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Animal welfare

Animal welfare is the well-being of non-human animals. Formal standards of animal welfare vary between contexts, but are debated mostly by animal welfare groups, legislators, and academics. Animal welfare science uses measures such as longevity, disease, immunosuppression, behavior, physiology, and reproduction, although there is debate about which of these best indicate animal welfare.

Respect for animal welfare is often based on the belief that nonhuman animals are sentient and that consideration should be given to their well-being or suffering, especially when they are under the care of humans. These concerns can include how animals are slaughtered for food, how they are used in scientific research, how they are kept (as pets, in zoos, farms, circuses, etc.), and how human activities affect the welfare and survival of wild species.

There are two forms of criticism of the concept of animal welfare, coming from diametrically opposite positions. One view, held by some thinkers in history, holds that humans have no duties of any kind to animals. The other view is based on the animal rights position that animals should not be regarded as property and any use of animals by humans is unacceptable. Accordingly, some animal rights proponents argue that the perception of better animal welfare facilitates continued and increased exploitation of animals. Some authorities therefore treat animal welfare and animal rights as two opposing positions. Others see animal welfare gains as incremental steps towards animal rights.

The predominant view of modern neuroscientists, notwithstanding philosophical problems with the definition of consciousness even in humans, is that consciousness exists in nonhuman animals; however, some still maintain that consciousness is a philosophical question that may never be scientifically resolved. Remarkably, a new study has managed to overcome some of the difficulties in testing this question empirically and devised a unique way to dissociate conscious from nonconscious perception in animals. In this study conducted in rhesus monkeys, the researchers built experiments predicting completely opposite behavioral outcomes to consciously vs. non-consciously perceived stimuli. Strikingly, the monkeys' behaviors displayed these exact opposite signatures, just like aware and unaware humans tested in the study.

History, principles, and practice
Animal protection laws were enacted as early as the 1st millennium BCE in India. Several Indian kings built hospitals for animals, and emperor Ashoka (304–232 BCE) issued orders against hunting and animal slaughter, in line with ahimsa, the doctrine of non-violence. In the 13th century CE, Genghis Khan protected wildlife in Mongolia during the breeding season (March to October).

Early legislation in the Western world on behalf of animals includes the Ireland Parliament (Thomas Wentworth) "An Act against Plowing by the Tayle, and pulling the Wooll off living Sheep", 1635, and the Massachusetts Colony (Nathaniel Ward) "Off the Bruite Creatures" Liberty 92 and 93 in the "Massachusetts Body of Liberties" of 1641.

In 1776, English clergyman Humphrey Primatt authored A Dissertation on the Duty of Mercy and Sin of Cruelty to Brute Animals, one of the first books published in support of animal welfare. Marc Bekoff has noted that "Primatt was largely responsible for bringing animal welfare to the attention of the general public."

Since 1822, when Irish MP Richard Martin brought the "Cruel Treatment of Cattle Act 1822" through Parliament offering protection from cruelty to cattle, horses, and sheep, an animal welfare movement has been active in England. Martin was among the founders of the world's first animal welfare organization, the Society for the Prevention of Cruelty to Animals, or SPCA, in 1824. In 1840, Queen Victoria gave the society her blessing, and it became the RSPCA. The society used members' donations to employ a growing network of inspectors, whose job was to identify abusers, gather evidence, and report them to the authorities.

In 1837, the German minister Albert Knapp founded the first German animal welfare society.

One of the first national laws to protect animals was the UK "Cruelty to Animals Act 1835" followed by the "Protection of Animals Act 1911". In the US it was many years until there was a national law to protect animals—the "Animal Welfare Act of 1966"—although there were a number of states that passed anti-cruelty laws between 1828 and 1898. In India, animals are protected by the "Prevention of Cruelty to Animals Act, 1960".

Significant progress in animal welfare did not take place until the late 20th century. In 1965, the UK government commissioned an investigation—led by professor Roger Brambell—into the welfare of intensively farmed animals, partly in response to concerns raised in Ruth Harrison's 1964 book, Animal Machines. On the basis of Brambell's report, the UK government set up the Farm Animal Welfare Advisory Committee in 1967, which became the Farm Animal Welfare Council in 1979. The committee's first guidelines recommended that animals require the freedom to "stand up, lie down, turn around, groom themselves and stretch their limbs." The guidelines have since been elaborated upon to become known as the Five Freedoms.

In the UK, the "Animal Welfare Act 2006" consolidated many different forms of animal welfare legislation.

A number of animal welfare organisations are campaigning to achieve a Universal Declaration on Animal Welfare (UDAW) at the United Nations. In principle, the Universal Declaration would call on the United Nations to recognise animals as sentient beings, capable of experiencing pain and suffering, and to recognise that animal welfare is an issue of importance as part of the social development of nations worldwide. The campaign to achieve the UDAW is being coordinated by World Animal Protection, with a core working group including Compassion in World Farming, the RSPCA, and the Humane Society International (the international branch of HSUS).

The 2019 UN Global Sustainable Development Report identified animal welfare as one of several key missing issues in the 2030 Agenda for Sustainable Development.

Animal welfare science
Animal welfare science is an emerging field that seeks to answer questions raised by the keeping and use of animals, such as whether hens are frustrated when confined in cages, whether the psychological well-being of animals in laboratories can be maintained, and whether zoo animals are stressed by the transport required for international conservation. Ireland leads research into farm animal welfare with the recently published Research Report on Farm Animal Welfare.

Animal welfare issues

 * Animal testing
 * Abandoned pets
 * Bambi effect
 * Behavioral enrichment
 * Blood sport
 * Cruelty to animals
 * Feral cat
 * Hunting
 * Overpopulation in companion animals
 * Overview of discretionary invasive procedures on animals
 * Poaching
 * Puppy mills
 * Whaling
 * Hypertype

Farmed animals
A major concern for the welfare of farmed animals is factory farming in which large numbers of animals are reared in confinement at high stocking densities. Issues include the limited opportunities for natural behaviors, for example, in battery cages, veal and gestation crates, instead producing abnormal behaviors such as tail-biting, cannibalism, and feather pecking, and routine invasive procedures such as beak trimming, castration, and ear notching.More extensive methods of farming, e.g. free range, can also raise welfare concerns such as the mulesing of sheep and predation of stock by wild animals. Biosecurity is also a risk with free range farming, as it allows for more contact between livestock and wild animal populations, which may carry zoonoses.

Farmed animals are artificially selected for production parameters which sometimes impinge on the animals' welfare. For example, broiler chickens are bred to be very large to produce the greatest quantity of meat per animal. Broilers bred for fast growth have a high incidence of leg deformities because the large breast muscles cause distortions of the developing legs and pelvis, and the birds cannot support their increased body weight. As a consequence, they frequently become lame or suffer from broken legs. The increased body weight also puts a strain on their hearts and lungs, and ascites often develop. In the UK alone, up to 20 million broilers each year die from the stress of catching and transporting before reaching the slaughterhouse. Animal welfare violations have been observed more in intensively bred chicken, pig and cattle species, respectively, and studies and laws have been enacted in this regard. However, animal welfare in semi-intensive species such as sheep and goats is nowadays being scrutinised and gaining importance.

Another concern about the welfare of farmed animals is the method of slaughter, especially ritual slaughter. While the killing of animals need not necessarily involve suffering, the general public considers that killing an animal reduces its welfare. This leads to further concerns about premature slaughtering such as chick culling by the laying hen industry, in which males are slaughtered immediately after hatching because they are superfluous; this policy occurs in other farmed animal industries such as the production of goat and cattle milk, raising the same concerns.

