The Golden Rule | Our Daily Bread – odb.org

The concept of The Golden Ruletreat others as you would like to be treatedappears in many religions. So what makes Jesus version of the saying so exceptional?

Its uniqueness lies in a single word, therefore, that signals the generosity of our heavenly Father. Here is what Jesus said: If you then, being evil, know how to give good gifts to your children, how much more will your Father who is in heaven give good things to those who ask Him! Therefore, whatever you want men to do to you, do also to them (Matt. 7:11-12 italics added).

All of us fall short of what we know to be true: We do not love others the way God loves us. Jesus lived out that admirable ethic with perfect love by living and dying for all our sins.

We have a loving, giving Father who set aside His own self-interest to reveal the full measure of His love through His Son Jesus. Gods generosity is the dynamic by which we treat others as we would like to be treated. We love and give to others because He first loved us (1 John 4:19).

Our heavenly Father asks us to live up to His commands, but He also gives us His power and love to carry it out. We need only to ask Him for it.

Heavenly Father, I know that I lack Your patience and mercy and love. Please show Your perfect love through me in some small way today. In Your Son Jesus name I pray.

We have committed The Golden Rule to memory; now let us commit it to life. E. Markham

In the reading today, we see how our Lord emphasized the importance of persistence in prayer. The actual Greek grammar might be better translated as Seek and keep on seeking. Knock and keep on knocking. Ask and keep on asking. Sometimes sincere believers may believe that a sign of faith is to ask God once for a request and never repeat it. But the teachings of the New Testament do not support such a concept. In the parable of the judge and the widow who repeatedly asked him to hear her case, the idea of persistence is central (Luke 18:1-8). As is the case with Job, King David, and other biblical characters, faith is often expressed through repeated prayers and pleading.

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The Golden Rule | Our Daily Bread - odb.org

Matriarchy – Wikipedia

Matriarchy is a social system in which females hold primary power, predominate in roles of political leadership, moral authority, social privilege and control of property at the specific exclusion of men, at least to a large degree. While those definitions apply in general English, definitions specific to the disciplines of anthropology and feminism differ in some respects.

Most anthropologists hold that there are no known societies that are unambiguously matriarchal, but some authors believe exceptions may exist or may have. Matriarchies may also be confused with matrilineal, matrilocal, and matrifocal societies. A few people consider any non-patriarchal system to be matriarchal, thus including genderally equalitarian systems (Peggy Reeves Sanday favors redefining and reintroducing the word matriarchy, especially in reference to contemporary matrilineal societies such as the Minangkabau[1]), but most academics exclude them from matriarchies strictly defined.

In 19th century Western scholarship, the hypothesis of matriarchy representing an early, mainly prehistoric, stage of human development gained popularity. Possibilities of so-called primitive societies were cited and the hypothesis survived into the 20th century, including in the context of second-wave feminism. This hypothesis was criticized by some authors such as Cynthia Eller in The Myth of Matriarchal Prehistory and remains as a largely unsolved question to this day. Some older myths describe matriarchies. Several modern feminists have advocated for matriarchy now or in the future and it has appeared in feminist literature. In several theologies, matriarchy has been portrayed as negative.

According to the Oxford English Dictionary (OED), matriarchy is a "form of social organization in which the mother or oldest female is the head of the family, and descent and relationship are reckoned through the female line; government or rule by a woman or women."[2] A popular definition, according to James Peoples and Garrick Bailey, is "female dominance".[3] Within the academic discipline of cultural anthropology, according to the OED, matriarchy is a "culture or community in which such a system prevails"[2] or a "family, society, organization, etc., dominated by a woman or women."[2] In general anthropology, according to William A. Haviland, matriarchy is "rule by women".[4] A matriarchy is a society in which females, especially mothers, have the central roles of political leadership, moral authority, and control of property, but does not include a society that occasionally is led by a female for nonmatriarchal reasons or an occupation in which females generally predominate without reference to matriarchy, such as prostitution or women's auxiliaries of organizations run by men.[citation needed] According to Lawrence A. Kuzner in 1997, A. R. Radcliffe-Brown argued in 1924 that the definitions of matriarchy and patriarchy had "logical and empirical failings.... [and] were too vague to be scientifically useful".[5]

Most academics exclude egalitarian nonpatriarchal systems from matriarchies more strictly defined. According to Heide Gttner-Abendroth, a reluctance to accept the existence of matriarchies might be based on a specific culturally biased notion of how to define matriarchy: because in a patriarchy men rule over women, a matriarchy has frequently been conceptualized as women ruling over men,[6] while she believed that matriarchies are egalitarian.[6][7]

The word matriarchy, for a society politically led by females, especially mothers, who also control property, is often interpreted to mean the genderal opposite of patriarchy, but it is not an opposite (linguistically, it is not a parallel term).[8][9][10] According to Peoples and Bailey, the view of anthropologist Peggy Reeves Sanday is that matriarchies are not a mirror form of patriarchies but rather that a matriarchy "emphasizes maternal meanings where 'maternal symbols are linked to social practices influencing the lives of both sexes and where women play a central role in these practices'".[11] Journalist Margot Adler wrote, "literally,... ["matriarchy"] means government by mothers, or more broadly, government and power in the hands of women."[12]Barbara Love and Elizabeth Shanklin wrote, "by 'matriarchy,' we mean a non-alienated society: a society in which women, those who produce the next generation, define motherhood, determine the conditions of motherhood, and determine the environment in which the next generation is reared."[13] According to Cynthia Eller, "'matriarchy' can be thought of... as a shorthand description for any society in which women's power is equal or superior to men's and in which the culture centers around values and life events described as 'feminine.'"[14] Eller wrote that the idea of matriarchy mainly rests on two pillars, romanticism and modern social criticism.[15] The notion of matriarchy was meant to describe something like a utopia placed in the past in order to legitimate contemporary social criticism.[citation needed] With respect to a prehistoric matriarchal Golden Age, according to Barbara Epstein, "matriarchy... means a social system organized around matriliny and goddess worship in which women have positions of power."[16] According to Adler, in the Marxist tradition, it usually refers to a pre-class society "where women and men share equally in production and power."[17]

According to Adler, "a number of feminists note that few definitions of the word [matriarchy], despite its literal meaning, include any concept of power, and they suggest that centuries of oppression have made it impossible for women to conceive of themselves with such power."[17]

Matriarchy has often been presented as negative, in contrast to patriarchy as natural and inevitable for society, thus that matriarchy is hopeless. Love and Shanklin wrote:

When we hear the word "matriarchy", we are conditioned to a number of responses: that matriarchy refers to the past and that matriarchies have never existed; that matriarchy is a hopeless fantasy of female domination, of mothers dominating children, of women being cruel to men. Conditioning us negatively to matriarchy is, of course, in the interests of patriarchs. We are made to feel that patriarchy is natural; we are less likely to question it, and less likely to direct our energies to ending it.[18]

The Matriarchal Studies school led by Gttner-Abendroth calls for an even more inclusive redefinition of the term: Gttner-Abendroth defines Modern Matriarchal Studies as the "investigation and presentation of non-patriarchal societies", effectively defining matriarchy as non-patriarchy.[19] She has also defined matriarchy as characterized by the sharing of power equally between the two genders.[20] According to Diane LeBow, "matriarchal societies are often described as... egalitarian...",[21] although anthropologist Ruby Rohrlich has written of "the centrality of women in an egalitarian society."[22][a]

Matriarchy is also the public formation in which the woman occupies the ruling position in a family.[2] For this usage, some scholars now prefer the term matrifocal to matriarchal.[citation needed] Some, including Daniel Moynihan, claimed that there is a matriarchy among Black families in the United States,[23][b] because a quarter of them were headed by single women;[24] thus, families composing a substantial minority of a substantial minority could be enough for the latter to constitute a matriarchy within a larger non-matriarchal society.

Etymologically, it is from Latin mter (genitive mtris), "mother" and Greek arkhein, "to rule".[25] The notion of matriarchy was defined by Joseph-Franois Lafitau (16811746), who first named it gincocratie.[26] According to the OED, the earliest known attestation of the word matriarchy is in 1885.[2] By contrast, gyncocracy, meaning 'rule of women', has been in use since the 17th century, building on the Greek word found in Aristotle and Plutarch.[27][28]

Terms with similar etymology are also used in various social sciences and humanities to describe matriarchal or matriological aspects of social, cultural and political processes. Adjective matriological is derived from the noun matriology that comes from Latin word mter (mother) and Greek word (logos, teaching about). The term matriology was used in theology and history of religion as a designation for the study of particular motherly aspects of various female deities. The term was subsequently borrowed by other social sciences and humanities and its meaning was widened in order to describe and define particular female-dominated and female-centered aspects of cultural and social life. The male alternative for matriology is patriology.[citation needed]

In their works, Johann Jakob Bachofen and Lewis Morgan used such terms and expressions as mother-right, female rule, gyneocracy, and female authority. All these terms meant the same: the rule by females (mother or wife).[citation needed] Although Bachofen and Lewis Morgan confined the "mother right" inside households, it was the basis of female influence upon the whole society.[citation needed] The authors of the classics did not think that gyneocracy meant 'female government' in politics.[citation needed] They were aware of the fact that the sexual structure of government had no relation to domestic rule and to roles of both sexes.[citation needed]

A matriarchy is also sometimes called a gynarchy, a gynocracy, a gynecocracy, or a gynocentric society, although these terms do not definitionally emphasize motherhood. Cultural anthropologist Jules de Leeuwe argued that some societies were "mainly gynecocratic"[29] (others being "mainly androcratic").[29][c]

Gynecocracy, gynaecocracy, gynocracy, gyneocracy, and gynarchy generally mean 'government by women over women and men'.[30][31][32][33] All of these words are synonyms in their most important definitions. While these words all share that principal meaning, they differ a little in their additional meanings, so that gynecocracy also means 'women's social supremacy',[34]gynaecocracy also means 'government by one woman', 'female dominance', and, derogatorily, 'petticoat government',[35] and gynocracy also means 'women as the ruling class'.[36]Gyneocracy is rarely used in modern times.[37] None of these definitions are limited to mothers.

