title: Wilderness

text: The United States was one of the first countries to officially designate land as "wilderness" through the Wilderness Act of 1964. The Wilderness Act is an important part of wilderness designation because it created the legal definition of wilderness and established the National Wilderness Preservation System. The Wilderness Act defines wilderness as "an area where the earth and its community of life are untrammelled by man, where man himself is a visitor who does not remain."


title: Wilderness

text: Wilderness designation helps preserve the natural state of the land and protects flora and fauna by prohibiting development and providing for non-mechanized recreation only.


title: Wilderness

text: The first administratively protected wilderness area in the United States was the Gila National Forest. In 1922, Aldo Leopold, then a ranking member of the U.S. Forest Service, proposed a new management strategy for the Gila National Forest. His proposal was adopted in 1924, and 750,000 acres of the Gila National Forest became the Gila Wilderness.


title: Wilderness

text: The Great Swamp in New Jersey was the first formally designated wilderness refuge in the United States. It was declared a wildlife refuge on 3 November 1960. In 1966 it was declared a National Natural Landmark and, in 1968, it was given wilderness status. Properties in the swamp had been acquired by a small group of residents of the area, who donated the assembled properties to the federal government as a park for perpetual protection. Today the refuge amounts to that are within thirty miles of Manhattan.


title: Wilderness

text: While wilderness designations were originally granted by an Act of Congress for Federal land that retained a "primeval character", meaning that it had not suffered from human habitation or development, the Eastern Wilderness Act of 1975 extended the protection of the NWPS to areas in the eastern states that were not initially considered for inclusion in the Wilderness Act. This act allowed lands that did not meet the constraints of size, roadlessness, or human impact to be designated as wilderness areas under the belief that they could be returned to a "primeval" state through preservation.


title: Wilderness

text: Approximately are designated as wilderness in the United States. This accounts for 4.82% of the country's total land area; however, 54% of that amount is found in Alaska (recreation and development in Alaskan wilderness is often less restrictive), while only 2.58% of the lower continental United States is designated as wilderness. As of 2019 there are 803 designated wilderness areas in the United States ranging in size from Florida's Pelican Island at to Alaska's Wrangell-Saint Elias at .


title: Wilderness

text: In Western Australia, a wilderness area is an area that has a wilderness quality rating of 12 or greater and meets a minimum size threshold of 80 km in temperate areas or 200 km in arid and tropical areas. A wilderness area is gazetted under section 62(1)(a) of the Conservation and Land Management Act 1984 by the Minister on any land that is vested in the Conservation Commission of Western Australia.


title: Wilderness

text: At the forefront of the international wilderness movement has been The WILD Foundation, its founder Ian Player and its network of sister and partner organizations around the globe. The pioneer World Wilderness Congress in 1977 introduced the wilderness concept as an issue of international importance, and began the process of defining the term in biological and social contexts. Today, this work is continued by many international groups who still look to the World Wilderness Congress as the international venue for wilderness and to The WILD Foundation network for wilderness tools and action. The WILD Foundation also publishes the standard references for wilderness professionals and others involved in the issues: "Wilderness Management: Stewardship and Protection of Resources and Values", the "International Journal of Wilderness", "A Handbook on International Wilderness Law and Policy" and "Protecting Wild Nature on Native Lands" are the backbone of information and management tools for international wilderness issues.


title: Wilderness

text: The Wilderness Specialist Group within the World Commission on Protected Areas (WTF/WCPA) of the International Union for Conservation of Nature (IUCN) plays a critical role in defining legal and management guidelines for wilderness at the international level and is also a clearing-house for information on wilderness issues. The IUCN Protected Areas Classification System defines wilderness as "A large area of unmodified or slightly modified land, and/or sea retaining its natural character and influence, without permanent or significant habitation, which is protected and managed so as to preserve its natural condition (Category 1b)." The WILD Foundation founded the WTF/WCPA in 2002 and remains co-chair.


title: Wilderness

text: The most recent efforts to map wilderness show that less than one quarter (~23%) of the world's wilderness area now remains, and that there have been catastrophic declines in wilderness extent over the last two decades. Over 3 million square kilometers (10 percent) of wilderness was converted to human land-uses. The Amazon and Congo rain forests suffered the most loss. Human pressure is extending into almost every corner of the planet. The loss of wilderness could have serious implications for biodiversity conservation.


title: Wilderness

text: According to a previous study, "Wilderness: Earth's Last Wild Places," carried out by Conservation International, 46% of the world's land mass is wilderness. For purposes of this report, "wilderness" was defined as an area that "has 70% or more of its original vegetation intact, covers at least and must have fewer than five people per square kilometer." However, an IUCN/UNEP report published in 2003, found that only 10.9% of the world's land mass is currently a Category 1 Protected Area, that is, either a "strict nature reserve" (5.5%) or "protected wilderness" (5.4%). Such areas remain relatively untouched by humans. Of course, there are large tracts of lands in national parks and other protected areas that would also qualify as wilderness. However, many protected areas have some degree of human modification or activity, so a definitive estimate of true wilderness is difficult.


title: Wilderness

text: The Wildlife Conservation Society generated a "human footprint" using a number of indicators, the absence of which indicate wildness: human population density, human access via roads and rivers, human infrastructure for agriculture and settlements and the presence of industrial power (lights visible from space). The society estimates that 26% of the Earth's land mass falls into the category of "Last of the wild." The wildest regions of the world include the Arctic Tundra, the Siberia Taiga, the Amazon rainforest, the Tibetan Plateau, the Australia Outback and deserts such as the Sahara, and the Gobi. However, from the 1970s, numerous geoglyphs have been discovered on deforested land in the Amazon rainforest, leading to claims about Pre-Columbian civilizations. The BBC's "Unnatural Histories" claimed that the Amazon rainforest, rather than being a pristine wilderness, has been shaped by man for at least 11,000 years through practices such as forest gardening and terra preta.


title: Wilderness

text: The percentage of land area designated wilderness does not necessarily reflect a measure of its biodiversity. Of the last natural wilderness areas, the taiga—which is mostly wilderness—represents 11% of the total land mass in the Northern Hemisphere. Tropical rainforest represent a further 7% of the world's land base. Estimates of the Earth's remaining wilderness underscore the rate at which these lands are being developed, with dramatic declines in biodiversity as a consequence.


title: Wilderness

text: The American concept of wilderness has been criticized by some nature writers. For example, William Cronon writes that what he calls a wilderness ethic or cult may "teach us to be dismissive or even contemptuous of such humble places and experiences", and that "wilderness tends to privilege some parts of nature at the expense of others", using as an example "the mighty canyon more inspiring than the humble marsh." This is most clearly visible with the fact that nearly all U.S. National Parks preserve spectacular canyons and mountains, and it was not until the 1940s that a swamp became a national park—the Everglades. In the mid-20th century national parks started to protect biodiversity, not simply attractive scenery.


title: Wilderness

text: Cronon also believes the passion to save wilderness "poses a serious threat to responsible environmentalism" and writes that it allows people to "give ourselves permission to evade responsibility for the lives we actually lead... to the extent that we live in an urban-industrial civilization but at the same time pretend to ourselves that our real home is in the wilderness".


title: Wilderness

text: Michael Pollan has argued that the wilderness ethic leads people to dismiss areas whose wildness is less than absolute. In his book "Second Nature", Pollan writes that "once a landscape is no longer 'virgin' it is typically written off as fallen, lost to nature, irredeemable." Another challenge to the conventional notion of wilderness comes from Robert Winkler in his book, "Going Wild: Adventures with Birds in the Suburban Wilderness". "On walks in the unpeopled parts of the suburbs," Winkler writes, "I’ve witnessed the same wild creatures, struggles for survival, and natural beauty that we associate with true wilderness." Attempts have been made, as in the Pennsylvania Scenic Rivers Act, to distinguish "wild" from various levels of human influence: in the Act, "wild rivers" are "not impounded", "usually not accessible except by trail", and their watersheds and shorelines are "essentially primitive".


title: Wilderness

text: Another source of criticism is that the criteria for wilderness designation is vague and open to interpretation. For example, the Wilderness Act states that wilderness must be roadless. The definition given for roadless is "the absences of roads which have been improved and maintained by mechanical means to insure relatively regular and continuous use". However, there have been added sub-definitions that have, in essence, made this standard unclear and open to interpretation, and some are drawn to narrowly exclude existing roads.


title: Wilderness

text: Coming from a different direction, some criticism from the Deep Ecology movement argues against conflating "wilderness" with "wilderness reservations", viewing the latter term as an oxymoron that, by allowing the law as a human construct to define nature, unavoidably voids the very freedom and independence of human control that defines wilderness. True wilderness requires the ability of life to undergo speciation with as little interference from humanity as possible. Anthropologist and scholar on wilderness Layla Abdel-Rahim argues that it is necessary to understand the principles that govern the economies of mutual aid and diversification in wilderness from a non-anthropocentric perspective.