A 2023 report by the Animal Welfare Institute found that animal welfare claims by companies selling meat and poultry products lack adequate substantiation in roughly 85% of analyzed cases.

Cetaceans
Captive cetaceans are kept for display, research and naval operations. To enhance their welfare, humans feed them fish that are dead but are disease-free, protect them from predators and injury, monitor their health, and provide activities for behavioral enrichment. Some are kept in lagoons with natural soil and vegetated sides. Most are in concrete tanks which are easy to clean but echo their natural sounds back to them. They cannot develop their own social groups, and related cetaceans are typically separated for display and breeding. Military dolphins used in naval operations swim free during operations and training and return to pens otherwise. Captive cetaceans are trained to present themselves for blood samples, health exams, and noninvasive breath samples above their blow holes. Staff can monitor the captives afterward for signs of infection from the procedure.

Research on wild cetaceans leaves them free to roam and make sounds in their natural habitat, eat live fish, face predators and injury, and form social groups voluntarily. However, boat engines of researchers, whale watchers and others add substantial noise to their natural environment, reducing their ability to echolocate and communicate. Electric engines are far quieter, but are not widely used for either research or whale watching, even for maintaining position, which does not require much power. Vancouver Port offers discounts for ships with quiet propeller and hull designs. Other areas have reduced speeds. Boat engines also have unshielded propellers, which cause serious injuries to cetaceans who come close to the propeller. The US Coast Guard has proposed rules on propeller guards to protect human swimmers, but has not adopted any rules. The US Navy uses propeller guards to protect manatees in Georgia. Ducted propellers provide more efficient drive at speeds up to 10 knots, and protect animals beneath and beside them, but need grilles to prevent injuries to animals drawn into the duct. Attaching satellite trackers and obtaining biopsies to measure pollution loads and DNA involve either capture and release, or shooting the cetaceans from a distance with dart guns. A cetacean was killed by a fungal infection after being darted, due to either an incompletely sterilized dart or an infection from the ocean entering the wound caused by the dart. Researchers on wild cetaceans have not yet been able to use drones to capture noninvasive breath samples.

Other harms to wild cetaceans include commercial whaling, aboriginal whaling, drift netting, ship collisions, water pollution, noise from sonar and reflection seismology, predators, loss of prey, and disease. Efforts to enhance the life of wild cetaceans, besides reducing those harms, include offering human music. Canadian rules do not forbid playing quiet music, though they forbid "noise that may resemble whale songs or calls, underwater".

Wild animal welfare
In addition to cetaceans, the welfare of other wild animals has also been studied, though to a lesser extent than that of animals in farms. Research in wild animal welfare has two focuses: the welfare of wild animals kept in captivity and the welfare of animals living in the wild. The former has addressed the situation of animals kept both for human use, as in zoos or circuses, or in rehabilitation centers. The latter has examined how the welfare of non-domesticated animals living in wild or urban areas are affected by humans or natural factors causing wild animal suffering.

Some of the proponents of these views have advocated carrying out conservation efforts in ways that respect the welfare of wild animals, within the framework of the disciplines of compassionate conservation and conservation welfare, while others have argued in favor of improving the welfare of wild animals for the sake of the animals, regardless of whether there are any conservation issues involved at all. The welfare economist Yew-Kwang Ng, in his 1995 "Towards welfare biology: Evolutionary economics of animal consciousness and suffering", proposed welfare biology as a research field to study "living things and their environment with respect to their welfare (defined as net happiness, or enjoyment minus suffering)."

European Union
The European Commission's activities in this area start with the recognition that animals are sentient beings. The general aim is to ensure that animals do not endure avoidable pain or suffering, and obliges the owner/keeper of animals to respect minimum welfare requirements. European Union legislation regarding farm animal welfare is regularly re-drafted according to science-based evidence and cultural views. For example, in 2009, legislation was passed which aimed to reduce animal suffering during slaughter and on 1 January 2012, the European Union Council Directive 1999/74/EC came into act, which means that conventional battery cages for laying hens are now banned across the Union.

United Kingdom
The Animal Welfare Act 2006 makes owners and keepers responsible for ensuring that the welfare needs of their animals are met. These include the need: for a suitable environment (place to live), for a suitable diet, to exhibit normal behavior patterns, to be housed with, or apart from, other animals (if applicable), and to be protected from pain, injury, suffering and disease. Anyone who is cruel to an animal, or does not provide for its welfare needs, may be banned from owning animals, fined up to £20,000 and/or sent to prison for a maximum of six months.

In the UK, the welfare of research animals being used for "regulated procedures" was historically protected by the Animals (Scientific Procedures) Act 1986 (ASPA) which is administrated by the Home Office. The Act defines "regulated procedures" as animal experiments that could potentially cause "pain, suffering, distress or lasting harm" to "protected animals". Initially, "protected animals" encompassed all living vertebrates other than humans, but, in 1993, an amendment added a single invertebrate species, the common octopus.

Primates, cats, dogs, and horses have additional protection over other vertebrates under the Act. Revised legislation came into force in January 2013. This has been expanded to protect "...all living vertebrates, other than man, and any living cephalopod. Fish and amphibia are protected once they can feed independently and cephalopods at the point when they hatch. Embryonic and foetal forms of mammals, birds and reptiles are protected during the last third of their gestation or incubation period." The definition of regulated procedures was also expanded: "A procedure is regulated if it is carried out on a protected animal and may cause that animal a level of pain, suffering, distress or lasting harm equivalent to, or higher than, that caused by inserting a hypodermic needle according to good veterinary practice." It also includes modifying the genes of a protected animal if this causes the animal pain, suffering, distress, or lasting harm. The ASPA also considers other issues such as animal sources, housing conditions, identification methods, and the humane killing of animals.

Those applying for a license must explain why such research cannot be done through non-animal methods. The project must also pass an ethical review panel which aims to decide if the potential benefits outweigh any suffering for the animals involved.

United States
In the United States, a federal law called the Humane Slaughter Act was designed to decrease suffering of livestock during slaughter.

The Georgia Animal Protection Act of 1986 was a state law enacted in response to the inhumane treatment of companion animals by a pet store chain in Atlanta. The Act provided for the licensing and regulation of pet shops, stables, kennels, and animal shelters, and established, for the first time, minimum standards of care. Additional provisions, called the Humane Euthanasia Act, were added in 1990, and then further expanded and strengthened with the Animal Protection Act of 2000.

In 2002, voters passed (by a margin of 55% for and 45% against) Amendment 10 to the Florida Constitution banning the confinement of pregnant pigs in gestation crates. In 2006, Arizona voters passed Proposition 204 with 62% support; the legislation prohibits the confinement of calves in veal crates and breeding sows in gestation crates. In 2007, the Governor of Oregon signed legislation prohibiting the confinement of pigs in gestation crates and in 2008, the Governor of Colorado signed legislation that phased out both gestation crates and veal crates. Also during 2008, California passed Proposition 2, known as the "Prevention of Farm Animal Cruelty Act", which orders new space requirements for farm animals starting in 2015.

In the US, every institution that uses vertebrate animals for federally funded laboratory research must have an Institutional Animal Care and Use Committee (IACUC). Each local IACUC reviews research protocols and conducts evaluations of the institution's animal care and use which includes the results of inspections of facilities that are required by law. The IACUC committee must assess the steps taken to "enhance animal well-being" before research can take place. This includes research on farm animals.