Some question whether a queen ruling without a king is sufficient to constitute female government, given the amount of participation of other men in most such governments. One view is that it is sufficient. "By the end of [Queen] Elizabeth's reign, gynecocracy was a fait accompli", according to historian Paula Louise Scalingi.[38][d] Gynecocracy is defined by Scalingi as "government by women",[39] similar to dictionary definitions[31][32][33] (one dictionary adding 'women's social supremacy' to the governing role).[34] Scalingi reported arguments for and against the validity of gynocracy[40] and said, "the humanists treated the question of female rule as part of the larger controversy over sexual equality."[41] Possibly, queenship, because of the power wielded by men in leadership and assisting a queen, leads to queen bee syndrome, contributing to the difficulty of other women in becoming heads of the government.[citation needed]

Some matriarchies have been described by historian Helen Diner as "a strong gynocracy"[42] and "women monopolizing government"[43] and she described matriarchal Amazons as "an extreme, feminist wing"[44][e] of humanity and that North African women "ruled the country politically,"[42] and, according to Adler, Diner "envision[ed] a dominance matriarchy".[45]

Gynocentrism is the 'dominant or exclusive focus on women', is opposed to androcentrism, and "invert[s]... the privilege of the... [male/female] binary...[,] [some feminists] arguing for 'the superiority of values embodied in traditionally female experience'".[46]

Some people who sought evidence for the existence of a matriarchy often mixed matriarchy with anthropological terms and concepts describing specific arrangements in the field of family relationships and the organization of family life, such as matrilineality and matrilocality. These terms refer to intergenerational relationships (as matriarchy may), but do not distinguish between males and females insofar as they apply to specific arrangements for sons as well as daughters from the perspective of their relatives on their mother's side. Accordingly, these concepts do not represent matriarchy as 'power of women over men'.[47]

Anthropologists have begun to use the term matrifocality.[citation needed] There is some debate concerning the terminological delineation between matrifocality and matriarchy.[citation needed] Matrifocal societies are those in which women, especially mothers, occupy a central position.[citation needed] Anthropologist R. T. Smith refers to matrifocality as the kinship structure of a social system whereby the mothers assume structural prominence.[48] The term does not necessarily imply domination by women or mothers.[48] In addition, some authors depart from the premise of a mother-child dyad as the core of a human group where the grandmother was the central ancestor with her children and grandchildren clustered around her in an extended family.[49]

The term matricentric means 'having a mother as head of the family or household'.[citation needed]

Matristic: Feminist scholars and archeologists such as Marija Gimbutas, Gerda Lerner, and Riane Eisler[50] label their notion of a "woman-centered" society surrounding Mother Goddess worship during prehistory (in Paleolithic and Neolithic Europe) and in ancient civilizations by using the term matristic rather than matriarchal.[citation needed]

Matrilineality, in which descent is traced through the female line, is sometimes conflated with historical matriarchy.[51] Sanday favors redefining and reintroducing the word matriarchy, especially in reference to contemporary matrilineal societies such as the Minangkabau.[52] The 19th-century belief that matriarchal societies existed was due to the transmission of "economic and social power... through kinship lines"[53] so that "in a matrilineal society all power would be channeled through women. Women may not have retained all power and authority in such societies..., but they would have been in a position to control and dispense power."[53]

A matrilocal society is one in which a couple resides close to the bride's family rather than the bridegroom's family; the term is by anthropologists.[citation needed]

Most anthropologists hold that there are no known societies that are unambiguously matriarchal.[54][55][56] According to J. M. Adovasio, Olga Soffer, and Jake Page, no true matriarchy is known actually to have existed.[51] Anthropologist Joan Bamberger argued that the historical record contains no primary sources on any society in which women dominated.[57] Anthropologist Donald Brown's list of human cultural universals (viz., features shared by nearly all current human societies) includes men being the "dominant element" in public political affairs,[58] which he asserts is the contemporary opinion of mainstream anthropology.[citation needed] There are some disagreements and possible exceptions. A belief that women's rule preceded men's rule was, according to Haviland, "held by many nineteenth-century intellectuals".[4] The hypothesis survived into the 20th century and was notably advanced in the context of feminism and especially second-wave feminism, but the hypothesis is mostly discredited today, most experts saying that it was never true.[59]

Matriarchs, according to Peoples and Bailey, do exist; there are "individual matriarchs of families and kin groups."[3]

The royal lineage of Ethiopia, including for the Kandake, was passed through the woman only.[citation needed]

The Cambridge Ancient History (1975)[60] stated that "the predominance of a supreme goddess is probably a reflection from the practice of matriarchy which at all times characterized Elamite civilization to a greater or lesser degree".[f]

Tacitus noted in his Germania that in "the nations of the Sitones a woman is the ruling sex."[61][g]

Legends of Amazon women originated not from South America, but rather Scythia (present day Russia.) Historians note that the Sarmatians (present day Ukraine) are also descendants of the Amazonian women tribe.

Possible matriarchies in Burma are, according to Jorgen Bisch, the Padaungs[62] and, according to Andrew Marshall, the Kayaw.[63]

The Mosuo culture, which is in China near Tibet, is frequently described as matriarchal.[64] The Mosuo themselves often use this description and they believe it increases interest in their culture and thus attracts tourism. The term matrilineal is sometimes used, and, while more accurate, still doesn't reflect the full complexity of their social organization. In fact, it is not easy to categorize Mosuo culture within traditional Western definitions. They have aspects of a matriarchal culture: Women are often the head of the house, inheritance is through the female line, and women make business decisions. However, unlike in a true matriarchy, political power tends to be in the hands of males.[65]

In India, of communities recognized in the national Constitution as Scheduled Tribes, "some... [are] matriarchal and matrilineal"[66] "and thus have been known to be more egalitarian".[67] According to interviewer Anuj Kumar, Manipur, India, "has a matriarchal society",[68] but this may not be a scholarly assessment.

Manipur, in north-east India, is not at all a matriarchy. Though mothers there are in forefront of most of the social activism, the society has always been a patriarchal. Their women power is visible because of historical reason. Manipur was ruled by strong dynasties. The need for expansions of borders, crushing any outsider threats etc. engaged the men. And so women had to take charge of home-front.[citation needed]

In the Dakshina Kannada district of Karnataka, many societies are matrilineal.[citation needed]

In Kerala, the Nair communities are matrilineal. Descent and relationship are determined through the female line.[citation needed]

Anthropologist Peggy Reeves Sanday said the Minangkabau society may be a matriarchy.[69]

According to William S. Turley, "the role of women in traditional Vietnamese culture was determined [partly] by... indigenous customs bearing traces of matriarchy",[70] affecting "different social classes"[70] to "varying degrees".[70] According to Peter C. Phan, that "the first three persons leading insurrections against China were women... suggest[s]... that ancient Vietnam was a matriarchal society"[71] and "the ancient Vietnamese family system was most likely matriarchal, with women ruling over the clan or tribe"[72] until the Vietnamese "adopt[ed]... the patriarchal system introduced by the Chinese",[72] although "this patriarchal system... was not able to dislodge the Vietnamese women from their relatively high position in the family and society, especially among the peasants and the lower classes",[72] with modern "culture and legal codes... [promoting more] rights and privileges" for women than in Chinese culture.[73] According to Chiricosta, the legend of u C is said to be evidence of "the presence of an original 'matriarchy' in North Vietnam and [it] led to the double kinship system, which developed there.... [and which] combined matrilineal and patrilineal patterns of family structure and assigned equal importance to both lines."[74][h][i] Chiricosta said that other scholars relied on "this 'matriarchal' aspect of the myth to differentiate Vietnamese society from the pervasive spread of Chinese Confucian patriarchy"[75][j] and that "resistance to China's colonization of Vietnam... [combined with] the view that Vietnam was originally a matriarchy... [led to viewing] women's struggles for liberation from (Chinese) patriarchy as a metaphor for the entire nation's struggle for Vietnamese independence."[76] According to Keith Weller Taylor, "the matriarchal flavor of the time is... attested by the fact that Trung Trac's mother's tomb and spirit temple have survived, although nothing remains of her father",[77] and the "society of the Trung sisters" was "strongly matrilineal".[78] According to Donald M. Seekins, an indication of "the strength of matriarchal values"[79] was that a woman, Trng Trc, with her younger sister Trng Nh, raised an army of "over 80,000 soldiers.... [in which] many of her officers were women",[79] with which they defeated the Chinese.[79] According to Seekins, "in [the year] 40, Trung Trac was proclaimed queen, and a capital was built for her"[79] and modern Vietnam considers the Trung sisters to be heroines.[79] According to Karen G. Turner, in the 3rd century A.D., Lady Triu "seem[ed]... to personify the matriarchal culture that mitigated Confucianized patriarchal norms.... [although] she is also painted as something of a freak... with her... savage, violent streak."[80]

The Hopi (in what is now the Hopi Reservation in northeastern Arizona), according to Alice Schlegel, had as its "gender ideology... one of female superiority, and it operated within a social actuality of sexual equality."[81] According to LeBow (based on Schlegel's work), in the Hopi, "gender roles... are egalitarian.... [and] [n]either sex is inferior."[82][k] LeBow concluded that Hopi women "participate fully in... political decision-making."[83][l] According to Schlegel, "the Hopi no longer live as they are described here"[84] and "the attitude of female superiority is fading".[84] Schlegel said the Hopi "were and still are matrilinial"[85] and "the household... was matrilocal".[85] Schlegel explains why there was female superiority as that the Hopi believed in "life as the highest good... [with] the female principle... activated in women and in Mother Earth... as its source"[86] and that the Hopi "were not in a state of continual war with equally matched neighbors"[87] and "had no standing army"[87] so that "the Hopi lacked the spur to masculine superiority"[87] and, within that, as that women were central to institutions of clan and household and predominated "within the economic and social systems (in contrast to male predominance within the political and ceremonial systems)",[87] the Clan Mother, for example, being empowered to overturn land distribution by men if she felt it was unfair,[86] since there was no "countervailing... strongly centralized, male-centered political structure".[86]

The Iroquois Confederacy or League, combining 56 Native American Haudenosaunee nations or tribes before the U.S. became a nation, operated by The Great Binding Law of Peace, a constitution by which women participated in the League's political decision-making, including deciding whether to proceed to war,[88] through what may have been a matriarchy[89] or gyneocracy.[90] According to Doug George-Kanentiio, in this society, mothers exercise central moral and political roles. The dates of this constitution's operation are unknown; the League was formed in approximately 10001450, but the constitution was oral until written in about 1880.[92] The League still exists.