title: Wilderness

text: Others have criticized the American concept of wilderness as rooted in white supremacy, ignoring Native American perspectives on the natural environment and excluding people of color from narratives about human interactions with the environment. Many early conservationists, such as Madison Grant, were also heavily involved in the eugenics movement. Grant, who worked alongside President Theodore Roosevelt to create the Bronx Zoo, also wrote "The Passing of the Great Race", a book on eugenics that was later praised by Adolf Hitler. Grant is also known to have featured Ota Benga, a Mbuti man from Central Africa, in the Bronx Zoo monkey house exhibit. John Muir, another important figure in the early conservation movement, referred to African-Americans as "making a great deal of noise and doing little work", and compared Native Americans to unclean animals who did not belong in the wilderness. Environmental history professor Miles A. Powell of Nanyang Technological University has argued that much of the early conservation movement was deeply tied to and inspired by a desire to preserve the Nordic race. Prakash Kashwan, a political science professor at the University of Connecticut who specializes in environmental policies and environmental justice, argues that the racist ideas of many early conservationists created a narrative of wilderness that has led to "fortress conservation" policies that have driven Native Americans off of their land. Kashwan has proposed conservation practices that would allow Indigenous people to continue using the land as a more just and more effective alternative to fortress conservation. The idea that the natural world is primarily made up of remote wilderness areas has also been criticized as classist, with environmental sociologist Dorceta Taylor arguing that this leads to experiencing wilderness becoming a privilege, as working-class people are often unable to afford transportation to wilderness areas. She further argues that, due to poverty and lack of access to transportation caused by systemic racism, this perception is also rooted in racism.


title: Wilderness

text: Another critique of wilderness is that it perpetuates the human-nature dichotomy. The idea that nature and humans are separate entities can be traced back to European colonial views. To European settlers, land was an inherited right and was to be used to profit. While native groups saw their relationship with the land in a more holistic view, they were eventually subjected to European property systems. Colonists from Europe saw the American landscape as wild, savage, dark, [etc.] and thus needed to be tamed in order for it to be safe and habitable. Once cleared and settled, these areas were depicted as "Eden itself". Yet the native peoples of those lands saw "wilderness" as that when the connection between humans and nature is broken. For native communities, human intervention was a part of their ecological practices.


title: Wilderness

text: There is a historical belief that wilderness must not only be tamed to be protected but that humans also need to be outside of it. In order to clear certain areas for conservation, such as national parks, involved the removal of native communities from their land. Some authors have come to describe this type of conservation as conservation-far, where humans and nature are kept separate. The other end of the conservation spectrum then, would be conservation-near, which would mimic native ecological practices of humans integrated into the care of nature.


title: Wilderness

text: Most scientists and conservationists agree that no place on earth is completely untouched by humanity, either due to past occupation by indigenous people, or through global processes such as climate change or pollution. Activities on the margins of specific wilderness areas, such as fire suppression and the interruption of animal migration, also affect the interior of wildernesses.


title: Diamond Star Halos

text: Diamond Star Halos is the twelfth studio album by the English rock band Def Leppard. It was released on 27 May 2022 through Bludgeon Riffola and Mercury Records, and is the band's first studio album in nearly seven years since 2015's "Def Leppard". The album takes its name from the 1971 T. Rex single "Get It On" and includes imagery from Anton Corbijn, Maryam Malakpour, and Oliver and Joshua Munden.


title: Diamond Star Halos

text: "Ultimate Classic Rock"s Michael Gallucci called the album "most obvious callback to glam's glory days as well as their own past triumphs", claiming that the band have learned to not "mess with what works" unlike past projects "Slang" and "X". Having noted influences of glam rock stars David Bowie, Mott the Hoople and T. Rex, Gallucci also wrote that while, "like most tribute albums, the take-and-give results on "Diamond Star Halos" don't always match what was heard the first time around", "the band hasn't sounded this invigorated on record since the early '90s." "The Arts Desk"s Joe Muggs wrote that "this album starts and ends so brilliantly", starting with "a salvo of three tracks that remind you exactly why Def Leppard became one of the biggest bands in the world in the mid Eighties" and ending with "heavily Queen-indebted high drama closer 'From Here to Eternity'", a "grand way to close a record", contrasting with a middle section that is "way too generic, slightly countrified and very American soft rock" and "can't really live up" to "these great bookends".


title: Diamond Star Halos

text: "Blabbermouth.net"s Dom Lawson explains the band's appeal as being because they "have never stopped behaving like the wide-eyed, priapic teenagers they were when they penned 'Hello America' all those years ago" rather than "resting on their laurels, touring the world on an endless nostalgia trip and never again making a new album", and that while the band are "relaxed" and the album "low on shiny bells and high-tech whistles", "it compensates by being (mainly) full of simple, heartfelt and punchy songs" and "is a very good time had by all." "Louder Sound"s Neil Jeffries called "SOS Emergency", "All We Need", "Open Your Eyes", "Gimme a Kiss", and "Unbreakable" "especially strong" and "stadium pleasers in the grand Leppard tradition"; and the album "best appreciated as a double album: three sides, each begun by three rockers and ending with a change of pace, then a shorter fourth side that abandons the pattern and goes out on the high of [Rick] Savage's 'From Here to Eternity', an epic track with a swinging, Pink Floyd-like tempo." "The Telegraph"s James Hall also emphasised the album's "[not messing] with the formula" in comparison to "Slang", save for the "fascinating curveballs" brought in the form of the Alison Krauss-featuring "This Guitar" and "Lifeless", the former of which Hall called the better of the two and "a subtle (by Def Leppard standards) ballad that could well turn out to be a smash in the Nashville country charts." AllMusic's Stephen Thomas Erlewine wrote that "Leppard crank up the hooks, melodies, and amplifiers, adding little bits of distinctive flair along the way", noting that "its individual moments may not be excessive" but "the cumulative effect is almost overwhelming, especially as Def Leppard gives it their all in each cut."


title: Paul Smith (fashion designer)

text: Sir Paul Brierley Smith (born 5 July 1946) is a British fashion designer. His reputation is founded on his designs for men's clothing, but his business has expanded into other areas as well. Smith was made a Royal Designer for Industry in 1991.


title: Paul Smith (fashion designer)

text: His eponymous fashion company was founded in 1970 and has expanded into over 70 countries, selling its products via standalone stores, departments in high-end stores or malls, along with airport terminals, as well as the e-commerce section of its international website. Some of his brand's stores are recognized for their uniqueness and eccentricity, including the much-photographed vibrant, fluorescent pink flagship store in Los Angeles.


title: Paul Smith (fashion designer)

text: Smith was born in 1946 in Beeston, Nottinghamshire, England, the son of Harold Smith, and is the youngest of three children. One of his early ambitions was to become a professional cyclist. He left school at the age of 15 to work in a Nottingham clothing warehouse, while practising cycling outside of work hours. He cycled to and from work until the age of 17, when he was in a major cycling accident that put him in hospital for close to six months. During his recovery, friends inspired him to enter the world of art and fashion. Smith has regularly referenced cycling in his work over the years.


title: Paul Smith (fashion designer)

text: He started to take classes in tailoring and eventually began working with a Savile Row tailor, Lincroft Kilgour.


title: Paul Smith (fashion designer)

text: Smith opened his own shop called Paul Smith Vêtements Pour Homme in Nottingham in 1970, which sold established clothing labels, alongside pieces that Smith had designed. The store was just 3 square metres and was located at 6 Byard Lane in Nottingham.


title: Paul Smith (fashion designer)

text: In 1976, Smith travelled to Paris to showcase his first men's collection, which featured a mix of casual and semi-formal wear. After that the Paul Smith brand continued to grow and he opened his flagship London store in 1979 on Floral Street in Covent Garden, London.


title: Paul Smith (fashion designer)

text: 'Paul Smith Women' his first womenswear collection was launched in 1993, after reports of women coming into his stores buying smaller sizes to wear themselves.


title: Paul Smith (fashion designer)

text: The first Japan store opened in Tokyo in 1984, growing over the years to 165 stores across the country.


title: Paul Smith (fashion designer)

text: Smith opened his first shop in New York on Fifth Avenue in 1987. The company now has four shops in the state, the flagship on Greene Street as well as Williamsburg, Bleecker Street and Brookfield Place.


title: Paul Smith (fashion designer)

text: In 1993, Smith took over a 'workwear' clothing company R. Newbold (established in 1885) and incorporated many of their designs into his new collection.


title: Paul Smith (fashion designer)

text: His childrenswear collection started in 1990 with the launch of a one-off collection for boys, including casual and tailored pieces. In 2010, Smith launched 'Paul Smith Junior' as a seasonal collection which often included remakes of his adult collections.


title: Paul Smith (fashion designer)

text: In 1995, the Design Museum exhibited 'True Brit', a show marking 25 years of his business. The show then went on to Glasgow for the 'Festival of Design' and then moved to his hometown of Nottingham and put on display in Nottingham Castle.


title: Paul Smith (fashion designer)

text: In 2016, Smith's second book, "Paul Smith's Cycling Scrapbook" was released, which documents a personal history of the sport he is very passionate about.


title: Paul Smith (fashion designer)

text: In January 2016, Smith combined his men's and women's fashion shows, showcasing during Paris Fashion Week.


title: Paul Smith (fashion designer)

text: Smith was appointed Commander of the Order of the British Empire (CBE) in the 1994 New Year Honours for services to fashion. He was knighted in the 2000 Birthday Honours and appointed Member of the Order of the Companions of Honour (CH) in the 2020 Birthday Honours for services to fashion.


title: Paul Smith (fashion designer)

text: Smith's first collaboration with Maharam, the US textile brand, originally used in one of his suit designs, the two continue to work together on new ranges.


title: Paul Smith (fashion designer)

text: Smith redesigned the Lasonic i931 boombox, giving it a white look with Smith's trademark multicolour look.


title: Paul Smith (fashion designer)

text: For the 60th anniversary of Penguin Classics, Paul Smith was asked to choose and redesign one cover, he chose Lady Chatterley's Lover by DH Lawrence.


title: Paul Smith (fashion designer)

text: Smith began working with the UK-based boutique cycle clothing retailer, Rapha. Smith designed a range of cycle clothing in association with Rapha, including a jersey to celebrate the rare start of the Tour de France in London.


title: Paul Smith (fashion designer)

text: Curated by the Isle of Man Post Office, Smith designed a set of stamps to mark the launch of the London Olympics.