According to the National Institutes of Health Office of Laboratory Animal Welfare, researchers must try to minimize distress in animals whenever possible: "Animals used in research and testing may experience pain from induced diseases, procedures, and toxicity. The Public Health Service (PHS) Policy and Animal Welfare Regulations (AWRs) state that procedures that cause more than momentary or slight pain or distress should be performed with appropriate sedation, analgesia, or anesthesia.

However, research and testing studies sometimes involve pain that cannot be relieved with such agents because they would interfere with the scientific objectives of the study. Accordingly, federal regulations require that IACUCs determine that discomfort to animals will be limited to that which is unavoidable for the conduct of scientifically valuable research, and that unrelieved pain and distress will only continue for the duration necessary to accomplish the scientific objectives. The PHS Policy and AWRs further state that animals that would otherwise suffer severe or chronic pain and distress that cannot be relieved should be painlessly killed at the end of the procedure, or if appropriate, during the procedure."

The National Research Council's Guide for the Care and Use of Laboratory Animals also serves as a guide to improve welfare for animals used in research in the US. The Federation of Animal Science Societies' Guide for the Care and Use of Agricultural Animals in Research and Teaching is a resource addressing welfare concerns in farm animal research. Laboratory animals in the US are also protected under the Animal Welfare Act. The United States Department of Agriculture Animal and Plant Health Inspection Service (APHIS) enforces the Animal Welfare Act. APHIS inspects animal research facilities regularly and reports are published online.

According to the U.S. Department of Agriculture (USDA), the total number of animals used in the U.S. in 2005 was almost 1.2 million, but this does not include rats, mice, and birds which are not covered by welfare legislation but make up approximately 90% of research animals.

Approaches and definitions
There are many different approaches to describing and defining animal welfare.

Positive conditions – Providing good animal welfare is sometimes defined by a list of positive conditions which should be provided to the animal. This approach is taken by the Five Freedoms and the three principles of professor John Webster.

The Five Freedoms are:
 * Freedom from thirst and hunger – by ready access to fresh water and a diet to maintain full health and vigour
 * Freedom from discomfort – by providing an appropriate environment including shelter and a comfortable resting area
 * Freedom from pain, injury, and disease – by prevention or rapid diagnosis and treatment
 * Freedom to express most normal behavior – by providing sufficient space, proper facilities, and company of the animal's own kind
 * Freedom from fear and distress – by ensuring conditions and treatment which avoid mental suffering

John Webster defines animal welfare by advocating three positive conditions: Living a natural life, being fit and healthy, and being happy.

High production – In the past, many have seen farm animal welfare chiefly in terms of whether the animal is producing well. The argument is that an animal in poor welfare would not be producing well, however, many farmed animals will remain highly productive despite being in conditions where good welfare is almost certainly compromised, e.g., layer hens in battery cages.

Emotion in animals – Others in the field, such as professor Ian Duncan and professor Marian Dawkins, focus more on the feelings of the animal. This approach indicates the belief that animals should be considered as sentient beings. Duncan wrote, "Animal welfare is to do with the feelings experienced by animals: the absence of strong negative feelings, usually called suffering, and (probably) the presence of positive feelings, usually called pleasure. In any assessment of welfare, it is these feelings that should be assessed." Dawkins wrote, "Let us not mince words: Animal welfare involves the subjective feelings of animals."

Welfare biology – Yew-Kwang Ng defines animal welfare in terms of welfare economics: "Welfare biology is the study of living things and their environment with respect to their welfare (defined as net happiness, or enjoyment minus suffering). Despite difficulties of ascertaining and measuring welfare and relevancy to normative issues, welfare biology is a positive science."

Dictionary definition – In the Saunders Comprehensive Veterinary Dictionary, animal welfare is defined as "the avoidance of abuse and exploitation of animals by humans by maintaining appropriate standards of accommodation, feeding and general care, the prevention and treatment of disease and the assurance of freedom from harassment, and unnecessary discomfort and pain."

American Veterinary Medical Association (AVMA) has defined animal welfare as: "An animal is in a good state of welfare if (as indicated by scientific evidence) it is healthy, comfortable, well nourished, safe, able to express innate behavior, and if it is not suffering from unpleasant states such as pain, fear, and distress." They have offered the following eight principles for developing and evaluating animal welfare policies.
 * The responsible use of animals for human purposes, such as companionship, food, fiber, recreation, work, education, exhibition, and research conducted for the benefit of both humans and animals, is consistent with the Veterinarian's Oath.
 * Decisions regarding animal care, use, and welfare shall be made by balancing scientific knowledge and professional judgment with consideration of ethical and societal values.
 * Animals must be provided water, food, proper handling, health care, and an environment appropriate to their care and use, with thoughtful consideration for their species-typical biology and behavior.
 * Animals should be cared for in ways that minimize fear, pain, stress, and suffering.
 * Procedures related to animal housing, management, care, and use should be continuously evaluated, and when indicated, refined or replaced.
 * Conservation and management of animal populations should be humane, socially responsible, and scientifically prudent.
 * Animals shall be treated with respect and dignity throughout their lives and, when necessary, provided a humane death.
 * The veterinary profession shall continually strive to improve animal health and welfare through scientific research, education, collaboration, advocacy, and the development of legislation and regulations.

Terrestrial Animal Health Code of World Organisation for Animal Health defines animal welfare as "how an animal is coping with the conditions in which it lives. An animal is in a good state of welfare if (as indicated by scientific evidence) it is healthy, comfortable, well nourished, safe, able to express innate behaviour, and if it is not suffering from unpleasant states such as pain, fear, and distress. Good animal welfare requires disease prevention and veterinary treatment, appropriate shelter, management, nutrition, humane handling and humane slaughter/killing. Animal welfare refers to the state of the animal; the treatment that an animal receives is covered by other terms such as animal care, animal husbandry, and humane treatment."

Coping – Professor Donald Broom defines the welfare of an animal as "Its state as regards its attempts to cope with its environment. This state includes how much it is having to do to cope, the extent to which it is succeeding in or failing to cope, and its associated feelings." He states that "welfare will vary over a continuum from very good to very poor and studies of welfare will be most effective if a wide range of measures is used." John Webster criticized this definition for making "no attempt to say what constitutes good or bad welfare."

Attitudes
Animal welfare often refers to a utilitarian attitude towards the well-being of nonhuman animals. It believes the animals can be exploited if the animal suffering and the costs of use is less than the benefits to humans. This attitude is also known simply as welfarism.

An example of welfarist thought is Hugh Fearnley-Whittingstall's meat manifesto. Point three of eight is: "Think about the animals that the meat you eat comes from. Are you at all concerned about how they have been treated? Have they lived well? Have they been fed on safe, appropriate foods? Have they been cared for by someone who respects them and enjoys contact with them? Would you like to be sure of that? Perhaps it's time to find out a bit more about where the meat you eat comes from. Or to buy from a source that reassures you about these points."

Robert Garner describes the welfarist position as the most widely held in modern society. He states that one of the best attempts to clarify this position is given by philosopher Robert Nozick:

"Consider the following (too minimal) position about the treatment of animals. So that we can easily refer to it, let us label this position 'utilitarianism for animals, Kantianism for people.' It says: (1) maximize the total happiness of all living beings; (2) place stringent side constraints on what one may do to human beings. Human beings may not be used or sacrificed for the benefit of others; animals may be used or sacrificed for the benefit of other people or animals only if those benefits are greater than the loss inflicted."

Welfarism is often contrasted with the animal rights and animal liberation positions, which hold that animals should not be used by humans and should not be regarded as human property. However, it has been argued that both welfarism and animal liberation only make sense if it is assumed that animals have "subjective welfare".