George-Kanentiio explains:

In our society, women are the center of all things. Nature, we believe, has given women the ability to create; therefore it is only natural that women be in positions of power to protect this function....We traced our clans through women; a child born into the world assumed the clan membership of its mother. Our young women were expected to be physically strong....The young women received formal instruction in traditional planting....Since the Iroquois were absolutely dependent upon the crops they grew, whoever controlled this vital activity wielded great power within our communities. It was our belief that since women were the givers of life they naturally regulated the feeding of our people....In all countries, real wealth stems from the control of land and its resources. Our Iroquois philosophers knew this as well as we knew natural law. To us it made sense for women to control the land since they were far more sensitive to the rhythms of the Mother Earth. We did not own the land but were custodians of it. Our women decided any and all issues involving territory, including where a community was to be built and how land was to be used....In our political system, we mandated full equality. Our leaders were selected by a caucus of women before the appointments were subject to popular review....Our traditional governments are composed of an equal number of men and women. The men are chiefs and the women clan-mothers....As leaders, the women closely monitor the actions of the men and retain the right to veto any law they deem inappropriate....Our women not only hold the reigns of political and economic power, they also have the right to determine all issues involving the taking of human life. Declarations of war had to be approved by the women, while treaties of peace were subject to their deliberations.

The controversy surrounding prehistoric or "primal" matriarchy began in reaction to the book by Bachofen, Mother Right: An Investigation of the Religious and Juridical Character of Matriarchy in the Ancient World, in 1861. Several generations of ethnologists were inspired by his pseudo-evolutionary theory of archaic matriarchy. Following him and Jane Ellen Harrison, several generations of scholars, usually arguing from known myths or oral traditions and examination of Neolithic female cult-figures, suggested that many ancient societies might have been matriarchal, or even that there existed a wide-ranging matriarchal society prior to the ancient cultures of which we are aware. According to Uwe Wesel, Bachofen's myth interpretations have proved to be untenable.[93] The concept was further investigated by Lewis Morgan.[94] Many researchers studied the phenomenon of matriarchy afterward, but the basis was laid by the classics of sociology. The notion of a "woman-centered" society was developed by Bachofen, whose three-volume Myth, Religion, and Mother Right (1861) impacted the way classicists such as Harrison, Arthur Evans, Walter Burkert, and James Mellaart[95] looked at the evidence of matriarchal religion in pre-Hellenic societies.[96] According to historian Susan Mann, as of 2000, "few scholars these days find... [a "notion of a stage of primal matriarchy"] persuasive."[97]

The following excerpts from Lewis Morgan's Ancient Society will explain the use of the terms: "In a work of vast research, Bachofen has collected and discussed the evidence of female authority, mother-right, and of female rule, gynecocracy."[pageneeded] "Common lands and joint tillage would lead to joint-tenant houses and communism in living; so that gyneocracy seems to require for its creation, descent in the female line. Women thus entrenched in large households, supplied from common stores, in which their own gens so largely predominated in numbers, would produce the phenomena of mother right and gyneocracy, which Bachofen has detected and traced with the aid of fragments of history and of tradition."[pageneeded]

Kurt Derungs is a non-academic author advocating an "anthropology of landscape" based on allegedly matriarchal traces in toponymy and folklore.[citation needed]

Friedrich Engels, in 1884, claimed that, in the earliest stages of human social development, there was group marriage and that therefore paternity was disputable, whereas maternity was not, so that a family could be traced only through the female line, and claimed that this was connected with the dominance of women over men or a Mutterrecht, which notion Engels took from Bachofen, who claimed, based on his interpretations of myths, that myths reflected a memory of a time when women dominated over men.[98][99] Engels speculated that the domestication of animals increased wealth claimed by men.[citation needed] Engels said that men wanted control over women for use as laborers and because they wanted to pass on their wealth to their children, requiring monogamy.[citation needed] Engels did not explain how this could happen in a matriarchal society, but said that women's status declined until they became mere objects in the exchange trade between men and patriarchy was established,[citation needed] causing the global defeat of the female sex[100] and the rise of individualism,[101] competition, and dedication to achievement.[citation needed] According to Eller, Engels may have been influenced with respect to women's status by August Bebel,[102] according to whom this matriarchy resulted in communism while patriarchy did not.[103]

Austrian writer Bertha Diener, also known as Helen Diner, wrote Mothers and Amazons (1930), which was the first work to focus on women's cultural history. Hers is regarded as a classic of feminist matriarchal study.[104] Her view is that in the past all human societies were matriarchal; then, at some point, most shifted to patriarchal and degenerated. The controversy was reinforced further by the publication of The White Goddess by Robert Graves (1948) and his later analysis of classical Greek mythology and the vestiges of earlier myths that had been rewritten after a profound change in the religion of Greek civilization that occurred within its very early historical times. From the 1950s, Marija Gimbutas developed a theory of an Old European culture in Neolithic Europe which had matriarchal traits, replaced by the patriarchal system of the Proto-Indo-Europeans with the spread of Indo-European languages beginning in the Bronze Age. According to Epstein, anthropologists in the 20th century said that "the goddess worship or matrilocality that evidently existed in many paleolithic societies was not necessarily associated with matriarchy in the sense of women's power over men. Many societies can be found that exhibit those qualities along with female subordination."[105] From the 1970s, these ideas were taken up by popular writers of second-wave feminism and expanded with the speculations of Margaret Murray on witchcraft, by the Goddess movement, and in feminist Wicca, as well as in works by Eisler, Elizabeth Gould Davis, and Merlin Stone.

"A Golden Age of matriarchy" was, according to Epstein, prominently presented by Charlene Spretnak and "encouraged" by Stone and Eisler,[106] but, at least for the Neolithic Age, has been denounced as feminist wishful thinking in The Inevitability of Patriarchy, Why Men Rule, Goddess Unmasked,[107] and The Myth of Matriarchal Prehistory and is not emphasized in third-wave feminism. According to Eller, Gimbutas had a large part in constructing a myth of historical matriarchy by examining Eastern European cultures that she asserts, by and large, never really bore any resemblance in character to the alleged universal matriarchy suggested by Gimbutas and Graves. She asserts that in "actually documented primitive societies" of recent (historical) times, paternity is never ignored and that the sacred status of goddesses does not automatically increase female social status, and believes that this affirms that utopian matriarchy is simply an inversion of antifeminism.[citation needed]

The original evidence recognized by Gimbutas, however, of Neolithic societies being more egalitarian than the Bronze Age Indo-European and Semitic patriarchies remains valid.[citation needed] Gimbutas herself has not described these societies as matriarchal, preferring the term woman-centered or matristic.[citation needed] J.F. del Giorgio insists on a matrifocal, matrilocal, matrilineal Paleolithic society.[108]

According to Rohrlich, "many scholars are convinced that Crete was a matriarchy, ruled by a queen-priestess"[109] and the "Cretan civilization" was "matriarchal" before "1500 B.C.," when it was overrun and colonized.[110]

Also according to Rohrlich, "in the early Sumerian city-states 'matriarchy seems to have left something more than a trace.'"[111]

One common misconception among historians of the Bronze Age such as Stone and Eisler is the notion that the Semites were matriarchal while the Indo-Europeans practiced a patriarchal system. An example of this view is found in Stone's When God Was a Woman,[pageneeded] wherein she attempts to make out a case that the worship of Yahweh was an Indo-European invention superimposed on an ancient matriarchal Semitic nation. Evidence from the Amorites and pre-Islamic Arabs, however, indicates that the primitive Semitic family was in fact patriarchal and patrilineal. Meanwhile, the Indo-Europeans were known to have practiced multiple succession systems, and there is much better evidence of matrilineal customs among the Indo-European Celts and Germans than among any ancient Semitic peoples.

Women were running Sparta while the men were often away fighting. Gorgo, Queen of Sparta, responded to a question from a woman in Attica along the lines of, "why Spartan women were the only women in the world who could rule men?" Gorgo replied, "because we are the only women who are mothers of men".

Arising in the period ranging from the Iron Age to the Middle Ages, several early northwestern European mythologies from the Irish (e.g., Macha and Scthach), the Brittonic (e.g., Rhiannon), and the Germanic (e.g., Grendel's mother and Nerthus) contain ambiguous episodes of primal female power which have been interpreted as folk evidence of a real potential for matriarchal attitudes in pre-Christian European Iron Age societies. Often transcribed from a retrospective, patriarchal, Romanised, and Catholic perspective, they hint at an earlier, culturally disturbing, era when female power could have predominated. The first-centuryattested historic British figure of Boudicca indicates that Brittonnic society permitted explicit female autocracy or a form of gender equality in a form which contrasted strongly with the patriarchal structure of Mediterranean civilisation.[citation needed]

In 1995, in Kenya, according to Emily Wax, Umoja, a village only for women from one tribe with about 36 residents, was established under a matriarch.[112] Men of the same tribe established a village nearby from which to observe the women's village,[112] the men's leader objecting to the matriarch's questioning the culture[113] and men suing to close the women's village.[113] The village was still operational in 2005 when Wax reported on it.[112]

Spokespersons for various indigenous peoples at the United Nations and elsewhere have highlighted the central role of women in their societies, referring to them as matriarchies, or as matriarchal in character.[114][115]

A legendary matriarchy related by several writers was Amazon society. According to Phyllis Chesler, "in Amazon societies, women were... mothers and their society's only political and religious leaders",[116] as well as the only warriors and hunters;[117] "queens were elected"[118] and apparently "any woman could aspire to and achieve full human expression."[119]Herodotus reported that the Sarmatians were descendants of Amazons and Scythians, and that their females observed their ancient maternal customs, "frequently hunting on horseback with their husbands; in war taking the field; and wearing the very same dress as the men".[citation needed] Moreover, said Herodotus, "no girl shall wed till she has killed a man in battle".[citation needed] Amazons came to play a role in Roman historiography. Julius Caesar spoke of the conquest of large parts of Asia by Semiramis and the Amazons.[citation needed] Although Strabo was sceptical about their historicity, the Amazons were taken as historical throughout late Antiquity.[120] Several Church Fathers spoke of the Amazons as a real people.[citation needed] Medieval authors continued a tradition of locating the Amazons in the North, Adam of Bremen placing them at the Baltic Sea and Paulus Diaconus in the heart of Germania.[121]

Robert Graves suggested that a myth displaced earlier myths that had to change when a major cultural change brought patriarchy to replace a matriarchy.[citation needed] According to this myth, in Greek mythology, Zeus is said to have swallowed his pregnant lover, the titan goddess Metis, who was carrying their daughter, Athena. The mother and child created havoc inside Zeus. Either Hermes or Hephaestus split Zeus's head, allowing Athena, in full battle armor, to burst forth from his forehead. Athena was thus described as being "born" from Zeus. The outcome pleased Zeus as it didn't fulfill the prophecy of Themis which (according to Aeschylus) predicted that Zeus will one day bear a son that would overthrow him.[citation needed]

According to Adler, "there is plenty of evidence of ancient societies where women held greater power than in many societies today. For example, Jean Markale's studies of Celtic societies show that the power of women was reflected not only in myth and legend but in legal codes pertaining to marriage, divorce, property ownership, and the right to rule."[122]

