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Friday, February 14, 2020

Social Darwinism

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Social_Darwinism

Social Darwinism is any of various theories of society which emerged in the United Kingdom, North America, and Western Europe in the 1870s, claiming to apply biological concepts of natural selection and survival of the fittest to sociology and politics. Social Darwinists argue that the strong should see their wealth and power increase while the weak should see their wealth and power decrease. Different social-Darwinist groups have differing views about which groups of people are considered to be the strong and which groups of people are considered to be the weak, and they also hold different opinions about the precise mechanisms that should be used to reward strength and punish weakness. Many such views stress competition between individuals in laissez-faire capitalism, while others were used in support of authoritarianism, eugenics, racism, imperialism, fascism, Nazism, and struggle between national or racial groups.

As a scientific concept, Social Darwinism broadly declined in popularity following World War I and was largely discredited by the end of World War II, partially due to its association with Nazism and partially due to a growing scientific consensus that it was scientifically groundless. Later theories that were categorised as social Darwinism were generally described as such as a critique by their opponents; their proponents did not identify themselves by such a label. Creationists have often maintained that social Darwinism—leading to policies designed to reward the most competitive—is a logical consequence of "Darwinism" (the theory of natural selection in biology). Biologists and historians have stated that this is a fallacy of appeal to nature, since the theory of natural selection is merely intended as a description of a biological phenomenon and should not be taken to imply that this phenomenon is good or that it ought to be used as a moral guide in human society. While most scholars recognize some historical links between the popularisation of Darwin's theory and forms of social Darwinism, they also maintain that social Darwinism is not a necessary consequence of the principles of biological evolution.

Scholars debate the extent to which the various social Darwinist ideologies reflect Charles Darwin's own views on human social and economic issues. His writings have passages that can be interpreted as opposing aggressive individualism, while other passages appear to promote it. Darwin's early evolutionary views and his opposition to slavery ran counter to many of the claims that social Darwinists would eventually make about the mental capabilities of the poor and colonial indigenes. After the publication of On the Origin of Species in 1859, one strand of Darwins' followers, led by Sir John Lubbock, argued that natural selection ceased to have any noticeable effect on humans once organised societies had been formed. However, some scholars argue that Darwin's view gradually changed and came to incorporate views from other theorists such as Herbert Spencer. Spencer published his Lamarckian evolutionary ideas about society before Darwin first published his hypothesis in 1859, and both Spencer and Darwin promoted their own conceptions of moral values. Spencer supported laissez-faire capitalism on the basis of his Lamarckian belief that struggle for survival spurred self-improvement which could be inherited. An important proponent in Germany was Ernst Haeckel, who popularized Darwin's thought and his personal interpretation of it, and used it as well to contribute to a new creed, the monist movement.

Origin of the term

The term Darwinism was coined by Thomas Henry Huxley in his March 1861 review of On the Origin of Species, and by the 1870s it was used to describe a range of concepts of evolution or development, without any specific commitment to Charles Darwin's theory of natural selection.

The first use of the phrase "social Darwinism" was in Joseph Fisher's 1877 article on The History of Landholding in Ireland which was published in the Transactions of the Royal Historical Society. Fisher was commenting on how a system for borrowing livestock which had been called "tenure" had led to the false impression that the early Irish had already evolved or developed land tenure;
These arrangements did not in any way affect that which we understand by the word " tenure", that is, a man's farm, but they related solely to cattle, which we consider a chattel. It has appeared necessary to devote some space to this subject, inasmuch as that usually acute writer Sir Henry Maine has accepted the word " tenure " in its modern interpretation, and has built up a theory under which the Irish chief " developed " into a feudal baron. I can find nothing in the Brehon laws to warrant this theory of social Darwinism, and believe further study will show that the Cáin Saerrath and the Cáin Aigillne relate solely to what we now call chattels, and did not in any way affect what we now call the freehold, the possession of the land.
— Joseph Fisher[20]
Despite the fact that Social Darwinism bears Charles Darwin's name, it is also linked today with others, notably Herbert Spencer, Thomas Malthus, and Francis Galton, the founder of eugenics. In fact, Spencer was not described as a social Darwinist until the 1930s, long after his death. The social Darwinism term first appeared in Europe in 1880, and journalist Emilie Gautier had coined the term with reference to a health conference in Berlin 1877. Around 1900 it was used by sociologists, some being opposed to the concept. The term was popularized in the United States in 1944 by the American historian Richard Hofstadter who used it in the ideological war effort against fascism to denote a reactionary creed which promoted competitive strife, racism and chauvinism. Hofstadter later also recognized (what he saw as) the influence of Darwinist and other evolutionary ideas upon those with collectivist views, enough to devise a term for the phenomenon, "Darwinist collectivism". Before Hofstadter's work the use of the term "social Darwinism" in English academic journals was quite rare. In fact,
... there is considerable evidence that the entire concept of "social Darwinism" as we know it today was virtually invented by Richard Hofstadter. Eric Foner, in an introduction to a then-new edition of Hofstadter's book published in the early 1990s, declines to go quite that far. "Hofstadter did not invent the term Social Darwinism", Foner writes, "which originated in Europe in the 1860s and crossed the Atlantic in the early twentieth century. But before he wrote, it was used only on rare occasions; he made it a standard shorthand for a complex of late-nineteenth-century ideas, a familiar part of the lexicon of social thought."
— Jeff Riggenbach

