title: Immigration

text: Legislation regarding the protection of rights of immigrants and equal access to justice differs per nation. International law -- the product of the United Nations and other multinational organizations -- creates protocols governing immigrant rights. International law and the European Convention of Human Rights state that immigrants can only be detained for ‘legitimate aims’ of the state. It also notes that vulnerable people should be protected from unreasonable punishment and lengthy detention. International law outlines requirements for due process and suitable conditions. However, nations are sovereign, and the protocols of international law cannot be enforced upon them. Nations have the freedom to handle immigrants as they choose, and to structure how any legal aid is distributed. Human rights organizations strongly criticize individual nation-states for the limitations of their immigration policies and practices.


title: Immigration

text: Treatment of migrants in host countries, both by governments, employers, and original population, is a topic of continual debate and criticism, and the violation of migrant human rights is an ongoing crisis. The United Nations Convention on the Protection of the Rights of All Migrant Workers and Members of Their Families, has been ratified by 48 states, most of which are heavy exporters of cheap labor. Major migrant-receiving countries and regions—including Western Europe, North America, Pacific Asia, Australia, and the Gulf States—have not ratified the convention, even though they are host to the majority of international migrant workers. Although freedom of movement is often recognized as a civil right in many documents such as the Universal Declaration of Human Rights (1948) and the International Covenant on Civil and Political Rights (1966), the freedom only applies to movement within national borders and the ability to return to one's home state.


title: Immigration

text: Some proponents of immigration argue that the freedom of movement both within and between countries is a basic human right, and that the restrictive immigration policies, typical of nation-states, violate this human right of freedom of movement. Such arguments are common among ideologies like anarchism and libertarianism. As philosopher and open borders activist Jacob Appel has written, "Treating human beings differently, simply because they were born on the opposite side of a national boundary, is hard to justify under any mainstream philosophical, religious or ethical theory."


title: Immigration

text: Where immigration is permitted, it is typically selective. , family reunification accounted for approximately two-thirds of legal immigration to the US every year. Ethnic selection, such as the White Australia policy, has generally disappeared, but priority is usually given to the educated, skilled, and wealthy. Less privileged individuals, including the mass of poor people in low-income countries, cannot avail themselves of the legal and protected immigration opportunities offered by wealthy states. This inequality has also been criticized as conflicting with the principle of equal opportunities. The fact that the door is closed for the unskilled, while at the same time many developed countries have a huge demand for unskilled labor, is a major factor in illegal immigration. The contradictory nature of this policy—which specifically disadvantages the unskilled immigrants while exploiting their labor—has also been criticized on ethical grounds.


title: Immigration

text: Immigration policies which selectively grant freedom of movement to targeted individuals are intended to produce a net economic gain for the host country. They can also mean net loss for a poor donor country through the loss of the educated minority—a "brain drain". This can exacerbate the global inequality in standards of living that provided the motivation for the individual to migrate in the first place. One example of competition for skilled labour is active recruitment of health workers from developing countries by developed countries. There may however also be a "brain gain" to emigration, as migration opportunities lead to greater investments in education in developing countries. Overall, research suggests that migration is beneficial both to the receiving and sending countries.


title: Immigration

text: A survey of leading economists shows a consensus behind the view that high-skilled immigration makes the average American better off. A survey of the same economists also shows support behind the notion that low-skilled immigration makes the average American better off and makes many low-skilled American workers substantially worse off unless they are compensated by others. A survey of European economists shows a consensus that freer movement of people to live and work across borders within Europe makes the average European better off, and strong support behind the notion that it has not made low-skilled Europeans worse off. According to David Card, Christian Dustmann, and Ian Preston, "most existing studies of the economic impacts of immigration suggest these impacts are small, and on average benefit the native population" . In a survey of the existing literature, Örn B Bodvarsson and Hendrik Van den Berg write, "a comparison of the evidence from all the studies... makes it clear that, with very few exceptions, there is no strong statistical support for the view held by many members of the public, mainly that immigration has an adverse effect on native-born workers in the destination country."


title: Immigration

text: Whereas the impact on the average native tends to be small and positive, studies show more mixed results for low-skilled natives, but whether the effects are positive or negative, they tend to be small either way. Research indicates that immigrants are more likely to work in risky jobs than U.S.-born workers, partly due to differences in average characteristics, such as immigrants' lower English language ability and educational attainment. According to a 2017 survey of the existing economic literature, studies on high-skilled migrants "rarely find adverse wage and employment consequences, and longer time horizons tend to show greater gains".


title: Immigration

text: Competition from immigrants in a particular profession may aggravate underemployment in that profession, but increase wages for other natives; for instance, a 2017 study in "Science" found that "the influx of foreign-born computer scientists since the early 1990s... increased the size of the US IT sector... benefited consumers via lower prices and more efficient products... raised overall worker incomes by 0.2 to 0.3% but decreased wages of U.S. computer scientists by 2.6 to 5.1%." A 2019 study found that foreign college workers in STEM occupations did not displace native college workers in STEM occupations, but instead had a positive impact on the latter group's wages. A 2021 study similarly found that highly educated immigrants to Switzerland caused wages to increase for highly educated Swiss natives. A 2019 study found that greater immigration led to less off-shoring by firms.


title: Immigration

text: Research also suggests that diversity and immigration have a net positive effect on productivity and economic prosperity. Immigration has also been associated with reductions in offshoring. A study found that the Age of Mass Migration (1850–1920) contributed to "higher incomes, higher productivity, more innovation, and more industrialization" in the short-run and "higher incomes, less poverty, less unemployment, higher rates of urbanization, and greater educational attainment" in the long-run for the United States. Research also shows that migration to Latin America during the Age of Mass Migration had a positive impact on long-run economic development.


title: Immigration

text: Studies show that the elimination of barriers to migration would have profound effects on world GDP, with estimates of gains ranging between 67 and 147.3%. Research also finds that migration leads to greater trade in goods and services, and increases in financial flows between the sending and receiving countries. Using 130 years of data on historical migrations to the United States, one study finds "that a doubling of the number of residents with ancestry from a given foreign country relative to the mean increases by 4.2 percentage points the probability that at least one local firm invests in that country, and increases by 31% the number of employees at domestic recipients of FDI from that country. The size of these effects increases with the ethnic diversity of the local population, the geographic distance to the origin country, and the ethno-linguistic fractionalization of the origin country." A 2017 study found that "immigrants' genetic diversity is significantly positively correlated with measures of U.S. counties' economic development [during the Age of Mass Migration]. There exists also a significant positive relationship between immigrants' genetic diversity in 1870 and contemporaneous measures of U.S. counties' average income."


title: Immigration

text: Some research suggests that immigration can offset some of the adverse effects of automation on native labor outcomes. By increasing overall demand, immigrants could push natives out of low-skilled manual labor into better paying occupations. A 2018 study in the "American Economic Review" found that the Bracero program (which allowed almost half a million Mexican workers to do seasonal farm labor in the United States) did not have any adverse impact on the labor market outcomes of American-born farm workers. A 2019 study by economic historians found that immigration restrictions implemented in the 1920s had an adverse impact on US-born workers' earnings.


title: Immigration

text: A 2016 paper by University of Southern Denmark and University of Copenhagen economists found that the 1924 immigration restrictions enacted in the United States impaired the economy.


title: Immigration

text: Overall immigration was found to account for a relatively small share of the rise of native wage inequality, but low-skill immigration has been linked to greater income inequality in the native population. Greater openness to low-skilled immigration in wealthy countries would drastically reduce global income inequality.


title: Immigration

text: A 2011 literature review of the economic impacts of immigration found that the net fiscal impact of migrants varies across studies but that the most credible analyses typically find small and positive fiscal effects on average. According to the authors, "the net social impact of an immigrant over his or her lifetime depends substantially and in predictable ways on the immigrant's age at arrival, education, reason for migration, and similar". According to a 2007 literature review by the Congressional Budget Office, "Over the past two decades, most efforts to estimate the fiscal impact of immigration in the United States have concluded that, in aggregate and over the long term, tax revenues of all types generated by immigrants—both legal and unauthorized—exceed the cost of the services they use." A 2022 study found that the sharp reduction in refugee admissions adversely affected public coffers at all levels of government in the United States.


title: Immigration

text: A 2018 study found that inflows of asylum seekers into Western Europe from 1985 to 2015 had a net positive fiscal impact. Research has shown that EU immigrants made a net positive fiscal contribution to Denmark and the United Kingdom. A 2017 study found that when Romanian and Bulgarian immigrants to the United Kingdom gained permission to acquire welfare benefits in 2014 that it had no discernible impact on the immigrants' use of welfare benefits. A paper by a group of French economists found that over the period 1980–2015, "international migration had a positive impact on the economic and fiscal performance of OECD countries."


title: Immigration

text: A 2017 survey of leading economists found that 34% of economists agreed with the statement "The influx of refugees into Germany beginning in the summer of 2015 will generate net economic benefits for German citizens over the succeeding decade", whereas 38% were uncertain and 6% disagreed. Studies of refugees' impact on native welfare are scant but the existing literature shows mixed results (negative, positive and no significant effects on native welfare). According to economist Michael Clemens, "when economists have studied past influxes of refugees and migrants they have found the labor market effects, while varied, are very limited, and can in fact be positive." A 2018 study in the "Economic Journal" found that Vietnamese refugees to the United States had a positive impact on American exports, as exports to Vietnam grew most in US states with larger Vietnamese populations. A 2018 study in the journal "Science Advances" found that asylum seekers entering Western Europe in the period 1985–2015 had a positive macroeconomic and fiscal impact. A 2019 study found that the mass influx of 1.3 million Syrian refugees to Jordan (total population: 6.6 million) did not have harm the labor market outcomes of native Jordanians. A 2020 study found that Syrian refugees to Turkey improved the productivity of Turkish firms.


