title: Compass

text: A compass should be laid down on a level surface so that the needle only rests or hangs on the bearing fused to the compass casing – if used at a tilt, the needle might touch the casing on the compass and not move freely, hence not pointing to the magnetic north accurately, giving a faulty reading. To see if the needle is well leveled, look closely at the needle, and tilt it slightly to see if the needle is swaying side to side freely and the needle is not contacting the casing of the compass. If the needle tilts to one direction, tilt the compass slightly and gently to the opposing direction until the compass needle is horizontal, lengthwise. Items to avoid around compasses are magnets of any kind and any electronics. Magnetic fields from electronics can easily disrupt the needle, preventing it from aligning with the Earth's magnetic fields, causing inaccurate readings. The Earth's natural magnetic forces are considerably weak, measuring at 0.5 gauss and magnetic fields from household electronics can easily exceed it, overpowering the compass needle. Exposure to strong magnets, or magnetic interference can sometimes cause the magnetic poles of the compass needle to differ or even reverse. Avoid iron rich deposits when using a compass, for example, certain rocks which contain magnetic minerals, like Magnetite. This is often indicated by a rock with a surface which is dark and has a metallic luster, not all magnetic mineral bearing rocks have this indication. To see if a rock or an area is causing interference on a compass, get out of the area, and see if the needle on the compass moves. If it does, it means that the area or rock the compass was previously at is causing interference and should be avoided.


title: Adolf Dassler

text: Adolf "Adi" Dassler (3 November 1900 – 6 September 1978) was a German cobbler, inventor and entrepreneur who founded the German sportswear company Adidas. He was also the younger brother of Rudolf Dassler, founder of Puma. Dassler was an innovator in athletic shoe design and one of the early promoters who obtained endorsements from athletes to drive sale of his products. As a result of his concepts, Adi Dassler built the largest manufacturer of sportswear and equipment. At the time of his death, Adidas had 17 factories and annual sales of one billion marks.


title: Adolf Dassler

text: Adi supported himself while attempting to start up his business by repairing shoes in town. Facing the realities of post-war Germany where there was no reliable supply for material for production or credit to obtain factory equipment or supplies, he began by scavenging army debris in the war-torn countryside: Army helmets and bread pouches supplied leather for soles; parachutes could supply silk for slippers. Dassler became quite adept at modifying available devices to help mechanize production in the absence of electricity. Using belts, for example, he rigged a leather milling machine to a mounted, stationary bicycle powered by the firm's first employee. The business would be driven by Adi's vision of specialized sport designs. He produced one of the earliest spiked shoes, with spikes forged by the smithy of the family of his friend Fritz Zehlein. He constantly experimented with various materials (such as shark skin and kangaroo leather) to create strong but lightweight shoes. Years later his widow, Käthe Dassler, said: "Developing shoes was his hobby, not his job. He did it very scientifically."


title: Adolf Dassler

text: After the war, Rudolf was determined to become a policeman. But after he completed his training, he joined Adi's firm on 1 July 1923. With the support of the Zehlein smithy producing spikes, Adi was able to register Gebrüder Dassler, Sportschuhfabrik, Herzogenaurach ("Dassler Brothers Sports Shoe Factory, Herzogenaurach") on 1 July 1924, where they were operating in a former washroom that was converted to a small workshop with manual electricity generation. By 1925 the Dasslers were making leather Fußballschuhe (football boots) with nailed studs and track shoes with hand-forged spikes.


title: Adolf Dassler

text: Two factors paved the way for the transformation of the business from a small regional factory, which they moved to in 1927 from their parents' home, to the international shoe distributor it would become. First was the interest showed by former Olympian and then coach of the German Olympic track-and-field team, Josef Waitzer. On learning of the plant and Adi's experiments, Waitzer travelled from Munich to Herzogenaurach to see for himself. A long friendship developed between the two, based on interest in improving athletic performance with improved footwear, and Waitzer became something of a consultant to the company. The relationship would prove extremely valuable in giving Adi access to the athletes (German and foreign) at the 1936 Berlin Olympics. As early as the 1928 Amsterdam games, however, the Dasslers' footwear was being used in international competitions. Lina Radke, for example, the German middle distance runner who won gold in 1928, wore Dassler track shoes. Likewise, a German gold medal runner wore Dassler shoes at the 1932 Los Angeles games. The second key factor for the shoe firm in the early 1930s was the role sport played in the racial-nationalist philosophy of Hitler. With the rise of the National Socialist German Workers Party, athletic teamwork was prioritized. The Dassler brothers did not fail to see how their economic interest would benefit from politics; all three Dassler brothers joined the Nazi Party on 1 May 1933—three months after Hitler was appointed Chancellor. Rudolf was said to be most ardent believer of the three. But it was Adi who decided that becoming a coach of and supplier to clubs in the Hitler Youth movement was essential to expanded production, and he joined in 1935. (In his denazification proceedings after the war, Adi pointed out that he confined himself to coaching and avoided political rallies. He also testified that he was involved in clubs of other political affiliations, such as a liberal gymnastic club, Herzogenaurach's conservative KHC football club and a workers' sports club named "The Union".) Both Adi and Rudolf were members of the National Socialist Motor Corps, and in their correspondence both used the complimentary closing, "Heil Hitler."


title: Adolf Dassler

text: In the early 1930s Adi Dassler enrolled in the Schuhfachschule (the Footwear Technical College) in Pirmasens. One of the instructors was Franz Martz, a master producer of lasts. Dassler became a frequent house guest of Martz, who permitted Dassler's attentions to his fifteen-year-old daughter, Käthe Martz. On 17 March 1934, the two wed. Unlike Rudolf's wife Friedl (née Strasser), Käthe was somewhat self-assertive and suspicious of the brusque ways of Franconians. She would have frequent run-ins with Adi's parents and Rudolf and his wife, all of whom lived in the same house. Years later, in a letter to Puma's American distributor, Rudolf explained the rift with his brother as solely to be blamed on Käthe, who he claimed "tried to interfere in business matters …"; he claimed that the brothers' relations were "ideal" until 1933. Käthe would give birth to their son Horst in March 1936, their first daughter Inge in June 1938 and their second daughter Karin in 1941. After the war, Brigit was born in May 1946 and Sigrid in 1953.


title: Adolf Dassler

text: Dassler saw the 1936 Berlin Olympics as the key springboard for international exposure. Although his relation with Waitzer ensured that most German athletes would wear Dassler footwear, Dassler had another athlete principally in mind—Jesse Owens, the American track-and-field star. Dassler found his way to meeting Owens and wordlessly offered his shoes to the American star. Owens accepted the gesture and wore the distinctive shoes (with two leather strips on the sides and dark spikes) when he defeated Luz Long in the long jump (shattering his own record in the process), in his two individual gold-winning performances in track and as a member of America's Gold medal upset of the German relay team.


title: Adolf Dassler

text: Dasslers' association with Owens proved crucial to the success of the firm. Not only did it immediately catapult the company into an international player in the sportswear field spiking sales overall, but it quite literally later saved the firm. When American troops discovered that the Dassler factory was where the shoes for Owens' Olympic victories were made, they decided to let the works remain standing, and, indeed, many of the troops became good customers. Large orders for basketball, baseball and hockey footwear gave the Dasslers "the first boost on the road to becoming a worldwide success story."


title: Adolf Dassler

text: Once war began the Dasslers' ability to profit from Nazi enthusiasm for sport ended as the Reich became a total war machine. The Dassler firm was permitted to operate, but its production was severely curtailed. Then on 7 August 1940 Adi received notice of his conscription into the Wehrmacht. Although he reported in December to begin training as a radio technician, he was relieved of duty on 28 February 1941 on the ground that his services were essential in Gebrüder Dassler. Rudolf, who had already served four years during the Great War, was drafted in January 1943.


title: Adolf Dassler

text: In the early years of the war, the firm was partially converted to a factory for the production of military material. Nevertheless, staff was reduced and supply was hard to come by. But it still continued to produce Waitzer shoes, although some of its football line became known as "Kampf" and "Blitz." By October 1942 worker shortage became so severe that Adi Dassler himself formally requested the use of five Soviet prisoners of war to man his production line.


title: Adolf Dassler

text: Wartime conditions exacerbated the simmering dispute between Rudolf and Adi's families. The house that Christoph, Pauline, sons Rudolf and Adi and their wives, and five grandchildren all lived in together seemed stifling, and forced family association at work was further complicated by sister Marie's employment there. Rudolf, angry that his younger brother was determined to be the leader of the Dassler firm (and therefore released from the Wehrmacht), began to assert himself among family members. He used this assumed authority to deny employment to two of Marie's sons, asserting that "there were enough family problems at the company." The decision devastated his sister, since those not employed in permitted industries were nearly guaranteed to be drafted as the army's manpower needs became a gaping maw. Indeed, Marie's sons were eventually conscripted, and they never returned from the war. Fritz Dassler, who was not on speaking terms with Adi, made a similar decision laying off a teenaged seamstress who worked for his lederhosen-turned-army-pouch manufacturer, but had worked previously for four years for Adi. Adi managed to make room at the shoe factory to protect her for the rest of the war.


title: Adolf Dassler

text: Rudolf's rage boiled over when he was called up again in January 1943 as part of a total mobilization program. He later expressed (to the Puma American distributors) the belief that he was unfairly repaid for getting his brother "released for the factory" in 1942 and claimed that for his own immediate conscription he "had to thank my brother and his [Nazi] party friends …" Stationed in Tuschin in April 1943, Rudolf wrote to his brother: "I will not hesitate to seek the closure of the factory so that you be forced to take up an occupation that will allow you to play the leader and, as a first-class sportsman, to carry a gun." Six months later the factory was indeed shut down, but as part of the Reich's "Totaler Krieg—Kürzester Krieg" (Total War—Shortest War) campaign, part of which involved converting all industry to military production. On leave at the time of the shut down, Rudolf intended to take some of the leather inventory for his own later use. Stunned to find that Adi had already done so, he denounced his brother to the "Kreisleitung" (the county level Party leaders), according to Käthe, who treated her husband "in the most demeaning manner."