Usage

Social Darwinism has many definitions, and some of them are incompatible with each other. As such, social Darwinism has been criticized for being an inconsistent philosophy, which does not lead to any clear political conclusions. For example, The Concise Oxford Dictionary of Politics states:
Part of the difficulty in establishing sensible and consistent usage is that commitment to the biology of natural selection and to 'survival of the fittest' entailed nothing uniform either for sociological method or for political doctrine. A 'social Darwinist' could just as well be a defender of laissez-faire as a defender of state socialism, just as much an imperialist as a domestic eugenist.
The term "Social Darwinism" has rarely been used by advocates of the supposed ideologies or ideas; instead it has almost always been used pejoratively by its opponents. The term draws upon the common meaning of Darwinism, which includes a range of evolutionary views, but in the late 19th century was applied more specifically to natural selection as first advanced by Charles Darwin to explain speciation in populations of organisms. The process includes competition between individuals for limited resources, popularly but inaccurately described by the phrase "survival of the fittest", a term coined by sociologist Herbert Spencer

Creationists have often maintained that Social Darwinism—leading to policies designed to reward the most competitive—is a logical consequence of "Darwinism" (the theory of natural selection in biology). Biologists and historians have stated that this is a fallacy of appeal to nature and should not be taken to imply that this phenomenon ought to be used as a moral guide in human society.[10] While there are historical links between the popularization of Darwin's theory and forms of social Darwinism, social Darwinism is not a necessary consequence of the principles of biological evolution.

While the term has been applied to the claim that Darwin's theory of evolution by natural selection can be used to understand the social endurance of a nation or country, Social Darwinism commonly refers to ideas that predate Darwin's publication of On the Origin of Species. Others whose ideas are given the label include the 18th century clergyman Thomas Malthus, and Darwin's cousin Francis Galton who founded eugenics towards the end of the 19th century.

The expansion of the British Empire fitted in with the broader notion of social Darwinism used from the 1870s onwards to account for the remarkable and universal phenomenon of "the Anglo-Saxon overflowing his boundaries", as phrased by the late-Victorian sociologist Benjamin Kidd in Social Evolution, published in 1894. The concept also proved useful to justify what was seen by some as the inevitable extermination of "the weaker races who disappear before the stronger" not so much "through the effects of … our vices upon them" as "what may be called the virtues of our civilisation." Winston Churchill, a political proponent of eugenics, maintained that if fewer ‘feebleminded’ individuals were born, less crime would take place.

Proponents


Herbert Spencer's ideas, like those of evolutionary progressivism, stemmed from his reading of Thomas Malthus, and his later theories were influenced by those of Darwin. However, Spencer's major work, Progress: Its Law and Cause (1857), was released two years before the publication of Darwin's On the Origin of Species, and First Principles was printed in 1860.

In The Social Organism (1860), Spencer compares society to a living organism and argues that, just as biological organisms evolve through natural selection, society evolves and increases in complexity through analogous processes.

In many ways, Spencer's theory of cosmic evolution has much more in common with the works of Lamarck and Auguste Comte's positivism than with Darwin's.