New welfarism
New welfarism was coined by Gary L. Francione in 1996. It is a view that the best way to prevent animal suffering is to abolish the causes of animal suffering, but advancing animal welfare is a goal to pursue in the short term. Thus, for instance, new welfarists want to phase out fur farms and animal experiments but in the short-term they try to improve conditions for the animals in these systems, so they lobby to make cages less constrictive and to reduce the numbers of animals used in laboratories.

Within the context of animal research, many scientific organisations believe that improved animal welfare will provide improved scientific outcomes. If an animal in a laboratory is suffering stress or pain it could negatively affect the results of the research.

Increased affluence in many regions for the past few decades afforded consumers the disposable income to purchase products from high welfare systems. The adaptation of more economically efficient farming systems in these regions were at the expense of animal welfare and to the financial benefit of consumers, both of which were factors in driving the demand for higher welfare for farm animals. A 2006 survey concluded that a majority (63%) of EU citizens "show some willingness to change their usual place of shopping in order to be able to purchase more animal welfare-friendly products." The volume of scientific research on animal welfare has also increased significantly in some countries.

Denial of duties to animals
Some individuals in history have, at least in principle, rejected the view that humans have duties of any kind to animals.

Augustine of Hippo seemed to take such a position in his writings against those he saw as heretics: "For we see and hear by their cries that animals die with pain, although man disregards this in a beast, with which, as not having a rational soul, we have no community of rights."

Animal rights
Animal rights advocates, such as Gary L. Francione and Tom Regan, argue that the animal welfare position (advocating for the betterment of the condition of animals, but without abolishing animal use) is inconsistent in logic and ethically unacceptable. Philosopher Steven Best suggests that an emphasis on "welfarism" has the effect of legitimizing "any human use of animals" so long as humans aren't "cruel" to them and do whatever is necessary to avoid inflicting "unnecessary harm". Sociologist David Nibert writes that animal welfare reforms, usually implemented by wealthier countries, are often "modest" and "mostly localized," and are vastly surpassed by the ongoing expansion of the capitalist–driven animal–industrial complex, with the number of CAFOs and the animals to fill them dramatically increasing, along with growing numbers of humans consuming animal products. However, there are some animal right groups, such as PETA, which support animal welfare measures in the short term to alleviate animal suffering until all animal use is ended.

According to PETA's Ingrid Newkirk in an interview with Wikinews, there are two issues in animal welfare and animal rights. "If I only could have one thing, it would be to end suffering", said Newkirk. "If you could take things from animals and kill animals all day long without causing them suffering, then I would take it... Everybody should be able to agree that animals should not suffer if you kill them or steal from them by taking the fur off their backs or take their eggs, whatever. But you shouldn't put them through torture to do that."

Abolitionism holds that focusing on animal welfare not only fails to challenge animal suffering, but may actually prolong it by making the exercise of property rights over animals appear less unattractive. The abolitionists' objective is to secure a moral and legal paradigm shift, whereby animals are no longer regarded as property. In recent years documentaries such as watchdominion.com have been produced, exposing the suffering occurring in animal agriculture facilities that are marketed as having high welfare standards.

Global
World Organisation for Animal Health (OIE): The intergovernmental organisation responsible for improving animal health worldwide. The OIE has been established "for the purpose of projects of international public utility relating to the control of animal diseases, including those affecting humans and the promotion of animal welfare and animal production food safety."

World Animal Protection: Protects animals across the globe. World Animal Protection's objectives include helping people understand the critical importance of good animal welfare, encouraging nations to commit to animal-friendly practices, and building the scientific case for the better treatment of animals. They are global in a sense that they have consultative status at the Council of Europe and collaborate with national governments, the United Nations, the Food and Agriculture Organization and the World Organization for Animal Health.

Non-government organizations
Animal Welfare Institute (AWI): An American non-profit charitable organization founded by Christine Stevens in 1951 with the goal of reducing suffering inflicted on animals by humans. It is one of the oldest animal welfare organizations in the US.

Canadian Council on Animal Care: The national organization responsible for overseeing the care and use of animals involved in Canadian Science.

Canadian Federation of Humane Societies (CFHS): The only national organization representing humane societies and SPCAs in Canada. They provide leadership on animal welfare issues and spread the message across Canada.

The Canadian Veterinary Medical Association: Brings in veterinary involvement to animal welfare. Their objective is to share this concern of animals with all members of the profession, with the general public, with government at all levels, and with other organizations such as the CFHS, which have similar concerns.

Compassion in World Farming: Founded over 40 years ago in 1967 by a British farmer who became horrified by the development of modern, intensive factory farming. "Today we campaign peacefully to end all cruel factory farming practices. We believe that the biggest cause of cruelty on the planet deserves a focused, specialised approach – so we only work on farm animal welfare."

The Movement for Compassionate Living: Exists to- "Promote simple vegan living and self-reliance as a remedy against the exploitation of humans, animals and the Earth. Promote the use of trees and vegan-organic farming to meet the needs of society for food and natural resources. Promote a land-based society where as much of our food and resources as possible are produced locally."

National Animal Interest Alliance: An animal welfare organization in the United States founded in 1991 promotes the welfare of animals, strengthens the human-animal bond, and safeguards the rights of responsible animal owners, enthusiasts and professionals through research, public information and sound public policy. They host an online library of information about various animal-related subjects serving as a resource for groups and individuals dedicated to responsible animal care and well-being.

National Farm Animal Care Council: Their objectives are to facilitate collaboration among members with respect to farm animal care issues in Canada, to facilitate information sharing and communication, and to monitor trends and initiatives in both the domestic and international market place.

National Office of Animal Health: A British organisation that represents its members drawn from the animal medicines industry.

Ontario Society for the Prevention of Cruelty to Animals: A registered charity comprising over 50 communities.

Royal Society for the Prevention of Cruelty to Animals: A well-known animal welfare charity in England and Wales, founded in 1824.

Universities Federation for Animal Welfare: A UK registered charity, established in 1926, that works to develop and promote improvements in the welfare of all animals through scientific and educational activity worldwide.

Links to animal welfare and rights by country

 * Animal welfare and rights in Brazil
 * Animal welfare and rights in China
 * Animal rights in Colombia
 * Animal welfare in Egypt
 * Animal welfare and rights in Germany
 * Animal welfare and rights in India
 * Animal welfare and rights in Israel
 * Animal welfare and rights in Japan
 * Animal welfare and rights in Malaysia
 * Animal welfare in Nazi Germany
 * Animal welfare in New Zealand
 * Animal welfare and rights in South Korea
 * Animal welfare in Thailand
 * Animal welfare in the United Kingdom
 * Animal welfare in the United States

title: Animal welfare


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Splitting field

In abstract algebra, a splitting field of a polynomial with coefficients in a field is the smallest field extension of that field over which the polynomial splits, i.e., decomposes into linear factors.

Definition
A splitting field of a polynomial p(X) over a field K is a field extension L of K over which p factors into linear factors

 * $$p(X) = c \prod_{i=1}^{\deg p} (X - a_i)$$

where $$c \in K$$ and for each $$i$$ we have $$X - a_i \in L[X]$$ with ai not necessarily distinct and such that the roots ai generate L over K. The extension L is then an extension of minimal degree over K in which p splits. It can be shown that such splitting fields exist and are unique up to isomorphism. The amount of freedom in that isomorphism is known as the Galois group of p (if we assume it is separable).

A splitting field of a set of P of polynomials is the smallest field over which each of the polynomials in P splits.

Properties
An extension L that is a splitting field for a set of polynomials p(X) over K is called a normal extension of K.

