spaces with vectors in M itself, this is mostly ignored, and vectors with lower indices are referred to as covariant vectors. In this latter interpretation, the covariant vectors are (almost always implicitly) identified with vectors (linear functionals) in the dual of Minkowski space. The ones with upper indices are contravariant vectors. In the same fashion, the inverse of the map from tangent to cotangent spaces, explicitly given by the inverse of η in matrix representation, can be used to define raising of an index. The components of this inverse are denoted ημν. It happens that ημν = ημν. These maps between a vector space and its dual can be denoted η♭ (eta-flat) and η♯ (eta-sharp) by the musical analogy. Contravariant and covariant vectors are geometrically very different objects. The first can and should be thought of as arrows. A linear function can be characterized by two objects: its kernel, which is a hyperplane passing through the origin, and its norm. Geometrically thus, covariant vectors should be viewed as a set of hyperplanes, with spacing depending on the norm (bigger = smaller spacing), with one of them (the kernel) passing through the origin. The mathematical term for a covariant vector is 1-covector or 1-form (though the latter is usually reserved for covector fields). One quantum mechanical analogy explored in the literature is that of a de Broglie wave (scaled by a factor of Planck's reduced constant) associated with a momentum four-vector to illustrate how one could imagine a covariant version of a contravariant vector. The inner product of two contravariant vectors could equally well be thought of as the action of the covariant version of one of them on the contravariant version of the other. The inner product is then how many times the arrow pierces the planes. The mathematical reference, Lee (2003), offers the same geometrical view of these objects (but mentions no piercing). The electromagnetic field tensor is a differential 2-form, which geometrical description can as well be found in MTW. One may, of course, ignore geometrical views altogether (as is the style in e.g. Weinberg (2002) and Landau & Lifshitz 2002) and proceed algebraically in a purely formal fashion. The time-proven robustness of the formalism itself, sometimes referred to as index gymnastics, ensures that moving vectors around and changing from contravariant to covariant vectors and vice versa (as well as higher order tensors) is mathematically sound. Incorrect expressions tend to reveal themselves quickly. Given a bilinear form η : M × M → R , {\displaystyle \ \eta :M\times M\rightarrow \mathbb {R} \ ,} the lowered version of a vector can be thought of as the partial evaluation of η , {\displaystyle \ \eta \ ,} that is, there is an associated partial evaluation map η ( ⋅ , − ) : M → M ∗ , v ↦ η ( v , ⋅ ) . {\displaystyle \eta (\cdot ,-):M\rightarrow M^{*}\ ~,\quad v\mapsto \eta (v,\cdot )~.} The lowered vector η ( v , ⋅ ) ∈ M ∗ {\displaystyle \ \eta (v,\cdot )\in M^{*}\ } is then the dual map u ↦ η ( v , u ) . {\displaystyle \ u\mapsto \eta (v,u)~.} Note it does not matter which argument is partially evaluated due to the symmetry of η . {\displaystyle \ \eta ~.} Non-degeneracy is then equivalent to injectivity of the partial evaluation map, or equivalently non-degeneracy indicates that the kernel of the map is trivial. In finite dimension, as is the case here, and noting that the dimension of a finite-dimensional space is equal to the dimension of the dual, this is enough to conclude the partial evaluation map is a linear isomorphism from M {\displaystyle \ M\ } to M ∗ . {\displaystyle \ M^{*}~.} This then allows the definition of the inverse partial evaluation map, η − 1 : M ∗ → M , {\displaystyle \eta ^{-1}:M^{*}\rightarrow M\ ,} which allows the inverse metric to be defined as η − 1 : M ∗ × M ∗ → R , η − 1 ( α , β ) = η ( η − 1 ( α ) , η − 1 ( β ) ) {\displaystyle \eta ^{-1}:M^{*}\times M^{*}\rightarrow \mathbb {R} \ ~,\quad \eta ^{-1}\!(\alpha ,\beta )\ =\ \eta {\bigl (}\ \eta ^{-1}\!(\alpha ),\ \eta ^{-1}\!(\beta )\ {\bigr )}\ } where the two different usages of η − 1 {\displaystyle \;\eta ^{-1}\ } can be told apart by the argument each is evaluated on. This can then be used to raise indices. If a coordinate basis is used, the metric η−1 is indeed the matrix inverse to η . The present purpose is to show semi-rigorously how formally one may apply the Minkowski metric to two vectors and obtain a real number, i.e. to display the role of the differentials and how they disappear in a calculation. The setting is that of smooth manifold theory, and concepts such as convector fields and exterior derivatives are introduced. A full-blown version of the Minkowski metric in coordinates as a tensor field on spacetime has the appearance η μ ν d x μ ⊗ d x ν = η μ ν d x μ ⊙ d x ν = η μ ν d x μ d x ν . {\displaystyle \eta _{\mu \nu }\operatorname {d} x^{\mu }\otimes \operatorname {d} x^{\nu }=\eta _{\mu \nu }\operatorname {d} x^{\mu }\odot \operatorname {d} x^{\nu }=\eta _{\mu \nu }\operatorname {d} x^{\mu }\operatorname {d} x^{\nu }~.} Explanation: The coordinate differentials are 1-form fields. They are defined as the exterior derivative of the coordinate functions xμ. These quantities evaluated at a point p provide a basis for the cotangent space at p. The tensor product (denoted by the symbol ⊗) yields a tensor field of type (0, 2), i.e. the type that expects two contravariant vectors as arguments. On the right-hand side, the symmetric product (denoted by the symbol ⊙ or by juxtaposition) has been taken. The equality holds since, by definition, the Minkowski metric is symmetric. The notation on the far right is also sometimes used for the related, but different, line element. It is not a tensor. For elaboration on the differences and similarities, see Misner, Thorne & Wheeler (1973, Box 3.2 and section 13.2.) Tangent vectors are, in this formalism, given in terms of a basis of differential operators of the first order, ∂ ∂ x μ | p , {\displaystyle \left.{\frac {\partial }{\partial x^{\mu }}}\right|_{p}\ ,} where p is an event. This operator applied to a function f gives the directional derivative of f at p in the direction of increasing xμ with xν, ν ≠ μ fixed. They provide a basis for the tangent space at p. The exterior derivative df of a function f is a covector field, i.e. an assignment of a cotangent vector to each point p, by definition such that d f ( X ) = X f , {\displaystyle \operatorname {d} f(X)=X\ f,} for each vector field X. A vector field is an assignment of a tangent vector to each point p. In coordinates X can be expanded at each point p in the basis given by the ∂/∂xν | p . Applying this with f = xμ, the coordinate function itself, and X = ∂/ ∂xν , called a coordinate vector field, one obtains d x μ ( ∂ ∂ x ν ) = ∂ x μ ∂ x ν = δ ν μ . {\displaystyle \operatorname {d} x^{\mu }\left({\frac {\partial }{\partial x^{\nu }}}\right)={\frac {\partial x^{\mu }}{\partial x^{\nu }}}=\delta _{\nu }^{\mu }~.} Since this relation holds at each point p, the dxμ|p provide a basis for the cotangent space at each p and the bases d xμ|p and ∂/∂xν |p are dual to each other, d x μ | p ( ∂ ∂ x ν | p ) = δ ν μ . {\displaystyle {\Bigl .}\operatorname {d} x^{\mu }{\Bigr |}_{p}\left(\left.{\frac {\partial }{\partial x^{\nu }}}\right|_{p}\right)=\delta _{\nu }^{\mu }~.} at each p. Furthermore, one has α ⊗ β ( a , b ) = α ( a ) β ( b ) {\displaystyle \alpha \ \otimes \ \beta (a,b)\ =\ \alpha (a)\ \beta (b)\ } for general one-forms on a tangent space α, β and general tangent vectors a, b. (This can be taken as a definition, but may also be proved in a more general setting.) Thus when the metric tensor is fed two vectors fields a, b, both expanded in terms of the basis coordinate vector fields, the result is η μ ν d x μ ⊗ d x ν ( a , b ) = η μ ν a μ b ν , {\displaystyle \eta _{\mu \nu }\ \operatorname {d} x^{\mu }\otimes \operatorname {d} x^{\nu }(a,b)\ =\ \eta _{\mu \nu }\ a^{\mu }\ b^{\nu }\ ,} where aμ, bν are the component functions of the vector fields. The above equation holds at each point p, and the relation may as well be interpreted as the Minkowski metric at p applied to two tangent vectors at p. As mentioned, in a vector space, such as modeling the spacetime of special relativity, tangent vectors can be canonically identified with vectors in the space itself, and vice versa. This means that the tangent spaces at each point are canonically identified with each other and with the vector space itself. This explains how the right-hand side of the above equation can be employed directly, without regard to the spacetime point the metric is to be evaluated and from where (which tangent space) the vectors come from. This situation changes in general relativity. There one has g μ ν ( p ) d x μ | p d x ν | p ( a , b ) = g μ ν ( p ) a μ b ν , {\displaystyle g_{\mu \nu }\!(p)\ {\Bigl .}\operatorname {d} x^{\mu }{\Bigr |}_{p}\ \left.\operatorname {d} x^{\nu }\right|_{p}(a,b)\ =\ g_{\mu \nu }\!(p)\ a^{\mu }\ b^{\nu }\ ,} where now η → g(p), i.e., g is still a metric tensor but now depending on spacetime and is a solution of Einstein's field equations. Moreover, a, b must be tangent vectors at spacetime point p and can no longer be moved around freely. Let x, y ∈ M. Here, Suppose x ∈ M is timelike. Then the simultaneous hyperplane for x is {y : η(x, y) = 0}. Since this hyperplane varies as x varies, there is a relativity of simultaneity in Minkowski space. Generalizations A Lorentzian manifold is a generalization of Minkowski space in two ways. The total number of spacetime dimensions is not restricted to be 4 (2 or more) and a Lorentzian manifold need not be flat, i.e. it allows for curvature. Complexified Minkowski space is defined as Mc = M ⊕ iM. Its real part is the Minkowski space of four-vectors, such as the four-velocity and the four-momentum, which are independent of the choice of orientation of the space. The imaginary part, on the other hand, may consist of four pseudovectors, such as angular velocity and magnetic moment, which change their direction with a change of orientation. A pseudoscalar i is introduced, which also changes sign with a change of orientation. Thus, elements of Mc are independent of the choice of the orientation. The inner product-like structure on Mc is defined as u ⋅ v = η(u, v) for any u,v ∈ Mc. A relativistic pure spin of an electron or any half spin particle is described by ρ ∈ Mc as ρ = u + is, where u is the four-velocity of the particle, satisfying u2 = 1 and s is the 4D spin vector, which is also the Pauli–Lubanski pseudovector satisfying s2 = −1 and u ⋅ s = 0. Minkowski space refers to a mathematical formulation in four dimensions. However, the mathematics can easily be extended or simplified to create an analogous generalized Minkowski space in any number of dimensions. If n ≥ 2, n-dimensional Minkowski space is a vector space of real dimension n on which there is a constant Minkowski metric of signature (n − 1, 1) or (1, n − 1). These generalizations are used in theories where spacetime is assumed to have more or less than 4 dimensions. String theory and M-theory are two examples where n > 4. In string theory there appear conformal field theories with 1 + 1 spacetime dimensions. de Sitter space can be formulated as a submanifold of generalized Minkowski space as can the model spaces of hyperbolic geometry (see below). As a flat spacetime, the three spatial components of Minkowski spacetime always obey the Pythagorean theorem. Minkowski space is a suitable basis for special relativity, a good description of physical systems over finite distances in systems without significant gravitation. However, in order to take gravity into account, physicists use the theory of general relativity, which is formulated in the mathematics of differential geometry of differential manifolds. When this geometry is used as a model of spacetime, it is known as curved spacetime. Even in curved spacetime, Minkowski space is still a good description in an infinitesimal region surrounding any point (barring gravitational singularities).[nb 5] More abstractly, it can be said that in the presence of gravity spacetime is described by a curved 4-dimensional manifold for which the tangent space to any point is a 4-dimensional Minkowski space. Thus, the structure of Minkowski space is still essential in the description of general relativity. Geometry The meaning of the term geometry for the Minkowski space depends heavily on the context. Minkowski space is not endowed with Euclidean geometry, and not with any of the generalized Riemannian geometries with intrinsic curvature, those exposed by the model spaces in hyperbolic geometry (negative curvature) and the geometry modeled by the sphere (positive curvature). The reason is the indefiniteness of the Minkowski metric. Minkowski space is, in particular, not a metric space and not a Riemannian manifold with a Riemannian metric. However, Minkowski space contains submanifolds endowed with a Riemannian metric yielding hyperbolic geometry. Model spaces of hyperbolic geometry of low dimension, say 2 or 3, cannot be isometrically embedded in Euclidean space with one more dimension, i.e. R 3 {\displaystyle \mathbb {R} ^{3}} or R 4 {\displaystyle \mathbb {R} ^{4}} respectively, with the Euclidean metric g ¯ {\displaystyle {\overline {g}}} , preventing easy visualization.[nb 6] By comparison, model spaces with positive curvature are just spheres in Euclidean space of one higher dimension. Hyperbolic spaces can be isometrically embedded in spaces of one more dimension when the embedding space is endowed with the Minkowski metric η {\displaystyle \eta } . Define H R 1 ( n ) ⊂ M n + 1 {\displaystyle \mathbf {H} _{R}^{1(n)}\subset \mathbf {M} ^{n+1}} to be the upper sheet ( c t > 0 {\displaystyle ct>0} ) of the hyperboloid H R 1 ( n ) = { ( c t , x 1 , … , x n ) ∈ M n : c 2 t 2 − ( x 1 ) 2 − ⋯ − ( x n ) 2 = R 2 , c t > 0 } {\displaystyle \mathbf {H} _{R}^{1(n)}=\left\{\left(ct,x^{1},\ldots ,x^{n}\right)\in \mathbf {M} ^{n}:c^{2}t^{2}-\left(x^{1}\right)^{2}-\cdots -\left(x^{n}\right)^{2}=R^{2},ct>0\right\}} in generalized Minkowski space M n + 1 {\displaystyle \mathbf {M} ^{n+1}} of spacetime dimension n + 1. {\displaystyle n+1.} This is one of the surfaces of transitivity of the generalized Lorentz group. The induced metric on this submanifold, h R 1 ( n ) = ι ∗ η , {\displaystyle h_{R}^{1(n)}=\iota ^{*}\eta ,} the pullback of the Minkowski metric η {\displaystyle \eta } under inclusion, is a Riemannian metric. With this metric H R 1 ( n ) {\displaystyle \mathbf {H} _{R}^{1(n)}} is a Riemannian manifold. It is one of the model spaces of Riemannian geometry, the hyperboloid model of hyperbolic space. It is a space of constant negative curvature − 1 / R 2 {\displaystyle -1/R^{2}} . The 1 in the upper index refers to an enumeration of the different model spaces of hyperbolic geometry, and the n for its dimension. A 2 ( 2 ) {\displaystyle 2(2)} corresponds to the Poincaré disk model, while 3 ( n ) {\displaystyle 3(n)} corresponds to the Poincaré half-space model of dimension n . {\displaystyle n.} In the definition above ι : H R 1 ( n ) → M n + 1 {\displaystyle \iota :\mathbf {H} _{R}^{1(n)}\rightarrow \mathbf {M} ^{n+1}} is the inclusion map and the superscript star denotes the pullback. The present purpose is to describe this and similar operations as a preparation for the actual demonstration that H R 1 ( n ) {\displaystyle \mathbf {H} _{R}^{1(n)}} actually is a hyperbolic space. Behavior of tensors under inclusion: For inclusion maps from a submanifold S into M and a covariant tensor α of order k on M it holds that ι ∗ α ( X 1 , X 2 , … , X k ) = α ( ι ∗ X 1 , ι ∗ X 2 , … , ι ∗ X k ) = α ( X 1 , X 2 , … , X k ) , {\displaystyle \iota ^{*}\alpha \left(X_{1},\,X_{2},\,\ldots ,\,X_{k}\right)=\alpha \left(\iota _{*}X_{1},\,\iota _{*}X_{2},\,\ldots ,\,\iota _{*}X_{k}\right)=\alpha \left(X_{1},\,X_{2},\,\ldots ,\,X_{k}\right),} where X1, X1, ..., Xk are vector fields on S. The subscript star denotes the pushforward (to be introduced later), and it is in this special case simply the identity map (as is the inclusion map). The latter equality holds because a tangent space to a submanifold at a point is in a canonical way a subspace of the tangent space of the manifold itself at the point in question. One may simply write ι ∗ α = α | S , {\displaystyle \iota ^{*}\alpha =\alpha |_{S},} meaning (with slight abuse of notation) the restriction of α to accept as input vectors tangent to some s ∈ S only. Pullback of tensors under general maps: The pullback of a covariant k-tensor α (one taking only contravariant vectors as arguments) under a map F: M → N is a linear map F ∗ : T F ( p ) k N → T p k M , {\displaystyle F^{*}\colon T_{F(p)}^{k}N\rightarrow T_{p}^{k}M,} where for any vector space V, T k V = V ∗ ⊗ V ∗ ⊗ ⋯ ⊗ V ∗ ⏟ k times . {\displaystyle T^{k}V=\underbrace {V^{*}\otimes V^{*}\otimes \cdots \otimes V^{*}} _{k{\text{ times}}}.} It is defined by F ∗ ( α ) ( X 1 , X 2 , … , X k ) = α ( F ∗ X 1 , F ∗ X 2 , … , F ∗ X k ) , {\displaystyle F^{*}(\alpha )\left(X_{1},\,X_{2},\,\ldots ,\,X_{k}\right)=\alpha \left(F_{*}X_{1},\,F_{*}X_{2},\,\ldots ,\,F_{*}X_{k}\right),} where the subscript star denotes the pushforward of the map F, and X1, X2, ..., Xk are vectors in TpM. (This is in accord with what was detailed about the pullback of the inclusion map. In the general case here, one cannot proceed as simply because F∗X1 ≠ X1 in general.) The pushforward of vectors under general maps: Heuristically, pulling back a tensor to p ∈ M from F(p) ∈ N feeding it vectors residing at p ∈ M is by definition the same as pushing forward the vectors from p ∈ M to F(p) ∈ N feeding them to the tensor residing at F(p) ∈ N. Further unwinding the definitions, the pushforward F∗: TMp → TNF(p) of a vector field under a map F: M → N between manifolds is defined by F ∗ ( X ) f = X ( f ∘ F ) , {\displaystyle F_{*}(X)f=X(f\circ F),} where f is a function on N. When M = Rm, N= Rn the pushforward of F reduces to DF: Rm → Rn, the ordinary differential, which is given by the Jacobian matrix of partial derivatives of the component functions. The differential is the best linear approximation of a function F from Rm to Rn. The pushforward is the smooth manifold version of this. It acts between tangent spaces, and is in coordinates represented by the Jacobian matrix of the coordinate representation of the function. The corresponding pullback is the dual map from the dual of the range tangent space to the dual of the domain tangent space, i.e. it is a linear map, F ∗ : T F ( p ) ∗ N → T p ∗ M . {\displaystyle F^{*}\colon T_{F(p)}^{*}N\rightarrow T_{p}^{*}M.} In order to exhibit the metric, it is necessary to pull it back via a suitable parametrization. A parametrization of a submanifold S of a manifold M is a map U ⊂ Rm → M whose range is an open subset of S. If S has the same dimension as M, a parametrization is just the inverse of a coordinate map φ: M → U ⊂ Rm. The parametrization to be used is the inverse of hyperbolic stereographic projection. This is illustrated in the figure to the right for n = 2. It is instructive to compare to stereographic projection for spheres. Stereographic projection σ: HnR → Rn and its inverse σ−1: Rn → HnR are given by σ ( τ , x ) = u = R x R + τ , σ − 1 ( u ) = ( τ , x ) = ( R R 2 + | u | 2 R 2 − | u | 2 , 2 R 2 u R 2 − | u | 2 ) , {\displaystyle {\begin{aligned}\sigma (\tau ,\mathbf {x} )=\mathbf {u} &={\frac {R\mathbf {x} }{R+\tau }},\\\sigma ^{-1}(\mathbf {u} )=(\tau ,\mathbf {x} )&=\left(R{\frac {R^{2}+|u|^{2}}{R^{2}-|u|^{2}}},{\frac {2R^{2}\mathbf {u} }{R^{2}-|u|^{2}}}\right),\end{aligned}}} where, for simplicity, τ ≡ ct. The (τ, x) are coordinates on Mn+1 and the u are coordinates on Rn. Let H R n = { ( τ , x 1 , … , x n ) ⊂ M : − τ 2 + ( x 1 ) 2 + ⋯ + ( x n ) 2 = − R 2 , τ > 0 } {\displaystyle \mathbf {H} _{R}^{n}=\left\{\left(\tau ,x^{1},\ldots ,x^{n}\right)\subset \mathbf {M} :-\tau ^{2}+\left(x^{1}\right)^{2}+\cdots +\left(x^{n}\right)^{2}=-R^{2},\tau >0\right\}} and let S = ( − R , 0 , … , 0 ) . {\displaystyle S=(-R,0,\ldots ,0).} If P = ( τ , x 1 , … , x n ) ∈ H R n , {\displaystyle P=\left(\tau ,x^{1},\ldots ,x^{n}\right)\in \mathbf {H} _{R}^{n},} then it is geometrically clear that the vector P S → {\displaystyle {\overrightarrow {PS}}} intersects the hyperplane { ( τ , x 1 , … , x n ) ∈ M : τ = 0 } {\displaystyle \left\{\left(\tau ,x^{1},\ldots ,x^{n}\right)\in M:\tau =0\right\}} once in point denoted U = ( 0 , u 1 ( P ) , … , u n ( P ) ) ≡ ( 0 , u ) . {\displaystyle U=\left(0,u^{1}(P),\ldots ,u^{n}(P)\right)\equiv (0,\mathbf {u} ).} One has S + S U → = U ⇒ S U → = U − S , S + S P → = P ⇒ S P → = P − S {\displaystyle {\begin{aligned}S+{\overrightarrow {SU}}&=U\Rightarrow {\overrightarrow {SU}}=U-S,\\S+{\overrightarrow {SP}}&=P\Rightarrow {\overrightarrow {SP}}=P-S\end{aligned}}} or S U → = ( 0 , u ) − ( − R , 0 ) = ( R , u ) , S P → = ( τ , x ) − ( − R , 0 ) = ( τ + R , x ) . . {\displaystyle {\begin{aligned}{\overrightarrow {SU}}&=(0,\mathbf {u} )-(-R,\mathbf {0} )=(R,\mathbf {u} ),\\{\overrightarrow {SP}}&=(\tau ,\mathbf {x} )-(-R,\mathbf {0} )=(\tau +R,\mathbf {x} ).\end{aligned}}.} By construction of stereographic projection one has S U → = λ ( τ ) S P → . {\displaystyle {\overrightarrow {SU}}=\lambda (\tau ){\overrightarrow {SP}}.} This leads to the system of equations R = λ ( τ + R ) , u = λ x . {\displaystyle {\begin{aligned}R&=\lambda (\tau +R),\\\mathbf {u} &=\lambda \mathbf {x} .\end{aligned}}} The first of these is solved for λ and one obtains for stereographic projection σ ( τ , x ) = u = R x R + τ . {\displaystyle \sigma (\tau ,\mathbf {x} )=\mathbf {u} ={\frac {R\mathbf {x} }{R+\tau }}.} Next, the inverse σ−1(u) = (τ, x) must be calculated. Use the same considerations as before, but now with U = ( 0 , u ) P = ( τ ( u ) , x ( u ) ) . , {\displaystyle {\begin{aligned}U&=(0,\mathbf {u} )\\P&=(\tau (\mathbf {u} ),\mathbf {x} (\mathbf {u} )).\end{aligned}},} one gets τ = R ( 1 − λ ) λ , x = u λ , {\displaystyle {\begin{aligned}\tau &={\frac {R(1-\lambda )}{\lambda }},\\\mathbf {x} &={\frac {\mathbf {u} }{\lambda }},\end{aligned}}} but now with λ depending on u. The condition for P lying in the hyperboloid is − τ 2 + | x | 2 = − R 2 , {\displaystyle -\tau ^{2}+|\mathbf {x} |^{2}=-R^{2},} or − R 2 ( 1 − λ ) 2 λ 2 + | u | 2 λ 2 = − R 2 , {\displaystyle -{\frac {R^{2}(1-\lambda )^{2}}{\lambda ^{2}}}+{\frac {|\mathbf {u} |^{2}}{\lambda ^{2}}}=-R^{2},} leading to λ = R 2 − | u | 2 2 R 2 . {\displaystyle \lambda ={\frac {R^{2}-|u|^{2}}{2R^{2}}}.} With this λ, one obtains σ − 1 ( u ) = ( τ , x ) = ( R R 2 + | u | 2 R 2 − | u | 2 , 2 R 2 u R 2 − | u | 2 ) . {\displaystyle \sigma ^{-1}(\mathbf {u} )=(\tau ,\mathbf {x} )=\left(R{\frac {R^{2}+|u|^{2}}{R^{2}-|u|^{2}}},{\frac {2R^{2}\mathbf {u} }{R^{2}-|u|^{2}}}\right).} One has h R 1 ( n ) = η | H R 1 ( n ) = ( d x 1 ) 2 + ⋯ + ( d x n ) 2 − d τ 2 {\displaystyle h_{R}^{1(n)}=\eta |_{\mathbf {H} _{R}^{1(n)}}=\left(dx^{1}\right)^{2}+\cdots +\left(dx^{n}\right)^{2}-d\tau ^{2}} and the map σ − 1 : R n → H R 1 ( n ) ; σ − 1 ( u ) = ( τ ( u ) , x ( u ) ) = ( R R 2 + | u | 2 R 2 − | u | 2 , 2 R 2 u R 2 − | u | 2 ) . {\displaystyle \sigma ^{-1}:\mathbf {R} ^{n}\rightarrow \mathbf {H} _{R}^{1(n)};\quad \sigma ^{-1}(\mathbf {u} )=(\tau (\mathbf {u} ),\,\mathbf {x} (\mathbf {u} ))=\left(R{\frac {R^{2}+|u|^{2}}{R^{2}-|u|^{2}}},\,{\frac {2R^{2}\mathbf {u} }{R^{2}-|u|^{2}}}\right).} The pulled back metric can be obtained by straightforward methods of calculus; ( σ − 1 ) ∗ η | H R 1 ( n ) = ( d x 1 ( u ) ) 2 + ⋯ + ( d x n ( u ) ) 2 − ( d τ ( u ) ) 2 . {\displaystyle \left.\left(\sigma ^{-1}\right)^{*}\eta \right|_{\mathbf {H} _{R}^{1(n)}}=\left(dx^{1}(\mathbf {u} )\right)^{2}+\cdots +\left(dx^{n}(\mathbf {u} )\right)^{2}-\left(d\tau (\mathbf {u} )\right)^{2}.} One computes according to the standard rules for computing differentials (though one is really computing the rigorously defined exterior derivatives), d x 1 ( u ) = d ( 2 R 2 u 1 R 2 − | u | 2 ) = ∂ ∂ u 1 2 R 2 u 1 R 2 − | u | 2 d u 1 + ⋯ + ∂ ∂ u n 2 R 2 u 1 R 2 − | u | 2 d u n + ∂ ∂ τ 2 R 2 u 1 R 2 − | u | 2 d τ , ⋮ d x n ( u ) = d ( 2 R 2 u n R 2 − | u | 2 ) = ⋯ , d τ ( u ) = d ( R R 2 + | u | 2 R 2 − | u | 2 ) = ⋯ , {\displaystyle {\begin{aligned}dx^{1}(\mathbf {u} )&=d\left({\frac {2R^{2}u^{1}}{R^{2}-|u|^{2}}}\right)={\frac {\partial }{\partial u^{1}}}{\frac {2R^{2}u^{1}}{R^{2}-|u|^{2}}}du^{1}+\cdots +{\frac {\partial }{\partial u^{n}}}{\frac {2R^{2}u^{1}}{R^{2}-|u|^{2}}}du^{n}+{\frac {\partial }{\partial \tau }}{\frac {2R^{2}u^{1}}{R^{2}-|u|^{2}}}d\tau ,\\&\ \ \vdots \\dx^{n}(\mathbf {u} )&=d\left({\frac {2R^{2}u^{n}}{R^{2}-|u|^{2}}}\right)=\cdots ,\\d\tau (\mathbf {u} )&=d\left(R{\frac {R^{2}+|u|^{2}}{R^{2}-|u|^{2}}}\right)=\cdots ,\end{aligned}}} and substitutes the results into the right hand side. This yields ( σ − 1 ) ∗ h R 1 ( n ) = 4 R 2 [ ( d u 1 ) 2 + ⋯ + ( d u n ) 2 ] ( R 2 − | u | 2 ) 2 ≡ h R 2 ( n ) . {\displaystyle \left(\sigma ^{-1}\right)^{*}h_{R}^{1(n)}={\frac {4R^{2}\left[\left(du^{1}\right)^{2}+\cdots +\left(du^{n}\right)^{2}\right]}{\left(R^{2}-|u|^{2}\right)^{2}}}\equiv h_{R}^{2(n)}.} One has ∂ ∂ u 1 2 R 2 u 1 R 2 − | u | 2 d u 1 = 2 ( R 2 − | u | 2 ) + 4 R 2 ( u 1 ) 2 ( R 2 − | u | 2 ) 2 d u 1 , ∂ ∂ u 2 2 R 2 u 1 R 2 − | u | 2 d u 2 = 4 R 2 u 1 u 2 ( R 2 − | u | 2 ) 2 d u 2 , {\displaystyle {\begin{aligned}{\frac {\partial }{\partial u^{1}}}{\frac {2R^{2}u^{1}}{R^{2}-|u|^{2}}}du^{1}&={\frac {2\left(R^{2}-|u|^{2}\right)+4R^{2}\left(u^{1}\right)^{2}}{\left(R^{2}-|u|^{2}\right)^{2}}}du^{1},\\{\frac {\partial }{\partial u^{2}}}{\frac {2R^{2}u^{1}}{R^{2}-|u|^{2}}}du^{2}&={\frac {4R^{2}u^{1}u^{2}}{\left(R^{2}-|u|^{2}\right)^{2}}}du^{2},\end{aligned}}} and ∂ ∂ τ 2 R 2 u 1 R 2 − | u | 2 d τ 2 = 0. {\displaystyle {\frac {\partial }{\partial \tau }}{\frac {2R^{2}u^{1}}{R^{2}-|u|^{2}}}d\tau ^{2}=0.} With this one may write d x 1 ( u ) = 2 R 2 ( R 2 − | u | 2 ) d u 1 + 4 R 2 u 1 ( u ⋅ d u ) ( R 2 − | u | 2 ) 2 , {\displaystyle dx^{1}(\mathbf {u} )={\frac {2R^{2}\left(R^{2}-|u|^{2}\right)du^{1}+4R^{2}u^{1}(\mathbf {u} \cdot d\mathbf {u} )}{\left(R^{2}-|u|^{2}\right)^{2}}},} from which ( d x 1 ( u ) ) 2 = 4 R 2 ( r 2 − | u | 2 ) 2 ( d u 1 ) 2 + 16 R 4 ( R 2 − | u | 2 ) ( u ⋅ d u ) u 1 d u 1 + 16 R 4 ( u 1 ) 2 ( u ⋅ d u ) 2 ( R 2 − | u | 2 ) 4 . {\displaystyle \left(dx^{1}(\mathbf {u} )\right)^{2}={\frac {4R^{2}\left(r^{2}-|u|^{2}\right)^{2}\left(du^{1}\right)^{2}+16R^{4}\left(R^{2}-|u|^{2}\right)\left(\mathbf {u} \cdot d\mathbf {u} \right)u^{1}du^{1}+16R^{4}\left(u^{1}\right)^{2}\left(\mathbf {u} \cdot d\mathbf {u} \right)^{2}}{\left(R^{2}-|u|^{2}\right)^{4}}}.} Summing this formula one obtains ( d x 1 ( u ) ) 2 + ⋯ + ( d x n ( u ) ) 2 = 4 R 2 ( R 2 − | u | 2 ) 2 [ ( d u 1 ) 2 + ⋯ + ( d u n ) 2 ] + 16 R 4 ( R 2 − | u | 2 ) ( u ⋅ d u ) ( u ⋅ d u ) + 16 R 4 | u | 2 ( u ⋅ d u ) 2 ( R 2 − | u | 2 ) 4 = 4 R 2 ( R 2 − | u | 2 ) 2 [ ( d u 1 ) 2 + ⋯ + ( d u n ) 2 ] ( R 2 − | u | 2 ) 4 + R 2 16 R 4 ( u ⋅ d u ) ( R 2 − | u | 2 ) 4 . {\displaystyle {\begin{aligned}&\left(dx^{1}(\mathbf {u} )\right)^{2}+\cdots +\left(dx^{n}(\mathbf {u} )\right)^{2}\\={}&{\frac {4R^{2}\left(R^{2}-|u|^{2}\right)^{2}\left[\left(du^{1}\right)^{2}+\cdots +\left(du^{n}\right)^{2}\right]+16R^{4}\left(R^{2}-|u|^{2}\right)(\mathbf {u} \cdot d\mathbf {u} )(\mathbf {u} \cdot d\mathbf {u} )+16R^{4}|u|^{2}(\mathbf {u} \cdot d\mathbf {u} )^{2}}{\left(R^{2}-|u|^{2}\right)^{4}}}\\={}&{\frac {4R^{2}\left(R^{2}-|u|^{2}\right)^{2}\left[\left(du^{1}\right)^{2}+\cdots +\left(du^{n}\right)^{2}\right]}{\left(R^{2}-|u|^{2}\right)^{4}}}+R^{2}{\frac {16R^{4}(\mathbf {u} \cdot d\mathbf {u} )}{\left(R^{2}-|u|^{2}\right)^{4}}}.\end{aligned}}} Similarly, for τ one gets d τ = ∑ i = 1 n ∂ ∂ u i R R 2 + | u | 2 R 2 + | u | 2 d u i + ∂ ∂ τ R R 2 + | u | 2 R 2 + | u | 2 d τ = ∑ i = 1 n R 4 4 R 2 u i d u i ( R 2 − | u | 2 ) , {\displaystyle d\tau =\sum _{i=1}^{n}{\frac {\partial }{\partial u^{i}}}R{\frac {R^{2}+|u|^{2}}{R^{2}+|u|^{2}}}du^{i}+{\frac {\partial }{\partial \tau }}R{\frac {R^{2}+|u|^{2}}{R^{2}+|u|^{2}}}d\tau =\sum _{i=1}^{n}R^{4}{\frac {4R^{2}u^{i}du^{i}}{\left(R^{2}-|u|^{2}\right)}},} yielding − d τ 2 = − ( R 4 R 4 ( u ⋅ d u ) ( R 2 − | u | 2 ) 2 ) 2 = − R 2 16 R 4 ( u ⋅ d u ) 2 ( R 2 − | u | 2 ) 4 . {\displaystyle -d\tau ^{2}=-\left(R{\frac {4R^{4}\left(\mathbf {u} \cdot d\mathbf {u} \right)}{\left(R^{2}-|u|^{2}\right)^{2}}}\right)^{2}=-R^{2}{\frac {16R^{4}(\mathbf {u} \cdot d\mathbf {u} )^{2}}{\left(R^{2}-|u|^{2}\right)^{4}}}.} Now add this contribution to finally get ( σ − 1 ) ∗ h R 1 ( n ) = 4 R 2 [ ( d u 1 ) 2 + ⋯ + ( d u n ) 2 ] ( R 2 − | u | 2 ) 2 ≡ h R 2 ( n ) . {\displaystyle \left(\sigma ^{-1}\right)^{*}h_{R}^{1(n)}={\frac {4R^{2}\left[\left(du^{1}\right)^{2}+\cdots +\left(du^{n}\right)^{2}\right]}{\left(R^{2}-|u|^{2}\right)^{2}}}\equiv h_{R}^{2(n)}.} This last equation shows that the metric on the ball is identical to the Riemannian metric h2(n)R in the Poincaré ball model, another standard model of hyperbolic geometry. The pullback can be computed in a different fashion. By definition, ( σ − 1 ) ∗ h R 1 ( n ) ( V , V ) = h R 1 ( n ) ( ( σ − 1 ) ∗ V , ( σ − 1 ) ∗ V ) = η | H R 1 ( n ) ( ( σ − 1 ) ∗ V , ( σ − 1 ) ∗ V ) . {\displaystyle \left(\sigma ^{-1}\right)^{*}h_{R}^{1(n)}(V,\,V)=h_{R}^{1(n)}\left(\left(\sigma ^{-1}\right)_{*}V,\,\left(\sigma ^{-1}\right)_{*}V\right)=\eta |_{\mathbf {H} _{R}^{1(n)}}\left(\left(\sigma ^{-1}\right)_{*}V,\,\left(\sigma ^{-1}\right)_{*}V\right).} In coordinates, ( σ − 1 ) ∗ V = ( σ − 1 ) ∗ V i ∂ ∂ u i = V i ∂ x j ∂ u i ∂ ∂ x j + V i ∂ τ ∂ u i ∂ ∂ τ = V i ∂ x j ∂ u i ∂ ∂ x j + V i ∂ τ ∂ u i ∂ ∂ τ = V x j ∂ ∂ x j + V τ ∂ ∂ τ . {\displaystyle \left(\sigma ^{-1}\right)_{*}V=\left(\sigma ^{-1}\right)_{*}V^{i}{\frac {\partial }{\partial u^{i}}}=V^{i}{\frac {\partial x^{j}}{\partial u^{i}}}{\frac {\partial }{\partial x^{j}}}+V^{i}{\frac {\partial \tau }{\partial u^{i}}}{\frac {\partial }{\partial \tau }}=V^{i}{\frac {\partial }{x}}^{j}{\partial u^{i}}{\frac {\partial }{\partial x^{j}}}+V^{i}{\frac {\partial }{\tau }}{\partial u^{i}}{\frac {\partial }{\partial \tau }}=Vx^{j}{\frac {\partial }{\partial x^{j}}}+V\tau {\frac {\partial }{\partial \tau }}.} One has from the formula for σ–1 V x j = V i ∂ ∂ u i ( 2 R 2 u j R 2 − | u | 2 ) = 2 R 2 V j R 2 − | u | 2 − 4 R 2 u j ⟨ V , u ⟩ ( R 2 − | u | 2 ) 2 , ( here V | u | 2 = 2 ∑ k = 1 n V k u k ≡ 2 ⟨ V , u ⟩ ) V τ = V ( R R 2 + | u | 2 R 2 − | u | 2 ) = 4 R 3 ⟨ V , u ⟩ ( R 2 − | u | 2 ) 2 . {\displaystyle {\begin{aligned}Vx^{j}&=V^{i}{\frac {\partial }{\partial u^{i}}}\left({\frac {2R^{2}u^{j}}{R^{2}-|u|^{2}}}\right)={\frac {2R^{2}V^{j}}{R^{2}-|u|^{2}}}-{\frac {4R^{2}u^{j}\langle \mathbf {V} ,\,\mathbf {u} \rangle }{\left(R^{2}-|u|^{2}\right)^{2}}},\quad \left({\text{here }}V|u|^{2}=2\sum _{k=1}^{n}V^{k}u^{k}\equiv 2\langle \mathbf {V} ,\,\mathbf {u} \rangle \right)\\V\tau &=V\left(R{\frac {R^{2}+|u|^{2}}{R^{2}-|u|^{2}}}\right)={\frac {4R^{3}\langle \mathbf {V} ,\,\mathbf {u} \rangle }{\left(R^{2}-|u|^{2}\right)^{2}}}.\end{aligned}}} Lastly, η ( σ ∗ − 1 V , σ ∗ − 1 V ) = ∑ j = 1 n ( V x j ) 2 − ( V τ ) 2 = 4 R 4 | V | 2 ( R 2 − | u | 2 ) 2 = h R 2 ( n ) ( V , z , V ) , {\displaystyle \eta \left(\sigma _{*}^{-1}V,\,\sigma _{*}^{-1}V\right)=\sum _{j=1}^{n}\left(Vx^{j}\right)^{2}-(V\tau )^{2}={\frac {4R^{4}|V|^{2}}{\left(R^{2}-|u|^{2}\right)^{2}}}=h_{R}^{2(n)}(V,z,V),} and the same conclusion is reached. See also Remarks Notes References External links Media related to Minkowski diagrams at Wikimedia Commons |
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[SOURCE: https://en.wikipedia.org/wiki/Sue_Desmond-Hellmann] | [TOKENS: 1392] |
Contents Sue Desmond-Hellmann Sue Desmond-Hellmann (born 1958) is an American oncologist and biotechnology leader who was the chief executive officer of the Bill & Melinda Gates Foundation from 2014 to 2020. In March 2024, she was elected as a board member of OpenAI. She was previously Chancellor of the University of California, San Francisco (UCSF), the first woman to hold the position, and Arthur and Toni Rembe Rock Distinguished Professor, and before that president of product development at Genentech, where she played a role in the development of the first gene-targeted cancer drugs, Avastin and Herceptin. Early life and education Born in Napa, California, Desmond-Hellmann grew up in Reno, Nevada, as one of seven children. Her father worked as a pharmacist and her mother was an English teacher. She graduated from Bishop Manogue High School in 1975. She earned a bachelor of science degree in pre-medicine and an M.D. from the University of Nevada, Reno and received her residency training at UCSF, where she was chief resident. She is board-certified in internal medicine and medical oncology, and also holds a master's degree in public health from the University of California, Berkeley School of Public Health. Career Desmond-Hellmann was an associate adjunct professor of epidemiology and biostatistics At UCSF. She joined the UCSF medical faculty during the HIV/AIDS epidemic in San Francisco, and worked on Kaposi's sarcoma. Beginning in 1989 both she and her husband, an infectious disease doctor, spent two years as visiting faculty at the Uganda Cancer Institute, studying and treating patients with infectious diseases and Kaposi's sarcoma in a project funded by the Rockefeller Foundation. She then spent two years in private practice. Returning to clinical research, Desmond-Hellmann became associate director of clinical cancer research at Bristol-Myers Squibb Pharmaceutical Research Institute. While there, she was the project team leader for Taxol. In 1995, Desmond-Hellmann joined Genentech as a clinical scientist. She was named chief medical officer the following year, and in 1999 became executive vice president of development and product operations. From March 2004 to April 2009 she was president of product development, playing a role in the development of two of the first gene-targeted therapies for cancer, Avastin and Herceptin. She left after the company was acquired by Roche Pharmaceuticals. At that point her compensation was $8 million a year. From 2005 to 2008, Desmond-Hellmann served a three-year term as a member of the American Association for Cancer Research board of directors, and from 2001 to 2009, she served on the executive committee of the board of directors of the Biotechnology Industry Organization. She also served a three-year term on the Economic Advisory Council of the Federal Reserve Bank of San Francisco beginning in January 2009. She was on the corporate board of Affymetrix from 2004 to 2009, and on the board of Procter & Gamble from 2012 to 2013. After being invited to apply, on August 3, 2009, Desmond-Hellmann became the ninth Chancellor of UCSF, and the first woman to hold the position. Desmond-Hellmann became the first Chancellor drawn from outside academia. Her starting salary was $450,000 a year. In June 2010, one day after being questioned by The New York Times, Desmond-Hellmann sold her stock in the Altria Group, which owns Phillip Morris USA and other tobacco companies, and subsequently donated $134,000 to the tobacco control center at UCSF. She said that many of her holdings had been purchased on her behalf by her stockbroker and that she was too busy to oversee all her investments, although she had included the stock on her financial disclosure statement. In January 2012, Desmond-Hellmann proposed changing the relationship between UCSF, a health sciences university, and the University of California. She proposed creating partnerships between UCSF and private pharmaceutical corporations and other sources of funding, in order to increase its revenues and resolve its projected financial instability. Desmond-Hellmann served as UCSF Chancellor until March 2014, holding the Arthur and Toni Rembe Rock Distinguished Professorship during her tenure. In 2011, Desmond-Hellmann co-chaired a National Academy of Sciences committee that recommended creating a Google Maps-like data network aimed at developing more diagnostics and treatments tailored to individual patients — a concept known as precision medicine. The so-called "knowledge network" would integrate the wealth of data emerging on the molecular basis of disease with information on environmental factors and patients' electronic medical records and would allow scientists to share emerging research findings faster, thereby accelerating the development of tailored treatments. It also would allow clinicians to make more informed decisions about treatments, reduce health care costs and ultimately improve care. The NAS report, titled "Toward Precision Medicine: Building a Knowledge Network for Biomedical Research and a New Taxonomy of Disease", was described by Keith Yamamoto, Vice Chancellor for Research at UCSF, as "the most important National Academy of Sciences Framework Analysis since that advisory body recommended that the United States go forward with the Human Genome Project". On December 17, 2013, The Bill & Melinda Gates Foundation announced that it had selected Desmond-Hellmann as its next chief executive officer. She assumed her role on May 1, 2014, the first head of the foundation to be neither a former Microsoft executive nor a friend of the Gates', and the first physician. In 2017, Desmond-Hellmann became a member of the Prix Galien USA Committee, succeeding Roy Vagelos as Chair of that Committee in 2018. She is also Chair of the Prix Galien International and Member of the Prix Galien Africa Committee. In December 2019, Desmond-Hellmann announced plans to step down from her role as BMGF CEO "for health and family reasons". Mark Suzman will leave his role of BMGF president of Global Policy & Advocacy and chief strategy officer to become the new BMGF CEO on February 1, 2020. In 2021, Desmond-Hellmann was appointed by President Joe Biden to the President’s Council of Advisors on Science and Technology (PCAST), co-chaired by Frances Arnold, Eric Lander and Maria Zuber. In March 2024, Desmond-Hellman was appointed to OpenAI's Board of Directors. In 2024 Desmond-Hellmann received the Clark Kerr Award for distinguished leadership in higher education from the UC Berkeley Academic Senate. Other activities Personal life Desmond-Hellmann married Nicholas Hellmann in 1987. References External links |
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[SOURCE: https://en.wikipedia.org/wiki/AT%26T_Mobility] | [TOKENS: 6997] |
Contents AT&T Mobility AT&T Mobility, LLC, also known as AT&T Wireless and marketed as simply AT&T, is an American telecommunications company. Formed in April 2000 as Cingular Wireless LLC, It is a wholly owned subsidiary of AT&T Inc. and provides wireless services in the United States. AT&T Mobility is the third largest wireless carrier in the United States, with 120.1 million subscribers as of December 31, 2025. The company is headquartered in Brookhaven, Georgia. Originally known as Cingular Wireless (a joint venture between SBC Communications and BellSouth) from 2000 to 2007, the company acquired the old AT&T Wireless in 2004; SBC later acquired the original AT&T and adopted its name. Cingular became wholly owned by AT&T in December 2006 as a result of AT&T's acquisition of BellSouth. In January 2007, Cingular confirmed it would rebrand itself under the AT&T name. Although the legal corporate name change occurred immediately, for both regulatory and brand-awareness reasons both brands were used in the company's signage and advertising during a transition period. The transition concluded in late June, just prior to the rollout of the Apple iPhone. On March 20, 2011, AT&T Mobility announced its intention to acquire T-Mobile US from Deutsche Telekom for $39 billion. If it had received government and regulatory approval, AT&T would have had more than 130 million subscribers. However, the U.S. Department of Justice, the Federal Communications Commission (FCC), and AT&T Mobility's competitors (such as Sprint Corporation) opposed the move on the grounds that it would substantially reduce competition in the cellular network market. In December 2011, in the face of both governmental and widespread consumer opposition, AT&T withdrew its offer to complete the merger. Services AT&T offers three tiers of its Unlimited Your Way plan, AT&T Unlimited Premium PL, AT&T Unlimited Extra EL, and AT&T Unlimited Starter SL. Customers can also choose from either the AT&T Value Plus VL, or AT&T 4 GB plans. All plans come with unlimited talk and text, with unlimited data on all except the AT&T 4 GB plan. The higher tier plans include premium data that offers superior service, up to the allotted limit on each line during a bill cycle, plus other features like Mobile Hotspot and more. The AT&T Unlimited Premium® PL plan also includes unlimited talk, text, and data in 20 Latin American countries including the Dominican Republic, included at no extra charge. As of January 8, 2016, AT&T no longer offers two-year contracts for subsidized smartphones on consumer accounts. Customers who currently have two-year contracts are grandfathered until they upgrade to a new device, in which case they will have to choose from AT&T's NEXT installment plans for smartphones. Unlimited data plans may be throttled based on the terms of the plan. AT&T also allows existing customers to stay on legacy right plans; however, reserves the right to terminate or require a plan change per its terms of service. Within AT&T's 21-state landline footprint, other AT&T services are offered at the AT&T retail stores, including signing up for home phone, internet, and U-verse. AT&T stores outside of its footprint offer wireless services. AT&T also provides free-email services to its customers. Employees A large number of AT&T Mobility employees are unionized, belonging to the Communications Workers of America. The CWA represented roughly 15,000 of the previous 20,000 formerly AT&T Wireless employees as of early 2006. As of the end of 2009, the CWA website claims that roughly 40,000 workers of AT&T Mobility are represented by the union. History Cingular Wireless was a wireless telecommunications company that was founded in April 2000 as a joint venture of SBC Communications and BellSouth. The joint venture created the nation's second-largest carrier. Cingular grew out of a conglomeration of more than 100 companies, including 12 well-known regional companies with Bell roots. The 12 companies included: SBC Wireless had previously operated in several northeast markets under the "Cellular One" brand, while BellSouth's wireless operations incorporated the former Houston Cellular. Cingular's lineage can be traced back to Advanced Mobile Phone Service, which was a subsidiary of AT&T created in 1978 to provide cellular service nationwide. AMPS was divided among the Regional Bell Operating Companies as part of the Bell System divestiture. With the exception of Pacific Bell and BellSouth Mobility DCS, the digital network consisted of D-AMPS technology. The Pacific Bell and BellSouth Mobility DCS networks used GSM technology on the PCS frequency band (1900 MHz). In October 2007, AT&T's president and chief executive officer Stan Sigman announced his retirement. Ralph de la Vega, group president-Regional Telecom & Entertainment, was named as president and CEO of AT&T Mobility.[citation needed] In February 2004, after a bidding war with Britain's Vodafone Plc (at the time a part-owner of Verizon Wireless), Cingular announced that it would purchase its struggling competitor, AT&T Wireless Services, for $41 billion. This was more than twice the company's trading value. The merger was completed on October 26, 2004. The combined company had a customer base of 46 million people at the time, making Cingular the largest wireless provider in the United States. AT&T Wireless was then legally renamed New Cingular Wireless Services. Shortly after, new commercials were shown with the "AT&T" transforming into the Cingular logo, and with the Cingular logo's text turned blue to acknowledge the change. Some of the companies that comprised Cingular, such as BellSouth Mobility, ceased to exist when they were legally merged into the operating company subsidiary AT&T Wireless PCS, which was New Cingular Wireless PCS.[citation needed] First announced on June 22, 2005, Cingular Wireless announced the intention to divest its Caribbean and Bermuda operations and licenses which it acquired from the acquisition of AT&T Wireless, to Irish-owned and Jamaica-based Digicel Group under undisclosed financial terms. In 2006, one year following the deal, a high-ranking source allegedly close to the sale pointed the Barbados Daily Nation Newspaper towards some SEC filings made by Cingular which were said to establish an idea of the approximate sale price of the deal. According to the SEC filings Cingular was paid around $122 million, with much of that cost going towards the purchase of the former AT&T Wireless assets in Barbados by Digicel.[citation needed] At the time of the merger, there were two networks: the historic AT&T Blue Network and the Cingular Orange Network. Both networks contained a mix of both TDMA and GSM facilities. Approximately 50,000 cell sites had to be melded together. From a technical standpoint, the "blue" and "orange" networks were considered different networks until integration was completed in 2005. Enhanced Network Selection (ENS) was used to home cellular devices on either the "blue" or "orange" network during this process. On November 21, 2005, Ed Whitacre, then CEO of the newly merged SBC/AT&T, announced plans to market Cingular's service under the AT&T brand. BellSouth spokesman Jeff Battcher countered that the terms of the joint venture allow either party to sell the service under another name, and that he believes they will be using the brand to market to business customers. Cingular president Stan Sigman concurred with BellSouth's position, indicating that the Cingular brand would continue but be sold under the AT&T brand where offered in packages with other AT&T services, such as data and wireline telephony. However, AT&T announced on March 5, 2006, that AT&T would merge with BellSouth. The acquisition was finalized on December 29, 2006, when the FCC gave its final approval. The following month, AT&T announced that it would phase out the Cingular brand across all of its services and replace it with AT&T, with an accompanying advertising campaign branding the combined company as "The New AT&T." Commercials featured the orange Cingular "Jack" logo encircling the AT&T globe logo several times, dragging its blue bars behind it to form the globe's blue stripes, before finally disappearing behind it, being backed by the chorus of the Oasis song "All Around the World". AT&T added the color orange to its signage to reflect the change; AT&T would eventually remove orange in 2015 following another rebranding related to its acquisition of DirecTV. In November 2007, AT&T merged with Dobson Communications, who owned Cellular One and was a roaming partner of AT&T, for $2.8 billion. The sale added 1.7 million subscribers and expanded AT&T coverage in various suburban and rural markets (including Alaska). On November 7, 2008, AT&T announced its intent to acquire Centennial Wireless for $944 million, expanding its coverage in the Midwest, southern U.S., and Puerto Rico. On March 20, 2011, AT&T and Deutsche Telekom announced that AT&T had agreed to acquire T-Mobile USA from Deutsche Telekom in a deal estimated to be worth $39 billion in cash and stock. AT&T said the deal was expected to close in 12 months and was subject to regulatory approval. As of June 2011, it was being examined by the FCC. On August 31, 2011, the United States Department of Justice formally announced that it had filed a lawsuit to block the merger. On November 22, 2011, FCC Chairman Julius Genachowski recommended sending AT&T's proposed T-Mobile acquisition to an administrative law judge for review and a hearing. On November 23, 2011, AT&T withdrew its application with the FCC regarding the acquisition of T-Mobile USA. They also indicated that they would recognize a $4 billion accounting charge in the event of a deal collapse. That charge covers a $3 billion cash breakup fee and $1 billion as the market value for the spectrum they were required to transfer to T-Mobile if the deal failed to complete. On August 2, 2012, AT&T announced its intent to acquire NextWave Wireless. On January 22, 2013, AT&T announced its intent to acquire the U.S. retail wireless operations of Atlantic Tele-Network, doing business as Alltel, for $780 million. On June 24, 2014, Plateau Wireless announced the sale of assets and operations in eastern New Mexico and west Texas to AT&T, including wireless spectrum and 40,000 customers. In November 2014 and January 2015, AT&T acquired the Mexican wireless carriers Iusacell and Nextel Mexico to form AT&T Mexico. On October 9, 2019, Liberty Cablevision of Puerto Rico's parent company (Liberty Latin America), announced the acquisition of AT&T Wireless Services in Puerto Rico and the U.S. Virgin Islands, in a $1.95 billion deal. The sale was completed on November 2, 2020. In May 2021, the company began promoting AT&T and Liberty as a unified brand. In September 2021, Liberty began phasing out the AT&T brand and introduced a new logo. On February 22, 2024, a massive outage affected customers nationwide. Network In California, Nevada, Northern New Jersey and New York City, Cingular and T-Mobile USA maintained and shared a GSM-1900 network prior to the acquisition of AT&T Wireless, through a joint venture known as GSM Facilities. The network sharing agreement allowed Cingular to offer local service in northern New Jersey and New York City and T-Mobile USA to offer service in California and Nevada. On May 25, 2004, Cingular and T-Mobile USA announced their intention to dissolve the agreement contingent on Cingular's successful acquisition of AT&T Wireless, the Cingular network was transferred to T-Mobile USA, with Cingular continuing work on the GSM facilities at AT&T Wireless sites. AT&T has a global sub-sea Tier-1 fiber network switching facility on St. Croix in the U.S. Virgin Islands, in conjunction with University of the Virgin Islands Research and Technology Park. The following is a list of known frequencies that AT&T employs in the United States. The following chart lists the networks that AT&T previously operated. As a result of its formation through mergers and acquisitions, as well as the rapid technological change in the wireless industry, AT&T operates the second-largest digital voice and data network within its United States footprint. AT&T's network footprint supports 4G and uses LTE/LTE-Advanced for simultaneous packet switched voice and data communications. AT&T is also in the process of rolling out its 5G network based on the NR specification. Cingular, the predecessor to AT&T, supported legacy D-AMPS/TDMA and analog wireless networks. In March 2006, Cingular announced that these networks would be shut down by February 2008. As of March 31, 2007, Cingular ended TDMA supported for GoPhone (pre-paid) customers. On July 15, 2007, AT&T TDMA on 1900 MHz was retired, while TDMA on 850 MHz remained. On February 18, 2008, AT&T Mobility officially ended service on their AMPS and remaining TDMA network, except for in areas previously operated by Dobson Communications; the Dobson AMPS and TDMA network was shut down March 1, 2008. Networks formerly operated by AT&T predecessors including Cingular also include various paging services and the Cingular Interactive division, which became Velocita Wireless. Velocita was later purchased by Sprint Nextel. AT&T also offered Enhanced Push To Talk (PTT) services on smartphones. The original PTT service was sunset. The AT&T wireless data network began in 2002 as a Cingular initiative called "Project Genesis" that involved a GPRS overlay of the entire wireless network. Project Genesis was completed by the end of 2004. Later, this network was upgraded to EDGE across the GSM footprint. In 2005, AT&T launched a broadband network known as "BroadbandConnect", based on UMTS and HSDPA, to counter Verizon Wireless and Sprint's EV-DO networks. UMTS service was launched on December 6, 2005, in Seattle, Portland, San Francisco, Salt Lake City, San Jose, San Diego, Las Vegas, Phoenix, Puerto Rico, Austin, Houston, Dallas, Detroit, Chicago, Boston, Baltimore, and Washington, D.C., and expanded to all major metropolitan markets by the end of 2006. As of early 2009, AT&T Mobility has completed its upgrade of the 3G to HSUPA, In 2011, it was reported that AT&T would upgrade its network to HSPA+ throughout the year, which it would market as offering 4G-grade speeds. On September 18, 2011, AT&T first launched LTE service in 5 U.S. metropolitan areas, with plans for serving 15 markets by the end of the year. AT&T's LTE rollout was noticeably slower than that of its competitor, Verizon Wireless, with the company stating that its then-proposed acquisition of T-Mobile USA would be necessary. In November 2012, AT&T promoted the network as serving 150 million users, with plans to double its coverage by 2014. On January 1, 2017, AT&T discontinued its 2G GSM network. In April 2017, AT&T announced that it would upgrade its existing LTE networks in selected markets to support LTE Advanced and LTE Advanced Pro features, marketed as "5G Evolution" (5G E). In January 2018, AT&T stated that it intended to deploy 5G NR service by the end of the year. On February 22, 2022, AT&T discontinued its 3G UMTS network AT&T operates the second-largest 5G network in the U.S. with approximately 30% of the nation covered. AT&T uses low, mid, and high band frequencies. Mid and high band 5G is marketed as 5G+ and offers much faster speeds than low band. Continuous expansion of the 5G network, especially mid-band 5G+, is planned through 2023. AT&T plans to cover 200 million people with 5G+ by the end of 2023. Marketing During the first quarter of 2006, Telephia reported that during an extensive nationwide test of major wireless carriers in 350 metropolitan markets around the country, Cingular dropped the fewest calls across the country. In turn, Cingular began aggressively advertising the "Allover Network", citing Telephia as "the leading independent research company." Telephia's report was in stark contrast to the Consumers Union publication, Consumer Reports, based on a