Jeff Riggenbach argues that Spencer's view was that culture and education made a sort of Lamarckism possible and notes that Herbert Spencer was a proponent of private charity. However, the legacy of his social Darwinism was less than charitable.


Spencer's work also served to renew interest in the work of Malthus. While Malthus's work does not itself qualify as social Darwinism, his 1798 work An Essay on the Principle of Population, was incredibly popular and widely read by social Darwinists. In that book, for example, the author argued that as an increasing population would normally outgrow its food supply, this would result in the starvation of the weakest and a Malthusian catastrophe.

According to Michael Ruse, Darwin read Malthus' famous Essay on a Principle of Population in 1838, four years after Malthus' death. Malthus himself anticipated the social Darwinists in suggesting that charity could exacerbate social problems.

Another of these social interpretations of Darwin's biological views, later known as eugenics, was put forth by Darwin's cousin, Francis Galton, in 1865 and 1869. Galton argued that just as physical traits were clearly inherited among generations of people, the same could be said for mental qualities (genius and talent). Galton argued that social morals needed to change so that heredity was a conscious decision in order to avoid both the over-breeding by less fit members of society and the under-breeding of the more fit ones. 


In Galton's view, social institutions such as welfare and insane asylums were allowing inferior humans to survive and reproduce at levels faster than the more "superior" humans in respectable society, and if corrections were not soon taken, society would be awash with "inferiors". Darwin read his cousin's work with interest, and devoted sections of Descent of Man to discussion of Galton's theories. Neither Galton nor Darwin, though, advocated any eugenic policies restricting reproduction, due to their Whiggish distrust of government.

Friedrich Nietzsche's philosophy addressed the question of artificial selection, yet Nietzsche's principles did not concur with Darwinian theories of natural selection. Nietzsche's point of view on sickness and health, in particular, opposed him to the concept of biological adaptation as forged by Spencer's "fitness". Nietzsche criticized Haeckel, Spencer, and Darwin, sometimes under the same banner by maintaining that in specific cases, sickness was necessary and even helpful. Thus, he wrote:
Wherever progress is to ensue, deviating natures are of greatest importance. Every progress of the whole must be preceded by a partial weakening. The strongest natures retain the type, the weaker ones help to advance it. Something similar also happens in the individual. There is rarely a degeneration, a truncation, or even a vice or any physical or moral loss without an advantage somewhere else. In a warlike and restless clan, for example, the sicklier man may have occasion to be alone, and may therefore become quieter and wiser; the one-eyed man will have one eye the stronger; the blind man will see deeper inwardly, and certainly hear better. To this extent, the famous theory of the survival of the fittest does not seem to me to be the only viewpoint from which to explain the progress of strengthening of a man or of a race.
Ernst Haeckel's recapitulation theory was not Darwinism, but rather attempted to combine the ideas of Goethe, Lamarck and Darwin. It was adopted by emerging social sciences to support the concept that non-European societies were "primitive", in an early stage of development towards the European ideal, but since then it has been heavily refuted on many fronts. Haeckel's works led to the formation of the Monist League in 1904 with many prominent citizens among its members, including the Nobel Prize winner Wilhelm Ostwald

The simpler aspects of social Darwinism followed the earlier Malthusian ideas that humans, especially males, require competition in their lives in order to survive in the future. Further, the poor should have to provide for themselves and not be given any aid. However, amidst this climate, most social Darwinists of the early twentieth century actually supported better working conditions and salaries. Such measures would grant the poor a better chance to provide for themselves yet still distinguish those who are capable of succeeding from those who are poor out of laziness, weakness, or inferiority.

Hypotheses relating social change and evolution

"Social Darwinism" was first described by Eduard Oscar Schmidt of the University of Strasbourg, reporting at a scientific and medical conference held in Munich in 1877. He noted how socialists, although opponents of Darwin's theory, used it to add force to their political arguments. Schmidt's essay first appeared in English in Popular Science in March 1879. There followed an anarchist tract published in Paris in 1880 entitled "Le darwinisme social" by Émile Gautier. However, the use of the term was very rare—at least in the English-speaking world (Hodgson, 2004)—until the American historian Richard Hofstadter published his influential Social Darwinism in American Thought (1944) during World War II

Hypotheses of social evolution and cultural evolution were common in Europe. The Enlightenment thinkers who preceded Darwin, such as Hegel, often argued that societies progressed through stages of increasing development. Earlier thinkers also emphasized conflict as an inherent feature of social life. Thomas Hobbes's 17th century portrayal of the state of nature seems analogous to the competition for natural resources described by Darwin. Social Darwinism is distinct from other theories of social change because of the way it draws Darwin's distinctive ideas from the field of biology into social studies. 