Given an algebraically closed field A containing K, there is a unique splitting field L of p between K and A, generated by the roots of p. If K is a subfield of the complex numbers, the existence is immediate. On the other hand, the existence of algebraic closures in general is often proved by 'passing to the limit' from the splitting field result, which therefore requires an independent proof to avoid circular reasoning.

Given a separable extension K′ of K, a Galois closure L of K′ is a type of splitting field, and also a Galois extension of K containing K′ that is minimal, in an obvious sense. Such a Galois closure should contain a splitting field for all the polynomials p over K that are minimal polynomials over K of elements of K′.

Motivation
Finding roots of polynomials has been an important problem since the time of the ancient Greeks. Some polynomials, however, such as $x^{2} + 1$ over $R$, the real numbers, have no roots. By constructing the splitting field for such a polynomial one can find the roots of the polynomial in the new field.

The construction
Let F be a field and p(X) be a polynomial in the polynomial ring F[X] of degree n. The general process for constructing K, the splitting field of p(X) over F, is to construct a chain of fields $$F=K_0 \subseteq K_1 \subseteq \cdots \subseteq K_{r-1} \subseteq K_r=K$$ such that Ki is an extension of Ki −1 containing a new root of p(X). Since p(X) has at most n roots the construction will require at most n extensions. The steps for constructing Ki are given as follows:
 * Factorize p(X) over Ki into irreducible factors $$f_1(X)f_2(X) \cdots f_k(X)$$.
 * Choose any nonlinear irreducible factor f(X).
 * Construct the field extension Ki +1 of Ki as the quotient ring Ki +1 = Ki [X] / (f(X)) where (f(X)) denotes the ideal in Ki [X] generated by f(X).
 * Repeat the process for Ki +1 until p(X) completely factors.

The irreducible factor f(X) used in the quotient construction may be chosen arbitrarily. Although different choices of factors may lead to different subfield sequences, the resulting splitting fields will be isomorphic.

Since f(X) is irreducible, (f(X)) is a maximal ideal of Ki [X] and Ki [X] / (f(X)) is, in fact, a field, the residue field for that maximal ideal. Moreover, if we let $$\pi : K_i[X] \to K_i[X]/(f(X))$$ be the natural projection of the ring onto its quotient then
 * $$f(\pi(X)) = \pi(f(X)) = f(X)\ \bmod\ f(X) = 0$$

so π(X) is a root of f(X) and of p(X).

The degree of a single extension $$[K_{i+1} : K_i]$$ is equal to the degree of the irreducible factor f(X). The degree of the extension [K : F] is given by $$[K_r : K_{r-1}] \cdots [K_2 : K_1] [K_1 : F]$$ and is at most n!.

The field Ki [X]/(f(X))
As mentioned above, the quotient ring Ki +1 = Ki [X]/(f(X)) is a field when f(X) is irreducible. Its elements are of the form

 * $$c_{n-1}\alpha^{n-1} + c_{n-2}\alpha^{n-2} + \cdots + c_1\alpha + c_0$$

where the cj are in Ki and α = π(X). (If one considers Ki +1 as a vector space over Ki then the powers α j for 0 ≤ j ≤ n−1 form a basis.)

The elements of Ki +1 can be considered as polynomials in α of degree less than n. Addition in Ki +1 is given by the rules for polynomial addition, and multiplication is given by polynomial multiplication modulo f(X). That is, for g(α) and h(α) in Ki +1 their product is g(α)h(α) = r(α) where r(X) is the remainder of g(X)h(X) when divided by f(X) in Ki [X].

The remainder r(X) can be computed through polynomial long division; however there is also a straightforward reduction rule that can be used to compute r(α) = g(α)h(α) directly. First let

 * $$f(X) = X^n + b_{n-1} X^{n-1} + \cdots + b_1 X + b_0.$$

The polynomial is over a field so one can take f(X) to be monic without loss of generality. Now α is a root of f(X), so

 * $$\alpha^n = -(b_{n-1} \alpha^{n-1} + \cdots + b_1 \alpha + b_0).$$

If the product g(α)h(α) has a term αm with m ≥ n it can be reduced as follows:

 * $$\alpha^n\alpha^{m-n} = -(b_{n-1} \alpha^{n-1} + \cdots + b_1 \alpha + b_0) \alpha^{m-n} = -(b_{n-1} \alpha^{m-1} + \cdots + b_1 \alpha^{m-n+1} + b_0 \alpha^{m-n})$$.

As an example of the reduction rule, take Ki = Q[X], the ring of polynomials with rational coefficients, and take f(X) = X 7 − 2. Let $$g(\alpha) = \alpha^5 + \alpha^2$$ and h(α) = α 3 +1 be two elements of Q[X]/(X 7 − 2). The reduction rule given by f(X) is α7 = 2 so

 * $$g(\alpha)h(\alpha) = (\alpha^5 + \alpha^2)(\alpha^3 + 1) = \alpha^8 + 2 \alpha^5 + \alpha^2 = (\alpha^7)\alpha + 2\alpha^5 + \alpha^2 = 2 \alpha^5 + \alpha^2 + 2\alpha.$$

The complex numbers
Consider the polynomial ring R[x], and the irreducible polynomial x2 + 1. The quotient ring R[x] / (x2 + 1) is given by the congruence x2 ≡ −1. As a result, the elements (or equivalence classes) of R[x] / (x2 + 1) are of the form a + bx where a and b belong to R. To see this, note that since x2 ≡ −1 it follows that x3 ≡ −x, x4 ≡ 1, x5 ≡ x, etc.; and so, for example p + qx + rx2 + sx3 ≡ p + qx + r(−1) + s(−x) = (p − r) + (q − s)x.

The addition and multiplication operations are given by firstly using ordinary polynomial addition and multiplication, but then reducing modulo x2 + 1, i.e. using the fact that x2 ≡ −1, x3 ≡ −x, x4 ≡ 1, x5 ≡ x, etc. Thus:
 * $$(a_1 + b_1x) + (a_2 + b_2x) = (a_1 + a_2) + (b_1 + b_2)x, $$
 * $$(a_1 + b_1x)(a_2 + b_2x) = a_1a_2 + (a_1b_2 + b_1a_2)x + (b_1b_2)x^2 \equiv (a_1a_2 - b_1b_2) + (a_1b_2 + b_1a_2)x \, . $$

If we identify a + bx with (a,b) then we see that addition and multiplication are given by
 * $$(a_1,b_1) + (a_2,b_2) = (a_1 + a_2,b_1 + b_2), $$
 * $$(a_1,b_1)\cdot (a_2,b_2) = (a_1a_2 - b_1b_2,a_1b_2 + b_1a_2). $$

We claim that, as a field, the quotient ring R[x] / (x2 + 1) is isomorphic to the complex numbers, C. A general complex number is of the form a + bi, where a and b are real numbers and i2 = −1. Addition and multiplication are given by

 * $$(a_1 + b_1 i) + (a_2 + b_2 i) = (a_1 + a_2) + i(b_1 + b_2),$$
 * $$(a_1 + b_1 i) \cdot (a_2 + b_2 i) = (a_1a_2 - b_1b_2) + i(a_1b_2 + a_2b_1).$$

If we identify a + bi with (a, b) then we see that addition and multiplication are given by

 * $$(a_1,b_1) + (a_2,b_2) = (a_1 + a_2,b_1 + b_2),$$
 * $$(a_1,b_1)\cdot (a_2,b_2) = (a_1a_2 - b_1b_2,a_1b_2 + b_1a_2).$$

The previous calculations show that addition and multiplication behave the same way in R[x] / (x2 + 1) and C. In fact, we see that the map between R[x] / (x2 + 1) and C given by a + bx → a + bi is a homomorphism with respect to addition and multiplication. It is also obvious that the map a + bx → a + bi is both injective and surjective; meaning that a + bx → a + bi is a bijective homomorphism, i.e., an isomorphism. It follows that, as claimed: R[x] / (x2 + 1) ≅ C.

