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In 1832, a young man aged 20 died after an obscure duel. In the few writings that he left and in his final letter which he composed in the night before the duel, he laid the foundations of a number of theories which totally changed Mathematics.His name was Évariste Galois.The genius emergesAlready at a very young age, Galois showed his exceptional talent at various occasions.He found a copy of Adrien-Marie Legendre's Éléments de Géométrie, which, it is said, he read "like a novel" and mastered at the first reading. At 15, he was reading the original papers of Joseph-Louis Lagrange, such as the Réflexions sur la résolution algébrique des équations which likely motivated his later work on equation theory, and Leçons sur le calcul des fonctions, work intended for professional mathematicians, yet his classwork remained uninspired, and his teachers accused him of affecting ambition and originality in a negative way.[1]Later Galois tried to enter the prestigious École Polytechnique at several occasions, but it never worked out:On 28 July 1829, Galois' father committed suicide after a bitter political dispute with the village priest. A couple of days later, Galois made his second and last attempt to enter the Polytechnique, and failed yet again. It is undisputed that Galois was more than qualified; however, accounts differ on why he failed. More plausible accounts state that Galois made too many logical leaps and baffled the incompetent examiner, which enraged Galois. The recent death of his father may have also influenced his behavior.[2][3]His novel take on Mathematics indeed further obstructed his tries to be a part of professional mathematical life at many points in his short life.For example, one of the best and famous scientists of the day, Siméon Denis Poisson, found Galois’s manuscript on equations unreadable, and this was a common feeling mathematicians had when they browsed through a text of Galois.The Mathematics appeared to come from another planet, displaying techniques so novel that the world in the 1800s simply was not ready to capture.Even today, if one reads proofs and ideas by Galois, one is stunned by the level and originality of his writings. In this modern era of Mathematics which has so much evolved in comparison to Mathematics before 1900, the proofs are ingenious, and breath taking.(And then thinking the guy was in his late teens when he composed the ideas, while being actively involved in the revolution, in the 1830s !)This is not the place to summarize Galois’s ideas, even in a nutshell, but let me say that he almost single-handedly founded Group Theory and Galois theory — two of the most important topics in modern day Mathematics.While still in his late teens, he solved one of the holy grails in Mathematics, by obtaining necessary and sufficient conditions for a polynomial to be solvable by radicals.This problem stood for 350 years before Galois (and, independently Niels Henrik Abel) came along !RevolutionGalois’s life was characterized by revolution. Besides his uncanny futuristic Mathematics, he was involved in protests, and sometimes incarcerated. (He also wanted to participate in the July revolution of 1830, but was prevented by the director of his school.)On the following Bastille Day (14 July 1831), Galois was at the head of a protest, wearing the uniform of the disbanded artillery, and came heavily armed with several pistols, a rifle, and a dagger. He was again arrested. On 23 October, he was sentenced to six months in prison for illegally wearing a uniform. He was released on 29 April 1832. During his imprisonment, he continued developing his mathematical ideas.[4][5][6]About a girlHis fatal duel took place on May 30, 1832. It is not sure what the motives were, but it has often been speculated that a love affair lay at its origins. (Some days before his death, he wrote a letter to his friend Chevalier about a broken love affair.) I also read that the duel was the outcome of a fight over a prostitute. We will perhaps never know for sure.[Artist’s interpretation of an unknown prostitute.]In any case, his opponent was a better shooter, and Galois was fatally wounded. He was found by a passing farmer. The next morning he died.Galois knew that this was going to happen, so he decided to spend the night before the duel writing down his (final) mathematical ideas in a letter which he sent to his friend Chevalier, together with three attached manuscripts.The great mathematician, physicist and philosopher Hermann Weyl said of this testament:[7]"This letter, if judged by the novelty and profundity of ideas it contains, is perhaps the most substantial piece of writing in the whole literature of mankind."Clearly, this is a bold statement of Weyl, but nevertheless, I think it is also clear that Évariste Galois deserves to be officially nominated for the title of smartest mind ever.It is almost scary to imagine what could have happened to Mathematics (and Science) if he would have lived for another 40 years.Duel with me on Quora …Feel also free to check out my Quora blog Cayne is Able for much, much more.References: Google Images and Wikipedia.The pastel pencil painting is called “Faceless girl (with stockings),” and was composed some years ago by me. (The model was Alexandra X.)Footnotes[1] http://Stewart, Ian (1973). Galois Theory. London: Chapman and Hall. pp. xvii–xxii.