survey of 50,000 of its members in 18 cities, which criticized Cingular for static and dropped calls. Furthermore, J.D. Power and Associates consistently ranked Cingular at or near the bottom of every geographical region in its 2006 Wireless Call Quality Study, which is based on a smaller survey of 23,000 wireless users. This campaign had to come to an abrupt end. Telephia, which tests wireless networks by making over 6 million calls per year in what it claims is the world's largest wireless network test program, initially refused to provide details on its study, and a spokesman for the company has said, according to the Boston Globe, that "Cingular shouldn't have even mentioned the company's name to a reporter." The research company later stated that Cingular did, indeed, have a "statistically significant lower dropped-call rate than the competition across some market/time period groupings", but that Telephia had "no knowledge of the specific methodology (markets, time periods or statistical thresholds) that Cingular used for its 'lowest dropped call' claim." While AT&T has abandoned its verbal claim of "The Fewest Dropped Calls" in its commercials, it continues to show situations where two persons are speaking with each other on their phones, and one of the users' call drops. AT&T now states "We are still continuing to run ads that emphasize the importance of not dropping calls. That campaign is continuing." On June 29, 2007, Apple's iPhone was introduced to the United States market, and AT&T was the exclusive carrier for the device within the United States until February 10, 2011, when the iPhone 4 was launched on the Verizon network. Teething problems with AT&T's billing process emerged soon after the iPhone's release, as early adopters started receiving exceptionally detailed monthly telephone bills with one of the most notable being the 300-page iPhone bill that was featured in an online video by YouTube influencer iJustine. Apple launched the iPhone 3G with AT&T on July 11, 2008. Although specific AT&T sales numbers are unavailable, Apple announced that over 1 million iPhone 3G devices were sold during the first three days — in contrast, according to Steve Jobs, Apple's CEO, "It took 74 days to sell the first one million original iPhones." In August 2008, Best Buy announced that it would begin selling the iPhone 3G for use on the AT&T network. In September 2008, AT&T announced that it would also sell the iPhone 3G in Puerto Rico and the U.S. Virgin Islands. The iPhone 4 was released on June 24, 2010. According to Apple, over 1.7 million iPhone 4 units were sold in the first few days, which is the most out of any phone ever sold. These sales propelled AT&T to strong Q2 results. The iPhone 5 was released on September 12, 2012. Apple reported selling 5 million iPhone 5's in the first weekend. AT&T activated 8.5 million iPhones in Q4 of 2012. On February 18, 2010, AT&T announced that on March 7, 2010, it would introduce its first smart phone based on Google's Android operating system, the Motorola Backflip. On March 22, 2010, AT&T announced that its second Android handset would be the Dell Aero, a revised version of the Dell Mini 3. However, the second Android phone AT&T released was the HTC Aria which was announced on June 14, 2010, and released on June 20, 2010. The Samsung Captivate, which is part of the Galaxy S family, was released on AT&T's network on July 18, 2010. In addition to devices released on AT&T were a line of handsets manufactured by Motorola. The Motorola Flipout, followed by the Motorola Flipside and the Motorola Bravo all run Android 2.1 and were all released Q4 2010. Three new 4G Android devices were announced for release within the first and second quarter of the fiscal year 2011, including the Motorola Atrix 4G, the HTC Inspire 4G, and the Samsung Infuse 4G. HTC Inspire 4G being the first, preceded by the Motorola Atrix 4G are, available through AT&T's 4G network. These three devices are all running Android 2.2 (Froyo) and are expected to be upgraded to Android 2.3 Gingerbread later in the year, along with an update to "enable" 4G uploads. Unlike other United States networks with Android-based phones, AT&T did not allow non-market apps to be installed. However, on May 16, 2011, AT&T announced that some current and future Android devices will come with an option to allow the installation of unofficial applications. In a BBDO campaign for 4G and 4G LTE started in November 2012, Beck Bennett interviewed children in commercials directed by Jorma Taccone, with the slogan "It's not complicated." The children were asked whether fast or slow is better, or whether two is better than one. Taccone said "The spots are 'guided' improv", meaning the children were allowed to be natural until others had to step in and help. In the NFS games Underground 2 to Carbon, the network (as Cingular) was shown as the mobile internet provider in the ingame voice/text message. Current services AT&T reintroduced unlimited plans in 2016; on launch, users were required to subscribe to an AT&T-owned pay television service (DirecTV or U-verse) in order to be eligible. In April 2017, the Unlimited Plus plan was reduced in price, and a complimentary subscription to HBO (either as part of an AT&T-owned pay television service, or standalone via HBO GO) was added to both plans. In June 2018, the two plans were discontinued for new subscribers and replaced by similar "Unlimited & More" plans, which both include AT&T's new "Watch TV" service (which includes a selection of entertainment cable networks) at no charge, and Unlimited & More Premium allowing users to also choose a premium subscription service (such as Cinemax, HBO, Showtime, Spotify, Starz, Amazon Music Unlimited, Pandora Premium, or VRV) as an add-on. The basic Unlimited & More plan is restricted to standard definition video streaming. AT&T Prepaid (stylized AT&T PREPAID; formerly GoPhone) is a prepaid mobile phone service from AT&T Mobility. The GoPhone name and product were originally conceived and implemented by McCaw Cellular by its founder Craig McCaw and first used in commerce in 1987 by his company. It was later bought by AT&T in 1995 and used by the pre-2004 "AT&T Wireless" after Cingular's purchase of AT&T Wireless in 2004 for $41 billion. At that time, Cingular was jointly owned by SBC Communications (Southwestern Bell Corporation) of San Antonio, Texas, which owned 60 percent, and BellSouth of Atlanta, Georgia. The original GoPhone service was discontinued and Cingular renamed its prepaid services under GoPhone. The GoPhone brand name was still in use even after "Cingular" renamed itself "AT&T Mobility" until 2017 when it was rebranded AT&T PREPAID. As of January 2019, AT&T Prepaid has 6 million subscribers. NumberSync was introduced in 2015. The service allows AT&T postpaid wireless customers to use one telephone number to send and receive calls and text messages across all of their supported devices. Controversies In 2011, following a similar change by T-Mobile USA, AT&T began marketing both its HSPA and HSPA+ services as "4G", and distributed phone software patches changing their network indicators to identify these services as such. With the ITU having expanded its definition of 4G to include HSPA+, AT&T decided to label 14 Mbit/s HSPA devices and service as HSPA+, and thus 4G. Standard HSPA service, however, never met 4G standards, nor are these HSPA devices (non-Evolved) actually capable of operating at HSPA+ speeds. Media outlets considered this branding to be deceptive. Concerns were also expressed over the possibility of confusion when actual 4G VoLTE networks were to be eventually deployed. In 2017, AT&T began to similarly use the trademark 5G Evolution (5G E) to refer to LTE networks upgraded to support higher data speeds via LTE Advanced and LTE Advanced Pro features, such as 4x4 MIMO antennas, 256-QAM, and three-way carrier aggregation. AT&T promotes these networks as having a theoretical top speed of 400 Mbit/s. In late-2018, AT&T distributed phone software patches changing network indicators to refer to these networks as such. 5G Evolution is entirely unrelated to actual 5G wireless standards; AT&T states that these technologies "serve as the runway to 5G by boosting the existing LTE network and priming it for the future of connectivity", and argued that "the customer doesn't need to think about the exact technology – they only care on the performance and what it enables." AT&T marketing likewise promotes this network with the slogan "The First Step to 5G". AT&T once again faced allegations that the branding was misleading, because it is merely a rebranding of existing 4G networks in order to ride upon consumer anticipation of actual 5G technology. T-Mobile US and Verizon Wireless have deployed similar late-stage upgrades in a larger number of markets than AT&T, but promote them as being upgrades to their 4G LTE service. T-Mobile mocked the branding via a video on Twitter, showing a person applying a sticky note reading "9G" over the LTE indicator on an iPhone, captioned "didn't realize it was this easy, brb updating". Technology website The Verge noted that the South American wireless carrier Claro had been using the branding "4.5G" (stylized to make the 4 slightly smaller than the 5) to promote similar upgrades to its LTE service, but felt that this brand was "not as baldfaced a deception as AT&T's 5G E". In February 2019, Sprint Corporation sued AT&T Mobility for false advertising, presenting evidence that consumers were being misled into believing these services were of equal or higher performance than actual 5G networks. Sprint sought an injunction to halt AT&T's promotion of the network with this trademark. However, the two parties later settled, with AT&T being allowed to continue to promote their network with the trademark. In May 2020, following complaints by T-Mobile to the National Advertising Division, the National Advertising Review Board (NARB) recommended that AT&T stop using "5G Evolution" or "The First Step to 5G" in advertising, as "the term 'Evolution' is not likely to alert consumers to the fact that the service is not 5G." AT&T stated that it would not use "5G Evolution" or the slogan in future advertising, but that it will still use the 5G E logo, and not remove the indicator from devices. Cingular Wireless began its sponsorship of the #31 Chevrolet, owned by Richard Childress Racing, in the NASCAR Winston Cup Series in 2002. Two years later, when Nextel Communications (now Sprint Corporation) purchased the naming rights to NASCAR's top division (rebranding the division as the Nextel Cup, and later the Sprint Cup), Cingular and Alltel, sponsor of the #12 Dodge (owned by Penske Racing and driven by Ryan Newman), were allowed to stay as sponsors under a grandfather clause. In early 2007, following its purchase by AT&T, Cingular began a re-branding effort to the AT&T Mobility brand. NASCAR quickly claimed that a clause in their contract with Sprint Nextel (the Viceroy rule) would not allow Cingular to change either the name or brand advertised on the #31 car. After trying and failing to persuade NASCAR to approve the addition of the AT&T globe logo to the rear of the car, AT&T filed a lawsuit against NASCAR on March 16, 2007. On May 18, AT&T won a preliminary injunction in the United States District Court for the Northern District of Georgia in Atlanta and, following a failed emergency motion for a stay by NASCAR on May 19, re-branded the #31 car, driven by Jeff Burton, in time for the Nextel All-Star Challenge that evening. NASCAR was later granted an appeal to be heard on August 2. On June 17, NASCAR announced it had filed a US$100 million lawsuit against AT&T and would like AT&T and all other rival telecommunications companies out of the sport in 2008. On August 13, a ruling by the United States Court of Appeals for the Eleventh Circuit cleared the way for NASCAR to prevent AT&T from featuring its logo on the car. The 11th Circuit dismissed a lower court's ruling that prevented NASCAR from stopping AT&T's plans. The appeals court remanded the case to the district court. At first practice for the Sharpie 500 at Bristol Motor Speedway on August 24, the #31 car was colored orange and black, but was bare; that is, associate sponsors appeared, but no primary sponsors were on the car, similar to Formula One cars run in races where tobacco advertising is prohibited. The pit crew wore grey Richard Childress Racing shirts and Burton had a plain orange fire suit with associate sponsors. The car, which carried a "subliminal advertising" scheme, arrived in a black hauler with only the number 31 on the side. NASCAR officials said the car would not have made it through inspection with the AT&T logos. During that weekend, AT&T claimed that two alternate paint schemes proposed by AT&T — one advertising its "go phone" and another with the old Cingular slogan "more bars in more places" that AT&T recently brought back — were rejected by NASCAR. The Go Phone scheme had been used in the past. NASCAR later denied these claims. On September 7, 2007, a settlement was reached where AT&T Mobility could remain on the #31 car until the end of 2008, but the associate sponsorship of the #29 Nationwide Series Holiday Inn Chevrolet was not affected, because it is in a lower series. No division of AT&T have sponsored any organization in NASCAR since, even though the Viceroy rule changed from telecommunications companies to beverages when Monster Energy took over sponsorship of the Cup Series in 2017 before NASCAR removed series title sponsorship in the Cup Series altogether, effectively removing any restrictions on which brands can sponsor teams, pursuant to NASCAR approval. In fact, AT&T's parent division had sued a NASCAR team and driver it sponsored, Mike Borkowski, on performance grounds. In 2012, AT&T came under scrutiny for throttling the speed of data delivered to consumers with an unlimited data plan. The company has claimed that, despite its claim of network speeds, it is within its legal rights to reduce the speed of data to consumers who reach preset thresholds. In May 2012, Matt Spaccarelli, a truck driver, won a small claims lawsuit against the company for slowing down his service. A Simi Valley, California judge awarded Spaccarelli $850, agreeing that "unlimited" service shouldn't be subject to slowdowns. Additionally, AT&T's user agreement does not permit class-action suits against the company. In 2014, the FTC sued AT&T for deceptive business practices. In November 2019, AT&T agreed to pay $60 million to settle the suit, which must be distributed as a "partial refund" to customers who signed up for the affected plans prior to 2011. It also agreed to prominently disclose any throttling restrictions it imposes on its wireless plans in the future. In May 2013, AT&T added a 61 cent "Mobility Administrative Fee" per-month per-line to all of its wireless postpaid lines, including lines still under service contract. The fee appears "below the line" making it appear like a tax at the bottom of a customer's phone bill. This fee is thought to bring more than a half-billion dollars in a year for AT&T, which claims the fee is for covering the cost of cell sites and maintenance. In June 2018, AT&T raised the administrative fee to $1.99 from 76 cents per-line. In April 2024, AT&T was fined $57 million by the FCC for illegally sharing access to customers' real-time location data. In response, AT&T criticized the FCC's decision, claiming it lacked "both legal and factual merit." Other AT&T’s subsidiaries/brands References External links |
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Contents Internet The Internet (or internet)[a] is the global system of interconnected computer networks that uses the Internet protocol suite (TCP/IP)[b] to communicate between networks and devices. It is a network of networks that comprises private, public, academic, business, and government networks of local to global scope, linked by electronic, wireless, and optical networking technologies. The Internet carries a vast range of information services and resources, such as the interlinked hypertext documents and applications of the World Wide Web (WWW), electronic mail, discussion groups, internet telephony, streaming media and file sharing. Most traditional communication media, including telephone, radio, television, paper mail, newspapers, and print publishing, have been transformed by the Internet, giving rise to new media such as email, online music, digital newspapers, news aggregators, and audio and video streaming websites. The Internet has enabled and accelerated new forms of personal interaction through instant messaging, Internet forums, and social networking services. Online shopping has also grown to occupy a significant market across industries, enabling firms to extend brick and mortar presences to serve larger markets. Business-to-business and financial services on the Internet affect supply chains across entire industries. The origins of the Internet date back to research that enabled the time-sharing of computer resources, the development of packet switching, and the design of computer networks for data communication. The set of communication protocols to enable internetworking on the Internet arose from research and development commissioned in the 1970s by the Defense Advanced Research Projects Agency (DARPA) of the United States Department of Defense in collaboration with universities and researchers across the United States and in the United Kingdom and France. The Internet has no single centralized governance in either technological implementation or policies for access and usage. Each constituent network sets its own policies. The overarching definitions of the two principal name spaces on the Internet, the Internet Protocol address (IP address) space and the Domain Name System (DNS), are directed by a maintainer organization, the Internet Corporation for Assigned Names and Numbers (ICANN). The technical underpinning and standardization of the core protocols is an activity of the non-profit Internet Engineering Task Force (IETF). Terminology The word internetted was used as early as 1849, meaning interconnected or interwoven. The word Internet was used in 1945 by the United States War Department in a radio operator's manual, and in 1974 as the shorthand form of Internetwork. Today, the term Internet most commonly refers to the global system of interconnected computer networks, though it may also refer to any group of smaller networks. The word Internet may be capitalized as a proper noun, although this is becoming less common. This reflects the tendency in English to capitalize new terms and move them to lowercase as they become familiar. The word is sometimes still capitalized to distinguish the global internet from smaller networks, though many publications, including the AP Stylebook since 2016, recommend the lowercase form in every case. In 2016, the Oxford English Dictionary found that, based on a study of around 2.5 billion printed and online sources, "Internet" was capitalized in 54% of cases. The terms Internet and World Wide Web are often used interchangeably; it is common to speak of "going on the Internet" when using a web browser to view web pages. However, the World Wide Web, or the Web, is only one of a large number of Internet services. It is the global collection of web pages, documents and other web resources linked by hyperlinks and URLs. History In the 1960s, computer scientists began developing systems for time-sharing of computer resources. J. C. R. Licklider proposed the idea of a universal network while working at Bolt Beranek & Newman and, later, leading the Information Processing Techniques Office at the Advanced Research Projects Agency (ARPA) of the United States Department of Defense. Research into packet switching,[c] one of the fundamental Internet technologies, started in the work of Paul Baran at RAND in the early 1960s and, independently, Donald Davies at the United Kingdom's National Physical Laboratory in 1965. After the Symposium on Operating Systems Principles in 1967, packet switching from the proposed NPL network was incorporated into the design of the ARPANET, an experimental resource sharing network proposed by ARPA. ARPANET development began with two network nodes which were interconnected between the University of California, Los Angeles and the Stanford Research Institute on 29 October 1969. The third site was at the University of California, Santa Barbara, followed by the University of Utah. By the end of 1971, 15 sites were connected to the young ARPANET. Thereafter, the ARPANET gradually developed into a decentralized communications network, connecting remote centers and military bases in the United States. Other user networks and research networks, such as the Merit Network and CYCLADES, were developed in the late 1960s and early 1970s. Early international collaborations for the ARPANET were rare. Connections were made in 1973 to Norway (NORSAR and, later, NDRE) and to Peter Kirstein's research group at University College London, which provided a gateway to British academic networks, the first internetwork for resource sharing. ARPA projects, the International Network Working Group and commercial initiatives led to the development of various protocols and standards by which multiple separate networks could become a single network, or a network of networks. In 1974, Vint Cerf at Stanford University and Bob Kahn at DARPA published a proposal for "A Protocol for Packet Network Intercommunication". Cerf and his graduate students used the term internet as a shorthand for internetwork in RFC 675. The Internet Experiment Notes and later RFCs repeated this use. The work of Louis Pouzin and Robert Metcalfe had important influences on the resulting TCP/IP design. National PTTs and commercial providers developed the X.25 standard and deployed it on public data networks. The ARPANET initially served as a backbone for the interconnection of regional academic and military networks in the United States to enable resource sharing. Access to the ARPANET was expanded in 1981 when the National Science Foundation (NSF) funded the Computer Science Network (CSNET). In 1982, the Internet Protocol Suite (TCP/IP) was standardized, which facilitated worldwide proliferation of interconnected networks. TCP/IP network access expanded again in 1986 when the National Science Foundation Network (NSFNet) provided access to supercomputer sites in the United States for researchers, first at speeds of 56 kbit/s and later at 1.5 Mbit/s and 45 Mbit/s. The NSFNet expanded into academic and research organizations in Europe, Australia, New Zealand and Japan in 1988–89. Although other network protocols such as UUCP and PTT public data networks had global reach well before this time, this marked the beginning of the Internet as an intercontinental network. Commercial Internet service providers emerged in 1989 in the United States and Australia. The ARPANET was decommissioned in 1990. The linking of commercial networks and enterprises by the early 1990s, as well as the advent of the World Wide Web, marked the beginning of the transition to the modern Internet. Steady advances in semiconductor technology and optical networking created new economic opportunities for commercial involvement in the expansion of the network in its core and for delivering services to the public. In mid-1989, MCI Mail and Compuserve established connections to the Internet, delivering email and public access products to the half million users of the Internet. Just months later, on 1 January 1990, PSInet launched an alternate Internet backbone for commercial use; one of the networks that added to the core of the commercial Internet of later years. In March 1990, the first high-speed T1 (1.5 Mbit/s) link between the NSFNET and Europe was installed between Cornell University and CERN, allowing much more robust communications than were capable with satellites. Later in 1990, Tim Berners-Lee began writing WorldWideWeb, the first web browser, after two years of lobbying CERN management. By Christmas 1990, Berners-Lee had built all the tools necessary for a working Web: the HyperText Transfer Protocol (HTTP) 0.9, the HyperText Markup Language (HTML), the first Web browser (which was also an HTML editor and could access Usenet newsgroups and FTP files), the first HTTP server software (later known as CERN httpd), the first web server, and the first Web pages that described the project itself. In 1991 the Commercial Internet eXchange was founded, allowing PSInet to communicate with the other commercial networks CERFnet and Alternet. Stanford Federal Credit Union was the first financial institution to offer online Internet banking services to all of its members in October 1994. In 1996, OP Financial Group, also a cooperative bank, became the second online bank in the world and the first in Europe. By 1995, the Internet was fully commercialized in the U.S. when the NSFNet was decommissioned, removing the last restrictions on use of the Internet to carry commercial traffic. As technology advanced and commercial opportunities fueled reciprocal growth, the volume of Internet traffic started experiencing similar characteristics as that of the scaling of MOS transistors, exemplified by Moore's law, doubling every 18 months. This growth, formalized as Edholm's law, was catalyzed by advances in MOS technology, laser light wave systems, and noise performance. Since 1995, the Internet has tremendously impacted culture and commerce, including the rise of near-instant communication by email, instant messaging, telephony (Voice over Internet Protocol or VoIP), two-way interactive video calls, and the World Wide Web. Increasing amounts of data are transmitted at higher and higher speeds over fiber optic networks operating at 1 Gbit/s, 10 Gbit/s, or more. The Internet continues to grow, driven by ever-greater amounts of online information and knowledge, commerce, entertainment and social networking services. During the late 1990s, it was estimated that traffic on the public Internet grew by 100 percent per year, while the mean annual growth in the number of Internet users was thought to be between 20% and 50%. This growth is often attributed to the lack of central administration, which allows organic growth of the network, as well as the non-proprietary nature of the Internet protocols, which encourages vendor interoperability and prevents any one company from exerting too much control over the network. In November 2006, the Internet was included on USA Today's list of the New Seven Wonders. As of 31 March 2011[update], the estimated total number of Internet users was 2.095 billion (30% of world population). It is estimated that in 1993 the Internet carried only 1% of the information flowing through two-way telecommunication. By 2000 this figure had grown to 51%, and by 2007 more than 97% of all telecommunicated information was carried over the Internet. Modern smartphones can access the Internet through cellular carrier networks, and internet usage by mobile and tablet devices exceeded desktop worldwide for the first time in October 2016. As of 2018[update], 80% of the world's population were covered by a 4G network. The International Telecommunication Union (ITU) estimated that, by the end of 2017, 48% of individual users regularly connect to the Internet, up from 34% in 2012. Mobile Internet connectivity has played an important role in expanding access in recent years, especially in Asia and the Pacific and in Africa. The number of unique mobile cellular subscriptions increased from 3.9 billion in 2012 to 4.8 billion in 2016, two-thirds of the world's population, with more than half of subscriptions located in Asia and the Pacific. The limits that users face on accessing information via mobile applications coincide with a broader process of fragmentation of the Internet. Fragmentation restricts access to media content and tends to affect the poorest users the most. One solution, zero-rating, is the practice of Internet service providers allowing users free connectivity to access specific content or applications without cost. Social impact The Internet has enabled new forms of social interaction, activities, and social associations, giving rise to the scholarly study of the sociology of the Internet. Between 2000 and 2009, the number of Internet users globally rose from 390 million to 1.9 billion. By 2010, 22% of the world's population had access to computers with 1 billion Google searches every day, 300 million Internet users reading blogs, and 2 billion videos viewed daily on YouTube. In 2014 the world's Internet users surpassed 3 billion or 44 percent of world population, but two-thirds came from the richest countries, with 78 percent of Europeans using the Internet, followed by 57 percent of the Americas. However, by 2018, Asia alone accounted for 51% of all Internet users, with 2.2 billion out of the 4.3 billion Internet users in the world. China's Internet users surpassed a major milestone in 2018, when the country's Internet regulatory authority, China Internet Network Information Centre, announced that China had 802 million users. China was followed by India, with some 700 million users, with the United States third with 275 million users. However, in terms of penetration, in 2022, China had a 70% penetration rate compared to India's 60% and the United States's 90%. In 2022, 54% of the world's Internet users were based in Asia, 14% in Europe, 7% in North America, 10% in Latin America and the Caribbean, 11% in Africa, 4% in the Middle East and 1% in Oceania. In 2019, Kuwait, Qatar, the Falkland Islands, Bermuda and Iceland had the highest Internet penetration by the number of users, with 93% or more of the population with access. As of 2022, it was estimated that 5.4 billion people use the Internet, more than two-thirds of the world's population. Early computer systems were limited to the characters in the American Standard Code for Information Interchange (ASCII), a subset of the Latin alphabet. After English (27%), the most requested languages on the World Wide Web are Chinese (25%), Spanish (8%), Japanese (5%), Portuguese and German (4% each), Arabic, French and Russian (3% each), and Korean (2%). Modern character encoding standards, such as Unicode, allow for development and communication in the world's widely used languages. However, some glitches such as mojibake (incorrect display of some languages' characters) still remain. Several neologisms exist that refer to Internet users: Netizen (as in "citizen of the net") refers to those actively involved in improving online communities, the Internet in general or surrounding political affairs and rights such as free speech, Internaut refers to operators or technically highly capable users of the Internet, digital citizen refers to a person using the Internet in order to engage in society, politics, and government participation. The Internet allows greater flexibility in working hours and location, especially with the spread of unmetered high-speed connections. The Internet can be accessed almost anywhere by numerous means, including through mobile Internet devices. Mobile phones, datacards, handheld game consoles and cellular routers allow users to connect to the Internet wirelessly.[citation needed] Educational material at all levels from pre-school (e.g. CBeebies) to post-doctoral (e.g. scholarly literature through Google Scholar) is available on websites. The internet has facilitated the development of virtual universities and distance education, enabling both formal and informal education. The Internet allows researchers to conduct research remotely via virtual laboratories, with profound changes in reach and generalizability of findings as well as in communication between scientists and in the publication of results. By the late 2010s the Internet had been described as "the main source of scientific information "for the majority of the global North population".: 111 Wikis have also been used in the academic community for sharing and dissemination of information across institutional and international boundaries. In those settings, they have been found useful for collaboration on grant writing, strategic planning, departmental documentation, and committee work. The United States Patent and Trademark Office uses a wiki to allow the public to collaborate on finding prior art relevant to examination of pending patent applications. Queens, New York has used a wiki to allow citizens to collaborate on the design and planning of a local park. The English Wikipedia has the largest user base among wikis on the World Wide Web and ranks in the top 10 among all sites in terms of traffic. The Internet has been a major outlet for leisure activity since its inception, with entertaining social experiments such as MUDs and MOOs being conducted on university servers, and humor-related Usenet groups receiving much traffic. Many Internet forums have sections devoted to games and funny videos. Another area of leisure activity on the Internet is multiplayer gaming. This form of recreation creates communities, where people of all ages and origins enjoy the fast-paced world of multiplayer games. These range from MMORPG to first-person shooters, from role-playing video games to online gambling. While online gaming has been around since the 1970s, modern modes of online gaming began with subscription services such as GameSpy and MPlayer. Streaming media is the real-time delivery of digital media for immediate consumption or enjoyment by end users. Streaming companies (such as Netflix, Disney+, Amazon's Prime Video, Mubi, Hulu, and Apple TV+) now dominate the entertainment industry, eclipsing traditional broadcasters. Audio streamers such as Spotify and Apple Music also have significant market share in the audio entertainment market. Video sharing websites are also a major factor in the entertainment ecosystem. YouTube was founded on 15 February 2005 and is now the leading website for free streaming video with more than two billion users. It uses a web player to stream and show video files. YouTube users watch hundreds of millions, and upload hundreds of thousands, of videos daily. Other video sharing websites include Vimeo, Instagram and TikTok.[citation needed] Although many governments have attempted to restrict both Internet pornography and online gambling, this has generally failed to stop their widespread popularity. A number of advertising-funded ostensible video sharing websites known as "tube sites" have been created to host shared pornographic video content. Due to laws requiring the documentation of the origin of pornography, these websites now largely operate in conjunction with pornographic movie studios and their own independent creator networks, acting as de-facto video streaming services. Major players in this field include the market leader Aylo, the operator of PornHub and numerous other branded sites, as well as other independent operators such as xHamster and Xvideos. As of 2023[update], Internet traffic to pornographic video sites rivalled that of mainstream video streaming and sharing services. Remote work is facilitated by tools such as groupware, virtual private networks, conference calling, videotelephony, and VoIP so that work may be performed from any location, such as the worker's home.[citation needed] The spread of low-cost Internet access in developing countries has opened up new possibilities for peer-to-peer charities, which allow individuals to contribute small amounts to charitable projects for other individuals. Websites, such as DonorsChoose and GlobalGiving, allow small-scale donors to direct funds to individual projects of their choice. A popular twist on Internet-based philanthropy is the use of peer-to-peer lending for charitable purposes. Kiva pioneered this concept in 2005, offering the first web-based service to publish individual loan profiles for funding. The low cost and nearly instantaneous sharing of ideas, knowledge, and skills have made collaborative work dramatically easier, with the help of collaborative software, which allow groups to easily form, cheaply communicate, and share ideas. An example of collaborative software is the free software movement, which has produced, among other things, Linux, Mozilla Firefox, and OpenOffice.org (later forked into LibreOffice).[citation needed] Content management systems allow collaborating teams to work on shared sets of documents simultaneously without accidentally destroying each other's work.[citation needed] The internet also allows for cloud computing, virtual private networks, remote desktops, and remote work.[citation needed] The online disinhibition effect describes the tendency of many individuals to behave more stridently or offensively online than they would in person. A significant number of feminist women have been the target of various forms of harassment, including insults and hate speech, to, in extreme cases, rape and death threats, in response to posts they have made on social media. Social media companies have been criticized in the past for not doing enough to aid victims of online abuse. Children also face dangers online such as cyberbullying and approaches by sexual predators, who sometimes pose as children themselves. Due to naivety, they may also post personal information about themselves online, which could put them or their families at risk unless warned not to do so. Many parents choose to enable Internet filtering or supervise their children's online activities in an attempt to protect their children from pornography or violent content on the Internet. The most popular social networking services commonly forbid users under the age of 13. However, these policies can be circumvented by registering an account with a false birth date, and a significant number of children aged under 13 join such sites.[citation needed] Social networking services for younger children, which claim to provide better levels of protection for children, also exist. Internet usage has been correlated to users' loneliness. Lonely people tend to use the Internet as an outlet for their feelings and to share their stories with others, such as in the "I am lonely will anyone speak to me" thread.[citation needed] Cyberslacking can become a drain on corporate resources; employees spend a significant amount of time surfing the Web while at work. Internet addiction disorder is excessive computer use that interferes with daily life. Nicholas G. Carr believes that Internet use has other effects on individuals, for instance improving skills of scan-reading and interfering with the deep thinking that leads to true creativity. Electronic business encompasses business processes spanning the entire value chain: purchasing, supply chain management, marketing, sales, customer service, and business relationship. E-commerce seeks to add revenue streams using the Internet to build and enhance relationships with clients and partners. According to International Data Corporation, the size of worldwide e-commerce, when global business-to-business and -consumer transactions are combined, equate to $16 trillion in 2013. A report by Oxford Economics added those two together to estimate the total size of the digital economy at $20.4 trillion, equivalent to roughly 13.8% of global sales. While much has been written of the economic advantages of Internet-enabled commerce, there is also evidence that some aspects of the Internet such as maps and location-aware services may serve to reinforce economic inequality and the digital divide. Electronic commerce may be responsible for consolidation and the decline of mom-and-pop, brick and mortar businesses resulting in increases in income inequality. A 2013 Institute for Local Self-Reliance report states that brick-and-mortar retailers employ 47 people for every $10 million in sales, while Amazon employs only 14. Similarly, the 700-employee room rental start-up Airbnb was valued at $10 billion in 2014, about half as much as Hilton Worldwide, which employs 152,000 people. At that time, Uber employed 1,000 full-time employees and was valued at $18.2 billion, about the same valuation as Avis Rent a Car and The Hertz Corporation combined, which together employed almost 60,000 people. Advertising on popular web pages can be lucrative, and e-commerce. Online advertising is a form of marketing and advertising which uses the Internet to deliver promotional marketing messages to consumers. It includes email marketing, search engine marketing (SEM), social media marketing, many types of display advertising (including web banner advertising), and mobile advertising. In 2011, Internet advertising revenues in the United States surpassed those of cable television and nearly exceeded those of broadcast television.: 19 Many common online advertising practices are controversial and increasingly subject to regulation. The Internet has achieved new relevance as a political tool. The presidential campaign of Howard Dean in 2004 in the United States was notable for its success in soliciting donation via the Internet. Many political groups use the Internet to achieve a new method of organizing for carrying out their mission, having given rise to Internet activism. Social media websites, such as Facebook and Twitter, helped people organize the Arab Spring, by helping activists organize protests, communicate grievances, and disseminate information. Many have understood the Internet as an extension of the Habermasian notion of the public sphere, observing how network communication technologies provide something like a global civic forum. However, incidents of politically motivated Internet censorship have now been recorded in many countries, including western democracies. E-government is the use of technological communications devices, such as the Internet, to provide public services to citizens and other persons in a country or region. E-government offers opportunities for more direct and convenient citizen access to government and for government provision of services directly to citizens. Cybersectarianism is a new organizational form that involves: highly dispersed small groups of practitioners that may remain largely anonymous within the larger social context and operate in relative secrecy, while still linked remotely to a larger network of believers who share a set of practices and texts, and often a common devotion to a particular leader. Overseas supporters provide funding and support; domestic practitioners distribute tracts, participate in acts of resistance, and share information on the internal situation with outsiders. Collectively, members and practitioners of such sects construct viable virtual communities of faith, exchanging personal testimonies and engaging in the collective study via email, online chat rooms, and web-based message boards. In particular, the British government has raised concerns about the prospect of young British Muslims being indoctrinated into Islamic extremism by material on the Internet, being persuaded to join terrorist groups such as the so-called "Islamic State", and then potentially committing acts of terrorism on returning to Britain after fighting in Syria or Iraq.[citation needed] Applications and services The Internet carries many applications and services, most prominently the World Wide Web, including social media, electronic mail, mobile applications, multiplayer online games, Internet telephony, file sharing, and streaming media services. The World Wide Web is a global collection of documents, images, multimedia, applications, and other resources, logically interrelated by hyperlinks and referenced with Uniform Resource Identifiers (URIs), which provide a global system of named references. URIs symbolically identify services, web servers, databases, and the documents and resources that they can provide. HyperText Transfer Protocol (HTTP) is the main access protocol of the World Wide Web. Web services also use HTTP for communication between software systems for information transfer, sharing and exchanging business data and logistics and is one of many languages or protocols that can be used for communication on the Internet. World Wide Web browser software, such as Microsoft Edge, Mozilla Firefox, Opera, Apple's Safari, and Google Chrome, enable users to navigate from one web page to another via the hyperlinks embedded in the documents. These documents may also contain computer data, including graphics, sounds, text, video, multimedia and interactive content. Client-side scripts can include animations, games, office applications and scientific demonstrations. Email is an important communications service available via the Internet. The concept of sending electronic text messages between parties, analogous to mailing letters or memos, predates the creation of the Internet. Internet telephony is a common communications service realized with the Internet. The name of the principal internetworking protocol, the Internet Protocol, lends its name to voice over Internet Protocol (VoIP).[citation needed] VoIP systems now dominate many markets, being as easy and convenient as a traditional telephone, while having substantial cost savings, especially over long distances. File sharing is the practice of transferring large amounts of data in the form of computer files across the Internet, for example via file servers. The load of bulk downloads to many users can be eased by the use of "mirror" servers or peer-to-peer networks. Access to the file may be controlled by user authentication, the transit of the file over the Internet may be obscured by encryption, and money may change hands for access to the file. The price can be paid by the remote charging of funds from, for example, a credit card whose details are also passed—usually fully encrypted—across the Internet. The origin and authenticity of the file received may be checked by a digital signature. Governance The Internet is a global network that comprises many voluntarily interconnected autonomous networks. It operates without a central governing body. The technical underpinning and standardization of the core protocols (IPv4 and IPv6) is an activity of the Internet Engineering Task Force (IETF), a non-profit organization of loosely affiliated international participants that anyone may associate with by contributing technical expertise. While the hardware components in the Internet infrastructure can often be used to support other software systems, it is the design and the standardization process of the software that characterizes the Internet and provides the foundation for its scalability and success. The responsibility for the architectural design of the Internet software systems has been assumed by the IETF. The IETF conducts standard-setting work groups, open to any individual, about the various aspects of Internet architecture. The resulting contributions and standards are published as Request for Comments (RFC) documents on the IETF web site. The principal methods of networking that enable the Internet are contained in specially designated RFCs that constitute the Internet Standards. Other less rigorous documents are simply informative, experimental, or historical, or document the best current practices when implementing Internet technologies. To maintain interoperability, the principal name spaces of the Internet are administered by the Internet Corporation for Assigned Names and Numbers (ICANN). ICANN is governed by an international board of directors drawn from across the Internet technical, business, academic, and other non-commercial communities. The organization coordinates the assignment of unique identifiers for use on the Internet, including domain names, IP addresses, application port numbers in the transport protocols, and many other parameters. Globally unified name spaces are essential for maintaining the global reach of the Internet. This role of ICANN distinguishes it as perhaps the only central coordinating body for the global Internet. The National Telecommunications and Information Administration, an agency of the United States Department of Commerce, had final approval over changes to the DNS root zone until the IANA stewardship transition on 1 October 2016. Regional Internet registries (RIRs) were established for five regions of the world to assign IP address blocks and other Internet parameters to local registries, such as Internet service providers, from a designated pool of addresses set aside for each region:[citation needed] The Internet Society (ISOC) was founded in 1992 with a mission to "assure the open development, evolution and use of the Internet for the benefit of all people throughout the world". Its members include individuals as well as corporations, organizations, governments, and universities. Among other activities ISOC provides an administrative home for a number of less formally organized groups that are involved in developing and managing the Internet, including: the Internet Engineering Task Force (IETF), Internet Architecture Board (IAB), Internet Engineering Steering Group (IESG), Internet Research Task Force (IRTF), and Internet Research Steering Group (IRSG). On 16 November 2005, the United Nations-sponsored World Summit on the Information Society in Tunis established the Internet Governance Forum (IGF) to discuss Internet-related issues.[citation needed] Infrastructure The communications infrastructure of the Internet consists of its hardware components and a system of software layers that control various aspects of the architecture. As with any computer network, the Internet physically consists of routers, media (such as cabling and radio links), repeaters, and modems. However, as an example of internetworking, many of the network nodes are not necessarily Internet equipment per se. Internet packets are carried by other full-fledged networking protocols, with the Internet acting as a homogeneous networking standard, running across heterogeneous hardware, with the packets guided to their destinations by IP routers.[citation needed] Internet service providers (ISPs) establish worldwide connectivity between individual networks at various levels of scope. At the top of the routing hierarchy are the tier 1 networks, large telecommunication companies that exchange traffic directly with each other via very high speed fiber-optic cables and governed by peering agreements. Tier 2 and lower-level networks buy Internet transit from other providers to reach at least some parties on the global Internet, though they may also engage in peering. End-users who only access the Internet when needed to perform a function or obtain information, represent the bottom of the routing hierarchy.[citation needed] An ISP may use a single upstream provider for connectivity, or implement multihoming to achieve redundancy and load balancing. Internet exchange points are major traffic exchanges with physical connections to multiple ISPs. Large organizations, such as academic institutions, large enterprises, and governments, may perform the same function as ISPs, engaging in peering and purchasing transit on behalf of their internal networks. Research networks tend to interconnect with large subnetworks such as GEANT, GLORIAD, Internet2, and the UK's national research and education network, JANET.[citation needed] Common methods of Internet access by users include broadband over coaxial cable, fiber optics or copper wires, Wi-Fi, satellite, and cellular telephone technology.[citation needed] Grassroots efforts have led to wireless community networks. Commercial Wi-Fi services that cover large areas are available in many cities, such as New York, London, Vienna, Toronto, San Francisco, Philadelphia, Chicago and Pittsburgh. Most servers that provide internet services are today hosted in data centers, and content is often accessed through high-performance content delivery networks. Colocation centers often host private peering connections between their customers, internet transit providers, cloud providers, meet-me rooms for connecting customers together, Internet exchange points, and landing points and terminal equipment for fiber optic submarine communication cables, connecting the internet. Internet Protocol Suite The Internet standards describe a framework known as the Internet protocol suite (also called TCP/IP, based on the first two components.) This is a suite of protocols that are ordered into a set of four conceptional layers by the scope of their operation, originally documented in RFC 1122 and RFC 1123:[citation needed] The most prominent component of the Internet model is the Internet Protocol. IP enables internetworking, essentially establishing the Internet itself. Two versions of the Internet Protocol exist, IPv4 and IPv6.[citation needed] Aside from the complex array of physical connections that make up its infrastructure, the Internet is facilitated by bi- or multi-lateral commercial contracts (e.g., peering agreements), and by technical specifications or protocols that describe the exchange of data over the network.[citation needed] For locating individual computers on the network, the Internet provides IP addresses. IP addresses are used by the Internet infrastructure to direct internet packets to their destinations. They consist of fixed-length numbers, which are found within the packet. IP addresses are generally assigned to equipment either automatically via Dynamic Host Configuration Protocol, or are configured.[citation needed] Domain Name Systems convert user-inputted domain names (e.g. "en.wikipedia.org") into IP addresses.