In 1847, Cauchy used this approach to define the complex numbers.

Cubic example
Let $K$ be the rational number field $Q$ and $p(x) = x^{3} − 2$. Each root of $p$ equals $\sqrt{2$ times a cube root of unity. Therefore, if we denote the cube roots of unity by

 * $$\omega_1 = 1,\,$$
 * $$\omega_2 = -\frac{1}{2} + \frac{\sqrt{3}}{2} i,$$
 * $$\omega_3 = -\frac{1}{2} - \frac{\sqrt{3}}{2} i.$$

any field containing two distinct roots of $p$ will contain the quotient between two distinct cube roots of unity. Such a quotient is a primitive cube root of unity—either $$\omega_2$$ or $$\omega_3=1/\omega_2$$. It follows that a splitting field $L$ of $p$ will contain ω2, as well as the real cube root of 2; conversely, any extension of $Q$ containing these elements contains all the roots of $p$. Thus

 * $$L = \mathbf{Q}(\sqrt[3]{2}, \omega_2) = \{ a + b\sqrt[3]{2} + c{\sqrt[3]{2}}^2 + d\omega_2 + e\sqrt[3]{2}\omega_2 + f{\sqrt[3]{2}}^2 \omega_2 \mid a,b,c,d,e,f \in \mathbf{Q} \}$$

Note that applying the construction process outlined in the previous section to this example, one begins with $$K_0 = \mathbf{Q}$$ and constructs the field $$K_1 = \mathbf{Q}[X] / (X^3 - 2)$$. This field is not the splitting field, but contains one (any) root. However, the polynomial $$Y^3 - 2$$ is not irreducible over $$K_1$$ and in fact:

 * $$Y^3 -2 = (Y - X)(Y^2 + XY + X^2).$$

Note that $$X$$ is not an indeterminate, and is in fact an element of $$K_1$$. Now, continuing the process, we obtain $$K_2 = K_1[Y] / (Y^2 + XY + X^2)$$, which is indeed the splitting field and is spanned by the $$\mathbf{Q}$$-basis $$\{1, X, X^2, Y, XY, X^2 Y\}$$. Notice that if we compare this with $$L$$ from above we can identify $$X = \sqrt[3]{2}$$ and $$Y = \omega_2$$.

Other examples

 * The splitting field of xq − x over Fp is the unique finite field Fq for q = pn. Sometimes this field is denoted by GF(q).

 * The splitting field of x2 + 1 over F7 is F49; the polynomial has no roots in F7, i.e., −1 is not a square there, because 7 is not congruent to 1 modulo 4.

 * The splitting field of x2 − 1 over F7 is F7 since x2 − 1 = (x + 1)(x − 1) already splits into linear factors.

 * We calculate the splitting field of f(x) = x3 + x + 1 over F2. It is easy to verify that f(x) has no roots in F2; hence f(x) is irreducible in F2[x]. Put r = x + (f(x)) in F2[x]/(f(x)) so F2(r ) is a field and x3 + x + 1 = (x + r)(x2 + ax + b) in F2(r )[x]. Note that we can write + for − since the characteristic is two. Comparing coefficients shows that a = r and b = 1 + r 2. The elements of F2(r ) can be listed as c + dr + er 2, where c, d, e are in F2. There are eight elements: 0, 1, r, 1 + r, r 2, 1 + r 2, r + r 2 and 1 + r + r 2. Substituting these in x2 + rx + 1 + r 2 we reach (r 2)2 + r(r 2) + 1 + r 2 = r 4 + r 3 + 1 + r 2 = 0, therefore x3 + x + 1 = (x + r)(x + r 2)(x + (r + r 2)) for r in F2[x]/(f(x)); E = F2(r ) is a splitting field of x3 + x + 1 over F2.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Splitting field


text:
Drygalski Island

Drygalski Island is an ice-capped island that is 11 nmi long and rises to 325 m in the Davis Sea of the Southern Ocean, about 85 km north of the coast of Queen Mary Land and 45 km north-northeast of Cape Filchner. The island has an area of 220 km2.

Drygalski Island was first viewed from the continental Antarctic coast in November 1912 by members of the Western Base Party of the Australian Antarctic Expedition (1911-1914), and observed more closely from Sir Douglas Mawson's ship Aurora on the homeward journey in January 1914. Because Drygalski Island was thought to be "Drygalski's High Land", charted by Professor Erich von Drygalski of the German Antarctic Expedition (1901-1903) in 1902, Drygalski's name was given by Sir Douglas Mawson to the island.

A temporary field station named Mir was opened from 20 May to 6 August in 1960 on the island by the Soviet Union to study meteorological conditions.

title: Drygalski Island


text:
Azazel

In the Hebrew Bible, the name Azazel (עֲזָאזֵל ʿĂzāʾzēl; عزازيل) represents a desolate place where a scapegoat bearing the sins of the Jews was sent during Yom Kippur. During the late Second Temple period (after the closure of the Hebrew Bible canon), Azazel came to be viewed as a fallen angel responsible for introducing humans to forbidden knowledge, as described in the Book of Enoch. His role as a fallen angel partly remains in Christian and Islamic traditions.

Torah
In the Hebrew Bible, the term is used three times in the Book of Leviticus, where two male goats were to be sacrificed to Yahweh and one of the two was selected by lot, for Yahweh is seen as speaking through the lots. One goat is selected by lot and sent into the wilderness לַעֲזָאזֵל, "for Azazel". This goat was then cast out in the desert as part of Yom Kippur. The scapegoat ritual can be traced back to 24th century BC Ebla, from where it spread throughout the ancient Near East.

In older English versions, such as the King James Version, the phrase la-azazel is translated as "as a scapegoat"; however, in most modern English Bible translations, it is represented as a name in the text: "Aaron shall offer the bull as a sin offering for himself, and shall make atonement for himself and for his house. He shall take the two goats and set them before the Lord at the entrance of the tent of meeting; and Aaron shall cast lots on the two goats, one lot for the Lord and the other lot for Azazel. Aaron shall present the goat on which the lot fell for the Lord, and offer it as a sin offering; but the goat on which the lot fell for Azazel shall be presented alive before the Lord to make atonement over it, that it may be sent away into the wilderness to Azazel."

A baraita, apparently interpreting ʿazazel as ʿaz (rugged) + El (God), understands it to refer to the rugged and rough mountain cliff from which the goat was cast down.

Wilhelm Gesenius also thought the term referred to the object, and emended the name to עזלזל "utter removal", theoretically the name of a demon. However, neither this demon nor the root עזל are attested.

In the Septuagint and later translations
The translators of the Greek Septuagint understood the Hebrew term as meaning "the sent away" (apparently reading either עז אזל "goat that leaves" or "the mighty sent" or עזלזל v.s.), and read: "8and Aaron shall cast lots upon the two goats, one lot for the Lord and the other lot for the scapegoat (Greek apodiopompaio dat.).9And Aaron shall present the goat on which the lot fell for the Lord, and offer it as a sin offering; 10but the goat on which the lot of the sent away one fell shall be presented alive before the Lord to make atonement over it, that it may be sent away (Greek eis ten apopompen acc.) into the wilderness."