title: Adolf Dassler

text: In December 1943 the shoe-making machinery of the Dassler firm was replaced by spot-welding machines. The Army determined that the Dassler plant would thereafter make "Panzerschreck", a shoulder-fired tube copied after captured American bazookas. Like the American proto-type, the weapon was designed to be relatively light weight and able to penetrate tank armor. Stationary testing suggested it could penetrate 230 mm (9"), 15–75 mm (½" to 3") deeper than the American bazooka. The Army's contractor was Schriker & Co., located in nearby Vach, which shifted assembly to Herzogenaurach to avoid Allied air raids. Parts were transported by rail to the Dassler plant where they were welded. The simple design of the weapon allowed the contractor to quickly train former seamstresses to spot weld sights and blast shields onto the pipes provided. The more complicated production of rockets continued in Vach. The weapons were to be distributed to tank-destroying detachments, and by March 1945 92,000 "Panzerschrecks" were in active use at the fronts of the rapidly constricting periphery of German territory. Although the weapon was remarkably effective and easily produced, its availability came too late in the war to save the Reich.


title: Adolf Dassler

text: Back in Tuschin, Rudolf continued to make good on his resolve to wrest the plant from his brother. Using contacts at the "Luftwaffe" he attempted to have the production of "Panzerschrecks" replaced by government-ordered production of army boots under a patent he personally held. The patent proved defective, and his plan came to nothing. Unable to obtain permission to leave the Polish outpost, Rudolf turned to his own devising. Several weeks before 19 January 1945, when the Soviets overran Tuschin (which then reverted to its original name, Tuszyn) and decimated his unit, Rudolf had fled to Herzogenaurach (where a doctor provided him a certificate of military incapacity owing to a frozen foot). The now-defunct unit had been folded into the "Schutzstaffel" (SS). The sources for what Rudolf did between his desertion from Tuschin and the funeral of Rudolf's and Adi's father on 4 April 1945 is among the disputed records in the American denazification panels. On the day after the funeral he was arrested and taken to the Bärenschanze prison run by the Gestapo in Nürnberg. He remained there until the Allied liberation in early May.


title: Adolf Dassler

text: When American troops reached Herzogenaurach, tanks paused before the Dassler factory pondering whether to blow it up. Käthe immediately approached the troops and argued that the plant was simply a sports shoes producer. The troops spared the plant, taking over the family house in the process. Two weeks after the liberation of Herzogenaurach, Rudolf returned. As the American denazification process proceeded, the threat of liability from their Nazi past drove an irreconcilable rift between brothers Rudolf and Adi, each seeking to save himself.


title: Adolf Dassler

text: On 25 July 1945, about two months after the arrival of U.S. troops, Rudolf was arrested by the American occupation authorities, on suspicion that he worked for the "Sicherheitsdienst" (the secret service of the "Reichsführer-SS" commonly known as the SD) engaged in counterespionage and censorship, and was sent to an internment camp in Hammelburg. Rudolf began to prepare a defense that he did not voluntarily help the Reich and did not in any event engage in SS or SD activities. The American investigators soon discovered his early Nazi party membership and proof that he volunteered for the Wehrmacht in 1941. They even knew that in Tuschin his job was to keep track of "personal and smuggling cases." His key problem, however, was in explaining his activities after he had been summoned to Nuremberg in March by the Gestapo. Rudolf maintained that he had been summoned on 13 March for an investigation of his earlier unauthorized departure from Tuschin and did nothing but report daily to the Gestapo while they investigated him for over two weeks. He claimed that he escaped on 20 March. Rudolf used written statements of his former superior in Tuschin (who was in the same camp and alleged to be the intelligence chief of the region) and a driver he encountered after he was arrested by the Gestapo in April (who was also incarcerated with Rudolf). Rudolf made much use of the latter's testimony and averred that he had been sentenced by the Gestapo to the Dachau concentration camp. Rudolf claimed that en route the driver was ordered to shoot all the prisoners, disregarded the order, continued toward Dachau but was stopped by advancing Allied troops to whom he released the prisoners, including Rudolf. The American investigator in charge of the case did not credit any of this testimony, which he regarded as mere cover for the unlawful activity of all three. He noted that both Rudolf's wife and his brother Adi testified that Rudolf worked for the Gestapo. The investigation ground on for nearly a year. During the time it became apparent that it was not possible to hold all the prisoners for a detailed examination of the case, and the authorities decided to release all persons not deemed to be a security threat. Accordingly, Rudolf was released on 31 July 1946.


title: Adolf Dassler

text: Before Rudolf was released, Adi himself had to appear before the denazification panel. The result was announced on 13 July 1946: Adi was declared a "Belasteter", the second most serious category of Nazi offenders, which included profiteers, and subjected the convict up to 10 years in prison,


title: Adolf Dassler

text: but the immediate threat was that he would be removed from management of the firm. His early membership in the Nazi Party and the Hitler Youth were not contestable. But on appeal he amassed a portfolio of testimony attesting to his good conduct during the war. Adi's staunchest supporter was Herzogenaurach's mayor, whom the Allied forces trusted. A nearby mayor, who was half-Jewish, testified that Adi warned him of a potential Gestapo arrest and hid him on his own property. A longtime Communist party member testified that Adi was never involved in political activities. Adi moreover showed that, far from profiting from the forced weapons production, the firm lost 100,000 marks. Despite Adi's evidence, the committee did not acquit him. Instead, they reclassified him as "Minderbelasteter" (Lesser Offender), a category of lesser culpability resulting in probation of two to three years with various conditions but still requiring that Adi not operate Dassler Shoes. Adi hired counsel to appeal the decision; Rudolf, who had just been released, saw this as his opportunity to wrest control of the business from Adi.


title: Adolf Dassler

text: In the course of the appeal proceedings Rudolf Dassler inserted statements that claimed that Adi Dassler had organized the production of weapons himself and for his own profit and that Rudolf would have resisted the change in production if he were present. He also claimed that his brother had falsely denounced him and that Adi had made political speeches to employees at the plant. Among other proofs submitted by Adi's counsel was a strong denial of all Rudolf's claims by Käthe. On 11 November 1946 the Spruchkammer Höchstadt sitting in Herzogenaurach changed Adi's status to "Mitläufer" (follower), relieving him of most of his civil disabilities, but still required some supervision. On 3 February 1947, ownership was returned and he was formally granted permission to resume management of the firm.


title: Adolf Dassler

text: Rudolf's belief that Adi had denounced him and his conduct during his brother's appeal made further relations between them impossible. In fact, it irreparably divided the family. Mother Paulina sided with Rudolf and Friedl, who cared for her the rest of her life. Their sister Marie, who never forgave Rudolf for the death of her sons, sided with Adi and Käthe. Rudolf, his wife and two children left the family home and moved across the river, where he would take over the second factory of the Dassler firm. In their separation Adi retained the first factory and the family villa. As for the rest of the firm's assets, the two divided them one-by-one. Once the brothers divided their businesses they never spoke again.


title: Adolf Dassler

text: After the war, the Dassler firm found itself with some of the same problems that it faced at the beginning. A world war had decimated the German economy and supplies for the shoe factory were hard to come by. In addition, the firm had to convert back from weapons to shoe production. This time, however, the American occupying authorities were interested in reviving economic activity, so they gave the firm active encouragement. American officers had commandeered the Dassler house for their residence on 16 April 1945, and, thus, Adi had close contact with officials who gave him access to unneeded war material for production. Until a source of leather became available Adi made use of the rubber from fuel tanks and rafts and canvas from tents to make shoes. Adi was thus able to produce shoes, and save for the months in 1946 while under the classification of "Belasteter" he was able to manage the business (from July 1946 to February 1947 under the supervision of a trustee) until the separation from his brother in 1948.


title: Adolf Dassler

text: During the negotiations to separate the firm, Rudolf and Adi allowed the employees to determine which resulting firm they would work for. Because Rudolf had mainly concerned himself with sales and administration, most of the sales staff opted to join Rudolf at the Würtzburger Strasse factory. The rest, including almost all the technicians and those involved in product development and production, remained with Adi. Adi thus ended up with nearly two-thirds of the employees. To partially fill the void left by the departure of the administrative personnel Käthe and her sister Marianne Martz joined the firm and acted in a variety of capacities.


title: Adolf Dassler

text: Meanwhile, Adi was concerned in designing a distinctive look for his shoes, at least partially so that it would be possible to show which athletes used his footwear. He fell upon the idea of coloring the straps used for reinforcement on the sides of the shoes a different color than the shoes themselves. He experimented with different numbers of straps and ultimately decided on three. The "three stripes" became a distinctive mark of Adidas shoes. In March 1949 Dassler registered the three stripe logo as the company's trademark. As for the company's name, the plan was to use a contraction of Adi's nickname and last name (much as Rudolf originally contemplated by naming his firm "Ruda" before deciding on "Puma"), but "Addas" was rejected on the ground that it was used by a children's shoe manufacturer. Accordingly, in his 18 August 1949 company registration, Adi added a handwritten "i" between Ad- and -das to maintain the contraction (Adi Dassler). As a result, the company became known as "Adolf Dassler adidas Schuhfabrik".


title: Adolf Dassler

text: Like the Dasslers, Sepp Herberger joined the Nazi Party in 1933. In 1936 after Germany's humiliating quarter final defeat by Norway at the Berlin Games, the Nazi sports authorities appointed him to coach the national football team. Herberger began an association with the Dassler firm having been cultivated by Rudolf Dassler. After the breakup Herberger sided with the Puma firm, until Rudolf once again felt his authority challenged and insulted him. Herberger switched his allegiance to Adidas. The nature of the dispute is unknown; some thought it involved the payments owed if the German team wore Puma shoes.


title: Adolf Dassler

text: In many respects the fit was better with Adi, who was quiet, willing to learn the needs of football players and more innovative than his brother. Herberger's drive to make Germany a dominant force in international football predated the war. He learned of 18 year old Fritz Walter in 1938 and began grooming him for the team. When war came Herberger was able to keep Walter out of the army. After the war, Herberger was deemed a "Mitlaufer" and the post-war German authorities continued him as the coach of the national team. Adi soon became a regular part of the entourage of the national team, who sat beside Herberger and adjusted players' shoes mid-game.