[citation needed] Internet Protocol version 4 (IPv4) defines an IP address as a 32-bit number. IPv4 is the initial version used on the first generation of the Internet and is still in dominant use. It was designed in 1981 to address up to ≈4.3 billion (109) hosts. However, the explosive growth of the Internet has led to IPv4 address exhaustion, which entered its final stage in 2011, when the global IPv4 address allocation pool was exhausted. Because of the growth of the Internet and the depletion of available IPv4 addresses, a new version of IP IPv6, was developed in the mid-1990s, which provides vastly larger addressing capabilities and more efficient routing of Internet traffic. IPv6 uses 128 bits for the IP address and was standardized in 1998. IPv6 deployment has been ongoing since the mid-2000s and is currently in growing deployment around the world, since Internet address registries began to urge all resource managers to plan rapid adoption and conversion. By design, IPv6 is not directly interoperable with IPv4. Instead, it establishes a parallel version of the Internet not directly accessible with IPv4 software. Thus, translation facilities exist for internetworking, and some nodes have duplicate networking software for both networks. Essentially all modern computer operating systems support both versions of the Internet Protocol.[citation needed] Network infrastructure, however, has been lagging in this development.[citation needed] A subnet or subnetwork is a logical subdivision of an IP network.: 1, 16 Computers that belong to a subnet are addressed with an identical most-significant bit-group in their IP addresses. This results in the logical division of an IP address into two fields, the network number or routing prefix and the rest field or host identifier. The rest field is an identifier for a specific host or network interface.[citation needed] The routing prefix may be expressed in Classless Inter-Domain Routing (CIDR) notation written as the first address of a network, followed by a slash character (/), and ending with the bit-length of the prefix. For example, 198.51.100.0/24 is the prefix of the Internet Protocol version 4 network starting at the given address, having 24 bits allocated for the network prefix, and the remaining 8 bits reserved for host addressing. Addresses in the range 198.51.100.0 to 198.51.100.255 belong to this network. The IPv6 address specification 2001:db8::/32 is a large address block with 296 addresses, having a 32-bit routing prefix.[citation needed] For IPv4, a network may also be characterized by its subnet mask or netmask, which is the bitmask that when applied by a bitwise AND operation to any IP address in the network, yields the routing prefix. Subnet masks are also expressed in dot-decimal notation like an address. For example, 255.255.255.0 is the subnet mask for the prefix 198.51.100.0/24.[citation needed] Computers and routers use routing tables in their operating system to forward IP packets to reach a node on a different subnetwork. Routing tables are maintained by manual configuration or automatically by routing protocols. End-nodes typically use a default route that points toward an ISP providing transit, while ISP routers use the Border Gateway Protocol to establish the most efficient routing across the complex connections of the global Internet.[citation needed] The default gateway is the node that serves as the forwarding host (router) to other networks when no other route specification matches the destination IP address of a packet. Security Internet resources, hardware, and software components are the target of criminal or malicious attempts to gain unauthorized control to cause interruptions, commit fraud, engage in blackmail or access private information. Malware is malicious software used and distributed via the Internet. It includes computer viruses which are copied with the help of humans, computer worms which copy themselves automatically, software for denial of service attacks, ransomware, botnets, and spyware that reports on the activity and typing of users.[citation needed] Usually, these activities constitute cybercrime. Defense theorists have also speculated about the possibilities of hackers using cyber warfare using similar methods on a large scale. Malware poses serious problems to individuals and businesses on the Internet. According to Symantec's 2018 Internet Security Threat Report (ISTR), malware variants number has increased to 669,947,865 in 2017, which is twice as many malware variants as in 2016. Cybercrime, which includes malware attacks as well as other crimes committed by computer, was predicted to cost the world economy US$6 trillion in 2021, and is increasing at a rate of 15% per year. Since 2021, malware has been designed to target computer systems that run critical infrastructure such as the electricity distribution network. Malware can be designed to evade antivirus software detection algorithms. The vast majority of computer surveillance involves the monitoring of data and traffic on the Internet. In the United States for example, under the Communications Assistance For Law Enforcement Act, all phone calls and broadband Internet traffic (emails, web traffic, instant messaging, etc.) are required to be available for unimpeded real-time monitoring by Federal law enforcement agencies. Under the Act, all U.S. telecommunications providers are required to install packet sniffing technology to allow Federal law enforcement and intelligence agencies to intercept all of their customers' broadband Internet and VoIP traffic.[d] The large amount of data gathered from packet capture requires surveillance software that filters and reports relevant information, such as the use of certain words or phrases, the access to certain types of web sites, or communicating via email or chat with certain parties. Agencies, such as the Information Awareness Office, NSA, GCHQ and the FBI, spend billions of dollars per year to develop, purchase, implement, and operate systems for interception and analysis of data. Similar systems are operated by Iranian secret police to identify and suppress dissidents. The required hardware and software were allegedly installed by German Siemens AG and Finnish Nokia. Some governments, such as those of Myanmar, Iran, North Korea, Mainland China, Saudi Arabia and the United Arab Emirates, restrict access to content on the Internet within their territories, especially to political and religious content, with domain name and keyword filters. In Norway, Denmark, Finland, and Sweden, major Internet service providers have voluntarily agreed to restrict access to sites listed by authorities. While this list of forbidden resources is supposed to contain only known child pornography sites, the content of the list is secret. Many countries, including the United States, have enacted laws against the possession or distribution of certain material, such as child pornography, via the Internet but do not mandate filter software. Many free or commercially available software programs, called content-control software are available to users to block offensive specific on individual computers or networks in order to limit access by children to pornographic material or depiction of violence.[citation needed] Performance As the Internet is a heterogeneous network, its physical characteristics, including, for example the data transfer rates of connections, vary widely. It exhibits emergent phenomena that depend on its large-scale organization. PB per monthYear020,00040,00060,00080,000100,000120,000140,000199019952000200520102015Petabytes per monthGlobal Internet Traffic Volume The volume of Internet traffic is difficult to measure because no single point of measurement exists in the multi-tiered, non-hierarchical topology. Traffic data may be estimated from the aggregate volume through the peering points of the Tier 1 network providers, but traffic that stays local in large provider networks may not be accounted for.[citation needed] An Internet blackout or outage can be caused by local signaling interruptions. Disruptions of submarine communications cables may cause blackouts or slowdowns to large areas, such as in the 2008 submarine cable disruption. Less-developed countries are more vulnerable due to the small number of high-capacity links. Land cables are also vulnerable, as in 2011 when a woman digging for scrap metal severed most connectivity for the nation of Armenia. Internet blackouts affecting almost entire countries can be achieved by governments as a form of Internet censorship, as in the blockage of the Internet in Egypt, whereby approximately 93% of networks were without access in 2011 in an attempt to stop mobilization for anti-government protests. Estimates of the Internet's electricity usage have been the subject of controversy, according to a 2014 peer-reviewed research paper that found claims differing by a factor of 20,000 published in the literature during the preceding decade, ranging from 0.0064 kilowatt hours per gigabyte transferred (kWh/GB) to 136 kWh/GB. The researchers attributed these discrepancies mainly to the year of reference (i.e. whether efficiency gains over time had been taken into account) and to whether "end devices such as personal computers and servers are included" in the analysis. In 2011, academic researchers estimated the overall energy used by the Internet to be between 170 and 307 GW, less than two percent of the energy used by humanity. This estimate included the energy needed to build, operate, and periodically replace the estimated 750 million laptops, a billion smart phones and 100 million servers worldwide as well as the energy that routers, cell towers, optical switches, Wi-Fi transmitters and cloud storage devices use when transmitting Internet traffic. According to a non-peer-reviewed study published in 2018 by The Shift Project (a French think tank funded by corporate sponsors), nearly 4% of global CO2 emissions could be attributed to global data transfer and the necessary infrastructure. The study also said that online video streaming alone accounted for 60% of this data transfer and therefore contributed to over 300 million tons of CO2 emission per year, and argued for new "digital sobriety" regulations restricting the use and size of video files. See also Notes References Sources Further reading External links |
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Contents Online wedding Something most often seen in massively multiplayer online role-playing games (MMORPGs), online weddings date back to the beginning of online communities and early online games such as MUDs. Two people who wish their avatars, or characters, to be married will create an event that resembles a standard wedding. This became very popular with the introduction of Ultima Online, which not only provided rings, outfits and decorations, but sometimes even Gamemasters to officiate. This tradition has carried forward into several other MMORPGs and virtual communities. Some games offer special Bonuses to players who participate in a virtual wedding. In many cases the participants do not know each other outside the virtual community. Some couples may not even know each other's true name, gender, etc. Some do, in fact, extend this union outside the virtual, but most do not. There is no legal recognition for virtual marriages. Some couples have joined in what appear to be legally binding unions through other mediums such as instant messaging or videoconferencing. These ceremonies are presided by the same appropriate officials and witnesses needed for a standard union. Some of these unions occur across state or even national borders. History In 1997 gaming magazine Next Generation reported that 20 virtual weddings had taken place in Meridian 59, an MMORPG which was commercially launched in September of the previous year. The Lord of the Rings Online In April 2007 Salon.com reported that The Lord of the Rings Online had dropped a planned feature for in-game players marriage because of the controversy around the possibility of same-sex and inter-species weddings. One developer stated that the design rule was for weddings to be allowed if examples could be found in the book, as between elves and humans. The online magazine for gaymers GayGamer.net commented that, while Tolkien was a devout Roman Catholic, his stance on gay marriage isn't known as the topic wasn't a public issue at the time. Video game critic Ian Bogost compared it to the case of The Sims 2, a blockbuster video game that did allow same-sex marriage. References |
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Contents Lod Lod (Hebrew: לוד, fully vocalized: לֹד), also known as Lydda (Ancient Greek: Λύδδα) and Lidd (Arabic: اللِّدّ, romanized: al-Lidd, or اللُّدّ, al-Ludd), is a city 15 km (9+1⁄2 mi) southeast of Tel Aviv and 40 km (25 mi) northwest of Jerusalem in the Central District of Israel. It is situated between the lower Shephelah on the east and the coastal plain on the west. The city had a population of 90,814 in 2023. Lod has been inhabited since at least the Neolithic period. It is mentioned a few times in the Hebrew Bible and in the New Testament. Between the 5th century BCE and up until the late Roman period, it was a prominent center for Jewish scholarship and trade. Around 200 CE, the city became a Roman colony and was renamed Diospolis (Ancient Greek: Διόσπολις, lit. 'city of Zeus'). Tradition identifies Lod as the 4th century martyrdom site of Saint George; the Church of Saint George and Mosque of Al-Khadr located in the city is believed to have housed his remains. Following the Arab conquest of the Levant, Lod served as the capital of Jund Filastin; however, a few decades later, the seat of power was transferred to Ramla, and Lod slipped in importance. Under Crusader rule, the city was a Catholic diocese of the Latin Church and it remains a titular see to this day.[citation needed] Lod underwent a major change in its population in the mid-20th century. Exclusively Palestinian Arab in 1947, Lod was part of the area designated for an Arab state in the United Nations Partition Plan for Palestine; however, in July 1948, the city was occupied by the Israel Defense Forces, and most of its Arab inhabitants were expelled in the Palestinian expulsion from Lydda and Ramle. The city was largely resettled by Jewish immigrants, most of them expelled from Arab countries. Today, Lod is one of Israel's mixed cities, with an Arab population of 30%. Lod is one of Israel's major transportation hubs. The main international airport, Ben Gurion Airport, is located 8 km (5 miles) north of the city. The city is also a major railway and road junction. Religious references The Hebrew name Lod appears in the Hebrew Bible as a town of Benjamin, founded along with Ono by Shamed or Shamer (1 Chronicles 8:12; Ezra 2:33; Nehemiah 7:37; 11:35). In Ezra 2:33, it is mentioned as one of the cities whose inhabitants returned after the Babylonian captivity. Lod is not mentioned among the towns allocated to the tribe of Benjamin in Joshua 18:11–28. The name Lod derives from a tri-consonantal root not extant in Northwest Semitic, but only in Arabic (“to quarrel; withhold, hinder”). An Arabic etymology of such an ancient name is unlikely (the earliest attestation is from the Achaemenid period). In the New Testament, the town appears in its Greek form, Lydda, as the site of Peter's healing of Aeneas in Acts 9:32–38. The city is also mentioned in an Islamic hadith as the location of the battlefield where the false messiah (al-Masih ad-Dajjal) will be slain before the Day of Judgment. History The first occupation dates to the Neolithic in the Near East and is associated with the Lodian culture. Occupation continued in the Levant Chalcolithic. Pottery finds have dated the initial settlement in the area now occupied by the town to 5600–5250 BCE. In the Early Bronze, it was an important settlement in the central coastal plain between the Judean Shephelah and the Mediterranean coast, along Nahal Ayalon. Other important nearby sites were Tel Dalit, Tel Bareqet, Khirbat Abu Hamid (Shoham North), Tel Afeq, Azor and Jaffa. Two architectural phases belong to the late EB I in Area B. The first phase had a mudbrick wall, while the late phase included a circulat stone structure. Later excavations have produced an occupation later, Stratum IV. It consists of two phases, Stratum IVb with mudbrick wall on stone foundations and rounded exterior corners. In Stratum IVa there was a mudbrick wall with no stone foundations, with imported Egyptian potter and local pottery imitations. Another excavations revealed nine occupation strata. Strata VI-III belonged to Early Bronze IB. The material culture showed Egyptian imports in strata V and IV. Occupation continued into Early Bronze II with four strata (V-II). There was continuity in the material culture and indications of centralized urban planning. North to the tell were scattered MB II burials. The earliest written record is in a list of Canaanite towns drawn up by the Egyptian pharaoh Thutmose III at Karnak in 1465 BCE. From the fifth century BCE until the Roman period, the city was a centre of Jewish scholarship and commerce. According to British historian Martin Gilbert, during the Hasmonean period, Jonathan Maccabee and his brother, Simon Maccabaeus, enlarged the area under Jewish control, which included conquering the city. The Jewish community in Lod during the Mishnah and Talmud era is described in a significant number of sources, including information on its institutions, demographics, and way of life. The city reached its height as a Jewish center between the First Jewish-Roman War and the Bar Kokhba revolt, and again in the days of Judah ha-Nasi and the start of the Amoraim period. The city was then the site of numerous public institutions, including schools, study houses, and synagogues. In 43 BC, Cassius, the Roman governor of Syria, sold the inhabitants of Lod into slavery, but they were set free two years later by Mark Antony. During the First Jewish–Roman War, the Roman proconsul of Syria, Cestius Gallus, razed the town on his way to Jerusalem in Tishrei 66 CE. According to Josephus, "[he] found the city deserted, for the entire population had gone up to Jerusalem for the Feast of Tabernacles. He killed fifty people whom he found, burned the town and marched on". Lydda was occupied by Emperor Vespasian in 68 CE. In the period following the destruction of Jerusalem in 70 CE, Rabbi Tarfon, who appears in many Tannaitic and Jewish legal discussions, served as a rabbinic authority in Lod. During the Kitos War, 115–117 CE, the Roman army laid siege to Lod, where the rebel Jews had gathered under the leadership of Julian and Pappos. Torah study was outlawed by the Romans and pursued mostly in the underground. The distress became so great, the patriarch Rabban Gamaliel II, who was shut up there and died soon afterwards, permitted fasting on Ḥanukkah. Other rabbis disagreed with this ruling. Lydda was next taken and many of the Jews were executed; the "slain of Lydda" are often mentioned in words of reverential praise in the Talmud. In 200 CE, emperor Septimius Severus elevated the town to the status of a city, calling it Colonia Lucia Septimia Severa Diospolis. The name Diospolis ("City of Zeus") may have been bestowed earlier, possibly by Hadrian. At that point, most of its inhabitants were Christian. The earliest known bishop is Aëtius, a friend of Arius. During the following century (200-300CE), it's said that Joshua ben Levi founded a yeshiva in Lod. In December 415, the Council of Diospolis was held here to try Pelagius; he was acquitted. In the sixth century, the city was renamed Georgiopolis after St. George, a soldier in the guard of the emperor Diocletian, who was born there between 256 and 285 CE. The Church of Saint George and Mosque of Al-Khadr is named for him. The 6th-century Madaba map shows Lydda as an unwalled city with a cluster of buildings under a black inscription reading "Lod, also Lydea, also Diospolis". An isolated large building with a semicircular colonnaded plaza in front of it might represent the St George shrine. After the Muslim conquest of Palestine by Amr ibn al-'As in 636 CE, Lod which was referred to as "al-Ludd" in Arabic served as the capital of Jund Filastin ("Military District of Palaestina") before the seat of power was moved to nearby Ramla during the reign of the Umayyad Caliph Suleiman ibn Abd al-Malik in 715–716. The population of al-Ludd was relocated to Ramla, as well. With the relocation of its inhabitants and the construction of the White Mosque in Ramla, al-Ludd lost its importance and fell into decay. The city was visited by the local Arab geographer al-Muqaddasi in 985, when it was under the Fatimid Caliphate, and was noted for its Great Mosque which served the residents of al-Ludd, Ramla, and the nearby villages. He also wrote of the city's "wonderful church (of St. George) at the gate of which Christ will slay the Antichrist." The Crusaders occupied the city in 1099 and named it St Jorge de Lidde. It was briefly conquered by Saladin, but retaken by the Crusaders in 1191. For the English Crusaders, it was a place of great significance as the birthplace of Saint George. The Crusaders made it the seat of a Latin Church diocese, and it remains a titular see. It owed the service of 10 knights and 20 sergeants, and it had its own burgess court during this era. In 1226, Ayyubid Syrian geographer Yaqut al-Hamawi visited al-Ludd and stated it was part of the Jerusalem District during Ayyubid rule. Sultan Baybars brought Lydda again under Muslim control by 1267–8. According to Qalqashandi, Lydda was an administrative centre of a wilaya during the fourteenth and fifteenth century in the Mamluk empire. Mujir al-Din described it as a pleasant village with an active Friday mosque. During this time, Lydda was a station on the postal route between Cairo and Damascus. In 1517, Lydda was incorporated into the Ottoman Empire as part of the Damascus Eyalet, and in the 1550s, the revenues of Lydda were designated for the new waqf of Hasseki Sultan Imaret in Jerusalem, established by Hasseki Hurrem Sultan (Roxelana), the wife of Suleiman the Magnificent. By 1596 Lydda was a part of the nahiya ("subdistrict") of Ramla, which was under the administration of the liwa ("district") of Gaza. It had a population of 241 households and 14 bachelors who were all Muslims, and 233 households who were Christians. They paid a fixed tax-rate of 33,3 % on agricultural products, including wheat, barley, summer crops, vineyards, fruit trees, sesame, special product ("dawalib" =spinning wheels), goats and beehives, in addition to occasional revenues and market toll, a total of 45,000 Akçe. All of the revenue went to the Waqf. In 1051 AH/1641/2, the Bedouin tribe of al-Sawālima from around Jaffa attacked the villages of Subṭāra, Bayt Dajan, al-Sāfiriya, Jindās, Lydda and Yāzūr belonging to Waqf Haseki Sultan. The village appeared as Lydda, though misplaced, on the map of Pierre Jacotin compiled in 1799. Missionary William M. Thomson visited Lydda in the mid-19th century, describing it as a "flourishing village of some 2,000 inhabitants, imbosomed in noble orchards of olive, fig, pomegranate, mulberry, sycamore, and other trees, surrounded every way by a very fertile neighbourhood. The inhabitants are evidently industrious and thriving, and the whole country between this and Ramleh is fast being filled up with their flourishing orchards. Rarely have I beheld a rural scene more delightful than this presented in early harvest ... It must be seen, heard, and enjoyed to be appreciated." In 1869, the population of Ludd was given as: 55 Catholics, 1,940 "Greeks", 5 Protestants and 4,850 Muslims. In 1870, the Church of Saint George was rebuilt. In 1892, the first railway station in the entire region was established in the city. In the second half of the 19th century, Jewish merchants migrated to the city, but left after the 1921 Jaffa riots. In 1882, the Palestine Exploration Fund's Survey of Western Palestine described Lod as "A small town, standing among enclosure of prickly pear, and having fine olive groves around it, especially to the south. The minaret of the mosque is a very conspicuous object over the whole of the plain. The inhabitants are principally Moslim, though the place is the seat of a Greek bishop resident of Jerusalem. The Crusading church has lately been restored, and is used by the Greeks. Wells are found in the gardens...." From 1918, Lydda was under the administration of the British Mandate in Palestine, as per a League of Nations decree that followed the Great War. During the Second World War, the British set up supply posts in and around Lydda and its railway station, also building an airport that was renamed Ben Gurion Airport after the death of Israel's first prime minister in 1973. At the time of the 1922 census of Palestine, Lydda had a population of 8,103 inhabitants (7,166 Muslims, 926 Christians, and 11 Jews), the Christians were 921 Orthodox, 4 Roman Catholics and 1 Melkite. This had increased by the 1931 census to 11,250 (10,002 Muslims, 1,210 Christians, 28 Jews, and 10 Bahai), in a total of 2475 residential houses. In 1938, Lydda had a population of 12,750. In 1945, Lydda had a population of 16,780 (14,910 Muslims, 1,840 Christians, 20 Jews and 10 "other"). Until 1948, Lydda was an Arab town with a population of around 20,000—18,500 Muslims and 1,500 Christians. In 1947, the United Nations proposed dividing Mandatory Palestine into two states, one Jewish state and one Arab; Lydda was to form part of the proposed Arab state. In the ensuing war, Israel captured Arab towns outside the area the UN had allotted it, including Lydda. In December 1947, thirteen Jewish passengers in a seven-car convoy to Ben Shemen Youth Village were ambushed and murdered.In a separate incident, three Jewish youths, two men and a woman were captured, then raped and murdered in a neighbouring village. Their bodies were paraded in Lydda’s principal street. The Israel Defense Forces entered Lydda on 11 July 1948. The following day, under the impression that it was under attack, the 3rd Battalion was ordered to shoot anyone "seen on the streets". According to Israel, 250 Arabs were killed. Other estimates are higher: Arab historian Aref al Aref estimated 400, and Nimr al Khatib 1,700. In 1948, the population rose to 50,000 during the Nakba, as Arab refugees fleeing other areas made their way there. A key event was the Palestinian expulsion from Lydda and Ramle, with the expulsion of 50,000-70,000 Palestinians from Lydda and Ramle by the Israel Defense Forces. All but 700 to 1,056 were expelled by order of the Israeli high command, and forced to walk 17 km (10+1⁄2 mi) to the Jordanian Arab Legion lines. Estimates of those who died from exhaustion and dehydration vary from a handful to 355. The town was subsequently sacked by the Israeli army. Some scholars, including Ilan Pappé, characterize this as ethnic cleansing. The few hundred Arabs who remained in the city were soon outnumbered by the influx of Jews who immigrated to Lod from August 1948 onward, most of them from Arab countries. As a result, Lod became a predominantly Jewish town. After the establishment of the state, the biblical name Lod was readopted. The Jewish immigrants who settled Lod came in waves, first from Morocco and Tunisia, later from Ethiopia, and then from the former Soviet Union. Since 2008, many urban development projects have been undertaken to improve the image of the city. Upscale neighbourhoods have been built, among them Ganei Ya'ar and Ahisemah, expanding the city to the east. According to a 2010 report in the Economist, a three-meter-high wall was built between Jewish and Arab neighbourhoods and construction in Jewish areas was given priority over construction in Arab neighborhoods. The newspaper says that violent crime in the Arab sector revolves mainly around family feuds over turf and honour crimes. In 2010, the Lod Community Foundation organised an event for representatives of bicultural youth movements, volunteer aid organisations, educational start-ups, businessmen, sports organizations, and conservationists working on programmes to better the city. In the 2021 Israel–Palestine crisis, a state of emergency was declared in Lod after Arab rioting led to the death of an Israeli Jew. The Mayor of Lod, Yair Revivio, urged Prime Minister of Israel Benjamin Netanyahu to deploy Israel Border Police to restore order in the city. This was the first time since 1966 that Israel had declared this kind of emergency lockdown. International media noted that both Jewish and Palestinian mobs were active in Lod, but the "crackdown came for one side" only. Demographics In the 19th century and until the Lydda Death March, Lod was an exclusively Muslim-Christian town, with an estimated 6,850 inhabitants, of whom approximately 2,000 (29%) were Christian. According to the Israel Central Bureau of Statistics (CBS), the population of Lod in 2010 was 69,500 people. According to the 2019 census, the population of Lod was 77,223, of which 53,581 people, comprising 69.4% of the city's population, were classified as "Jews and Others", and 23,642 people, comprising 30.6% as "Arab". Education According to CBS, 38 schools and 13,188 pupils are in the city. They are spread out as 26 elementary schools and 8,325 elementary school pupils, and 13 high schools and 4,863 high school pupils. About 52.5% of 12th-grade pupils were entitled to a matriculation certificate in 2001.[citation needed] Economy The airport and related industries are a major source of employment for the residents of Lod. Other important factories in the city are the communication equipment company "Talard", "Cafe-Co" - a subsidiary of the Strauss Group and "Kashev" - the computer center of Bank Leumi. A Jewish Agency Absorption Centre is also located in Lod. According to CBS figures for 2000, 23,032 people were salaried workers and 1,405 were self-employed. The mean monthly wage for a salaried worker was NIS 4,754, a real change of 2.9% over the course of 2000. Salaried men had a mean monthly wage of NIS 5,821 (a real change of 1.4%) versus NIS 3,547 for women (a real change of 4.6%). The mean income for the self-employed was NIS 4,991. About 1,275 people were receiving unemployment benefits and 7,145 were receiving an income supplement. Art and culture In 2009-2010, Dor Guez held an exhibit, Georgeopolis, at the Petach Tikva art museum that focuses on Lod. Archaeology A well-preserved mosaic floor dating to the Roman period was excavated in 1996 as part of a salvage dig conducted on behalf of the Israel Antiquities Authority and the Municipality of Lod, prior to widening HeHalutz Street. According to Jacob Fisch, executive director of the Friends of the Israel Antiquities Authority, a worker at the construction site noticed the tail of a tiger and halted work. The mosaic was initially covered over with soil at the conclusion of the excavation for lack of funds to conserve and develop the site. The mosaic is now part of the Lod Mosaic Archaeological Center. The floor, with its colorful display of birds, fish, exotic animals and merchant ships, is believed to have been commissioned by a wealthy resident of the city for his private home. The Lod Community Archaeology Program, which operates in ten Lod schools, five Jewish and five Israeli Arab, combines archaeological studies with participation in digs in Lod. Sports The city's major football club, Hapoel Bnei Lod, plays in Liga Leumit (the second division). Its home is at the Lod Municipal Stadium. The club was formed by a merger of Bnei Lod and Rakevet Lod in the 1980s. Two other clubs in the city play in the regional leagues: Hapoel MS Ortodoxim Lod in Liga Bet and Maccabi Lod in Liga Gimel. Hapoel Lod played in the top division during the 1960s and 1980s, and won the State Cup in 1984. The club folded in 2002. A new club, Hapoel Maxim Lod (named after former mayor Maxim Levy) was established soon after, but folded in 2007. Notable people Twin towns-sister cities Lod is twinned with: See also References Bibliography External links |
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[SOURCE: https://en.wikipedia.org/wiki/Reciprocity_in_network] | [TOKENS: 1033] |
Contents Reciprocity (network science) In network science, reciprocity is a measure of the likelihood of vertices in a directed network to be mutually linked. Like the clustering coefficient, scale-free degree distribution, or community structure, reciprocity is a quantitative measure used to study complex networks. Motivation In real network problems, people are interested in determining the likelihood of occurring double links (with opposite directions) between vertex pairs. This problem is fundamental for several reasons. First, in the networks that transport information or material (such as email networks, World Wide Web (WWW), World Trade Web, or Wikipedia ), mutual links facilitate the transportation process. Second, when analyzing directed networks, people often treat them as undirected ones for simplicity; therefore, the information obtained from reciprocity studies helps to estimate the error introduced when a directed network is treated as undirected (for example, when measuring the clustering coefficient). Finally, detecting nontrivial patterns of reciprocity can reveal possible mechanisms and organizing principles that shape the observed network's topology. Definitions A traditional way to define the reciprocity r {\displaystyle r} is using the ratio of the number of links pointing in both directions L < − > {\displaystyle L^{<->}} to the total number of links L r = L < − > L {\displaystyle r={\frac {L^{<->}}{L}}} With this definition, r = 1 {\displaystyle r=1} is for a purely bidirectional network while r = 0 {\displaystyle r=0} for a purely unidirectional one. Real networks have an intermediate value between 0 and 1. However, this definition of reciprocity has some defects. It cannot tell the relative difference of reciprocity compared with purely random network with the same number of vertices and edges. The useful information from reciprocity is not the value itself, but whether mutual links occur more or less often than expected by chance. Besides, in those networks containing self-linking loops (links starting and ending at the same vertex), the self-linking loops should be excluded when calculating L {\displaystyle L} . In order to overcome the defects of the above definition, Garlaschelli and Loffredo defined reciprocity as the correlation coefficient between the entries of the adjacency matrix of a directed graph ( a i j = 1 {\displaystyle a_{ij}=1} if a link from i {\displaystyle i} to j {\displaystyle j} exists, and a i j = 0 {\displaystyle a_{ij}=0} if not): ρ ≡ ∑ i ≠ j ( a i j − a ¯ ) ( a j i − a ¯ ) ∑ i ≠ j ( a i j − a ¯ ) 2 {\displaystyle \rho \equiv {\frac {\sum _{i\neq j}(a_{ij}-{\bar {a}})(a_{ji}-{\bar {a}})}{\sum _{i\neq j}(a_{ij}-{\bar {a}})^{2}}}} , where the average value a ¯ ≡ ∑ i ≠ j a i j N ( N − 1 ) = L N ( N − 1 ) {\displaystyle {\bar {a}}\equiv {\frac {\sum _{i\neq j}a_{ij}}{N(N-1)}}={\frac {L}{N(N-1)}}} . a ¯ {\displaystyle {\bar {a}}} measures the ratio of observed to possible directed links (link density), and self-linking loops are now excluded from L {\displaystyle L} since i {\displaystyle i} is not equal to j {\displaystyle j} . The definition can be written in the following simple form: ρ = r − a ¯ 1 − a ¯ {\displaystyle \rho ={\frac {r-{\bar {a}}}{1-{\bar {a}}}}} The new definition of reciprocity gives an absolute quantity which directly allows one to distinguish between reciprocal ( ρ > 0 {\displaystyle \rho >0} ) and antireciprocal ( ρ < 0 {\displaystyle \rho <0} ) networks, with mutual links occurring more and less often than random respectively. If all the links occur in reciprocal pairs, ρ = 1 {\displaystyle \rho =1} ; if r = 0 {\displaystyle r=0} , ρ = ρ m i n {\displaystyle \rho =\rho _{min}} . ρ m i n ≡ − a ¯ 1 − a ¯ {\displaystyle \rho _{min}\equiv {\frac {-{\bar {a}}}{1-{\bar {a}}}}} This is another advantage of using ρ {\displaystyle \rho } , since it incorporates the idea that complete antireciprocality is more statistically significant in networks with larger density, while it must be regarded as a less pronounced effect in sparser networks. References |
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[SOURCE: https://en.wikipedia.org/wiki/Artificial_Intelligence] | [TOKENS: 16553] |
Contents Artificial intelligence Artificial intelligence (AI) is the capability of computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of research in computer science that develops and studies methods and software that enable machines to perceive their environment and use learning and intelligence to take actions that maximize their chances of achieving defined goals. High-profile applications of AI include advanced web search engines (e.g., Google Search); recommendation systems (used by YouTube, Amazon, and Netflix); virtual assistants (e.g., Google Assistant, Siri, and Alexa); autonomous vehicles (e.g., Waymo); generative and creative tools (e.g., language models and AI art); and superhuman play and analysis in strategy games (e.g., chess and Go). However, many AI applications are not perceived as AI: "A lot of cutting edge AI has filtered into general applications, often without being called AI because once something becomes useful enough and common enough it's not labeled AI anymore." Various subfields of AI research are centered around particular goals and the use of particular tools. The traditional goals of AI research include learning, reasoning, knowledge representation, planning, natural language processing, perception, and support for robotics.[a] To reach these goals, AI researchers have adapted and integrated a wide range of techniques, including search and mathematical optimization, formal logic, artificial neural networks, and methods based on statistics, operations research, and economics.[b] AI also draws upon psychology, linguistics, philosophy, neuroscience, and other fields. Some companies, such as OpenAI, Google DeepMind and Meta, aim to create artificial general intelligence (AGI) – AI that can complete virtually any cognitive task at least as well as a human. Artificial intelligence was founded as an academic discipline in 1956, and the field went through multiple cycles of optimism throughout its history, followed by periods of disappointment and loss of funding, known as AI winters. Funding and interest vastly increased after 2012 when graphics processing units started being used to accelerate neural networks, and deep learning outperformed previous AI techniques. This growth accelerated further after 2017 with the transformer architecture. In the 2020s, an ongoing period of rapid progress in advanced generative AI became known as the AI boom. Generative AI's ability to create and modify content has led to several unintended consequences and harms. Ethical concerns have been raised about AI's long-term effects and potential existential risks, prompting discussions about regulatory policies to ensure the safety and benefits of the technology. Goals The general problem of simulating (or creating) intelligence has been broken into subproblems. These consist of particular traits or capabilities that researchers expect an intelligent system to display. The traits described below have received the most attention and cover the scope of AI research.[a] Early researchers developed algorithms that imitated step-by-step reasoning that humans use when they solve puzzles or make logical deductions. By the late 1980s and 1990s, methods were developed for dealing with uncertain or incomplete information, employing concepts from probability and economics. Many of these algorithms are insufficient for solving large reasoning problems because they experience a "combinatorial explosion": They become exponentially slower as the problems grow. Even humans rarely use the step-by-step deduction that early AI research could model. They solve most of their problems using fast, intuitive judgments. Accurate and efficient reasoning is an unsolved problem. Knowledge representation and knowledge engineering allow AI programs to answer questions intelligently and make deductions about real-world facts. Formal knowledge representations are used in content-based indexing and retrieval, scene interpretation, clinical decision support, knowledge discovery (mining "interesting" and actionable inferences from large databases), and other areas. A knowledge base is a body of knowledge represented in a form that can be used by a program. An ontology is the set of objects, relations, concepts, and properties used by a particular domain of knowledge. Knowledge bases need to represent things such as objects, properties, categories, and relations between objects; situations, events, states, and time; causes and effects; knowledge about knowledge (what we know about what other people know); default reasoning (things that humans assume are true until they are told differently and will remain true even when other facts are changing); and many other aspects and domains of knowledge. Among the most difficult problems in knowledge representation are the breadth of commonsense knowledge (the set of atomic facts that the average person knows is enormous); and the sub-symbolic form of most commonsense knowledge (much of what people know is not represented as "facts" or "statements" that they could express verbally). There is also the difficulty of knowledge acquisition, the problem of obtaining knowledge for AI applications.[c] An "agent" is any entity (artificial or not) that perceives and takes actions in the world. A rational agent has goals or preferences and takes actions to make them happen.[d] In automated planning, the agent has a specific goal. In automated decision-making, the agent has preferences—there are some situations it would prefer to be in, and some situations it is trying to avoid. The decision-making agent assigns a number to each situation (called the "utility") that measures how much the agent prefers it. For each possible action, it can calculate the "expected utility": the utility of all possible outcomes of the action, weighted by the probability that the outcome will occur. It can then choose the action with the maximum expected utility. In classical planning, the agent knows exactly what the effect of any action will be. In most real-world problems, however, the agent may not be certain about the situation they are in (it is "unknown" or "unobservable") and it may not know for certain what will happen after each possible action (it is not "deterministic"). It must choose an action by making a probabilistic guess and then reassess the situation to see if the action worked. Alongside thorough testing and improvement based on previous decisions, having an explanation for why the agent took certain decisions is a way to build trust, especially when the decisions have to be relied upon. In some problems, the agent's preferences may be uncertain, especially if there are other agents or humans involved. These can be learned (e.g., with inverse reinforcement learning), or the agent can seek information to improve its preferences. Information value theory can be used to weigh the value of exploratory or experimental actions. The space of possible future actions and situations is typically intractably large, so the agents must take actions and evaluate situations while being uncertain of what the outcome will be. A Markov decision process has a transition model that describes the probability that a particular action will change the state in a particular way and a reward function that supplies the utility of each state and the cost of each action. A policy associates a decision with each possible state. The policy could be calculated (e.g., by iteration), be heuristic, or it can be learned. Game theory describes the rational behavior of multiple interacting agents and is used in AI programs that make decisions that involve other agents. Machine learning is the study of programs that can improve their performance on a given task automatically. It has been a part of AI from the beginning.[e] There are several kinds of machine learning. Unsupervised learning analyzes a stream of data and finds patterns and makes predictions without any other guidance. Supervised learning requires labeling the training data with the expected answers, and comes in two main varieties: classification (where the program must learn to predict what category the input belongs in) and regression (where the program must deduce a numeric function based on numeric input). In reinforcement learning, the agent is rewarded for good responses and punished for bad ones. The agent learns to choose responses that are classified as "good". Transfer learning is when the knowledge gained from one problem is applied to a new problem. Deep learning is a type of machine learning that runs inputs through biologically inspired artificial neural networks for all of these types of learning. Computational learning theory can assess learners by computational complexity, by sample complexity (how much data is required), or by other notions of optimization. Natural language processing (NLP) allows programs to read, write and communicate in human languages. Specific problems include speech recognition, speech synthesis, machine translation, information extraction, information retrieval and question answering. Early work, based on Noam Chomsky's generative grammar and semantic networks, had difficulty with word-sense disambiguation[f] unless restricted to small domains called "micro-worlds" (due to the common sense knowledge problem). Margaret Masterman believed that it was meaning and not grammar that was the key to understanding languages, and that thesauri and not dictionaries should be the basis of computational language structure. Modern deep learning techniques for NLP include word embedding (representing words, typically as vectors encoding their meaning), transformers (a deep learning architecture using an attention mechanism), and others. In 2019, generative pre-trained transformer (or "GPT") language models began to generate coherent text, and by 2023, these models were able to get human-level scores on the bar exam, SAT test, GRE test, and many other real-world applications. Machine perception is the ability to use input from sensors (such as cameras, microphones, wireless signals, active lidar, sonar, radar, and tactile sensors) to deduce aspects of the world. Computer vision is the ability to analyze visual input. The field includes speech recognition, image classification, facial recognition, object recognition, object tracking, and robotic perception. Affective computing is a field that comprises systems that recognize, interpret, process, or simulate human feeling, emotion, and mood. For example, some virtual assistants are programmed to speak conversationally or even to banter humorously; it makes them appear more sensitive to the emotional dynamics of human interaction, or to otherwise facilitate human–computer interaction. However, this tends to give naïve users an unrealistic conception of the intelligence of existing computer agents. Moderate successes related to affective computing include textual sentiment analysis and, more recently, multimodal sentiment analysis, wherein AI classifies the effects displayed by a videotaped subject. A machine with artificial general intelligence would be able to solve a wide variety of problems with breadth and versatility similar to human intelligence. Techniques AI research uses a wide variety of techniques to accomplish the goals above.[b] AI can solve many problems by intelligently searching through many possible solutions. There are two very different kinds of search used in AI: state space search and local search. State space search searches through a tree of possible states to try to find a goal state. For example, planning algorithms search through trees of goals and subgoals, attempting to find a path to a target goal, a process called means-ends analysis. Simple exhaustive searches are rarely sufficient for most real-world problems: the search space (the number of places to search) quickly grows to astronomical numbers. The result is a search that is too slow or never completes. "Heuristics" or "rules of thumb" can help prioritize choices that are more likely to reach a goal. Adversarial search is used for game-playing programs, such as chess or Go. It searches through a tree of possible moves and countermoves, looking for a winning position. Local search uses mathematical optimization to find a solution to a problem. It begins with some form of guess and refines it incrementally. Gradient descent is a type of local search that optimizes a set of numerical parameters by incrementally adjusting them to minimize a loss function. Variants of gradient descent are commonly used to train neural networks, through the backpropagation algorithm. Another type of local search is evolutionary computation, which aims to iteratively improve a set of candidate solutions by "mutating" and "recombining" them, selecting only the fittest to survive each generation. Distributed search processes can coordinate via swarm intelligence algorithms. Two popular swarm algorithms used in search are particle swarm optimization (inspired by bird flocking) and ant colony optimization (inspired by ant trails). Formal logic is used for reasoning and knowledge representation. Formal logic comes in two main forms: propositional logic (which operates on statements that are true or false and uses logical connectives such as "and", "or", "not" and "implies") and predicate logic (which also operates on objects, predicates and relations and uses quantifiers such as "Every X is a Y" and "There are some Xs that are Ys"). Deductive reasoning in logic is the process of proving a new statement (conclusion) from other statements that are given and assumed to be true (the premises). Proofs can be structured as proof trees, in which nodes are labelled by sentences, and children nodes are connected to parent nodes by inference rules. Given a problem and a set of premises, problem-solving reduces to searching for a proof tree whose root node is labelled by a solution of the problem and whose leaf nodes are labelled by premises or axioms. In the case of Horn clauses, problem-solving search can be performed by reasoning forwards from the premises or backwards from the problem. In the more general case of the clausal form of first-order logic, resolution is a single, axiom-free rule of inference, in which a problem is solved by proving a contradiction from premises that include the negation of the problem to be solved. Inference in both Horn clause logic and first-order logic is undecidable, and therefore intractable. However, backward reasoning with Horn clauses, which underpins computation in the logic programming language Prolog, is Turing complete. Moreover, its efficiency is competitive with computation in other symbolic programming languages. Fuzzy logic assigns a "degree of truth" between 0 and 1. It can therefore handle propositions that are vague and partially true. Non-monotonic logics, including logic programming with negation as failure, are designed to handle default reasoning. Other specialized versions of logic have been developed to describe many complex domains. Many problems in AI (including reasoning, planning, learning, perception, and robotics) require the agent to operate with incomplete or uncertain information. AI researchers have devised a number of tools to solve these problems using methods from probability theory and economics. Precise mathematical tools have been developed that analyze how an agent can make choices and plan, using decision theory, decision analysis, and information value theory. These tools include models such as Markov decision processes, dynamic decision networks, game theory and mechanism design. Bayesian networks are a tool that can be used for reasoning (using the Bayesian inference algorithm),[g] learning (using the expectation–maximization algorithm),[h] planning (using decision networks) and perception (using dynamic Bayesian networks). Probabilistic algorithms can also be used for filtering, prediction, smoothing, and finding explanations for streams of data, thus helping perception systems analyze processes that occur over time (e.g., hidden Markov models or Kalman filters). The simplest AI applications can be divided into two types: classifiers (e.g., "if shiny then diamond"), on one hand, and controllers (e.g., "if diamond then pick up"), on the other hand. Classifiers are functions that use pattern matching to determine the closest match. They can be fine-tuned based on chosen examples using supervised learning. Each pattern (also called an "observation") is labeled with a certain predefined class. All the observations combined with their class labels are known as a data set. When a new observation is received, that observation is classified based on previous experience. There are many kinds of classifiers in use. The decision tree is the simplest and most widely used symbolic machine learning algorithm. K-nearest neighbor algorithm was the most widely used analogical AI until the mid-1990s, and Kernel methods such as the support vector machine (SVM) displaced k-nearest neighbor in the 1990s. The naive Bayes classifier is reportedly the "most widely used learner" at Google, due in part to its scalability. Neural networks are also used as classifiers. An artificial neural network is based on a collection of nodes also known as artificial neurons, which loosely model the neurons in a biological brain. It is trained to recognise patterns; once trained, it can recognise those patterns in fresh data. There is an input, at least one hidden layer of nodes and an output. Each node applies a function and once the weight crosses its specified threshold, the data is transmitted to the next layer. A network is typically called a deep neural network if it has at least 2 hidden layers. Learning algorithms for neural networks use local search to choose the weights that will get the right output for each input during training. The most common training technique is the backpropagation algorithm. Neural networks learn to model complex relationships between inputs and outputs and find patterns in data. In theory, a neural network can learn any function. In feedforward neural networks the signal passes in only one direction. The term perceptron typically refers to a single-layer neural network. In contrast, deep learning uses many layers. Recurrent neural networks (RNNs) feed the output signal back into the input, which allows short-term memories of previous input events. Long short-term memory networks (LSTMs) are recurrent neural networks that better preserve longterm dependencies and are less sensitive to the vanishing gradient problem. Convolutional neural networks (CNNs) use layers of kernels to more efficiently process local patterns. This local processing is especially important in image processing, where the early CNN layers typically identify simple local patterns such as edges and curves, with subsequent layers detecting more complex patterns like textures, and eventually whole objects. Deep learning uses several layers of neurons between the network's inputs and outputs. The multiple layers can progressively extract higher-level features from the raw input. For example, in image processing, lower layers may identify edges, while higher layers may identify the concepts relevant to a human such as digits, letters, or faces. Deep learning has profoundly improved the performance of programs in many important subfields of artificial intelligence, including computer vision, speech recognition, natural language processing, image classification, and others. The reason that deep learning performs so well in so many applications is not known as of 2021. The sudden success of deep learning in 2012–2015 did not occur because of some new discovery or theoretical breakthrough (deep neural networks and backpropagation had been described by many people, as far back as the 1950s)[i] but because of two factors: the incredible increase in computer power (including the hundred-fold increase in speed by switching to GPUs) and the availability of vast amounts of training data, especially the giant curated datasets used for benchmark testing, such as ImageNet.