Bamberger (1974) examines several matriarchal myths from South American cultures and concludes that portraying the women from this matriarchal period as evil often serves to restrain contemporary women.[clarification needed][citation needed]

While matriarchy has mostly fallen out of use for the anthropological description of existing societies, it remains current as a concept in feminism.[123][124]

In first-wave feminist discourse, either Elizabeth Cady Stanton or Margaret Fuller (it is unclear who was first) introduced the concept of matriarchy[125] and the discourse was joined in by Matilda Joslyn Gage.[126]Victoria Woodhull, in 1871, called for men to open the U.S. government to women or a new constitution and government would be formed in a year;[127] and, on a basis of equality, she ran to be elected President in 1872.[128][129]Charlotte Perkins Gilman, in 1911 and 1914,[130] argued for "a woman-centered, or better mother-centered, world"[131] and described "'government by women'".[132] She argued that a government led by either sex must be assisted by the other,[133] both genders being "useful... and should in our governments be alike used",[134] because men and women have different qualities.[135]

Cultural feminism includes "matriarchal worship", according to Prof. James Penner.[136]

In feminist literature, matriarchy and patriarchy are not conceived as simple mirrors of each other.[137] While matriarchy sometimes means "the political rule of women",[138] that meaning is often rejected, on the ground that matriarchy is not a mirroring of patriarchy.[139] Patriarchy is held to be about power over others while matriarchy is held to be about power from within,[137]Starhawk having written on that distinction[137][140] and Adler having argued that matriarchal power is not possessive and not controlling, but is harmonious with nature.[m]

For radical feminists, the importance of matriarchy is that "veneration for the female principle... somewhat lightens an oppressive system."[142]

Feminist utopias are a form of advocacy. According to Tineke Willemsen, "a feminist utopia would... be the description of a place where at least women would like to live."[143] Willemsen continues, among "type[s] of feminist utopias[,]... [one] stem[s] from feminists who emphasize the differences between women and men. They tend to formulate their ideal world in terms of a society where women's positions are better than men's. There are various forms of matriarchy, or even a utopia that resembles the Greek myth of the Amazons.... [V]ery few modern utopias have been developed in which women are absolute autocrats."[144]

A minority of feminists, generally radical,[123][124] have argued that women should govern societies of women and men. In all of these advocacies, the governing women are not limited to mothers:

Some such advocacies are informed by work on past matriarchy:

Some fiction caricatured the current gender hierarchy by describing a matriarchal alternative without advocating for it. According to Karin Schnpflug, "Gerd Brantenberg's Egalia's Daughters is a caricature of powered gender relations which have been completely reversed, with the female sex on the top and the male sex a degraded, oppressed group";[193] "gender inequality is expressed through power inversion"[194] and "all gender roles are reversed and women rule over a class of intimidated, effeminate men".[195] "Egalia is not a typical example of gender inequality in the sense that a vision of a desirable matriarchy is created; Egalia is more a caricature of male hegemony by twisting gender hierarchy but not really offering a 'better world.'"[195][196]

On egalitarian matriarchy,[197]Heide Gttner-Abendroth's International Academy for Modern Matriarchal Studies and Matriarchal Spirituality (HAGIA) organized conferences in Luxembourg in 2003[198] and Texas in 2005,[199][200] with papers published.[201] Gttner-Abendroth argued that "matriarchies are all egalitarian at least in terms of genderthey have no gender hierarchy.... [, that, f]or many matriarchal societies, the social order is completely egalitarian at both local and regional levels",[202] that, "for our own path toward new egalitarian societies, we can gain... insight from... ["tested"] matriarchal patterns",[203] and that "matriarchies are not abstract utopias, constructed according to philosophical concepts that could never be implemented."[204]

According to Eller, "a deep distrust of men's ability to adhere to"[205] future matriarchal requirements may invoke a need "to retain at least some degree of female hegemony to insure against a return to patriarchal control",[205] "feminists... [having] the understanding that female dominance is better for societyand better for menthan the present world order",[206] as is equalitarianism. On the other hand, Eller continued, if men can be trusted to accept equality, probably most feminists seeking future matriarchy would accept an equalitarian model.[206]

"Demographic[ally]",[207] "feminist matriarchalists run the gamut"[207] but primarily are "in white, well-educated, middle-class circles";[207] many of the adherents are "religiously inclined"[207] while others are "quite secular".[207]

Biology as a ground for holding either males or females superior over the other has been criticized as invalid, such as by Andrea Dworkin[208] and by Robin Morgan.[209] A claim that women have unique characteristics that prevent women's assimilation with men has been apparently rejected by Ti-Grace Atkinson.[210] On the other hand, not all advocates based their arguments on biology or essentialism.

A criticism by Mansfield of choosing who governs according to gender or sex is that the best qualified people should be chosen, regardless of gender or sex.[211] On the other hand, Mansfield considered merit insufficient for office, because a legal right granted by a sovereign (e.g., a king), was more important than merit.[212]

Diversity within a proposed community can, according to Becki L. Ross, make it especially challenging to complete forming the community.[213] However, some advocacy includes diversity, in the views of Dworkin[145] and Farley.[214]

Prof. Christine Stansell, a feminist, wrote that, for feminists to achieve state power, women must democratically cooperate with men. "Women must take their place with a new generation of brothers in a struggle for the world's fortunes. Herland, whether of virtuous matrons or daring sisters, is not an option.... [T]he well-being and liberty of women cannot be separated from democracy's survival."[215] (Herland was feminist utopian fiction by Charlotte Perkins Gilman in 1911, featuring a community entirely of women except for three men who seek it out,[216] strong women in a matriarchal utopia[217] expected to last for generations,[218] although Charlotte Perkins Gilman was herself a feminist advocate of society being gender-integrated and of women's freedom.)[219]

Other criticisms of superiority are that it is reverse sexism or discriminatory against men, it is opposed by most people including most feminists, women do not want such a position,[r] governing takes women away from family responsibilities, women are too likely to be unable to serve politically because of menstruation and pregnancy,[225] public affairs are too sordid for women[226] and would cost women their respect[227] and femininity (apparently including fertility),[228] superiority is not traditional,[229][s] women lack the political capacity and authority men have,[t] it is impractical because of a shortage of women with the ability to govern at that level of difficulty[227] as well as the desire and ability to wage war,[u][v][w] women are less aggressive, or less often so, than are men[236] and politics is aggressive,[237] women legislating would not serve men's interests[227][238][239] or would serve only petty interests,[227] it is contradicted by current science on genderal differences,[240] it is unnatural,[241][242][x][244] and, in the views of a playwright and a novelist, "women cannot govern on their own."[245] On the other hand, another view is that "women have 'empire' over men"[246] because of nature and "men... are actually obeying" women.[246]

Pursuing a future matriarchy would tend to risk sacrificing feminists' position in present social arrangements, and many feminists are not willing to take that chance, according to Eller.[205] "Political feminists tend to regard discussions of what utopia would look like as a good way of setting themselves up for disappointment", according to Eller,[247] and argue that immediate political issues must get the highest priority.[247]

"Matriarchists", as typified by comic character Wonder Woman were criticized by Kathie Sarachild, Carol Hanisch, and some others.[248]

Some theologies and theocracies limit or forbid women from being in civil government or public leadership or forbid them from voting,[249] effectively criticizing and forbidding matriarchy. Within none of the following religions is the respective view necessarily universally held:

Feminist thealogy, according to Eller, conceptualized humanity as beginning with "female-ruled or equalitarian societies",[302] until displaced by patriarchies,[303] and that in the millennial future "'gynocentric,' life-loving values"[303] will return to prominence.[303] This, according to Eller, produces "a virtually infinite number of years of female equality or superiority coming both at the beginning and end of historical time."[304]

Among criticisms is that a future matriarchy, according to Eller, as a reflection of spirituality, is conceived as ahistorical,[206] and thus may be unrealistic, unreachable, or even meaningless as a goal to secular feminists.

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Live by the Golden Rule (pledge/petition/proclamation …

Sign the petition Petition results Who What & Why All Life strives to incorporate the principle of the Golden Rule. Directing our attention toward understanding this most basic principle gives us a reasonable, common sense and compassionate direction in anything we do. Remembering and putting the Golden Rule to use each day in our own lives transforms our relationship with ourselves, with others and with our environment, the planet Earth. An invitation to All:

1stStrive and Incorporate: strive to understand the meaning of the Golden Rule for myself and how I wish to incorporate it in my life, recognizing that this effort is sometimes hard and yet always helpful.

2ndInvite and Request: invite/petition/request those who represent me to do the same: live by the Golden Rule. My representatives will change the world for the better when they apply it within their organizations, such as in any of the religious traditions, teachings and in communities; environmental, civic, economic, educational, political, or social entities.

3rdStand in Unity: join with those on this planet who wish to take real responsibility toward compassion and fairness; and to build an understanding with my neighbors about what is to be done in each new situation based upon the principle of the Golden Rule. Simply stated,

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Golden calf – Wikipedia

According to the Bible, the golden calf ( ggel hazhv) was an icon (a cult image) made by the Israelites during Moses' absence, when he went up to Mount Sinai. In Hebrew, the incident is known as haggel ( ) or "The Sin of the Calf". It is first mentioned in Exodus 32:4.

Bull worship was common in many cultures. In Egypt, whence according to the Exodus narrative the Hebrews had recently come, the Apis Bull was a comparable object of worship, which some believe the Hebrews were reviving in the wilderness;[1] alternatively, some believe the God of Israel was associated with or pictured as a calf/bull deity through the process of religious assimilation and syncretism. Among the Egyptians' and Hebrews' neighbors in the ancient Near East and in the Aegean, the Aurochs, the wild bull, was widely worshipped, often as the Lunar Bull and as the creature of El.

When Moses went up into Biblical Mount Sinai to receive the Ten Commandments (Exodus 24:12-18), he left the Israelites for forty days and forty nights. The Israelites feared that he would not return and demanded that Aaron make them "gods" to go before them (Exodus 32:1). Aaron gathered up the Israelites' golden earrings and ornaments, constructed a "molten calf" and they declared: "These [be] thy gods, O Israel, which brought thee up out of the land of Egypt." (Exodus 32:4)

Aaron built an altar before the calf and proclaimed the next day to be a feast to the LORD. So they rose up early the next day and "offered burnt-offerings, and brought peace-offerings; and the people sat down to eat and to drink, and rose up to play." (Exodus 32:6) God told Moses what the Israelites were up to back in camp, that they had turned aside quickly out of the way which God commanded them and he was going to destroy them and start a new people from Moses. Moses besought and pleaded that they should be spared (Exodus 32:11-14), and God "repented of the evil which He said He would do unto His people."