title: Adolf Dassler

text: West Germany (established in May 1949) was not eligible for the 1950 World Cup (the first after the war), and so all preparations were made with a view toward the 1954 matches in Bern, Switzerland. By that time Adidas's football boots were considerably lighter than the ones made before the war, based on English designs. At the World Cup Adi had a secret weapon, which he revealed when West Germany made the finals against the overwhelmingly favored Hungarian team, which was undefeated since May 1950 and had defeated West Germany 8–3 in group play. Despite this defeat, West Germany made the knock-out rounds by twice defeating Turkey handily. The team defeated Yugoslavia and Austria to reach the final (a remarkable achievement), where the hope of many German fans was simply that the team "avoid another humiliating defeat" at the hands of the Hungarians. The day of the final began with light rain, which brightened the prospects of the West German team who called it ""Fritz Walter-Wetter"" because the team's best player excelled in muddy conditions. Dassler informed Herberger before the match of his latest innovation—"screw in studs." Unlike the traditional boot which had fixed leather spike studs, Dassler's shoe allowed spikes of various lengths to be affixed depending on the state of the pitch. As the playing field at Wankdorf Stadium drastically deteriorated, Herberger famously announced, "Adi, screw them on." The longer spikes improved the footing of West German players compared to the Hungarians whose mud-caked boots were also much heavier. The West Germans staged a come from behind upset, winning 3-2, in what became known as the "Miracle in Bern." Herberger publicly praised Dassler as a key contributor to the win, and Adidas's fame rose both in West Germany, where the win was considered a key post-war event in restoring German self-esteem and abroad, where in the first televised World Cup final viewers were introduced to "the ultimate breakthrough."


title: Adolf Dassler

text: Dassler was married to Käthe until his death from heart failure in 1978. They had 5 children. In 1973, their son Horst Dassler founded Arena, a producer of swimming equipment. Käthe Dassler died on 31 December 1984.


title: Adolf Dassler

text: After Adolf Dassler's death, his son Horst and his wife, Käthe, took over the management. Horst died on 11 April 1987.


title: Adolf Dassler

text: Adidas was transformed into a private limited company in 1989, but remained family property until its IPO in 1995. The last of the family members who worked for Adidas was Frank Dassler (the grandson of Rudolf), head of the legal department since 2004, who resigned in January 2018.


title: Adolf Dassler

text: In 2006, a sculpture of Dassler was unveiled in the Adi Dassler Stadium in Herzogenaurach. It was created by the artist Josef Tabachnyk.


title: Latitude

text: In geography, latitude is a coordinate that specifies the north–south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pole, with 0° at the Equator. Lines of constant latitude, or "parallels", run east–west as circles parallel to the equator. Latitude and "longitude" are used together as a coordinate pair to specify a location on the surface of the Earth.


title: Latitude

text: On its own, the term "latitude" normally refers to the "geodetic latitude" as defined below. Briefly, the geodetic latitude of a point is the angle formed between the vector perpendicular (or "normal") to the ellipsoidal surface from the point, and the plane of the equator.


title: Latitude

text: Two levels of abstraction are employed in the definitions of latitude and longitude. In the first step the physical surface is modeled by the geoid, a surface which approximates the mean sea level over the oceans and its continuation under the land masses. The second step is to approximate the geoid by a mathematically simpler reference surface. The simplest choice for the reference surface is a sphere, but the geoid is more accurately modeled by an ellipsoid. The definitions of latitude and longitude on such reference surfaces are detailed in the following sections. Lines of constant latitude and longitude together constitute a graticule on the reference surface. The latitude of a point on the "actual" surface is that of the corresponding point on the reference surface, the correspondence being along the normal to the reference surface, which passes through the point on the physical surface. Latitude and longitude together with some specification of height constitute a geographic coordinate system as defined in the specification of the ISO 19111 standard.


title: Latitude

text: Since there are many different reference ellipsoids, the precise latitude of a feature on the surface is not unique: this is stressed in the ISO standard which states that "without the full specification of the coordinate reference system, coordinates (that is latitude and longitude) are ambiguous at best and meaningless at worst". This is of great importance in accurate applications, such as a Global Positioning System (GPS), but in common usage, where high accuracy is not required, the reference ellipsoid is not usually stated.


title: Latitude

text: In English texts, the latitude angle, defined below, is usually denoted by the Greek lower-case letter phi ( or ). It is measured in degrees, minutes and seconds or decimal degrees, north or south of the equator. For navigational purposes positions are given in degrees and decimal minutes. For instance, The Needles lighthouse is at 50°39.734′ N 001°35.500′ W.


title: Latitude

text: This article relates to coordinate systems for the Earth: it may be adapted to cover the Moon, planets and other celestial objects (planetographic latitude).


title: Latitude

text: More precise measurement of latitude requires an understanding of the gravitational field of the Earth, either to set up theodolites or to determine GPS satellite orbits. The study of the figure of the Earth together with its gravitational field is the science of geodesy.


title: Latitude

text: The graticule is formed by the lines of constant latitude and constant longitude, which are constructed with reference to the rotation axis of the Earth. The primary reference points are the poles where the axis of rotation of the Earth intersects the reference surface. Planes which contain the rotation axis intersect the surface at the meridians; and the angle between any one meridian plane and that through Greenwich (the Prime Meridian) defines the longitude: meridians are lines of constant longitude. The plane through the centre of the Earth and perpendicular to the rotation axis intersects the surface at a great circle called the Equator. Planes parallel to the equatorial plane intersect the surface in circles of constant latitude; these are the parallels. The Equator has a latitude of 0°, the North Pole has a latitude of 90° North (written 90° N or +90°), and the South Pole has a latitude of 90° South (written 90° S or −90°). The latitude of an arbitrary point is the angle between the equatorial plane and the normal to the surface at that point: the normal to the surface of the sphere is along the radial vector.


title: Latitude

text: The latitude, as defined in this way for the sphere, is often termed the spherical latitude, to avoid ambiguity with the geodetic latitude and the auxiliary latitudes defined in subsequent sections of this article.


title: Latitude

text: The plane of the Earth's orbit about the Sun is called the ecliptic, and the plane perpendicular to the rotation axis of the Earth is the equatorial plane. The angle between the ecliptic and the equatorial plane is called variously the axial tilt, the obliquity, or the inclination of the ecliptic, and it is conventionally denoted by . The latitude of the tropical circles is equal to and the latitude of the polar circles is its complement (90° - "i"). The axis of rotation varies slowly over time and the values given here are those for the current epoch. The time variation is discussed more fully in the article on axial tilt.


title: Latitude

text: The figure shows the geometry of a cross-section of the plane perpendicular to the ecliptic and through the centres of the Earth and the Sun at the December solstice when the Sun is overhead at some point of the Tropic of Capricorn. The south polar latitudes below the Antarctic Circle are in daylight, whilst the north polar latitudes above the Arctic Circle are in night. The situation is reversed at the June solstice, when the Sun is overhead at the Tropic of Cancer. Only at latitudes in between the two tropics is it possible for the Sun to be directly overhead (at the zenith).


title: Latitude

text: On map projections there is no universal rule as to how meridians and parallels should appear. The examples below show the named parallels (as red lines) on the commonly used Mercator projection and the Transverse Mercator projection. On the former the parallels are horizontal and the meridians are vertical, whereas on the latter there is no exact relationship of parallels and meridians with horizontal and vertical: both are complicated curves.


title: Latitude

text: In 1687 Isaac Newton published the "Philosophiæ Naturalis Principia Mathematica", in which he proved that a rotating self-gravitating fluid body in equilibrium takes the form of an oblate ellipsoid. (This article uses the term "ellipsoid" in preference to the older term "spheroid".) Newton's result was confirmed by geodetic measurements in the 18th century. (See Meridian arc.) An oblate ellipsoid is the three-dimensional surface generated by the rotation of an ellipse about its shorter axis (minor axis). "Oblate ellipsoid of revolution" is abbreviated to 'ellipsoid' in the remainder of this article. (Ellipsoids which do not have an axis of symmetry are termed triaxial.)


title: Latitude

text: Many different reference ellipsoids have been used in the history of geodesy. In pre-satellite days they were devised to give a good fit to the geoid over the limited area of a survey but, with the advent of GPS, it has become natural to use reference ellipsoids (such as WGS84) with centre at the centre of mass of the Earth and minor axis aligned to the rotation axis of the Earth. These geocentric ellipsoids are usually within of the geoid. Since latitude is defined with respect to an ellipsoid, the position of a given point is different on each ellipsoid: one cannot exactly specify the latitude and longitude of a geographical feature without specifying the ellipsoid used. Many maps maintained by national agencies are based on older ellipsoids, so one must know how the latitude and longitude values are transformed from one ellipsoid to another. GPS handsets include software to carry out datum transformations which link WGS84 to the local reference ellipsoid with its associated grid.


title: Latitude

text: The shape of an ellipsoid of revolution is determined by the shape of the ellipse which is rotated about its minor (shorter) axis. Two parameters are required. One is invariably the equatorial radius, which is the semi-major axis, . The other parameter is usually (1) the polar radius or semi-minor axis, ; or (2) the (first) flattening, ; or (3) the eccentricity, . These parameters are not independent: they are related by


title: Latitude

text: Many other parameters (see ellipse, ellipsoid) appear in the study of geodesy, geophysics and map projections but they can all be expressed in terms of one or two members of the set , , and . Both and are small and often appear in series expansions in calculations; they are of the order and 0.0818 respectively. Values for a number of ellipsoids are given in Figure of the Earth. Reference ellipsoids are usually defined by the semi-major axis and the "inverse" flattening, . For example, the defining values for the WGS84 ellipsoid, used by all GPS devices, are


title: Latitude

text: The difference between the semi-major and semi-minor axes is about and as fraction of the semi-major axis it equals the flattening; on a computer monitor the ellipsoid could be sized as 300 by 299 pixels. This would barely be distinguishable from a 300-by-300-pixel sphere, so illustrations usually exaggerate the flattening.