[j] Generative pre-trained transformers (GPT) are large language models (LLMs) that generate text based on the semantic relationships between words in sentences. Text-based GPT models are pre-trained on a large corpus of text that can be from the Internet. The pretraining consists of predicting the next token (a token being usually a word, subword, or punctuation). Throughout this pretraining, GPT models accumulate knowledge about the world and can then generate human-like text by repeatedly predicting the next token. Typically, a subsequent training phase makes the model more truthful, useful, and harmless, usually with a technique called reinforcement learning from human feedback (RLHF). Current GPT models are prone to generating falsehoods called "hallucinations". These can be reduced with RLHF and quality data, but the problem has been getting worse for reasoning systems. Such systems are used in chatbots, which allow people to ask a question or request a task in simple text. Current models and services include ChatGPT, Claude, Gemini, Copilot, and Meta AI. Multimodal GPT models can process different types of data (modalities) such as images, videos, sound, and text. In the late 2010s, graphics processing units (GPUs) that were increasingly designed with AI-specific enhancements and used with specialized TensorFlow software had replaced previously used central processing unit (CPUs) as the dominant means for large-scale (commercial and academic) machine learning models' training. Specialized programming languages such as Prolog were used in early AI research, but general-purpose programming languages like Python have become predominant. The transistor density in integrated circuits has been observed to roughly double every 18 months—a trend known as Moore's law, named after the Intel co-founder Gordon Moore, who first identified it. Improvements in GPUs have been even faster, a trend sometimes called Huang's law, named after Nvidia co-founder and CEO Jensen Huang. Applications AI and machine learning technology is used in most of the essential applications of the 2020s, including: The deployment of AI may be overseen by a chief automation officer (CAO). It has been suggested that AI can overcome discrepancies in funding allocated to different fields of research. AlphaFold 2 (2021) demonstrated the ability to approximate, in hours rather than months, the 3D structure of a protein. In 2023, it was reported that AI-guided drug discovery helped find a class of antibiotics capable of killing two different types of drug-resistant bacteria. In 2024, researchers used machine learning to accelerate the search for Parkinson's disease drug treatments. Their aim was to identify compounds that block the clumping, or aggregation, of alpha-synuclein (the protein that characterises Parkinson's disease). They were able to speed up the initial screening process ten-fold and reduce the cost by a thousand-fold. Game playing programs have been used since the 1950s to demonstrate and test AI's most advanced techniques. Deep Blue became the first computer chess-playing system to beat a reigning world chess champion, Garry Kasparov, on 11 May 1997. In 2011, in a Jeopardy! quiz show exhibition match, IBM's question answering system, Watson, defeated the two greatest Jeopardy! champions, Brad Rutter and Ken Jennings, by a significant margin. In March 2016, AlphaGo won 4 out of 5 games of Go in a match with Go champion Lee Sedol, becoming the first computer Go-playing system to beat a professional Go player without handicaps. Then, in 2017, it defeated Ke Jie, who was the best Go player in the world. Other programs handle imperfect-information games, such as the poker-playing program Pluribus. DeepMind developed increasingly generalistic reinforcement learning models, such as with MuZero, which could be trained to play chess, Go, or Atari games. In 2019, DeepMind's AlphaStar achieved grandmaster level in StarCraft II, a particularly challenging real-time strategy game that involves incomplete knowledge of what happens on the map. In 2021, an AI agent competed in a PlayStation Gran Turismo competition, winning against four of the world's best Gran Turismo drivers using deep reinforcement learning. In 2024, Google DeepMind introduced SIMA, a type of AI capable of autonomously playing nine previously unseen open-world video games by observing screen output, as well as executing short, specific tasks in response to natural language instructions. Large language models, such as GPT-4, Gemini, Claude, Llama or Mistral, are increasingly used in mathematics. These probabilistic models are versatile, but can also produce wrong answers in the form of hallucinations. They sometimes need a large database of mathematical problems to learn from, but also methods such as supervised fine-tuning or trained classifiers with human-annotated data to improve answers for new problems and learn from corrections. A February 2024 study showed that the performance of some language models for reasoning capabilities in solving math problems not included in their training data was low, even for problems with only minor deviations from trained data. One technique to improve their performance involves training the models to produce correct reasoning steps, rather than just the correct result. The Alibaba Group developed a version of its Qwen models called Qwen2-Math, that achieved state-of-the-art performance on several mathematical benchmarks, including 84% accuracy on the MATH dataset of competition mathematics problems. In January 2025, Microsoft proposed the technique rStar-Math that leverages Monte Carlo tree search and step-by-step reasoning, enabling a relatively small language model like Qwen-7B to solve 53% of the AIME 2024 and 90% of the MATH benchmark problems. Alternatively, dedicated models for mathematical problem solving with higher precision for the outcome including proof of theorems have been developed such as AlphaTensor, AlphaGeometry, AlphaProof and AlphaEvolve all from Google DeepMind, Llemma from EleutherAI or Julius. When natural language is used to describe mathematical problems, converters can transform such prompts into a formal language such as Lean to define mathematical tasks. The experimental model Gemini Deep Think accepts natural language prompts directly and achieved gold medal results in the International Math Olympiad of 2025. Some models have been developed to solve challenging problems and reach good results in benchmark tests, others to serve as educational tools in mathematics. Topological deep learning integrates various topological approaches. Finance is one of the fastest growing sectors where applied AI tools are being deployed: from retail online banking to investment advice and insurance, where automated "robot advisers" have been in use for some years. According to Nicolas Firzli, director of the World Pensions & Investments Forum, it may be too early to see the emergence of highly innovative AI-informed financial products and services. He argues that "the deployment of AI tools will simply further automatise things: destroying tens of thousands of jobs in banking, financial planning, and pension advice in the process, but I'm not sure it will unleash a new wave of [e.g., sophisticated] pension innovation." Various countries are deploying AI military applications. The main applications enhance command and control, communications, sensors, integration and interoperability. Research is targeting intelligence collection and analysis, logistics, cyber operations, information operations, and semiautonomous and autonomous vehicles. AI technologies enable coordination of sensors and effectors, threat detection and identification, marking of enemy positions, target acquisition, coordination and deconfliction of distributed Joint Fires between networked combat vehicles, both human-operated and autonomous. AI has been used in military operations in Iraq, Syria, Israel and Ukraine. Generative artificial intelligence, also known as generative AI or GenAI, is a subfield of artificial intelligence that uses generative models to generate text, images, videos, audio, software code or other forms of data. These models learn the underlying patterns and structures of their training data, and use them to generate new data in response to input, which often takes the form of natural language prompts. The prevalence of generative AI tools has increased significantly since the AI boom in the 2020s. This boom was made possible by improvements in deep neural networks, particularly large language models (LLMs), which are based on the transformer architecture. Generative AI applications include chatbots such as ChatGPT, Claude, Copilot, DeepSeek, Google Gemini and Grok; text-to-image models such as Stable Diffusion, Midjourney, and DALL-E; and text-to-video models such as Veo, LTX and Sora. Companies in a variety of sectors have used generative AI, including those in software development, healthcare, finance, entertainment, customer service, sales and marketing, art, writing, and product design. AI agents are software entities designed to perceive their environment, make decisions, and take actions autonomously to achieve specific goals. These agents can interact with users, their environment, or other agents. AI agents are used in various applications, including virtual assistants, chatbots, autonomous vehicles, game-playing systems, and industrial robotics. AI agents operate within the constraints of their programming, available computational resources, and hardware limitations. This means they are restricted to performing tasks within their defined scope and have finite memory and processing capabilities. In real-world applications, AI agents often face time constraints for decision-making and action execution. Many AI agents incorporate learning algorithms, enabling them to improve their performance over time through experience or training. Using machine learning, AI agents can adapt to new situations and optimise their behaviour for their designated tasks. Microsoft introduced Copilot Search in February 2023 under the name Bing Chat, as a built-in feature for Microsoft Edge and Bing mobile app. Copilot Search provides AI-generated summaries and step-by-step reasoning based of information from web publishers, ranked in Bing Search. For safety, Copilot uses AI-based classifiers and filters to reduce potentially harmful content. Google officially pushed its AI Search at its Google I/O event on 20 May 2025. It keeps people looking at Google instead of clicking on a search result. AI Overviews uses Gemini 2.5 to provide contextual answers to user queries based on web content. Applications of AI in this domain include AI-enabled menstruation and fertility trackers that analyze user data to offer predictions, AI-integrated sex toys (e.g., teledildonics), AI-generated sexual education content, and AI agents that simulate sexual and romantic partners (e.g., Replika). AI is also used for the production of non-consensual deepfake pornography, raising significant ethical and legal concerns. AI technologies have also been used to attempt to identify online gender-based violence and online sexual grooming of minors. There are also thousands of successful AI applications used to solve specific problems for specific industries or institutions. In a 2017 survey, one in five companies reported having incorporated "AI" in some offerings or processes. A few examples are energy storage, medical diagnosis, military logistics, applications that predict the result of judicial decisions, foreign policy, or supply chain management. AI applications for evacuation and disaster management are growing. AI has been used to investigate patterns in large-scale and small-scale evacuations using historical data from GPS, videos or social media. Furthermore, AI can provide real-time information on the evacuation conditions. In agriculture, AI has helped farmers to increase yield and identify areas that need irrigation, fertilization, pesticide treatments. Agronomists use AI to conduct research and development. AI has been used to predict the ripening time for crops such as tomatoes, monitor soil moisture, operate agricultural robots, conduct predictive analytics, classify livestock pig call emotions, automate greenhouses, detect diseases and pests, and save water. Artificial intelligence is used in astronomy to analyze increasing amounts of available data and applications, mainly for "classification, regression, clustering, forecasting, generation, discovery, and the development of new scientific insights." For example, it is used for discovering exoplanets, forecasting solar activity, and distinguishing between signals and instrumental effects in gravitational wave astronomy. Additionally, it could be used for activities in space, such as space exploration, including the analysis of data from space missions, real-time science decisions of spacecraft, space debris avoidance, and more autonomous operation. During the 2024 Indian elections, US$50 million was spent on authorized AI-generated content, notably by creating deepfakes of allied (including sometimes deceased) politicians to better engage with voters, and by translating speeches to various local languages. Ethics AI has potential benefits and potential risks. AI may be able to advance science and find solutions for serious problems: Demis Hassabis of DeepMind hopes to "solve intelligence, and then use that to solve everything else". However, as the use of AI has become widespread, several unintended consequences and risks have been identified. In-production systems can sometimes not factor ethics and bias into their AI training processes, especially when the AI algorithms are inherently unexplainable in deep learning. Machine learning algorithms require large amounts of data. The techniques used to acquire this data have raised concerns about privacy, surveillance and copyright. AI-powered devices and services, such as virtual assistants and IoT products, continuously collect personal information, raising concerns about intrusive data gathering and unauthorized access by third parties. The loss of privacy is further exacerbated by AI's ability to process and combine vast amounts of data, potentially leading to a surveillance society where individual activities are constantly monitored and analyzed without adequate safeguards or transparency. Sensitive user data collected may include online activity records, geolocation data, video, or audio. For example, in order to build speech recognition algorithms, Amazon has recorded millions of private conversations and allowed temporary workers to listen to and transcribe some of them. Opinions about this widespread surveillance range from those who see it as a necessary evil to those for whom it is clearly unethical and a violation of the right to privacy. AI developers argue that this is the only way to deliver valuable applications and have developed several techniques that attempt to preserve privacy while still obtaining the data, such as data aggregation, de-identification and differential privacy. Since 2016, some privacy experts, such as Cynthia Dwork, have begun to view privacy in terms of fairness. Brian Christian wrote that experts have pivoted "from the question of 'what they know' to the question of 'what they're doing with it'." Generative AI is often trained on unlicensed copyrighted works, including in domains such as images or computer code; the output is then used under the rationale of "fair use". Experts disagree about how well and under what circumstances this rationale will hold up in courts of law; relevant factors may include "the purpose and character of the use of the copyrighted work" and "the effect upon the potential market for the copyrighted work". Website owners can indicate that they do not want their content scraped via a "robots.txt" file. However, some companies will scrape content regardless because the robots.txt file has no real authority. In 2023, leading authors (including John Grisham and Jonathan Franzen) sued AI companies for using their work to train generative AI. Another discussed approach is to envision a separate sui generis system of protection for creations generated by AI to ensure fair attribution and compensation for human authors. The commercial AI scene is dominated by Big Tech companies such as Alphabet Inc., Amazon, Apple Inc., Meta Platforms, and Microsoft. Some of these players already own the vast majority of existing cloud infrastructure and computing power from data centers, allowing them to entrench further in the marketplace. In January 2024, the International Energy Agency (IEA) released Electricity 2024, Analysis and Forecast to 2026, forecasting electric power use. This is the first IEA report to make projections for data centers and power consumption for artificial intelligence and cryptocurrency. The report states that power demand for these uses might double by 2026, with additional electric power usage equal to electricity used by the whole Japanese nation. Prodigious power consumption by AI is responsible for the growth of fossil fuel use, and might delay closings of obsolete, carbon-emitting coal energy facilities. There is a feverish rise in the construction of data centers throughout the US, making large technology firms (e.g., Microsoft, Meta, Google, Amazon) into voracious consumers of electric power. Projected electric consumption is so immense that there is concern that it will be fulfilled no matter the source. A ChatGPT search involves the use of 10 times the electrical energy as a Google search. The large firms are in haste to find power sources – from nuclear energy to geothermal to fusion. The tech firms argue that – in the long view – AI will be eventually kinder to the environment, but they need the energy now. AI makes the power grid more efficient and "intelligent", will assist in the growth of nuclear power, and track overall carbon emissions, according to technology firms. A 2024 Goldman Sachs Research Paper, AI Data Centers and the Coming US Power Demand Surge, found "US power demand (is) likely to experience growth not seen in a generation...." and forecasts that, by 2030, US data centers will consume 8% of US power, as opposed to 3% in 2022, presaging growth for the electrical power generation industry by a variety of means. Data centers' need for more and more electrical power is such that they might max out the electrical grid. The Big Tech companies counter that AI can be used to maximize the utilization of the grid by all. In 2024, the Wall Street Journal reported that big AI companies have begun negotiations with the US nuclear power providers to provide electricity to the data centers. In March 2024 Amazon purchased a Pennsylvania nuclear-powered data center for US$650 million. Nvidia CEO Jensen Huang said nuclear power is a good option for the data centers. In September 2024, Microsoft announced an agreement with Constellation Energy to re-open the Three Mile Island nuclear power plant to provide Microsoft with 100% of all electric power produced by the plant for 20 years. Reopening the plant, which suffered a partial nuclear meltdown of its Unit 2 reactor in 1979, will require Constellation to get through strict regulatory processes which will include extensive safety scrutiny from the US Nuclear Regulatory Commission. If approved (this will be the first ever US re-commissioning of a nuclear plant), over 835 megawatts of power – enough for 800,000 homes – of energy will be produced. The cost for re-opening and upgrading is estimated at US$1.6 billion and is dependent on tax breaks for nuclear power contained in the 2022 US Inflation Reduction Act. The US government and the state of Michigan are investing almost US$2 billion to reopen the Palisades Nuclear reactor on Lake Michigan. Closed since 2022, the plant is planned to be reopened in October 2025. The Three Mile Island facility will be renamed the Crane Clean Energy Center after Chris Crane, a nuclear proponent and former CEO of Exelon who was responsible for Exelon's spinoff of Constellation. After the last approval in September 2023, Taiwan suspended the approval of data centers north of Taoyuan with a capacity of more than 5 MW in 2024, due to power supply shortages. Taiwan aims to phase out nuclear power by 2025. On the other hand, Singapore imposed a ban on the opening of data centers in 2019 due to electric power, but in 2022, lifted this ban. Although most nuclear plants in Japan have been shut down after the 2011 Fukushima nuclear accident, according to an October 2024 Bloomberg article in Japanese, cloud gaming services company Ubitus, in which Nvidia has a stake, is looking for land in Japan near a nuclear power plant for a new data center for generative AI. Ubitus CEO Wesley Kuo said nuclear power plants are the most efficient, cheap and stable power for AI. On 1 November 2024, the Federal Energy Regulatory Commission (FERC) rejected an application submitted by Talen Energy for approval to supply some electricity from the nuclear power station Susquehanna to Amazon's data center. According to the Commission Chairman Willie L. Phillips, it is a burden on the electricity grid as well as a significant cost shifting concern to households and other business sectors. In 2025, a report prepared by the International Energy Agency estimated the greenhouse gas emissions from the energy consumption of AI at 180 million tons. By 2035, these emissions could rise to 300–500 million tonnes depending on what measures will be taken. This is below 1.5% of the energy sector emissions. The emissions reduction potential of AI was estimated at 5% of the energy sector emissions, but rebound effects (for example if people switch from public transport to autonomous cars) can reduce it. YouTube, Facebook and others use recommender systems to guide users to more content. These AI programs were given the goal of maximizing user engagement (that is, the only goal was to keep people watching). The AI learned that users tended to choose misinformation, conspiracy theories, and extreme partisan content, and, to keep them watching, the AI recommended more of it. Users also tended to watch more content on the same subject, so the AI led people into filter bubbles where they received multiple versions of the same misinformation. This convinced many users that the misinformation was true, and ultimately undermined trust in institutions, the media and the government. The AI program had correctly learned to maximize its goal, but the result was harmful to society. After the U.S. election in 2016, major technology companies took some steps to mitigate the problem. In the early 2020s, generative AI began to create images, audio, and texts that are virtually indistinguishable from real photographs, recordings, or human writing, while realistic AI-generated videos became feasible in the mid-2020s. It is possible for bad actors to use this technology to create massive amounts of misinformation or propaganda; one such potential malicious use is deepfakes for computational propaganda. AI pioneer and Nobel Prize-winning computer scientist Geoffrey Hinton expressed concern about AI enabling "authoritarian leaders to manipulate their electorates" on a large scale, among other risks. The ability to influence electorates has been proved in at least one study. This same study shows more inaccurate statements from the models when they advocate for candidates of the political right. AI researchers at Microsoft, OpenAI, universities and other organisations have suggested using "personhood credentials" as a way to overcome online deception enabled by AI models. Machine learning applications can be biased[k] if they learn from biased data. The developers may not be aware that the bias exists. Discriminatory behavior by some LLMs can be observed in their output. Bias can be introduced by the way training data is selected and by the way a model is deployed. If a biased algorithm is used to make decisions that can seriously harm people (as it can in medicine, finance, recruitment, housing or policing) then the algorithm may cause discrimination. The field of fairness studies how to prevent harms from algorithmic biases. On 28 June 2015, Google Photos's new image labeling feature mistakenly identified Jacky Alcine and a friend as "gorillas" because they were black. The system was trained on a dataset that contained very few images of black people, a problem called "sample size disparity". Google "fixed" this problem by preventing the system from labelling anything as a "gorilla". Eight years later, in 2023, Google Photos still could not identify a gorilla, and neither could similar products from Apple, Facebook, Microsoft and Amazon. COMPAS is a commercial program widely used by U.S. courts to assess the likelihood of a defendant becoming a recidivist. In 2016, Julia Angwin at ProPublica discovered that COMPAS exhibited racial bias, despite the fact that the program was not told the races of the defendants. Although the error rate for both whites and blacks was calibrated equal at exactly 61%, the errors for each race were different—the system consistently overestimated the chance that a black person would re-offend and would underestimate the chance that a white person would not re-offend. In 2017, several researchers[l] showed that it was mathematically impossible for COMPAS to accommodate all possible measures of fairness when the base rates of re-offense were different for whites and blacks in the data. A program can make biased decisions even if the data does not explicitly mention a problematic feature (such as "race" or "gender"). The feature will correlate with other features (like "address", "shopping history" or "first name"), and the program will make the same decisions based on these features as it would on "race" or "gender". Moritz Hardt said "the most robust fact in this research area is that fairness through blindness doesn't work." Criticism of COMPAS highlighted that machine learning models are designed to make "predictions" that are only valid if we assume that the future will resemble the past. If they are trained on data that includes the results of racist decisions in the past, machine learning models must predict that racist decisions will be made in the future. If an application then uses these predictions as recommendations, some of these "recommendations" will likely be racist. Thus, machine learning is not well suited to help make decisions in areas where there is hope that the future will be better than the past. It is descriptive rather than prescriptive.[m] Bias and unfairness may go undetected because the developers are overwhelmingly white and male: among AI engineers, about 4% are black and 20% are women. There are various conflicting definitions and mathematical models of fairness. These notions depend on ethical assumptions, and are influenced by beliefs about society. One broad category is distributive fairness, which focuses on the outcomes, often identifying groups and seeking to compensate for statistical disparities. Representational fairness tries to ensure that AI systems do not reinforce negative stereotypes or render certain groups invisible. Procedural fairness focuses on the decision process rather than the outcome. The most relevant notions of fairness may depend on the context, notably the type of AI application and the stakeholders. The subjectivity in the notions of bias and fairness makes it difficult for companies to operationalize them. Having access to sensitive attributes such as race or gender is also considered by many AI ethicists to be necessary in order to compensate for biases, but it may conflict with anti-discrimination laws. At the 2022 ACM Conference on Fairness, Accountability, and Transparency a paper reported that a CLIP‑based (Contrastive Language-Image Pre-training) robotic system reproduced harmful gender‑ and race‑linked stereotypes in a simulated manipulation task. The authors recommended robot‑learning methods which physically manifest such harms be "paused, reworked, or even wound down when appropriate, until outcomes can be proven safe, effective, and just." Many AI systems are so complex that their designers cannot explain how they reach their decisions. Particularly with deep neural networks, in which there are many non-linear relationships between inputs and outputs. But some popular explainability techniques exist. It is impossible to be certain that a program is operating correctly if no one knows how exactly it works. There have been many cases where a machine learning program passed rigorous tests, but nevertheless learned something different than what the programmers intended. For example, a system that could identify skin diseases better than medical professionals was found to actually have a strong tendency to classify images with a ruler as "cancerous", because pictures of malignancies typically include a ruler to show the scale. Another machine learning system designed to help effectively allocate medical resources was found to classify patients with asthma as being at "low risk" of dying from pneumonia. Having asthma is actually a severe risk factor, but since the patients having asthma would usually get much more medical care, they were relatively unlikely to die according to the training data. The correlation between asthma and low risk of dying from pneumonia was real, but misleading. People who have been harmed by an algorithm's decision have a right to an explanation. Doctors, for example, are expected to clearly and completely explain to their colleagues the reasoning behind any decision they make. Early drafts of the European Union's General Data Protection Regulation in 2016 included an explicit statement that this right exists.[n] Industry experts noted that this is an unsolved problem with no solution in sight. Regulators argued that nevertheless the harm is real: if the problem has no solution, the tools should not be used. DARPA established the XAI ("Explainable Artificial Intelligence") program in 2014 to try to solve these problems. Several approaches aim to address the transparency problem. SHAP enables to visualise the contribution of each feature to the output. LIME can locally approximate a model's outputs with a simpler, interpretable model. Multitask learning provides a large number of outputs in addition to the target classification. These other outputs can help developers deduce what the network has learned. Deconvolution, DeepDream and other generative methods can allow developers to see what different layers of a deep network for computer vision have learned, and produce output that can suggest what the network is learning. For generative pre-trained transformers, Anthropic developed a technique based on dictionary learning that associates patterns of neuron activations with human-understandable concepts. Artificial intelligence provides a number of tools that are useful to bad actors, such as authoritarian governments, terrorists, criminals or rogue states. A lethal autonomous weapon is a machine that locates, selects and engages human targets without human supervision.[o] Widely available AI tools can be used by bad actors to develop inexpensive autonomous weapons and, if produced at scale, they are potentially weapons of mass destruction. Even when used in conventional warfare, they currently cannot reliably choose targets and could potentially kill an innocent person. In 2014, 30 nations (including China) supported a ban on autonomous weapons under the United Nations' Convention on Certain Conventional Weapons, however the United States and others disagreed. By 2015, over fifty countries were reported to be researching battlefield robots. AI tools make it easier for authoritarian governments to efficiently control their citizens in several ways. Face and voice recognition allow widespread surveillance. Machine learning, operating this data, can classify potential enemies of the state and prevent them from hiding. Recommendation systems can precisely target propaganda and misinformation for maximum effect. Deepfakes and generative AI aid in producing misinformation. Advanced AI can make authoritarian centralized decision-making more competitive than liberal and decentralized systems such as markets. It lowers the cost and difficulty of digital warfare and advanced spyware. All these technologies have been available since 2020 or earlier—AI facial recognition systems are already being used for mass surveillance in China. There are many other ways in which AI is expected to help bad actors, some of which can not be foreseen. For example, machine-learning AI is able to design tens of thousands of toxic molecules in a matter of hours. Economists have frequently highlighted the risks of redundancies from AI, and speculated about unemployment if there is no adequate social policy for full employment. In the past, technology has tended to increase rather than reduce total employment, but economists acknowledge that "we're in uncharted territory" with AI. A survey of economists showed disagreement about whether the increasing use of robots and AI will cause a substantial increase in long-term unemployment, but they generally agree that it could be a net benefit if productivity gains are redistributed. Risk estimates vary; for example, in the 2010s, Michael Osborne and Carl Benedikt Frey estimated 47% of U.S. jobs are at "high risk" of potential automation, while an OECD report classified only 9% of U.S. jobs as "high risk".[p] The methodology of speculating about future employment levels has been criticised as lacking evidential foundation, and for implying that technology, rather than social policy, creates unemployment, as opposed to redundancies. In April 2023, it was reported that 70% of the jobs for Chinese video game illustrators had been eliminated by generative artificial intelligence. Unlike previous waves of automation, many middle-class jobs may be eliminated by artificial intelligence; The Economist stated in 2015 that "the worry that AI could do to white-collar jobs what steam power did to blue-collar ones during the Industrial Revolution" is "worth taking seriously". Jobs at extreme risk range from paralegals to fast food cooks, while job demand is likely to increase for care-related professions ranging from personal healthcare to the clergy. In July 2025, Ford CEO Jim Farley predicted that "artificial intelligence is going to replace literally half of all white-collar workers in the U.S." From the early days of the development of artificial intelligence, there have been arguments, for example, those put forward by Joseph Weizenbaum, about whether tasks that can be done by computers actually should be done by them, given the difference between computers and humans, and between quantitative calculation and qualitative, value-based judgement. Recent public debates in artificial intelligence have increasingly focused on its broader societal and ethical implications. It has been argued AI will become so powerful that humanity may irreversibly lose control of it. This could, as physicist Stephen Hawking stated, "spell the end of the human race". This scenario has been common in science fiction, when a computer or robot suddenly develops a human-like "self-awareness" (or "sentience" or "consciousness") and becomes a malevolent character.[q] These sci-fi scenarios are misleading in several ways. First, AI does not require human-like sentience to be an existential risk. Modern AI programs are given specific goals and use learning and intelligence to achieve them. Philosopher Nick Bostrom argued that if one gives almost any goal to a sufficiently powerful AI, it may choose to destroy humanity to achieve it (he used the example of an automated paperclip factory that destroys the world to get more iron for paperclips). Stuart Russell gives the example of household robot that tries to find a way to kill its owner to prevent it from being unplugged, reasoning that "you can't fetch the coffee if you're dead." In order to be safe for humanity, a superintelligence would have to be genuinely aligned with humanity's morality and values so that it is "fundamentally on our side". Second, Yuval Noah Harari argues that AI does not require a robot body or physical control to pose an existential risk. The essential parts of civilization are not physical. Things like ideologies, law, government, money and the economy are built on language; they exist because there are stories that billions of people believe. The current prevalence of misinformation suggests that an AI could use language to convince people to believe anything, even to take actions that are destructive. Geoffrey Hinton said in 2025 that modern AI is particularly "good at persuasion" and getting better all the time. He asks "Suppose you wanted to invade the capital of the US. Do you have to go there and do it yourself? No. You just have to be good at persuasion." The opinions amongst experts and industry insiders are mixed, with sizable fractions both concerned and unconcerned by risk from eventual superintelligent AI. Personalities such as Stephen Hawking, Bill Gates, and Elon Musk, as well as AI pioneers such as Geoffrey Hinton, Yoshua Bengio, Stuart Russell, Demis Hassabis, and Sam Altman, have expressed concerns about existential risk from AI. In May 2023, Geoffrey Hinton announced his resignation from Google in order to be able to "freely speak out about the risks of AI" without "considering how this impacts Google". He notably mentioned risks of an AI takeover, and stressed that in order to avoid the worst outcomes, establishing safety guidelines will require cooperation among those competing in use of AI. In 2023, many leading AI experts endorsed the joint statement that "Mitigating the risk of extinction from AI should be a global priority alongside other societal-scale risks such as pandemics and nuclear war". Some other researchers were more optimistic. AI pioneer Jürgen Schmidhuber did not sign the joint statement, emphasising that in 95% of all cases, AI research is about making "human lives longer and healthier and easier." While the tools that are now being used to improve lives can also be used by bad actors, "they can also be used against the bad actors." Andrew Ng also argued that "it's a mistake to fall for the doomsday hype on AI—and that regulators who do will only benefit vested interests." Yann LeCun ", a Turing Award winner, disagreed with the idea that AI will subordinate humans "simply because they are smarter, let alone destroy [us]", "scoff[ing] at his peers' dystopian scenarios of supercharged misinformation and even, eventually, human extinction." In the early 2010s, experts argued that the risks are too distant in the future to warrant research or that humans will be valuable from the perspective of a superintelligent machine. However, after 2016, the study of current and future risks and possible solutions became a serious area of research. Friendly AI are machines that have been designed from the beginning to minimize risks and to make choices that benefit humans. Eliezer Yudkowsky, who coined the term, argues that developing friendly AI should be a higher research priority: it may require a large investment and it must be completed before AI becomes an existential risk. Machines with intelligence have the potential to use their intelligence to make ethical decisions. The field of machine ethics provides machines with ethical principles and procedures for resolving ethical dilemmas. The field of machine ethics is also called computational morality, and was founded at an AAAI symposium in 2005. Other approaches include Wendell Wallach's "artificial moral agents" and Stuart J. Russell's three principles for developing provably beneficial machines. Active organizations in the AI open-source community include Hugging Face, Google, EleutherAI and Meta. Various AI models, such as Llama 2, Mistral or Stable Diffusion, have been made open-weight, meaning that their architecture and trained parameters (the "weights") are publicly available. Open-weight models can be freely fine-tuned, which allows companies to specialize them with their own data and for their own use-case. Open-weight models are useful for research and innovation but can also be misused. Since they can be fine-tuned, any built-in security measure, such as objecting to harmful requests, can be trained away until it becomes ineffective. Some researchers warn that future AI models may develop dangerous capabilities (such as the potential to drastically facilitate bioterrorism) and that once released on the Internet, they cannot be deleted everywhere if needed. They recommend pre-release audits and cost-benefit analyses. Artificial intelligence projects can be guided by ethical considerations during the design, development, and implementation of an AI system. An AI framework such as the Care and Act Framework, developed by the Alan Turing Institute and based on the SUM values, outlines four main ethical dimensions, defined as follows: Other developments in ethical frameworks include those decided upon during the Asilomar Conference, the Montreal Declaration for Responsible AI, and the IEEE's Ethics of Autonomous Systems initiative, among others; however, these principles are not without criticism, especially regarding the people chosen to contribute to these frameworks. Promotion of the wellbeing of the people and communities that these technologies affect requires consideration of the social and ethical implications at all stages of AI system design, development and implementation, and collaboration between job roles such as data scientists, product managers, data engineers, domain experts, and delivery managers. The UK AI Safety Institute released in 2024 a testing toolset called 'Inspect' for AI safety evaluations available under an MIT open-source licence which is freely available on GitHub and can be improved with third-party packages. It can be used to evaluate AI models in a range of areas including core knowledge, ability to reason, and autonomous capabilities. The regulation of artificial intelligence is the development of public sector policies and laws for promoting and regulating AI; it is therefore related to the broader regulation of algorithms. The regulatory and policy landscape for AI is an emerging issue in jurisdictions globally. According to AI Index at Stanford, the annual number of AI-related laws passed in the 127 survey countries jumped from one passed in 2016 to 37 passed in 2022 alone. Between 2016 and 2020, more than 30 countries adopted dedicated strategies for AI. Most EU member states had released national AI strategies, as had Canada, China, India, Japan, Mauritius, the Russian Federation, Saudi Arabia, United Arab Emirates, U.S., and Vietnam. Others were in the process of elaborating their own AI strategy, including Bangladesh, Malaysia and Tunisia. The Global Partnership on Artificial Intelligence was launched in June 2020, stating a need for AI to be developed in accordance with human rights and democratic values, to ensure public confidence and trust in the technology. Henry Kissinger, Eric Schmidt, and Daniel Huttenlocher published a joint statement in November 2021 calling for a government commission to regulate AI. In 2023, OpenAI leaders published recommendations for the governance of superintelligence, which they believe may happen in less than 10 years. In 2023, the United Nations also launched an advisory body to provide recommendations on AI governance; the body comprises technology company executives, government officials and academics. On 1 August 2024, the EU Artificial Intelligence Act entered into force, establishing the first comprehensive EU-wide AI regulation. In 2024, the Council of Europe created the first international legally binding treaty on AI, called the "Framework Convention on Artificial Intelligence and Human Rights, Democracy and the Rule of Law". It was adopted by the European Union, the United States, the United Kingdom, and other signatories. In a 2022 Ipsos survey, attitudes towards AI varied greatly by country; 78% of Chinese citizens, but only 35% of Americans, agreed that "products and services using AI have more benefits than drawbacks". A 2023 Reuters/Ipsos poll found that 61% of Americans agree, and 22% disagree, that AI poses risks to humanity. In a 2023 Fox News poll, 35% of Americans thought it "very important", and an additional 41% thought it "somewhat important", for the federal government to regulate AI, versus 13% responding "not very important" and 8% responding "not at all important". In November 2023, the first global AI Safety Summit was held in Bletchley Park in the UK to discuss the near and far term risks of AI and the possibility of mandatory and voluntary regulatory frameworks. 28 countries including the United States, China, and the European Union issued a declaration at the start of the summit, calling for international co-operation to manage the challenges and risks of artificial intelligence. In May 2024 at the AI Seoul Summit, 16 global AI tech companies agreed to safety commitments on the development of AI. History The study of mechanical or "formal" reasoning began with philosophers and mathematicians in antiquity. The study of logic led directly to Alan Turing's theory of computation, which suggested that a machine, by shuffling symbols as simple as "0" and "1", could simulate any conceivable form of mathematical reasoning. This, along with concurrent discoveries in cybernetics, information theory and neurobiology, led researchers to consider the possibility of building an "electronic brain".[r] They developed several areas of research that would become part of AI, such as McCulloch and Pitts design for "artificial neurons" in 1943, and Turing's influential 1950 paper 'Computing Machinery and Intelligence', which introduced the Turing test and showed that "machine intelligence" was plausible. The field of AI research was founded at a workshop at Dartmouth College in 1956.[s] The attendees became the leaders of AI research in the 1960s.[t] They and their students produced programs that the press described as "astonishing":[u] computers were learning checkers strategies, solving word problems in algebra, proving logical theorems and speaking English.[v] Artificial intelligence laboratories were set up at a number of British and U.S. universities in the latter 1950s and early 1960s. Researchers in the 1960s and the 1970s were convinced that their methods would eventually succeed in creating a machine with general intelligence and considered this the goal of their field. In 1965 Herbert Simon predicted, "machines will be capable, within twenty years, of doing any work a man can do". In 1967 Marvin Minsky agreed, writing that "within a generation ... the problem of creating 'artificial intelligence' will substantially be solved". They had, however, underestimated the difficulty of the problem.[w] In 1974, both the U.S. and British governments cut off exploratory research in response to the criticism of Sir James Lighthill and ongoing pressure from the U.S. Congress to fund more productive projects. Minsky and Papert's book Perceptrons was understood as proving that artificial neural networks would never be useful for solving real-world tasks, thus discrediting the approach altogether. The "AI winter", a period when obtaining funding for AI projects was difficult, followed. In the early 1980s, AI research was revived by the commercial success of expert systems, a form of AI program that simulated the knowledge and analytical skills of human experts. By 1985, the market for AI had reached over a billion dollars. At the same time, Japan's fifth generation computer project inspired the U.S. and British governments to restore funding for academic research. However, beginning with the collapse of the Lisp Machine market in 1987, AI once again fell into disrepute, and a second, longer-lasting winter began. Up to this point, most of AI's funding had gone to projects that used high-level symbols to represent mental objects like plans, goals, beliefs, and known facts. In the 1980s, some researchers began to doubt that this approach would be able to imitate all the processes of human cognition, especially perception, robotics, learning and pattern recognition, and began to look into "sub-symbolic" approaches. Rodney Brooks rejected "representation" in general and focussed directly on engineering machines that move and survive.[x] Judea Pearl, Lotfi Zadeh, and others developed methods that handled incomplete and uncertain information by making reasonable guesses rather than precise logic. But the most important development was the revival of "connectionism", including neural network research, by Geoffrey Hinton and others. In 1990, Yann LeCun successfully showed that convolutional neural networks can recognize handwritten digits, the first of many successful applications of neural networks. AI gradually restored its reputation in the late 1990s and early 21st century by exploiting formal mathematical methods and by finding specific solutions to specific problems. This "narrow" and "formal" focus allowed researchers to produce verifiable results and collaborate with other fields (such as statistics, economics and mathematics). By 2000, solutions developed by AI researchers were being widely used, although in the 1990s they were rarely described as "artificial intelligence" (a tendency known as the AI effect). However, several academic researchers became concerned that AI was no longer pursuing its original goal of creating versatile, fully intelligent machines. Beginning around 2002, they founded the subfield of artificial general intelligence (or "AGI"), which had several well-funded institutions by the 2010s. Deep learning began to dominate industry benchmarks in 2012 and was adopted throughout the field. For many specific tasks, other methods were abandoned.[y] Deep learning's success was based on both hardware improvements (faster computers, graphics processing units, cloud computing) and access to large amounts of data (including curated datasets, such as ImageNet). Deep learning's success led to an enormous increase in interest and funding in AI.