Moses went down from the mountain, but upon seeing the calf, he became angry and threw down the two Tablets of Stone, breaking them. Moses burnt the golden calf in a fire, ground it to powder, scattered it on water, and forced the Israelites to drink it. When Moses asked him, Aaron admitted collecting the gold, and throwing it into the fire, and said it came out as a calf (Exodus 32:21-24).

The bible records that the tribe of Levi did not worship the golden calf. When Moses stood in the gate of the camp, and said: 'Whosoever is on the LORD's side, let him come unto me.' And all the sons of Levi gathered themselves together unto him. And he said unto them: 'Thus saith the LORD, the God of Israel: Put ye every man his sword upon his thigh, and go to and fro from gate to gate throughout the camp, and slay every man his brother, and every man his companion, and every man his neighbour.' And the sons of Levi did according to the word of Moses; and there fell of the people that day about three thousand men. (Exodus 32:26-28)

The golden calf is mentioned in Nehemiah 9:1621.

"But they, our ancestors, became arrogant and stiff-necked, and they did not obey your commands. They refused to listen and failed to remember the miracles you performed among them. They became stiff-necked and in their rebellion appointed a leader in order to return to their slavery. But you are a forgiving God, gracious and compassionate, slow to anger and abounding in love. Therefore you did not desert them, even when they cast for themselves an image of a calf and said, 'This is your god, who brought you up out of Egypt,' or when they committed awful blasphemies. "Because of your great compassion you did not abandon them in the wilderness. By day the pillar of cloud did not fail to guide them on their path, nor the pillar of fire by night to shine on the way they were to take. You gave your good Spirit to instruct them. You did not withhold your manna from their mouths, and you gave them water for their thirst. For forty years you sustained them in the wilderness; they lacked nothing, their clothes did not wear out nor did their feet become swollen."

The language suggests that there are some inconsistencies in the other accounts of the Israelites and their use of the calf. As the version in Exodus and 1 Kings are written by Deuteronomistic historians based in the southern kingdom of Judah, there is a proclivity to expose the Israelites as unfaithful. The inconsistency is primarily located in Exodus 32.4 where "gods" is plural despite the construction of a single calf. When Ezra retells the story, he uses the single, capitalized God.[2]

Conversely, a more biblically conservative view offers a tenable explanation accounting for the discrepancy between "gods" in Exodus 32 and "God" in Nehemiah 9:18. In both instances, the Hebrew 'elohim' is used. Since ancient Hebrew failed to distinguish 'elohim' God (known as the majestic plural) from 'elohim' gods, Biblical translations are either determined by a) context or b) the local verb(s). In the original account in Exodus 32, the local verb is in the 3rd person plural. In Nehemiah 9, the verb connected to 'elohim' is singular. For the JEDP (i.e. Deuteronomistic) theorist, this inconsistency is confirmatory since the theory maintains a roughly equivalent date for the composition of Exodus and Nehemiah. More conservative scholarship would argue that these two texts were composed about 1000 years apart: Exodus (by Moses) circa 1500 BCE, and Nehemiah circa 500 BCE. The biblically conservative framework would therefore account for the verbal inconsistency from Exodus to Nehemiah as a philological evolution over the approximate millennium separating the two books.

According to 1 Kings 12:2630, after Jeroboam establishes the northern Kingdom of Israel, he contemplates the sacrificial practices of the Israelites.

Jeroboam thought to himself, "The kingdom will now likely revert to the house of David. If these people go up to offer sacrifices at the temple of the LORD in Jerusalem, they will again give their allegiance to their lord, Rehoboam king of Judah. They will kill me and return to King Rehoboam." After seeking advice, the king made two golden calves. He said to the people, "It is too much for you to go up to Jerusalem. Here are your gods, Israel, who brought you up out of Egypt." One he set up in Bethel, and the other in Dan. And this thing became a sin; the people came to worship the one at Bethel and went as far as Dan to worship the other.

His concern was that the tendency to offer sacrifices in Jerusalem, which is in the southern Kingdom of Judah, would lead to a return to King Rehoboam. He makes two golden calves and places them in Bethel and Dan. He erects the two calves in what he figures (in some interpretations) as substitutes for the cherubim built by King Solomon in Jerusalem.[3]

Richard Elliott Friedman says "at a minimum we can say that the writer of the golden calf account in Exodus seems to have taken the words that were traditionally ascribed to Jeroboam and placed them in the mouths of the people." Friedman believes that the story was turned into a polemic, exaggerating the throne platform decoration into idolatry, by a family of priests sidelined by Jeroboam.[4]

The declarations of Aaron and Jeroboam are almost identical:

After making the golden calf or golden calves both Aaron and Jeroboam celebrate festivals. Aaron builds an altar and Jeroboam ascends an altar (Exod 32:56; 1 Kings 12:3233).[5]

The incident of the worship of the Golden Calf is narrated in the Qur'an and other Islamic literature. The Qur'an narrates that after they refused to enter the promised land, God decreed that as punishment the Israelites would wander for forty years. Moses continued to lead the Israelites to Mount Sinai for Divine guidance. According to Islamic literature, God ordered Moses to fast for thirty days, and upon near completion of the thirty days, Moses ate a scented plant to improve the odour of his mouth. God commanded Moses to fast for ten more days, before receiving the guidance for the Israelites. When Moses completed the fasts, he approached God for guidance. During this time, Moses had instructed the Israelites that Aaron (Harun) was to lead them. The Israelites grew restless, since Moses had not returned to them, and after thirty days, a man the Qur'an names Samiri raised doubts among the Israelites. Samiri claimed that Moses had forsaken the Israelites and ordered his followers among the Israelites to light a fire and bring him all the jewelry and gold ornaments they had.[6] Samiri fashioned the gold into a golden calf along with the dust on which the angel Gabriel had trodden, which he proclaimed to be the God of Moses and the God who had guided them out of Egypt.[7] There is a sharp contrast between the Qur'anic and the biblical accounts the prophet Aaron's actions. The Qur'an mentions that Aaron attempted to guide and warn the people from worshipping the Golden Calf. However, the Israelites refused to stop until Moses had returned.[8] The righteous separated themselves from the pagans. God informed Moses that He had tried the Israelites in his absence and that they had failed by worshipping the Golden Calf.

Returning to the Israelites in great anger, Moses asked Aaron why he had not stopped the Israelites when he had seen them worshipping the Golden Calf. The Qur'an reports that Aaron stated that he did not act due to the fear that Moses would blame him for causing divisions among the Israelites. Moses realized his helplessness in the situation, and both prayed to God for forgiveness. Moses then questioned Samiri for the creation of the Golden Calf; Samiri justified his actions by stating that he had thrown the dust of the ground upon which Gabriel had tread on into the fire because his soul had suggested it to him.[6] Moses informed him that he would be banished and that they would burn the Golden Calf and spread its dust into the sea. Moses ordered seventy delegates to repent to God and pray for forgiveness.[9] The delegates traveled alongside Moses to Mount Sinai, where they witnessed the speech between him and God but refused to believe until they had witnessed God with their sight. As punishment, God struck the delegates with lightning and killed them with a violent earthquake.[10] Moses prayed to God for their forgiveness. God forgave and resurrected them and they continued on their journey.

In the Islamic view, the Calf-worshipers' sin had been shirk (Arabic: ), the sin of idolatry or polytheism. Shirk is the deification or worship of anyone or anything other than the singular God (Allah), or more literally the establishment of "partners" placed beside God, a most serious and unforgivable sin, with the Calf-worshipers' being ultimately forgiven being a mark of special forbearance by Allah.

Despite a seemingly simplistic faade, the golden calf narrative is complex. According to Michael Coogan, it seems that the golden calf was not an idol for another god, and thus a false god.[11] He cites Exodus 32:4-5 as evidence: He [Aaron] took the gold from them, formed it in a mold, and cast an image of a calf; and they said, "These are your gods, O Israel, who brought you up out of the land of Egypt!" When Aaron saw this, he built an altar before it; and Aaron made proclamation and said, "Tomorrow shall be a festival to the Lord." Importantly, there is a single calf in this narrative, though the people refer to it as representative of the "gods." While a reference to singular god does not necessarily imply Yahweh worship, it does not rule out the possibility that it is Yahweh that the people are worshiping, as the reference to a plurality of "gods" would. Additionally, the festival "to the Lord" in verse 5 is sometimes translated as "to Yahweh".[11] It should also be noted that "in the chronology of the narrative of the Ten Commandments" the commandment against the creation of graven images had not yet been given to the people when they pressed upon Aaron to help them make the calf, and that such behavior was not yet explicitly outlawed.[11]

Another understanding of the golden calf narrative is that the calf was meant to be the pedestal of Yahweh. In Near Eastern art, gods were often depicted standing on an animal, rather than seated on a throne.[11] This reading suggests that the golden calf was merely an alternative to the ark of the covenant or the cherubim upon which Yahweh was enthroned.[11]

The reason for this complication may be understood as 1.) a criticism of Aaron, as the founder of one priestly house that rivaled the priestly house of Moses, and/or 2.) as "an attack on the northern kingdom of Israel."[11] The second explanation relies on the "sin of Jeroboam," who was the first king of the northern kingdom, as the cause of the northern kingdoms fall to Assyria in 722 BCE.[11] Jeroboams "sin" was creating two calves of gold, and sending one to Bethel as a worship site in the south of the Kingdom, and the other to Dan as a worship site in the north, so that the people of the northern kingdom would not have to continue to go to Jerusalem to worship (see 1 Kings 12.2630). According to Coogan, this episode is part of the Deuteronomistic history, written in the southern kingdom of Judah, after the fall of the Northern kingdom, which was biased against the northern kingdom.[11] Coogan maintains that Jeroboam was merely presenting an alternative to the cherubim of the Temple in Jerusalem, and that calves did not indicate non-Yahwehistic worship.[11]

The documentary hypothesis can be used to further understand the layers of this narrative: it is plausible that the earliest story of the golden calf was preserved by E (Israel source) and originated in the Northern kingdom. When E and J (Judah source) were combined after the fall of northern kingdom, "the narrative was reworked to portray the northern kingdom in a negative light," and the worship of the calf was depicted as "polytheism, with the suggestion of a sexual orgy" (see Exodus 32.6). When compiling the narratives, P (a later Priest source from Jerusalem) may have minimized Aarons guilt in the matter, but preserved the negativity associated with the calf.[11]

Alternatively it could be said that there is no golden calf story in the J source, and if it is correct that the Jeroboam story was the original as stated by Friedman, then it is unlikely that the Golden Calf events as described in Exodus occurred at all. Friedman states that the smashing of the Ten Commandments by Moses when he beheld the worship of the golden calf, is really an attempt to cast into doubt the validity of Judah's central shrine, the Ark of the Covenant. "The author of E, in fashioning the golden calf story, attacked both the Israelite and Judean religious establishments." [12]

As to the likelihood that these events ever took place, on the one hand there are two versions of the ten commandments story, in E (Exodus 20) and J (Exodus 34), this gives some antiquity and there may be some original events serving as a basis to the stories. The Golden Calf story is only in the E version and a later editor added in an explanation that God made a second pair of tablets to give continuity to the J story.[13] The actual Ten Commandments as given in Exodus 20 were also inserted by the redactor who combined the various sources.[14]

Archaeologists Israel Finkelstein and Neil Asher Silberman say that while archaeology has found traces left by small bands of hunter-gatherers in the Sinai, there is no evidence at all for the large body of people described in the Exodus story: "The conclusion that Exodus did not happen at the time and in the manner described in the Bible seems irrefutable... repeated excavations and surveys throughout the entire area have not provided even the slightest evidence."[15]

A metaphoric interpretation emphasizes the "gold" part of "golden calf" to criticize the pursuit of wealth.