title: Latitude

text: The graticule on the ellipsoid is constructed in exactly the same way as on the sphere. The normal at a point on the surface of an ellipsoid does not pass through the centre, except for points on the equator or at the poles, but the definition of latitude remains unchanged as the angle between the normal and the equatorial plane. The terminology for latitude must be made more precise by distinguishing:


title: Latitude

text: Geographic latitude must be used with care, as some authors use it as a synonym for geodetic latitude whilst others use it as an alternative to the astronomical latitude.


title: Latitude

text: The importance of specifying the reference datum may be illustrated by a simple example. On the reference ellipsoid for WGS84, the centre of the Eiffel Tower has a geodetic latitude of 48° 51′ 29″ N, or 48.8583° N and longitude of 2° 17′ 40″ E or 2.2944°E. The same coordinates on the datum ED50 define a point on the ground which is distant from the tower. A web search may produce several different values for the latitude of the tower; the reference ellipsoid is rarely specified.


title: Latitude

text: therefore equal to the angle subtended at the centre by the meridian arc from the equator to the point concerned. If the meridian distance is denoted by then


title: Latitude

text: where denotes the mean radius of the Earth. is equal to . No higher accuracy is appropriate for since higher-precision results necessitate an ellipsoid model. With this value for the meridian length of 1 degree of latitude on the sphere is (60.0 nautical miles). The length of 1 minute of latitude is (1.00 nautical miles), while the length of 1 second of latitude is (see nautical mile).


title: Latitude

text: In Meridian arc and standard texts it is shown that the distance along a meridian from latitude to the equator is given by ( in radians)


title: Latitude

text: The evaluation of the meridian distance integral is central to many studies in geodesy and map projection. It can be evaluated by expanding the integral by the binomial series and integrating term by term: see Meridian arc for details. The length of the meridian arc between two given latitudes is given by replacing the limits of the integral by the latitudes concerned. The length of a "small" meridian arc is given by


title: Latitude

text: The distance in metres (correct to 0.01 metre) between latitudes formula_7 − 0.5 degrees and formula_7 + 0.5 degrees on the WGS84 spheroid is


title: Latitude

text: The variation of this distance with latitude (on WGS84) is shown in the table along with the length of a degree of longitude (east–west distance):


title: Latitude

text: A calculator for any latitude is provided by the U.S. Government's National Geospatial-Intelligence Agency (NGA).


title: Latitude

text: The following graph illustrates the variation of both a degree of latitude and a degree of longitude with latitude.


title: Latitude

text: There are six auxiliary latitudes that have applications to special problems in geodesy, geophysics and the theory of map projections:


title: Latitude

text: The definitions given in this section all relate to locations on the reference ellipsoid but the first two auxiliary latitudes, like the geodetic latitude, can be extended to define a three-dimensional geographic coordinate system as discussed below. The remaining latitudes are not used in this way; they are used "only" as intermediate constructs in map projections of the reference ellipsoid to the plane or in calculations of geodesics on the ellipsoid. Their numerical values are not of interest. For example, no one would need to calculate the authalic latitude of the Eiffel Tower.


title: Latitude

text: The expressions below give the auxiliary latitudes in terms of the geodetic latitude, the semi-major axis, , and the eccentricity, . (For inverses see below.) The forms given are, apart from notational variants, those in the standard reference for map projections, namely "Map projections: a working manual" by J. P. Snyder. Derivations of these expressions may be found in Adams and online publications by Osborne and Rapp.


title: Latitude

text: The geocentric latitude is the angle between the equatorial plane and the radius from the centre to a point of interest.


title: Latitude

text: When the point is on the surface of the ellipsoid, the relation between the geocentric latitude () and the geodetic latitude () is:


title: Latitude

text: For points not on the surface of the ellipsoid, the relationship involves additionally the ellipsoidal height "h":


title: Latitude

text: The geodetic and geocentric latitudes are equal at the equator and at the poles but at other latitudes they differ by a few minutes of arc. Taking the value of the squared eccentricity as 0.0067 (it depends on the choice of ellipsoid) the maximum difference of formula_13 may be shown to be about 11.5 minutes of arc at a geodetic latitude of approximately 45° 6′.


title: Latitude

text: The parametric latitude or reduced latitude, , is defined by the radius drawn from the centre of the ellipsoid to that point on the surrounding sphere (of radius ) which is the projection parallel to the Earth's axis of a point on the ellipsoid at latitude . It was introduced by Legendre and Bessel who solved problems for geodesics on the ellipsoid by transforming them to an equivalent problem for spherical geodesics by using this smaller latitude. Bessel's notation, , is also used in the current literature. The parametric latitude is related to the geodetic latitude by:


title: Latitude

text: The alternative name arises from the parameterization of the equation of the ellipse describing a meridian section. In terms of Cartesian coordinates , the distance from the minor axis, and , the distance above the equatorial plane, the equation of the ellipse is:


title: Latitude

text: The parametric latitude is not used in the theory of map projections. Its most important application is in the theory of ellipsoid geodesics, (Vincenty, Karney).


title: Latitude

text: The rectifying latitude, , is the meridian distance scaled so that its value at the poles is equal to 90 degrees or radians:


title: Latitude

text: defines a projection from the ellipsoid to the sphere such that all meridians have true length and uniform scale. The sphere may then be projected to the plane with an equirectangular projection to give a double projection from the ellipsoid to the plane such that all meridians have true length and uniform meridian scale. An example of the use of the rectifying latitude is the equidistant conic projection. (Snyder, Section 16). The rectifying latitude is also of great importance in the construction of the Transverse Mercator projection.


title: Latitude

text: The authalic latitude (after the Greek for "same area"), , gives an area-preserving transformation to a sphere.


title: Latitude

text: The conformal latitude defines a transformation from the ellipsoid to a sphere of "arbitrary" radius such that the angle of intersection between any two lines on the ellipsoid is the same as the corresponding angle on the sphere (so that the shape of "small" elements is well preserved). A further conformal transformation from the sphere to the plane gives a conformal double projection from the ellipsoid to the plane. This is not the only way of generating such a conformal projection. For example, the 'exact' version of the Transverse Mercator projection on the ellipsoid is not a double projection. (It does, however, involve a generalisation of the conformal latitude to the complex plane).


title: Latitude

text: The isometric latitude, , is used in the development of the ellipsoidal versions of the normal Mercator projection and the Transverse Mercator projection. The name "isometric" arises from the fact that at any point on the ellipsoid equal increments of and longitude give rise to equal distance displacements along the meridians and parallels respectively. The graticule defined by the lines of constant and constant , divides the surface of the ellipsoid into a mesh of squares (of varying size). The isometric latitude is zero at the equator but rapidly diverges from the geodetic latitude, tending to infinity at the poles. The conventional notation is given in Snyder (page 15):


title: Latitude

text: For the "normal" Mercator projection (on the ellipsoid) this function defines the spacing of the parallels: if the length of the equator on the projection is (units of length or pixels) then the distance, , of a parallel of latitude from the equator is


title: Latitude

text: The formulae in the previous sections give the auxiliary latitude in terms of the geodetic latitude. The expressions for the geocentric and parametric latitudes may be inverted directly but this is impossible in the four remaining cases: the rectifying, authalic, conformal, and isometric latitudes. There are two methods of proceeding.


title: Latitude

text: The plot to the right shows the difference between the geodetic latitude and the auxiliary latitudes other than the isometric latitude (which diverges to infinity at the poles) for the case of the WGS84 ellipsoid. The differences shown on the plot are in arc minutes.


title: Latitude

text: In the Northern hemisphere (positive latitudes), "θ" ≤ "χ" ≤ "μ" ≤ "ξ" ≤ "β" ≤ "ϕ"; in the Southern hemisphere (negative latitudes), the inequalities are reversed, with equality at the equator and the poles. Although the graph appears symmetric about 45°, the minima of the curves actually lie between 45° 2′ and 45° 6′. Some representative data points are given in the table below. The conformal and geocentric latitudes are nearly indistinguishable, a fact that was exploited in the days of hand calculators to expedite the construction of map projections.


title: Latitude

text: The geodetic latitude, or any of the auxiliary latitudes defined on the reference ellipsoid, constitutes with longitude a two-dimensional coordinate system on that ellipsoid. To define the position of an arbitrary point it is necessary to extend such a coordinate system into three dimensions. Three latitudes are used in this way: the geodetic, geocentric and parametric latitudes are used in geodetic coordinates, spherical polar coordinates and ellipsoidal coordinates respectively.


title: Latitude

text: At an arbitrary point consider the line which is normal to the reference ellipsoid. The geodetic coordinates are the latitude and longitude of the point on the ellipsoid and the distance . This height differs from the height above the geoid or a reference height such as that above mean sea level at a specified location. The direction of will also differ from the direction of a vertical plumb line. The relation of these different heights requires knowledge of the shape of the geoid and also the gravity field of the Earth.


title: Latitude

text: The geocentric latitude is the complement of the "polar angle" or "colatitude" in conventional spherical polar coordinates in which the coordinates of a point are where is the distance of from the centre , is the angle between the radius vector and the polar axis and is longitude. Since the normal at a general point on the ellipsoid does not pass through the centre it is clear that points on the normal, which all have the same geodetic latitude, will have differing geocentric latitudes. Spherical polar coordinate systems are used in the analysis of the gravity field.


title: Latitude

text: The parametric latitude can also be extended to a three-dimensional coordinate system. For a point not on the reference ellipsoid (semi-axes and ) construct an auxiliary ellipsoid which is confocal (same foci , ) with the reference ellipsoid: the necessary condition is that the product of semi-major axis and eccentricity is the same for both ellipsoids. Let be the semi-minor axis () of the auxiliary ellipsoid. Further let be the parametric latitude of on the auxiliary ellipsoid. The set define the ellipsoidal-harmonic coordinates or simply "ellipsoidal coordinates" (although that term is also used to refer to geodetic coordinate). These coordinates are the natural choice in models of the gravity field for a rotating ellipsoidal body.