title: Paul Smith (fashion designer)

text: Smith started a collaboration with Anglepoise, reimagining their Type 75 lamp as Edition One, he has since gone on to creating multiple editions.


title: Paul Smith (fashion designer)

text: Smith designed a series of T-shirts in collaboration with the release of David Bowie's final album ★ (Blackstar).


title: Paul Smith (fashion designer)

text: Smith worked with Kask for the first time to design their 'Protone' aero helmet. In 2018 a second helmet was released.


title: Paul Smith (fashion designer)

text: The first collaboration between Paul Smith & Caran d'Ache, launched 10 colours of their '849' pen. They went on to work together again in 2016.


title: Paul Smith (fashion designer)

text: For the 120th anniversary of Globe-Trotter, Smith collaborated with the company by redesigning their 20" trolley case, this was first showcased at the Salone del Mobile.


title: Paul Smith (fashion designer)

text: Celebrating 30 years of New Balance's 576 sneaker (trainer), Smith redesigned with his iconic stripe design, along with a series of footballs and football boot.


title: Paul Smith (fashion designer)

text: In tribute to his close friend Tony Gross, the company collaborated with Cutler & Gross on a limited edition collection of eyewear for his spring/summer 2019 show in Paris.


title: Paul Smith (fashion designer)

text: Smith worked with James Turner of Sports Purpose to cover a 1965 Porsche 911 with multicoloured stripes, which went on to compete at Le Mans Classic and Goodwood Festival of Speed.


title: Paul Smith (fashion designer)

text: Smith designed a Mini Electric using sustainable principles, with recycled and natural materials for example cork. Smith's Mini Strip was designed to break "the unwritten law that even small cars have to be shiny, polished luxury products."


title: Chirality (physics)

text: A chiral phenomenon is one that is not identical to its mirror image (see the article on mathematical chirality). The spin of a particle may be used to define a handedness, or helicity, for that particle, which, in the case of a massless particle, is the same as chirality. A symmetry transformation between the two is called parity transformation. Invariance under parity transformation by a Dirac fermion is called chiral symmetry.


title: Chirality (physics)

text: The helicity of a particle is positive (“right-handed”) if the direction of its spin is the same as the direction of its motion. It is negative (“left-handed”) if the directions of spin and motion are opposite. So a standard clock, with its spin vector defined by the rotation of its hands, has left-handed helicity if tossed with its face directed forwards.


title: Chirality (physics)

text: Mathematically, "helicity" is the sign of the projection of the spin vector onto the momentum vector: “left” is negative, “right” is positive.


title: Chirality (physics)

text: The chirality of a particle is more abstract: It is determined by whether the particle transforms in a right- or left-handed representation of the Poincaré group.


title: Chirality (physics)

text: For massless particles – photons, gluons, and (hypothetical) gravitons – chirality is the same as helicity; a given massless particle appears to spin in the same direction along its axis of motion regardless of point of view of the observer.


title: Chirality (physics)

text: For massive particles – such as electrons, quarks, and neutrinos – chirality and helicity must be distinguished: In the case of these particles, it is possible for an observer to change to a reference frame moving faster than the spinning particle, in which case the particle will then appear to move backwards, and its helicity (which may be thought of as “apparent chirality”) will be reversed. That is, helicity is a constant of motion, but it is not Lorentz invariant. Chirality is Lorentz invariant, but is not a constant of motion - a propagating massive left-handed spinor will evolve into a right handed spinor over time, and vice versa.


title: Chirality (physics)

text: A "massless" particle moves with the speed of light, so no real observer (who must always travel at less than the speed of light) can be in any reference frame where the particle appears to reverse its relative direction of spin, meaning that all real observers see the same helicity. Because of this, the direction of spin of massless particles is not affected by a change of viewpoint (Lorentz boost) in the direction of motion of the particle, and the sign of the projection (helicity) is fixed for all reference frames: The helicity of massless particles is a "relativistic invariant" (a quantity whose value is the same in all inertial reference frames) which always matches the massless particles' chirality.


title: Chirality (physics)

text: The discovery of neutrino oscillation implies that neutrinos have mass, so the photon is the only known massless particle. Gluons are also expected to be massless, although the assumption that they are has not been conclusively tested. Hence, these are the only two particles now known for which helicity could be identical to chirality, and only the photon has been confirmed by measurement. All other observed particles have mass and thus may have different helicities in different reference frames.


title: Chirality (physics)

text: Particle physicists have only observed or inferred left-chiral fermions and right-chiral antifermions engaging in the charged weak interaction. Even in the case of the electrically neutral weak interaction, which can engage with both left- and right-chiral fermions, in most circumstances two left-handed fermions interact more strongly than right-handed or opposite-handed fermions, implying that the universe has a preference for left-handed chirality. This preferential treatment of one chirality over another violates a symmetry that holds for all other forces of nature.


title: Chirality (physics)

text: Chirality for a Dirac fermion is defined through the operator, which has eigenvalues ±1. Any Dirac field can thus be projected into its left- or right-handed component by acting with the projection operators or on .


title: Chirality (physics)

text: The coupling of the charged weak interaction to fermions is proportional to the first projection operator, which is responsible for this interaction's parity symmetry violation.


title: Chirality (physics)

text: A common source of confusion is due to conflating the , chirality operator with the helicity operator. Since the helicity of massive particles is frame-dependent, it might seem that the same particle would interact with the weak force according to one frame of reference, but not another. The resolution to this paradox is that "the chirality operator is equivalent to helicity for massless fields only", for which helicity is not frame-dependent. By contrast, for massive particles, "chirality is not the same as helicity", so there is no frame dependence of the weak interaction: A particle that couples to the weak force in one frame does so in every frame.


title: Chirality (physics)

text: A theory that is asymmetric with respect to chiralities is called a "chiral theory", while a non-chiral (i.e., parity-symmetric) theory is sometimes called a "vector theory". Many pieces of the Standard Model of physics are non-chiral, which is traceable to anomaly cancellation in chiral theories. Quantum chromodynamics is an example of a "vector theory", since both chiralities of all quarks appear in the theory, and couple to gluons in the same way.


title: Chirality (physics)

text: The electroweak theory, developed in the mid 20th century, is an example of a "chiral theory". Originally, it assumed that neutrinos were massless, and only assumed the existence of left-handed neutrinos (along with their complementary right-handed antineutrinos). After the observation of neutrino oscillations, which imply that neutrinos are massive (like all other fermions) the revised theories of the electroweak interaction now include both right- and left-handed neutrinos. However, it is still a chiral theory, as it does not respect parity symmetry.


title: Chirality (physics)

text: The exact nature of the neutrino is still unsettled and so the electroweak theories that have been proposed are somewhat different, but most accommodate the chirality of neutrinos in the same way as was already done for all other fermions.


title: Chirality (physics)

text: Vector gauge theories with massless Dirac fermion fields exhibit chiral symmetry, i.e., rotating the left-handed and the right-handed components independently makes no difference to the theory. We can write this as the action of rotation on the fields:


title: Chirality (physics)

text: More generally, we write the right-handed and left-handed states as a projection operator acting on a spinor. The right-handed and left-handed projection operators are


title: Chirality (physics)

text: Massive fermions do not exhibit chiral symmetry, as the mass term in the Lagrangian, , breaks chiral symmetry explicitly.


title: Chirality (physics)

text: Spontaneous chiral symmetry breaking may also occur in some theories, as it most notably does in quantum chromodynamics.


title: Chirality (physics)

text: The chiral symmetry transformation can be divided into a component that treats the left-handed and the right-handed parts equally, known as vector symmetry, and a component that actually treats them differently, known as axial symmetry. (cf. Current algebra.) A scalar field model encoding chiral symmetry and its breaking is the chiral model.


title: Chirality (physics)

text: The most common application is expressed as equal treatment of clockwise and counter-clockwise rotations from a fixed frame of reference.


title: Chirality (physics)

text: The general principle is often referred to by the name chiral symmetry. The rule is absolutely valid in the classical mechanics of Newton and Einstein, but results from quantum mechanical experiments show a difference in the behavior of left-chiral versus right-chiral subatomic particles.


title: Chirality (physics)

text: Consider quantum chromodynamics (QCD) with two "massless" quarks and (massive fermions do not exhibit chiral symmetry). The Lagrangian reads


title: Chirality (physics)

text: The Lagrangian is unchanged under a rotation of "q" by any 2×2 unitary matrix , and "q" by any 2×2 unitary matrix .


title: Chirality (physics)

text: This symmetry of the Lagrangian is called "flavor chiral symmetry", and denoted as . It decomposes into


title: Chirality (physics)

text: However, it does not correspond to a conserved quantity, because the associated axial current is not conserved. It is explicitly violated by a quantum anomaly.


title: Chirality (physics)

text: formula_15 formed through nonperturbative action of QCD gluons, into the diagonal vector subgroup SU(2) known as isospin. The Goldstone bosons corresponding to the three broken generators are the three pions.


title: Chirality (physics)

text: As a consequence, the effective theory of QCD bound states like the baryons, must now include mass terms for them, ostensibly disallowed by unbroken chiral symmetry. Thus, this chiral symmetry breaking induces the bulk of hadron masses, such as those for the nucleons — in effect, the bulk of the mass of all visible matter.


title: Chirality (physics)

text: In the real world, because of the nonvanishing and differing masses of the quarks, SU(2) × SU(2) is only an approximate symmetry to begin with, and therefore the pions are not massless, but have small masses: they are pseudo-Goldstone bosons.