This usage can be found in Spanish[16] where Mammon, the Gospel personification of idolatry of wealth, is not so current.

People and things in the Quran

Groups and tribes

Note: The names are sorted alphabetically. Standard form: Islamic name / Bibilical name (title or relationship)

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Rockwell’s "Golden Rule" – Norman Rockwell Museum – The Home …

This week the United Nations rededicated a large mosaic of Norman Rockwells iconic 1961 illustration, Golden Rule, which hangs in their New York City Headquarters.The workoriginally presented to the UN in 1985 as a gift on behalf of the United States by then First Lady Nancy Reaganwas restored by Williamstown Art Conservation Center, which over the years has repaired numerous objects from Norman Rockwell Museums collection as well (including Rockwells 1953 United Nationsdrawing, which was the artists earliest conceptions for Golden Rule). Here is a little more background on both artworks, currently on view and part of the collection of Norman Rockwell Museum.

United Nations

Conceived in 1952 and executed in 1953, this drawing was inspired by the United Nations humanitarian mission. Though it was carefully researched and developed, Rockwells idea never made it to canvas. He said he didnt quite know why he grew tired of the pieceperhaps it was too ambitious. At the height of the Cold War and two years into the Korean War, his concept was to picture the United Nations as the worlds hope for the futurehe included sixty-five people representing the worlds nations, waiting for the delegates to straighten out the world, so that they might live in peace and without fear. In the end Rockwell abandoned the illustration, saying that it seemed empty and pretentious, although he would reference it again many years later.

Golden Rule

In the 1960s, the mood of the country was changing, and Norman Rockwells opportunity to be rid of the art intelligentsias claim that he was old-fashioned was on the horizon. His 1961 Golden Rule was a precursor to the type of subject he would soon illustrate. A group of people of different religions, races and ethnicity served as the backdrop for the inscription Do Unto Other as You Would Have Them Do Unto You. Rockwell was a compassionate and liberal man, and this simple phrase reflected his philosophy. Having traveled all his life and been welcomed wherever he went, Rockwell felt like a citizen of the world, and his politics reflected that value system.

Id been reading up on comparative religion. The thing is that all major religions have the Golden Rule in Common. Do unto others as you would have them do unto you. Not always the same words but the same meaning.Norman Rockwell, The Norman Rockwell Album.

From photographs hed taken on his 1955 round-the-world Pam Am trip, Rockwell referenced native costumes and accessories and how they were worn. He picked up a few costumes and devised some from ordinary objects in his studio, such as using a lampshade as a fez. Many of Rockwells models were local exchange students and visitors. In a 1961 interview, indicating the man wearing a wide brimmed hat in the upper right corner, Rockwell said, Hes part Brazilian, part Hungarian, I think. Then there is Choi, a Korean. Hes a student at Ohio State University. Here is a Japanese student at Bennington College and here is a Jewish student. He was taking summer school courses at the Indian Hill Museum School. Pointing to the rabbi, he continued, Hes the retired postmaster of Stockbridge. He made a pretty good rabbi, in real life, a devout Catholic. I got all my Middle East faces from Abdalla who runs the Elm Street market, just one block from my house. Some of the models used were also from Rockwells earlier illustration,United Nations.

See the originals: Golden Rule and United Nations are currently on view at Norman Rockwell Museum.

View the restoration of RockwellsUnited Nations painting below:

Related Links:

Golden Rule, iconic Norman Rockwell mosaic, rededicated at UN Headquarters, UN News Centre, February 5, 2014

The Golden Rule: Restoring the Norman Rockwell Mosaic at the United Nations, Art Conservator, Summer 2013

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Rockwell's "Golden Rule" - Norman Rockwell Museum - The Home ...

Golden Rule: Treat People as You’d Like to Be Treated

By Cherie Burbach

One of the key principles in getting along with people is the Golden Rule. It helps you relate to people and gives you and instant guide to follow when it comes to your behavior.The Golden Rule is generally defined as treating others as you would like to be treated. Many religions have a version of this life philosophy, which provides a basic approach on how to interact with others. Specifically, the Bible says that "as you wish that others would do to you, do so to them" (Luke 6:31).

Why Don't More People Practice the Golden Rule?

In terms of friendship, the Golden Rule provides a guide on how to be a friend. If you want someone to laugh with, care about, and be there for you, then you need to do this for other people. Why then, is this so difficult for people to grasp? After all, if everyone lived by this rule, there would be no conflict or hurt feelings between friends.

One possible reason is that people don't always know how to treat themselves, and as a result treat others poorly as well.

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Rules of Texting in A New Relationship

Perhaps they had a hard time with self-esteem or did not receive the unconditional love that every child should have. Learning the Golden Rule as an adult may take some time in that case, and a friendship or two may end because of poor behavior. When the person realizes what it takes to be a true friend, his or her behavior changes and strong friendships can be built.

Another reason people ignore the golden rule is that they don't see the benefit in "giving" to someone else. They view generosity of spirit as an emotional cost that they don't feel will ever be returned. Folks like these often want to be on the receiving end of the Golden Rule but don't reciprocate.

The Golden Rule and Social Grace

While the Golden Rule is the guide for kindness toward others, social grace expands on that to include manners and etiquette in society. Things like making proper introductions and maintaining good cell phone etiquette fall under the heading of social grace, while listening and being empathetic falls under the Golden Rule. The difference is that social grace is the outward behavior toward a stranger, and the Golden Rule is what happens with your heart.

For example, you might introduce someone properly and make small talk with them at a party, which is perfectly acceptable in terms of social grace. But to take that same scenario further and relate it to the Golden Rule, you would give that same person the benefit of the doubt, refrain from gossip, and treat them well not because someone at the party expects you to, but because you genuinely want to.

The Golden Rule and Arguments

When you look at arguments from the perspective of the Golden Rule, it means you treat your friend with respect even when you're angry. You don't send off a nasty email to them or call them out in front of other friends, but you wait until the two of you are alone and can discuss things calmly (or at least, privately.)

Sometimes people try and manipulate others not involved in the argument to get "on their side" when they have an argument with a friend. They might tell their side of things to as many people as they can in an effort to get sympathy, and they pull others in before their friend can even respond. Behaving in this way can add a sticking point to whatever the original argument was about, and may serve as a catalyst to end the friendship. When a friend cannot apply the Golden Rule to arguments, the other friend may just step back from the relationship because there is no respect there.

How to Use the Golden Rule as a Guide in Your Friendship

One of the best things about the Golden Rule is that it can change your relationships for the better, with a simple change in perspective. To use this rule as a guide for your friendship:

Using the Golden Rule will help you have better friendships, but it must start with you. Change your approach and attitude, and your actions will follow.

Also Known As: respect, do unto others

Examples:

"Claire just went off on Judy in front of everyone. I doubt she would have appreciated that if Judy had done that to her. Time for a little lesson on the Golden Rule."

"I just got a lesson in the Golden Rule when Jane stood me up for our lunch date. I've done that to her about five times in the past. Now I know what it feels like."

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Golden Rule: Treat People as You'd Like to Be Treated

Golden ratio – Wikipedia

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure on the right illustrates the geometric relationship. Expressed algebraically, for quantities a and b with a>b>0,

where the Greek letter phi ( {displaystyle varphi } or {displaystyle phi } ) represents the golden ratio. Its value is:

The golden ratio is also called the golden mean or golden section (Latin: sectio aurea).[1][2][3] Other names include extreme and mean ratio,[4]medial section, divine proportion, divine section (Latin: sectio divina), golden proportion, golden cut,[5] and golden number.[6][7][8]

Some twentieth-century artists and architects, including Le Corbusier and Dal, have proportioned their works to approximate the golden ratioespecially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratiobelieving this proportion to be aesthetically pleasing. The golden ratio appears in some patterns in nature, including the spiral arrangement of leaves and other plant parts.

Mathematicians since Euclid have studied the properties of the golden ratio, including its appearance in the dimensions of a regular pentagon and in a golden rectangle, which may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has also been used to analyze the proportions of natural objects as well as man-made systems such as financial markets, in some cases based on dubious fits to data.[9]

Two quantities a and b are said to be in the golden ratio if

One method for finding the value of is to start with the left fraction. Through simplifying the fraction and substituting in b/a = 1/,

Therefore,

Multiplying by gives

which can be rearranged to

Using the quadratic formula, two solutions are obtained:

and

Because is the ratio between positive quantities is necessarily positive:

This derivation can also be found with a compass-and-straightedge construction:

The golden ratio has been claimed to have held a special fascination for at least 2,400 years, though without reliable evidence.[11] According to Mario Livio:

Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.[12]

Ancient Greek mathematicians first studied what we now call the golden ratio because of its frequent appearance in geometry. The division of a line into "extreme and mean ratio" (the golden section) is important in the geometry of regular pentagrams and pentagons. Euclid's Elements (Greek: ) provides the first known written definition of what is now called the golden ratio: "A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser."[13] Euclid explains a construction for cutting (sectioning) a line "in extreme and mean ratio", i.e., the golden ratio.[14] Throughout the Elements, several propositions (theorems in modern terminology) and their proofs employ the golden ratio.[15]

The golden ratio is explored in Luca Pacioli's book De divina proportione of 1509.