title: Immigration

text: A 2017 paper by Evans and Fitzgerald found that refugees to the United States pay "$21,000 more in taxes than they receive in benefits over their first 20 years in the U.S." An internal study by the Department of Health and Human Services under the Trump administration, which was suppressed and not shown to the public, found that refugees to the United States brought in $63 billion more in government revenues than they cost the government. According to University of California, Davis, labor economist Giovanni Peri, the existing literature suggests that there are no economic reasons why the American labor market could not easily absorb 100,000 Syrian refugees in a year. A 2017 paper looking at the long-term impact of refugees on the American labor market over the period 1980–2010 found "that there is no adverse long-run impact of refugees on the U.S. labor market." A 2022 study by economist Michael Clemens found that the sharp reduction in refugee admissions in the United States since 2017 had cost the U.S. economy over $9.1 billion per year and cost public coffers over $2 billion per year.


title: Immigration

text: Refugees integrate more slowly into host countries' labor markets than labor migrants, in part due to the loss and depreciation of human capital and credentials during the asylum procedure. Refugees tend to do worse in economic terms than natives, even when they have the same skills and language proficiencies of natives. For instance, a 2013 study of Germans in West-Germany who had been displaced from Eastern Europe during and after World War II showed that the forced German migrants did far worse economically than their native West-German counterparts decades later. Second-generation forced German migrants also did worse in economic terms than their native counterparts. A study of refugees to the United States found that "refugees that enter the U.S. before age 14 graduate high school and enter college at the same rate as natives. Refugees that enter as older teenagers have lower attainment with much of the difference attributable to language barriers and because many in this group are not accompanied by a parent to the U.S." Refugees that entered the U.S. at ages 18–45, have "much lower levels of education and poorer language skills than natives and outcomes are initially poor with low employment, high welfare use and low earnings." But the authors of the study find that "outcomes improve considerably as refugees age."


title: Immigration

text: A 2017 study found that the 0.5 million Portuguese who returned to Portugal from Mozambique and Angola in the mid-1970s lowered labor productivity and wages. A 2018 paper found that the areas in Greece that took on a larger share of Greek Orthodox refugees from the Greco-Turkish War of 1919–1922 "have today higher earnings, higher levels of household wealth, greater educational attainment, as well as larger financial and manufacturing sectors."


title: Immigration

text: Research on the economic effects of undocumented immigrants is scant but existing studies suggests that the effects are positive for the native population, and public coffers. A 2015 study shows that "increasing deportation rates and tightening border control weakens low-skilled labor markets, increasing unemployment of native low-skilled workers. Legalization, instead, decreases the unemployment rate of low-skilled natives and increases income per native." Studies show that legalization of undocumented immigrants would boost the U.S. economy; a 2013 study found that granting legal status to undocumented immigrants would raise their incomes by a quarter (increasing U.S. GDP by approximately $1.4 trillion over a ten-year period), and a 2016 study found that "legalization would increase the economic contribution of the unauthorized population by about 20%, to 3.6% of private-sector GDP." A 2018 National Bureau of Economic Research paper found that undocumented immigrants to the United States "generate higher surplus for US firms relative to natives, hence restricting their entry has a depressing effect on job creation and, in turn, on native labor markets."


title: Immigration

text: In the US the Immigration Reform and Control Act was passed to help remove the illegal aliens. They were trying to do this by granting legal status or by imposing penalties against the employers who would knowingly work illegal immigrants. However, IRCA did not address the reality or price which caused an issue in the accomplishing of the objectives.


title: Immigration

text: A 2017 study in the "Journal of Public Economics" found that more intense immigration enforcement increased the likelihood that US-born children with undocumented immigrant parents would live in poverty.


title: Immigration

text: A paper by Spanish economists found that upon legalizing the undocumented immigrant population in Spain, the fiscal revenues increased by around €4,189 per newly legalized immigrant. The paper found that the wages of the newly legalized immigrants increased after legalization, some low-skilled natives had worse labor market outcomes and high-skilled natives had improved labor market outcomes.


title: Immigration

text: A 2018 study found no evidence that apprehensions of undocumented immigrants in districts in the United States improved the labor market outcomes for American natives. A 2020 study found that immigration enforcement in the US leads to declining production in the US dairy industry and that dairy operators respond to immigration enforcement by automating their operations (rather than hire new labor).


title: Immigration

text: A 2021 study in the "American Economic Journal" found that undocumented immigrants had beneficial effects on the employment and wages of American natives. Stricter immigration enforcement adversely affected employment and wages of American natives.


title: Immigration

text: Research suggests that migration is beneficial both to the receiving and sending countries. According to one study, welfare increases in both types of countries: "welfare impact of observed levels of migration is substantial, at about 5% to 10% for the main receiving countries and about 10% in countries with large incoming remittances". According to Branko Milanović, country of residency is by far the most important determinant of global income inequality, which suggests that the reduction in labor barriers would significantly reduce global income inequality. A study of equivalent workers in the United States and 42 developing countries found that "median wage gap for a male, unskilled (9 years of schooling), 35-year-old, urban formal sector worker born and educated in a developing country is P$15,400 per year at purchasing power parity". A 2014 survey of the existing literature on emigration finds that a 10 percent emigrant supply shock would increase wages in the sending country by 2–5.5%.


title: Immigration

text: According to economists Michael Clemens and Lant Pritchett, "permitting people to move from low-productivity places to high-productivity places appears to be by far the most efficient generalized policy tool, at the margin, for poverty reduction". A successful two-year in situ anti-poverty program, for instance, helps poor people make in a year what is the equivalent of working one day in the developed world. A slight reduction in the barriers to labor mobility between the developing and developed world would do more to reduce poverty in the developing world than any remaining trade liberalization.


title: Immigration

text: Research on a migration lottery allowing Tongans to move to New Zealand found that the lottery winners saw a 263% increase in income from migrating (after only one year in New Zealand) relative to the unsuccessful lottery entrants. A longer-term study on the Tongan lottery winners finds that they "continue to earn almost 300 percent more than non-migrants, have better mental health, live in households with more than 250 percent higher expenditure, own more vehicles, and have more durable assets". A conservative estimate of their lifetime gain to migration is NZ$315,000 in net present value terms (approximately US$237,000).


title: Immigration

text: A 2017 study of Mexican immigrant households in the United States found that by virtue of moving to the United States, the households increase their incomes more than fivefold immediately. The study also found that the "average gains accruing to migrants surpass those of even the most successful current programs of economic development."


title: Immigration

text: A 2017 study of European migrant workers in the UK shows that upon accession to the EU, the migrant workers see a substantial positive impact on their earnings. The data indicate that acquiring EU status raises earnings for the workers by giving them the right to freely change jobs.


title: Immigration

text: A 2017 study in the "Quarterly Journal of Economics" found that immigrants from middle- and low-income countries to the United States increased their wages by a factor of two to three upon migration.


title: Immigration

text: A 2017 survey of the existing economic literature found that "high-skilled migrants boost innovation and productivity outcomes." According to a 2013 survey of the existing economic literature, "much of the existing research points towards positive net contributions by immigrant entrepreneurs." Areas where immigrant are more prevalent in the United States have substantially more innovation (as measured by patenting and citations). Immigrants to the United States create businesses at higher rates than natives. A 2010 study showed "that a 1 percentage point increase in immigrant college graduates' population share increases patents per capita by 9–18 percent." Mass migration can also boost innovation and growth, as shown by the Jewish, Huguenot and Bohemian diasporas in Berlin and Prussia, German Jewish Émigrés in the US, the Mariel boatlift, the exodus of Soviet Jews to Israel in the 1990s, European migration to Argentina during the Age of Mass Migration (1850–1914), west-east migration in the wake of German reunification, German migration to Russian Empire, and Polish immigration to Germany after joining the EU. A 2018 study in the "Economic Journal" found that "a 10% increase in immigration from exporters of a given product is associated with a 2% increase in the likelihood that the host country starts exporting that good 'from scratch' in the next decade."


title: Immigration

text: Immigrants have been linked to greater invention and innovation. According to one report, "immigrants have started more than half (44 of 87) of America's startup companies valued at $1 billion dollars or more and are key members of management or product development teams in over 70 percent (62 of 87) of these companies." One analysis found that immigrant-owned firms had a higher innovation rate (on most measures of innovation) than firms owned by U.S.-born entrepreneurs. Research also shows that labor migration increases human capital. Foreign doctoral students are a major source of innovation in the American economy. In the United States, immigrant workers hold a disproportionate share of jobs in science, technology, engineering, and math (STEM): "In 2013, foreign-born workers accounted for 19.2 percent of STEM workers with a bachelor's degree, 40.7 percent of those with a master's degree, and more than half—54.5 percent—of those with a PhD"


title: Immigration

text: A number of countries across the globe offer Economic Citizenship Programs where in return for investing into the local economy, foreign investors are awarded citizenship. Such programs encourage innovation and entrepreneurship from foreign investors and high net worth individuals who as new citizens in the country can offer unique perspectives. St. Kitts and Nevis was the first country to offer economic citizenship back in 1984 creating a new market for citizenship and by the early 2000s other Caribbean countries joined them.