[z] The amount of machine learning research (measured by total publications) increased by 50% in the years 2015–2019. In 2016, issues of fairness and the misuse of technology were catapulted into center stage at machine learning conferences, publications vastly increased, funding became available, and many researchers re-focussed their careers on these issues. The alignment problem became a serious field of academic study. In the late 2010s and early 2020s, AGI companies began to deliver programs that created enormous interest. In 2015, AlphaGo, developed by DeepMind, beat the world champion Go player. The program taught only the game's rules and developed a strategy by itself. GPT-3 is a large language model that was released in 2020 by OpenAI and is capable of generating high-quality human-like text. ChatGPT, launched on 30 November 2022, became the fastest-growing consumer software application in history, gaining over 100 million users in two months. It marked what is widely regarded as AI's breakout year, bringing it into the public consciousness. These programs, and others, inspired an aggressive AI boom, where large companies began investing billions of dollars in AI research. According to AI Impacts, about US$50 billion annually was invested in "AI" around 2022 in the U.S. alone and about 20% of the new U.S. Computer Science PhD graduates have specialized in "AI". About 800,000 "AI"-related U.S. job openings existed in 2022. According to PitchBook research, 22% of newly funded startups in 2024 claimed to be AI companies. Philosophy Philosophical debates have historically sought to determine the nature of intelligence and how to make intelligent machines. Another major focus has been whether machines can be conscious, and the associated ethical implications. Many other topics in philosophy are relevant to AI, such as epistemology and free will. Rapid advancements have intensified public discussions on the philosophy and ethics of AI. Alan Turing wrote in 1950 "I propose to consider the question 'can machines think'?" He advised changing the question from whether a machine "thinks", to "whether or not it is possible for machinery to show intelligent behaviour". He devised the Turing test, which measures the ability of a machine to simulate human conversation. Since we can only observe the behavior of the machine, it does not matter if it is "actually" thinking or literally has a "mind". Turing notes that we can not determine these things about other people but "it is usual to have a polite convention that everyone thinks." Russell and Norvig agree with Turing that intelligence must be defined in terms of external behavior, not internal structure. However, they are critical that the test requires the machine to imitate humans. "Aeronautical engineering texts", they wrote, "do not define the goal of their field as making 'machines that fly so exactly like pigeons that they can fool other pigeons.'" AI founder John McCarthy agreed, writing that "Artificial intelligence is not, by definition, simulation of human intelligence". McCarthy defines intelligence as "the computational part of the ability to achieve goals in the world". Another AI founder, Marvin Minsky, similarly describes it as "the ability to solve hard problems". Artificial Intelligence: A Modern Approach defines it as the study of agents that perceive their environment and take actions that maximize their chances of achieving defined goals. The many differing definitiuons of AI have been critically analyzed. During the 2020s AI boom, the term has been used as a marketing buzzword to promote products and services which do not use AI. The International Organization for Standardization describes an AI system as a "an engineered system that generates outputs such as content, forecasts, recommendations, or decisions for a given set of human‑defined objectives, and can operate with varying levels of automation". The EU AI Act defines an AI system as "a machine-based system that is designed to operate with varying levels of autonomy and that may exhibit adaptiveness after deployment, and that, for explicit or implicit objectives, infers, from the input it receives, how to generate outputs such as predictions, content, recommendations, or decisions that can influence physical or virtual environments". In the United States, influential but non‑binding guidance such as the National Institute of Standards and Technology's AI Risk Management Framework describes an AI system as "an engineered or machine-based system that can, for a given set of objectives, generate outputs such as predictions, recommendations, or decisions influencing real or virtual environments. AI systems are designed to operate with varying levels of autonomy". No established unifying theory or paradigm has guided AI research for most of its history.[aa] The unprecedented success of statistical machine learning in the 2010s eclipsed all other approaches (so much so that some sources, especially in the business world, use the term "artificial intelligence" to mean "machine learning with neural networks"). This approach is mostly sub-symbolic, soft and narrow. Critics argue that these questions may have to be revisited by future generations of AI researchers. Symbolic AI (or "GOFAI") simulated the high-level conscious reasoning that people use when they solve puzzles, express legal reasoning and do mathematics. They were highly successful at "intelligent" tasks such as algebra or IQ tests. In the 1960s, Newell and Simon proposed the physical symbol systems hypothesis: "A physical symbol system has the necessary and sufficient means of general intelligent action." However, the symbolic approach failed on many tasks that humans solve easily, such as learning, recognizing an object or commonsense reasoning. Moravec's paradox is the discovery that high-level "intelligent" tasks were easy for AI, but low level "instinctive" tasks were extremely difficult. Philosopher Hubert Dreyfus had argued since the 1960s that human expertise depends on unconscious instinct rather than conscious symbol manipulation, and on having a "feel" for the situation, rather than explicit symbolic knowledge. Although his arguments had been ridiculed and ignored when they were first presented, eventually, AI research came to agree with him.[ab] The issue is not resolved: sub-symbolic reasoning can make many of the same inscrutable mistakes that human intuition does, such as algorithmic bias. Critics such as Noam Chomsky argue continuing research into symbolic AI will still be necessary to attain general intelligence, in part because sub-symbolic AI is a move away from explainable AI: it can be difficult or impossible to understand why a modern statistical AI program made a particular decision. The emerging field of neuro-symbolic artificial intelligence attempts to bridge the two approaches. "Neats" hope that intelligent behavior is described using simple, elegant principles (such as logic, optimization, or neural networks). "Scruffies" expect that it necessarily requires solving a large number of unrelated problems. Neats defend their programs with theoretical rigor, scruffies rely mainly on incremental testing to see if they work. This issue was actively discussed in the 1970s and 1980s, but eventually was seen as irrelevant. Modern AI has elements of both. Finding a provably correct or optimal solution is intractable for many important problems. Soft computing is a set of techniques, including genetic algorithms, fuzzy logic and neural networks, that are tolerant of imprecision, uncertainty, partial truth and approximation. Soft computing was introduced in the late 1980s and most successful AI programs in the 21st century are examples of soft computing with neural networks. AI researchers are divided as to whether to pursue the goals of artificial general intelligence and superintelligence directly or to solve as many specific problems as possible (narrow AI) in hopes these solutions will lead indirectly to the field's long-term goals. General intelligence is difficult to define and difficult to measure, and modern AI has had more verifiable successes by focusing on specific problems with specific solutions. The sub-field of artificial general intelligence studies this area exclusively. There is no settled consensus in philosophy of mind on whether a machine can have a mind, consciousness and mental states in the same sense that human beings do. This issue considers the internal experiences of the machine, rather than its external behavior. Mainstream AI research considers this issue irrelevant because it does not affect the goals of the field: to build machines that can solve problems using intelligence. Russell and Norvig add that "[t]he additional project of making a machine conscious in exactly the way humans are is not one that we are equipped to take on." However, the question has become central to the philosophy of mind. It is also typically the central question at issue in artificial intelligence in fiction. David Chalmers identified two problems in understanding the mind, which he named the "hard" and "easy" problems of consciousness. The easy problem is understanding how the brain processes signals, makes plans and controls behavior. The hard problem is explaining how this feels or why it should feel like anything at all, assuming we are right in thinking that it truly does feel like something (Dennett's consciousness illusionism says this is an illusion). While human information processing is easy to explain, human subjective experience is difficult to explain. For example, it is easy to imagine a color-blind person who has learned to identify which objects in their field of view are red, but it is not clear what would be required for the person to know what red looks like. Computationalism is the position in the philosophy of mind that the human mind is an information processing system and that thinking is a form of computing. Computationalism argues that the relationship between mind and body is similar or identical to the relationship between software and hardware and thus may be a solution to the mind–body problem. This philosophical position was inspired by the work of AI researchers and cognitive scientists in the 1960s and was originally proposed by philosophers Jerry Fodor and Hilary Putnam. Philosopher John Searle characterized this position as "strong AI": "The appropriately programmed computer with the right inputs and outputs would thereby have a mind in exactly the same sense human beings have minds."[ac] Searle challenges this claim with his Chinese room argument, which attempts to show that even a computer capable of perfectly simulating human behavior would not have a mind. It is difficult or impossible to reliably evaluate whether an advanced AI is sentient (has the ability to feel), and if so, to what degree. But if there is a significant chance that a given machine can feel and suffer, then it may be entitled to certain rights or welfare protection measures, similarly to animals. Sapience (a set of capacities related to high intelligence, such as discernment or self-awareness) may provide another moral basis for AI rights. Robot rights are also sometimes proposed as a practical way to integrate autonomous agents into society. In 2017, the European Union considered granting "electronic personhood" to some of the most capable AI systems. Similarly to the legal status of companies, it would have conferred rights but also responsibilities. Critics argued in 2018 that granting rights to AI systems would downplay the importance of human rights, and that legislation should focus on user needs rather than speculative futuristic scenarios. They also noted that robots lacked the autonomy to take part in society on their own. Progress in AI increased interest in the topic. Proponents of AI welfare and rights often argue that AI sentience, if it emerges, would be particularly easy to deny. They warn that this may be a moral blind spot analogous to slavery or factory farming, which could lead to large-scale suffering if sentient AI is created and carelessly exploited. Future A superintelligence is a hypothetical agent that would possess intelligence far surpassing that of the brightest and most gifted human mind. If research into artificial general intelligence produced sufficiently intelligent software, it might be able to reprogram and improve itself. The improved software would be even better at improving itself, leading to what I. J. Good called an "intelligence explosion" and Vernor Vinge called a "singularity". However, technologies cannot improve exponentially indefinitely, and typically follow an S-shaped curve, slowing when they reach the physical limits of what the technology can do. Robot designer Hans Moravec, cyberneticist Kevin Warwick and inventor Ray Kurzweil have predicted that humans and machines may merge in the future into cyborgs that are more capable and powerful than either. This idea, called transhumanism, has roots in the writings of Aldous Huxley and Robert Ettinger. Edward Fredkin argues that "artificial intelligence is the next step in evolution", an idea first proposed by Samuel Butler's "Darwin among the Machines" as far back as 1863, and expanded upon by George Dyson in his 1998 book Darwin Among the Machines: The Evolution of Global Intelligence. In fiction Thought-capable artificial beings have appeared as storytelling devices since antiquity, and have been a persistent theme in science fiction. A common trope in these works began with Mary Shelley's Frankenstein, where a human creation becomes a threat to its masters. This includes such works as Arthur C. Clarke's and Stanley Kubrick's 2001: A Space Odyssey (both 1968), with HAL 9000, the murderous computer in charge of the Discovery One spaceship, as well as The Terminator (1984) and The Matrix (1999). In contrast, the rare loyal robots such as Gort from The Day the Earth Stood Still (1951) and Bishop from Aliens (1986) are less prominent in popular culture. Isaac Asimov introduced the Three Laws of Robotics in many stories, most notably with the "Multivac" super-intelligent computer. Asimov's laws are often brought up during lay discussions of machine ethics; while almost all artificial intelligence researchers are familiar with Asimov's laws through popular culture, they generally consider the laws useless for many reasons, one of which is their ambiguity. Several works use AI to force us to confront the fundamental question of what makes us human, showing us artificial beings that have the ability to feel, and thus to suffer. This appears in Karel Čapek's R.U.R., the films A.I. Artificial Intelligence and Ex Machina, as well as the novel Do Androids Dream of Electric Sheep?, by Philip K. Dick. Dick considers the idea that our understanding of human subjectivity is altered by technology created with artificial intelligence. See also Explanatory notes References External links |
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[SOURCE: https://en.wikipedia.org/wiki/List_of_Python_software#Python_implementations] | [TOKENS: 116] |
Contents List of Python software The Python programming language is actively used by many people, both in industry and academia, for a wide variety of purposes. Integrated Development Environments (IDEs) for Python Unit testing frameworks Python package managers and Python distributions Applications Web applications Video games Web frameworks Graphics frameworks UI frameworks Scientific packages Machine learning and artificial intelligence Mathematical libraries Numerical libraries Additional development packages Embedded as a scripting language Python is, or can be used as the scripting language in these notable software products: Commercial uses Python implementations Implementations of Python include: Historic Python implementations include: See also References External links |
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[SOURCE: https://en.wikipedia.org/wiki/Visa_Inc.] | [TOKENS: 8054] |
Contents Visa Inc. Visa Inc. (/ˈviːzə, ˈviːsə/) is an American multinational payment card services corporation headquartered in San Francisco, California. It facilitates electronic funds transfers throughout the world, most commonly through Visa-branded credit cards, debit cards and prepaid cards. Visa does not issue cards, extend credit, or set rates and fees for consumers; rather, Visa provides financial institutions with Visa-branded payment products that they then use to offer credit, debit, prepaid and cash access programs to their customers. In 2025, Visa's global network (known as VisaNet) processed 257.5 billion transactions worth US$14.2 trillion. Visa was founded in 1958 by Bank of America (BofA) as the BankAmericard credit card program. In response to competitor Master Charge (now Mastercard), BofA began to license the BankAmericard program to other financial institutions in 1966. By 1970, BofA gave up direct control of the BankAmericard program, forming a cooperative with the other various BankAmericard issuer banks to take over its management. It was then renamed Visa in 1976. Nearly all Visa transactions worldwide are processed through the company's directly operated VisaNet at one of four secure data centers, located in Ashburn, Virginia, and Highlands Ranch, Colorado, in the United States; London, England; and in Singapore. These facilities are heavily secured against natural disasters, crime, and terrorism; can operate independently of each other and from external utilities if necessary; and can handle up to 30,000 simultaneous transactions and up to 100 billion computations every second. Visa is the world's second-largest card payment organization (debit and credit cards combined), after being surpassed by China UnionPay in 2015, based on annual value of card payments transacted and number of issued cards. However, because UnionPay's size is based primarily on the size of its domestic market in China, Visa is still considered the dominant bankcard company in the rest of the world, where it commands a 50% market share of total card payments. History On September 18, 1958, Bank of America (BofA) officially launched its BankAmericard credit card program in Fresno, California. In the weeks leading up to the launch of BankAmericard, BofA had saturated Fresno mailboxes with an initial mass mailing (or "drop", as they came to be called) of 65,000 unsolicited credit cards. BankAmericard was the brainchild of BofA's in-house product development think tank, the Customer Services Research Group, and its leader, Joseph P. Williams. Williams convinced senior BofA executives in 1956 to let him pursue what became the world's first successful mass mailing of unsolicited credit cards (actual working cards, not mere applications) to a large population. Williams' pioneering accomplishment was that he brought about the successful implementation of the all-purpose credit card (in the sense that his project was not canceled outright), not in coming up with the idea. By the mid-1950s, the typical middle-class American already maintained revolving credit accounts with several different merchants, which was clearly inconvenient and inefficient due to the need to carry so many cards and pay so many separate bills each month. The need for a unified financial instrument was already evident to the American financial services industry, but no one could figure out how to do it. There were already charge cards like Diners Club (which had to be paid in full at the end of each billing cycle), and "by the mid-1950s, there had been at least a dozen attempts to create an all-purpose credit card." However, these prior attempts had been carried out by small banks which lacked the resources to make them work. Williams and his team studied these failures carefully and believed they could avoid replicating those banks' mistakes; they also studied existing revolving credit operations at Sears and Mobil Oil to learn why they were successful. Fresno was selected for its population of 250,000 (big enough to make a credit card work, small enough to control initial startup cost), BofA's market share of that population (45%), and relative isolation, to control public relations damage in case the project failed. According to Williams, Florsheim Shoes was the first major retail chain which agreed to accept BankAmericard at its stores. The 1958 test at first went smoothly, but then BofA panicked when it confirmed rumors that another bank was about to initiate its own drop in San Francisco, BofA's home market. By March 1959, drops began in San Francisco and Sacramento; by June, BofA was dropping cards in Los Angeles; by October, the entire state of California had been saturated with over 2 million credit cards and BankAmericard was being accepted by 20,000 merchants. However, the program was riddled with problems, as Williams (who had never worked in a bank's loan department) had been too earnest and trusting in his belief in the basic goodness of the bank's customers, and he resigned in December 1959. Twenty-two percent of accounts were delinquent, not the 4% expected, and police departments around the state were confronted by numerous incidents of the brand new crime of credit card fraud. Both politicians and journalists joined the general uproar against Bank of America and its newfangled credit card, especially when it was pointed out that the cardholder agreement held customers liable for all charges, even those resulting from fraud. BofA officially lost over $8.8 million on the launch of BankAmericard, but when the full cost of advertising and overhead was included, the bank's actual loss was probably around $20 million. However, after Williams and some of his closest associates left, BofA management realized that BankAmericard was salvageable. They conducted a "massive effort" to clean up after Williams, imposed proper financial controls, published an open letter to 3 million households across the state apologizing for the credit card fraud and other issues their card raised and eventually were able to make the new financial instrument work. By May 1961, the BankAmericard program became profitable for the first time. At the time, BofA deliberately kept this information secret and allowed then-widespread negative impressions to linger in order to ward off competition. This strategy worked until 1966, when BankAmericard's profitability had become far too big to hide. The original goal of BofA was to offer the BankAmericard product across California, but in 1966, BofA began to sign licensing agreements with a group of banks outside of California, in response to a new competitor, Master Charge (now Mastercard), which had been created by an alliance of several regional bankcard associations to compete against BankAmericard. BofA itself (like all other U.S. banks at the time) could not expand directly into other states due to federal restrictions not repealed until 1994. Over the following 11 years, various banks licensed the card system from Bank of America, thus forming a network of banks backing the BankAmericard system across the United States. The "drops" of unsolicited credit cards continued unabated, thanks to BofA and its licensees and competitors until they were outlawed in 1970, but not before over 100 million credit cards had been distributed into the American population. During the late 1960s, BofA also licensed the BankAmericard program to banks in several other countries, which began issuing cards with localized brand names. For example:[citation needed] In 1968, a manager at the National Bank of Commerce (later Rainier Bancorp), Dee Hock, was asked to supervise that bank's launch of its own licensed version of BankAmericard in the Pacific Northwest market. Although Bank of America had cultivated the public image that BankAmericard's troubled startup issues were now safely in the past, Hock realized that the BankAmericard licensee program itself was in terrible disarray because it had developed and grown very rapidly in an ad hoc fashion. For example, "interchange" transaction issues between banks were becoming a very serious problem, which had not been seen before when Bank of America was the sole issuer of BankAmericards. Hock suggested to other licensees that they form a committee to investigate and analyze the various problems with the licensee program; they promptly made him the chair of that committee. After lengthy negotiations, the committee led by Hock was able to persuade Bank of America that a bright future lay ahead for BankAmericard — outside Bank of America. In June 1970, Bank of America gave up control of the BankAmericard program. The various BankAmericard issuer banks took control of the program, creating National BankAmericard Inc. (NBI), an independent Delaware corporation which would be in charge of managing, promoting and developing the BankAmericard system within the United States. In other words, BankAmericard was transformed from a franchising system into a jointly controlled consortium or alliance, like its competitor Master Charge. Hock became NBI's first president and CEO. However, Bank of America retained the right to directly license BankAmericard to banks outside the United States and continued to issue and support such licenses. By 1972, licenses had been granted in 15 countries. The international licensees soon encountered a variety of problems with their licensing programs, and they hired Hock as a consultant to help them restructure their relationship with BofA as he had done for the domestic licensees. As a result, in 1974, the International Bankcard Company (IBANCO), a multinational member corporation, was founded in order to manage the international BankAmericard program. In 1976, the directors of IBANCO determined that bringing the various international networks together into a single network with a single name internationally would be in the best interests of the corporation; however, in many countries, there was still great reluctance to issue a card associated with Bank of America, even though the association was entirely nominal in nature. For this reason, in 1976, BankAmericard, Barclaycard, Carte Bleue, Chargex, Sumitomo Card, and all other licensees united under the new name, "Visa", which retained the distinctive blue, white and gold flag. NBI became Visa USA and IBANCO became Visa International. The term Visa was conceived by the company's founder, Dee Hock. He believed that the word was instantly recognizable in many languages in many countries and that it also denoted universal acceptance. The announcement of the transition came on December 16, 1976, with VISA cards to replace expiring BankAmericard cards starting on March 1, 1977 (initially with both the BankAmericard name and the VISA name on the same card), and the various Bank of America issued cards worldwide being phased out by the end of October 1979. In October 2007, Bank of America announced it was resurrecting the BankAmericard brand name as the "BankAmericard Rewards Visa". In March 2022, following the Russian invasion of Ukraine, Visa announced that it would suspend all business operations in Russia. Prior to October 3, 2007, Visa comprised four non-stock, separately incorporated companies that employed 6,000 people worldwide: the worldwide parent entity Visa International Service Association (Visa), Visa USA Inc., Visa Canada Association, and Visa Europe Ltd. The latter three separately incorporated regions had the status of group members of Visa International Service Association.[citation needed] The unincorporated regions Visa Latin America (LAC), Visa Asia Pacific and Visa Central and Eastern Europe, Middle East and Africa (CEMEA) were divisions within Visa.[citation needed] Initially, signed copies of sales drafts were included in each customer's monthly billing statement for verification purposes—an industry practice known as "country club billing". By the late 1970s, however, billing statements no longer contained these enclosures, but rather a summary statement showing posting date, purchase date, reference number, merchant name, and the dollar amount of each purchase. At the same time, many issuers, particularly Bank of America, were in the process of changing their methods of finance charge calculation. Initially, a "previous balance" method was used—calculation of finance charge on the unpaid balance shown on the prior month's statement. Later, it was decided to use "average daily balance" which resulted in increased revenue for the issuers by calculating the number of days each purchase was included on the prior month's statement. Several years later, "new average daily balance"—in which transactions from previous and current billing cycles were used in the calculation—was introduced. By the early 1980s, many issuers introduced the concept of the annual fee as yet another revenue enhancer.[citation needed] On October 11, 2006, Visa announced that some of its businesses would be merged and become a publicly traded company, Visa Inc. Under the IPO restructuring, Visa Canada, Visa International, and Visa USA were merged into the new public company. Visa's Western Europe operation became a separate company, owned by its member banks who will also have a minority stake in Visa Inc. In total, more than 35 investment banks participated in the deal in several capacities, most notably as underwriters. On October 3, 2007, Visa completed its corporate restructuring with the formation of Visa Inc. The new company was the first step towards Visa's IPO. The second step came on November 9, 2007, when the new Visa Inc. submitted its $10 billion IPO filing with the U.S. Securities and Exchange Commission (SEC). On February 25, 2008, Visa announced it would go ahead with an IPO of half its shares. The IPO took place on March 18, 2008. Visa sold 406 million shares at US$44 per share ($2 above the high end of the expected $37–42 pricing range), raising US$17.9 billion in what was then the largest initial public offering in U.S. history. On March 20, 2008, the IPO underwriters (including JP Morgan, Goldman Sachs & Co., Bank of America Securities LLC, Citi, HSBC, Merrill Lynch & Co., UBS Investment Bank and Wachovia Securities) exercised their overallotment option, purchasing an additional 40.6 million shares, bringing Visa's total IPO share count to 446.6 million, and bringing the total proceeds to US$19.1 billion. Visa now trades under the ticker symbol "V" on the New York Stock Exchange. Visa Europe Ltd. was a membership association and cooperative of over 3,700 European banks and other payment service providers that operated Visa branded products and services within Europe. Visa Europe was a company entirely separate from Visa Inc. having gained independence of Visa International Service Association in October 2007 when Visa Inc. became a publicly traded company on the New York Stock Exchange. Visa Inc. announced the plan to acquire Visa Europe on November 2, 2015, creating a single global company. On April 21, 2016, the agreement was amended in response to the feedback of European Commission. The acquisition of Visa Europe was completed on June 21, 2016. On January 13, 2020, Plaid announced that it had signed a definitive agreement to be acquired by Visa for $5.3 billion. The deal was double the company's most recent Series C round valuation of $2.65 billion, and was expected to close in the next 3–6 months, subject to regulatory review and closing conditions. According to the deal, Visa would pay $4.9 billion in cash and approximately $400 million of retention equity and deferred equity, according to a presentation deck prepared by Visa. On November 5, 2020, the United States Department of Justice filed a lawsuit seeking to block the acquisition, arguing that Visa is a monopolist trying to eliminate a competitive threat by purchasing Plaid. Visa said it disagreed with the lawsuit and "intends to defend the transaction vigorously." On January 12, 2021, Visa and Plaid announced they had abandoned the deal. On February 3, 2021, Visa announced a partnership with First Boulevard, a neobank promoting cryptocurrency, which has been touted as a means of building generational wealth for Black Americans. The partnership would allow their users to buy, sell, hold, and trade digital assets through Anchorage Digital. On March 29, 2021, Visa announced the acceptance of stablecoin USDC to settle transactions on its network. Registered in the United States as a 501(c)(3) entity, the Visa Foundation was created with the mission of supporting inclusive economies. In particular, economies in which individuals, businesses and communities can thrive with the support of grants and investments. Supporting resiliency, as well as the growth, of micro and small businesses that benefit women is a priority of the Visa Foundation. Furthermore, the Foundation prioritizes providing support to the community from a broad standpoint, as well as responding to disasters during crisis. In December 2020, Visa Announced the launch of a new accelerator program across Asia Pacific to further develop the region's financial technology ecosystem. The accelerator program aims to find and partner with startup companies providing financial and payments technologies that could potentially leverage on Visa's network of bank and merchant partners in the region. Finance For the fiscal year 2022, Visa reported earnings of US$14.96 billion, with an annual revenue of US$29.31 billion, an increase of 21.6% over the previous fiscal cycle. As of 2022, the company ranked 147th on the Fortune 500 list of the largest United States corporations by revenue. Visa's shares traded at over $143 per share, and its market capitalization was valued at over US$280.2 billion in September 2018. Criticism and controversy Visa Europe began suspending payments to WikiLeaks on December 7, 2010. The company said it was awaiting an investigation into 'the nature of its business and whether it contravenes Visa operating rules' – though it did not go into details. In return DataCell, the IT company that enables WikiLeaks to accept credit and debit card donations, announced that it would take legal action against Visa Europe. On December 8, the group Anonymous performed a DDoS attack on visa.com, bringing the site down. Although the Norway-based financial services company Teller AS, which Visa ordered to look into WikiLeaks and its fundraising body, the Sunshine Press, found no proof of any wrongdoing, Salon reported in January 2011 that Visa Europe "would continue blocking donations to the secret-spilling site until it completes its own investigation". The United Nations High Commissioner for Human Rights Navi Pillay stated that Visa may be "violating WikiLeaks' right to freedom of expression" by withdrawing their services. In July 2012, the Reykjavík District Court in Iceland decided that Valitor (the Icelandic partner of Visa and MasterCard) was violating the law when it prevented donations to the site by credit card. It was ruled that the donations be allowed to return to the site within 14 days or they would be fined in the amount of US$6,000 per day. In 2011, MasterCard and Visa were sued in a class action by ATM operators claiming the credit card networks' rules effectively fix ATM access fees. The suit claimed that this is a restraint on trade in violation of US federal law. The lawsuit was filed by the National ATM Council and independent operators of automated teller machines. More specifically, it is alleged that MasterCard's and Visa's network rules prohibit ATM operators from offering lower prices for transactions over PIN-debit networks that are not affiliated with Visa or MasterCard. The suit says that this price-fixing artificially raises the price that consumers pay using ATMs, limits the revenue that ATM-operators earn, and violates the Sherman Act's prohibition against unreasonable restraints of trade. Johnathan Rubin, an attorney for the plaintiffs said, "Visa and MasterCard are the ringleaders, organizers, and enforcers of a conspiracy among U.S. banks to fix the price of ATM access fees in order to keep the competition at bay." In 2017, a US district court denied the ATM operators' request to stop Visa from enforcing the ATM fees. In 1996, a class of U.S. merchants, including Walmart, brought an antitrust lawsuit against Visa and MasterCard over their "Honor All Cards" policy, which forced merchants who accepted Visa and MasterCard branded credit cards to also accept their respective debit cards (such as the "Visa Check Card"). Over 4 million class members were represented by the plaintiffs. According to a website associated with the suit, Visa and MasterCard settled the plaintiffs' claims in 2003 for a total of $3.05 billion. Visa's share of this settlement is reported to have been the larger.[citation needed] In 1998, the U.S. Department of Justice sued Visa over rules prohibiting its issuing banks from doing business with American Express and Discover. The Department of Justice won its case at trial in 2001 and the verdict was upheld on appeal. American Express and Discover filed suit as well. In October 2010, Visa and MasterCard reached a settlement with the Department of Justice in another antitrust case. The companies agreed to allow merchants displaying their logos to decline certain types of cards (because interchange fees differ), or to offer consumers discounts for using cheaper cards. On November 27, 2012, a federal judge entered an order granting preliminary approval to a proposed settlement to a class-action lawsuit filed in 2005 by merchants and trade associations against Mastercard and Visa. The suit was filed due to alleged price-fixing practices employed by Mastercard and Visa. About one-quarter of the named class plaintiffs have decided to opt "out of the settlement". Opponents object to provisions that would bar future lawsuits and even prevent merchants from opting out of significant portions of the proposed settlement. Plaintiffs allege that Visa and Mastercard fixed interchange fees, also known as swipe fees, that are charged to merchants for the privilege of accepting payment cards. In their complaint, the plaintiffs also alleged that the defendants unfairly interfere with merchants from encouraging customers to use less expensive forms of payment such as lower-cost cards, cash, and checks. A settlement of US$6.24 billion was scheduled for the court to approve or deny, on November 7, 2019. Separately, in October 2025, merchants agreed to a $231.7 million settlement beforea U.S. District Judge, as B & R Supermarket, Inc., et al v. Visa, Inc. et al, for costs imposed in frauds related to counterfeit, lost, or stolen cards, with Visa agreeing to pay $119.7 million of the total settlement. In June 2016, the Wall Street Journal reported that Walmart threatened to stop accepting Visa cards in Canada. Visa objected saying that consumers should not be dragged into a dispute between the companies. In January 2017, Walmart Canada and Visa reached a deal to allow the continued acceptance of Visa. In March 2019, U.S. retailer Kroger announced that its 250-strong Smith's chain would stop accepting Visa credit cards as of April 3, 2019, due to the cards' high swipe fees. Kroger's California-based Foods Co stores stopped accepting Visa cards in August 2018. Mike Schlotman, Kroger's executive vice president/chief financial officer, said Visa had been "misusing its position and charging retailers excessive fees for a long time." In response, Visa issued a statement saying it was "unfair and disappointing that Kroger is putting shoppers in the middle of a business dispute." As of October 31, 2019, Kroger has settled their dispute with Visa and is now accepting the payment method. In January 2020 Visa announced it would acquire Plaid for $5.3 billion. In November 2020, the United States Department of Justice (DOJ) sued to block Visa's acquisition of fintech startup Plaid, claiming that the merger would violate antitrust laws. The DOJ argues that the merger would eliminate Plaid's potential ability to compete in the online debit market, thereby creating a monopoly for Visa. Visa CEO at the time Alfred Kelly described the acquisition bid as an "insurance policy" to neutralize a "threat to our important US debit business." In January 2021, Visa along with Plaid both mutually agreed to abandon its proposed acquisition. In March 2021, the United States Justice Department announced its investigation with Visa to discover if the company is engaging in anticompetitive practices in the debit card market. The main question at hand is whether or not Visa is limiting merchants' ability to route debit card transactions over card networks that are often less expensive, focusing more so on online debit card transactions. The probe highlights the role of network fees, which are invisible to consumers and place pressure on merchants, who mitigate the fees by raising prices of goods for customers. The probe was confirmed through a regulatory filing on March 19, 2021, stating they will be cooperating with the Justice Department. Visa's shares fell more than 6% following the announcement. On September 24, 2024, the Justice Department sued Visa, alleging that Visa used illegal tactics to maintain a monopoly in debit-card payments. In 2015, the Australian Federal Court ordered Visa to pay a pecuniary penalty of $20 million (including legal fees) for engaging in anti-competitive conduct against dynamic currency conversion operators, in proceedings brought by the Australian Competition and Consumer Commission. In 2002, the European Commission exempted Visa's multilateral interchange fees from Article 81 of the EC Treaty that prohibits anti-competitive arrangements. However, this exemption expired on December 31, 2007. In the United Kingdom, Mastercard has reduced its interchange fees while it is under investigation by the Office of Fair Trading. In January 2007, the European Commission issued the results of a two-year inquiry into the retail banking sector. The report focuses on payment cards and interchange fees. Upon publishing the report, Commissioner Neelie Kroes said the "present level of interchange fees in many of the schemes we have examined does not seem justified." The report called for further study of the issue. On March 26, 2008, the European Commission opened an investigation into Visa's multilateral interchange fees for cross-border transactions within the EEA as well as into the "Honor All Cards" rule (under which merchants are required to accept all valid Visa-branded cards).[needs update] The antitrust authorities of EU member states (other than the United Kingdom) also investigated Mastercard's and Visa's interchange fees. For example, on January 4, 2007, the Polish Office of Competition and Consumer Protection fined twenty banks a total of PLN 164 million (about $56 million) for jointly setting Mastercard's and Visa's interchange fees. In December 2010, Visa reached a settlement with the European Union in yet another antitrust case, promising to reduce debit card payments to 0.2 percent of a purchase. A senior official from the European Central Bank called for a break-up of the Visa/Mastercard duopoly by creation of a new European debit card for use in the Single Euro Payments Area (SEPA). After Visa's blocking of payments to WikiLeaks, members of the European Parliament expressed concern that payments from European citizens to a European corporation could apparently be blocked by the US, and called for a further reduction in the dominance of Visa and Mastercard in the European payment system. Visa's interchange fee of 1.5–1.6% in Poland started discussion about the need for increased government regulation surrounding the topic. The high fees encouraged merchants to create new payment systems, which avoid using Visa as a middleman. For example, mobile applications were created by major banks, proprietary payment systems were created by franchises, and public transport authorities created ticketing systems. In May 2024, the UK Payment Systems Regulator (PSR) proposed new rules requiring Visa and Mastercard to increase transparency regarding the fees they charge merchants. The proposed regulations mandate that the two companies, regularly disclose detailed financial information to the PSR. The regulations also require Visa and Mastercard to consult with merchants and retailers before implementing any fee changes. The proposal followed a PSR review revealing that Visa and Mastercard had raised their scheme and processing fees by more than 30% in real terms over the previous five years. Despite these increases, the PSR found limited evidence that service quality had improved proportionately. In November 2024, the European Commission launched a further investigation into whether the scheme fees imposed by Visa and Mastercard impact negatively on retailers. Some retailers had in recent years complained about the fees, citing a lack of transparency. The Commission took its investigation further in June 2025, asking for a retailer view and for comments from the card operators about whether "a standardized summary of fees" would help to promote transparency. Corporate affairs Visa was traditionally headquartered in San Francisco until 1985, when it moved to San Mateo. Around 1993, Visa began consolidating various scattered offices in San Mateo to a location in nearby Foster City. Visa became Foster City's largest employer. In 2009, Visa moved its corporate headquarters back to San Francisco when it leased the top three floors of the 595 Market Street office building, although most of its employees remained at its Foster City campus. In 2012, Visa decided to consolidate its headquarters in Foster City where 3,100 of its 7,700 global workers are employed. Visa owns four buildings at the intersection of Metro Center Boulevard and Vintage Park Drive. As of October 1, 2012, Visa's headquarters were located in Foster City. In December 2012, Visa Inc. confirmed that it will build a global information technology center off of the US 183 Expressway in northwest Austin, Texas. By 2019, Visa had leased space in four buildings near Austin and employed nearly 2,000 people. On November 6, 2019, Visa announced plans to move its headquarters back to San Francisco by 2024 upon completion of a new "13-story, 300,000-square-foot building". Visa also announced that it would redesign its current four-building complex in Foster City to 575,000 square feet, for offices for 3,000 employees in its product and technology teams. The existing complex has over 970,000 square feet of space, but Visa declined to explain how it would dispose of almost 400,000 square feet of excess space. On June 6, 2024, Visa opened its new headquarters building at 300 Toni Stone Crossing in the Mission Rock development in San Francisco's Mission Bay neighborhood. The building was officially designated as the Market Support Center on its opening date, rather than a "headquarters" building as indicated in its original 2019 announcement. The company's 2024 filings with the U.S. Securities and Exchange Commission designate a post office box as its official address. Despite that ambiguity, the office of Visa's chief executive officer is based in the Market Support Center. The building features outdoor terraces, a rooftop deck, and views of San Francisco Giants baseball games and other events at Oracle Park across McCovey Cove. Visa is mainly owned by institutional investors, who own over 95% of shares. The largest shareholders in December 2023 were: Operations Visa offers through its issuing members the following types of cards: Visa operates the Plus automated teller machine network and the Interlink EFTPOS point-of-sale network, which facilitate the "debit" protocol used with debit cards and prepaid cards. They also provide commercial payment solutions for small businesses, midsize and large corporations, and governments. Visa teamed with Apple in September 2014, to incorporate a new mobile wallet feature into Apple's new iPhone models, enabling users to more readily use their Visa, and other credit/debit cards. Visa has a set of rules that govern the participation of financial institutions in its payment system. Acquiring banks are responsible for ensuring that their merchants comply with the rules. Rules address how a cardholder must be identified for security, how transactions may be denied by the bank, and how banks may cooperate for fraud prevention, and how to keep that identification and fraud protection standard and non-discriminatory. Other rules govern what creates an enforceable proof of authorization by the cardholder. The rules generally prohibit merchants from imposing a minimum or maximum purchase amount in order to accept a Visa card and from charging cardholders a fee for using a Visa card, but rules and laws vary by country. Court decisions, legal settlements, and state statutes regulating surcharges and fees vary across the United States. It is illegal in three U.S. states and one territory (Connecticut, Massachusetts, Maine, and Puerto Rico) for merchants to impose surcharges for the use of a credit card. In those U.S. states where surcharges are permitted by law, merchants wishing to apply surcharges are required to abide by rules set by Visa. Visa permits merchants to ask for photo ID, although the merchant rule book states that merchants are not generally allowed to require photo ID to complete a transaction. However, Visa may grant a merchant permission to require photo ID for purposes of fraud control. The Dodd–Frank Act allows U.S. merchants to set a minimum purchase amount on credit card transactions, not to exceed $10. Some countries have banned the no-surcharge rule, most notably in Australia retailers may apply surcharges to any credit-card transaction, Visa or otherwise. In the UK the law was changed in January 2018 to prevent retailers from adding a surcharge to a transaction as per 'The Consumer Rights (Payment Surcharges) Regulations 2012'. Other complications include the addition of exceptions for non-signed purchases by telephone or on the Internet and an additional security system called "Verified by Visa" for purchases on the Internet. In September 2014, Visa Inc, launched a new service to replace account information on plastic cards with tokens – a digital account number. Products Depending on the geographical location, Visa card issuers issue the following tiers of cards, from the lowest to the highest: This is the standard Visa-branded debit card. A Visa-branded debit card issued worldwide since the 1990s. Its distinguishing feature is that it does not allow "card not present" transactions while its floor limit is set to zero, which triggers automatic authorisation of each transaction with the issuing bank and effectively makes it impossible for the user to overdraw the account. The card has often been issued to younger customers or those who may pose a risk of overdrawing the account. Since mid-2000s, the card has mostly been replaced by Visa Debit. A Visa-branded stored-value card. In September 2007, Visa introduced Visa payWave (later known as Visa Contactless), a contactless payment technology feature that allows cardholders to wave their card in front of contactless payment terminals without the need to physically swipe or insert the card into a point-of-sale device. This is similar to the Mastercard Contactless service and the American Express ExpressPay, with both using RFID technology. All of them uses the same EMV Contactless logo to denote the capability of the card. In Europe, Visa has introduced the V Pay card, which is a chip-only and PIN-only debit card. In Australia, take up has been the highest in the world, with more than 50% of in store Visa transactions made by Visa payWave in 2016. mVisa is a mobile payment app allowing payment via smartphones using QR code. This QR code payment method was first introduced in India in 2015. It was later expanded to a number of other countries, including in Africa and South East Asia. In 2013, Visa launched Visa Checkout, an online payment system that removes the need to share card details with retailers. The Visa Checkout service allows users to enter all their personal details and card information, then use a single username and password to make purchases from online retailers. The service works with Visa credit, debit, and prepaid cards. On November 27, 2013, V.me went live in the UK, France, Spain and Poland, with Nationwide Building Society being the first financial institution in Britain to support it, although Nationwide subsequently withdrew this service in 2016. After Visa's acquisition of TrialPay on February 27, 2015, Visa created the Visa Commerce Network. Visa Commerce Network provides businesses the ability to provide rewards, through the use of loyalty programs. Trademark and design The blue and gold in Visa's logo were chosen to represent the blue sky and gold-colored hills of California, where the Bank of America was founded. In 2005, Visa changed its logo, removing the horizontal stripes in favor of a simple white background with the name Visa in blue with an orange flick on the 'V'. The orange flick was removed in favor of the logo being a solid blue gradient in 2014 and solid blue in 2021. In 2015, the gold and blue stripes were restored as card branding on Visa Debit and Visa Electron, although not as the company's logotype. In 1983, most Visa cards around the world began to feature a hologram of a dove on its face, generally under the last four digits of the Visa number. This was implemented as a security feature – true holograms would appear three-dimensional and the image would change as the card was turned. At the same time, the Visa logo, which had previously covered the whole card face, was reduced in size to a strip on the card's right incorporating the hologram. This allowed issuing banks to customize the appearance of the card. Similar changes were implemented with MasterCard cards. Today, cards may be co-branded with various merchants, airlines, etc., and marketed as "reward cards". On older Visa cards, holding the face of the card under an ultraviolet light will reveal the dove picture, dubbed the Ultra-Sensitive Dove, as an additional security test. (On newer Visa cards, the UV dove is replaced by a small V over the Visa logo.) Beginning in 2005, the Visa standard was changed to allow for the hologram to be placed on the back of the card, or to be replaced with a holographic magnetic stripe ("HoloMag"). The HoloMag card was shown to occasionally cause interference with card readers, so Visa eventually withdrew designs of HoloMag cards and reverted to traditional magnetic strips. Signatures Visa made a statement on January 12, 2018, that the signature requirement would become optional for all EMV contact or contactless chip-enabled merchants in North America starting in April 2018. It was noted that the signatures are no longer necessary to fight fraud and the fraud capabilities have advanced allowing this elimination leading to a faster in-store purchase experience. Visa was the last of the major credit card issuers to relax the signature requirements. The first to eliminate the signature was MasterCard Inc. followed by Discover Financial Services and American Express Co. Sponsorships See also References External links |