title: Chirality (physics)

text: For more "light" quark species, flavors in general, the corresponding chiral symmetries are "U"("N") × "U"("N"), decomposing into


title: Chirality (physics)

text: Most usually,  = 3 is taken, the "u, d", and "s" quarks taken to be light (the Eightfold way (physics)), so then approximately massless for the symmetry to be meaningful to a lowest order, while the other three quarks are sufficiently heavy to barely have a residual chiral symmetry be visible for practical purposes.


title: Chirality (physics)

text: In theoretical physics, the electroweak model breaks parity maximally. All its fermions are chiral Weyl fermions, which means that the charged weak gauge bosons W and W only couple to left-handed quarks and leptons.


title: Chirality (physics)

text: Some theorists found this objectionable, and so conjectured a GUT extension of the weak force which has new, high energy W' and Z' bosons, which "do" couple with right handed quarks and leptons:


title: Chirality (physics)

text: Here, SU(2) (pronounced “SU(2) left”) is none other than SU(2) from above, while "B−L" is the baryon number minus the lepton number. The electric charge formula in this model is given by


title: Chirality (physics)

text: where formula_20 and formula_21 are the left and right weak isospin values of the fields in the theory.


title: Chirality (physics)

text: There is also the chromodynamic SU(3). The idea was to restore parity by introducing a left-right symmetry. This is a group extension of formula_22 (the left-right symmetry) by


title: Chirality (physics)

text: This has two connected components where formula_22 acts as an automorphism, which is the composition of an involutive outer automorphism of SU(3) with the interchange of the left and right copies of SU(2) with the reversal of U(1) . It was shown by Mohapatra & Senjanovic (1975) that left-right symmetry can be spontaneously broken to give a chiral low energy theory, which is the Standard Model of Glashow, Weinberg, and Salam, and also connects the small observed neutrino masses to the breaking of left-right symmetry via the seesaw mechanism.


title: Chirality (physics)

text: The Higgs bosons needed to implement the breaking of left-right symmetry down to the Standard Model are


title: Chirality (physics)

text: This then provides three sterile neutrinos which are perfectly consistent with neutrino oscillation data. Within the seesaw mechanism, the sterile neutrinos become superheavy without affecting physics at low energies.


title: Chirality (physics)

text: Because the left-right symmetry is spontaneously broken, left-right models predict domain walls. This left-right symmetry idea first appeared in the Pati–Salam model (1974) and Mohapatra–Pati models (1975).


title: Parity of zero

text: In mathematics, zero is an even number. In other words, its parity—the quality of an integer being even or odd—is even. This can be easily verified based on the definition of "even": it is an integer multiple of 2, specifically . As a result, zero shares all the properties that characterize even numbers: for example, 0 is neighbored on both sides by odd numbers, any decimal integer has the same parity as its last digit—so, since 10 is even, 0 will be even, and if is even then has the same parity as —and always have the same parity.


title: Parity of zero

text: Zero also fits into the patterns formed by other even numbers. The parity rules of arithmetic, such as , require 0 to be even. Zero is the additive identity element of the group of even integers, and it is the starting case from which other even natural numbers are recursively defined. Applications of this recursion from graph theory to computational geometry rely on zero being even. Not only is 0 divisible by 2, it is divisible by every power of 2, which is relevant to the binary numeral system used by computers. In this sense, 0 is the "most even" number of all.


title: Parity of zero

text: Among the general public, the parity of zero can be a source of confusion. In reaction time experiments, most people are slower to identify 0 as even than 2, 4, 6, or 8. Some teachers —and some children in mathematics classes—think that zero is odd, or both even and odd, or neither. Researchers in mathematics education propose that these misconceptions can become learning opportunities. Studying equalities like can address students' doubts about calling 0 a number and using it in arithmetic. Class discussions can lead students to appreciate the basic principles of mathematical reasoning, such as the importance of definitions. Evaluating the parity of this exceptional number is an early example of a pervasive theme in mathematics: the abstraction of a familiar concept to an unfamiliar setting.


title: Parity of zero

text: The standard definition of "even number" can be used to directly prove that zero is even. A number is called "even" if it is an integer multiple of 2. As an example, the reason that 10 is even is that it equals . In the same way, zero is an integer multiple of 2, namely so zero is even.


title: Parity of zero

text: It is also possible to explain why zero is even without referring to formal definitions. The following explanations make sense of the idea that zero is even in terms of fundamental number concepts. From this foundation, one can provide a rationale for the definition itself—and its applicability to zero.


title: Parity of zero

text: Given a set of objects, one uses a number to describe how many objects are in the set. Zero is the count of "no objects"; in more formal terms, it is the number of objects in the empty set. The concept of parity is used for making groups of two objects. If the objects in a set can be marked off into groups of two, with none left over, then the number of objects is even. If an object is left over, then the number of objects is odd. The empty set contains zero groups of two, and no object is left over from this grouping, so zero is even.


title: Parity of zero

text: These ideas can be illustrated by drawing objects in pairs. It is difficult to depict zero groups of two, or to emphasize the nonexistence of a leftover object, so it helps to draw other groupings and to compare them with zero. For example, in the group of five objects, there are two pairs. More importantly, there is a leftover object, so 5 is odd. In the group of four objects, there is no leftover object, so 4 is even. In the group of just one object, there are no pairs, and there is a leftover object, so 1 is odd. In the group of zero objects, there is no leftover object, so 0 is even.


title: Parity of zero

text: There is another concrete definition of evenness: if the objects in a set can be placed into two groups of equal size, then the number of objects is even. This definition is equivalent to the first one. Again, zero is even because the empty set can be divided into two groups of zero items each.


title: Parity of zero

text: Numbers can also be visualized as points on a number line. When even and odd numbers are distinguished from each other, their pattern becomes obvious, especially if negative numbers are included:


title: Parity of zero

text: The even and odd numbers alternate. Starting at any even number, counting up or down by twos reaches the other even numbers, and there is no reason to skip over zero.


title: Parity of zero

text: With the introduction of multiplication, parity can be approached in a more formal way using arithmetic expressions. Every integer is either of the form or the former numbers are even and the latter are odd. For example, 1 is odd because and 0 is even because Making a table of these facts then reinforces the number line picture above.


title: Parity of zero

text: The precise definition of a mathematical term, such as "even" meaning "integer multiple of two", is ultimately a convention. Unlike "even", some mathematical terms are purposefully constructed to exclude trivial or degenerate cases. Prime numbers are a famous example. Before the 20th century, definitions of primality were inconsistent, and significant mathematicians such as Goldbach, Lambert, Legendre, Cayley, and Kronecker wrote that 1 was prime. The modern definition of "prime number" is "positive integer with exactly 2 factors", so 1 is not prime. This definition can be rationalized by observing that it more naturally suits mathematical theorems that concern the primes. For example, the fundamental theorem of arithmetic is easier to state when 1 is not considered prime.


title: Parity of zero

text: It would be possible to similarly redefine the term "even" in a way that no longer includes zero. However, in this case, the new definition would make it more difficult to state theorems concerning the even numbers. Already the effect can be seen in the algebraic rules governing even and odd numbers. The most relevant rules concern addition, subtraction, and multiplication:


title: Parity of zero

text: Inserting appropriate values into the left sides of these rules, one can produce 0 on the right sides:


title: Parity of zero

text: The above rules would therefore be incorrect if zero were not even. At best they would have to be modified. For example, one test study guide asserts that even numbers are characterized as integer multiples of two, but zero is "neither even nor odd". Accordingly, the guide's rules for even and odd numbers contain exceptions:


title: Parity of zero

text: Making an exception for zero in the definition of evenness forces one to make such exceptions in the rules for even numbers. From another perspective, taking the rules obeyed by positive even numbers and requiring that they continue to hold for integers forces the usual definition and the evenness of zero.


title: Parity of zero

text: Countless results in number theory invoke the fundamental theorem of arithmetic and the algebraic properties of even numbers, so the above choices have far-reaching consequences. For example, the fact that positive numbers have unique factorizations means that one can determine whether a number has an even or odd number of distinct prime factors. Since 1 is not prime, nor does it have prime factors, it is a product of 0 distinct primes; since 0 is an even number, 1 has an even number of distinct prime factors. This implies that the Möbius function takes the value , which is necessary for it to be a multiplicative function and for the Möbius inversion formula to work.


title: Parity of zero

text: A number is odd if there is an integer such that . One way to prove that zero is not odd is by contradiction: if then , which is not an integer. Since zero is not odd, if an unknown number is proven to be odd, then it cannot be zero. This apparently trivial observation can provide a convenient and revealing proof explaining why an odd number is nonzero.


title: Parity of zero

text: A classic result of graph theory states that a graph of odd order (having an odd number of vertices) always has at least one vertex of even degree. (The statement itself requires zero to be even: the empty graph has an even order, and an isolated vertex has an even degree.) In order to prove the statement, it is actually easier to prove a stronger result: any odd-order graph has an "odd number" of even degree vertices. The appearance of this odd number is explained by a still more general result, known as the handshaking lemma: any graph has an even number of vertices of odd degree. Finally, the even number of odd vertices is naturally explained by the degree sum formula.


title: Parity of zero

text: Sperner's lemma is a more advanced application of the same strategy. The lemma states that a certain kind of coloring on a triangulation of a simplex has a subsimplex that contains every color. Rather than directly construct such a subsimplex, it is more convenient to prove that there exists an odd number of such subsimplices through an induction argument. A stronger statement of the lemma then explains why this number is odd: it naturally breaks down as when one considers the two possible orientations of a simplex.