title: Immigration

text: A 2015 study finds "some evidence that larger immigrant population shares (or inflows) yield positive impacts on institutional quality. At a minimum, our results indicate that no negative impact on economic freedom is associated with more immigration." Another study, looking at the increase in Israel's population in the 1990s due to the unrestricted immigration of Jews from the Soviet Union, finds that the mass immigration did not undermine political institutions, and substantially increased the quality of economic institutions. A 2017 study in the "British Journal of Political Science" argued that the British American colonies without slavery adopted better democratic institutions in order to attract migrant workers to their colonies. A 2018 study fails to find evidence that immigration to the United States weakens economic freedom. A 2019 study of Jordan found that the massive influx of refugees into Jordan during the Gulf War had long-lasting positive effects on Jordanian economic institutions.


title: Immigration

text: Some research has found that as immigration and ethnic heterogeneity increase, government funding of welfare and public support for welfare decrease. Ethnic nepotism may be an explanation for this phenomenon. Other possible explanations include theories regarding in-group and out-group effects and reciprocal altruism.


title: Immigration

text: Research however also challenges the notion that ethnic heterogeneity reduces public goods provision. Studies that find a negative relationship between ethnic diversity and public goods provision often fail to take into account that strong states were better at assimilating minorities, thus decreasing diversity in the long run. Ethnically diverse states today consequently tend to be weaker states. Because most of the evidence on fractionalization comes from sub-Saharan Africa and the United States, the generalizability of the findings is questionable. A 2018 study in the "American Political Science Review" cast doubts on findings that ethnoracial homogeneity led to greater public goods provision.


title: Immigration

text: Research finds that Americans' attitudes towards immigration influence their attitudes towards welfare spending.


title: Immigration

text: A 2016 study found that immigration in the period 1940–2010 in the United States increased the high school completion of natives: "An increase of one percentage point in the share of immigrants in the population aged 11–64 increases the probability that natives aged 11–17 eventually complete 12 years of schooling by 0.3 percentage point." A 2019 NBER paper found little evidence that exposure to foreign-born students had an impact on US-born students.


title: Immigration

text: Studies have found that non-native speakers of English in the UK have no causal impact on the performance of other pupils, immigrant children have no significant impact on the test scores of Dutch children, no effect on grade repetition among native students exposed to migrant students in Austrian schools, that the presence of Latin American children in schools had no significant negative effects on peers, but that students with limited English skills had slight negative effects on peers, and that the influx of Haitians to Florida public schools after the 2010 Haiti earthquake had no effects on the educational outcomes of incumbent students.


title: Immigration

text: A 2018 study found that the "presence of immigrant students who have been in the country for some time is found to have no effect on natives. However, a small negative effect of recent immigrants on natives' language scores is reported." Another 2018 study found that the presence of immigrant students to Italy was associated with "small negative average effects on maths test scores that are larger for low ability native students, strongly non-linear and only observable in classes with a high (top 20%) immigrant concentration. These outcomes are driven by classes with a high average linguistic distance between immigrants and natives, with no apparent additional role played by ethnic diversity."


title: Immigration

text: A 2019 review of existing research in the "Annual Review of Sociology" on immigrant assimilation in the United States, the United Kingdom, France, Germany, Sweden, Norway, Belgium, the Netherlands and Spain concluded "we find an overall pattern of intergenerational assimilation in terms of socioeconomic attainment, social relations, and cultural beliefs."


title: Immigration

text: A 2018 study in the "American Sociological Review" found that within racial groups, most immigrants to the United States had fully assimilated within a span of 20 years. Immigrants arriving in the United States after 1994 assimilate more rapidly than immigrants who arrived in previous periods. Measuring assimilation can be difficult due to "ethnic attrition", which refers to when descendants of migrants cease to self-identify with the nationality or ethnicity of their ancestors. This means that successful cases of assimilation will be underestimated. Research shows that ethnic attrition is sizable in Hispanic and Asian immigrant groups in the United States. By taking account of ethnic attrition, the assimilation rate of Hispanics in the United States improves significantly. A 2016 paper challenges the view that cultural differences are necessarily an obstacle to long-run economic performance of migrants. It finds that "first generation migrants seem to be less likely to success the more culturally distant they are, but this effect vanishes as time spent in the US increases."


title: Immigration

text: A 2018 study found that Chinese nationals in the United States who received permanent residency permits from the US government amid the Tiananmen Square protests (and subsequent Chinese government clampdown) experienced significant employment and earnings gains relative to similar immigrant groups who did not have the same residency rights.


title: Immigration

text: During the Age of Mass Migration, infant arrivals to the United States had greater economic success over their lifetime than teenage arrivals.


title: Immigration

text: A 2015 report by the National Institute of Demographic Studies finds that an overwhelming majority of second-generation immigrants of all origins in France feel French, despite the persistent discrimination in education, housing and employment that many of the minorities face.


title: Immigration

text: Research shows that country of origin matters for speed and depth of immigrant assimilation but that there is considerable assimilation overall. Research finds that first generation immigrants from countries with less egalitarian gender cultures adopt gender values more similar to natives over time. According to one study, "this acculturation process is almost completed within one generational succession: The gender attitudes of second generation immigrants are difficult to distinguish from the attitudes of members of mainstream society. This holds also for children born to immigrants from very gender traditional cultures and for children born to less well integrated immigrant families." Similar results are found on a study of Turkish migrants to Western Europe. The assimilation on gender attitudes has been observed in education, as one study finds "that the female advantage in education observed among the majority population is usually present among second-generation immigrants."


title: Immigration

text: A 2017 study of Switzerland found that naturalization strongly improves long-term social integration of immigrants: "The integration returns to naturalization are larger for more marginalized immigrant groups and when naturalization occurs earlier, rather than later in the residency period." A separate study of Switzerland found that naturalization improved the economic integration of immigrants: "winning Swiss citizenship in the referendum increased annual earnings by an average of approximately 5,000 U.S. dollars over the subsequent 15 years. This effect is concentrated among more marginalized immigrants."


title: Immigration

text: First-generation immigrants tend to hold less accepting views of homosexuality but opposition weakens with longer stays. Second-generation immigrants are overall more accepting of homosexuality, but the acculturation effect is weaker for Muslims and to some extent, Eastern Orthodox migrants.


title: Immigration

text: A study of Bangladeshi migrants in East London found they shifted towards the thinking styles of the wider non-migrant population in just a single generation.


title: Immigration

text: A study on Germany found that foreign-born parents are more likely to integrate if their children are entitled to German citizenship at birth. A 2017 study found that "faster access to citizenship improves the economic situation of immigrant women, especially their labour market attachment with higher employment rates, longer working hours and more stable jobs. Immigrants also invest more in host country-specific skills like language and vocational training. Faster access to citizenship seems a powerful policy instrument to boost economic integration in countries with traditionally restrictive citizenship policies." Naturalization is associated with large and persistent wage gains for the naturalized citizens in most countries. One study of Denmark found that providing immigrants with voting rights reduced their crime rate.


title: Immigration

text: Studies on programs that randomly allocate refugee immigrants across municipalities find that the assignment of neighborhood impacts immigrant crime propensity, education and earnings. A 2019 study found that refugees who resettled in areas with many conationals were more likely to be economically integrated.


title: Immigration

text: Research suggests that bilingual schooling reduces barriers between speakers from two different communities.


title: Immigration

text: Research suggests that a vicious cycle of bigotry and isolation could reduce assimilation and increase bigotry towards immigrants in the long-term. For instance, University of California, San Diego political scientist Claire Adida, Stanford University political scientist David Laitin and Sorbonne University economist Marie-Anne Valfort argue "fear-based policies that target groups of people according to their religion or region of origin are counter-productive. Our own research, which explains the failed integration of Muslim immigrants in France, suggests that such policies can feed into a vicious cycle that damages national security. French Islamophobia—a response to cultural difference—has encouraged Muslim immigrants to withdraw from French society, which then feeds back into French Islamophobia, thus further exacerbating Muslims' alienation, and so on. Indeed, the failure of French security in 2015 was likely due to police tactics that intimidated rather than welcomed the children of immigrants—an approach that makes it hard to obtain crucial information from community members about potential threats."


title: Immigration

text: A study which examined Catalan nationalism examined the Catalan Government's policy towards the integration of immigrants during the start of the 1990s. At this time the Spanish region of Catalonia was experiencing a large influx in the number of immigrants from Northern Africa, Latin America and Asia. The Spanish government paid little attention to this influx of immigrants. However, Catalan politicians began discussing how the increase in immigrants would effect Catalan identity. Members of the Catalan parliament petitioned for a plan to integrate these immigrants into Catalan society. Crucially, the plan did not include policies regarding naturalisation, which were key immigration policies of the Spanish government. The plan of the Catalan parliament aimed to create a shared Catalan identity which included both the native Catalan population and immigrant communities. This meant that immigrants were encouraged to relate as part of the Catalan community but also encouraged to retain their own culture and traditions. In this way assimilation of immigrant cultures in Catalonia was avoided.


title: Immigration

text: A 2018 study in the "British Journal of Political Science" found that immigrants in Norway became more politically engaged the earlier that they were given voting rights.


title: Immigration

text: A 2019 study in the "European Economic Review" found that language training improved the economic assimilation of immigrants in France.


title: Immigration

text: A 2020 paper on reforms of refugee policy in Denmark found that language training boosted the economic and social integration of refugees, whereas cuts to refugees' welfare benefits had no impact, except to temporarily increase property crimes.


title: Immigration

text: There is some research that suggests that immigration adversely affects social capital. One study, for instance, found that "larger increases in US states' Mexican population shares correspond to larger decreases in social capital over the period" 1986–2004. A 2017 study in the "Journal of Comparative Economics" found that "individuals whose ancestors migrated from countries with higher autocracy levels are less likely to trust others and to vote in presidential elections in the U.S. The impact of autocratic culture on trust can last for at least three generations while the impact on voting disappears after one generation. These impacts on trust and voting are also significant across Europe." A 2019 study found that "humans are inclined to react negatively to threats to homogeneity... in the short term. However, these negative outcomes are compensated in the long term by the beneficial influence of intergroup contact, which alleviates initial negative influences."