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Contents Ghillie Dhu The Ghillie Dhu or Gille Dubh (Scottish Gaelic pronunciation: [ˈkʲiʎə ˈt̪u]) is a solitary male fairy described in Scottish folklore. He was said to be dark-haired, and clothed in leaves and moss, from which the ghillie suit got its name. He appears primarily in accounts from the late 18th century, living in a birch wood in the north-west Highlands of Scotland. He was said to fiercely protect the forest from outsiders, but with accounts of him treating children with kindness. Etymology Ghillie is an English equivalent of the Scottish Gaelic word gille. English lexicographer Edward Dwelly lists gille as a "lad", "youth", or "boy"; with dubh meaning "dark" or "dark-haired". Folk beliefs According to folklorist Katharine Briggs, the Ghillie Dhu was a gentle and kind-hearted mountain spirit, or a "rather unusual nature fairy." He was generally timid, yet he could also be "wild". Generally of a dishevelled appearance, he used green moss and leaves taken from trees as clothing. As indicated by his name, he had black hair. He was of a small stature. His fondness of children is similar to that displayed by the little known Hyter sprite of English mythology. He was said to live in the birch woods near Loch a Druing, in the north-west Highland area of Gairloch. The woods are in a dip alongside a hilly area around 2 miles (3.2 kilometres) from where Rua Reidh Lighthouse was later built. He was mainly reported in the latter part of the 18th century. He was described by Osgood Mackenzie, a Scottish landowner and horticulturist, in his 1921 memoirs. The best known account of the Ghillie Dhu involves a girl named Jessie Macrae, who lived near the woods. She wandered into the woods and became lost as the sun went down. Her sobs reportedly drew the attention of the Ghillie Dhu, who comforted her and either led her home before darkness fell, or stayed with her all night and led her home in the morning. Over a period of four decades the fairy was reportedly seen by many people but Jessie was the only person with whom he conversed. At some point, landowner Sir Hector Mackenzie of Gairloch invited a group of five Mackenzie dignitaries to hunt and capture the Ghillie Dhu, which he believed posed a threat. Despite searching extensively throughout the night, the hunters could not find their prey; according to mythology scholar Patricia Monaghan, the Ghillie Dhu was never seen again. Origins After researching folklore traditions gathered primarily from Gaelic areas of Scotland, an authority on congenital disorders, Susan Schoon Eberly, has speculated the tale of the Ghillie Dhu may have a basis in a human being with a medical condition; other academics, such as Carole G. Silver, Professor of English at Stern College for Women, agree and suggest he was a dwarf. Eberly maintained several other solitary or individual fairies, including the Brownie and the Manx Fenodyree, could also have a medical, rather than supernatural, explanation. Bibliography References See also |
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Contents Avi Loeb Abraham "Avi" Loeb (Hebrew: אברהם (אבי) לייב; born February 26, 1962) is an Israeli and American theoretical physicist who works on astrophysics and cosmology. Loeb is the Frank B. Baird Jr. Professor of Science at Harvard University. He chaired the Department of Astronomy from 2011 to 2020, and founded the Black Hole Initiative in 2016. Loeb is a fellow of the American Academy of Arts and Sciences, the American Physical Society, and the International Academy of Astronautics. In 2015, he was appointed as the science theory director for the Breakthrough Initiatives of the Breakthrough Prize Foundation. Loeb has published popular science books including Extraterrestrial: The First Sign of Intelligent Life Beyond Earth (2021) and Interstellar: The Search for Extraterrestrial Life and Our Future in the Stars (2023). Since 2017, Loeb has made a series of claims that alien space craft may be in the Solar System. He has argued that ʻOumuamua and other interstellar objects, including the reputedly interstellar meteor CNEOS 2014-01-08, are potential examples of such craft. These claims have been widely rejected by the scientific community. In 2023, he claimed to have recovered spherules formed by the impact of CNEOS 2014-01-08 that he alleged could be evidence of an alien starship, but the location in the ocean where he recovered the spherules was based on mistaking a seismic signal from a truck for the impact of the meteor. During an appearance on Joe Rogan's podcast, he also claimed that whether an ancient "sophisticated civilization" existed on Earth before humanity is a credible question to ask. Loeb tends to publicize his results before undergoing peer review, contributing to a climate of sensationalism around his claims. Life and career Loeb was born in Beit Hanan, Israel, in 1962. He took part in the national Talpiot program research program of the Israeli Defense Forces at age 18. While in Talpiot, he obtained a BSc degree in physics and mathematics in 1983, an MSc degree in physics in 1985, and a PhD in plasma physics in 1986, all from the Hebrew University of Jerusalem (HUJI). During his doctoral studies, Loeb conducted research at the Soreq Nuclear Research Center in Yavne. His PhD thesis focused on the modeling of plasma acceleration of charged particles. From 1983 to 1988, he led the first international project supported by the U.S. Strategic Defense Initiative on a new propulsion method for high-speed projectiles. Between 1988 and 1993, Loeb was a long-term member at the Institute for Advanced Study at Princeton, where he started to work in theoretical astrophysics under the supervision of John Bahcall. In 1993, he moved to Harvard University as an assistant professor in the department of astronomy, and was tenured three years later. Since 2007, he has been Director of the Institute for Theory and Computation at the Harvard-Smithsonian Center for Astrophysics. Since 2012, Loeb became the Frank B. Baird Jr. Professor of Science at Harvard. Loeb has written eight books, including the textbooks How Did the First Stars and Galaxies Form? and The First Galaxies in the Universe. He has co-authored many papers on topics in astrophysics and cosmology, including the first stars, the epoch of reionization, the formation and evolution of massive black holes, the search for extraterrestrial life, gravitational lensing by planets, gamma-ray bursts at high redshifts, the use of the Lyman-alpha forest to measure the acceleration/deceleration of the universe in real time, the future collision between the Milky Way and Andromeda galaxies, the future state of extragalactic astronomy, astrophysical implications of black hole recoil in galaxy mergers, tidal disruption of stars, and imaging black hole silhouettes. Together with his postdoc James Guillochon, Loeb predicted the existence of a new population of stars moving near the speed of light throughout the universe. Together with his postdoc John Forbes and Howard Chen of Northwestern University, Loeb made another prediction that sub-Neptune-sized exoplanets have been transformed into rocky super-Earths by the activity of Sagittarius A*. Together with Paolo Pani, Loeb showed in 2013 that primordial black holes in the range between the masses of the Moon and the Sun cannot make up dark matter. In 2025, Loeb, in collaboration with Oem Trivedi, proposed that dark matter could consist of remnants of Planck Stars formed after the evaporation of primordial black holes. Loeb led a team that reported tentative evidence for the birth of a black hole in the young nearby supernova SN 1979C. In collaboration with Dan Maoz, Loeb demonstrated in 2013 that biomarkers, such as molecular oxygen (O2), can be detected by the James Webb Space Telescope (JWST) in the atmosphere of Earth-mass planets in the habitable zone of white dwarfs. In 2018, he served a term as chair of the board on Physics and Astronomy (BPA) of the National Academies of Sciences, Engineering, and Medicine (NASEM). In 2013, Loeb wrote about the "Habitable Epoch of the Early Universe", noting that the Cosmic Microwave Background would temporarily have been at temperatures compatible with liquid water around 15 million years after the Big Bang. In April 2021, he presented an updated summary of his ideas of life in the early universe. In 2020, Loeb published a paper about the possibility that life can propagate from one planet to another, followed by the opinion piece "Noah's Spaceship" about directed panspermia. Loeb's claims about alien life have attracted sustained criticism from other scientists. Steve Desch, an astrophysicist at Arizona State University referred to Loeb's claims as "ridiculous sensationalism" which represent "a real breakdown of the peer review process and the scientific method". Some of Loeb's claims have been described as conspiracy theories, with USA Today referring to Loeb's speculation about 3I/ATLAS as an "outlandish conspiracy theor[y]." Other scientists have described Loeb's theories as "nonsense", comparable to the idea that "the moon is made of cheese." In 2024, Loeb delivered a speech in which he declared his view that the Messiah will be an alien who arrives from outer space. ʻOumuamua was the first confirmed interstellar object detected in the Solar System. In December 2017, Loeb cited ʻOumuamua's unusually elongated shape as one of the reasons the Green Bank Telescope in West Virginia should listen for radio emissions from it to see if there were any unexpected signs that it might be of artificial origin, although earlier limited observations by other radio telescopes such as the SETI Institute's Allen Telescope Array had produced no such results. The Green Bank Telescope observed the asteroid for six hours, detecting no radio signals. On October 26, 2018, Loeb and his postdoctoral student Shmuel Bialy submitted a paper exploring the possibility that ʻOumuamua is an artificial thin solar sail accelerated by solar radiation pressure in an effort to help explain the object's non-gravitational acceleration. The consensus among other astrophysicists was that the available evidence is insufficient to consider such a premise, and that a tumbling solar sail would not be able to accelerate. In response, Loeb wrote an article detailing six anomalous properties of ʻOumuamua that make it unusual, unlike any comets or asteroids seen before. By 2021, there was widespread consensus in the scientific community that 1I/ʻOumuamua had properties entirely consistent with a naturally occurring object, perhaps made of nitrogen ice, or a comet-like body that was altered by warming as it travelled through the solar system. On November 27, 2018, Loeb and Amir Siraj, a Harvard undergraduate, proposed a search for ʻOumuamua-like objects that might be trapped in the Solar System as a result of losing orbital energy through a close encounter with Jupiter. They identified four candidates (2011 SP25, 2017 RR2, 2017 SV13, and 2018 TL6) for trapped interstellar objects that dedicated missions could visit. The authors pointed out that future sky surveys, such as with Large Synoptic Survey Telescope, could find many more. In public interviews and private communications with reporters and academic colleagues, Loeb has become more vocal about the prospects of proving the existence of alien life. On April 16, 2019, Loeb and Siraj reported the discovery of a meteor of interstellar origin. Extraterrestrial: The First Sign of Intelligent Life Beyond Earth, a popular science account of ʻOumuamua by Loeb, was published in 2021. A followup book, Interstellar: The Search for Extraterrestrial Life and Our Future in the Stars, was published on August 29, 2023. In July 2021, Loeb founded the Galileo Project for the Systematic Scientific Search for Evidence of Extraterrestrial Technological Artifacts. The project was inspired by the detection of ʻOumuamua and by release of the Office of the Director of National Intelligence report on Unidentified Aerial Phenomena (UAP). As stated on the project's website, the aim is: Given the recently discovered abundance of Earth-Sun systems, the Galileo Project is dedicated to the proposition that humans can no longer ignore the possible existence of Extraterrestrial Technological Civilizations (ETCs), and that science should not dogmatically reject potential extraterrestrial explanations because of social stigma or cultural preferences, factors which are not conducive to the scientific method of unbiased, empirical inquiry. We now must 'dare to look through new telescopes', both literally and figuratively. The three main avenues of research are: Unlike other similar projects, the goal of the Galileo Project is to search for physical objects, and not electromagnetic signals, associated with extraterrestrial technological equipment. The project was covered by many independent publishers, among them Nature, Science, New York Post, Scientific American, The Guardian, etc. To allegations that studies of UFOs is pseudoscience, Loeb answers that the project aims not to study UFOs based on previous data, but to study Unidentified Aerial Phenomena "using the standard scientific method based on a transparent analysis of open scientific data to be collected using optimized instruments". In 2014, the US Department of Defense observed a fireball entering the atmosphere. Loeb made a series of claims about this event, from the meteor being from outside the Solar System to its likely area of impact based on, among other things, a seismic signal that occurred around the same time, all culminating in 2023, when Loeb announced that he had found interstellar material on the ocean floor that he asserted came from the meteor and could be remnants of an extraterrestrial starship. These claims were criticized by other scientists as hasty, sensational, and part of a pattern of improper behavior. Peter Brown, a meteor physicist at the University of Western Ontario, argued the material can be explained as non-interstellar, noting that measurements from Defense Department data are opaque and error-prone. Brown further said he was disturbed by Loeb's lack of engagement with relevant experts. In March 2022, the U.S. Space Force affirmed that their 2014 data indicated an interstellar origin, while the following month NASA stated the evidence for this was inconclusive. Astrophysicist Steve Desch, at Arizona State University, commented "[Loeb's claims are] polluting good science—conflating the good science we do with this ridiculous sensationalism and sucking all the oxygen out of the room", and said several of his colleagues are consequently refusing to engage with Loeb in the peer review process. Monica Grady from the Open University argued that the evidence for Loeb's claims is "rather shaky" and pointed more plausibly to terrestrial pollution. Patricio A. Gallardo in an American Astronomical Society paper similarly concluded the samples were consistent with coal ash contamination. Loeb subsequently authored a preprint saying chemical analysis ruled out coal ash contamination and indicated extrasolar origins. Loeb and Morgan MacLeod proposed a tidal disruption mechanism that could cause meteors to be ejected into trajectories leading to the described observations. In 2024 planetary seismologist Benjamin Fernando led a team that analyzed the seismic signals that led Loeb to search that specific region of the ocean, and they concluded that the seismic signals from one of the sensors used was in fact caused not by a meteor, but by a truck driving near the sensor, so that, "Not only did they use the wrong signal, they were looking in the wrong place." In 2025, ATLAS (Asteroid Terrestrial-impact Last Alert System), the NASA-funded survey telescope in Rio Hurtado, Chile, observed a comet approaching from the constellation of Sagittarius at an interstellar velocity. Loeb hypothesized in the press that it, the third known interstellar object, could be an alien device with potentially malevolent intent. He based these speculations on his calculations of the likelihood of a comet of natural origins having these characteristics. "The retrograde orbital plane of 3I/ATLAS around the Sun lies within 5 degrees of that of Earth... The likelihood for that coincidence out of all random orientations is 0.2 percent," Loeb told Newsweek. He further claimed that the brightness of 3I/ATLAS implies an object that is around 20 kilometers in diameter which is "too large for an interstellar asteroid." 3I/ATLAS' trajectory will bring it close to Venus, Mars and Jupiter, a path Loeb calculated as having a probability of just 0.005 percent. "It might have targeted the inner Solar System as expected from alien technology," he added. Richard Moissl, Head of Planetary Defence at the European Space Agency told Newsweek: "There have been no signs pointing to non-natural origins of 3I/ATLAS in the available observations." Since then, observations have reported evidence of 3I/ATLAS containing water, which is a substance commonly found in comets. Independent assessments have resoundingly rejected the idea that 3I/ATLAS is anything except a comet. Nicola Fox, associate administrator of NASA's Science Mission Directorate said that "We certainly haven't seen any technosignatures or anything from it that would lead us to believe it was anything other than a comet". Similarly, NASA Associate Administrator Amit Kshatriya stated that "all evidence points to it being a comet." In the face of this growing body of evidence, Loeb conceded that 3I/ATLAS is "most likely" a comet, though he continued to speculate about its supposed technological nature regardless. Media appearances In 2006, Loeb was featured in a Time magazine cover story on the first stars, and in a Scientific American article on the Dark Ages of the universe. In 2008, he was featured in a Smithsonian magazine cover story on black holes, and in two Astronomy magazine cover stories, one on the collision between the Milky Way and the Andromeda Galaxy and the second on the future state of our universe. In 2009, Loeb reviewed in a Scientific American article a new technique for imaging black hole silhouettes. Loeb received considerable media attention after proposing in 2011 (with E.L. Turner) a new technique for detecting artificially-illuminated objects in the Solar System and beyond, and showing in 2012 (with I. Ginsburg) that planets may transit hypervelocity stars or get kicked to a fraction of the speed of light near the black hole at the center of the Milky Way. He has been profiled a number of times, including in Science magazine, Discover, and The New York Times. He has been interviewed by Astronomy magazine, by Lex Fridman, Let's Get Haunted, Joe Rogan, Mick West, and by the H3 Podcast. On August 24, 2023, The New York Times published an article about Loeb and his search for signs of extraterrestrial life. Loeb also regularly writes opinion essays on science and policy. In February 2026 a large poem about Avi Loeb titled The Avi Loeb Interstellar was printed by Jane Hirshfield in Poets for Science and later published by Dr. Loeb to his Medium page. Honors and awards Loeb has received many honors, including: See also Selected publications References External links |
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[SOURCE: https://en.wikipedia.org/wiki/Linearized_gravity] | [TOKENS: 1881] |
Contents Linearized gravity In the theory of general relativity, linearized gravity is the application of perturbation theory to the metric tensor that describes the geometry of spacetime. As a consequence, linearized gravity is an effective method for modeling the effects of gravity when the gravitational field is weak. The usage of linearized gravity is integral to the study of gravitational waves and weak-field gravitational lensing. Weak-field approximation The Einstein field equation (EFE) describing the geometry of spacetime using the MTW sign convention, including the metric signature (−+++), is where R μ ν {\displaystyle R_{\mu \nu }} is the Ricci tensor, R {\displaystyle R} is the Ricci scalar, T μ ν {\displaystyle T_{\mu \nu }} is the energy–momentum tensor, κ {\displaystyle \kappa } is the Einstein gravitational constant, and g μ ν {\displaystyle g_{\mu \nu }} is the spacetime metric tensor that represents the solutions of the equation. Although succinct when written out using Einstein notation, hidden within the Ricci tensor and Ricci scalar are exceptionally nonlinear dependencies on the metric tensor that render the prospect of finding exact solutions impractical in most systems. However, when describing systems for which the curvature of spacetime is small (meaning that terms in the EFE that are quadratic in g μ ν {\displaystyle g_{\mu \nu }} do not significantly contribute to the equations of motion), one can model the solution of the field equations as being the Minkowski metric[note 1] η μ ν {\displaystyle \eta _{\mu \nu }} plus a small perturbation term h μ ν {\displaystyle h_{\mu \nu }} . In other words: In this regime, substituting the general metric g μ ν {\displaystyle g_{\mu \nu }} for this perturbative approximation results in a simplified expression for the Ricci tensor: where h = η μ ν h μ ν {\displaystyle h=\eta ^{\mu \nu }h_{\mu \nu }} is the trace of the perturbation, ∂ μ {\displaystyle \partial _{\mu }} denotes the partial derivative with respect to the x μ {\displaystyle x^{\mu }} coordinate of spacetime, and ◻ = η μ ν ∂ μ ∂ ν {\displaystyle \square =\eta ^{\mu \nu }\partial _{\mu }\partial _{\nu }} is the d'Alembert operator. Together with the Ricci scalar, the left side of the field equation reduces to and thus the EFE is reduced to a linear second order partial differential equation in terms of h μ ν {\displaystyle h_{\mu \nu }} . The process of decomposing the general spacetime g μ ν {\displaystyle g_{\mu \nu }} into the Minkowski metric plus a perturbation term is not unique. This is because different choices for coordinates may give different forms for h μ ν {\displaystyle h_{\mu \nu }} . In order to capture this phenomenon, the concept of gauge symmetry is introduced. Gauge symmetries are a mathematical device for describing a system that does not change when the underlying coordinate system is "shifted" by an infinitesimal amount. So although the perturbation metric h μ ν {\displaystyle h_{\mu \nu }} is not consistently defined between different coordinate systems, the overall system which it describes is. To capture this formally, the non-uniqueness of the perturbation h μ ν {\displaystyle h_{\mu \nu }} is represented as being a consequence of the diverse collection of diffeomorphisms on spacetime that leave h μ ν {\displaystyle h_{\mu \nu }} sufficiently small. Therefore, it is required that h μ ν {\displaystyle h_{\mu \nu }} be defined in terms of a general set of diffeomorphisms, then select the subset of these that preserve the small scale that is required by the weak-field approximation. One may thus define ϕ {\displaystyle \phi } to denote an arbitrary diffeomorphism that maps the flat Minkowski spacetime to the more general spacetime represented by the metric g μ ν {\displaystyle g_{\mu \nu }} . With this, the perturbation metric may be defined as the difference between the pullback of g μ ν {\displaystyle g_{\mu \nu }} and the Minkowski metric: The diffeomorphisms ϕ {\displaystyle \phi } may thus be chosen such that | h μ ν | ≪ 1 {\displaystyle |h_{\mu \nu }|\ll 1} . Given then a vector field ξ μ {\displaystyle \xi ^{\mu }} defined on the flat background spacetime, an additional family of diffeomorphisms ψ ϵ {\displaystyle \psi _{\epsilon }} may be defined as those generated by ξ μ {\displaystyle \xi ^{\mu }} and parameterized by ϵ > 0 {\displaystyle \epsilon >0} . These new diffeomorphisms will be used to represent the coordinate transformations for "infinitesimal shifts" as discussed above. Together with ϕ {\displaystyle \phi } , a family of perturbations is given by Therefore, in the limit ϵ → 0 {\displaystyle \epsilon \rightarrow 0} , where L ξ {\displaystyle {\mathcal {L}}_{\xi }} is the Lie derivative along the vector field ξ μ {\displaystyle \xi _{\mu }} . The Lie derivative works out to yield the final gauge transformation of the perturbation metric h μ ν {\displaystyle h_{\mu \nu }} : which precisely define the set of perturbation metrics that describe the same physical system. In other words, it characterizes the gauge symmetry of the linearized field equations. By exploiting gauge invariance, certain properties of the perturbation metric can be guaranteed by choosing a suitable vector field ξ μ {\displaystyle \xi ^{\mu }} . To study how the perturbation h μ ν {\displaystyle h_{\mu \nu }} distorts measurements of length, it is useful to define the following spatial tensor: (Note that the indices span only spatial components: i , j ∈ { 1 , 2 , 3 } {\displaystyle i,j\in \{1,2,3\}} ). Thus, by using s i j {\displaystyle s_{ij}} , the spatial components of the perturbation can be decomposed as where Ψ = 1 3 δ k l h k l {\displaystyle \Psi ={\frac {1}{3}}\delta ^{kl}h_{kl}} . The tensor s i j {\displaystyle s_{ij}} is, by construction, traceless and is referred to as the strain since it represents the amount by which the perturbation stretches and contracts measurements of space. In the context of studying gravitational radiation, the strain is particularly useful when utilized with the transverse gauge. This gauge is defined by choosing the spatial components of ξ μ {\displaystyle \xi ^{\mu }} to satisfy the relation then choosing the time component ξ 0 {\displaystyle \xi ^{0}} to satisfy After performing the gauge transformation using the formula in the previous section, the strain becomes spatially transverse: with the additional property: The synchronous gauge simplifies the perturbation metric by requiring that the metric not distort measurements of time. More precisely, the synchronous gauge is chosen such that the non-spatial components of h μ ν ( ϵ ) {\displaystyle h_{\mu \nu }^{(\epsilon )}} are zero, namely This can be achieved by requiring the time component of ξ μ {\displaystyle \xi ^{\mu }} to satisfy and requiring the spatial components to satisfy The harmonic gauge (also referred to as the Lorenz gauge[note 2]) is selected whenever it is necessary to reduce the linearized field equations as much as possible. This can be done if the condition is true. To achieve this, ξ μ {\displaystyle \xi _{\mu }} is required to satisfy the relation Consequently, by using the harmonic gauge, the Einstein tensor G μ ν = R μ ν − 1 2 R g μ ν {\displaystyle G_{\mu \nu }=R_{\mu \nu }-{\frac {1}{2}}Rg_{\mu \nu }} reduces to Therefore, by writing it in terms of a "trace-reversed" metric, h ¯ μ ν ( ϵ ) = h μ ν ( ϵ ) − 1 2 h ( ϵ ) η μ ν {\displaystyle {\bar {h}}_{\mu \nu }^{(\epsilon )}=h_{\mu \nu }^{(\epsilon )}-{\frac {1}{2}}h^{(\epsilon )}\eta _{\mu \nu }} , the linearized field equations reduce to This can be solved exactly, to produce the wave solutions that define gravitational radiation. See also Notes Further reading External links |
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[SOURCE: https://en.wikipedia.org/wiki/Lod#cite_ref-Shahinp260_65-0] | [TOKENS: 4733] |
Contents Lod Lod (Hebrew: לוד, fully vocalized: לֹד), also known as Lydda (Ancient Greek: Λύδδα) and Lidd (Arabic: اللِّدّ, romanized: al-Lidd, or اللُّدّ, al-Ludd), is a city 15 km (9+1⁄2 mi) southeast of Tel Aviv and 40 km (25 mi) northwest of Jerusalem in the Central District of Israel. It is situated between the lower Shephelah on the east and the coastal plain on the west. The city had a population of 90,814 in 2023. Lod has been inhabited since at least the Neolithic period. It is mentioned a few times in the Hebrew Bible and in the New Testament. Between the 5th century BCE and up until the late Roman period, it was a prominent center for Jewish scholarship and trade. Around 200 CE, the city became a Roman colony and was renamed Diospolis (Ancient Greek: Διόσπολις, lit. 'city of Zeus'). Tradition identifies Lod as the 4th century martyrdom site of Saint George; the Church of Saint George and Mosque of Al-Khadr located in the city is believed to have housed his remains. Following the Arab conquest of the Levant, Lod served as the capital of Jund Filastin; however, a few decades later, the seat of power was transferred to Ramla, and Lod slipped in importance. Under Crusader rule, the city was a Catholic diocese of the Latin Church and it remains a titular see to this day.[citation needed] Lod underwent a major change in its population in the mid-20th century. Exclusively Palestinian Arab in 1947, Lod was part of the area designated for an Arab state in the United Nations Partition Plan for Palestine; however, in July 1948, the city was occupied by the Israel Defense Forces, and most of its Arab inhabitants were expelled in the Palestinian expulsion from Lydda and Ramle. The city was largely resettled by Jewish immigrants, most of them expelled from Arab countries. Today, Lod is one of Israel's mixed cities, with an Arab population of 30%. Lod is one of Israel's major transportation hubs. The main international airport, Ben Gurion Airport, is located 8 km (5 miles) north of the city. The city is also a major railway and road junction. Religious references The Hebrew name Lod appears in the Hebrew Bible as a town of Benjamin, founded along with Ono by Shamed or Shamer (1 Chronicles 8:12; Ezra 2:33; Nehemiah 7:37; 11:35). In Ezra 2:33, it is mentioned as one of the cities whose inhabitants returned after the Babylonian captivity. Lod is not mentioned among the towns allocated to the tribe of Benjamin in Joshua 18:11–28. The name Lod derives from a tri-consonantal root not extant in Northwest Semitic, but only in Arabic (“to quarrel; withhold, hinder”). An Arabic etymology of such an ancient name is unlikely (the earliest attestation is from the Achaemenid period). In the New Testament, the town appears in its Greek form, Lydda, as the site of Peter's healing of Aeneas in Acts 9:32–38. The city is also mentioned in an Islamic hadith as the location of the battlefield where the false messiah (al-Masih ad-Dajjal) will be slain before the Day of Judgment. History The first occupation dates to the Neolithic in the Near East and is associated with the Lodian culture. Occupation continued in the Levant Chalcolithic. Pottery finds have dated the initial settlement in the area now occupied by the town to 5600–5250 BCE. In the Early Bronze, it was an important settlement in the central coastal plain between the Judean Shephelah and the Mediterranean coast, along Nahal Ayalon. Other important nearby sites were Tel Dalit, Tel Bareqet, Khirbat Abu Hamid (Shoham North), Tel Afeq, Azor and Jaffa. Two architectural phases belong to the late EB I in Area B. The first phase had a mudbrick wall, while the late phase included a circulat stone structure. Later excavations have produced an occupation later, Stratum IV. It consists of two phases, Stratum IVb with mudbrick wall on stone foundations and rounded exterior corners. In Stratum IVa there was a mudbrick wall with no stone foundations, with imported Egyptian potter and local pottery imitations. Another excavations revealed nine occupation strata. Strata VI-III belonged to Early Bronze IB. The material culture showed Egyptian imports in strata V and IV. Occupation continued into Early Bronze II with four strata (V-II). There was continuity in the material culture and indications of centralized urban planning. North to the tell were scattered MB II burials. The earliest written record is in a list of Canaanite towns drawn up by the Egyptian pharaoh Thutmose III at Karnak in 1465 BCE. From the fifth century BCE until the Roman period, the city was a centre of Jewish scholarship and commerce. According to British historian Martin Gilbert, during the Hasmonean period, Jonathan Maccabee and his brother, Simon Maccabaeus, enlarged the area under Jewish control, which included conquering the city. The Jewish community in Lod during the Mishnah and Talmud era is described in a significant number of sources, including information on its institutions, demographics, and way of life. The city reached its height as a Jewish center between the First Jewish-Roman War and the Bar Kokhba revolt, and again in the days of Judah ha-Nasi and the start of the Amoraim period. The city was then the site of numerous public institutions, including schools, study houses, and synagogues. In 43 BC, Cassius, the Roman governor of Syria, sold the inhabitants of Lod into slavery, but they were set free two years later by Mark Antony. During the First Jewish–Roman War, the Roman proconsul of Syria, Cestius Gallus, razed the town on his way to Jerusalem in Tishrei 66 CE. According to Josephus, "[he] found the city deserted, for the entire population had gone up to Jerusalem for the Feast of Tabernacles. He killed fifty people whom he found, burned the town and marched on". Lydda was occupied by Emperor Vespasian in 68 CE. In the period following the destruction of Jerusalem in 70 CE, Rabbi Tarfon, who appears in many Tannaitic and Jewish legal discussions, served as a rabbinic authority in Lod. During the Kitos War, 115–117 CE, the Roman army laid siege to Lod, where the rebel Jews had gathered under the leadership of Julian and Pappos. Torah study was outlawed by the Romans and pursued mostly in the underground. The distress became so great, the patriarch Rabban Gamaliel II, who was shut up there and died soon afterwards, permitted fasting on Ḥanukkah. Other rabbis disagreed with this ruling. Lydda was next taken and many of the Jews were executed; the "slain of Lydda" are often mentioned in words of reverential praise in the Talmud. In 200 CE, emperor Septimius Severus elevated the town to the status of a city, calling it Colonia Lucia Septimia Severa Diospolis. The name Diospolis ("City of Zeus") may have been bestowed earlier, possibly by Hadrian. At that point, most of its inhabitants were Christian. The earliest known bishop is Aëtius, a friend of Arius. During the following century (200-300CE), it's said that Joshua ben Levi founded a yeshiva in Lod. In December 415, the Council of Diospolis was held here to try Pelagius; he was acquitted. In the sixth century, the city was renamed Georgiopolis after St. George, a soldier in the guard of the emperor Diocletian, who was born there between 256 and 285 CE. The Church of Saint George and Mosque of Al-Khadr is named for him. The 6th-century Madaba map shows Lydda as an unwalled city with a cluster of buildings under a black inscription reading "Lod, also Lydea, also Diospolis". An isolated large building with a semicircular colonnaded plaza in front of it might represent the St George shrine. After the Muslim conquest of Palestine by Amr ibn al-'As in 636 CE, Lod which was referred to as "al-Ludd" in Arabic served as the capital of Jund Filastin ("Military District of Palaestina") before the seat of power was moved to nearby Ramla during the reign of the Umayyad Caliph Suleiman ibn Abd al-Malik in 715–716. The population of al-Ludd was relocated to Ramla, as well. With the relocation of its inhabitants and the construction of the White Mosque in Ramla, al-Ludd lost its importance and fell into decay. The city was visited by the local Arab geographer al-Muqaddasi in 985, when it was under the Fatimid Caliphate, and was noted for its Great Mosque which served the residents of al-Ludd, Ramla, and the nearby villages. He also wrote of the city's "wonderful church (of St. George) at the gate of which Christ will slay the Antichrist." The Crusaders occupied the city in 1099 and named it St Jorge de Lidde. It was briefly conquered by Saladin, but retaken by the Crusaders in 1191. For the English Crusaders, it was a place of great significance as the birthplace of Saint George. The Crusaders made it the seat of a Latin Church diocese, and it remains a titular see. It owed the service of 10 knights and 20 sergeants, and it had its own burgess court during this era. In 1226, Ayyubid Syrian geographer Yaqut al-Hamawi visited al-Ludd and stated it was part of the Jerusalem District during Ayyubid rule. Sultan Baybars brought Lydda again under Muslim control by 1267–8. According to Qalqashandi, Lydda was an administrative centre of a wilaya during the fourteenth and fifteenth century in the Mamluk empire. Mujir al-Din described it as a pleasant village with an active Friday mosque. During this time, Lydda was a station on the postal route between Cairo and Damascus. In 1517, Lydda was incorporated into the Ottoman Empire as part of the Damascus Eyalet, and in the 1550s, the revenues of Lydda were designated for the new waqf of Hasseki Sultan Imaret in Jerusalem, established by Hasseki Hurrem Sultan (Roxelana), the wife of Suleiman the Magnificent. By 1596 Lydda was a part of the nahiya ("subdistrict") of Ramla, which was under the administration of the liwa ("district") of Gaza. It had a population of 241 households and 14 bachelors who were all Muslims, and 233 households who were Christians. They paid a fixed tax-rate of 33,3 % on agricultural products, including wheat, barley, summer crops, vineyards, fruit trees, sesame, special product ("dawalib" =spinning wheels), goats and beehives, in addition to occasional revenues and market toll, a total of 45,000 Akçe. All of the revenue went to the Waqf. In 1051 AH/1641/2, the Bedouin tribe of al-Sawālima from around Jaffa attacked the villages of Subṭāra, Bayt Dajan, al-Sāfiriya, Jindās, Lydda and Yāzūr belonging to Waqf Haseki Sultan. The village appeared as Lydda, though misplaced, on the map of Pierre Jacotin compiled in 1799. Missionary William M. Thomson visited Lydda in the mid-19th century, describing it as a "flourishing village of some 2,000 inhabitants, imbosomed in noble orchards of olive, fig, pomegranate, mulberry, sycamore, and other trees, surrounded every way by a very fertile neighbourhood. The inhabitants are evidently industrious and thriving, and the whole country between this and Ramleh is fast being filled up with their flourishing orchards. Rarely have I beheld a rural scene more delightful than this presented in early harvest ... It must be seen, heard, and enjoyed to be appreciated." In 1869, the population of Ludd was given as: 55 Catholics, 1,940 "Greeks", 5 Protestants and 4,850 Muslims. In 1870, the Church of Saint George was rebuilt. In 1892, the first railway station in the entire region was established in the city. In the second half of the 19th century, Jewish merchants migrated to the city, but left after the 1921 Jaffa riots. In 1882, the Palestine Exploration Fund's Survey of Western Palestine described Lod as "A small town, standing among enclosure of prickly pear, and having fine olive groves around it, especially to the south. The minaret of the mosque is a very conspicuous object over the whole of the plain. The inhabitants are principally Moslim, though the place is the seat of a Greek bishop resident of Jerusalem. The Crusading church has lately been restored, and is used by the Greeks. Wells are found in the gardens...." From 1918, Lydda was under the administration of the British Mandate in Palestine, as per a League of Nations decree that followed the Great War. During the Second World War, the British set up supply posts in and around Lydda and its railway station, also building an airport that was renamed Ben Gurion Airport after the death of Israel's first prime minister in 1973. At the time of the 1922 census of Palestine, Lydda had a population of 8,103 inhabitants (7,166 Muslims, 926 Christians, and 11 Jews), the Christians were 921 Orthodox, 4 Roman Catholics and 1 Melkite. This had increased by the 1931 census to 11,250 (10,002 Muslims, 1,210 Christians, 28 Jews, and 10 Bahai), in a total of 2475 residential houses. In 1938, Lydda had a population of 12,750. In 1945, Lydda had a population of 16,780 (14,910 Muslims, 1,840 Christians, 20 Jews and 10 "other"). Until 1948, Lydda was an Arab town with a population of around 20,000—18,500 Muslims and 1,500 Christians. In 1947, the United Nations proposed dividing Mandatory Palestine into two states, one Jewish state and one Arab; Lydda was to form part of the proposed Arab state. In the ensuing war, Israel captured Arab towns outside the area the UN had allotted it, including Lydda. In December 1947, thirteen Jewish passengers in a seven-car convoy to Ben Shemen Youth Village were ambushed and murdered.In a separate incident, three Jewish youths, two men and a woman were captured, then raped and murdered in a neighbouring village. Their bodies were paraded in Lydda’s principal street. The Israel Defense Forces entered Lydda on 11 July 1948. The following day, under the impression that it was under attack, the 3rd Battalion was ordered to shoot anyone "seen on the streets". According to Israel, 250 Arabs were killed. Other estimates are higher: Arab historian Aref al Aref estimated 400, and Nimr al Khatib 1,700. In 1948, the population rose to 50,000 during the Nakba, as Arab refugees fleeing other areas made their way there. A key event was the Palestinian expulsion from Lydda and Ramle, with the expulsion of 50,000-70,000 Palestinians from Lydda and Ramle by the Israel Defense Forces. All but 700 to 1,056 were expelled by order of the Israeli high command, and forced to walk 17 km (10+1⁄2 mi) to the Jordanian Arab Legion lines. Estimates of those who died from exhaustion and dehydration vary from a handful to 355. The town was subsequently sacked by the Israeli army. Some scholars, including Ilan Pappé, characterize this as ethnic cleansing. The few hundred Arabs who remained in the city were soon outnumbered by the influx of Jews who immigrated to Lod from August 1948 onward, most of them from Arab countries. As a result, Lod became a predominantly Jewish town. After the establishment of the state, the biblical name Lod was readopted. The Jewish immigrants who settled Lod came in waves, first from Morocco and Tunisia, later from Ethiopia, and then from the former Soviet Union. Since 2008, many urban development projects have been undertaken to improve the image of the city. Upscale neighbourhoods have been built, among them Ganei Ya'ar and Ahisemah, expanding the city to the east. According to a 2010 report in the Economist, a three-meter-high wall was built between Jewish and Arab neighbourhoods and construction in Jewish areas was given priority over construction in Arab neighborhoods. The newspaper says that violent crime in the Arab sector revolves mainly around family feuds over turf and honour crimes. In 2010, the Lod Community Foundation organised an event for representatives of bicultural youth movements, volunteer aid organisations, educational start-ups, businessmen, sports organizations, and conservationists working on programmes to better the city. In the 2021 Israel–Palestine crisis, a state of emergency was declared in Lod after Arab rioting led to the death of an Israeli Jew. The Mayor of Lod, Yair Revivio, urged Prime Minister of Israel Benjamin Netanyahu to deploy Israel Border Police to restore order in the city. This was the first time since 1966 that Israel had declared this kind of emergency lockdown. International media noted that both Jewish and Palestinian mobs were active in Lod, but the "crackdown came for one side" only. Demographics In the 19th century and until the Lydda Death March, Lod was an exclusively Muslim-Christian town, with an estimated 6,850 inhabitants, of whom approximately 2,000 (29%) were Christian. According to the Israel Central Bureau of Statistics (CBS), the population of Lod in 2010 was 69,500 people. According to the 2019 census, the population of Lod was 77,223, of which 53,581 people, comprising 69.4% of the city's population, were classified as "Jews and Others", and 23,642 people, comprising 30.6% as "Arab". Education According to CBS, 38 schools and 13,188 pupils are in the city. They are spread out as 26 elementary schools and 8,325 elementary school pupils, and 13 high schools and 4,863 high school pupils. About 52.5% of 12th-grade pupils were entitled to a matriculation certificate in 2001.[citation needed] Economy The airport and related industries are a major source of employment for the residents of Lod. Other important factories in the city are the communication equipment company "Talard", "Cafe-Co" - a subsidiary of the Strauss Group and "Kashev" - the computer center of Bank Leumi. A Jewish Agency Absorption Centre is also located in Lod. According to CBS figures for 2000, 23,032 people were salaried workers and 1,405 were self-employed. The mean monthly wage for a salaried worker was NIS 4,754, a real change of 2.9% over the course of 2000. Salaried men had a mean monthly wage of NIS 5,821 (a real change of 1.4%) versus NIS 3,547 for women (a real change of 4.6%). The mean income for the self-employed was NIS 4,991. About 1,275 people were receiving unemployment benefits and 7,145 were receiving an income supplement. Art and culture In 2009-2010, Dor Guez held an exhibit, Georgeopolis, at the Petach Tikva art museum that focuses on Lod. Archaeology A well-preserved mosaic floor dating to the Roman period was excavated in 1996 as part of a salvage dig conducted on behalf of the Israel Antiquities Authority and the Municipality of Lod, prior to widening HeHalutz Street. According to Jacob Fisch, executive director of the Friends of the Israel Antiquities Authority, a worker at the construction site noticed the tail of a tiger and halted work. The mosaic was initially covered over with soil at the conclusion of the excavation for lack of funds to conserve and develop the site. The mosaic is now part of the Lod Mosaic Archaeological Center. The floor, with its colorful display of birds, fish, exotic animals and merchant ships, is believed to have been commissioned by a wealthy resident of the city for his private home. The Lod Community Archaeology Program, which operates in ten Lod schools, five Jewish and five Israeli Arab, combines archaeological studies with participation in digs in Lod. Sports The city's major football club, Hapoel Bnei Lod, plays in Liga Leumit (the second division). Its home is at the Lod Municipal Stadium. The club was formed by a merger of Bnei Lod and Rakevet Lod in the 1980s. Two other clubs in the city play in the regional leagues: Hapoel MS Ortodoxim Lod in Liga Bet and Maccabi Lod in Liga Gimel. Hapoel Lod played in the top division during the 1960s and 1980s, and won the State Cup in 1984. The club folded in 2002. A new club, Hapoel Maxim Lod (named after former mayor Maxim Levy) was established soon after, but folded in 2007. Notable people Twin towns-sister cities Lod is twinned with: See also References Bibliography External links |
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[SOURCE: https://en.wikipedia.org/wiki/REFAL] | [TOKENS: 1047] |
Contents Refal Refal ("Recursive functions algorithmic language"; Russian: РЕФАЛ) "is a functional programming language oriented toward symbolic computations", including "string processing, language translation, [and] artificial intelligence". It is one of the oldest members of this family, first conceived of in 1966 as a theoretical tool, with the first implementation appearing in 1968. Refal was intended to combine mathematical simplicity with practicality for writing large and sophisticated programs. One of the first functional programming languages to do so, and unlike Lisp of its time, Refal is based on pattern matching. Its pattern matching works in conjunction with term rewriting. The basic data structure of Lisp and Prolog is a linear list built by cons operation in a sequential manner, thus with O(n) access to list's nth element. Refal's lists are built and scanned from both ends, with pattern matching working for nested lists as well as the top-level one. In effect, the basic data structure of Refal is a tree rather than a list. This gives freedom and convenience in creating data structures while using only mathematically simple control mechanisms of pattern matching and substitution. Refal also includes a feature called the freezer to support efficient partial evaluation. Refal can be applied to the processing and transformation of tree structures, similarly to XSLT. Basics A Refal Hello World example is shown below. The program above includes two functions named Go and Hello. A function is written as the name of the function followed by the function body in curly braces. The Go function is marked as the entry point of the program using the $ENTRY directive. One could think of expressions in the function bodies as function "calls" in Lisp-like syntax. For example, the Hello function appears to call the built-in Prout function with the string 'Hello world' as the argument. The meaning and the mechanism of the call, however, is quite different. To illustrate the difference, consider the following function that determines whether a string is a palindrome. This example shows a function with a more complex body, consisting of four sentences (clauses). A sentence begins with a pattern followed by an equal sign followed by a general expression on the right hand side. A sentence is terminated with a semicolon. For example, the pattern of the second sentence of the function is "s.1" and the expression is "True". As the example shows, patterns include pattern variables that have the form of a character identifying the type of the variable (what the variable matches) followed by the variable identifier. The variables that begin with an "s" match a single symbol, those that begin with an "e" match an arbitrary expression. The variable identifier can be an arbitrary alphanumeric sequence optionally separated from the type identifier by a dot. A function executes by comparing its argument with the patterns of its sentences in the order they appear in the definition, until the first pattern that matches. The function then replaces the argument with the expression on the right hand side of the matched sentence. If the result of a function application includes a subexpression in angle brackets (as it will after the third sentence of our example is applied), the result is further processed by Refal by invoking the function identified by the first symbol in the brackets. Execution stops when the result has no more angle brackets to expand in this way. The function Pal can thus be read informally as: "If the expression is empty, replace it with True. Otherwise if the expression is a single symbol, replace it with True. Otherwise if the expression is a symbol followed by an arbitrary expression e.2 followed by the same symbol, replace it with the expression <Pal e.2>. (In other words, throw away the two identical symbols at the beginning and the end and recurse). Otherwise replace the expression with False. (The pattern e.1 always matches)." The following are three step-by-step execution traces annotated with the sentence numbers applied at each step to produce the next We can now see that the Hello World example in fact executes as the sequence of the following expression transformations: Other examples Here 0 matches 0 the number and produces 1. On any other symbol which is a number, multiply it with the result of (Fact (- s.N 1)) Note the prefix style of operators. As can be seen s.n acts as the loop counter. Here the function is defined as, if given two terms, and the terms are same then the first clause matches and produces True. else the second clause matches and produces False. An important property of Refal is that all functions in refal are single argument. (But may be decomposed into terms in an expression as above.) Defining control structures is easy Here the e1 is evaluated only when the expression entered matches 'True' Then e1 Else e2 the same for e2. (Using '_' in place of space char so as to make the function call clear.) The first clause matches whenever the function Squeeze encounters double blanks in its input expression, and replaces it with a single blank. The second clause matches only when the first one did not, and returns the resultant value which is the current expression. References External links |
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[SOURCE: https://en.wikipedia.org/wiki/Minecraft#cite_ref-NLcitesBattleminer_424-0] | [TOKENS: 12858] |