The first known approximation of the (inverse) golden ratio by a decimal fraction, stated as "about 0.6180340", was written in 1597 by Michael Maestlin of the University of Tbingen in a letter to his former student Johannes Kepler.[16]

Since the 20th century, the golden ratio has been represented by the Greek letter (phi, after Phidias, a sculptor who is said to have employed it) or less commonly by (tau, the first letter of the ancient Greek root meaning cut).[1][17]

Timeline according to Priya Hemenway:[18]

De Divina Proportione, a three-volume work by Luca Pacioli, was published in 1509. Pacioli, a Franciscan friar, was known mostly as a mathematician, but he was also trained and keenly interested in art. De Divina Proportione explored the mathematics of the golden ratio. Though it is often said that Pacioli advocated the golden ratio's application to yield pleasing, harmonious proportions, Livio points out that the interpretation has been traced to an error in 1799, and that Pacioli actually advocated the Vitruvian system of rational proportions.[1] Pacioli also saw Catholic religious significance in the ratio, which led to his work's title. De Divina Proportione contains illustrations of regular solids by Leonardo da Vinci, Pacioli's longtime friend and collaborator.

The Parthenon's faade as well as elements of its faade and elsewhere are said by some to be circumscribed by golden rectangles.[25] Other scholars deny that the Greeks had any aesthetic association with golden ratio. For example, Midhat J. Gazal says, "It was not until Euclid, however, that the golden ratio's mathematical properties were studied. In the Elements (308 BC) the Greek mathematician merely regarded that number as an interesting irrational number, in connection with the middle and extreme ratios. Its occurrence in regular pentagons and decagons was duly observed, as well as in the dodecahedron (a regular polyhedron whose twelve faces are regular pentagons). It is indeed exemplary that the great Euclid, contrary to generations of mystics who followed, would soberly treat that number for what it is, without attaching to it other than its factual properties."[26] And Keith Devlin says, "Certainly, the oft repeated assertion that the Parthenon in Athens is based on the golden ratio is not supported by actual measurements. In fact, the entire story about the Greeks and golden ratio seems to be without foundation. The one thing we know for sure is that Euclid, in his famous textbook Elements, written around 300 BC, showed how to calculate its value."[27] Later sources like Vitruvius exclusively discuss proportions that can be expressed in whole numbers, i.e. commensurate as opposed to irrational proportions.

A 2004 geometrical analysis of earlier research into the Great Mosque of Kairouan reveals a consistent application of the golden ratio throughout the design, according to Boussora and Mazouz.[28] They found ratios close to the golden ratio in the overall proportion of the plan and in the dimensioning of the prayer space, the court, and the minaret. The authors note, however, that the areas where ratios close to the golden ratio were found are not part of the original construction, and theorize that these elements were added in a reconstruction.

The Swiss architect Le Corbusier, famous for his contributions to the modern international style, centered his design philosophy on systems of harmony and proportion. Le Corbusier's faith in the mathematical order of the universe was closely bound to the golden ratio and the Fibonacci series, which he described as "rhythms apparent to the eye and clear in their relations with one another. And these rhythms are at the very root of human activities. They resound in man by an organic inevitability, the same fine inevitability which causes the tracing out of the Golden Section by children, old men, savages and the learned."[29]

Le Corbusier explicitly used the golden ratio in his Modulor system for the scale of architectural proportion. He saw this system as a continuation of the long tradition of Vitruvius, Leonardo da Vinci's "Vitruvian Man", the work of Leon Battista Alberti, and others who used the proportions of the human body to improve the appearance and function of architecture. In addition to the golden ratio, Le Corbusier based the system on human measurements, Fibonacci numbers, and the double unit. He took suggestion of the golden ratio in human proportions to an extreme: he sectioned his model human body's height at the navel with the two sections in golden ratio, then subdivided those sections in golden ratio at the knees and throat; he used these golden ratio proportions in the Modulor system. Le Corbusier's 1927 Villa Stein in Garches exemplified the Modulor system's application. The villa's rectangular ground plan, elevation, and inner structure closely approximate golden rectangles.[30]

Another Swiss architect, Mario Botta, bases many of his designs on geometric figures. Several private houses he designed in Switzerland are composed of squares and circles, cubes and cylinders. In a house he designed in Origlio, the golden ratio is the proportion between the central section and the side sections of the house.[31]

In a recent book, author Jason Elliot speculated that the golden ratio was used by the designers of the Naqsh-e Jahan Square and the adjacent Lotfollah mosque.[32]

Patrice Foutakis examined the measurements of 15 temples, 18 monumental tombs, 8 sarcophagi and 58 grave stelae from the fifth century BC to the second century AD. The temples were the main place for communication between the humans and Gods, while the tombs, sarcophagi and grave stelae were connected with the mortals' passage from the material life to the eternal one. Should the golden ratio imply any divine, mystical or aesthetic property, then, according to the author, most of these constructions would be characterized by a golden-section rule. The result of this original research is that the golden ratio was totally absent from Greek architecture of the classical fifth century BC, and almost absent during the following six centuries. Four extremely rare and therefore valuable examples of golden-mean proportions were identified in an ancient tower in Modon (Peloponnese, Greece), in the Great Altar of Pergamon (Pergamon Museum, Berlin), in a grave stele from Edessa (Greece), and in a monumental tomb at Pella (Greece). Although these cases Foutakis claims to be evidence about a golden-section application in constructions of ancient Greece, he concludes that it was a marginal application indicating that the ancient Greeks did not pay any particular attention to the golden ratio as far as their architecture was concerned.[33]

The 16th-century philosopher Heinrich Agrippa drew a man over a pentagram inside a circle, implying a relationship to the golden ratio.[2]

Leonardo da Vinci's illustrations of polyhedra in De divina proportione (On the Divine Proportion) and his views that some bodily proportions exhibit the golden ratio have led some scholars to speculate that he incorporated the golden ratio in his paintings.[34] But the suggestion that his Mona Lisa, for example, employs golden ratio proportions, is not supported by anything in Leonardo's own writings.[35] Similarly, although the Vitruvian Man is often[36] shown in connection with the golden ratio, the proportions of the figure do not actually match it, and the text only mentions whole number ratios.[37]

Salvador Dal, influenced by the works of Matila Ghyka,[38] explicitly used the golden ratio in his masterpiece, The Sacrament of the Last Supper. The dimensions of the canvas are a golden rectangle. A huge dodecahedron, in perspective so that edges appear in golden ratio to one another, is suspended above and behind Jesus and dominates the composition.[1][39]

Mondrian has been said to have used the golden section extensively in his geometrical paintings,[40] though other experts (including critic Yve-Alain Bois) have disputed this claim.[1]

A statistical study on 565 works of art of different great painters, performed in 1999, found that these artists had not used the golden ratio in the size of their canvases. The study concluded that the average ratio of the two sides of the paintings studied is 1.34, with averages for individual artists ranging from 1.04 (Goya) to 1.46 (Bellini).[41] On the other hand, Pablo Tosto listed over 350 works by well-known artists, including more than 100 which have canvasses with golden rectangle and root-5 proportions, and others with proportions like root-2, 3, 4, and 6.[42]

According to Jan Tschichold,[44]

There was a time when deviations from the truly beautiful page proportions 2:3, 1:3, and the Golden Section were rare. Many books produced between 1550 and 1770 show these proportions exactly, to within half a millimeter.

Some sources claim that the golden ratio is commonly used in everyday design, for example in the shapes of postcards, playing cards, posters, wide-screen televisions, photographs, light switch plates and cars.[45][46][47][48][49]

Ern Lendvai analyzes Bla Bartk's works as being based on two opposing systems, that of the golden ratio and the acoustic scale,[50] though other music scholars reject that analysis.[1] French composer Erik Satie used the golden ratio in several of his pieces, including Sonneries de la Rose+Croix. The golden ratio is also apparent in the organization of the sections in the music of Debussy's Reflets dans l'eau (Reflections in Water), from Images (1st series, 1905), in which "the sequence of keys is marked out by the intervals 34, 21, 13 and 8, and the main climax sits at the phi position."[51]

The musicologist Roy Howat has observed that the formal boundaries of La Mer correspond exactly to the golden section.[52] Trezise finds the intrinsic evidence "remarkable," but cautions that no written or reported evidence suggests that Debussy consciously sought such proportions.[53]

Pearl Drums positions the air vents on its Masters Premium models based on the golden ratio. The company claims that this arrangement improves bass response and has applied for a patent on this innovation.[54]

Though Heinz Bohlen proposed the non-octave-repeating 833 cents scale based on combination tones, the tuning features relations based on the golden ratio. As a musical interval the ratio 1.618... is 833.090... cents (Play(helpinfo)).[55]

Adolf Zeising, whose main interests were mathematics and philosophy, found the golden ratio expressed in the arrangement of parts such as leaves and branches along the stems of plants and of veins in leaves. He extended his research to the skeletons of animals and the branchings of their veins and nerves, to the proportions of chemical compounds and the geometry of crystals, even to the use of proportion in artistic endeavors. In these patterns in nature he saw the golden ratio operating as a universal law.[56][57] In connection with his scheme for golden-ratio-based human body proportions, Zeising wrote in 1854 of a universal law "in which is contained the ground-principle of all formative striving for beauty and completeness in the realms of both nature and art, and which permeates, as a paramount spiritual ideal, all structures, forms and proportions, whether cosmic or individual, organic or inorganic, acoustic or optical; which finds its fullest realization, however, in the human form."[58]

In 2010, the journal Science reported that the golden ratio is present at the atomic scale in the magnetic resonance of spins in cobalt niobate crystals.[59]

Since 1991, several researchers have proposed connections between the golden ratio and human genome DNA.[60][61][62]

However, some have argued that many apparent manifestations of the golden ratio in nature, especially in regard to animal dimensions, are fictitious.[63]

The golden ratio is key to the golden section search.

Studies by psychologists, starting with Fechner, have been devised to test the idea that the golden ratio plays a role in human perception of beauty. While Fechner found a preference for rectangle ratios centered on the golden ratio, later attempts to carefully test such a hypothesis have been, at best, inconclusive.[1][64]

The golden ratio is an irrational number. Below are two short proofs of irrationality:

Recall that:

If we call the whole n and the longer part m, then the second statement above becomes

or, algebraically

To say that is rational means that is a fraction n/m where n and m are integers. We may take n/m to be in lowest terms and n and m to be positive. But if n/m is in lowest terms, then the identity labeled (*) above says m/(nm) is in still lower terms. That is a contradiction that follows from the assumption that is rational.

Another short proofperhaps more commonly knownof the irrationality of the golden ratio makes use of the closure of rational numbers under addition and multiplication. If 1 + 5 2 {displaystyle textstyle {frac {1+{sqrt {5}}}{2}}} is rational, then 2 ( 1 + 5 2 ) 1 = 5 {displaystyle textstyle 2left({frac {1+{sqrt {5}}}{2}}right)-1={sqrt {5}}} is also rational, which is a contradiction if it is already known that the square root of a non-square natural number is irrational.