title: Immigration

text: Research suggests that immigration has positive effects on native workers' health. As immigration rises, native workers are pushed into less demanding jobs, which improves native workers' health outcomes.


title: Immigration

text: A 2018 study found that immigration to the United Kingdom "reduced waiting times for outpatient referrals and did not have significant effects on waiting times in accident and emergency departments (A&E) and elective care." The study also found "evidence that immigration increased waiting times for outpatient referrals in more deprived areas outside of London" but that this increase disappears after 3 to 4 years.


title: Immigration

text: A 2018 systemic review and meta-analysis in "The Lancet" found that migrants generally have better health than the general population.


title: Immigration

text: In the EU, the use of personal health records for migrants is being tested in the new REHEALTH 2 project.


title: Immigration

text: A 2014 study of the United Kingdom found that immigration generally reduced local house prices in the areas they moved to, because natives at the top of the wage distribution respond to immigration by moving to other areas, reducing demand for housing. At the national level an increase in the number of immigrants has a positive effect on house prices.


title: Immigration

text: Bogus recruitment agencies and rogue recruitment agencies make fake promises of better opportunities, education, income, some of the abuses and crimes experienced by immigrants are the followed:


title: Immigration

text: In many countries there is a lack of prosecution of this crimes, since these countries obtain benefits and taxes paid by these companies that benefit the economies and also because of the current shortage of workers.


title: Immigration

text: Research suggests that police practices, such as racial profiling, over-policing in areas populated by minorities and in-group bias may result in disproportionately high numbers of racial minorities among crime suspects in Sweden, Italy, and England and Wales. Research also suggests that there may be possible discrimination by the judicial system, which contributes to a higher number of convictions for racial minorities in Sweden, the Netherlands, Italy, Germany, Denmark and France. A 2018 study found that the Dutch are less likely to reciprocate in games played with immigrants than the native Dutch.


title: Immigration

text: Several meta-analyses find extensive evidence of ethnic and racial discrimination in hiring in the North-American and European labor markets. A 2016 meta-analysis of 738 correspondence tests in 43 separate studies conducted in OECD countries between 1990 and 2015 finds that there is extensive racial discrimination in hiring decisions in Europe and North-America. Equivalent minority candidates need to send around 50% more applications to be invited for an interview than majority candidates.


title: Immigration

text: A 2014 meta-analysis found extensive evidence of racial and ethnic discrimination in the housing market of several European countries.


title: Immigration

text: Since 2010, the United Kingdom’s policies surrounding immigrant detention have come under fire for insufficiently protecting vulnerable groups. In the early 2000s, the United Kingdom adopted the Detention Duty Advice (DDA) scheme in order to provide free, government-funded, legal aid to immigrants. The DDA scheme at face value granted liberty on administrative grounds by considering immigrant merits, nature of their work, their financial means, and other factors that would then determine how much free legal aid detainees were granted. Recent research by the Organization for Economic Cooperation and Development (OECD), demonstrates that marginalized groups have been barred from legal assistance in detention centers. The barriers immigrants face in order to access justice through the DDA disproportionately impacted underrepresented groups of immigrants, and the language barrier and lack of interpreters led to further hurdles that detainees were unable to jump through.


title: Immigration

text: In Canada immigrant detainees face barriers to justice due to a lack of international enforcement. Canada’s immigration detention system has significant legal and normative problems, and the rubric of ‘access to justice’ that is presented by international law fails to identify these faults. There is a lack of access to legal aid for immigrants in detention, as well as inhumane treatment in detention centers. Research has demonstrated irreparable psychological, physical, and social damage to immigrants, and the international community ignores these injustices.


title: Immigration

text: A 2014 meta-analysis of racial discrimination in product markets found extensive evidence of minority applicants being quoted higher prices for products. A 1995 study found that car dealers "quoted significantly lower prices to white males than to black or female test buyers using identical, scripted bargaining strategies." A 2013 study found that eBay sellers of iPods received 21 percent more offers if a white hand held the iPod in the photo than a black hand.


title: Immigration

text: Research suggests that police practices, such as racial profiling, over-policing in areas populated by minorities and in-group bias may result in disproportionately high numbers of racial minorities among crime suspects. Research also suggests that there may be possible discrimination by the judicial system, which contributes to a higher number of convictions for racial minorities. A 2012 study found that "(i) juries formed from all-white jury pools convict black defendants significantly (16 percentage points) more often than white defendants, and (ii) this gap in conviction rates is entirely eliminated when the jury pool includes at least one black member." Research has found evidence of in-group bias, where "black (white) juveniles who are randomly assigned to black (white) judges are more likely to get incarcerated (as opposed to being placed on probation), and they receive longer sentences." In-group bias has also been observed when it comes to traffic citations, as black and white cops are more likely to cite out-groups.


title: Immigration

text: A 2015 study using correspondence tests "found that when considering requests from prospective students seeking mentoring in the future, faculty were significantly more responsive to White males than to all other categories of students, collectively, particularly in higher-paying disciplines and private institutions."


title: Immigration

text: According to an analysis of the National Study of College Experience, elite colleges may favor minority applicants due to affirmative action policies.


title: Immigration

text: A 2018 National Bureau of Economic Research paper found that math teachers discriminate against the children of immigrants. When the teachers were informed about negative stereotypes towards the children of immigrants, they gave higher grades to the children of immigrants.


title: Immigration

text: As of 2020, 2 percent of all students enrolled in U.S. higher education. That comes out to about 454,000 students. Fewer than half of the undocumented are eligible for the DACA program. DACA is formally known as Deferred Action for Childhood Arrivals.


title: Immigration

text: A 2014 meta-analysis found extensive evidence of racial discrimination in the American housing market. Minority applicants for housing needed to make many more enquiries to view properties. Geographical steering of African-Americans in US housing remained significant. A 2003 study finds "evidence that agents interpret an initial housing request as an indication of a customer's preferences, but also are more likely to withhold a house from all customers when it is in an integrated suburban neighborhood (redlining). Moreover, agents' marketing efforts increase with asking price for white, but not for black, customers; blacks are more likely than whites to see houses in suburban, integrated areas (steering); and the houses agents show are more likely to deviate from the initial request when the customer is black than when the customer is white. These three findings are consistent with the possibility that agents act upon the belief that some types of transactions are relatively unlikely for black customers (statistical discrimination)."


title: Immigration

text: A report by the federal Department of Housing and Urban Development where the department sent African-Americans and whites to look at apartments found that African-Americans were shown fewer apartments to rent and houses for sale.


title: Immigration

text: Several meta-analyses find extensive evidence of ethnic and racial discrimination in hiring in the American labor market. A 2016 meta-analysis of 738 correspondence tests—tests where identical CVs for stereotypically black and white names were sent to employers—in 43 separate studies conducted in OECD countries between 1990 and 2015 finds that there is extensive racial discrimination in hiring decisions in Europe and North-America. These correspondence tests showed that equivalent minority candidates need to send around 50% more applications to be invited for an interview than majority candidates. A study that examine the job applications of actual people provided with identical résumés and similar interview training showed that African-American applicants with no criminal record were offered jobs at a rate as low as white applicants who had criminal records.


title: Immigration

text: Remittances increase living standards in the country of origin. Remittances are a large share of the GDP of many developing countries. A study on remittances to Mexico found that remittances lead to a substantial increase in the availability of public services in Mexico, surpassing government spending in some localities.


title: Immigration

text: Research finds that emigration and low migration barriers has net positive effects on human capital formation in the sending countries. This means that there is a "brain gain" instead of a "brain drain" to emigration. Emigration has also been linked to innovation in cases where the migrants return to their home country after developing skills abroad.


title: Immigration

text: One study finds that sending countries benefit indirectly in the long-run on the emigration of skilled workers because those skilled workers are able to innovate more in developed countries, which the sending countries are able to benefit on as a positive externality. Greater emigration of skilled workers consequently leads to greater economic growth and welfare improvements in the long-run. The negative effects of high-skill emigration remain largely unfounded. According to economist Michael Clemens, it has not been shown that restrictions on high-skill emigration reduce shortages in the countries of origin.


title: Immigration

text: Research also suggests that emigration, remittances and return migration can have a positive impact on political institutions and democratization in the country of origin. According to Abel Escribà-Folch, Joseph Wright, and Covadonga Meseguer, remittances "provide resources that make political opposition possible, and they decrease government dependency, undermining the patronage strategies underpinning authoritarianism." Research also shows that remittances can lower the risk of civil war in the country of origin. Return migration from countries with liberal gender norms has been associated with the transfer of liberal gender norms to the home country.


title: Immigration

text: Research suggests that emigration causes an increase in the wages of those who remain in the country of origin. A 2014 survey of the existing literature on emigration finds that a 10 percent emigrant supply shock would increase wages in the sending country by 2–5.5%. A study of emigration from Poland shows that it led to a slight increase in wages for high- and medium-skilled workers for remaining Poles. A 2013 study finds that emigration from Eastern Europe after the 2004 EU enlargement increased the wages of remaining young workers in the country of origin by 6%, while it had no effect on the wages of old workers. The wages of Lithuanian men increased as a result of post-EU enlargement emigration. Return migration is associated with greater household firm revenues. Emigration leads to boosts in foreign direct investment to their home country.