Contents Minecraft Minecraft is a sandbox game developed and published by Mojang Studios. Following its initial public alpha release in 2009, it was formally released in 2011 for personal computers. The game has since been ported to numerous platforms, including mobile devices and various video game consoles. In Minecraft, players explore a procedurally generated world with virtually infinite terrain made up of voxels (cubes). They can discover and extract raw materials, craft tools and items, build structures, fight hostile mobs, and cooperate with or compete against other players in multiplayer. The game's large community offers a wide variety of user-generated content, such as modifications, servers, player skins, texture packs, and custom maps, which add new game mechanics and possibilities. Originally created by Markus "Notch" Persson using the Java programming language, Jens "Jeb" Bergensten was handed control over the game's development following its full release. In 2014, Mojang and the Minecraft intellectual property were purchased by Microsoft for US$2.5 billion; Xbox Game Studios hold the publishing rights for the Bedrock Edition, the unified cross-platform version which evolved from the Pocket Edition codebase[i] and replaced the legacy console versions. Bedrock is updated concurrently with Mojang's original Java Edition, although with numerous, generally small, differences. Minecraft is the best-selling video game in history with over 350 million copies sold. It has received critical acclaim, winning several awards and being cited as one of the greatest video games of all time. Social media, parodies, adaptations, merchandise, and the annual Minecon conventions have played prominent roles in popularizing it. The wider Minecraft franchise includes several spin-off games, such as Minecraft: Story Mode, Minecraft Dungeons, and Minecraft Legends. A film adaptation, titled A Minecraft Movie, was released in 2025 and became the second highest-grossing video game film of all time. Gameplay Minecraft is a 3D sandbox video game that has no required goals to accomplish, giving players a large amount of freedom in choosing how to play the game. The game features an optional achievement system. Gameplay is in the first-person perspective by default, but players have the option of third-person perspectives. The game world is composed of rough 3D objects—mainly cubes, referred to as blocks—representing various materials, such as dirt, stone, ores, tree trunks, water, and lava. The core gameplay revolves around picking up and placing these objects. These blocks are arranged in a voxel grid, while players can move freely around the world. Players can break, or mine, blocks and then place them elsewhere, enabling them to build things. Very few blocks are affected by gravity, instead maintaining their voxel position in the air. Players can also craft a wide variety of items, such as armor, which mitigates damage from attacks; weapons (such as swords or bows and arrows), which allow monsters and animals to be killed more easily; and tools (such as pickaxes or shovels), which break certain types of blocks more quickly. Some items have multiple tiers depending on the material used to craft them, with higher-tier items being more effective and durable. They may also freely craft helpful blocks—such as furnaces which can cook food and smelt ores, and torches that produce light—or exchange items with villagers (NPC) through trading emeralds for different goods and vice versa. The game has an inventory system, allowing players to carry a limited number of items. The in-game time system follows a day and night cycle, with one full cycle lasting for 20 real-time minutes. The game also contains a material called redstone, which can be used to make primitive mechanical devices, electrical circuits, and logic gates, allowing for the construction of many complex systems. New players are given a randomly selected default character skin out of nine possibilities, including Steve or Alex, but are able to create and upload their own skins. Players encounter various mobs (short for mobile entities) including animals, villagers, and hostile creatures. Passive mobs, such as cows, pigs, and chickens, spawn during the daytime and can be hunted for food and crafting materials, while hostile mobs—including large spiders, witches, skeletons, and zombies—spawn during nighttime or in dark places such as caves. Some hostile mobs, such as zombies and skeletons, burn under the sun if they have no headgear and are not standing in water. Other creatures unique to Minecraft include the creeper (an exploding creature that sneaks up on the player) and the enderman (a creature with the ability to teleport as well as pick up and place blocks). There are also variants of mobs that spawn in different conditions; for example, zombies have husk and drowned variants that spawn in deserts and oceans, respectively. The Minecraft environment is procedurally generated as players explore it using a map seed that is randomly chosen at the time of world creation (or manually specified by the player). Divided into biomes representing different environments with unique resources and structures, worlds are designed to be effectively infinite in traditional gameplay, though technical limits on the player have existed throughout development, both intentionally and not. Implementation of horizontally infinite generation initially resulted in a glitch termed the "Far Lands" at over 12 million blocks away from the world center, where terrain generated as wall-like, fissured patterns. The Far Lands and associated glitches were considered the effective edge of the world until they were resolved, with the current horizontal limit instead being a special impassable barrier called the world border, located 30 million blocks away. Vertical space is comparatively limited, with an unbreakable bedrock layer at the bottom and a building limit several hundred blocks into the sky. Minecraft features three independent dimensions accessible through portals and providing alternate game environments. The Overworld is the starting dimension and represents the real world, with a terrestrial surface setting including plains, mountains, forests, oceans, caves, and small sources of lava. The Nether is a hell-like underworld dimension accessed via an obsidian portal and composed mainly of lava. Mobs that populate the Nether include shrieking, fireball-shooting ghasts, alongside anthropomorphic pigs called piglins and their zombified counterparts. Piglins in particular have a bartering system, where players can give them gold ingots and receive items in return. Structures known as Nether Fortresses generate in the Nether, containing mobs such as wither skeletons and blazes, which can drop blaze rods needed to access the End dimension. The player can also choose to build an optional boss mob known as the Wither, using skulls obtained from wither skeletons and soul sand. The End can be reached through an end portal, consisting of twelve end portal frames. End portals are found in underground structures in the Overworld known as strongholds. To find strongholds, players must craft eyes of ender using an ender pearl and blaze powder. Eyes of ender can then be thrown, traveling in the direction of the stronghold. Once the player reaches the stronghold, they can place eyes of ender into each portal frame to activate the end portal. The dimension consists of islands floating in a dark, bottomless void. A boss enemy called the Ender Dragon guards the largest, central island. Killing the dragon opens access to an exit portal, which, when entered, cues the game's ending credits and the End Poem, a roughly 1,500-word work written by Irish novelist Julian Gough, which takes about nine minutes to scroll past, is the game's only narrative text, and the only text of significant length directed at the player.: 10–12 At the conclusion of the credits, the player is teleported back to their respawn point and may continue the game indefinitely. In Survival mode, players have to gather natural resources such as wood and stone found in the environment in order to craft certain blocks and items. Depending on the difficulty, monsters spawn in darker areas outside a certain radius of the character, requiring players to build a shelter in order to survive at night. The mode also has a health bar which is depleted by attacks from mobs, falls, drowning, falling into lava, suffocation, starvation, and other events. Players also have a hunger bar, which must be periodically refilled by eating food in-game unless the player is playing on peaceful difficulty. If the hunger bar is empty, the player starves. Health replenishes when players have a full hunger bar or continuously on peaceful. Upon losing all health, players die. The items in the players' inventories are dropped unless the game is reconfigured not to do so. Players then re-spawn at their spawn point, which by default is where players first spawn in the game and can be changed by sleeping in a bed or using a respawn anchor. Dropped items can be recovered if players can reach them before they despawn after 5 minutes. Players may acquire experience points (commonly referred to as "xp" or "exp") by killing mobs and other players, mining, smelting ores, animal breeding, and cooking food. Experience can then be spent on enchanting tools, armor and weapons. Enchanted items are generally more powerful, last longer, or have other special effects. The game features two more game modes based on Survival, known as Hardcore mode and Adventure mode. Hardcore mode plays identically to Survival mode, but with the game's difficulty setting locked to "Hard" and with permadeath, forcing them to delete the world or explore it as a spectator after dying. Adventure mode was added to the game in a post-launch update, and prevents the player from directly modifying the game's world. It was designed primarily for use in custom maps, allowing map designers to let players experience it as intended. In Creative mode, players have access to an infinite number of all resources and items in the game through the inventory menu and can place or mine them instantly. Players can toggle the ability to fly freely around the game world at will, and their characters usually do not take any damage nor are affected by hunger. The game mode helps players focus on building and creating projects of any size without disturbance. Multiplayer in Minecraft enables multiple players to interact and communicate with each other on a single world. It is available through direct game-to-game multiplayer, local area network (LAN) play, local split screen (console-only), and servers (player-hosted and business-hosted). Players can run their own server by making a realm, using a host provider, hosting one themselves or connect directly to another player's game via Xbox Live, PlayStation Network or Nintendo Switch Online. Single-player worlds have LAN support, allowing players to join a world on locally interconnected computers without a server setup. Minecraft multiplayer servers are guided by server operators, who have access to server commands such as setting the time of day and teleporting players. Operators can also set up restrictions concerning which usernames or IP addresses are allowed or disallowed to enter the server. Multiplayer servers have a wide range of activities, with some servers having their own unique rules and customs. The largest and most popular server is Hypixel, which has been visited by over 14 million unique players. Player versus player combat (PvP) can be enabled to allow fighting between players. In 2013, Mojang announced Minecraft Realms, a server hosting service intended to enable players to run server multiplayer games easily and safely without having to set up their own. Unlike a standard server, only invited players can join Realms servers, and these servers do not use server addresses. Minecraft: Java Edition Realms server owners can invite up to twenty people to play on their server, with up to ten players online at a time. Minecraft Realms server owners can invite up to 3,000 people to play on their server, with up to ten players online at one time. The Minecraft: Java Edition Realms servers do not support user-made plugins, but players can play custom Minecraft maps. Minecraft Bedrock Realms servers support user-made add-ons, resource packs, behavior packs, and custom Minecraft maps. At Electronic Entertainment Expo 2016, support for cross-platform play between Windows 10, iOS, and Android platforms was added through Realms starting in June 2016, with Xbox One and Nintendo Switch support to come later in 2017, and support for virtual reality devices. On 31 July 2017, Mojang released the beta version of the update allowing cross-platform play. Nintendo Switch support for Realms was released in July 2018. The modding community consists of fans, users and third-party programmers. Using a variety of application program interfaces that have arisen over time, they have produced a wide variety of downloadable content for Minecraft, such as modifications, texture packs and custom maps. Modifications of the Minecraft code, called mods, add a variety of gameplay changes, ranging from new blocks, items, and mobs to entire arrays of mechanisms. The modding community is responsible for a substantial supply of mods from ones that enhance gameplay, such as mini-maps, waypoints, and durability counters, to ones that add to the game elements from other video games and media. While a variety of mod frameworks were independently developed by reverse engineering the code, Mojang has also enhanced vanilla Minecraft with official frameworks for modification, allowing the production of community-created resource packs, which alter certain game elements including textures and sounds. Players can also create their own "maps" (custom world save files) that often contain specific rules, challenges, puzzles and quests, and share them for others to play. Mojang added an adventure mode in August 2012 and "command blocks" in October 2012, which were created specially for custom maps in Java Edition. Data packs, introduced in version 1.13 of the Java Edition, allow further customization, including the ability to add new achievements, dimensions, functions, loot tables, predicates, recipes, structures, tags, and world generation. The Xbox 360 Edition supported downloadable content, which was available to purchase via the Xbox Games Store; these content packs usually contained additional character skins. It later received support for texture packs in its twelfth title update while introducing "mash-up packs", which combined texture packs with skin packs and changes to the game's sounds, music and user interface. The first mash-up pack (and by extension, the first texture pack) for the Xbox 360 Edition was released on 4 September 2013, and was themed after the Mass Effect franchise. Unlike Java Edition, however, the Xbox 360 Edition did not support player-made mods or custom maps. A cross-promotional resource pack based on the Super Mario franchise by Nintendo was released exclusively for the Wii U Edition worldwide on 17 May 2016, and later bundled free with the Nintendo Switch Edition at launch. Another based on Fallout was released on consoles that December, and for Windows and Mobile in April 2017. In April 2018, malware was discovered in several downloadable user-made Minecraft skins for use with the Java Edition of the game. Avast stated that nearly 50,000 accounts were infected, and when activated, the malware would attempt to reformat the user's hard drive. Mojang promptly patched the issue, and released a statement stating that "the code would not be run or read by the game itself", and would run only when the image containing the skin itself was opened. In June 2017, Mojang released the "1.1 Discovery Update" to the Pocket Edition of the game, which later became the Bedrock Edition. The update introduced the "Marketplace", a catalogue of purchasable user-generated content intended to give Minecraft creators "another way to make a living from the game". Various skins, maps, texture packs and add-ons from different creators can be bought with "Minecoins", a digital currency that is purchased with real money. Additionally, users can access specific content with a subscription service titled "Marketplace Pass". Alongside content from independent creators, the Marketplace also houses items published by Mojang and Microsoft themselves, as well as official collaborations between Minecraft and other intellectual properties. By 2022, the Marketplace had over 1.7 billion content downloads, generating over $500 million in revenue. Development Before creating Minecraft, Markus "Notch" Persson was a game developer at King, where he worked until March 2009. At King, he primarily developed browser games and learned several programming languages. During his free time, he prototyped his own games, often drawing inspiration from other titles, and was an active participant on the TIGSource forums for independent developers. One such project was "RubyDung", a base-building game inspired by Dwarf Fortress, but with an isometric, three-dimensional perspective similar to RollerCoaster Tycoon. Among the features in RubyDung that he explored was a first-person view similar to Dungeon Keeper, though he ultimately discarded this idea, feeling the graphics were too pixelated at the time. Around March 2009, Persson left King and joined jAlbum, while continuing to work on his prototypes. Infiniminer, a block-based open-ended mining game first released in April 2009, inspired Persson's vision for RubyDung's future direction. Infiniminer heavily influenced the visual style of gameplay, including bringing back the first-person mode, the "blocky" visual style and the block-building fundamentals. However, unlike Infiniminer, Persson wanted Minecraft to have RPG elements. The first public alpha build of Minecraft was released on 17 May 2009 on TIGSource. Over the years, Persson regularly released test builds that added new features, including tools, mobs, and entire new dimensions. In 2011, partly due to the game's rising popularity, Persson decided to release a full 1.0 version—a second part of the "Adventure Update"—on 18 November 2011. Shortly after, Persson stepped down from development, handing the project's lead to Jens "Jeb" Bergensten. On 15 September 2014, Microsoft, the developer behind the Microsoft Windows operating system and Xbox video game console, announced a $2.5 billion acquisition of Mojang, which included the Minecraft intellectual property. Persson had suggested the deal on Twitter, asking a corporation to buy his stake in the game after receiving criticism for enforcing terms in the game's end-user license agreement (EULA), which had been in place for the past three years. According to Persson, Mojang CEO Carl Manneh received a call from a Microsoft executive shortly after the tweet, asking if Persson was serious about a deal. Mojang was also approached by other companies including Activision Blizzard and Electronic Arts. The deal with Microsoft was arbitrated on 6 November 2014 and led to Persson becoming one of Forbes' "World's Billionaires". After 2014, Minecraft's primary versions received usually annual major updates—free to players who have purchased the game— each primarily centered around a specific theme. For instance, version 1.13, the Update Aquatic, focused on ocean-related features, while version 1.16, the Nether Update, introduced significant changes to the Nether dimension. However, in late 2024, Mojang announced a shift in their update strategy; rather than releasing large updates annually, they opted for a more frequent release schedule with smaller, incremental updates, stating, "We know that you want new Minecraft content more often." The Bedrock Edition has also received regular updates, now matching the themes of the Java Edition updates. Other versions of the game, such as various console editions and the Pocket Edition, were either merged into Bedrock or discontinued and have not received further updates. On 7 May 2019, coinciding with Minecraft's 10th anniversary, a JavaScript recreation of an old 2009 Java Edition build named Minecraft Classic was made available to play online for free. On 16 April 2020, a Bedrock Edition-exclusive beta version of Minecraft, called Minecraft RTX, was released by Nvidia. It introduced physically-based rendering, real-time path tracing, and DLSS for RTX-enabled GPUs. The public release was made available on 8 December 2020. Path tracing can only be enabled in supported worlds, which can be downloaded for free via the in-game Minecraft Marketplace, with a texture pack from Nvidia's website, or with compatible third-party texture packs. It cannot be enabled by default with any texture pack on any world. Initially, Minecraft RTX was affected by many bugs, display errors, and instability issues. On 22 March 2025, a new visual mode called Vibrant Visuals, an optional graphical overhaul similar to Minecraft RTX, was announced. It promises modern rendering features—such as dynamic shadows, screen space reflections, volumetric fog, and bloom—without the need of RTX-capable hardware. Vibrant Visuals was released as a part of the Chase the Skies update on 17 June 2025 for Bedrock Edition and is planned to release on Java Edition at a later date. Development began for the original edition of Minecraft—then known as Cave Game, and now known as the Java Edition—in May 2009,[k] and ended on 13 May, when Persson released a test video on YouTube of an early version of the game, dubbed the "Cave game tech test" or the "Cave game tech demo". The game was named Minecraft: Order of the Stone the next day, after a suggestion made by a player. "Order of the Stone" came from the webcomic The Order of the Stick, and "Minecraft" was chosen "because it's a good name". The title was later shortened to just Minecraft, omitting the subtitle. Persson completed the game's base programming over a weekend in May 2009, and private testing began on TigIRC on 16 May. The first public release followed on 17 May 2009 as a developmental version shared on the TIGSource forums. Based on feedback from forum users, Persson continued updating the game. This initial public build later became known as Classic. Further developmental phases—dubbed Survival Test, Indev, and Infdev—were released throughout 2009 and 2010. The first major update, known as Alpha, was released on 30 June 2010. At the time, Persson was still working a day job at jAlbum but later resigned to focus on Minecraft full-time as sales of the alpha version surged. Updates were distributed automatically, introducing new blocks, items, mobs, and changes to game mechanics such as water flow. With revenue generated from the game, Persson founded Mojang, a video game studio, alongside former colleagues Jakob Porser and Carl Manneh. On 11 December 2010, Persson announced that Minecraft would enter its beta phase on 20 December. He assured players that bug fixes and all pre-release updates would remain free. As development progressed, Mojang expanded, hiring additional employees to work on the project. The game officially exited beta and launched in full on 18 November 2011. On 1 December 2011, Jens "Jeb" Bergensten took full creative control over Minecraft, replacing Persson as lead designer. On 28 February 2012, Mojang announced the hiring of the developers behind Bukkit, a popular developer API for Minecraft servers, to improve Minecraft's support of server modifications. This move included Mojang taking apparent ownership of the CraftBukkit server mod, though this apparent acquisition later became controversial, and its legitimacy was questioned due to CraftBukkit's open-source nature and licensing under the GNU General Public License and Lesser General Public License. In August 2011, Minecraft: Pocket Edition was released as an early alpha for the Xperia Play via the Android Market, later expanding to other Android devices on 8 October 2011. The iOS version followed on 17 November 2011. A port was made available for Windows Phones shortly after Microsoft acquired Mojang. Unlike Java Edition, Pocket Edition initially focused on Minecraft's creative building and basic survival elements but lacked many features of the PC version. Bergensten confirmed on Twitter that the Pocket Edition was written in C++ rather than Java, as iOS does not support Java. On 10 December 2014, a port of Pocket Edition was released for Windows Phone 8.1. In July 2015, a port of the Pocket Edition to Windows 10 was released as the Windows 10 Edition, with full crossplay to other Pocket versions. In January 2017, Microsoft announced that it would no longer maintain the Windows Phone versions of Pocket Edition. On 20 September 2017, with the "Better Together Update", the Pocket Edition was ported to the Xbox One, and was renamed to the Bedrock Edition. The console versions of Minecraft debuted with the Xbox 360 edition, developed by 4J Studios and released on 9 May 2012. Announced as part of the Xbox Live Arcade NEXT promotion, this version introduced a redesigned crafting system, a new control interface, in-game tutorials, split-screen multiplayer, and online play via Xbox Live. Unlike the PC version, its worlds were finite, bordered by invisible walls. Initially, the Xbox 360 version resembled outdated PC versions but received updates to bring it closer to Java Edition before eventually being discontinued. The Xbox One version launched on 5 September 2014, featuring larger worlds and support for more players. Minecraft expanded to PlayStation platforms with PlayStation 3 and PlayStation 4 editions released on 17 December 2013 and 4 September 2014, respectively. Originally planned as a PS4 launch title, it was delayed before its eventual release. A PlayStation Vita version followed in October 2014. Like the Xbox versions, the PlayStation editions were developed by 4J Studios. Nintendo platforms received Minecraft: Wii U Edition on 17 December 2015, with a physical release in North America on 17 June 2016 and in Europe on 30 June. The Nintendo Switch version launched via the eShop on 11 May 2017. During a Nintendo Direct presentation on 13 September 2017, Nintendo announced that Minecraft: New Nintendo 3DS Edition, based on the Pocket Edition, would be available for download immediately after the livestream, and a physical copy available on a later date. The game is compatible only with the New Nintendo 3DS or New Nintendo 2DS XL systems and does not work with the original 3DS or 2DS systems. On 20 September 2017, the Better Together Update introduced Bedrock Edition across Xbox One, Windows 10, VR, and mobile platforms, enabling cross-play between these versions. Bedrock Edition later expanded to Nintendo Switch and PlayStation 4, with the latter receiving the update in December 2019, allowing cross-platform play for users with a free Xbox Live account. The Bedrock Edition released a native version for PlayStation 5 on 22 October 2024, while the Xbox Series X/S version launched on 17 June 2025. On 18 December 2018, the PlayStation 3, PlayStation Vita, Xbox 360, and Wii U versions of Minecraft received their final update and would later become known as "Legacy Console Editions". On 15 January 2019, the New Nintendo 3DS version of Minecraft received its final update, effectively becoming discontinued as well. An educational version of Minecraft, designed for use in schools, launched on 1 November 2016. It is available on Android, ChromeOS, iPadOS, iOS, MacOS, and Windows. On 20 August 2018, Mojang announced that it would bring Education Edition to iPadOS in Autumn 2018. It was released to the App Store on 6 September 2018. On 27 March 2019, it was announced that it would be operated by JD.com in China. On 26 June 2020, a public beta for the Education Edition was made available to Google Play Store compatible Chromebooks. The full game was released to the Google Play Store for Chromebooks on 7 August 2020. On 20 May 2016, China Edition (also known as My World) was announced as a localized edition for China, where it was released under a licensing agreement between NetEase and Mojang. The PC edition was released for public testing on 8 August 2017. The iOS version was released on 15 September 2017, and the Android version was released on 12 October 2017. The PC edition is based on the original Java Edition, while the iOS and Android mobile versions are based on the Bedrock Edition. The edition is free-to-play and had over 700 million registered accounts by September 2023. This version of Bedrock Edition is exclusive to Microsoft's Windows 10 and Windows 11 operating systems. The beta release for Windows 10 launched on the Windows Store on 29 July 2015. After nearly a year and a half in beta, Microsoft fully released the version on 19 December 2016. Called the "Ender Update", this release implemented new features to this version of Minecraft like world templates and add-on packs. On 7 June 2022, the Java and Bedrock Editions of Minecraft were merged into a single bundle for purchase on Windows; those who owned one version would automatically gain access to the other version. Both game versions would otherwise remain separate. Around 2011, prior to Minecraft's full release, Mojang collaborated with The Lego Group to create a Lego brick-based Minecraft game called Brickcraft. This would have modified the base Minecraft game to use Lego bricks, which meant adapting the basic 1×1 block to account for larger pieces typically used in Lego sets. Persson worked on an early version called "Project Rex Kwon Do", named after the character of the same name from the film Napoleon Dynamite. Although Lego approved the project and Mojang assigned two developers for six months, it was canceled due to the Lego Group's demands, according to Mojang's Daniel Kaplan. Lego considered buying Mojang to complete the game, but when Microsoft offered over $2 billion for the company, Lego stepped back, unsure of Minecraft's potential. On 26 June 2025, a build of Brickcraft dated 28 June 2012 was published on a community archive website Omniarchive. Initially, Markus Persson planned to support the Oculus Rift with a Minecraft port. However, after Facebook acquired Oculus in 2013, he abruptly canceled the plans, stating, "Facebook creeps me out." In 2016, a community-made mod, Minecraft VR, added VR support for Java Edition, followed by Vivecraft for HTC Vive. Later that year, Microsoft introduced official Oculus Rift support for Windows 10 Edition, leading to the discontinuation of the Minecraft VR mod due to trademark complaints. Vivecraft was endorsed by Minecraft VR contributors for its Rift support. Also available is a Gear VR version, titled Minecraft: Gear VR Edition. Windows Mixed Reality support was added in 2017. On 7 September 2020, Mojang Studios announced that the PlayStation 4 Bedrock version would receive PlayStation VR support later that month. In September 2024, the Minecraft team announced they would no longer support PlayStation VR, which received its final update in March 2025. Music and sound design Minecraft's music and sound effects were produced by German musician Daniel Rosenfeld, better known as C418. To create the sound effects for the game, Rosenfeld made extensive use of Foley techniques. On learning the processes for the game, he remarked, "Foley's an interesting thing, and I had to learn its subtleties. Early on, I wasn't that knowledgeable about it. It's a whole trial-and-error process. You just make a sound and eventually you go, 'Oh my God, that's it! Get the microphone!' There's no set way of doing anything at all." He reminisced on creating the in-game sound for grass blocks, stating "It turns out that to make grass sounds you don't actually walk on grass and record it, because grass sounds like nothing. What you want to do is get a VHS, break it apart, and just lightly touch the tape." According to Rosenfeld, his favorite sound to design for the game was the hisses of spiders. He elaborates, "I like the spiders. Recording that was a whole day of me researching what a spider sounds like. Turns out, there are spiders that make little screeching sounds, so I think I got this recording of a fire hose, put it in a sampler, and just pitched it around until it sounded like a weird spider was talking to you." Many of the sound design decisions by Rosenfeld were done accidentally or spontaneously. The creeper notably lacks any specific noises apart from a loud fuse-like sound when about to explode; Rosenfeld later recalled "That was just a complete accident by Markus and me [sic]. We just put in a placeholder sound of burning a matchstick. It seemed to work hilariously well, so we kept it." On other sounds, such as those of the zombie, Rosenfeld remarked, "I actually never wanted the zombies so scary. I intentionally made them sound comical. It's nice to hear that they work so well [...]." Rosenfeld remarked that the sound engine was "terrible" to work with, remembering "If you had two song files at once, it [the game engine] would actually crash. There were so many more weird glitches like that the guys never really fixed because they were too busy with the actual game and not the sound engine." The background music in Minecraft consists of instrumental ambient music. To compose the music of Minecraft, Rosenfeld used the package from Ableton Live, along with several additional plug-ins. Speaking on them, Rosenfeld said "They can be pretty much everything from an effect to an entire orchestra. Additionally, I've got some synthesizers that are attached to the computer. Like a Moog Voyager, Dave Smith Prophet 08 and a Virus TI." On 4 March 2011, Rosenfeld released a soundtrack titled Minecraft – Volume Alpha; it includes most of the tracks featured in Minecraft, as well as other music not featured in the game. Kirk Hamilton of Kotaku chose the music in Minecraft as one of the best video game soundtracks of 2011. On 9 November 2013, Rosenfeld released the second official soundtrack, titled Minecraft – Volume Beta, which included the music that was added in a 2013 "Music Update" for the game. A physical release of Volume Alpha, consisting of CDs, black vinyl, and limited-edition transparent green vinyl LPs, was issued by indie electronic label Ghostly International on 21 August 2015. On 14 August 2020, Ghostly released Volume Beta on CD and vinyl, with alternate color LPs and lenticular cover pressings released in limited quantities. The final update Rosenfeld worked on was 2018's 1.13 Update Aquatic. His music remained the only music in the game until 2020's "Nether Update", introducing pieces from Lena Raine. Since then, other composers have made contributions, including Kumi Tanioka, Samuel Åberg, Aaron Cherof, and Amos Roddy, with Raine remaining as the new primary composer. Ownership of all music besides Rosenfeld's independently released albums has been retained by Microsoft, with their label publishing all of the other artists' releases. Gareth Coker also composed some of the music for the game's mini games from the Legacy Console editions. Rosenfeld had stated his intent to create a third album of music for the game in a 2015 interview with Fact, and confirmed its existence in a 2017 tweet, stating that his work on the record as of then had tallied up to be longer than the previous two albums combined, which in total clocks in at over 3 hours and 18 minutes. However, due to licensing issues with Microsoft, the third volume has since not seen release. On 8 January 2021, Rosenfeld was asked in an interview with Anthony Fantano whether or not there was still a third volume of his music intended for release. Rosenfeld responded, saying, "I have something—I consider it finished—but things have become complicated, especially as Minecraft is now a big property, so I don't know." Reception Minecraft has received critical acclaim, with praise for the creative freedom it grants players in-game, as well as the ease of enabling emergent gameplay. Critics have expressed enjoyment in Minecraft's complex crafting system, commenting that it is an important aspect of the game's open-ended gameplay. Most publications were impressed by the game's "blocky" graphics, with IGN describing them as "instantly memorable". Reviewers also liked the game's adventure elements, noting that the game creates a good balance between exploring and building. The game's multiplayer feature has been generally received favorably, with IGN commenting that "adventuring is always better with friends". Jaz McDougall of PC Gamer said Minecraft is "intuitively interesting and contagiously fun, with an unparalleled scope for creativity and memorable experiences". It has been regarded as having introduced millions of children to the digital world, insofar as its basic game mechanics are logically analogous to computer commands. IGN was disappointed about the troublesome steps needed to set up multiplayer servers, calling it a "hassle". Critics also said that visual glitches occur periodically. Despite its release out of beta in 2011, GameSpot said the game had an "unfinished feel", adding that some game elements seem "incomplete or thrown together in haste". A review of the alpha version, by Scott Munro of the Daily Record, called it "already something special" and urged readers to buy it. Jim Rossignol of Rock Paper Shotgun also recommended the alpha of the game, calling it "a kind of generative 8-bit Lego Stalker". On 17 September 2010, gaming webcomic Penny Arcade began a series of comics and news posts about the addictiveness of the game. The Xbox 360 version was generally received positively by critics, but did not receive as much praise as the PC version. Although reviewers were disappointed by the lack of features such as mod support and content from the PC version, they acclaimed the port's addition of a tutorial and in-game tips and crafting recipes, saying that they make the game more user-friendly. The Xbox One Edition was one of the best received ports, being praised for its relatively large worlds. The PlayStation 3 Edition also received generally favorable reviews, being compared to the Xbox 360 Edition and praised for its well-adapted controls. The PlayStation 4 edition was the best received port to date, being praised for having 36 times larger worlds than the PlayStation 3 edition and described as nearly identical to the Xbox One edition. The PlayStation Vita Edition received generally positive reviews from critics but was noted for its technical limitations. The Wii U version received generally positive reviews from critics but was noted for a lack of GamePad integration. The 3DS version received mixed reviews, being criticized for its high price, technical issues, and lack of cross-platform play. The Nintendo Switch Edition received fairly positive reviews from critics, being praised, like other modern ports, for its relatively larger worlds. Minecraft: Pocket Edition initially received mixed reviews from critics. Although reviewers appreciated the game's intuitive controls, they were disappointed by the lack of content. The inability to collect resources and craft items, as well as the limited types of blocks and lack of hostile mobs, were especially criticized. After updates added more content, Pocket Edition started receiving more positive reviews. Reviewers complimented the controls and the graphics, but still noted a lack of content. Minecraft surpassed over a million purchases less than a month after entering its beta phase in early 2011. At the same time, the game had no publisher backing and has never been commercially advertised except through word of mouth, and various unpaid references in popular media such as the Penny Arcade webcomic. By April 2011, Persson estimated that Minecraft had made €23 million (US$33 million) in revenue, with 800,000 sales of the alpha version of the game, and over 1 million sales of the beta version. In November 2011, prior to the game's full release, Minecraft beta surpassed 16 million registered users and 4 million purchases. By March 2012, Minecraft had become the 6th best-selling PC game of all time. As of 10 October 2014[update], the game had sold 17 million copies on PC, becoming the best-selling PC game of all time. On 25 February 2014, the game reached 100 million registered users. By May 2019, 180 million copies had been sold across all platforms, making it the single best-selling video game of all time. The free-to-play Minecraft China version had over 700 million registered accounts by September 2023. By 2023, the game had sold over 300 million copies. As of April 2025, Minecraft has sold over 350 million copies. The Xbox 360 version of Minecraft became profitable within the first day of the game's release in 2012, when the game broke the Xbox Live sales records with 400,000 players online. Within a week of being on the Xbox Live Marketplace, Minecraft sold a million copies. GameSpot announced in December 2012 that Minecraft sold over 4.48 million copies since the game debuted on Xbox Live Arcade in May 2012. In 2012, Minecraft was the most purchased title on Xbox Live Arcade; it was also the fourth most played title on Xbox Live based on average unique users per day. As of 4 April 2014[update], the Xbox 360 version has sold 12 million copies. In addition, Minecraft: Pocket Edition has reached a figure of 21 million in sales. The PlayStation 3 Edition sold one million copies in five weeks. The release of the game's PlayStation Vita version boosted Minecraft sales by 79%, outselling both PS3 and PS4 debut releases and becoming the largest Minecraft launch on a PlayStation console. The PS Vita version sold 100,000 digital copies in Japan within the first two months of release, according to an announcement by SCE Japan Asia. By January 2015, 500,000 digital copies of Minecraft were sold in Japan across all PlayStation platforms, with a surge in primary school children purchasing the PS Vita version. As of 2022, the Vita version has sold over 1.65 million physical copies in Japan, making it the best-selling Vita game in the country. Minecraft helped improve Microsoft's total first-party revenue by $63 million for the 2015 second quarter. The game, including all of its versions, had over 112 million monthly active players by September 2019. On its 11th anniversary in May 2020, the company announced that Minecraft had reached over 200 million copies sold across platforms with over 126 million monthly active players. By April 2021, the number of active monthly users had climbed to 140 million. In July 2010, PC Gamer listed Minecraft as the fourth-best game to play at work. In December of that year, Good Game selected Minecraft as their choice for Best Downloadable Game of 2010, Gamasutra named it the eighth best game of the year as well as the eighth best indie game of the year, and Rock, Paper, Shotgun named it the "game of the year". Indie DB awarded the game the 2010 Indie of the Year award as chosen by voters, in addition to two out of five Editor's Choice awards for Most Innovative and Best Singleplayer Indie. It was also awarded Game of the Year by PC Gamer UK. The game was nominated for the Seumas McNally Grand Prize, Technical Excellence, and Excellence in Design awards at the March 2011 Independent Games Festival and won the Grand Prize and the community-voted Audience Award. At Game Developers Choice Awards 2011, Minecraft won awards in the categories for Best Debut Game, Best Downloadable Game and Innovation Award, winning every award for which it was nominated. It also won GameCity's video game arts award. On 5 May 2011, Minecraft was selected as one of the 80 games that would be displayed at the Smithsonian American Art Museum as part of The Art of Video Games exhibit that opened on 16 March 2012. At the 2011 Spike Video Game Awards, Minecraft won the award for Best Independent Game and was nominated in the Best PC Game category. In 2012, at the British Academy Video Games Awards, Minecraft was nominated in the GAME Award of 2011 category and Persson received The Special Award. In 2012, Minecraft XBLA was awarded a Golden Joystick Award in the Best Downloadable Game category, and a TIGA Games Industry Award in the Best Arcade Game category. In 2013, it was nominated as the family game of the year at the British Academy Video Games Awards. During the 16th Annual D.I.C.E. Awards, the Academy of Interactive Arts & Sciences nominated the Xbox 360 version of Minecraft for "Strategy/Simulation Game of the Year". Minecraft Console Edition won the award for TIGA Game Of The Year in 2014. In 2015, the game placed 6th on USgamer's The 15 Best Games Since 2000 list. In 2016, Minecraft placed 6th on Time's The 50 Best Video Games of All Time list. Minecraft was nominated for the 2013 Kids' Choice Awards for Favorite App, but lost to Temple Run. It was nominated for the 2014 Kids' Choice Awards for Favorite Video Game, but lost to Just Dance 2014. The game later won the award for the Most Addicting Game at the 2015 Kids' Choice Awards. In addition, the Java Edition was nominated for "Favorite Video Game" at the 2018 Kids' Choice Awards, while the game itself won the "Still Playing" award at the 2019 Golden Joystick Awards, as well as the "Favorite Video Game" award at the 2020 Kids' Choice Awards. Minecraft also won "Stream Game of the Year" at inaugural Streamer Awards in 2021. The game later garnered a Nickelodeon Kids' Choice Award nomination for Favorite Video Game in 2021, and won the same category in 2022 and 2023. At the Golden Joystick Awards 2025, it won the Still Playing Award - PC and Console. Minecraft has been subject to several notable controversies. In June 2014, Mojang announced that it would begin enforcing the portion of Minecraft's end-user license agreement (EULA) which prohibits servers from giving in-game advantages to players in exchange for donations or payments. Spokesperson Owen Hill stated that servers could still require players to pay a fee to access the server and could sell in-game cosmetic items. The change was supported by Persson, citing emails he received from parents of children who had spent hundreds of dollars on servers. The Minecraft community and server owners protested, arguing that the EULA's terms were more broad than Mojang was claiming, that the crackdown would force smaller servers to shut down for financial reasons, and that Mojang was suppressing competition for its own Minecraft Realms subscription service. The controversy contributed to Notch's decision to sell Mojang. In 2020, Mojang announced an eventual change to the Java Edition to require a login from a Microsoft account rather than a Mojang account, the latter of which would be sunsetted. This also required Java Edition players to create Xbox network Gamertags. Mojang defended the move to Microsoft accounts by saying that improved security could be offered, including two-factor authentication, blocking cyberbullies in chat, and improved parental controls. The community responded with intense backlash, citing various technical difficulties encountered in the process and how account migration would be mandatory, even for those who do not play on servers. As of 10 March 2022, Microsoft required that all players migrate in order to maintain access the Java Edition of Minecraft. Mojang announced a deadline of 19 September 2023 for account migration, after which all legacy Mojang accounts became inaccessible and unable to be migrated. In June 2022, Mojang added a player-reporting feature in Java Edition. Players could report other players on multiplayer servers for sending messages prohibited by the Xbox Live Code of Conduct; report categories included profane language,[l] substance abuse, hate speech, threats of violence, and nudity. If a player was found to be in violation of Xbox Community Standards, they would be banned from all servers for a specific period of time or permanently. The update containing the report feature (1.19.1) was released on 27 July 2022. Mojang received substantial backlash and protest from community members, one of the most common complaints being that banned players would be forbidden from joining any server, even private ones. Others took issue to what they saw as Microsoft increasing control over its player base and exercising censorship, leading some to start a hashtag #saveminecraft and dub the version "1.19.84", a reference to the dystopian novel Nineteen Eighty-Four. The "Mob Vote" was an online event organized by Mojang in which the Minecraft community voted between three original mob concepts; initially, the winning mob was to be implemented in a future update, while the losing mobs were scrapped, though after the first mob vote this was changed, and losing mobs would now have a chance to come to the game in the future. The first Mob Vote was held during Minecon Earth 2017 and became an annual event starting with Minecraft Live 2020. The Mob Vote was often criticized for forcing players to choose one mob instead of implementing all three, causing divisions and flaming within the community, and potentially allowing internet bots and Minecraft content creators with large fanbases to conduct vote brigading. The Mob Vote was also blamed for a perceived lack of new content added to Minecraft since Microsoft's acquisition of Mojang in 2014. The 2023 Mob Vote featured three passive mobs—the crab, the penguin, and the armadillo—with voting scheduled to start on 13 October. In response, a Change.org petition was created on 6 October, demanding that Mojang eliminate the Mob Vote and instead implement all three mobs going forward. The petition received approximately 445,000 signatures by 13 October and was joined by calls to boycott the Mob Vote, as well as a partially tongue-in-cheek "revolutionary" propaganda campaign in which sympathizers created anti-Mojang and pro-boycott posters in the vein of real 20th century propaganda posters. Mojang did not release an official response to the boycott, and the Mob Vote otherwise proceeded normally, with the armadillo winning the vote. In September 2024, as part of a blog post detailing their future plans for Minecraft's development, Mojang announced the Mob Vote would be retired. Cultural impact In September 2019, The Guardian classified Minecraft as the best video game of the 21st century to date, and in November 2019, Polygon called it the "most important game of the decade" in its 2010s "decade in review". In June 2020, Minecraft was inducted into the World Video Game Hall of Fame. Minecraft is recognized as one of the first successful games to use an early access model to draw in sales prior to its full release version to help fund development. As Minecraft helped to bolster indie game development in the early 2010s, it also helped to popularize the use of the early access model in indie game development. Social media sites such as YouTube, Facebook, and Reddit have played a significant role in popularizing Minecraft. Research conducted by the Annenberg School for Communication at the University of Pennsylvania showed that one-third of Minecraft players learned about the game via Internet videos. In 2010, Minecraft-related videos began to gain influence on YouTube, often made by commentators. The videos usually contain screen-capture footage of the game and voice-overs. Common coverage in the videos includes creations made by players, walkthroughs of various tasks, and parodies of works in popular culture. By May 2012, over four million Minecraft-related YouTube videos had been uploaded. The game would go on to be a prominent fixture within YouTube's gaming scene during the entire 2010s; in 2014, it was the second-most searched term on the entire platform. By 2018, it was still YouTube's biggest game globally. Some popular commentators have received employment at Machinima, a now-defunct gaming video company that owned a highly watched entertainment channel on YouTube. The Yogscast is a British company that regularly produces Minecraft videos; their YouTube channel has attained billions of views, and their panel at Minecon 2011 had the highest attendance. Another well-known YouTube personality is Jordan Maron, known online as CaptainSparklez, who has also created many Minecraft music parodies, including "Revenge", a parody of Usher's "DJ Got Us Fallin' in Love". Minecraft's popularity on YouTube was described by Polygon as quietly dominant, although in 2019, thanks in part to PewDiePie's playthroughs of the game, Minecraft experienced a visible uptick in popularity on the platform. Longer-running series include Far Lands or Bust, dedicated to reaching the obsolete "Far Lands" glitch by foot on an older version of the game. YouTube announced that on 14 December 2021 that the total amount of Minecraft-related views on the website had exceeded one trillion. Minecraft has been referenced by other video games, such as Torchlight II, Team Fortress 2, Borderlands 2, Choplifter HD, Super Meat Boy, The Elder Scrolls V: Skyrim, The Binding of Isaac, The Stanley Parable, and FTL: Faster Than Light. Minecraft is officially represented in downloadable content for the crossover fighter Super Smash Bros. Ultimate, with Steve as a playable character with a moveset including references to building, crafting, and redstone, alongside an Overworld-themed stage. It was also referenced by electronic music artist Deadmau5 in his performances. The game is also referenced heavily in "Informative Murder Porn", the second episode of the seventeenth season of the animated television series South Park. In 2025, A Minecraft Movie was released. It made $313 million in the box office in the first week, a record-breaking opening for a video game adaptation. Minecraft has been noted as a cultural touchstone for Generation Z, as many of the generation's members played the game at a young age. The possible applications of Minecraft have been discussed extensively, especially in the fields of computer-aided design (CAD) and education. In a panel at Minecon 2011, a Swedish developer discussed the possibility of using the game to redesign public buildings and parks, stating that rendering using Minecraft was much more user-friendly for the community, making it easier to envision the functionality of new buildings and parks. In 2012, a member of the Human Dynamics group at the MIT Media Lab, Cody Sumter, said: "Notch hasn't just built a game. He's tricked 40 million people into learning to use a CAD program." Various software has been developed to allow virtual designs to be printed using professional 3D printers or personal printers such as MakerBot and RepRap. In September 2012, Mojang began the Block by Block project in cooperation with UN Habitat to create real-world environments in Minecraft. The project allows young people who live in those environments to participate in designing the changes they would like to see. Using Minecraft, the community has helped reconstruct the areas of concern, and citizens are invited to enter the Minecraft servers and modify their own neighborhood. Carl Manneh, Mojang's managing director, called the game "the perfect tool to facilitate this process", adding "The three-year partnership will support UN-Habitat's Sustainable Urban Development Network to upgrade 300 public spaces by 2016." Mojang signed Minecraft building community, FyreUK, to help render the environments into Minecraft. The first pilot project began in Kibera, one of Nairobi's informal settlements and is in the planning phase. The Block by Block project is based on an earlier initiative started in October 2011, Mina Kvarter (My Block), which gave young people in Swedish communities a tool to visualize how they wanted to change their part of town. According to Manneh, the project was a helpful way to visualize urban planning ideas without necessarily having a training in architecture. The ideas presented by the citizens were a template for political decisions. In April 2014, the Danish Geodata Agency generated all of Denmark in fullscale in Minecraft based on their own geodata. This is possible because Denmark is one of the flattest countries with the highest point at 171 meters (ranking as the country with the 30th smallest elevation span), where the limit in default Minecraft was around 192 meters above in-game sea level when the project was completed. Taking advantage of the game's accessibility where other websites are censored, the non-governmental organization Reporters Without Borders has used an open Minecraft server to create the Uncensored Library, a repository within the game of journalism by authors from countries (including Egypt, Mexico, Russia, Saudi Arabia and Vietnam) who have been censored and arrested, such as Jamal Khashoggi. The neoclassical virtual building was created over about 250 hours by an international team of 24 people. Despite its unpredictable nature, Minecraft speedrunning, where players time themselves from spawning into a new world to reaching The End and defeating the Ender Dragon boss, is popular. Some speedrunners use a combination of mods, external programs, and debug menus, while other runners play the game in a more vanilla or more consistency-oriented way. Minecraft has been used in educational settings through initiatives such as MinecraftEdu, founded in 2011 to make the game affordable and accessible for schools in collaboration with Mojang. MinecraftEdu provided features allowing teachers to monitor student progress, including screenshot submissions as evidence of lesson completion, and by 2012 reported that approximately 250,000 students worldwide had access to the platform. Mojang also developed Minecraft: Education Edition with pre-built lesson plans for up to 30 students in a closed environment. Educators have used Minecraft to teach subjects such as history, language arts, and science through custom-built environments, including reconstructions of historical landmarks and large-scale models of biological structures such as animal cells. The introduction of redstone blocks enabled the construction of functional virtual machines such as a hard drive and an 8-bit computer. Mods have been created to use these mechanics for teaching programming. In 2014, the British Museum announced a project to reproduce its building and exhibits in Minecraft in collaboration with the public. Microsoft and Code.org have offered Minecraft-based tutorials and activities designed to teach programming, reporting by 2018 that more than 85 million children had used their resources. In 2025, the Musée de Minéralogie in Paris held a temporary exhibition titled "Minerals in Minecraft." Following the initial surge in popularity of Minecraft in 2010, other video games were criticised for having various similarities to Minecraft, and some were described as being "clones", often due to a direct inspiration from Minecraft, or a superficial similarity. Examples include Ace of Spades, CastleMiner, CraftWorld, FortressCraft, Terraria, BlockWorld 3D, Total Miner, and Luanti (formerly Minetest). David Frampton, designer of The Blockheads, reported that one failure of his 2D game was the "low resolution pixel art" that too closely resembled the art in Minecraft, which resulted in "some resistance" from fans. A homebrew adaptation of the alpha version of Minecraft for the Nintendo DS, titled DScraft, has been released; it has been noted for its similarity to the original game considering the technical limitations of the system. In response to Microsoft's acquisition of Mojang and their Minecraft IP, various developers announced further clone titles developed specifically for Nintendo's consoles, as they were the only major platforms not to officially receive Minecraft at the time. These clone titles include UCraft (Nexis Games), Cube Life: Island Survival (Cypronia), Discovery (Noowanda), Battleminer (Wobbly Tooth Games), Cube Creator 3D (Big John Games), and Stone Shire (Finger Gun Games). Despite this, the fears of fans were unfounded, with official Minecraft releases on Nintendo consoles eventually resuming. Markus Persson made another similar game, Minicraft, for a Ludum Dare competition in 2011. In 2025, Persson announced through a poll on his X account that he was considering developing a spiritual successor to Minecraft. He later clarified that he was "100% serious", and that he had "basically announced Minecraft 2". Within days, however, Persson cancelled the plans after speaking to his team. In November 2024, artificial intelligence companies Decart and Etched released Oasis, an artificially generated version of Minecraft, as a proof of concept. Every in-game element is completely AI-generated in real time and the model does not store world data, leading to "hallucinations" such as items and blocks appearing that were not there before. In January 2026, indie game developer Unomelon announced that their voxel sandbox game Allumeria would be playable in Steam Next Fest that year. On 10 February, Mojang issued a DMCA takedown of Allumeria on Steam through Valve, alleging the game was infringing on Minecraft's copyright. Some reports suggested that the takedown may have used an automatic AI copyright claiming service. The DMCA was later withdrawn. Minecon was an annual official fan convention dedicated to Minecraft. The first full Minecon was held in November 2011 at the Mandalay Bay Hotel and Casino in Las Vegas. The event included the official launch of Minecraft; keynote speeches, including one by Persson; building and costume contests; Minecraft-themed breakout classes; exhibits by leading gaming and Minecraft-related companies; commemorative merchandise; and autograph and picture times with Mojang employees and well-known contributors from the Minecraft community. In 2016, Minecon was held in-person for the last time, with the following years featuring annual "Minecon Earth" livestreams on minecraft.net and YouTube instead. These livestreams, later rebranded to "Minecraft Live", included the mob/biome votes, and announcements of new game updates. In 2025, "Minecraft Live" became a biannual event as part of Minecraft's changing update schedule.[citation needed] Notes References External links |