title: Latitude

text: The above applies to a biaxial ellipsoid (a spheroid, as in oblate spheroidal coordinates); for a generalization, see triaxial ellipsoidal coordinates.


title: Latitude

text: The relations between the above coordinate systems, and also Cartesian coordinates are not presented here. The transformation between geodetic and Cartesian coordinates may be found in geographic coordinate conversion. The relation of Cartesian and spherical polars is given in spherical coordinate system. The relation of Cartesian and ellipsoidal coordinates is discussed in Torge.


title: Latitude

text: Astronomical latitude () is the angle between the equatorial plane and the true vertical direction at a point on the surface. The true vertical, the direction of a plumb line, is also the gravity direction (the resultant of the gravitational acceleration (mass-based) and the centrifugal acceleration) at that latitude. Astronomic latitude is calculated from angles measured between the zenith and stars whose declination is accurately known.


title: Latitude

text: In general the true vertical at a point on the surface does not exactly coincide with either the normal to the reference ellipsoid or the normal to the geoid. The angle between the astronomic and geodetic normals is called "vertical deflection" and is usually a few seconds of arc but it is important in geodesy. The reason why it differs from the normal to the geoid is, because the geoid is an idealized, theoretical shape "at mean sea level". Points on the real surface of the earth are usually above or below this idealized geoid surface and here the true vertical can vary slightly. Also, the true vertical at a point at a specific time is influenced by tidal forces, which the theoretical geoid averages out.


title: Latitude

text: Astronomical latitude is not to be confused with declination, the coordinate astronomers use in a similar way to specify the angular position of stars north/south of the celestial equator (see equatorial coordinates), nor with ecliptic latitude, the coordinate that astronomers use to specify the angular position of stars north/south of the ecliptic (see ecliptic coordinates).


title: Happier Than Ever

text: Happier Than Ever is the second studio album by American singer Billie Eilish, released by Darkroom and Interscope Records on July 30, 2021. Eilish co-wrote the album with her brother Finneas O'Connell, her frequent collaborator who also produced the album and played every instrument. Eilish cited self-reflection during the COVID-19 pandemic as the biggest inspiration for the LP.


title: Happier Than Ever

text: Primarily a downtempo pop record, "Happier Than Ever" is characterized by sparse, jazz-influenced, electropop arrangements set to meditative tempos, departing from the upbeat, trap-led sound of Eilish's debut album, "When We All Fall Asleep, Where Do We Go?" (2019). Consisting of torch songs about the downsides of stardom, "Happier Than Ever" draws heavily from Eilish's rise to fame and the drawbacks that come with it. Upon release, the album received acclaim from music critics, who praised its stylistic, restrained production, and insightful lyrics. At the 64th Annual Grammy Awards, the album and its title track received a total of seven nominations, including Album of the Year, Best Pop Vocal Album, Song of the Year and Record of the Year.


title: Happier Than Ever

text: Seven singles were released in promotion of the album: "My Future", "Therefore I Am", "Your Power", "Lost Cause", "NDA", the title track, and "Male Fantasy"; the first three peaked within the top 10 of the US "Billboard" Hot 100. "Therefore I Am" was the highest-charting song from the album, peaking at number two, followed by "My Future" at number six, and "Your Power" at number 10. "Happier Than Ever" debuted atop the "Billboard" 200 as Eilish's second number-one album in the United States, and topping the album charts in 27 other countries. Eilish performed the album's tracks in the Disney+ concert film, "", which was released on September 3, 2021. To further promote the album, Eilish embarked on her sixth concert tour, titled Happier Than Ever, The World Tour, which ran from February 3 to September 30, 2022.


title: Happier Than Ever

text: Eilish released her debut album "When We All Fall Asleep, Where Do We Go?" (which was also produced by her brother) on March 29, 2019. It was met with critical acclaim and commercial success, and spawned the "Billboard" Hot 100-topping single "Bad Guy", her first number-one on the chart. The album and the single helped Eilish win five awards at the 62nd Annual Grammy Awards, including the "big four" Album of the Year, Song of the Year, Record of the Year, and Best New Artist. Eilish released a number of singles since the album: the stand-alone "Everything I Wanted" (2019), the "James Bond" theme song "No Time to Die" (2020), and the Rosalía collaboration "Lo Vas a Olvidar" (2021), the first two of which won the Record of the Year and Best Song Written for Visual Media at the 63rd Grammy Awards, respectively. In a January 2020 interview, Eilish stated she would begin working on her upcoming second studio album during the year. In March, Eilish's brother Finneas O'Connell confirmed this, stating that it would be "pretty pure in its intention" like Eilish's debut, with the two continuing to make the type of music they like to "play live". In January 2021, Eilish stated that the album "feels exactly how I want it to", with her not wanting to change a single thing about it. Her documentary film, "", was released the following month. Later in February, Eilish announced the album would have 16 tracks.


title: Happier Than Ever

text: "Happier Than Ever" was recorded at Finneas' home recording studio, located in the basement of his Los Angeles residence. According to Eilish, recording took place between April 1, 2020, and February 16, 2021, in weekly schedules, starting with "My Future" and ending with "Oxytocin". The title track was the first song she wrote from the record, dating back to the European leg of her When We All Fall Asleep Tour. Eilish revealed that all of 16 songs on the final track listing were the only songs the duo worked on during the album's creation, yet there were two songs, namely "What I Wanna Hear" and "Born Blue", that were omitted from the record since she "just couldn't figure them out".


title: Happier Than Ever

text: Eilish has revealed that the creative process of "Happier Than Ever" felt "very natural", unlike her previous projects where she constantly felt anxious and under pressure. With earlier works, Eilish also felt that she was not good enough and simply was not talented, but has since gained much more confidence in her craft. According to Eilish, her record label did not have any input on the album, unlike her debut album where she felt pressure from deadlines, constant meetings and "an expectation that a star was about to be born", all of which she "literally hated".


title: Happier Than Ever

text: In an interview with Vevo, Eilish said that she wanted to create "a very timeless record", mostly being inspired by jazz singers that she listened to growing up such as Julie London, Peggy Lee and Frank Sinatra. She also said that the songs on the album are "all over the place and very, I think, versatile, different to one another, but also very cohesive," which she cited as one of her biggest goals. Another one of her goals she had during studio sessions was to surprise her fans as well as herself. She aimed to be uncomfortable during the creative process, using "NDA" as an example of a song that was not made in her "comfort zone". Eilish cited self-reflection as the biggest muse behind the record, and revealed before its release that "almost none of the songs on this album are joyful". She noted "Male Fantasy" as a song that "pretty much wrote itself" and helped her realize feelings she had not processed before.


title: Happier Than Ever

text: Musically, "Happier Than Ever" is a subdued, pop, electropop, downtempo, and jazz-pop record, incorporating elements of R&B, techno, country, bossa nova, bedroom pop, trip hop, folk, electro, trap, and 1990s sophisti-pop. It consists of torch songs set to slow tempos, with restrained, minimalistic arrangements of acoustic guitars, delicate synthesizers, and burbling beats. The lyrics deal with struggles faced by young women in the entertainment industry, fame, stardom, emotional abuse, power struggles, mistrust, and misogyny, imbued by Eilish's self-consciousness. In Robert Christgau's opinion, Eilish's songwriting had inspired Finneas to devise a sound for the album that is "calmer and less sprightly" than her earlier breakthrough work.


title: Happier Than Ever

text: The opening track, "Getting Older", is a song about abuse and was "particularly harrowing" to write. The song deals with sexual coercion. The second track, "I Didn't Change My Number", features a heavy beat. "Billie Bossa Nova", the third track, presents "a more mature side of Eilish". The fourth track, "My Future", starts as a slow synth ballad that "transitions into a laidback funk groove". Lyrically, the song is about self-discovery. "Oxytocin", the fifth track, has a techno pulse. The song references the titular hormone. The sixth track, "Goldwing", loops its a capella introduction throughout the song. The eighth track, "Halley's Comet", is a ballad featuring stripped-back vocals, light synths, and a backbeat. The ninth track, "Not My Responsibility", is a spoken word interlude with an ambient instrumental that debuted on Eilish's Where Do We Go? World Tour (2020).


title: Happier Than Ever

text: The interlude then transitions into the tenth track, "Overheated", which samples the production of its predecessor and explores stardom in the era of social media. The eleventh track "Everybody Dies", is an alt-pop ballad, driven by dark synths and light guitar strumming, with "Eilish's voice again standing out". The twelfth track, "Your Power", is a soft acoustic ballad about sexual abuse and being taken advantage of by your partner. The thirteenth track, "NDA" discusses the lack of privacy in her life due to her rise in fame over a dark electropop beat which transitions into the fourteenth track "Therefore I Am", which is lyrically about dismissing the haters and critics. The fifteenth track, "Happier Than Ever", is a rock opera song. It has been described as "a mopey breakup song", before breaking into "an electric-guitar-driven rager", while the rest of the tracks "bare different kinds of catharsis, teetering between sexy, electronic beats and warm folkiness, reminiscent of her earliest music." It has been dubbed an album highlight. The album closes with "Male Fantasy", a slow-tempo ballad that finds Billie reflecting on relationships and sexual growth.


title: Happier Than Ever

text: On April 26, 2021, Eilish began hinting at upcoming music, and revealed the title, "Happier Than Ever", in an Instagram post on April 26, including a 15-second snippet of the title track, which had been previously teased in the documentary film. The following day, Eilish announced "Happier Than Ever" as the album title, after billboards announcing its title and release date reportedly began appearing in various cities. "Happier Than Ever" was released on July 30, 2021. It was available in a variety of physical album formats, such as eight differently colored vinyl LPs, including retail-exclusives for Amazon, independent record stores, Target, Urban Outfitters and Walmart, ten CD variants, including autographed CDs at independent stores, a version with alternate packaging hand-painted by Eilish, three premium box sets, a Target-exclusive edition packaged with a poster, and multiple cassette tape variants, including a deluxe box set.