title: Parity of zero

text: The fact that zero is even, together with the fact that even and odd numbers alternate, is enough to determine the parity of every other natural number. This idea can be formalized into a recursive definition of the set of even natural numbers:


title: Parity of zero

text: This definition has the conceptual advantage of relying only on the minimal foundations of the natural numbers: the existence of 0 and of successors. As such, it is useful for computer logic systems such as LF and the Isabelle theorem prover. With this definition, the evenness of zero is not a theorem but an axiom. Indeed, "zero is an even number" may be interpreted as one of the Peano axioms, of which the even natural numbers are a model. A similar construction extends the definition of parity to transfinite ordinal numbers: every limit ordinal is even, including zero, and successors of even ordinals are odd.


title: Parity of zero

text: The classic point in polygon test from computational geometry applies the above ideas. To determine if a point lies within a polygon, one casts a ray from infinity to the point and counts the number of times the ray crosses the edge of polygon. The crossing number is even if and only if the point is outside the polygon. This algorithm works because if the ray never crosses the polygon, then its crossing number is zero, which is even, and the point is outside. Every time the ray does cross the polygon, the crossing number alternates between even and odd, and the point at its tip alternates between outside and inside.


title: Parity of zero

text: In graph theory, a bipartite graph is a graph whose vertices are split into two colors, such that neighboring vertices have different colors. If a connected graph has no odd cycles, then a bipartition can be constructed by choosing a base vertex "v" and coloring every vertex black or white, depending on whether its distance from "v" is even or odd. Since the distance between "v" and itself is 0, and 0 is even, the base vertex is colored differently from its neighbors, which lie at a distance of 1.


title: Parity of zero

text: In abstract algebra, the even integers form various algebraic structures that require the inclusion of zero. The fact that the additive identity (zero) is even, together with the evenness of sums and additive inverses of even numbers and the associativity of addition, means that the even integers form a group. Moreover, the group of even integers under addition is a subgroup of the group of all integers; this is an elementary example of the subgroup concept. The earlier observation that the rule "even − even = even" forces 0 to be even is part of a general pattern: any nonempty subset of an additive group that is closed under subtraction must be a subgroup, and in particular, must contain the identity.


title: Parity of zero

text: Since the even integers form a subgroup of the integers, they partition the integers into cosets. These cosets may be described as the equivalence classes of the following equivalence relation: if is even. Here, the evenness of zero is directly manifested as the reflexivity of the binary relation ~. There are only two cosets of this subgroup—the even and odd numbers—so it has index 2.


title: Parity of zero

text: Analogously, the alternating group is a subgroup of index 2 in the symmetric group on "n" letters. The elements of the alternating group, called even permutations, are the products of even numbers of transpositions. The identity map, an empty product of no transpositions, is an even permutation since zero is even; it is the identity element of the group.


title: Parity of zero

text: The rule "even × integer = even" means that the even numbers form an ideal in the ring of integers, and the above equivalence relation can be described as equivalence modulo this ideal. In particular, even integers are exactly those integers "k" where This formulation is useful for investigating integer zeroes of polynomials.


title: Parity of zero

text: There is a sense in which some multiples of 2 are "more even" than others. Multiples of 4 are called doubly even, since they can be divided by 2 twice. Not only is zero divisible by 4, zero has the unique property of being divisible by every power of 2, so it surpasses all other numbers in "evenness".


title: Parity of zero

text: One consequence of this fact appears in the bit-reversed ordering of integer data types used by some computer algorithms, such as the Cooley–Tukey fast Fourier transform. This ordering has the property that the farther to the left the first 1 occurs in a number's binary expansion, or the more times it is divisible by 2, the sooner it appears. Zero's bit reversal is still zero; it can be divided by 2 any number of times, and its binary expansion does not contain any 1s, so it always comes first.


title: Parity of zero

text: Although 0 is divisible by 2 more times than any other number, it is not straightforward to quantify exactly how many times that is. For any nonzero integer "n", one may define the 2-adic order of "n" to be the number of times "n" is divisible by 2. This description does not work for 0; no matter how many times it is divided by 2, it can always be divided by 2 again. Rather, the usual convention is to set the 2-order of 0 to be infinity as a special case. This convention is not peculiar to the 2-order; it is one of the axioms of an additive valuation in higher algebra.


title: Parity of zero

text: The powers of two—1, 2, 4, 8, ...—form a simple sequence of numbers of increasing 2-order. In the 2-adic numbers, such sequences actually converge to zero.


title: Parity of zero

text: The subject of the parity of zero is often treated within the first two or three years of primary education, as the concept of even and odd numbers is introduced and developed.


title: Parity of zero

text: The chart on the right depicts children's beliefs about the parity of zero, as they progress from Year 1 to Year 6 of the English education system. The data is from Len Frobisher, who conducted a pair of surveys of English schoolchildren. Frobisher was interested in how knowledge of single-digit parity translates to knowledge of multiple-digit parity, and zero figures prominently in the results.


title: Parity of zero

text: In a preliminary survey of nearly 400 seven-year-olds, 45% chose "even" over "odd" when asked the parity of zero. A follow-up investigation offered more choices: "neither", "both", and "don't know". This time the number of children in the same age range identifying zero as even dropped to 32%. Success in deciding that zero is even initially shoots up and then levels off at around 50% in Years 3 to 6. For comparison, the easiest task, identifying the parity of a single digit, levels off at about 85% success.


title: Parity of zero

text: In interviews, Frobisher elicited the students' reasoning. One fifth-year decided that 0 was even because it was found on the 2 times table. A couple of fourth-years realized that zero can be split into equal parts. Another fourth-year reasoned "1 is odd and if I go down it's even." The interviews also revealed the misconceptions behind incorrect responses. A second-year was "quite convinced" that zero was odd, on the basis that "it is the first number you count". A fourth-year referred to 0 as "none" and thought that it was neither odd nor even, since "it's not a number". In another study, Annie Keith observed a class of 15 second-graders who convinced each other that zero was an even number based on even-odd alternation and on the possibility of splitting a group of zero things in two equal groups.


title: Parity of zero

text: More in-depth investigations were conducted by Esther Levenson, Pessia Tsamir, and Dina Tirosh, who interviewed a pair of sixth-grade students in the USA who were performing highly in their mathematics class. One student preferred deductive explanations of mathematical claims, while the other preferred practical examples. Both students initially thought that 0 was neither even nor odd, for different reasons. Levenson et al. demonstrated how the students' reasoning reflected their concepts of zero and division.


title: Parity of zero

text: Deborah Loewenberg Ball analyzed US third grade students' ideas about even and odd numbers and zero, which they had just been discussing with a group of fourth-graders. The students discussed the parity of zero, the rules for even numbers, and how mathematics is done. The claims about zero took many forms, as seen in the list on the right. Ball and her coauthors argued that the episode demonstrated how students can "do mathematics in school", as opposed to the usual reduction of the discipline to the mechanical solution of exercises.


title: Parity of zero

text: One of the themes in the research literature is the tension between students' concept images of parity and their concept definitions. Levenson et al.'s sixth-graders both defined even numbers as multiples of 2 or numbers divisible by 2, but they were initially unable to apply this definition to zero, because they were unsure how to multiply or divide zero by 2. The interviewer eventually led them to conclude that zero was even; the students took different routes to this conclusion, drawing on a combination of images, definitions, practical explanations, and abstract explanations. In another study, David Dickerson and Damien Pitman examined the use of definitions by five advanced undergraduate mathematics majors. They found that the undergraduates were largely able to apply the definition of "even" to zero, but they were still not convinced by this reasoning, since it conflicted with their concept images.


title: Parity of zero

text: Researchers of mathematics education at the University of Michigan have included the true-or-false prompt "0 is an even number" in a database of over 250 questions designed to measure teachers' content knowledge. For them, the question exemplifies "common knowledge ... that any well-educated adult should have", and it is "ideologically neutral" in that the answer does not vary between traditional and reform mathematics. In a 2000–2004 study of 700 primary teachers in the United States, overall performance on these questions significantly predicted improvements in students' standardized test scores after taking the teachers' classes. In a more in-depth 2008 study, the researchers found a school where all of the teachers thought that zero was neither odd nor even, including one teacher who was exemplary by all other measures. The misconception had been spread by a math coach in their building.


title: Parity of zero

text: It is uncertain how many teachers harbor misconceptions about zero. The Michigan studies did not publish data for individual questions. Betty Lichtenberg, an associate professor of mathematics education at the University of South Florida, in a 1972 study reported that when a group of prospective elementary school teachers were given a true-or-false test including the item "Zero is an even number", they found it to be a "tricky question", with about two thirds answering "False".


title: Parity of zero

text: Mathematically, proving that zero is even is a simple matter of applying a definition, but more explanation is needed in the context of education. One issue concerns the foundations of the proof; the definition of "even" as "integer multiple of 2" is not always appropriate. A student in the first years of primary education may not yet have learned what "integer" or "multiple" means, much less how to multiply with 0. Additionally, stating a definition of parity for all integers can seem like an arbitrary conceptual shortcut if the only even numbers investigated so far have been positive. It can help to acknowledge that as the number concept is extended from positive integers to include zero and negative integers, number properties such as parity are also extended in a nontrivial way.


title: Parity of zero

text: Adults who do believe that zero is even can nevertheless be unfamiliar with thinking of it as even, enough so to measurably slow them down in a reaction time experiment. Stanislas Dehaene, a pioneer in the field of numerical cognition, led a series of such experiments in the early 1990s. A numeral is flashed to the subject on a monitor, and a computer records the time it takes the subject to push one of two buttons to identify the number as odd or even. The results showed that 0 was slower to process than other even numbers. Some variations of the experiment found delays as long as 60 milliseconds or about 10% of the average reaction time—a small difference but a significant one.