Following the Septuagint, the Vulgate, Martin Luther and the King James Version also give readings such as Young's Literal Translation: "And Aaron hath given lots over the two goats, one lot for Jehovah, and one lot for a goat of departure'". According to the Peshitta, Azazel is rendered Za-za-e'il "strong one against/of God" in Syriac. Pesher on the Periods A-B (4Q180) reads, "on Azazel (some read Uzael) and the angels". If the name is in fact Azazel's, it is spelled עזזאל, equivalent to the Peshitta's version. The Targum Neofiti reads עזזל, without the aleph.

Rabbinical Judaism
The Mishnah (Yoma 39a ) follows the Hebrew Bible text; two goats were procured, similar in respect of appearance, height, cost, and time of selection. Having one of these on his right and the other on his left, the high priest, who was assisted in this rite by two subordinates, put both his hands into a wooden case, and took out two labels, one inscribed "for Yahweh" and the other "for Azazel". The high priest then laid his hands with the labels upon the two goats and said, "A sin-offering to Yahweh" (thus speaking the Tetragrammaton); and the two men accompanying him replied, "Blessed be the name of His glorious kingdom for ever and ever." He then fastened a scarlet woolen thread to the head of the goat "for Azazel"; and laying his hands upon it again, recited the following confession of sin and prayer for forgiveness: "O Lord, I have acted iniquitously, trespassed, sinned before Thee: I, my household, and the sons of Aaron Thy holy ones. O Lord, forgive the iniquities, transgressions, and sins that I, my household, and Aaron's children, Thy holy people, committed before Thee, as is written in the law of Moses, Thy servant, 'for on this day He will forgive you, to cleanse you from all your sins before the Lord; ye shall be clean.'"

This prayer was responded to by the congregation present. A man was selected, preferably a priest, to take the goat to the precipice in the wilderness; and he was accompanied part of the way by the most eminent men of Jerusalem. Ten booths had been constructed at intervals along the road leading from Jerusalem to the steep mountain. At each one of these the man leading the goat was formally offered food and drink, which he, however, refused. When he reached the tenth booth those who accompanied him proceeded no further, but watched the ceremony from a distance. When he came to the precipice he divided the scarlet thread into two parts, one of which he tied to the rock and the other to the goat's horns, and then pushed the goat down (Yoma 6:1–8). The cliff was so high and rugged that before the goat had traversed half the distance to the plain below, its limbs were utterly shattered. Men were stationed at intervals along the way, and as soon as the goat was thrown down the precipice, they signaled to one another by means of kerchiefs or flags, until the information reached the high priest, whereat he proceeded with the other parts of the ritual.

The scarlet thread is symbolically referenced in ; and the Talmud states (ib. 39a) that during the forty years that Simeon the Just was High Priest of Israel, the thread actually turned white as soon as the goat was thrown over the precipice: a sign that the sins of the people were forgiven. In later times the change to white was not invariable: a proof of the people's moral and spiritual deterioration, that was gradually on the increase, until forty years before the destruction of the Second Temple, when the change of color was no longer observed (l.c. 39b).

Medieval Jewish commentators
The medieval scholar Nachmanides (1194–1270) identified the Hebrew text as also referring to a demon, and identified this "Azazel" with Samael. However, he did not see the sending of the goat as honoring Azazel as a deity, but as a symbolic expression of the idea that the people's sins and their evil consequences were to be sent back to the spirit of desolation and ruin, the source of all impurity. The very fact that the two goats were presented before God, before the one was sacrificed and the other sent into the wilderness, was proof that Azazel was not ranked alongside God, but regarded simply as the personification of wickedness in contrast with the righteous government of God.

Maimonides (1134–1204) says that as sins cannot be taken off one's head and transferred elsewhere, the ritual is symbolic, enabling the penitent to discard his sins: “These ceremonies are of a symbolic character and serve to impress man with a certain idea and to lead him to repent, as if to say, ‘We have freed ourselves of our previous deeds, cast them behind our backs and removed them from us as far as possible’.”

The rite, resembling, on one hand, the sending off of the basket with the woman embodying wickedness to the land of Shinar in the vision of Zechariah, and, on the other, the letting loose of the living bird into the open field in the case of the leper healed from the plague , was, indeed, viewed by the people of Jerusalem as a means of ridding themselves of the sins of the year. So would the crowd, called Babylonians or Alexandrians, pull the goat's hair to make it hasten forth, carrying the burden of sins away with it (Yoma vi. 4, 66b; "Epistle of Barnabas," vii.), and the arrival of the shattered animal at the bottom of the valley of the rock of Bet Ḥadudo, twelve miles away from the city, was signalized by the waving of shawls to the people of Jerusalem, who celebrated the event with boisterous hilarity and amid dancing on the hills (Yoma vi. 6, 8; Ta'an. iv. 8). Evidently the figure of Azazel was an object of general fear and awe rather than, as has been conjectured, a foreign product or the invention of a late lawgiver. More as a demon of the desert, it seems to have been closely interwoven with the mountainous region of Jerusalem.

Latin Bible
The Vulgate contains no mention of "Azazel" but only of caper emissarius, or "emissary goat", apparently reading עז אזל goat which leaves:

English versions, such as the King James Version, followed the Septuagint and Vulgate in understanding the term as relating to a goat. The modern English Standard Version provides the footnote "16:8 The meaning of Azazel is uncertain; possibly the name of a place or a demon, traditionally a scapegoat; also verses 10, 26". Most scholars accept the indication of some kind of demon or deity, however Judit M. Blair notes that this is an argument without supporting contemporary text evidence.

Ida Zatelli (1998) has suggested that the Hebrew ritual parallels pagan practice of sending a scapegoat into the desert on the occasion of a royal wedding found in two ritual texts in archives at Ebla (24th C. BC). A she-goat with a silver bracelet hung from her neck was driven forth into the wasteland of 'Alini' by the community. There is no mention of an "Azazel".

According to The Expositor's Bible Commentary, Azazel is the Hebrew word for scapegoat. This is the only place that the Hebrew word is found in the whole Hebrew Old Testament. It says that the Book of Enoch, (extra-biblical Jewish theological literature, dated around 200 B.C.) is full of demonology and reference to fallen angels. The EBC (Vol 2) says that this text uses late Aramaic forms for these names which indicates that The Book of Enoch most likely relies upon the Hebrew Leviticus text rather than the Leviticus text being reliant upon the Book of Enoch.

Christian commentators
Origen ("Contra Celsum," vi. 43) identifies Azazel with Satan.

In Mandaeism
Azazel is occasionally mentioned as Azaziʿil in Mandaean texts. In the Right Ginza, Azaziʿil is the name of an uthra (celestial being or angel).

In Islam
In Islam, Azazel appears in relation to the story of Harut and Marut, a pair of angels mentioned in the Quran. Although not explained by the Quran itself, Muslim exegetes such as Hisham ibn al-Kalbi and Abu Ishaq al-Tha'labi usually linked the reason of their abode to a narration related to the Watchers known from 3 Enoch. Just as in 3 Enoch, angels complained about humans iniquity, whereupon God offered a test, that the angels might choose three among them to descend to earth, endowed with bodily desires, and prove that they would do better than humans under the same conditions. Accordingly, they choose Aza, Azzaya and Azazel. However, Azazel repented his decision and God allowed him to turn back to heaven. The other two angels failed the test and their names were changed to Harut and Marut. They ended up on earth, introducing men to illicit magic.