The golden ratio is also an algebraic number and even an algebraic integer. It has minimal polynomial

Having degree 2, this polynomial actually has two roots, the other being the golden ratio conjugate.

The conjugate root to the minimal polynomial x2 - x - 1 is

The absolute value of this quantity ( 0.618) corresponds to the length ratio taken in reverse order (shorter segment length over longer segment length, b/a), and is sometimes referred to as the golden ratio conjugate.[10] It is denoted here by the capital Phi ( {displaystyle Phi } ):

Alternatively, {displaystyle Phi } can be expressed as

This illustrates the unique property of the golden ratio among positive numbers, that

or its inverse:

This means 0.61803...:1 = 1:1.61803....

The formula = 1 + 1/ can be expanded recursively to obtain a continued fraction for the golden ratio:[65]

and its reciprocal:

The convergents of these continued fractions (1/1, 2/1, 3/2, 5/3, 8/5, 13/8, ..., or 1/1, 1/2, 2/3, 3/5, 5/8, 8/13, ...) are ratios of successive Fibonacci numbers.

The equation 2 = 1 + likewise produces the continued square root, or infinite surd, form:

An infinite series can be derived to express phi:[66]

Also:

These correspond to the fact that the length of the diagonal of a regular pentagon is times the length of its side, and similar relations in a pentagram.

The number turns up frequently in geometry, particularly in figures with pentagonal symmetry. The length of a regular pentagon's diagonal is times its side. The vertices of a regular icosahedron are those of three mutually orthogonal golden rectangles.

There is no known general algorithm to arrange a given number of nodes evenly on a sphere, for any of several definitions of even distribution (see, for example, Thomson problem). However, a useful approximation results from dividing the sphere into parallel bands of equal surface area and placing one node in each band at longitudes spaced by a golden section of the circle, i.e. 360/ 222.5. This method was used to arrange the 1500 mirrors of the student-participatory satellite Starshine-3.[67]

Application examples you can see in the articles Pentagon with a given side length, Decagon with given circumcircle and Decagon with a given side length.

The both above displayed different algorithms produce geometric constructions that divides a line segment into two line segments where the ratio of the longer to the shorter line segment is the golden ratio.

The golden triangle can be characterized as an isosceles triangle ABC with the property that bisecting the angle C produces a new triangle CXB which is a similar triangle to the original.

If angle BCX = , then XCA = because of the bisection, and CAB = because of the similar triangles; ABC = 2 from the original isosceles symmetry, and BXC = 2 by similarity. The angles in a triangle add up to 180, so 5 = 180, giving = 36. So the angles of the golden triangle are thus 36-72-72. The angles of the remaining obtuse isosceles triangle AXC (sometimes called the golden gnomon) are 36-36-108.

Suppose XB has length 1, and we call BC length . Because of the isosceles triangles XC=XA and BC=XC, so these are also length. Length AC=AB, therefore equals +1. But triangle ABC is similar to triangle CXB, so AC/BC=BC/BX, AC/=/1, and so AC also equals 2. Thus 2 =+1, confirming that is indeed the golden ratio.

Similarly, the ratio of the area of the larger triangle AXC to the smaller CXB is equal to , while the inverse ratio is1.

In a regular pentagon the ratio between a side and a diagonal is {displaystyle Phi } (i.e. 1/), while intersecting diagonals section each other in the golden ratio.[8]

George Odom has given a remarkably simple construction for involving an equilateral triangle: if an equilateral triangle is inscribed in a circle and the line segment joining the midpoints of two sides is produced to intersect the circle in either of two points, then these three points are in golden proportion. This result is a straightforward consequence of the intersecting chords theorem and can be used to construct a regular pentagon, a construction that attracted the attention of the noted Canadian geometer H. S. M. Coxeter who published it in Odom's name as a diagram in the American Mathematical Monthly accompanied by the single word "Behold!" [68]

The golden ratio plays an important role in the geometry of pentagrams. Each intersection of edges sections other edges in the golden ratio. Also, the ratio of the length of the shorter segment to the segment bounded by the two intersecting edges (a side of the pentagon in the pentagram's center) is , as the four-color illustration shows.

The pentagram includes ten isosceles triangles: five acute and five obtuse isosceles triangles. In all of them, the ratio of the longer side to the shorter side is . The acute triangles are golden triangles. The obtuse isosceles triangles are golden gnomons.

The golden ratio properties of a regular pentagon can be confirmed by applying Ptolemy's theorem to the quadrilateral formed by removing one of its vertices. If the quadrilateral's long edge and diagonals are b, and short edges are a, then Ptolemy's theorem gives b2=a2+ab which yields

Consider a triangle with sides of lengths a, b, and c in decreasing order. Define the "scalenity" of the triangle to be the smaller of the two ratios a/b and b/c. The scalenity is always less than and can be made as close as desired to .[69]

If the side lengths of a triangle form a geometric progression and are in the ratio 1: r: r2, where r is the common ratio, then r must lie in the range 1 < r < , which is a consequence of the triangle inequality (the sum of any two sides of a triangle must be strictly bigger than the length of the third side). If r = then the shorter two sides are 1 and but their sum is 2, thus r < . A similar calculation shows that r > 1. A triangle whose sides are in the ratio 1: : is a right triangle (because 1 + = 2) known as a Kepler triangle.[70]

A golden rhombus is a rhombus whose diagonals are in the golden ratio. The rhombic triacontahedron is a convex polytope that has a very special property: all of its faces are golden rhombi. In the rhombic triacontahedron the dihedral angle between any two adjacent rhombi is 144, which is twice the isosceles angle of a golden triangle and four times its most acute angle.[71]

The mathematics of the golden ratio and of the Fibonacci sequence are intimately interconnected. The Fibonacci sequence is:

The closed-form expression for the Fibonacci sequence involves the golden ratio:

The golden ratio is the limit of the ratios of successive terms of the Fibonacci sequence (or any Fibonacci-like sequence), as originally shown by Kepler:[20]

Therefore, if a Fibonacci number is divided by its immediate predecessor in the sequence, the quotient approximates ; e.g., 987/6101.6180327868852. These approximations are alternately lower and higher than , and converge on as the Fibonacci numbers increase, and:

More generally:

where above, the ratios of consecutive terms of the Fibonacci sequence, is a case when a = 1 {displaystyle a=1} .

Furthermore, the successive powers of obey the Fibonacci recurrence:

This identity allows any polynomial in to be reduced to a linear expression. For example:

The reduction to a linear expression can be accomplished in one step by using the relationship

where F k {displaystyle F_{k}} is the kth Fibonacci number.

However, this is no special property of , because polynomials in any solution x to a quadratic equation can be reduced in an analogous manner, by applying:

for given coefficients a, b such that x satisfies the equation. Even more generally, any rational function (with rational coefficients) of the root of an irreducible nth-degree polynomial over the rationals can be reduced to a polynomial of degree n 1. Phrased in terms of field theory, if is a root of an irreducible nth-degree polynomial, then Q ( ) {displaystyle mathbb {Q} (alpha )} has degree n over Q {displaystyle mathbb {Q} } , with basis { 1 , , , n 1 } {displaystyle {1,alpha ,dots ,alpha ^{n-1}}} .

The golden ratio and inverse golden ratio = ( 1 5 ) / 2 {displaystyle varphi _{pm }=(1pm {sqrt {5}})/2} have a set of symmetries that preserve and interrelate them. They are both preserved by the fractional linear transformations x , 1 / ( 1 x ) , ( x 1 ) / x , {displaystyle x,1/(1-x),(x-1)/x,} this fact corresponds to the identity and the definition quadratic equation. Further, they are interchanged by the three maps 1 / x , 1 x , x / ( x 1 ) {displaystyle 1/x,1-x,x/(x-1)} they are reciprocals, symmetric about 1 / 2 {displaystyle 1/2} , and (projectively) symmetric about 2.

More deeply, these maps form a subgroup of the modular group PSL ( 2 , Z ) {displaystyle operatorname {PSL} (2,mathbf {Z} )} isomorphic to the symmetric group on 3 letters, S 3 , {displaystyle S_{3},} corresponding to the stabilizer of the set { 0 , 1 , } {displaystyle {0,1,infty }} of 3 standard points on the projective line, and the symmetries correspond to the quotient map S 3 S 2 {displaystyle S_{3}to S_{2}} the subgroup C 3 < S 3 {displaystyle C_{3}

The golden ratio has the simplest expression (and slowest convergence) as a continued fraction expansion of any irrational number (see Alternate forms above). It is, for that reason, one of the worst cases of Lagrange's approximation theorem and it is an extremal case of the Hurwitz inequality for Diophantine approximations. This may be why angles close to the golden ratio often show up in phyllotaxis (the growth of plants).[72]

The defining quadratic polynomial and the conjugate relationship lead to decimal values that have their fractional part in common with :

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Golden ratio - Wikipedia

Golden Rule Plumbing, Heating & Cooling

Plumbing Services

Whether your drainpipes have become clogged, or your water heater is leaking water, make sure that you have a reliable Des Moines plumber at your beck and call. We offer comprehensive plumbing repair, installation, replacement, and maintenance services that can keep your home free of water damage and bountifully supplied with hot and cold water. We want you to have a reliable plumbing system, and we have the quality workmanship and technical expertise to make sure that this is the case. Thousands of customers in Des Moines choose Golden Rule for their plumbing needs, and wed love an opportunity to earn your business.

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At Golden Rule Plumbing, Heating & Cooling, we also offer excellent air conditioning service in Des Moines, IA. Our service technicians can help with everything frominstallation and replacement to repair and maintenance. We not only install and service central air conditioners, which are probably the most common, but also heat pumps, ductless mini splits and geothermal systems. Having a great cooling system is essential to the comfort of your home in the summer.

One of our specialties is geothermal. This type of heating and cooling system delivers yearround comfort to your home while cutting down on energy consumption significantly. It is a great way not only to be more selfsufficient, but also to reduce your energy bill and to utilize a renewable resource. It involves the installation of underground piping as well as conventional HVAC components such as the heat pump and ductwork. You can depend on us for professional geothermal service throughout Des Moines.

A leak or clog at home is often a minor inconvenience. But when it occurs at your place of business or at the commercial property that you manage, it directly affects your livelihood. We can take care of your commercial plumbing and commercial HVAC services in Des Moines, IA, whether its the installation of a comprehensive new rooftop heating and cooling unit or the replacement of your existing water heater with a new tankless model, Golden Rule Plumbing, Heating & Cooling can help. Call us today.

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Golden Rule Plumbing, Heating & Cooling