title: Parity of zero

text: Dehaene's experiments were not designed specifically to investigate 0 but to compare competing models of how parity information is processed and extracted. The most specific model, the mental calculation hypothesis, suggests that reactions to 0 should be fast; 0 is a small number, and it is easy to calculate . (Subjects are known to compute and name the result of multiplication by zero faster than multiplication of nonzero numbers, although they are slower to verify proposed results like .) The results of the experiments suggested that something quite different was happening: parity information was apparently being recalled from memory along with a cluster of related properties, such as being prime or a power of two. Both the sequence of powers of two and the sequence of positive even numbers 2, 4, 6, 8, ... are well-distinguished mental categories whose members are prototypically even. Zero belongs to neither list, hence the slower responses.


title: Parity of zero

text: Repeated experiments have shown a delay at zero for subjects with a variety of ages and national and linguistic backgrounds, confronted with number names in numeral form, spelled out, and spelled in a mirror image. Dehaene's group did find one differentiating factor: mathematical expertise. In one of their experiments, students in the École Normale Supérieure were divided into two groups: those in literary studies and those studying mathematics, physics, or biology. The slowing at 0 was "essentially found in the [literary] group", and in fact, "before the experiment, some L subjects were unsure whether 0 was odd or even and had to be reminded of the mathematical definition".


title: Parity of zero

text: This strong dependence on familiarity again undermines the mental calculation hypothesis. The effect also suggests that it is inappropriate to include zero in experiments where even and odd numbers are compared as a group. As one study puts it, "Most researchers seem to agree that zero is not a typical even number and should not be investigated as part of the mental number line."


title: Parity of zero

text: Some of the contexts where the parity of zero makes an appearance are purely rhetorical. The issue provides material for Internet message boards and ask-the-expert websites. Linguist Joseph Grimes muses that asking "Is zero an even number?" to married couples is a good way to get them to disagree. People who think that zero is neither even nor odd may use the parity of zero as proof that every rule has a counterexample, or as an example of a trick question.


title: Parity of zero

text: Around the year 2000, media outlets noted a pair of unusual milestones: "1999/11/19" was the last calendar date composed of all odd digits that would occur for a very long time, and that "2000/02/02" was the first all-even date to occur in a very long time. Since these results make use of 0 being even, some readers disagreed with the idea.


title: Parity of zero

text: In standardized tests, if a question asks about the behavior of even numbers, it might be necessary to keep in mind that zero is even. Official publications relating to the GMAT and GRE tests both state that 0 is even.


title: Parity of zero

text: The parity of zero is relevant to odd–even rationing, in which cars may drive or purchase gasoline on alternate days, according to the parity of the last digit in their license plates. Half of the numbers in a given range end in 0, 2, 4, 6, 8 and the other half in 1, 3, 5, 7, 9, so it makes sense to include 0 with the other even numbers. However, in 1977, a Paris rationing system led to confusion: on an odd-only day, the police avoided fining drivers whose plates ended in 0, because they did not know whether 0 was even. To avoid such confusion, the relevant legislation sometimes stipulates that zero is even; such laws have been passed in New South Wales and Maryland.


title: Parity of zero

text: On U.S. Navy vessels, even-numbered compartments are found on the port side, but zero is reserved for compartments that intersect the centerline. That is, the numbers read 6-4-2-0-1-3-5 from port to starboard.


title: Parity of zero

text: In the game of roulette, the number 0 does not count as even or odd, giving the casino an advantage on such bets. Similarly, the parity of zero can affect payoffs in prop bets when the outcome depends on whether some randomized number is odd or even, and it turns out to be zero.


title: Parity of zero

text: The game of "odds and evens" is also affected: if both players cast zero fingers, the total number of fingers is zero, so the even player wins. One teachers' manual suggests playing this game as a way to introduce children to the concept that 0 is divisible by 2.


title: Harvesting lightning energy

text: Since the late 1980s, there have been several attempts to investigate the possibility of harvesting lightning energy. A single bolt of lightning carries a relatively large amount of energy (approximately 5 gigajoules or about the energy stored in 38 gallons or 172 litres of gasoline). However, this energy is concentrated in a small location and is passed during an extremely short period of time (microseconds); therefore, extremely high electrical power is involved. 5 gigajoules over 10 microseconds is equal to 500 terawatts. Because lightning bolts vary in voltage and current, a more average calculation would be 10 gigawatts. It has been proposed that the energy contained in lightning be used to generate hydrogen from water, to harness the energy from rapid heating of water due to lightning, or to use a group of lightning arresters to harness a strike, either directly or by converting it to heat or mechanical energy, or to use inductors spaced far enough away so that a safe fraction of the energy might be captured.


title: Harvesting lightning energy

text: A technology capable of harvesting lightning energy would need to be able to rapidly capture the high power involved in a lightning bolt. Several schemes have been proposed, but the ever-changing energy involved in each lightning bolt renders lightning power harvesting from ground-based rods impractical: too high and it will damage the storage; too low and it may not work. Additionally, lightning is sporadic, and therefore energy would have to be collected and stored; it is difficult to convert high-voltage electrical power to the lower-voltage power that can be stored.


title: Harvesting lightning energy

text: In the summer of 2007, an alternative energy company called Alternate Energy Holdings, Inc. (AEHI) tested a method for capturing the energy in lightning bolts. The design for the system had been purchased from an Illinois inventor named Steve LeRoy, who had reportedly been able to power a 60-watt light bulb for 20 minutes using the energy captured from a small flash of artificial lightning. The method involved a tower, a means of shunting off a large portion of the incoming energy, and a capacitor to store the rest. According to Donald Gillispie, CEO of AEHI, they "couldn't make it work," although "given enough time and money, you could probably scale this thing up... it's not black magic; it's truly math and science, and it could happen."


title: Harvesting lightning energy

text: According to Martin A. Uman, co-director of the Lightning Research Laboratory at the University of Florida and a leading authority on lightning, "a single lightning strike, while fast and bright, contains very little energy by the time it gets down to earth, and dozens of lightning towers like those used in the system tested by AEHI would be needed to operate five 100-watt light bulbs for the course of a year". When interviewed by "The New York Times", he stated that "the energy in a thunderstorm is comparable to that of an atomic bomb, but trying to harvest the energy of lightning from the ground is hopeless".


title: Harvesting lightning energy

text: Another major challenge when attempting to harvest energy from lightning is the impossibility of predicting when and where thunderstorms will occur. Even during a storm, it is very difficult to tell where exactly lightning will strike.


title: Harvesting lightning energy

text: To facilitate the harvesting of lightning, a laser-induced plasma channel (LIPC) could theoretically be used to allow lightning to strike in a predictable location. A high power laser could be used to form an ionized column of gas, which would act as an atmospheric conduit for electrical discharges of lightning, which would direct the lightning to a ground station for harvesting.


title: Harvesting lightning energy

text: Teramobile, an international project initiated jointly by a French-German collaboration of CNRS (France) and DFG (Germany), has managed to trigger electric activity in thunderclouds by ultrashort lasers. A large amount of power is necessary, 5 terawatts, over the short pulse duration. For the moment, the application of laser-channeled lightning is to use energy to divert the lightning and prevent damage instead of harvesting the lightning energy.


title: Judge Rotenberg Educational Center

text: The Judge Rotenberg Center (founded in 1971 as the Behavior Research Institute) is an institution in Canton, Massachusetts, United States, for people with developmental disabilities, emotional disorders, and autistic-like behaviors. The center has been condemned for torture by the United Nations Special Rapporteur on Torture. The JRC is known for its use of the graduated electronic decelerator (GED), a device that administers electric shocks to residents through a remote control. The device was designed by Matthew Israel, the institute's founder. While the FDA issued a formal ban on the GED in 2020, the device continued to be used on some residents pending an administrative stay for the duration of the COVID-19 pandemic. In July 2021, the D.C. Circuit Court of Appeals ruled that the FDA could not issue a "partial stay" but must issue a blanket ban or no ban at all, thus allowing the JRC to continue using the device on 55 people in the meantime.


title: Judge Rotenberg Educational Center

text: The Judge Rotenberg Center's behavior modification program uses the methods of applied behavior analysis and relies heavily on aversion therapy. Aversives used by the JRC include contingent food programs, long-term restraints, sensory deprivation, and GED shocks. While JRC claims to rely mainly on positive behavior support and contends that aversives are used only as a last resort when positive intervention has failed, multiple state reports have found that aversives are used for minor infractions, and that no significant positive behavior support programs exist.


title: Judge Rotenberg Educational Center

text: In a video that surfaced in 2011, JRC staff tied a boy with autism face-down to a four-point board and shocked him 31 times at the highest amperage setting. The first shock was given for failing to take off his coat when asked, and the remaining 30 shocks were given for screaming and tensing up while being shocked. The boy was later hospitalized with third degree burns and acute stress disorder, but no action was taken against any of the staff as neither the law nor JRC policy had been broken. In a separate incident, two residents were awoken from their beds at night, restrained, and shocked 29 and 77 times, respectively, due to false allegations that they had misbehaved. The center's founder, Matthew Israel, was indicted on criminal charges for ordering a video of the incident destroyed and was forced to resign his position at the JRC as part of a plea deal to avoid prosecution.


title: Judge Rotenberg Educational Center

text: There have been repeated attempts to shut down the center by autism rights advocates, disability rights advocates, and human rights advocates. Organizations that oppose the center include the Autistic Self Advocacy Network, Disability Rights International, and Community Alliance for the Ethical Treatment of Youth. Six residents have died at the institute since it was founded in 1971.


title: Judge Rotenberg Educational Center

text: In 1971, Matthew Israel founded the center as the Behavior Research Institute (BRI) in Providence, Rhode Island. Initially, it had just two residents, one with autism and the other with schizophrenia. In 1975, the BRI expanded to include group homes in Massachusetts, and in 1976 it opened another branch in California.