Enochic literature
In the Dead Sea Scrolls, the name Azazel occurs in the line 6 of 4Q203, The Book of Giants, which is a part of the Enochic literature found at Qumran. Despite the expectation of Brandt (1889) to date no evidence has surfaced of Azazel as a demon or god prior to the earliest Jewish sources among the Dead Sea Scrolls.

The Book of Enoch brings Azazel into connection with the Biblical story of the fall of the angels, located on Mount Hermon, a gathering-place of the demons of old. Here, Azazel is one of the leaders of the rebellious Watchers in the time preceding the Flood; he taught men the art of warfare, of making swords, knives, shields, and coats of mail, and taught women the art of deception by ornamenting the body, dyeing the hair, and painting the face and the eyebrows, and also revealed to the people the secrets of witchcraft and corrupted their manners, leading them into wickedness and impurity until at last he was, at Yahweh's command, bound hand and foot by the archangel Raphael and chained to the rough and jagged rocks of [Ha] Dudael (= Beth Ḥadudo), where he is to abide in utter darkness until the great Day of Judgment, when he will be cast into the fire to be consumed forever.

According to the Book of Enoch, Azazel (here spelled ‘ăzā’zyēl) was one of the chief Grigori, a group of fallen angels who married women. Many believe that this same story (without any mention of Azazel) is told in the Book of Genesis 6:2–4:

These "sons of God" have often been thought of as fallen angels, and are sometimes equated with the Nephilim. (On the other hand, it has also been argued that the phrase refers only to pious men, or else that it should be translated "sons of the rulers".)

In the Book of Enoch, Azazel is responsible for teaching people to make weapons and cosmetics, for which he was cast out of heaven. The Book of Enoch 8:1–3a reads, "And Azazel taught men to make swords and knives and shields and breastplates; and made known to them the metals [of the earth] and the art of working them; and bracelets and ornaments; and the use of antimony and the beautifying of the eyelids; and all kinds of costly stones and all colouring tinctures. And there arose much godlessness, and they committed fornication, and they were led astray and became corrupt in all their ways." The corruption brought on by Azazel and the Grigori degrades the human race, and the four archangels (Michael, Gabriel, Raphael, and Uriel) “saw much blood being shed upon the earth and all lawlessness being wrought upon the earth […] The souls of men [made] their suit, saying, "Bring our cause before the Most High; […] Thou seest what Azazel hath done, who hath taught all unrighteousness on earth and revealed the eternal secrets which were in heaven, which men were striving to learn." God sees the sin brought about by Azazel and has Raphael “bind Azazel hand and foot and cast him into the darkness: and make an opening in the desert – which is in Dudael – and cast him therein. And place upon him rough and jagged rocks, and cover him with darkness, and let him abide there forever, and cover his face that he may not see light.” Azazel's fate is foretold near the end of Enoch 2:8, where God says, “On the day of the great judgement he shall be cast into the fire.” He will be delivered to the angels of punishments (Satan).

Several scholars have previously discerned that some details of Azazel's punishment are reminiscent of the scapegoat rite. Thus, Lester Grabbe points to a number of parallels between the Azazel narrative in Enoch and the wording of Leviticus 16, including "the similarity of the names Asael and Azazel; the punishment in the desert; the placing of sin on Asael/Azazel; the resultant healing of the land." Daniel Stökl also observes that "the punishment of the demon resembles the treatment of the goat in aspects of geography, action, time and purpose." Thus, the place of Asael's punishment designated in Enoch as Dudael is reminiscent of the rabbinic terminology used for the designation of the ravine of the scapegoat in later rabbinic interpretations of the Yom Kippur ritual. Stökl remarks that "the name of place of judgment (Dudael) is conspicuously similar in both traditions and can likely be traced to a common origin."

Azazel in 1 Enoch has been compared to Greek Titan Prometheus. He might be a demonized counterpart of a heavenly creature, who provided knowledge for people to make weapons, thus causing bloodshed and injustice. The latter might be identified with Greek kings and generals, who suppressed the Jews with military forces, but learned how to make their weapons by this specific expelled creature.

In the fifth-century 3 Enoch, Azazel is one of the three angels (Azza [Shemhazai] and Uzza [Ouza] are the other two) who opposed Enoch's high rank when he became the angel Metatron. Whilst they were fallen at this time they were still in Heaven, but Metatron held a dislike for them, and had them cast out.

In the Apocalypse of Abraham
In the extra-canonical text the Apocalypse of Abraham (c.1st CE), Azazel appears as an unclean bird who came down upon the sacrifice which Abraham prepared. (This is in reference to Genesis 15:11: "Birds of prey came down on the carcasses, but Abram drove them away" [ NIV ]).

The text also associates Azazel with the serpent and hell. In Chapter 23, verse 7, it is described as having seven heads, 14 faces, "hands and feet like a man's [and] on his back six wings on the right and six on the left."

Abraham says that the wicked will "putrefy in the belly of the crafty worm Azazel, and be burned by the fire of Azazel's tongue" (Abr. 31:5), and earlier says to Azazel himself, "May you be the firebrand of the furnace of the earth! Go, Azazel, into the untrodden parts of the earth. For your heritage is over those who are with you" (Abr. 14:5–6).

Here there is the idea that God's heritage (the created world) is largely under the dominion of evil – i.e., it is "shared with Azazel" (Abr. 20:5), again identifying him with the devil, who was called "the prince of this world" by Jesus. ( niv )

title: Azazel


text:
Tomme de Savoie

Tomme de Savoie is an upland variety of Tomme cheese, specifically, one from Savoy in the French Alps. It is a mild, semi-firm cow's milk cheese with a beige interior and a thick brownish-grey rind. Tomme de Savoie dates back to ancient history.

Tomme de Savoie, like most Tommes, is usually made from the skimmed milk left over after the cream is used to make butter or richer cheeses. As a result, the cheese has a relatively low fat content (between 20 and 45%). The cheese is made year-round, and typically has a slightly different character depending on whether the cows are fed on winter hay or summer grass.

The cheese normally comes in discs approximately 18 cm across, 5 - 8 cm in thickness, and weighing between 1 and 2 kg. It is first pressed, and then matured for several months in a traditional cellar, producing the characteristically thick rind and flavor.

title: Tomme de Savoie


text:
Abelian extension

In abstract algebra, an abelian extension is a Galois extension whose Galois group is abelian. When the Galois group is also cyclic, the extension is also called a cyclic extension. Going in the other direction, a Galois extension is called solvable if its Galois group is solvable, i.e., if the group can be decomposed into a series of normal extensions of an abelian group. Every finite extension of a finite field is a cyclic extension.

Description
Class field theory provides detailed information about the abelian extensions of number fields, function fields of algebraic curves over finite fields, and local fields.

There are two slightly different definitions of the term cyclotomic extension. It can mean either an extension formed by adjoining roots of unity to a field, or a subextension of such an extension. The cyclotomic fields are examples. A cyclotomic extension, under either definition, is always abelian.

If a field K contains a primitive n-th root of unity and the n-th root of an element of K is adjoined, the resulting Kummer extension is an abelian extension (if K has characteristic p we should say that p doesn't divide n, since otherwise this can fail even to be a separable extension). In general, however, the Galois groups of n-th roots of elements operate both on the n-th roots and on the roots of unity, giving a non-abelian Galois group as semi-direct product. The Kummer theory gives a complete description of the abelian extension case, and the Kronecker–Weber theorem tells us that if K is the field of rational numbers, an extension is abelian if and only if it is a subfield of a field obtained by adjoining a root of unity.

There is an important analogy with the fundamental group in topology, which classifies all covering spaces of a space: abelian covers are classified by its abelianisation which relates directly to the first homology group.

title: Abelian extension