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Contents Elon Musk Elon Reeve Musk (/ˈiːlɒn/ EE-lon; born June 28, 1971) is a businessman and entrepreneur known for his leadership of Tesla, SpaceX, Twitter, and xAI. Musk has been the wealthiest person in the world since 2025; as of February 2026,[update] Forbes estimates his net worth to be around US$852 billion. Born into a wealthy family in Pretoria, South Africa, Musk emigrated in 1989 to Canada; he has Canadian citizenship since his mother was born there. He received bachelor's degrees in 1997 from the University of Pennsylvania before moving to California to pursue business ventures. In 1995, Musk co-founded the software company Zip2. Following its sale in 1999, he co-founded X.com, an online payment company that later merged to form PayPal, which was acquired by eBay in 2002. Musk also became an American citizen in 2002. In 2002, Musk founded the space technology company SpaceX, becoming its CEO and chief engineer; the company has since led innovations in reusable rockets and commercial spaceflight. Musk joined the automaker Tesla as an early investor in 2004 and became its CEO and product architect in 2008; it has since become a leader in electric vehicles. In 2015, he co-founded OpenAI to advance artificial intelligence (AI) research, but later left; growing discontent with the organization's direction and their leadership in the AI boom in the 2020s led him to establish xAI, which became a subsidiary of SpaceX in 2026. In 2022, he acquired the social network Twitter, implementing significant changes, and rebranding it as X in 2023. His other businesses include the neurotechnology company Neuralink, which he co-founded in 2016, and the tunneling company the Boring Company, which he founded in 2017. In November 2025, a Tesla pay package worth $1 trillion for Musk was approved, which he is to receive over 10 years if he meets specific goals. Musk was the largest donor in the 2024 U.S. presidential election, where he supported Donald Trump. After Trump was inaugurated as president in early 2025, Musk served as Senior Advisor to the President and as the de facto head of the Department of Government Efficiency (DOGE). After a public feud with Trump, Musk left the Trump administration and returned to managing his companies. Musk is a supporter of global far-right figures, causes, and political parties. His political activities, views, and statements have made him a polarizing figure. Musk has been criticized for COVID-19 misinformation, promoting conspiracy theories, and affirming antisemitic, racist, and transphobic comments. His acquisition of Twitter was controversial due to a subsequent increase in hate speech and the spread of misinformation on the service, following his pledge to decrease censorship. His role in the second Trump administration attracted public backlash, particularly in response to DOGE. The emails he sent to Jeffrey Epstein are included in the Epstein files, which were published between 2025–26 and became a topic of worldwide debate. Early life Elon Reeve Musk was born on June 28, 1971, in Pretoria, South Africa's administrative capital. He is of British and Pennsylvania Dutch ancestry. His mother, Maye (née Haldeman), is a model and dietitian born in Saskatchewan, Canada, and raised in South Africa. Musk therefore holds both South African and Canadian citizenship from birth. His father, Errol Musk, is a South African electromechanical engineer, pilot, sailor, consultant, emerald dealer, and property developer, who partly owned a rental lodge at Timbavati Private Nature Reserve. His maternal grandfather, Joshua N. Haldeman, who died in a plane crash when Elon was a toddler, was an American-born Canadian chiropractor, aviator and political activist in the technocracy movement who moved to South Africa in 1950. Elon has a younger brother, Kimbal, a younger sister, Tosca, and four paternal half-siblings. Musk was baptized as a child in the Anglican Church of Southern Africa. Despite both Elon and Errol previously stating that Errol was a part owner of a Zambian emerald mine, in 2023, Errol recounted that the deal he made was to receive "a portion of the emeralds produced at three small mines". Errol was elected to the Pretoria City Council as a representative of the anti-apartheid Progressive Party and has said that his children shared their father's dislike of apartheid. After his parents divorced in 1979, Elon, aged around 9, chose to live with his father because Errol Musk had an Encyclopædia Britannica and a computer. Elon later regretted his decision and became estranged from his father. Elon has recounted trips to a wilderness school that he described as a "paramilitary Lord of the Flies" where "bullying was a virtue" and children were encouraged to fight over rations. In one incident, after an altercation with a fellow pupil, Elon was thrown down concrete steps and beaten severely, leading to him being hospitalized for his injuries. Elon described his father berating him after he was discharged from the hospital. Errol denied berating Elon and claimed, "The [other] boy had just lost his father to suicide, and Elon had called him stupid. Elon had a tendency to call people stupid. How could I possibly blame that child?" Elon was an enthusiastic reader of books, and had attributed his success in part to having read The Lord of the Rings, the Foundation series, and The Hitchhiker's Guide to the Galaxy. At age ten, he developed an interest in computing and video games, teaching himself how to program from the VIC-20 user manual. At age twelve, Elon sold his BASIC-based game Blastar to PC and Office Technology magazine for approximately $500 (equivalent to $1,600 in 2025). Musk attended Waterkloof House Preparatory School, Bryanston High School, and then Pretoria Boys High School, where he graduated. Musk was a decent but unexceptional student, earning a 61/100 in Afrikaans and a B on his senior math certification. Musk applied for a Canadian passport through his Canadian-born mother to avoid South Africa's mandatory military service, which would have forced him to participate in the apartheid regime, as well as to ease his path to immigration to the United States. While waiting for his application to be processed, he attended the University of Pretoria for five months. Musk arrived in Canada in June 1989, connected with a second cousin in Saskatchewan, and worked odd jobs, including at a farm and a lumber mill. In 1990, he entered Queen's University in Kingston, Ontario. Two years later, he transferred to the University of Pennsylvania, where he studied until 1995. Although Musk has said that he earned his degrees in 1995, the University of Pennsylvania did not award them until 1997 – a Bachelor of Arts in physics and a Bachelor of Science in economics from the university's Wharton School. He reportedly hosted large, ticketed house parties to help pay for tuition, and wrote a business plan for an electronic book-scanning service similar to Google Books. In 1994, Musk held two internships in Silicon Valley: one at energy storage startup Pinnacle Research Institute, which investigated electrolytic supercapacitors for energy storage, and another at Palo Alto–based startup Rocket Science Games. In 1995, he was accepted to a graduate program in materials science at Stanford University, but did not enroll. Musk decided to join the Internet boom of the 1990s, applying for a job at Netscape, to which he reportedly never received a response. The Washington Post reported that Musk lacked legal authorization to remain and work in the United States after failing to enroll at Stanford. In response, Musk said he was allowed to work at that time and that his student visa transitioned to an H1-B. According to numerous former business associates and shareholders, Musk said he was on a student visa at the time. Business career In 1995, Musk, his brother Kimbal, and Greg Kouri founded the web software company Zip2 with funding from a group of angel investors. They housed the venture at a small rented office in Palo Alto. Replying to Rolling Stone, Musk denounced the notion that they started their company with funds borrowed from Errol Musk, but in a tweet, he recognized that his father contributed 10% of a later funding round. The company developed and marketed an Internet city guide for the newspaper publishing industry, with maps, directions, and yellow pages. According to Musk, "The website was up during the day and I was coding it at night, seven days a week, all the time." To impress investors, Musk built a large plastic structure around a standard computer to create the impression that Zip2 was powered by a small supercomputer. The Musk brothers obtained contracts with The New York Times and the Chicago Tribune, and persuaded the board of directors to abandon plans for a merger with CitySearch. Musk's attempts to become CEO were thwarted by the board. Compaq acquired Zip2 for $307 million in cash in February 1999 (equivalent to $590,000,000 in 2025), and Musk received $22 million (equivalent to $43,000,000 in 2025) for his 7-percent share. In 1999, Musk co-founded X.com, an online financial services and e-mail payment company. The startup was one of the first federally insured online banks, and, in its initial months of operation, over 200,000 customers joined the service. The company's investors regarded Musk as inexperienced and replaced him with Intuit CEO Bill Harris by the end of the year. The following year, X.com merged with online bank Confinity to avoid competition. Founded by Max Levchin and Peter Thiel, Confinity had its own money-transfer service, PayPal, which was more popular than X.com's service. Within the merged company, Musk returned as CEO. Musk's preference for Microsoft software over Unix created a rift in the company and caused Thiel to resign. Due to resulting technological issues and lack of a cohesive business model, the board ousted Musk and replaced him with Thiel in 2000.[b] Under Thiel, the company focused on the PayPal service and was renamed PayPal in 2001. In 2002, PayPal was acquired by eBay for $1.5 billion (equivalent to $2,700,000,000 in 2025) in stock, of which Musk—the largest shareholder with 11.72% of shares—received $175.8 million (equivalent to $320,000,000 in 2025). In 2017, Musk purchased the domain X.com from PayPal for an undisclosed amount, stating that it had sentimental value. In 2001, Musk became involved with the nonprofit Mars Society and discussed funding plans to place a growth-chamber for plants on Mars. Seeking a way to launch the greenhouse payloads into space, Musk made two unsuccessful trips to Moscow to purchase intercontinental ballistic missiles (ICBMs) from Russian companies NPO Lavochkin and Kosmotras. Musk instead decided to start a company to build affordable rockets. With $100 million of his early fortune, (equivalent to $180,000,000 in 2025) Musk founded SpaceX in May 2002 and became the company's CEO and Chief Engineer. SpaceX attempted its first launch of the Falcon 1 rocket in 2006. Although the rocket failed to reach Earth orbit, it was awarded a Commercial Orbital Transportation Services program contract from NASA, then led by Mike Griffin. After two more failed attempts that nearly caused Musk to go bankrupt, SpaceX succeeded in launching the Falcon 1 into orbit in 2008. Later that year, SpaceX received a $1.6 billion NASA contract (equivalent to $2,400,000,000 in 2025) for Falcon 9-launched Dragon spacecraft flights to the International Space Station (ISS), replacing the Space Shuttle after its 2011 retirement. In 2012, the Dragon vehicle docked with the ISS, a first for a commercial spacecraft. Working towards its goal of reusable rockets, in 2015 SpaceX successfully landed the first stage of a Falcon 9 on a land platform. Later landings were achieved on autonomous spaceport drone ships, an ocean-based recovery platform. In 2018, SpaceX launched the Falcon Heavy; the inaugural mission carried Musk's personal Tesla Roadster as a dummy payload. Since 2019, SpaceX has been developing Starship, a reusable, super heavy-lift launch vehicle intended to replace the Falcon 9 and Falcon Heavy. In 2020, SpaceX launched its first crewed flight, the Demo-2, becoming the first private company to place astronauts into orbit and dock a crewed spacecraft with the ISS. In 2024, NASA awarded SpaceX an $843 million (equivalent to $865,000,000 in 2025) contract to build a spacecraft that NASA will use to deorbit the ISS at the end of its lifespan. In 2015, SpaceX began development of the Starlink constellation of low Earth orbit satellites to provide satellite Internet access. After the launch of prototype satellites in 2018, the first large constellation was deployed in May 2019. As of May 2025[update], over 7,600 Starlink satellites are operational, comprising 65% of all operational Earth satellites. The total cost of the decade-long project to design, build, and deploy the constellation was estimated by SpaceX in 2020 to be $10 billion (equivalent to $12,000,000,000 in 2025).[c] During the Russian invasion of Ukraine, Musk provided free Starlink service to Ukraine, permitting Internet access and communication at a yearly cost to SpaceX of $400 million (equivalent to $440,000,000 in 2025). However, Musk refused to block Russian state media on Starlink. In 2023, Musk denied Ukraine's request to activate Starlink over Crimea to aid an attack against the Russian navy, citing fears of a nuclear response. Tesla, Inc., originally Tesla Motors, was incorporated in July 2003 by Martin Eberhard and Marc Tarpenning. Both men played active roles in the company's early development prior to Musk's involvement. Musk led the Series A round of investment in February 2004; he invested $6.35 million (equivalent to $11,000,000 in 2025), became the majority shareholder, and joined Tesla's board of directors as chairman. Musk took an active role within the company and oversaw Roadster product design, but was not deeply involved in day-to-day business operations. Following a series of escalating conflicts in 2007 and the 2008 financial crisis, Eberhard was ousted from the firm.[page needed] Musk assumed leadership of the company as CEO and product architect in 2008. A 2009 lawsuit settlement with Eberhard designated Musk as a Tesla co-founder, along with Tarpenning and two others. Tesla began delivery of the Roadster, an electric sports car, in 2008. With sales of about 2,500 vehicles, it was the first mass production all-electric car to use lithium-ion battery cells. Under Musk, Tesla has since launched several well-selling electric vehicles, including the four-door sedan Model S (2012), the crossover Model X (2015), the mass-market sedan Model 3 (2017), the crossover Model Y (2020), and the pickup truck Cybertruck (2023). In May 2020, Musk resigned as chairman of the board as part of the settlement of a lawsuit from the SEC over him tweeting that funding had been "secured" for potentially taking Tesla private. The company has also constructed multiple lithium-ion battery and electric vehicle factories, called Gigafactories. Since its initial public offering in 2010, Tesla stock has risen significantly; it became the most valuable carmaker in summer 2020, and it entered the S&P 500 later that year. In October 2021, it reached a market capitalization of $1 trillion (equivalent to $1,200,000,000,000 in 2025), the sixth company in U.S. history to do so. Musk provided the initial concept and financial capital for SolarCity, which his cousins Lyndon and Peter Rive founded in 2006. By 2013, SolarCity was the second largest provider of solar power systems in the United States. In 2014, Musk promoted the idea of SolarCity building an advanced production facility in Buffalo, New York, triple the size of the largest solar plant in the United States. Construction of the factory started in 2014 and was completed in 2017. It operated as a joint venture with Panasonic until early 2020. Tesla acquired SolarCity for $2 billion in 2016 (equivalent to $2,700,000,000 in 2025) and merged it with its battery unit to create Tesla Energy. The deal's announcement resulted in a more than 10% drop in Tesla's stock price; at the time, SolarCity was facing liquidity issues. Multiple shareholder groups filed a lawsuit against Musk and Tesla's directors, stating that the purchase of SolarCity was done solely to benefit Musk and came at the expense of Tesla and its shareholders. Tesla directors settled the lawsuit in January 2020, leaving Musk the sole remaining defendant. Two years later, the court ruled in Musk's favor. In 2016, Musk co-founded Neuralink, a neurotechnology startup, with an investment of $100 million. Neuralink aims to integrate the human brain with artificial intelligence (AI) by creating devices that are embedded in the brain. Such technology could enhance memory or allow the devices to communicate with software. The company also hopes to develop devices to treat neurological conditions like spinal cord injuries. In 2022, Neuralink announced that clinical trials would begin by the end of the year. In September 2023, the Food and Drug Administration approved Neuralink to initiate six-year human trials. Neuralink has conducted animal testing on macaques at the University of California, Davis. In 2021, the company released a video in which a macaque played the video game Pong via a Neuralink implant. The company's animal trials—which have caused the deaths of some monkeys—have led to claims of animal cruelty. The Physicians Committee for Responsible Medicine has alleged that Neuralink violated the Animal Welfare Act. Employees have complained that pressure from Musk to accelerate development has led to botched experiments and unnecessary animal deaths. In 2022, a federal probe was launched into possible animal welfare violations by Neuralink.[needs update] In 2017, Musk founded the Boring Company to construct tunnels; he also revealed plans for specialized, underground, high-occupancy vehicles that could travel up to 150 miles per hour (240 km/h) and thus circumvent above-ground traffic in major cities. Early in 2017, the company began discussions with regulatory bodies and initiated construction of a 30-foot (9.1 m) wide, 50-foot (15 m) long, and 15-foot (4.6 m) deep "test trench" on the premises of SpaceX's offices, as that required no permits. The Los Angeles tunnel, less than two miles (3.2 km) in length, debuted to journalists in 2018. It used Tesla Model Xs and was reported to be a rough ride while traveling at suboptimal speeds. Two tunnel projects announced in 2018, in Chicago and West Los Angeles, have been canceled. A tunnel beneath the Las Vegas Convention Center was completed in early 2021. Local officials have approved further expansions of the tunnel system. April 14, 2022 In early 2017, Musk expressed interest in buying Twitter and had questioned the platform's commitment to freedom of speech. By 2022, Musk had reached 9.2% stake in the company, making him the largest shareholder.[d] Musk later agreed to a deal that would appoint him to Twitter's board of directors and prohibit him from acquiring more than 14.9% of the company. Days later, Musk made a $43 billion offer to buy Twitter. By the end of April Musk had successfully concluded his bid for approximately $44 billion. This included approximately $12.5 billion in loans and $21 billion in equity financing. Having backtracked on his initial decision, Musk bought the company on October 27, 2022. Immediately after the acquisition, Musk fired several top Twitter executives including CEO Parag Agrawal; Musk became the CEO instead. Under Elon Musk, Twitter instituted monthly subscriptions for a "blue check", and laid off a significant portion of the company's staff. Musk lessened content moderation and hate speech also increased on the platform after his takeover. In late 2022, Musk released internal documents relating to Twitter's moderation of Hunter Biden's laptop controversy in the lead-up to the 2020 presidential election. Musk also promised to step down as CEO after a Twitter poll, and five months later, Musk stepped down as CEO and transitioned his role to executive chairman and chief technology officer (CTO). Despite Musk stepping down as CEO, X continues to struggle with challenges such as viral misinformation, hate speech, and antisemitism controversies. Musk has been accused of trying to silence some of his critics such as Twitch streamer Asmongold, who criticized him during one of his streams. Musk has been accused of removing their accounts' blue checkmarks, which hinders visibility and is considered a form of shadow banning, or suspending their accounts without justification. Other activities In August 2013, Musk announced plans for a version of a vactrain, and assigned engineers from SpaceX and Tesla to design a transport system between Greater Los Angeles and the San Francisco Bay Area, at an estimated cost of $6 billion. Later that year, Musk unveiled the concept, dubbed the Hyperloop, intended to make travel cheaper than any other mode of transport for such long distances. In December 2015, Musk co-founded OpenAI, a not-for-profit artificial intelligence (AI) research company aiming to develop artificial general intelligence, intended to be safe and beneficial to humanity. Musk pledged $1 billion of funding to the company, and initially gave $50 million. In 2018, Musk left the OpenAI board. Since 2018, OpenAI has made significant advances in machine learning. In July 2023, Musk launched the artificial intelligence company xAI, which aims to develop a generative AI program that competes with existing offerings like OpenAI's ChatGPT. Musk obtained funding from investors in SpaceX and Tesla, and xAI hired engineers from Google and OpenAI. December 16, 2022 Musk uses a private jet owned by Falcon Landing LLC, a SpaceX-linked company, and acquired a second jet in August 2020. His heavy use of the jets and the consequent fossil fuel usage have received criticism. Musk's flight usage is tracked on social media through ElonJet. In December 2022, Musk banned the ElonJet account on Twitter, and made temporary bans on the accounts of journalists that posted stories regarding the incident, including Donie O'Sullivan, Keith Olbermann, and journalists from The New York Times, The Washington Post, CNN, and The Intercept. In October 2025, Musk's company xAI launched Grokipedia, an AI-generated online encyclopedia that he promoted as an alternative to Wikipedia. Articles on Grokipedia are generated and reviewed by xAI's Grok chatbot. Media coverage and academic analysis described Grokipedia as frequently reusing Wikipedia content but framing contested political and social topics in line with Musk's own views and right-wing narratives. A study by Cornell University researchers and NBC News stated that Grokipedia cites sources that are blacklisted or considered "generally unreliable" on Wikipedia, for example, the conspiracy site Infowars and the neo-Nazi forum Stormfront. Wired, The Guardian and Time criticized Grokipedia for factual errors and for presenting Musk himself in unusually positive terms while downplaying controversies. Politics Musk is an outlier among business leaders who typically avoid partisan political advocacy. Musk was a registered independent voter when he lived in California. Historically, he has donated to both Democrats and Republicans, many of whom serve in states in which he has a vested interest. Since 2022, his political contributions have mostly supported Republicans, with his first vote for a Republican going to Mayra Flores in the 2022 Texas's 34th congressional district special election. In 2024, he started supporting international far-right political parties, activists, and causes, and has shared misinformation and numerous conspiracy theories. Since 2024, his views have been generally described as right-wing. Musk supported Barack Obama in 2008 and 2012, Hillary Clinton in 2016, Joe Biden in 2020, and Donald Trump in 2024. In the 2020 Democratic Party presidential primaries, Musk endorsed candidate Andrew Yang and expressed support for Yang's proposed universal basic income, and endorsed Kanye West's 2020 presidential campaign. In 2021, Musk publicly expressed opposition to the Build Back Better Act, a $3.5 trillion legislative package endorsed by Joe Biden that ultimately failed to pass due to unanimous opposition from congressional Republicans and several Democrats. In 2022, gave over $50 million to Citizens for Sanity, a conservative political action committee. In 2023, he supported Republican Ron DeSantis for the 2024 U.S. presidential election, giving $10 million to his campaign, and hosted DeSantis's campaign announcement on a Twitter Spaces event. From June 2023 to January 2024, Musk hosted a bipartisan set of X Spaces with Republican and Democratic candidates, including Robert F. Kennedy Jr., Vivek Ramaswamy, and Dean Phillips. In October 2025, former vice-president Kamala Harris commented that it was a mistake from the Democratic side to not invite Musk to a White House electric vehicle event organized in August 2021 and featuring executives from General Motors, Ford and Stellantis, despite Tesla being "the major American manufacturer of extraordinary innovation in this space." Fortune remarked that this was a nod to United Auto Workers and organized labor. Harris said presidents should put aside political loyalties when it came to recognizing innovation, and guessed that the non-invitation impacted Musk's perspective. Fortune noted that, at the time, Musk said, "Yeah, seems odd that Tesla wasn't invited." A month later, he criticized Biden as "not the friendliest administration." Jacob Silverman, author of the book Gilded Rage: Elon Musk and the Radicalization of Silicon Valley, said that the tech industry represented by Musk, Thiel, Andreessen and other capitalists, actually flourished under Biden, but the tech leaders chose Trump for their common ground on cultural issues. By early 2024, Musk had become a vocal and financial supporter of Donald Trump. In July 2024, minutes after the attempted assassination of Donald Trump, Musk endorsed him for president saying; "I fully endorse President Trump and hope for his rapid recovery." During the presidential campaign, Musk joined Trump on stage at a campaign rally, and during the campaign promoted conspiracy theories and falsehoods about Democrats, election fraud and immigration, in support of Trump. Musk was the largest individual donor of the 2024 election. In 2025, Musk contributed $19 million to the Wisconsin Supreme Court race, hoping to influence the state's future redistricting efforts and its regulations governing car manufacturers and dealers. In 2023, Musk said he shunned the World Economic Forum because it was boring. The organization commented that they had not invited him since 2015. He has participated in Dialog, dubbed "Tech Bilderberg" and organized by Peter Thiel and Auren Hoffman, though. Musk's international political actions and comments have come under increasing scrutiny and criticism, especially from the governments and leaders of France, Germany, Norway, Spain and the United Kingdom, particularly due to his position in the U.S. government as well as ownership of X. An NBC News analysis found he had boosted far-right political movements to cut immigration and curtail regulation of business in at least 18 countries on six continents since 2023. During his speech after the second inauguration of Donald Trump, Musk twice made a gesture interpreted by many as a Nazi or a fascist Roman salute.[e] He thumped his right hand over his heart, fingers spread wide, and then extended his right arm out, emphatically, at an upward angle, palm down and fingers together. He then repeated the gesture to the crowd behind him. As he finished the gestures, he said to the crowd, "My heart goes out to you. It is thanks to you that the future of civilization is assured." It was widely condemned as an intentional Nazi salute in Germany, where making such gestures is illegal. The Anti-Defamation League said it was not a Nazi salute, but other Jewish organizations disagreed and condemned the salute. American public opinion was divided on partisan lines as to whether it was a fascist salute. Musk dismissed the accusations of Nazi sympathies, deriding them as "dirty tricks" and a "tired" attack. Neo-Nazi and white supremacist groups celebrated it as a Nazi salute. Multiple European political parties demanded that Musk be banned from entering their countries. The concept of DOGE emerged in a discussion between Musk and Donald Trump, and in August 2024, Trump committed to giving Musk an advisory role, with Musk accepting the offer. In November and December 2024, Musk suggested that the organization could help to cut the U.S. federal budget, consolidate the number of federal agencies, and eliminate the Consumer Financial Protection Bureau, and that its final stage would be "deleting itself". In January 2025, the organization was created by executive order, and Musk was designated a "special government employee". Musk led the organization and was a senior advisor to the president, although his official role is not clear. In sworn statement during a lawsuit, the director of the White House Office of Administration stated that Musk "is not an employee of the U.S. DOGE Service or U.S. DOGE Service Temporary Organization", "is not the U.S. DOGE Service administrator", and has "no actual or formal authority to make government decisions himself". Trump said two days later that he had put Musk in charge of DOGE. A federal judge has ruled that Musk acted as the de facto leader of DOGE. Musk's role in the second Trump administration, particularly in response to DOGE, has attracted public backlash. He was criticized for his treatment of federal government employees, including his influence over the mass layoffs of the federal workforce. He has prioritized secrecy within the organization and has accused others of violating privacy laws. A Senate report alleged that Musk could avoid up to $2 billion in legal liability as a result of DOGE's actions. In May 2025, Bill Gates accused Musk of "killing the world's poorest children" through his cuts to USAID, which modeling by Boston University estimated had resulted in 300,000 deaths by this time, most of them of children. By November 2025, the estimated death toll had increased to 400,000 children and 200,000 adults. Musk announced on May 28, 2025, that he would depart from the Trump administration as planned when the special government employee's 130 day deadline expired, with a White House official confirming that Musk's offboarding from the Trump administration was already underway. His departure was officially confirmed during a joint Oval Office press conference with Trump on May 30, 2025. @realDonaldTrump is in the Epstein files. That is the real reason they have not been made public. June 5, 2025 After leaving office, Musk criticized the Trump administration's Big Beautiful Bill, calling it a "disgusting abomination" due to its provisions increasing the deficit. A feud began between Musk and Trump, with its most notable event being Musk alleging Trump had ties to sex offender Jeffrey Epstein on X (formerly Twitter) on June 5, 2025. Trump responded on Truth Social stating that Musk went "CRAZY" after the "EV Mandate" was purportedly taken away and threatened to cut Musk's government contracts. Musk then called for a third Trump impeachment. The next day, Trump stated that he did not wish to reconcile with Musk, and added that Musk would face "very serious consequences" if he funds Democratic candidates. On June 11, Musk publicly apologized for the tweets against Trump, saying they "went too far". Views November 6, 2022 Rejecting the conservative label, Musk has described himself as a political moderate, even as his views have become more right-wing over time. His views have been characterized as libertarian and far-right, and after his involvement in European politics, they have received criticism from world leaders such as Emmanuel Macron and Olaf Scholz. Within the context of American politics, Musk supported Democratic candidates up until 2022, at which point he voted for a Republican for the first time. He has stated support for universal basic income, gun rights, freedom of speech, a tax on carbon emissions, and H-1B visas. Musk has expressed concern about issues such as artificial intelligence (AI) and climate change, and has been a critic of wealth tax, short-selling, and government subsidies. An immigrant himself, Musk has been accused of being anti-immigration, and regularly blames immigration policies for illegal immigration. He is also a pronatalist who believes population decline is the biggest threat to civilization, and identifies as a cultural Christian. Musk has long been an advocate for space colonization, especially the colonization of Mars. He has repeatedly pushed for humanity colonizing Mars, in order to become an interplanetary species and lower the risks of human extinction. Musk has promoted conspiracy theories and made controversial statements that have led to accusations of racism, sexism, antisemitism, transphobia, disseminating disinformation, and support of white pride. While describing himself as a "pro-Semite", his comments regarding George Soros and Jewish communities have been condemned by the Anti-Defamation League and the Biden White House. Musk was criticized during the COVID-19 pandemic for making unfounded epidemiological claims, defying COVID-19 lockdowns restrictions, and supporting the Canada convoy protest against vaccine mandates. He has amplified false claims of white genocide in South Africa. Musk has been critical of Israel's actions in the Gaza Strip during the Gaza war, praised China's economic and climate goals, suggested that Taiwan and China should resolve cross-strait relations, and was described as having a close relationship with the Chinese government. In Europe, Musk expressed support for Ukraine in 2022 during the Russian invasion, recommended referendums and peace deals on the annexed Russia-occupied territories, and supported the far-right Alternative for Germany political party in 2024. Regarding British politics, Musk blamed the 2024 UK riots on mass migration and open borders, criticized Prime Minister Keir Starmer for what he described as a "two-tier" policing system, and was subsequently attacked as being responsible for spreading misinformation and amplifying the far-right. He has also voiced his support for far-right activist Tommy Robinson and pledged electoral support for Reform UK. In February 2026, Musk described Spanish Prime Minister Pedro Sánchez as a "tyrant" following Sánchez's proposal to prohibit minors under the age of 16 from accessing social media platforms. Legal affairs In 2018, Musk was sued by the U.S. Securities and Exchange Commission (SEC) for a tweet stating that funding had been secured for potentially taking Tesla private.[f] The securities fraud lawsuit characterized the tweet as false, misleading, and damaging to investors, and sought to bar Musk from serving as CEO of publicly traded companies. Two days later, Musk settled with the SEC, without admitting or denying the SEC's allegations. As a result, Musk and Tesla were fined $20 million each, and Musk was forced to step down for three years as Tesla chairman but was able to remain as CEO. Shareholders filed a lawsuit over the tweet, and in February 2023, a jury found Musk and Tesla not liable. Musk has stated in interviews that he does not regret posting the tweet that triggered the SEC investigation. In 2019, Musk stated in a tweet that Tesla would build half a million cars that year. The SEC reacted by asking a court to hold him in contempt for violating the terms of the 2018 settlement agreement. A joint agreement between Musk and the SEC eventually clarified the previous agreement details, including a list of topics about which Musk needed preclearance. In 2020, a judge blocked a lawsuit that claimed a tweet by Musk regarding Tesla stock price ("too high imo") violated the agreement. Freedom of Information Act (FOIA)-released records showed that the SEC concluded Musk had subsequently violated the agreement twice by tweeting regarding "Tesla's solar roof production volumes and its stock price". In October 2023, the SEC sued Musk over his refusal to testify a third time in an investigation into whether he violated federal law by purchasing Twitter stock in 2022. In February 2024, Judge Laurel Beeler ruled that Musk must testify again. In January 2025, the SEC filed a lawsuit against Musk for securities violations related to his purchase of Twitter. In January 2024, Delaware judge Kathaleen McCormick ruled in a 2018 lawsuit that Musk's $55 billion pay package from Tesla be rescinded. McCormick called the compensation granted by the company's board "an unfathomable sum" that was unfair to shareholders. The Delaware Supreme Court overturned McCormick's decision in December 2025, restoring Musk's compensation package and awarding $1 in nominal damages. Personal life Musk became a U.S. citizen in 2002. From the early 2000s until late 2020, Musk resided in California, where both Tesla and SpaceX were founded. He then relocated to Cameron County, Texas, saying that California had become "complacent" about its economic success. While hosting Saturday Night Live in 2021, Musk stated that he has Asperger syndrome (an outdated term for autism spectrum disorder). When asked about his experience growing up with Asperger's syndrome in a TED2022 conference in Vancouver, Musk stated that "the social cues were not intuitive ... I would just tend to take things very literally ... but then that turned out to be wrong — [people were not] simply saying exactly what they mean, there's all sorts of other things that are meant, and [it] took me a while to figure that out." Musk suffers from back pain and has undergone several spine-related surgeries, including a disc replacement. In 2000, he contracted a severe case of malaria while on vacation in South Africa. Musk has stated he uses doctor-prescribed ketamine for occasional depression and that he doses "a small amount once every other week or something like that"; since January 2024, some media outlets have reported that he takes ketamine, marijuana, LSD, ecstasy, mushrooms, cocaine and other drugs. Musk at first refused to comment on his alleged drug use, before responding that he had not tested positive for drugs, and that if drugs somehow improved his productivity, "I would definitely take them!". The New York Times' investigations revealed Musk's overuse of ketamine and numerous other drugs, as well as strained family relationships and concerns from close associates who have become troubled by his public behavior as he became more involved in political activities and government work. According to The Washington Post, President Trump described Musk as "a big-time drug addict". Through his own label Emo G Records, Musk released a rap track, "RIP Harambe", on SoundCloud in March 2019. The following year, he released an EDM track, "Don't Doubt Ur Vibe", featuring his own lyrics and vocals. Musk plays video games, which he stated has a "'restoring effect' that helps his 'mental calibration'". Some games he plays include Quake, Diablo IV, Elden Ring, and Polytopia. Musk once claimed to be one of the world's top video game players but has since admitted to "account boosting", or cheating by hiring outside services to achieve top player rankings. Musk has justified the boosting by claiming that all top accounts do it so he has to as well to remain competitive. In 2024 and 2025, Musk criticized the video game Assassin's Creed Shadows and its creator Ubisoft for "woke" content. Musk posted to X that "DEI kills art" and specified the inclusion of the historical figure Yasuke in the Assassin's Creed game as offensive; he also called the game "terrible". Ubisoft responded by saying that Musk's comments were "just feeding hatred" and that they were focused on producing a game not pushing politics. Musk has fathered at least 14 children, one of whom died as an infant. The Wall Street Journal reported in 2025 that sources close to Musk suggest that the "true number of Musk's children is much higher than publicly known". He had six children with his first wife, Canadian author Justine Wilson, whom he met while attending Queen's University in Ontario, Canada; they married in 2000. In 2002, their first child Nevada Musk died of sudden infant death syndrome at the age of 10 weeks. After his death, the couple used in vitro fertilization (IVF) to continue their family; they had twins in 2004, followed by triplets in 2006. The couple divorced in 2008 and have shared custody of their children. The elder twin he had with Wilson came out as a trans woman and, in 2022, officially changed her name to Vivian Jenna Wilson, adopting her mother's surname because she no longer wished to be associated with Musk. Musk began dating English actress Talulah Riley in 2008. They married two years later at Dornoch Cathedral in Scotland. In 2012, the couple divorced, then remarried the following year. After briefly filing for divorce in 2014, Musk finalized a second divorce from Riley in 2016. Musk then dated the American actress Amber Heard for several months in 2017; he had reportedly been "pursuing" her since 2012. In 2018, Musk and Canadian musician Grimes confirmed they were dating. Grimes and Musk have three children, born in 2020, 2021, and 2022.[g] Musk and Grimes originally gave their eldest child the name "X Æ A-12", which would have violated California regulations as it contained characters that are not in the modern English alphabet; the names registered on the birth certificate are "X" as a first name, "Æ A-Xii" as a middle name, and "Musk" as a last name. They received criticism for choosing a name perceived to be impractical and difficult to pronounce; Musk has said the intended pronunciation is "X Ash A Twelve". Their second child was born via surrogacy. Despite the pregnancy, Musk confirmed reports that the couple were "semi-separated" in September 2021; in an interview with Time in December 2021, he said he was single. In October 2023, Grimes sued Musk over parental rights and custody of X Æ A-Xii. Elon Musk has taken X Æ A-Xii to multiple official events in Washington, D.C. during Trump's second term in office. Also in July 2022, The Wall Street Journal reported that Musk allegedly had an affair with Nicole Shanahan, the wife of Google co-founder Sergey Brin, in 2021, leading to their divorce the following year. Musk denied the report. Musk also had a relationship with Australian actress Natasha Bassett, who has been described as "an occasional girlfriend". In October 2024, The New York Times reported Musk bought a Texas compound for his children and their mothers, though Musk denied having done so. Musk also has four children with Shivon Zilis, director of operations and special projects at Neuralink: twins born via IVF in 2021, a child born in 2024 via surrogacy and a child born in 2025.[h] On February 14, 2025, Ashley St. Clair, an influencer and author, posted on X claiming to have given birth to Musk's son Romulus five months earlier, which media outlets reported as Musk's supposed thirteenth child.[i] On February 22, 2025, it was reported that St Clair had filed for sole custody of her five-month-old son and for Musk to be recognised as the child's father. On March 31, 2025, Musk wrote that, while he was unsure if he was the father of St. Clair's child, he had paid St. Clair $2.5 million and would continue paying her $500,000 per year.[j] Later reporting from the Wall Street Journal indicated that $1 million of these payments to St. Clair were structured as a loan. In 2014, Musk and Ghislaine Maxwell appeared together in a photograph taken at an Academy Awards after-party, which Musk later described as a "photobomb". The January 2026 Epstein files contain emails between Musk and Epstein from 2012 to 2013, after Epstein's first conviction. Emails released on January 30, 2026, indicated that Epstein invited Musk to visit his private island on multiple occasions. The correspondence showed that while Epstein repeatedly encouraged Musk to attend, Musk did not visit the island. In one instance, Musk discussed the possibility of attending a party with his then-wife Talulah Riley and asked which day would be the "wildest party"; according to the emails, the visit did not take place after Epstein later cancelled the plans.[k] On Christmas day in 2012, Musk emailed Epstein asking "Do you have any parties planned? I’ve been working to the edge of sanity this year and so, once my kids head home after Christmas, I really want to hit the party scene in St Barts or elsewhere and let loose. The invitation is much appreciated, but a peaceful island experience is the opposite of what I’m looking for". Epstein replied that the "ratio on my island" might make Musk's wife uncomfortable to which Musk responded, "Ratio is not a problem for Talulah". On September 11, 2013, Epstein sent an email asking Musk if he had any plans for coming to New York for the opening of the United Nations General Assembly where many "interesting people" would be coming to his house to which Musk responded that "Flying to NY to see UN diplomats do nothing would be an unwise use of time". Epstein responded by stating "Do you think i am retarded. Just kidding, there is no one over 25 and all very cute." Musk has denied any close relationship with Epstein and described him as a "creep" who attempted to ingratiate himself with influential people. When Musk was asked in 2019 if he introduced Epstein to Mark Zuckerberg, Musk responded: "I don’t recall introducing Epstein to anyone, as I don’t know the guy well enough to do so." The released emails nonetheless showed cordial exchanges on a range of topics, including Musk's inquiry about parties on the island. The correspondence also indicated that Musk suggested hosting Epstein at SpaceX, while Epstein separately discussed plans to tour SpaceX and bring "the girls", though there is no evidence that such a visit occurred. Musk has described the release of the files a "distraction", later accusing the second Trump administration of suppressing them to protect powerful individuals, including Trump himself.[l] Wealth Elon Musk is the wealthiest person in the world, with an estimated net worth of US$690 billion as of January 2026, according to the Bloomberg Billionaires Index, and $852 billion according to Forbes, primarily from his ownership stakes in SpaceX and Tesla. Having been first listed on the Forbes Billionaires List in 2012, around 75% of Musk's wealth was derived from Tesla stock in November 2020, although he describes himself as "cash poor". According to Forbes, he became the first person in the world to achieve a net worth of $300 billion in 2021; $400 billion in December 2024; $500 billion in October 2025; $600 billion in mid-December 2025; $700 billion later that month; and $800 billion in February 2026. In November 2025, a Tesla pay package worth potentially $1 trillion for Musk was approved, which he is to receive over 10 years if he meets specific goals. Public image Although his ventures have been highly influential within their separate industries starting in the 2000s, Musk only became a public figure in the early 2010s. He has been described as an eccentric who makes spontaneous and impactful decisions, while also often making controversial statements, contrary to other billionaires who prefer reclusiveness to protect their businesses. Musk's actions and his expressed views have made him a polarizing figure. Biographer Ashlee Vance described people's opinions of Musk as polarized due to his "part philosopher, part troll" persona on Twitter. He has drawn denouncement for using his platform to mock the self-selection of personal pronouns, while also receiving praise for bringing international attention to matters like British survivors of grooming gangs. Musk has been described as an American oligarch due to his extensive influence over public discourse, social media, industry, politics, and government policy. After Trump's re-election, Musk's influence and actions during the transition period and the second presidency of Donald Trump led some to call him "President Musk", the "actual president-elect", "shadow president" or "co-president". Awards for his contributions to the development of the Falcon rockets include the American Institute of Aeronautics and Astronautics George Low Transportation Award in 2008, the Fédération Aéronautique Internationale Gold Space Medal in 2010, and the Royal Aeronautical Society Gold Medal in 2012. In 2015, he received an honorary doctorate in engineering and technology from Yale University and an Institute of Electrical and Electronics Engineers Honorary Membership. Musk was elected a Fellow of the Royal Society (FRS) in 2018.[m] In 2022, Musk was elected to the National Academy of Engineering. Time has listed Musk as one of the most influential people in the world in 2010, 2013, 2018, and 2021. Musk was selected as Time's "Person of the Year" for 2021. Then Time editor-in-chief Edward Felsenthal wrote that, "Person of the Year is a marker of influence, and few individuals have had more influence than Musk on life on Earth, and potentially life off Earth too." Notes References Works cited Further reading External links |
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