title: Immigration

text: Some research shows that the remittance effect is not strong enough to make the remaining natives in countries with high emigration flows better off.


title: Glutamic acid

text: Glutamic acid (symbol Glu or E; the ionic form is known as glutamate) is an α-amino acid that is used by almost all living beings in the biosynthesis of proteins. It is a non-essential nutrient for humans, meaning that the human body can synthesize enough for its use. It is also the most abundant excitatory neurotransmitter in the vertebrate nervous system. It serves as the precursor for the synthesis of the inhibitory gamma-aminobutyric acid (GABA) in GABA-ergic neurons.


title: Glutamic acid

text: Its molecular formula is . Glutamic acid exists in three optically isomeric forms; the dextrorotatory -form is usually obtained by hydrolysis of gluten or from the waste waters of beet-sugar manufacture or by fermentation. Its molecular structure could be idealized as HOOC−CH()−()−COOH, with two carboxyl groups −COOH and one amino group −. However, in the solid state and mildly acidic water solutions, the molecule assumes an electrically neutral zwitterion structure OOC−CH()−()−COOH. It is encoded by the codons GAA or GAG.


title: Glutamic acid

text: The acid can lose one proton from its second carboxyl group to form the conjugate base, the singly-negative anion glutamate OOC−CH()−()−COO. This form of the compound is prevalent in neutral solutions. The glutamate neurotransmitter plays the principal role in neural activation. This anion creates the savory "umami" flavor of foods and is found in glutamate flavorings such as MSG. In Europe it is classified as food additive E620. In highly alkaline solutions the doubly negative anion OOC−CH()−()−COO prevails. The radical corresponding to glutamate is called glutamyl.


title: Glutamic acid

text: When glutamic acid is dissolved in water, the amino group (−) may gain a proton (), and/or the carboxyl groups may lose protons, depending on the acidity of the medium.


title: Glutamic acid

text: In sufficiently acidic environments, the amino group gains a proton and the molecule becomes a cation with a single positive charge, HOOC−CH()−()−COOH.


title: Glutamic acid

text: At pH values between about 2.5 and 4.1, the carboxylic acid closer to the amine generally loses a proton, and the acid becomes the neutral zwitterion OOC−CH()−()−COOH. This is also the form of the compound in the crystalline solid state. The change in protonation state is gradual; the two forms are in equal concentrations at pH 2.10.


title: Glutamic acid

text: At even higher pH, the other carboxylic acid group loses its proton and the acid exists almost entirely as the glutamate anion OOC−CH()−()−COO, with a single negative charge overall. The change in protonation state occurs at pH 4.07. This form with both carboxylates lacking protons is dominant in the physiological pH range (7.35–7.45).


title: Glutamic acid

text: At even higher pH, the amino group loses the extra proton, and the prevalent species is the doubly-negative anion OOC−CH()−()−COO. The change in protonation state occurs at pH 9.47.


title: Glutamic acid

text: The carbon atom adjacent to the amino group is chiral (connected to four distinct groups). Glutamic acid can exist in three optical isomers, including the dextrorotatory -form, (−), and (+). The form is the one most widely occurring in nature, but the form occurs in some special contexts, such as the bacterial capsule and cell walls of the bacteria (which can manufacture it from the form with the enzyme glutamate racemase) and the liver of mammals.


title: Glutamic acid

text: Although they occur naturally in many foods, the flavor contributions made by glutamic acid and other amino acids were only scientifically identified early in the 20th century. The substance was discovered and identified in the year 1866 by the German chemist Karl Heinrich Ritthausen, who treated wheat gluten (for which it was named) with sulfuric acid. In 1908, Japanese researcher Kikunae Ikeda of the Tokyo Imperial University identified brown crystals left behind after the evaporation of a large amount of kombu broth as glutamic acid. These crystals, when tasted, reproduced the ineffable but undeniable flavor he detected in many foods, most especially in seaweed. Professor Ikeda termed this flavor umami. He then patented a method of mass-producing a crystalline salt of glutamic acid, monosodium glutamate.


title: Glutamic acid

text: Glutamic acid is produced on the largest scale of any amino acid, with an estimated annual production of about 1.5 million tons in 2006. Chemical synthesis was supplanted by the aerobic fermentation of sugars and ammonia in the 1950s, with the organism "Corynebacterium glutamicum" (also known as "Brevibacterium flavum") being the most widely used for production. Isolation and purification can be achieved by concentration and crystallization; it is also widely available as its hydrochloride salt.


title: Glutamic acid

text: Glutamate is a key compound in cellular metabolism. In humans, dietary proteins are broken down by digestion into amino acids, which serve as metabolic fuel for other functional roles in the body. A key process in amino acid degradation is transamination, in which the amino group of an amino acid is transferred to an α-ketoacid, typically catalysed by a transaminase. The reaction can be generalised as such:


title: Glutamic acid

text: A very common α-keto acid is α-ketoglutarate, an intermediate in the citric acid cycle. Transamination of α-ketoglutarate gives glutamate. The resulting α-ketoacid product is often a useful one as well, which can contribute as fuel or as a substrate for further metabolism processes. Examples are as follows:


title: Glutamic acid

text: Both pyruvate and oxaloacetate are key components of cellular metabolism, contributing as substrates or intermediates in fundamental processes such as glycolysis, gluconeogenesis, and the citric acid cycle.


title: Glutamic acid

text: Glutamate also plays an important role in the body's disposal of excess or waste nitrogen. Glutamate undergoes deamination, an oxidative reaction catalysed by glutamate dehydrogenase, as follows:


title: Glutamic acid

text: Ammonia (as ammonium) is then excreted predominantly as urea, synthesised in the liver. Transamination can thus be linked to deamination, effectively allowing nitrogen from the amine groups of amino acids to be removed, via glutamate as an intermediate, and finally excreted from the body in the form of urea.


title: Glutamic acid

text: Glutamate is also a neurotransmitter (see below), which makes it one of the most abundant molecules in the brain. Malignant brain tumors known as glioma or glioblastoma exploit this phenomenon by using glutamate as an energy source, especially when these tumors become more dependent on glutamate due to mutations in the gene IDH1.


title: Glutamic acid

text: Glutamate is the most abundant excitatory neurotransmitter in the vertebrate nervous system. At chemical synapses, glutamate is stored in vesicles. Nerve impulses trigger the release of glutamate from the presynaptic cell. Glutamate acts on ionotropic and metabotropic (G-protein coupled) receptors. In the opposing postsynaptic cell, glutamate receptors, such as the NMDA receptor or the AMPA receptor, bind glutamate and are activated. Because of its role in synaptic plasticity, glutamate is involved in cognitive functions such as learning and memory in the brain. The form of plasticity known as long-term potentiation takes place at glutamatergic synapses in the hippocampus, neocortex, and other parts of the brain. Glutamate works not only as a point-to-point transmitter, but also through spill-over synaptic crosstalk between synapses in which summation of glutamate released from a neighboring synapse creates extrasynaptic signaling/volume transmission. In addition, glutamate plays important roles in the regulation of growth cones and synaptogenesis during brain development as originally described by Mark Mattson.


title: Glutamic acid

text: Extracellular glutamate in "Drosophila" brains has been found to regulate postsynaptic glutamate receptor clustering, via a process involving receptor desensitization. A gene expressed in glial cells actively transports glutamate into the extracellular space, while, in the nucleus accumbens-stimulating group II metabotropic glutamate receptors, this gene was found to reduce extracellular glutamate levels. This raises the possibility that this extracellular glutamate plays an "endocrine-like" role as part of a larger homeostatic system.


title: Glutamic acid

text: Glutamate also serves as the precursor for the synthesis of the inhibitory gamma-aminobutyric acid (GABA) in GABA-ergic neurons. This reaction is catalyzed by glutamate decarboxylase (GAD), which is most abundant in the cerebellum and pancreas.


title: Glutamic acid

text: Stiff person syndrome is a neurologic disorder caused by anti-GAD antibodies, leading to a decrease in GABA synthesis and, therefore, impaired motor function such as muscle stiffness and spasm. Since the pancreas has abundant GAD, a direct immunological destruction occurs in the pancreas and the patients will have diabetes mellitus.


title: Glutamic acid

text: Glutamic acid, being a constituent of protein, is present in foods that contain protein, but it can only be tasted when it is present in an unbound form. Significant amounts of free glutamic acid are present in a wide variety of foods, including cheeses and soy sauce, and glutamic acid is responsible for umami, one of the five basic tastes of the human sense of taste. Glutamic acid often is used as a food additive and flavor enhancer in the form of its sodium salt, known as monosodium glutamate (MSG).


title: Glutamic acid

text: All meats, poultry, fish, eggs, dairy products, and kombu are excellent sources of glutamic acid. Some protein-rich plant foods also serve as sources. 30% to 35% of gluten (much of the protein in wheat) is glutamic acid. Ninety-five percent of the dietary glutamate is metabolized by intestinal cells in a first pass.


title: Glutamic acid

text: In recent years, there has been much research into the use of residual dipolar coupling (RDC) in nuclear magnetic resonance spectroscopy (NMR). A glutamic acid derivative, poly-γ-benzyl-L-glutamate (PBLG), is often used as an alignment medium to control the scale of the dipolar interactions observed.