Darwin, unlike Hobbes, believed that this struggle for natural resources allowed individuals with certain physical and mental traits to succeed more frequently than others, and that these traits accumulated in the population over time, which under certain conditions could lead to the descendants being so different that they would be defined as a new species.

However, Darwin felt that "social instincts" such as "sympathy" and "moral sentiments" also evolved through natural selection, and that these resulted in the strengthening of societies in which they occurred, so much so that he wrote about it in Descent of Man:
The following proposition seems to me in a high degree probable—namely, that any animal whatever, endowed with well-marked social instincts, the parental and filial affections being here included, would inevitably acquire a moral sense or conscience, as soon as its intellectual powers had become as well, or nearly as well developed, as in man. For, firstly, the social instincts lead an animal to take pleasure in the society of its fellows, to feel a certain amount of sympathy with them, and to perform various services for them.

Nazi Germany


Nazi Germany's justification for its aggression was regularly promoted in Nazi propaganda films depicting scenes such as beetles fighting in a lab setting to demonstrate the principles of "survival of the fittest" as depicted in Alles Leben ist Kampf (English translation: All Life is Struggle). Hitler often refused to intervene in the promotion of officers and staff members, preferring instead to have them fight amongst themselves to force the "stronger" person to prevail—"strength" referring to those social forces void of virtue or principle. Key proponents were Alfred Rosenberg, who was hanged later at Nuremberg. Such ideas also helped to advance euthanasia in Germany, especially Action T4, which led to the murder of mentally ill and disabled people in Germany.

The argument that Nazi ideology was strongly influenced by social Darwinist ideas is often found in historical and social science literature. For example, the philosopher and historian Hannah Arendt analysed the historical development from a politically indifferent scientific Darwinism via social Darwinist ethics to racist ideology.

By 1985, creationists were taking up the argument that Nazi ideology was directly influenced by Darwinian evolutionary theory. Such claims have been presented by creationists such as Jonathan Sarfati. Intelligent design creationism supporters have promoted this position as well. For example, it is a theme in the work of Richard Weikart, who is a historian at California State University, Stanislaus, and a senior fellow for the Center for Science and Culture of the Discovery Institute. It is also a main argument in the 2008 intelligent-design/creationist movie Expelled: No Intelligence Allowed. These claims are widely criticized. The Anti-Defamation League has rejected such attempts to link Darwin's ideas with Nazi atrocities, and has stated that "Using the Holocaust in order to tarnish those who promote the theory of evolution is outrageous and trivializes the complex factors that led to the mass extermination of European Jewry." Robert J. Richards describes the link as a myth that ignores far more obvious causes of Nazism - including the "pervasive anti-Semitic miasma created by Christian apologists" - and dismisses efforts to tie Darwin to Nazism as "crude lever" used by religious fundamentalists to try and reduce public support for Darwin's theories.

Similar criticisms are sometimes applied (or misapplied) to other political or scientific theories that resemble social Darwinism, for example criticisms leveled at evolutionary psychology. For example, a critical reviewer of Weikart's book writes that "(h)is historicization of the moral framework of evolutionary theory poses key issues for those in sociobiology and evolutionary psychology, not to mention bioethicists, who have recycled many of the suppositions that Weikart has traced."

Another example is recent scholarship that portrays Ernst Haeckel's Monist League as a mystical progenitor of the Völkisch movement and, ultimately, of the Nazi Party of Adolf Hitler. Scholars opposed to this interpretation, however, have pointed out that the Monists were freethinkers who opposed all forms of mysticism, and that their organizations were immediately banned following the Nazi takeover in 1933 because of their association with a wide variety of causes including feminism, pacifism, human rights, and early gay rights movements.

Other regional distributions


United States

Spencer proved to be a popular figure in the 1880s primarily because his application of evolution to areas of human endeavor promoted an optimistic view of the future as inevitably becoming better. In the United States, writers and thinkers of the gilded age such as Edward L. Youmans, William Graham Sumner, John Fiske, John W. Burgess, and others developed theories of social evolution as a result of their exposure to the works of Darwin and Spencer. 