title: Happier Than Ever

text: On December 2, Eilish announced that she has teamed up with an Italian fashion house Gucci for an eco-friendly limited vinyl edition of "Happier Than Ever". The set was released the following day, featuring vinyls created entirely from leftover recycled materials gathered during the original pressing of the record and a Gucci-branded nail stickers. The box and stickers were designed by the brand's creative director Alessandro Michele. Additionally, the colector's edition was sold in a physical Gucci stores throughout the world. The cover of this edition has a "psychedelic pattern" in the background. Next month, during the 30th anniversary of Interscope Records, the label announced a museum exhibit, "Artists Inspired by Music: Interscope Reimagined", featuring new cover arts of the projects released by the label. Those artworks were featured on the limited vinyl release. "Happier Than Ever" new cover was designed by American artist Lisa Yuskavage.


title: Happier Than Ever

text: Eilish appeared on the cover of June 2021 issue of "British Vogue", wearing a corset. The photoshoot provoked polarizing reactions. The singer also were interviewed for that magazine, and also for such publications as "the Guardian" and "Rolling Stone". To support the album in the United Kingdom, a television special titled "Billie Eilish: Up Close" was broadcast on BBC One on July 31, in tandem with Eilish's debut on the BBC Live Lounge. All of the album's tracks received lyric videos on YouTube upon its release. For the first anniversary of the album, Eilish shared voice memos of her recording takes for "Billie Bossa Nova", "Lost Cause", "Your Power", the title track, and "Male Fantasy".


title: Happier Than Ever

text: On June 16, 2021, Eilish performed a 27-minute set on Prime Day Show, including renditions of first four singles from "Happier Than Ever", "All the Good Girls Go to Hell", and "Everything I Wanted". The set was later released on Amazon Music to download and streaming as a digital EP. The artist partnered with an American video hosting service Vevo to create a series of "Official Vevo Live Performances" in promotion of "Happier Than Ever". So far, four renditions of the album songs were published on the singer's official YouTube account; in chronogical order: "Your Power" on July 18, "Male Fantasy" on August 4, "Lost Cause" on October 21, and "Billie Bossa Nova" on January 13, 2022. Two additional in-studio performances were uploaded to Eilish's channel, namely "NDA" on July 16, 2021, and an acoustic rendition of "Billie Bossa Nova" on December 20.


title: Happier Than Ever

text: On July 29, 2021, Eilish appeared on German program "Undersing", where she performed "NDA" and "Billie Bossa Nova". On August 5, the singer appeared in BBC Radio 1's Live Lounge with a 4-song set consisting of "Getting Older", "I Didn't Change My Number", "NDA", and a cover of Frances Langford's "I'm in the Mood for Love". Next month, she was on gigs such as iHeartRadio Music Festival and Life Is Beautiful Music & Art Festival, where she performed some of the album tracks. The same month, she also performed "Getting Older" and "Billie Bossa Nova" for TIME ABC. In November, Eilish was featured in "Sesame Street", where she gave an alternate rendition of the title track with Count von Count. The following month, the artist was performing a double duty in "Saturday Night Live" of the show's host and musical guest, in addition to various sketches, she performed "Happier Than Ever" and "Male Fantasy" in a scenery nodding to the tracks' music videos. To mark the album's one-year anniversary, Eilish and Finneas held performances at the Amoeba Music record store in Hollywood. The store's employees stated that 500 tickets were sold, as well as many guests were invited. The setlist included "Getting Older", "Billie Bossa Nova", and the title track. They also performed "TV", which is part of her second extended play "Guitar Songs".


title: Happier Than Ever

text: On July 22, 2021, Eilish teased a concert film that featured performances of all 16 tracks from the album, set for an exclusive release to Disney+ on September 3, 2021. Titled , it was directed by Robert Rodriguez and Patrick Osborne, and it features live action scenes blended with animation. The concert took place at the Hollywood Bowl without a live audience due to the COVID-19 pandemic; additional scenes were recorded at various landmarks around Los Angeles. Critics praised the film's performances, which they felt were of similar or better quality compared to the songs' studio versions.


title: Happier Than Ever

text: Eilish announced that she would embark on a world tour in support of "Happier Than Ever", through a video released on her YouTube channel, on May 21. The tickets were made available for sale one week later. The tour consisted of 72 concerts across North America, Europe, and Oceania. It began on February 3, 2022, in New Orleans, United States, and concluded on September 30, 2022, in Perth, Australia. Parts of the tour were held on festivals such as Coachella Valley Music and Arts Festival and Glastonbury Festival.


title: Happier Than Ever

text: To mark the tour's conclusion, Eilish worked with Apple Music to exclusively host a film of one of the concerts, specifically one of her shows at the O2 Arena in London. She billed the film as a way for fans who missed out on tickets to experience the tour for themselves, wanting more people to recognize her for her showmanship live. Months later, Eilish revealed the Happier Than Ever, The Hometown Encore, two concerts at the Kia Forum in Inglewood, California, from December 15 to 16, 2022. The shows intend to celebrate the success of the album and its corresponding world tour.


title: Happier Than Ever

text: Seven singles were released in support of "Happier Than Ever", with the first six managing to chart within top 40 on the "Billboard" Hot 100 in the United States. The album's lead single, "My Future", was released on July 30, 2020, one year before the album's scheduled release date. An accompanying animated music video was published the same day as the song and was directed by Australian animator Andrew Onorato. The single was critically acclaimed, even appearing at some publication's year-end lists as one of the best song of the year. It debuted at number six on the "Billboard" Hot 100, becoming her third top ten entry. Besides not receiving radio treatment in the United States, "My Future" is the only single of the album that appeared on physical discs. The second single, "Therefore I Am", was released on November 12, 2020, with an accompanying music video directed by Eilish herself. The song met with a positive critical reception and, commercially, became the biggest single of "Happier Than Ever". The single debuted at number 94 on the "Billboard" Hot 100, rising to number two the following week, making it the fourth-greatest leap in the Hot 100's history with a vault of 92 positions. The track was promoted through the 2020 American Music Awards live performance.


title: Happier Than Ever

text: "Your Power" arrived on April 29, 2021, as the album's third single with an accompanying music video. Well received by music critics, it was next single promoting the project that landed within the top ten of the US "Billboard" Hot 100. It was promoted by a performance on "The Late Show with Stephen Colbert", and became the second single after "Therefore I Am" that impacted American radios. On June 2, "Lost Cause" was released as the fourth single. The accompanying music video sparked a queerbaiting controversy. Without any radio impact dates or live performances, the track failed to chart any higher than 27 in the United States. The fifth single, "NDA", was released on July 9, along with another self-directed visual. Even though the song received an official studio performance video and radio release in the United States, the single barely scratched Hot 100's top 40, charting at number 39. Additionally, the single was not received as warmly by music critics as previous efforts, with "Rolling Stone India" calling it one of the worst songs of 2021. Due to the moderate success of those singles, Eilish received backlash from her fans, who dubbed the then-upcoming album as her "flop era".


title: Happier Than Ever

text: The final two songs of "Happier Than Ever", namely the title track and "Male Fantasy", were chosen as the album's sixth and seventh singles, respectively. Similarly to how the music video for "Bad Guy" was published on the same day as "When We All Fall Asleep, Where Do We Go?" (2019), the music video for "Happier Than Ever" was uploaded to Eilish's YouTube account on the same day as the release of its parent album, on July 30, 2021. The song was met with widespread critical acclaim, topping "Harper's Bazaar"s best songs of 2021 list. Eilish performed the single on numerous occasions, such as on "The Tonight Show Starring Jimmy Fallon" and "Jimmy Kimmel Live!". The track reached top ten in 17 countries, including the United Kingdom where it peaked at number 4, becoming her sixth UK top five single. However, in the United States, "Happier Than Ever" missed the top ten, debuting on the Hot 100 at number 11. On December 6, Eilish debuted the video for "Male Fantasy", with the song being issued as the seventh single. Even though critically acclaimed, the song did not manage to appear on many charts. Both "Male Fantasy" and "Happier Than Ever" were performed by Eilish on "Saturday Night Live" on December 11.


title: Happier Than Ever

text: Upon release, "Happier Than Ever" received critical acclaim from music critics, who admired its resolute portrayal of teenage stardom contrasting its muted sound. At Metacritic, which assigns a normalized rating out of 100 to reviews from publications, the album has a weighted mean score of 86 based on 27 reviews, indicating "universal acclaim".


title: Happier Than Ever

text: "NME" critic El Hunt lauded the album for proving Eilish "one of her generation's most significant pop artists", and wrote that its music is "softer" and "far more low-key" than her debut record. Alexis Petridis of "The Guardian" noted the "uniformly great" melodies and vocals, the "less flashy" production in "Happier Than Ever", observing a "more somber" tone. Sal Cinquemani of "Slant" felt the album is more "sonically diverse" than Eilish's debut record, expanding beyond its predecessor's trip-hop and trap elements. "The Daily Telegraph" Neil McCormick dubbed "Happier Than Ever" "the sound of a tortured teen alone in her bedroom late at night", its lyrics "pithy", and Eilish's vocals "delicate".


title: Happier Than Ever

text: Reviewing in his Substack-published "Consumer Guide" column, Robert Christgau gave "Happier Than Ever" an "A" and applauded Eilish for conceiving original ideas about fame through "sheer candor", highlighting her lyrics on "Getting Older", "Not My Responsibility", and "Everybody Dies". Louis Bruton of "The Irish Times" stated the album describes "the confinements and exploitations of being a celebrity and a teenager." Rob Sheffield, writing for "Rolling Stone", called it a "downright heroic", "dark, painful, confessional album where [Eilish is] choosing not to settle into the role of America's beloved kooky kid sister." David Smyth of "Evening Standard" complimented the style and non-mainstream appeal of the album's production. "Clash" Robin Murray called "Happier Than Ever" "a work of subtle evolution" and "a record of quite complexity".