title: Judge Rotenberg Educational Center

text: Israel opened the California branch of the BRI without a license to operate a group home, without a license to practice psychology in the state of California, and without a license to use aversives. The institute used aversives on residents there nonetheless. When the institute applied for a license to operate in 1977, the California Department of Health rejected the application, citing lack of meaningful peer review and the unnecessary use of painful aversives. The department also found that there was insufficient evidence to show that Israel was "reputable and responsible" and that he had the ability to comply with regulations. Without a license, the center was scheduled to shut down.


title: Judge Rotenberg Educational Center

text: The day after the scheduled shutdown, a group of parents reopened the institute as a co-op, moving Israel's official position of executive director to consultant. The organization then changed its name to the Behavior Research Institute of California, and applied for a license to operate a group home and a permit to use aversives. With the aid of then-California governor Pat Brown (whose law firm was hired to represent the center), they received the license to operate, as well as the only permit ever granted by the state of California for a group home to use physical aversives on its residents. The institute was awarded $35,000 a year per child by the state, the highest rate of any community facility in California.


title: Judge Rotenberg Educational Center

text: After the 1981 death of a resident, California launched an investigation into the institute and its practices. The investigation revealed various abuses against the residents, both physical and psychological. Residents were beaten, restrained, humiliated, and not adequately fed or cared for. Residents often bore extreme bruising, which staff had been trained to conceal from doctors and family members. As a result of the investigation, the institute was banned from using physical aversives, as well as from using restraints and withholding meals as punishment. Additionally, Matthew Israel was banned from entering the facility. Judy Weber, the mother of one of the institute's residents who would go on to become Israel's second wife, took over the operation of the center and later renamed it as Tobinworld. The center denied all allegations made by the state report.


title: Judge Rotenberg Educational Center

text: As early as 1979, authorities in New York State had published two reports on the Behavior Research Institute in which signs of physical and mental abuse were documented. One report found that the institute's methods were only effective through the means of coercion, and that the residents relapsed into their old behavior as soon as the immediate threat of punishment was gone. While corporal punishment was against the law in Massachusetts, the institute was granted special permission to use aversives in 1983. The institute was welcomed by some state officials due to its near-zero rejection rate. In 1993, the Massachusetts Department of Mental Retardation said that the institution had "repeatedly failed to comply with a number of state regulations" and threatened to take away its certification.


title: Judge Rotenberg Educational Center

text: In 1994, the center changed its name to the Judge Rotenberg Educational Center "to honor the memory of the judge [who] helped to preserve [the] program from extinction at the hands of state licensing officials in the 1980s." JRC moved from its original location near Providence, Rhode Island, to its current facilities in Canton, Massachusetts, in 1996. In 2011, Israel was forced to resign from his position as director of the Judge Rotenberg Center as part of a deferred prosecution agreement after being indicted on criminal charges related to the abuse of residents. Six residents have died of preventable causes at the center since it opened in 1971.


title: Judge Rotenberg Educational Center

text: As the result of a 2011 ruling by the Massachusetts Department of Early Education and Care, governor Deval Patrick's administration imposed regulations that only residents whose treatment plans approved the GED before that time were still permitted to receive it, but new residents enrolled into the JRC were no longer allowed, by law, to receive the GED as part of their plan.


title: Judge Rotenberg Educational Center

text: The Massachusetts Department of Developmental Services is responsible for providing the JRC with its license to use aversives, including electric shocks.


title: Judge Rotenberg Educational Center

text: The Judge Rotenberg Center provides behavioral treatment using the methodologies of Applied Behavior Analysis (ABA). JRC's behavior modification program relies heavily on aversion therapy, with treatment directed exclusively towards promoting normalization. Aversives used to modify behavior include: food deprivation, restraint, solitary confinement, and GED skin shocks. While the center often claims that it uses aversives only as last resort against self-harm and aggression, these claims have been refuted. Reports by multiple government agencies have found that the center regularly uses aversives on children with no history of self-harm or aggression, often for minor infractions. Several former residents of the center who used to be on the GED have successfully transitioned to positive behavior support programs elsewhere. There is medical consensus that positive-only support is both safer and more effective than the use of aversives.


title: Judge Rotenberg Educational Center

text: The center has stated that the GED was only used as a last resort to prevent violent or self-injurious behavior when positive behavioral support had failed. However, a 2006 report by the New York State Education Department found that the device was regularly used when there was no threat of serious physical harm or injury, including for:


title: Judge Rotenberg Educational Center

text: The report also found that despite the center's claims, no significant positive behavioral support program existed.


title: Judge Rotenberg Educational Center

text: Additionally, the report found that the GED could be programmed to give automated skin shocks in response to targeted behaviors. For example, some residents were made to sit on GED seats that would automatically administer skin shocks for the target behavior of standing up, while others wore waist holsters that would administer skin shocks if the resident pulled a hand out of the holster. Shocks were administered continuously until the target behavior stopped occurring. The center did not have approval from the United States Food and Drug Administration (FDA) to use the device in this way.


title: Judge Rotenberg Educational Center

text: An FDA investigation found that some parents and guardians were pressured into giving consent to put their child on the GED, that they were not provided with accurate information about the device's risks, and that other options were not exhausted before resorting to the GED. The agency also found that the GED could cause both physical and psychological harm, including pain, burns, tissue damage, depression, fear, and aggression. Furthermore, they concluded that the GED device may have caused one resident to enter a catatonic state, and that it can in some cases worsen the behaviors that it claims to treat.


title: Judge Rotenberg Educational Center

text: Greg Miller, a former teacher's assistant at the JRC, reported that staff were expected to administer shocks without consideration for the circumstances in which it occurred. Staff were monitored by cameras, and feared losing their jobs if they refused to deliver the expected shocks. "There were no exceptions..." he said. "we had to follow court-approved orders." Residents were made to wear the GED devices at all hours, even during showers and sleep. Residents report that they were sometimes awoken by shocks in the night, which were administered for reasons including nighttime incontinence, tensing up while asleep, and having broken a rule earlier in the day. Resident would also be shocked if they failed to stay awake at daytime. One resident reported that after being shocked while asleep, staff would not explain to her why she was shocked. After the incident, the fear of being shocked in her sleep produced extreme insomnia.William Pelham, a behavioral specialist and director of the Center for Children and Families at the State University of New York at Buffalo, argued that the center's use of electric shocks was harmful and unnecessary. "People don't use... shock anymore because they don't need to. It is not the standard of care. There are alternative procedures that do not involve aversives like electric shock." At the time of the ban, the JRC was the only institution in the United States using electric skin shocks as aversives.


title: Judge Rotenberg Educational Center

text: In the contingent food program, a resident's food is withheld to be used as a reward for good behavior. If a resident fails to meet all the goals laid out for them by the JRC each meal, they are made to discard the excess food not earned. If a resident fails to meet their daily minimum calorie intake (which may be as little as 20% of their prescribed calories), non-preferred make up food is dispensed to bring them up to the minimum. The non-preferred make up food is designed to be noxious so as to punish the resident; for example, it may be mashed up and sprinkled with liver powder. A 2006 investigation of the JRC concluded that the contingent food program posed an "unnecessary risk" to the residents' growth and development.


title: Judge Rotenberg Educational Center

text: A common sensory deprivation punishment involves forcing a resident to wear a helmet that restricts vision and hearing (through the use of white noise) for an extended period of time. The resident may also be restrained and subjected to other aversives during this time. In 1981, a resident died of asphyxiation during this procedure. The punishment continues to be used.


title: Judge Rotenberg Educational Center

text: At least one resident was subjected to a procedure called "isolation-deprivation" in which he was restrained by the wrists and ankles for 24 hours and boxes were stacked so as to prevent him from seeing anything in the room. During this time he received only lettuce with mayonnaise to eat. On some occasions he was not allowed to use the bathroom and was forced to soil his pants. Furthermore, staff were directed to pinch his feet once per hour and spray him with water whenever they walked by.


title: Judge Rotenberg Educational Center

text: The use of long term restraints is common at the JRC. Many residents are required to carry their own "restraint bags", which contain the materials required to restrain them. Commonly used restraints include the four-point board and the five-point restraint chair. Restraints may be used alone, or in combination with other aversives to hurt residents. For example, one resident's behavior plan specified that he was to receive five GED shocks while restrained to a four-point board as a consequence for pulling the fire alarm.


title: Judge Rotenberg Educational Center

text: In a behavior rehearsal lesson, a resident is provoked, tricked, or coerced into exhibiting a target behavior (e.g. eating nonfood items, destruction of property) so that the target behavior may be punished. If the resident refuses to perform the target behavior, they are punished for noncompliance, but if they perform the target behavior then they are punished much more harshly for breaking the rules. There is no way for the resident to escape punishment. The resident is repeatedly challenged to perform the behavior, and the lesson does not end until they sit perfectly still for ten minutes. The JRC contends that behavior rehearsal lessons are an effective way of reducing "high risk, low frequency" behaviors. at least nine residents at the JRC were approved for behavior rehearsal lessons.


title: Judge Rotenberg Educational Center

text: In addition to punishments, residents of the center are given the opportunity to earn rewards. State reports have found that despite the institute's claims, its reward programs are minimal. Things considered rewards at the JRC may include verbal praise, the opportunity to look out a window, and sometimes food. A child who cries is not to be given attention, as this is considered a reward, and the child may be punished for crying. One reward that a resident may win is the opportunity to visit the "Big Rewards Store" (BRS). The BRS contains a pool table and various arcade games, and is the only place in the center that residents may socialize freely.