title: Glutamic acid

text: The drug phencyclidine (more commonly known as PCP or 'Angel Dust') antagonizes glutamic acid non-competitively at the NMDA receptor. For the same reasons, dextromethorphan and ketamine also have strong dissociative and hallucinogenic effects. Acute infusion of the drug LY354740 (also known as eglumegad, an agonist of the metabotropic glutamate receptors 2 and 3) resulted in a marked diminution of yohimbine-induced stress response in bonnet macaques (Macaca radiata); chronic oral administration of LY354740 in those animals led to markedly reduced baseline cortisol levels (approximately 50 percent) in comparison to untreated control subjects. LY354740 has also been demonstrated to act on the metabotropic glutamate receptor 3 (GRM3) of human adrenocortical cells, downregulating aldosterone synthase, CYP11B1, and the production of adrenal steroids (i.e. aldosterone and cortisol). Glutamate does not easily pass the blood brain barrier, but, instead, is transported by a high-affinity transport system. It can also be converted into glutamine.


title: Cubic equation

text: The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the coefficients , , , and of the cubic equation are real numbers, then it has at least one real root (this is true for all odd-degree polynomial functions). All of the roots of the cubic equation can be found by the following means:


title: Cubic equation

text: The coefficients do not need to be real numbers. Much of what is covered below is valid for coefficients in any field with characteristic other than 2 and 3. The solutions of the cubic equation do not necessarily belong to the same field as the coefficients. For example, some cubic equations with rational coefficients have roots that are irrational (and even non-real) complex numbers.


title: Cubic equation

text: Cubic equations were known to the ancient Babylonians, Greeks, Chinese, Indians, and Egyptians. Babylonian (20th to 16th centuries BC) cuneiform tablets have been found with tables for calculating cubes and cube roots. The Babylonians could have used the tables to solve cubic equations, but no evidence exists to confirm that they did. The problem of doubling the cube involves the simplest and oldest studied cubic equation, and one for which the ancient Egyptians did not believe a solution existed. In the 5th century BC, Hippocrates reduced this problem to that of finding two mean proportionals between one line and another of twice its length, but could not solve this with a compass and straightedge construction, a task which is now known to be impossible. Methods for solving cubic equations appear in "The Nine Chapters on the Mathematical Art", a Chinese mathematical text compiled around the 2nd century BC and commented on by Liu Hui in the 3rd century. In the 3rd century AD, the Greek mathematician Diophantus found integer or rational solutions for some bivariate cubic equations (Diophantine equations). Hippocrates, Menaechmus and Archimedes are believed to have come close to solving the problem of doubling the cube using intersecting conic sections, though historians such as Reviel Netz dispute whether the Greeks were thinking about cubic equations or just problems that can lead to cubic equations. Some others like T. L. Heath, who translated all of Archimedes' works, disagree, putting forward evidence that Archimedes really solved cubic equations using intersections of two conics, but also discussed the conditions where the roots are 0, 1 or 2.


title: Cubic equation

text: In the 7th century, the Tang dynasty astronomer mathematician Wang Xiaotong in his mathematical treatise titled Jigu Suanjing systematically established and solved numerically 25 cubic equations of the form , 23 of them with , and two of them with .


title: Cubic equation

text: In the 11th century, the Persian poet-mathematician, Omar Khayyam (1048–1131), made significant progress in the theory of cubic equations. In an early paper, he discovered that a cubic equation can have more than one solution and stated that it cannot be solved using compass and straightedge constructions. He also found a geometric solution. In his later work, the "Treatise on Demonstration of Problems of Algebra", he wrote a complete classification of cubic equations with general geometric solutions found by means of intersecting conic sections.


title: Cubic equation

text: In the 12th century, the Indian mathematician Bhaskara II attempted the solution of cubic equations without general success. However, he gave one example of a cubic equation: . In the 12th century, another Persian mathematician, Sharaf al-Dīn al-Tūsī (1135–1213), wrote the "Al-Muʿādalāt" ("Treatise on Equations"), which dealt with eight types of cubic equations with positive solutions and five types of cubic equations which may not have positive solutions. He used what would later be known as the "Ruffini-Horner method" to numerically approximate the root of a cubic equation. He also used the concepts of maxima and minima of curves in order to solve cubic equations which may not have positive solutions. He understood the importance of the discriminant of the cubic equation to find algebraic solutions to certain types of cubic equations.


title: Cubic equation

text: In his book "Flos", Leonardo de Pisa, also known as Fibonacci (1170–1250), was able to closely approximate the positive solution to the cubic equation . Writing in Babylonian numerals he gave the result as 1,22,7,42,33,4,40 (equivalent to 1 + 22/60 + 7/60 + 42/60 + 33/60 + 4/60 + 40/60), which has a relative error of about 10.


title: Cubic equation

text: In the early 16th century, the Italian mathematician Scipione del Ferro (1465–1526) found a method for solving a class of cubic equations, namely those of the form . In fact, all cubic equations can be reduced to this form if one allows and to be negative, but negative numbers were not known to him at that time. Del Ferro kept his achievement secret until just before his death, when he told his student Antonio Fior about it.


title: Cubic equation

text: In 1535, Niccolò Tartaglia (1500–1557) received two problems in cubic equations from Zuanne da Coi and announced that he could solve them. He was soon challenged by Fior, which led to a famous contest between the two. Each contestant had to put up a certain amount of money and to propose a number of problems for his rival to solve. Whoever solved more problems within 30 days would get all the money. Tartaglia received questions in the form , for which he had worked out a general method. Fior received questions in the form , which proved to be too difficult for him to solve, and Tartaglia won the contest.


title: Cubic equation

text: Later, Tartaglia was persuaded by Gerolamo Cardano (1501–1576) to reveal his secret for solving cubic equations. In 1539, Tartaglia did so only on the condition that Cardano would never reveal it and that if he did write a book about cubics, he would give Tartaglia time to publish. Some years later, Cardano learned about del Ferro's prior work and published del Ferro's method in his book "Ars Magna" in 1545, meaning Cardano gave Tartaglia six years to publish his results (with credit given to Tartaglia for an independent solution). Cardano's promise to Tartaglia said that he would not publish Tartaglia's work, and Cardano felt he was publishing del Ferro's, so as to get around the promise. Nevertheless, this led to a challenge to Cardano from Tartaglia, which Cardano denied. The challenge was eventually accepted by Cardano's student Lodovico Ferrari (1522–1565). Ferrari did better than Tartaglia in the competition, and Tartaglia lost both his prestige and his income.


title: Cubic equation

text: Cardano noticed that Tartaglia's method sometimes required him to extract the square root of a negative number. He even included a calculation with these complex numbers in "Ars Magna", but he did not really understand it. Rafael Bombelli studied this issue in detail and is therefore often considered as the discoverer of complex numbers.


title: Cubic equation

text: François Viète (1540–1603) independently derived the trigonometric solution for the cubic with three real roots, and René Descartes (1596–1650) extended the work of Viète.


title: Cubic equation

text: If the coefficients of a cubic equation are rational numbers, one can obtain an equivalent equation with integer coefficients, by multiplying all coefficients by a common multiple of their denominators. Such an equation


title: Cubic equation

text: with integer coefficients, is said to be reducible if the polynomial on the left-hand side is the product of polynomials of lower degrees. By Gauss's lemma, if the equation is reducible, one can suppose that the factors have integer coefficients.


title: Cubic equation

text: Finding the roots of a reducible cubic equation is easier than solving the general case. In fact, if the equation is reducible, one of the factors must have degree one, and thus have the form


title: Cubic equation

text: with and being coprime integers. The rational root test allows finding and by examining a finite number of cases (because must be a divisor of , and must be a divisor of ).


title: Cubic equation

text: Thus, one root is formula_4 and the other roots are the roots of the other factor, which can be found by polynomial long division. This other factor is


title: Cubic equation

text: Then, the other roots are the roots of this quadratic polynomial and can be found by using the quadratic formula.


title: Cubic equation

text: are said to be depressed. They are much simpler than general cubics, but are fundamental, because the study of any cubic may be reduced by a simple change of variable to that of a depressed cubic.


title: Cubic equation

text: The roots formula_11 of the original equation are related to the roots formula_12 of the depressed equation by the relations


title: Cubic equation

text: The nature (real or not, distinct or not) of the roots of a cubic can be determined without computing them explicitly, by using the discriminant.


title: Cubic equation

text: The discriminant of a polynomial is a function of its coefficients that is zero if and only if the polynomial has a multiple root, or, if it is divisible by the square of a non-constant polynomial. In other words, the discriminant is nonzero if and only if the polynomial is square-free.


title: Cubic equation

text: If are the three roots (not necessarily distinct nor real) of the cubic formula_15 then the discriminant is


title: Cubic equation

text: It is the product of formula_21 and the discriminant of the corresponding depressed cubic. Using the formula relating the general cubic and the associated depressed cubic, this implies that the discriminant of the general cubic can be written as


title: Cubic equation

text: It follows that one of these two discriminants is zero if and only if the other is also zero, and, if the coefficients are real, the two discriminants have the same sign. In summary, the same information can be deduced from either one of these two discriminants.


title: Cubic equation

text: To prove the preceding formulas, one can use Vieta's formulas to express everything as polynomials in , and . The proof then results in the verification of the equality of two polynomials.


title: Cubic equation

text: If the coefficients of a polynomial are real numbers, and its discriminant formula_23 is not zero, there are two cases:


title: Cubic equation

text: This can be proved as follows. First, if is a root of a polynomial with real coefficients, then its complex conjugate is also a root. So the non-real roots, if any, occur as pairs of complex conjugate roots. As a cubic polynomial has three roots (not necessarily distinct) by the fundamental theorem of algebra, at least one root must be real.