In 1883, Sumner published a highly influential pamphlet entitled "What Social Classes Owe to Each Other", in which he insisted that the social classes owe each other nothing, synthesizing Darwin's findings with free enterprise Capitalism for his justification. According to Sumner, those who feel an obligation to provide assistance to those unequipped or under-equipped to compete for resources, will lead to a country in which the weak and inferior are encouraged to breed more like them, eventually dragging the country down. Sumner also believed that the best equipped to win the struggle for existence was the American businessman, and concluded that taxes and regulations serve as dangers to his survival. This pamphlet makes no mention of Darwinism, and only refers to Darwin in a statement on the meaning of liberty, that "There never has been any man, from the primitive barbarian up to a Humboldt or a Darwin, who could do as he had a mind to."

Sumner never fully embraced Darwinian ideas, and some contemporary historians do not believe that Sumner ever actually believed in social Darwinism. The great majority of American businessmen rejected the anti-philanthropic implications of the theory. Instead they gave millions to build schools, colleges, hospitals, art institutes, parks and many other institutions. Andrew Carnegie, who admired Spencer, was the leading philanthropist in the world (1890–1920), and a major leader against imperialism and warfare.

H. G. Wells was heavily influenced by Darwinist thoughts, and novelist Jack London wrote stories of survival that incorporated his views on social Darwinism. Film director Stanley Kubrick has been described as having held social Darwinist opinions.

Japan

Social Darwinism has influenced political, public health and social movements in Japan since the late 19th and early 20th century. Social Darwinism was originally brought to Japan through the works of Francis Galton and Ernst Haeckel as well as United States, British and French Lamarckian eugenic written studies of the late 19th and early 20th centuries. Eugenism as a science was hotly debated at the beginning of the 20th century, in Jinsei-Der Mensch, the first eugenics journal in the empire. As Japan sought to close ranks with the west, this practice was adopted wholesale along with colonialism and its justifications. 

China

Social Darwinism was formally introduced to China through the translation by Yan Fu of Huxley's Evolution and Ethics, in the course of an extensive series of translations of influential Western thought. Yan's translation strongly impacted Chinese scholars because he added national elements not found in the original. Yan Fu criticized Huxley from the perspective of Spencerian social Darwinism in his own annotations to the translation. He understood Spencer's sociology as "not merely analytical and descriptive, but prescriptive as well", and saw Spencer building on Darwin, whom Yan summarized thus:
Peoples and living things struggle for survival. At first, species struggle with species; they as [people] gradually progress, there is a struggle between one social group and another. The weak invariably become the prey of the strong, the stupid invariably become subservient to the clever."
By the 1920s, social Darwinism found expression in the promotion of eugenics by the Chinese sociologist Pan Guangdan. When Chiang Kai-shek started the New Life movement in 1934, he
. . . harked back to theories of Social Darwinism, writing that "only those who readapt themselves to new conditions, day by day, can live properly. When the life of a people is going through this process of readaptation, it has to remedy its own defects, and get rid of those elements which become useless. Then we call it new life."

Germany

Social evolution theories in Germany gained large popularity in the 1860s and had a strong antiestablishment connotation first. Social Darwinism allowed people to counter the connection of Thron und Altar, the intertwined establishment of clergy and nobility, and provided as well the idea of progressive change and evolution of society as a whole. Ernst Haeckel propagated both Darwinism as a part of natural history and as a suitable base for a modern Weltanschauung, a world view based on scientific reasoning in his Monist League. Friedrich von Hellwald had a strong role in popularizing it in Austria. Darwin's work served as a catalyst to popularize evolutionary thinking.

A sort of aristocratic turn, the use of the struggle for life as a base of Social Darwinism sensu stricto came up after 1900 with Alexander Tilles 1895 work Entwicklungsethik (Ethics of Evolution) which asked to move from Darwin till Nietzsche. Further interpretations moved to ideologies propagating a racist and hierarchical society and provided ground for the later radical versions of Social Darwinism.