title: Judge Rotenberg Educational Center

text: In its 2006 "Private Special Education School Program Review Report of Findings", the Massachusetts Department of Education found that unsigned Individualized Education Programs (IEPs) were being utilized for residents at JRC, and that the center did not have a written policy indicating that it must obtain consent before revising or changing an IEP. At various points in its history, investigations and lawsuits have been brought against the center's operations. Matthew Israel has cited Ivar Lovaas's use of a cattle prod on children with autism as justification for the center's use of electric skin shocks.


title: Judge Rotenberg Educational Center

text: As a result of the report, the state of New York restricted the institute's right to use aversives to cases where a resident was a danger to himself or others, and even then only after other means had failed. However, the institute soon after regained its right to use aversives on New York residents.


title: Judge Rotenberg Educational Center

text: In 1979, a staff member resigned and asked the district attorney to file child abuse charges against the institute, alleging that he had observed abuse there. On the prompting of various former staff, residents, and concerned family members, the California Department of Social Services launched an investigation into the institution. The ensuing investigation revealed various abuses by the institute including: improper and unsafe use of restraints, punishments designed to humiliate the residents, failure to provide proper nutrition, failure to provide proper medical care, and severe bruising/lacerations/scars from aversive interventions. In a 1982 report of the investigation, the California Department of Social Services documented various violations and abuses that had occurred at the institute. As a result of the investigation, the state of California revoked the institute's license to use aversives and forbade Matthew Israel from setting foot on the property.


title: Judge Rotenberg Educational Center

text: The investigation found that residents had received "excessive bruises" from "excessive and unnecessary aversives". Residents had cuts, scars, scabs, and open wounds from the use of aversives. Furthermore, staff took action to disguise these injuries from doctors and family members: Doctor's appointments were sometimes postponed due to the presence of excessive bruising, and aversive interventions were put on hold before scheduled visits with family for "public relations purposes". Residents were made to wear long sleeves to cover up the injuries, and social service employees were on some occasions denied the right to adequately inspect them for bruises.


title: Judge Rotenberg Educational Center

text: Residents were often put in positions where there was no way for them to avoid receiving an aversive: For example, deaf children were punished for failing to comply with verbal commands. Residents were also forced to take part in "behavior rehearsal" lessons where they were punished regardless of whether or not they behaved correctly. Additionally, residents were regularly spanked for crying in response to punishment. The report found that at least one resident's behavior substantially worsened at the institute due to "improper treatment" and "unprofessional use of aversives".


title: Judge Rotenberg Educational Center

text: The report found that staff pinched residents to make them repeat phrases uttered by staff, and threatened residents with the use of aversives if they did not comply with the staff's arbitrary demands. One resident was made to eat dinner outside with his arms restrained by his sides from a plate of food that had been placed on the ground. Other residents were deprived of the right to sleep in a bed: One was forced to sleep in a kneeling position while tied to a piece of furniture, while another was made to sleep on the floor with his arms restrained to nearby fixtures. Residents were sometimes made to soil themselves when staff refused to let them use the bathroom.


title: Judge Rotenberg Educational Center

text: Residents were restrained for punishment, as well as for the personal convenience of staff. Residents were restrained in unsafe ways, and sometimes received cuts and bruises. In 1981, a fourteen-year boy old died at the institute while restrained face down to a four-point board. The institute was not authorized to use restraints on any resident at this time, and continued to do so even after being informed that it was against the law.


title: Judge Rotenberg Educational Center

text: The institute was found to have removed records, making them inaccessible to investigators and family. Furthermore, they were found to have denied the right to view records to family members and investigators. In many cases, the institute's records were inaccurate. Examples include: denying a resident food as punishment while recording that he had been fed, recording that restraints had been checked when they had not been checked, and failing to properly record the administration of aversives. The institute retaliated against people who complained about their practices and refused to let the Department of Social Services investigate those complaints. Parents were told that their children would be expelled if they questioned or complained about the institute.


title: Judge Rotenberg Educational Center

text: The investigation found that residents were provoked into violent and aggressive behavior as part of the filming of a before-and-after video, where staged clips of the residents responding to provocation were shown as examples of how they had behaved before treatment. The residents were then taken off aversive therapy, rewarded heavily for several days, and asked to perform only tasks that placed little demand on them so that a video could be produced to show how they behaved after treatment. This film is often shown to parents of prospective residents and to reporters to convince them of the benefits of the institute.


title: Judge Rotenberg Educational Center

text: After the center received a phone call alleging that two residents had misbehaved earlier that evening, staff woke them from their beds, restrained them, and repeatedly gave them electric shocks. One of the residents received 77 shocks and the other received 29. After the incident, one of the residents had to be treated for burns. The phone call was later found to be a hoax perpetrated by a former resident who was pretending to be a supervisor. In December 2007, the center was found by the Massachusetts Department of Early Education and Care to have been abusive towards residents and had failed to protect their health.


title: Judge Rotenberg Educational Center

text: The incident led to two investigations – one by the federal government, and one by the state of Massachusetts. While the investigation was ongoing, Matthew Israel ordered tapes destroyed, despite a court order to keep them. In May 2011, Israel was indicted on charges of child endangerment, acting as an accessory after the fact, and obstruction of justice for misleading a grand jury over the JRC's destruction of tapes. In 2011, Israel was forced to resign his position at JRC in a deferred prosecution plea deal with the Massachusetts State Attorney General's office.


title: Judge Rotenberg Educational Center

text: In 1980, 25-year-old Robert Cooper died of a hemorrhagic bowel obstruction. The institution was criticized for driving him to the hospital in a private vehicle rather than calling for an ambulance.


title: Judge Rotenberg Educational Center

text: In 1981, Danny Aswad, a 14-year-old boy with autism, died at the JRC (then called the Behavior Research Institute) while restrained face-down to a bed. The institute was not authorized to use restraints on its residents at that time, and Aswad had previously had a rod surgically implanted in his back to treat a degenerative back disease that had resulted from his treatment there. The coroner's report concluded that Aswad had died of "mental retardation" and "cerebral malformation" and recorded his death as from natural causes.


title: Judge Rotenberg Educational Center

text: In 1985, Vincent Milletich, a 22-year-old man with autism, died at the institute. He had been restrained and forced to wear a white noise emitting sensory deprivation helmet when he died of asphyxiation after having an epileptic seizure. Milletich had a history of epileptic seizures, and had been made to wear the helmet as punishment for "making inappropriate sounds". The judge who presided over a hearing on Milletich's death declared that two staff doctors were negligent for approving the therapy, and that the center's director, Matthew Israel, had been negligent in authorizing the helmet's use. Milletich's mother said that she did not want charges pressed against the institute, but did sue the JRC for $10 million.


title: Judge Rotenberg Educational Center

text: In 1987, Abigail Gibson, a 29-year-old woman with a seizure disorder, was detained at the Behavioral Research Institute and subject to regular physical aversives by the program there. She had a heart attack in her room at night, and died two days later at Sturdy Memorial Hospital.


title: Judge Rotenberg Educational Center

text: In 1990, Linda Cornelison, a 19-year-old non-verbal and intellectually disabled resident, died of complications related to a ruptured bowel. At the time of her death, Cornelison was on a contingent food program where food was withheld as a punishment for undesired behavior. In the days leading up to her death, Cornelison's expressions of pain were interpreted as misbehavior by staff, who administered 56 physical aversives over five hours before calling an ambulance. Cornelison was unconscious when the ambulance arrived. An investigation of Cornelison's death, conducted by the Massachusetts Department of Mental Retardation, reported that the treatment was "inhumane beyond all reason" and violated "universal standards of human decency", but failed to find enough evidence to link the JRC to Cornelison's death. However, a Massachusetts court found in 1995 that the JRC had exhibited negligence. At the time of her death, Cornelison had been a resident of the institute for seven years, and had been subjected to 88,719 aversives.


title: Judge Rotenberg Educational Center

text: In 1998, disabled 16-year-old Silverio Gonzalez died in the institute's custody. He was housed there for 11 months before making an attempt to free himself by jumping from a transport bus. He died from head trauma from the fall. His mother, Olga Cepeda, sued the center after his death.


title: Judge Rotenberg Educational Center

text: In 2002, a teenager with autism from New York City named Andre McCollins was restrained on a four-point board and shocked 31 times over the course of seven hours. The first shock was given after he did not take off his coat when asked; subsequent shocks were given as punishments for screaming and tensing up while being shocked. In the video, McCollins can be heard shouting "Someone, help me, please!" The JRC staff listed this as a "major disruptive behavior", for which he was administered a GED shock. The day after the incident, McCollins' mother had to drive him to the hospital, as he was unable to speak and had burns on many parts of his body. The doctor diagnosed him with acute stress disorder, which was a direct result of the center's aversives. His mother subsequently claimed that "There is no counseling for the [residents] there... and the staff there lied to [her] all these years..."


title: Judge Rotenberg Educational Center

text: In 2012, a video of the incident was released as part of a lawsuit by McCollins' mother, which was settled for an undisclosed sum. The video aired on national news, and caught the attention of the hacker group Anonymous, which announced in a YouTube video that the center and those affiliated with it were targets. Anonymous hacked the JRC's website, retrieved confidential information about individuals and groups associated with it, and posted that information to Pastebin. The doxed information included the names and addresses of the center's sponsors, lobbyists, lawyers, supporters, and founder.


title: Judge Rotenberg Educational Center

text: In 2010, the American human rights organization, Disability Rights International, filed an appeal with the office of the United Nations Special Rapporteur on Torture, stating they believed the residents were being subjected to human rights abuses due to the center's use of aversives. The then-Special Rapporteur, Manfred Nowak, sent what he described as "an urgent appeal to the U.S. government asking them to investigate." In 2013, the Special Rapporteur declared that the use of the GED device violated the United Nations Convention Against Torture.