title: Cubic equation

text: If the three roots are real and distinct, the discriminant is a product of positive reals, that is formula_28


title: Cubic equation

text: If only one root, say , is real, then and are complex conjugates, which implies that is a purely imaginary number, and thus that is real and negative. On the other hand, and are complex conjugates, and their product is real and positive. Thus the discriminant is the product of a single negative number and several positive ones. That is formula_29


title: Cubic equation

text: If the discriminant of a cubic is zero, the cubic has a multiple root. If furthermore its coefficients are real, then all of its roots are real.


title: Cubic equation

text: The discriminant of the depressed cubic formula_30 is zero if formula_31 If is also zero, then , and 0 is a triple root of the cubic. If formula_32 and , then the cubic has a simple root


title: Cubic equation

text: This result can be proved by expanding the latter product or retrieved by solving the rather simple system of equations resulting from Vieta's formulas.


title: Cubic equation

text: By using the reduction of a depressed cubic, these results can be extended to the general cubic. This gives: If the discriminant of the cubic formula_36 is zero, then


title: Cubic equation

text: The above results are valid when the coefficients belong to a field of characteristic other than 2 or 3, but must be modified for characteristic 2 or 3, because of the involved divisions by 2 and 3.


title: Cubic equation

text: The reduction to a depressed cubic works for characteristic 2, but not for characteristic 3. However, in both cases, it is simpler to establish and state the results for the general cubic. The main tool for that is the fact that a multiple root is a common root of the polynomial and its formal derivative. In these characteristics, if the derivative is not a constant, it is a linear polynomial in characteristic 3, and is the square of a linear polynomial in characteristic 2. Therefore, for either characteristic 2 or 3, the derivative has only one root. This allows computing the multiple root, and the third root can be deduced from the sum of the roots, which is provided by Vieta's formulas.


title: Cubic equation

text: A difference with other characteristics is that, in characteristic 2, the formula for a double root involves a square root, and, in characteristic 3, the formula for a triple root involves a cube root.


title: Cubic equation

text: Gerolamo Cardano is credited with publishing the first formula for solving cubic equations, attributing it to Scipione del Ferro and Niccolo Fontana Tartaglia. The formula applies to depressed cubics, but, as shown in , it allows solving all cubic equations.


title: Cubic equation

text: is a cubic equation such that and are real numbers such that formula_45 is positive, then the equation has the real root


title: Cubic equation

text: As shown in , the two other roots are non-real complex conjugate numbers, in this case. It was later shown (Cardano did not know complex numbers) that the two other roots are obtained by multiplying one of the cube roots by the primitive cube root of unity formula_51 and the other cube root by the other primutive cube root of the unity formula_52 That is, the other roots of the equation are formula_53 and formula_54


title: Cubic equation

text: If formula_55 there are three real roots, but Galois theory allows proving that, if there is no rational root, the roots cannot be expressed by an algebraic expression involving only real numbers. Therefore, the equation cannot be solved in this case with the knowledge of Cardano's time. This case has thus been called "casus irreducibilis", meaning "irreducible case" in Latin.


title: Cubic equation

text: In "casus irreducibilis", Cardano's formula can still be used, but some care is needed in the use of cube roots. A first method is to define the symbols formula_56 and formula_57 as representing the principal values of the root function (that is the root that has the largest real part). With this convention Cardano's formula for the three roots remains valid, but is not purely algebraic, as the definition of a principal part is not purely algebraic, since it involves inequalities for comparing real parts. Also, the use of principal cube root may give a wrong result if the coefficients are non-real complex numbers. Moreover, if the coefficients belong to another field, the principal cube root is not defined in general.


title: Cubic equation

text: The second way for making Cardano's formula always correct, is to remark that the product of the two cube roots must be . It results that a root of the equation is


title: Cubic equation

text: In this formula, the symbols formula_56 and formula_57 denote any square root and any cube root. The other roots of the equation are obtained either by changing of cube root or, equivalently, by multiplying the cube root by a primitive cube root of unity, that is formula_61


title: Cubic equation

text: This formula for the roots is always correct except when , with the proviso that if , the square root is chosen so that . However, the formula is useless in these cases as the roots can be expressed without any cube root. Similarly, the formula is also useless in the other cases where no cube root is needed, that is when formula_62 and when the cubic polynomial is not irreducible.


title: Cubic equation

text: can be deduced from every variant of Cardano's formula by reduction to a depressed cubic. The variant that is presented here is valid not only for real coefficients, but also for coefficients belonging to any field of characteristic different of 2 and 3.


title: Cubic equation

text: where the symbols formula_56 and formula_57 are interpreted as "any" square root and "any" cube root, respectively (every nonzero complex number has two square roots and three cubic roots). The sign "" before the square root is either "" or ""; the choice is almost arbitrary, and changing it amounts to choosing a different square root. However, if a choice yields (this occurs if formula_72), then the other sign must be selected instead. If both choices yield , that is, if formula_73 a fraction occurs in following formulas; this fraction must be interpreted as equal to zero (see the end of this section).


title: Cubic equation

text: The other two roots can be obtained by changing the choice of the cube root in the definition of , or, equivalently by multiplying by a primitive cube root of unity, that is . In other words, the three roots are


title: Cubic equation

text: As for the special case of a depressed cubic, this formula applies but is useless when the roots can be expressed without cube roots. In particular, if formula_73 the formula gives that the three roots equal formula_77 which means that the cubic polynomial can be factored as formula_78 A straightforward computation allows verifying that the existence of this factorization is equivalent with formula_79


title: Cubic equation

text: When a cubic equation with real coefficients has three real roots, the formulas expressing these roots in terms of radicals involve complex numbers. Galois theory allows proving that when the three roots are real, and none is rational ("casus irreducibilis"), one cannot express the roots in terms of real radicals. Nevertheless, purely real expressions of the solutions may be obtained using trigonometric functions, specifically in terms of cosines and arccosines. More precisely, the roots of the depressed cubic


title: Cubic equation

text: This formula is due to François Viète. It is purely real when the equation has three real roots (that is formula_82). Otherwise, it is still correct but involves complex cosines and arccosines when there is only one real root, and it is nonsensical (division by zero) when .


title: Cubic equation

text: This formula can be straightforwardly transformed into a formula for the roots of a general cubic equation, using the back-substitution described in .


title: Cubic equation

text: The formula can be proved as follows: Starting from the equation , let us set The idea is to choose to make the equation coincide with the identity


title: Cubic equation

text: When there is only one real root (and ), this root can be similarly represented using hyperbolic functions, as


title: Cubic equation

text: If and the inequalities on the right are not satisfied (the case of three real roots), the formulas remain valid but involve complex quantities.


title: Cubic equation

text: When , the above values of are sometimes called the Chebyshev cube root. More precisely, the values involving cosines and hyperbolic cosines define, when , the same analytic function denoted , which is the proper Chebyshev cube root. The value involving hyperbolic sines is similarly denoted , when .


title: Cubic equation

text: For solving the cubic equation where , Omar Khayyám constructed the parabola , the circle that has as a diameter the line segment on the positive -axis, and a vertical line through the point where the circle and the parabola intersect above the -axis. The solution is given by the length of the horizontal line segment from the origin to the intersection of the vertical line and the -axis (see the figure).


title: Cubic equation

text: The left-hand side is the value of on the parabola. The equation of the circle being , the right hand side is the value of on the circle.


title: Cubic equation

text: A cubic equation with real coefficients can be solved geometrically using compass, straightedge, and an angle trisector if and only if it has three real roots.


title: Cubic equation

text: A cubic equation can be solved by compass-and-straightedge construction (without trisector) if and only if it has a rational root. This implies that the old problems of angle trisection and doubling the cube, set by ancient Greek mathematicians, cannot be solved by compass-and-straightedge construction.


title: Cubic equation

text: Viète's trigonometric expression of the roots in the three-real-roots case lends itself to a geometric interpretation in terms of a circle. When the cubic is written in depressed form (), , as shown above, the solution can be expressed as


title: Cubic equation

text: Here formula_92 is an angle in the unit circle; taking of that angle corresponds to taking a cube root of a complex number; adding for finds the other cube roots; and multiplying the cosines of these resulting angles by formula_93 corrects for scale.


title: Cubic equation

text: For the non-depressed case () (shown in the accompanying graph), the depressed case as indicated previously is obtained by defining such that so . Graphically this corresponds to simply shifting the graph horizontally when changing between the variables and , without changing the angle relationships. This shift moves the point of inflection and the centre of the circle onto the -axis. Consequently, the roots of the equation in sum to zero.


title: Cubic equation

text: When the graph of a cubic function is plotted in the Cartesian plane, if there is only one real root, it is the abscissa (-coordinate) of the horizontal intercept of the curve (point R on the figure). Further, if the complex conjugate roots are written as , then the real part is the abscissa of the tangency point H of the tangent line to cubic that passes through -intercept R of the cubic (that is the signed length RM, negative on the figure). The imaginary parts are the square roots of the tangent of the angle between this tangent line and the horizontal axis.


title: Cubic equation

text: With one real and two complex roots, the three roots can be represented as points in the complex plane, as can the two roots of the cubic's derivative. There is an interesting geometrical relationship among all these roots.


title: Cubic equation

text: The points in the complex plane representing the three roots serve as the vertices of an isosceles triangle. (The triangle is isosceles because one root is on the horizontal (real) axis and the other two roots, being complex conjugates, appear symmetrically above and below the real axis.) Marden's theorem says that the points representing the roots of the derivative of the cubic are the foci of the Steiner inellipse of the triangle—the unique ellipse that is tangent to the triangle at the midpoints of its sides. If the angle at the vertex on the real axis is less than then the major axis of the ellipse lies on the real axis, as do its foci and hence the roots of the derivative. If that angle is greater than , the major axis is vertical and its foci, the roots of the derivative, are complex conjugates. And if that angle is , the triangle is equilateral, the Steiner inellipse is simply the triangle's incircle, its foci coincide with each other at the incenter, which lies on the real axis, and hence the derivative has duplicate real roots.