title: Happier Than Ever

text: "Variety" Chris Willman highlighted the album's "trenchant observation", "self-aware humor", and "post-celebrity self-consciousness". Sarah Carson of "i" labeled the album a "great, understated, philosophical" project inclining towards sparse and acoustic pop music trends. Jesse Atkinson of "Gigwise" called the album's production extraordinary, admiring its interpretation of music genres. Giselle Au-Nhien Nguyen of "The Sydney Morning Herald" deemed the album a cohesive, "revealing and rewarding, listening experience" enhanced by Eilish's "acidic" delivery. In his "Slate" review, Carl Wilson liked the musical and lyrical maturity Eilish displays in "Happier Than Ever". "The New York Times" Lindsay Zoladz felt the album is "fixated on the tension between private and public knowledge, a social-media-era pop star's meditation on how much candor—if any—she owes her audience."


title: Happier Than Ever

text: A few reviews were critical of "Happier Than Ever". Alexandra Pollard of "The Independent" remarked that the album is "full of things most of us don't have to deal with", but Eilish turns them into relatable stories via "insightful" songs. She dismissed the tracks "Oxytocin" and "Goldwing" as insubstantial. In a mixed review, Matthew Kent of "The Line of Best Fit" commended Eilish's lyrics and Finneas' production, but regarded the album a less unique work, with its tracks "often blurring into each other." "Consequence" critic Mary Siroky, despite her overall warm review, also agreed that the album could be too cohesive with sonically indistinct songs. "The A.V. Club" Alex McLevy felt "there are just a few too many tracks on "Happier Than Ever", which starts off unstoppably strong, but starts to falter in the back half." "Stereogum" Tom Breihan wrote negatively, calling the album a boring, "shell-shocked" product of Eilish's attempts at making a second album as triumphant as her first.


title: Happier Than Ever

text: A few weeks before its release, with over 1.028 million pre-adds of "Happier Than Ever", Eilish reclaimed the Apple Music record for the most pre-saved album ever in the platform's history; Canadian singer the Weeknd had previously seized the record from Eilish's own "When We All Fall Asleep, Where Do We Go?" (2019) with his album "After Hours" (2020). The International Federation of the Phonographic Industry reported that Eilish was the third best-selling female artist of 2021, behind Taylor Swift and Adele.


title: Happier Than Ever

text: "Happier Than Ever" marked Eilish's second number-one album in the United States. It debuted atop the "Billboard" 200 with 238,000 album-equivalent units, the fifth largest week for an album in 2021. Of the 238,000 units, sales constitutes 154,000 copies, which is the third largest album sales week in 2021, and 84,000 units calculated from the 113.87 million on-demand streams the album received in its first week. The tally also consists of 73,000 vinyl LPs shipped in the same week.


title: Happier Than Ever

text: The album topped the "Billboard" 200 for its first three consecutive weeks, becoming the first album by a woman to do so since Swift's "Folklore" (2020), and the second album in 2021 to achieve the feat, after "" by American singer Morgan Wallen. Nine songs from the album charted on the all-genre "Billboard" Hot 100 simultaneously, whereas all of its tracks charted on the Hot Rock & Alternative Songs chart, with the title track, "Happier Than Ever", debuting at number one.


title: Happier Than Ever

text: In the United Kingdom, the album debuted at number one on the UK Albums Chart with 39,000 units, scoring Eilish's second number-one album in the country. With over 9,500 vinyl record sales, "Happier Than Ever" became the third-fastest selling vinyl album of the millennium by a female artist in the UK. The album debuted atop Germany's Offizielle Top 100 as Eilish's first number one album there. It eclipsed her debut album, which peaked at number three.


title: Happier Than Ever

text: In Australia, the album landed atop the ARIA Albums Chart, her second number one in the country, whilst five songs debuted on the ARIA Singles Chart; all of the album's five singles charted on the chart previously. "Happier Than Ever" entered at the number one spot of France's SNEP albums chart with 14,695 units, becoming her first French number-one album.


title: Six degrees of separation

text: Six degrees of separation is the idea that all people are six or fewer social connections away from each other. As a result, a chain of "friend of a friend" statements can be made to connect any two people in a maximum of six steps. It is also known as the six handshakes rule.


title: Six degrees of separation

text: The concept was originally set out in a 1929 short story by Frigyes Karinthy, where a group of people play a game trying to connect any person in the world to themselves by a chain of five others. It was popularized in John Guare's 1990 play "Six Degrees of Separation".


title: Six degrees of separation

text: The idea is sometimes generalized to the average social distance being logarithmic in the size of the population.


title: Six degrees of separation

text: Theories on optimal design of cities, city traffic flows, neighborhoods, and demographics were in vogue after World War I. These conjectures were expanded in 1929 by Hungarian author Frigyes Karinthy, who published a volume of short stories titled "Everything is Different." One of these pieces was titled "Chains," or "Chain-Links." The story investigated in abstract, conceptual, and fictional terms many of the problems that would captivate future generations of mathematicians, sociologists, and physicists within the field of network theory. Due to technological advances in communications and travel, friendship networks could grow larger and span greater distances. In particular, Karinthy believed that the modern world was 'shrinking' due to this ever-increasing connectedness of human beings. He posited that despite great physical distances between the globe's individuals, the growing density of human networks made the actual social distance far smaller.


title: Six degrees of separation

text: As a result of this hypothesis, Karinthy's characters believed that any two individuals could be connected through at most five acquaintances. In his story, the characters create a game out of this notion. He wrote:


title: Six degrees of separation

text: A fascinating game grew out of this discussion. One of us suggested performing the following experiment to prove that the population of the Earth is closer together now than they have ever been before. We should select any person from the 1.5 billion inhabitants of the Earth – anyone, anywhere at all. He bet us that, using no more than "five" individuals, one of whom is a personal acquaintance, he could contact the selected individual using nothing except the network of personal acquaintances.


title: Six degrees of separation

text: This idea influenced a great deal of early thought on social networks, both directly and indirectly. Karinthy has been regarded as the originator of the notion of six degrees of separation.


title: Six degrees of separation

text: A related theory deals with the quality of connections, rather than their existence. The theory of three degrees of influence was created by Nicholas A. Christakis and James H. Fowler.


title: Six degrees of separation

text: Michael Gurevich conducted seminal work in his empirical study of the structure of social networks in his 1961 Massachusetts Institute of Technology PhD dissertation under Ithiel de Sola Pool. Mathematician Manfred Kochen, an Austrian who had been involved in urban design, extrapolated these empirical results in a mathematical manuscript, "Contacts and Influences", concluding that in a U.S.-sized population without social structure, "it is practically certain that any two individuals can contact one another by means of at most two intermediaries. In a [socially] structured population it is less likely but still seems probable. And perhaps for the whole world's population, probably only one more bridging individual should be needed." They subsequently constructed Monte Carlo simulations based on Gurevich's data, which recognized that both weak and strong acquaintance links are needed to model social structure. The simulations, carried out on the relatively limited computers of 1973, were nonetheless able to predict that a more realistic three degrees of separation existed across the U.S. population, foreshadowing the findings of American psychologist Stanley Milgram.


title: Six degrees of separation

text: Milgram continued Gurevich's experiments in acquaintanceship networks at Harvard University in Cambridge, Massachusetts, U.S. Kochen and de Sola Pool's manuscript, "Contacts and Influences", was conceived while both were working at the University of Paris in the early 1950s, during a time when Milgram visited and collaborated in their research. Their unpublished manuscript circulated among academics for over 20 years before publication in 1978. It formally articulated the mechanics of social networks, and explored the mathematical consequences of these (including the degree of connectedness). The manuscript left many significant questions about networks unresolved, and one of these was the number of degrees of separation in actual social networks. Milgram took up the challenge on his return from Paris, leading to the experiments reported in "The Small World Problem" in popular science journal "Psychology Today", with a more rigorous version of the paper appearing in Sociometry two years later. The "Psychology Today" article generated enormous publicity for the experiments, which are well known today, long after much of the formative work has been forgotten.


title: Six degrees of separation

text: Milgram's article made famous his 1967 set of experiments to investigate de Sola Pool and Kochen's "small world problem." Mathematician Benoit Mandelbrot, born in Warsaw, growing up in Poland then France, was aware of the Statist rule of thumb, and was also a colleague of de Sola Pool, Kochen and Milgram at the University of Paris during the early 1950s (Kochen brought Mandelbrot to work at the Institute for Advanced Study and later IBM in the U.S.). This circle of researchers was fascinated by the interconnectedness and "social capital" of human networks. Milgram's study results showed that people in the United States seemed to be connected by approximately three friendship links, on average, without speculating on global linkages; he never actually used the term "six degrees of separation." Since the "Psychology Today" article gave the experiments wide publicity, Milgram, Kochen, and Karinthy all had been incorrectly attributed as the origin of the notion of six degrees; the most likely popularizer of the term "six degrees of separation" would be John Guare, who attributed the value '6' to Marconi.


title: Six degrees of separation

text: In 2003, Columbia University conducted an analogous experiment on social connectedness amongst Internet email users. Their effort was named the Columbia Small World Project, and included 24,163 e-mail chains, aimed at 18 targets from 13 countries. Almost 100,000 people registered, but only 384 (0.4%) reached the final target. Amongst the successful chains, while shorter lengths were more common some reached their target after only 7, 8, 9 or 10 steps. Dodds et al. noted that participants (all of whom volunteers) were strongly biased towards existing models of Internet users and that connectedness based on professional ties was much stronger than those within families or friendships. The authors cite "lack of interest" as the predominating factor in the high attrition rate, a finding consistent with earlier studies.


title: Six degrees of separation

text: Several studies, such as Milgram's small-world experiment, have been conducted to measure this connectedness empirically. The phrase "six degrees of separation" is often used as a synonym for the idea of the "small world" phenomenon.


title: Six degrees of separation

text: However, detractors argue that Milgram's experiment did not demonstrate such a link, and the "six degrees" claim has been decried as an "academic urban myth".


title: Six degrees of separation

text: In 2001, Duncan Watts, a professor at Columbia University, attempted to recreate Milgram's experiment on the Internet, using an e-mail message as the "package" that needed to be delivered, with 48,000 senders and 19 targets (in 157 countries). Watts found that the average (though not maximum) number of intermediaries was around six.


title: Six degrees of separation

text: A 2007 study by Jure Leskovec and Eric Horvitz examined a data set of instant messages composed of 30 billion conversations among 240 million people. They found the average path length among Microsoft Messenger users to be 6.