Social Darwinism came to play a major role in the ideology of Nazism, where it was combined with a similarly pseudo-scientific theory of racial hierarchy in order to identify the Germans as a part of what the Nazis regarded as an Aryan or Nordic master race. Nazi social Darwinist beliefs led them to retain business competition and private property as economic engines. Nazism likewise opposed social welfare based on a social Darwinist belief that the weak and feeble should perish. This association with Nazism, coupled with increasing recognition that it was scientifically unfounded, contributed to the broader rejection Social Darwinism after the end of World War II.

Criticism and controversy


Multiple incompatible definitions

Social Darwinism has many definitions, and some of them are incompatible with each other. As such, social Darwinism has been criticized for being an inconsistent philosophy, which does not lead to any clear political conclusions. For example, The Concise Oxford Dictionary of Politics states:
Part of the difficulty in establishing sensible and consistent usage is that commitment to the biology of natural selection and to 'survival of the fittest' entailed nothing uniform either for sociological method or for political doctrine. A 'social Darwinist' could just as well be a defender of laissez-faire as a defender of state socialism, just as much an imperialist as a domestic eugenist.

Nazism, eugenics, fascism, imperialism

Social Darwinism was predominantly found in laissez-faire societies where the prevailing view was that of an individualist order to society. As such, social Darwinism supposed that human progress would generally favor the most individualistic races, which were those perceived as stronger. A different form of social Darwinism was part of the ideological foundations of Nazism and other fascist movements. This form did not envision survival of the fittest within an individualist order of society, but rather advocated a type of racial and national struggle where the state directed human breeding through eugenics. Names such as "Darwinian collectivism" or "Reform Darwinism" have been suggested to describe these views, in order to differentiate them from the individualist type of social Darwinism.

As mentioned above, social Darwinism has often been linked to nationalism and imperialism. During the age of New Imperialism, the concepts of evolution justified the exploitation of "lesser breeds without the law" by "superior races". To elitists, strong nations were composed of white people who were successful at expanding their empires, and as such, these strong nations would survive in the struggle for dominance. With this attitude, Europeans, except for Christian missionaries, seldom adopted the customs and languages of local people under their empires.

Peter Kropotkin and mutual aid

Peter Kropotkin argued in his 1902 book Mutual Aid: A Factor of Evolution that Darwin did not define the fittest as the strongest, or most clever, but recognized that the fittest could be those who cooperated with each other. In many animal societies, "struggle is replaced by co-operation".
It may be that at the outset Darwin himself was not fully aware of the generality of the factor which he first invoked for explaining one series only of facts relative to the accumulation of individual variations in incipient species. But he foresaw that the term [evolution] which he was introducing into science would lose its philosophical and its only true meaning if it were to be used in its narrow sense only—that of a struggle between separate individuals for the sheer means of existence. And at the very beginning of his memorable work he insisted upon the term being taken in its "large and metaphorical sense including dependence of one being on another, and including (which is more important) not only the life of the individual, but success in leaving progeny." [Quoting Origin of Species, chap. iii, p. 62 of first edition.]
While he himself was chiefly using the term in its narrow sense for his own special purpose, he warned his followers against committing the error (which he seems once to have committed himself) of overrating its narrow meaning. In The Descent of Man he gave some powerful pages to illustrate its proper, wide sense. He pointed out how, in numberless animal societies, the struggle between separate individuals for the means of existence disappears, how struggle is replaced by co-operation, and how that substitution results in the development of intellectual and moral faculties which secure to the species the best conditions for survival. He intimated that in such cases the fittest are not the physically strongest, nor the cunningest, but those who learn to combine so as mutually to support each other, strong and weak alike, for the welfare of the community. "Those communities", he wrote, "which included the greatest number of the most sympathetic members would flourish best, and rear the greatest number of offspring" (2nd edit., p. 163). The term, which originated from the narrow Malthusian conception of competition between each and all, thus lost its narrowness in the mind of one who knew Nature.
Noam Chomsky discussed briefly Kropotkin's views in an 8 July 2011 YouTube video from Renegade Economist, in which he said Kropotkin argued
... the exact opposite [of Social Darwinism]. He argued that on Darwinian grounds, you would expect cooperation and mutual aid to develop leading towards community, workers' control and so on. Well, you know, he didn't prove his point. It's at least as well argued as Herbert Spencer is ...

Representation of a Lie group

From Wikipedia, the free encyclopedia https://en.wikipedia.org/wiki/Representation_of_a_Lie_group...