title: Cubic equation

text: Given a cubic irreducible polynomial over a field of characteristic different from 2 and 3, the Galois group over is the group of the field automorphisms that fix of the smallest extension of (splitting field). As these automorphisms must permute the roots of the polynomials, this group is either the group of all six permutations of the three roots, or the group of the three circular permutations.


title: Cubic equation

text: where is the leading coefficient of the cubic, and , and are the three roots of the cubic. As formula_95 changes of sign if two roots are exchanged, formula_95 is fixed by the Galois group only if the Galois group is


title: Cubic equation

text: . In other words, the Galois group is if and only if the discriminant is the square of an element of .


title: Cubic equation

text: As most integers are not squares, when working over the field of the rational numbers, the Galois group of most irreducible cubic polynomials is the group with six elements. An example of a Galois group with three elements is given by , whose discriminant is .


title: Cubic equation

text: This method is due to Scipione del Ferro and Tartaglia, but is named after Gerolamo Cardano who first published it in his book "Ars Magna" (1545).


title: Cubic equation

text: This method applies to a depressed cubic . The idea is to introduce two variables and such that and to substitute this in the depressed cubic, giving


title: Cubic equation

text: At this point Cardano imposed the condition . This removes the third term in previous equality, leading to the system of equations


title: Cubic equation

text: Knowing the sum and the product of and , one deduces that they are the two solutions of the quadratic equation


title: Cubic equation

text: The discriminant of this equation is formula_101, and assuming it is positive, real solutions to this equations are (after folding division by 4 under the square root):


title: Cubic equation

text: This works well when formula_106 but, if formula_55 the square root appearing in the formula is not real. As a complex number has three cube roots, using Cardano's formula without care would provide nine roots, while a cubic equation cannot have more than three roots. This was clarified first by Rafael Bombelli in his book "L'Algebra" (1572). The solution is to use the fact that , that is . This means that only one cube root needs to be computed, and leads to the second formula given in .


title: Cubic equation

text: The other roots of the equation can be obtained by changing of cube root, or, equivalently, by multiplying the cube root by each of the two primitive cube roots of unity, which are formula_108


title: Cubic equation

text: Vieta's substitution is a method introduced by François Viète (Vieta is his Latin name) in a text published posthumously in 1615, which provides directly the second formula of , and avoids the problem of computing two different cube roots.


title: Cubic equation

text: be any nonzero root of this quadratic equation. If , and are the three cube roots of , then the roots of the original depressed cubic are , , and . The other root of the quadratic equation is formula_112 This implies that changing the sign of the square root exchanges and for , and therefore does not change the roots. This method only fails when both roots of the quadratic equation are zero, that is when , in which case the only root of the depressed cubic is .


title: Cubic equation

text: In his paper "Réflexions sur la résolution algébrique des équations" ("Thoughts on the algebraic solving of equations"), Joseph Louis Lagrange introduced a new method to solve equations of low degree in a uniform way, with the hope that he could generalize it for higher degrees. This method works well for cubic and quartic equations, but Lagrange did not succeed in applying it to a quintic equation, because it requires solving a resolvent polynomial of degree at least six.


title: Cubic equation

text: Except that nobody succeeded before to solve the problem, this was the first indication of the non-existence of an algebraic formula for degrees 5 and higher; this was later proved as the Abel–Ruffini theorem. Nevertheless, the modern methods for solving solvable quintic equations are mainly based on Lagrange's method.


title: Cubic equation

text: In the case of cubic equations, Lagrange's method gives the same solution as Cardano's. Lagrange's method can be applied directly to the general cubic equation , but the computation is simpler with the depressed cubic equation, .


title: Cubic equation

text: Lagrange's main idea was to work with the discrete Fourier transform of the roots instead of with the roots themselves. More precisely, let be a primitive third root of unity, that is a number such that and (when working in the space of complex numbers, one has formula_113 but this complex interpretation is not used here). Denoting , and the three roots of the cubic equation to be solved, let


title: Cubic equation

text: be the discrete Fourier transform of the roots. If , and are known, the roots may be recovered from them with the inverse Fourier transform consisting of inverting this linear transformation; that is,


title: Cubic equation

text: By Vieta's formulas, is known to be zero in the case of a depressed cubic, and for the general cubic. So, only and need to be computed. They are not symmetric functions of the roots (exchanging and exchanges also and ), but some simple symmetric functions of and are also symmetric in the roots of the cubic equation to be solved. Thus these symmetric functions can be expressed in terms of the (known) coefficients of the original cubic, and this allows eventually expressing the as roots of a polynomial with known coefficients. This works well for every degree, but, in degrees higher than four, the resulting polynomial that has the as roots has a degree higher than that of the initial polynomial, and is therefore unhelpful for solving. This is the reason for which Lagrange's method fails in degrees five and higher.


title: Cubic equation

text: In the case of a cubic equation, formula_116 and formula_117 are such symmetric polynomials (see below). It follows that formula_118 and formula_119 are the two roots of the quadratic equation formula_120 Thus the resolution of the equation may be finished exactly as with Cardano's method, with formula_121 and formula_122 in place of and .


title: Cubic equation

text: In the case of the depressed cubic, one has formula_123 and formula_124 while in Cardano's method we have set formula_125 and formula_126 Thus, up to the exchange of and , we have formula_127 and formula_128 In other words, in this case, Cardano's method and Lagrange's method compute exactly the same things, up to a factor of three in the auxiliary variables, the main difference being that Lagrange's method explains why these auxiliary variables appear in the problem.


title: Cubic equation

text: This shows that and are symmetric functions of the roots. Using Newton's identities, it is straightforward to express them in terms of the elementary symmetric functions of the roots, giving


title: At the Mountains of Madness

text: At the Mountains of Madness is a science fiction-horror novella by American author H. P. Lovecraft, written in February/March 1931 and rejected that year by "Weird Tales" editor Farnsworth Wright on the grounds of its length. It was originally serialized in the February, March, and April 1936 issues of "Astounding Stories". It has been reproduced in numerous collections.


title: At the Mountains of Madness

text: The story details the events of a disastrous expedition to Antarctica in September 1930, and what is found there by a group of explorers led by the narrator, Dr. William Dyer of Miskatonic University. Throughout the story, Dyer details a series of previously untold events in the hope of deterring another group of explorers who wish to return to the continent. These events include the discovery of an ancient civilization older than the human race, and realization of Earth's past told through various sculptures and murals.


title: At the Mountains of Madness

text: The story was inspired by Lovecraft's interest in Antarctic exploration; the continent was still not fully explored in the 1930s. Lovecraft explicitly draws from Edgar Allan Poe's novel "The Narrative of Arthur Gordon Pym of Nantucket", and he may have used other stories for inspiration. Many story elements, such as the formless "shoggoth," recur in other Lovecraft works. The story has been adapted and used for graphic novels, video games, and musical works.


title: At the Mountains of Madness

text: The story is narrated in a first-person perspective by the geologist William Dyer, a professor at Arkham's Miskatonic University, in the hope to prevent an important and much publicized scientific expedition to Antarctica. Throughout the course of his explanation, Dyer relates how he led a group of scholars from Miskatonic University on a previous expedition to Antarctica, during which they discovered ancient ruins and a dangerous secret beyond a range of mountains higher than the Himalayas.


title: At the Mountains of Madness

text: A small advance group, led by Professor Lake, discovers the remains of fourteen prehistoric life-forms previously unknown to science, and also unidentifiable as either plants or animals. Six of the specimens have been badly damaged, while another eight have been preserved in pristine condition. The specimens' stratum places them far too early on the geologic time scale for the features of the specimens to have evolved. Some fossils of Cambrian age show signs of the use of tools to carve a specimen for food.


title: At the Mountains of Madness

text: When the main expedition loses contact with Lake's party, Dyer and his colleagues investigate. Lake's camp is devastated, with the majority of men and dogs slaughtered, while a man named Gedney and one of the dogs are absent. Near the expedition's campsite, they find six star-shaped snow mounds with one specimen under each. They also discover that the better preserved life-forms have vanished, and that some form of dissection experiment has been done on both an unnamed man and a dog. The missing man Gedney is suspected of having gone utterly insane and having killed and mutilated all the others.


title: At the Mountains of Madness

text: Dyer and a graduate student named Danforth fly an aeroplane across the mountains, which they identify as the outer walls of a vast, abandoned stone city, alien to any human architecture. For their resemblance to creatures of myth mentioned in the "Necronomicon", the builders of this lost civilization are dubbed the "Elder Things." By exploring these fantastic structures, the men learn through hieroglyphic murals that the Elder Things first came to Earth shortly after the Moon took form, and built their cities with the help of "shoggoths"—biological entities created to perform any task, assume any form, and reflect any thought. There is a hint that all Earthly life evolved from cellular material left over from the creation of the shoggoths.


title: At the Mountains of Madness

text: As more buildings are explored, the explorers learn about the Elder Things' conflict with both the Star-spawn of Cthulhu and the Mi-Go, who arrived on Earth shortly afterwards. The images also reflect a degradation of their civilization, once the shoggoths gain independence. As more resources are applied in maintaining order, the etchings become haphazard and primitive. The murals also allude to an unnamed evil lurking within an even larger mountain range located beyond the city. This mountain range rose in one night and certain phenomena and incidents deterred the Elder Things from exploring it. When Antarctica became uninhabitable, even for the Elder Things, they soon migrated into a large, subterranean ocean.