title: Six degrees of separation

text: It has been suggested by some commentators that interlocking networks of computer-mediated lateral communication could diffuse single messages to all interested users worldwide as per the six degrees of separation principle via information routing groups, which are networks specifically designed to exploit this principle and lateral diffusion.


title: Six degrees of separation

text: Bakhshandeh "et al." have addressed the search problem of identifying the degree of separation between two users in social networks such as Twitter. They have introduced new search techniques to provide optimal or near optimal solutions. The experiments are performed using Twitter, and they show an improvement of several orders of magnitude over greedy approaches. Their optimal algorithm finds an average degree of separation of 3.43 between two random Twitter users, requiring an average of only 67 requests for information over the Internet to Twitter. A near-optimal solution of length 3.88 can be found by making an average of 13.3 requests.


title: Six degrees of separation

text: No longer limited strictly to academic or philosophical thinking, the notion of six degrees recently has become influential throughout popular culture. Further advances in communication technology – and particularly the Internet – have drawn great attention to social networks and human interconnectedness. As a result, many popular media sources have addressed the term. The following provide a brief outline of the ways such ideas have shaped popular culture.


title: Six degrees of separation

text: American playwright John Guare wrote a play in 1990 and released a 1993 film that popularized it; it is Guare's most widely known work. The play ruminates upon the idea that any two individuals are connected by at most five others. As one of the characters states:


title: Six degrees of separation

text: I read somewhere that everybody on this planet is separated by only six other people. Six degrees of separation between us and everyone else on this planet. The President of the United States, a gondolier in Venice, just fill in the names. I find it A) extremely comforting that we're so close, and B) like Chinese water torture that we're so close because you have to find the right six people to make the right connection... I am bound to everyone on this planet by a trail of six people.


title: Six degrees of separation

text: Guare, in interviews, attributed his awareness of the "six degrees" to Marconi. Although this idea had been circulating in various forms for decades, it is Guare's piece that is most responsible for popularizing the phrase "six degrees of separation." Following Guare's lead, many future television and film sources would later incorporate the notion into their stories.


title: Six degrees of separation

text: J. J. Abrams, the executive producer of television series "Six Degrees" and "Lost", played the role of Doug in the film adaptation of this play.


title: Six degrees of separation

text: The game "Six Degrees of Kevin Bacon" was invented as a play on the concept: the goal is to link any actor to Kevin Bacon through no more than six connections, where two actors are connected if they have appeared in a movie or commercial together. It was created by three students at Albright College in Pennsylvania, who came up with the concept while watching "Footloose". On September 13, 2012, Google made it possible to search for any given actor's "Bacon Number" through their search engine.


title: Six degrees of separation

text: Upon the arrival of the 4G mobile network in the United Kingdom, Kevin Bacon appears in several commercials for the EE Network in which he links himself to several well known celebrities and TV shows in the UK.


title: Six degrees of separation

text: An early version involved former world Heavyweight boxing champion, John L. Sullivan, in which people would ask others to "shake the hand that shook the hand that shook the hand that shook the hand of 'the great John L.'"


title: Six degrees of separation

text: In 2013, Hungarian physicist Albert-László Barabási discovered that, on average, there are 19 degrees of separation between any two web pages.


title: Six degrees of separation

text: Several "degrees of Wikipedia" web services have been created, where the shortest paths between two Wikipedia articles can be discovered automatically.


title: Six degrees of separation

text: A Facebook platform application named "Six Degrees" was developed by Karl Bunyan, which calculates the degrees of separation between people. It had over 5.8 million users, as seen from the group's page. The average separation for all users of the application is 5.73 degrees, whereas the maximum degree of separation is 12. The application has a "Search for Connections" window to input any name of a Facebook user, to which it then shows the chain of connections. In June 2009, Bunyan shut down the application, presumably due to issues with Facebook's caching policy; specifically, the policy prohibited the storing of friend lists for more than 24 hours; following this would have made the application inaccurate. A new version of the application became available at Six Degrees after Karl Bunyan gave permission to a group of developers led by Todd Chaffee to re-develop the application based on Facebook's revised policy on caching data.


title: Six degrees of separation

text: The initial version of the application was built at a Facebook Developers Garage London hackathon with Mark Zuckerberg in attendance.


title: Six degrees of separation

text: Yahoo! Research Small World Experiment has been conducting an experiment and everyone with a Facebook account can take part in it. According to the research page, this research has the potential of resolving the still unresolved theory of six degrees of separation.


title: Six degrees of separation

text: Facebook's data team released two papers in November 2011 which document that amongst all Facebook users at the time of research (721 million users with 69 billion friendship links) there is an average distance of 4.74. Probabilistic algorithms were applied on statistical metadata to verify the accuracy of the measurements. It was also found that 99.91% of Facebook users were interconnected, forming a large connected component.


title: Six degrees of separation

text: Facebook reported that the distance had decreased to 4.57 in February 2016, when it had 1.6 billion users (about 22% of the world population).


title: Six degrees of separation

text: The LinkedIn professional networking site operates the degree of separation one is away from a person with which he or she wishes to communicate. On LinkedIn, one's network is made up of 1st-degree, 2nd-degree, and 3rd-degree connections and fellow members of LinkedIn Groups. In addition, LinkedIn notifies the user how many connections they and any other user have in common.


title: Six degrees of separation

text: SixDegrees.com was an early social-networking website that existed from 1997 to 2000. It allowed users to list friends, family members and acquaintances, send messages and post bulletin board items to people in their first, second, and third degrees, and see their connection to any other user on the site. At its height, it had 3,500,000 fully registered members. However, it was closed in 2000.


title: Six degrees of separation

text: Users on Twitter can follow other users creating a network. According to a 2010 study of 5.2 billion such relationships by social media monitoring firm Sysomos, the average distance on Twitter is 4.67. On average, about 50% of people on Twitter are only four steps away from each other, while nearly everyone is five steps or less away.


title: Six degrees of separation

text: In another work, researchers have shown that the average distance of 1,500 random users in Twitter is 3.435. They calculated the distance between each pair of users using all the active users in Twitter.


title: Six degrees of separation

text: Mathematicians use an analogous notion of "collaboration distance": two persons are linked if they are coauthors of an article. The collaboration distance with mathematician Paul Erdős is called the Erdős number. Erdős-Bacon numbers and Erdős-Bacon-Sabbath (EBS) numbers are further extensions of the same thinking.


title: Six degrees of separation

text: Watts and Strogatz showed that the average path length between two nodes in a random network is equal to , where = total nodes and = acquaintances per node. Thus if


title: Six degrees of separation

text: A 2007 article published in "The Industrial-Organizational Psychologist", by Jesse S. Michel from Michigan State University, applied Stanley Milgram's small world phenomenon (i.e., “small world problem”) to the field of I-O psychology through co-author publication linkages. Following six criteria, Scott Highhouse (Bowling Green State University professor and fellow of the Society of Industrial and Organizational Psychology) was chosen as the target. Co-author publication linkages were determined for (1) top authors within the I-O community, (2) quasi-random faculty members of highly productive I-O programs in North America, and (3) publication trends of the target. Results suggest that the small world phenomenon is alive and well with mean linkages of 3.00 to top authors, mean linkages of 2.50 to quasi-random faculty members, and a relatively broad and non-repetitive set of co-author linkages for the target. The author then provided a series of implications and suggestions for future research.


title: Liminality

text: In anthropology, liminality () is the quality of ambiguity or disorientation that occurs in the middle stage of a rite of passage, when participants no longer hold their pre-ritual status but have not yet begun the transition to the status they will hold when the rite is complete. During a rite's liminal stage, participants "stand at the threshold" between their previous way of structuring their identity, time, or community, and a new way (which completing the rite establishes).


title: Liminality

text: The concept of liminality was first developed in the early twentieth century by folklorist Arnold van Gennep and later taken up by Victor Turner. More recently, usage of the term has broadened to describe political and cultural change as well as rites. During liminal periods of all kinds, social hierarchies may be reversed or temporarily dissolved, continuity of tradition may become uncertain, and future outcomes once taken for granted may be thrown into doubt. The dissolution of order during liminality creates a fluid, malleable situation that enables new institutions and customs to become established. The term has also passed into popular usage and has been expanded to include liminoid experiences that are more relevant to post-industrial society.


title: Liminality

text: Van Gennep, who coined the term liminality, published in 1909 his "Rites de Passage", a work that explores and develops the concept of liminality in the context of rites in small-scale societies. Van Gennep began his book by identifying the various categories of rites. He distinguished between those that result in a change of status for an individual or social group, and those that signify transitions in the passage of time. In doing so, he placed a particular emphasis on rites of passage, and claimed that "such rituals marking, helping, or celebrating individual or collective passages through the cycle of life or of nature exist in every culture, and share a specific three-fold sequential structure".


title: Liminality

text: Turner confirmed his nomenclature for "the three phases of passage from one culturally defined state or status to another..."preliminal", "liminal", and "postliminal"".


title: Liminality

text: Beyond this structural template, Van Gennep also suggested four categories of rites that emerge as universal across cultures and societies. He suggested that there are four types of social rites of passage that are replicable and recognizable among many ethnographic populations. They include:


title: Liminality

text: Van Gennep considered rites of initiation to be the most typical rite. To gain a better understanding of "tripartite structure" of liminal situations, one can look at a specific rite of initiation: the initiation of youngsters into adulthood, which Turner considered the most typical rite. In such rites of passage, the experience is highly structured. The first phase (the rite of separation) requires the child to go through a separation from his family; this involves his/her "death" as a child, as childhood is effectively left behind. In the second stage, initiands (between childhood and adulthood) must pass a "test" to prove they are ready for adulthood. If they succeed, the third stage (incorporation) involves a celebration of the "new birth" of the adult and a welcoming of that being back into society.


title: Liminality

text: By constructing this three-part sequence, van Gennep identified a pattern he believed was inherent in all ritual passages. By suggesting that such a sequence is universal (meaning that all societies use rites to demarcate transitions), van Gennep made an important claim (one that not many anthropologists make, as they generally tend to demonstrate cultural diversity while shying away from universality).