[2] http://C., Bruno, Leonard (2003) [1999]. Math and mathematicians : the history of math discoveries around the world. Baker, Lawrence W. Detroit, Mich.: U X L. p. 173.[3] http://Stewart, Ian (1973). Galois Theory. London: Chapman and Hall. pp. xvii–xxii.[4] http://Bell, Eric Temple (1986). Men of Mathematics. New York: Simon and Schuster.[5] http://Escofier, Jean-Pierre (2001). Galois Theory. Springer. pp. 222–224.[6] http://C., Bruno, Leonard (2003) [1999]. Math and mathematicians : the history of math discoveries around the world. Baker, Lawrence W. Detroit, Mich.: U X L. p. 173.[7] Évariste Galois - Wikipedia

If you aspire to become one of those august personages who have read Hugh Everett’s thesis on the many worlds interpretation, it’s all at the link. The thesis is clear, straightforward, and requires only a knowledge of basic non-relativistic, particle quantum mechanics to get through it.But once you’ve read it all the way through, I don’t think you’ll find any explanation as to what …alleged “linking” (quantum superposition evolution) of states …… is.Quantum superposition evolution is just normal, unitary quantum mechanics. It’s what states do. In any interpretation.As for “linking”, the word is used precisely once in his whole thesis, in connection with von Neumann’s “cut” argument.So, a wild guess. I’ll assume the question is asking how the “splitting” of worlds happens. The one that appears in popular presentations of Everett’s ideas as if it’s an extra process added on top of the postulates of quantum mechanics, and why that process is considered any more valid than wavefunction collapse.Well … you won’t find anything about that in the thesis either. Because in Everett’s theory, there is absolutely no process of “splitting” that is added into the theory. Instead, it is derived as a consequence of standard quantum mechanics.The full story… well, read Everett’s thesis. But in a nutshell, he makes the rather simple and obvious move of modelling the observer as a quantum system (something absolutely forbidden by Bohr) and asking what such an observer would be able to “see”, or derive knowledge of, given its ability to interact with other parts of the wavefunction:His answer:There are, therefore, fundamental restrictions to the knowledge that an observer can obtain about the state of the universe. It is impossible for any observer to discover the total state function of any physical system, since the process of observation itself leaves no independent state for the system or the observer, but only a composite system state in which the object-system states are inextricably bound up with the observer states.As soon as the observation is performed, the composite state is split into a superposition for which each element describes a different object-system state and an observer with (different) knowledge of it. Only the totality of these observer states, with their diverse knowledge, contains complete information about the original object-system state - but there is no possible communication between the observers described by these separate states. Any single observer can therefore possess knowledge only of the relative state function (relative to his state) of any systems, which is in any case all that is of any importance to him.(Everett, pp.98–99)So, as Everett points out, once you consider what a quantum “observer”, built into the wavefunction would be able to “see”, one is able to derive as a consequence an effective process by which each observer + system can only gain knowledge of one part of the overall wavefunction (each part associated with its own outcome of a given experiment). And all this is derived from unitary quantum mechanics alone.So, to the original question, why is this any more valid than wavefunction collapse?It’s because while wavefunction collapse is added as an extra (problematic) postulate on top of unitary quantum mechanical evolution, Everett’s process is derived from unitary quantum mechanical evolution.

Broadly speaking, social capital refers to norms and networks with ties of mutual reciprocities and trust, that gives its members both tangible (economic benefits or other material gains) and intangible benefits (support in times of crisis, enjoyment of group values).However, rather than understanding social capital as a descriptor of social relations which are themselves hierarchical, social capital is often stretched in policy studies and academic works as structural constraints in social interactions. Social capital being a group resource enjoyed by individuals, it is only logical that the concept would reflect social and ethnic inequalities.Having said this,however, there is a difference in the contentions of social capital reflecting social inequality and social capital being an outcome of social inequality. The confusion between these two different standpoints probably derive from the initial confusion in formulation of the concept, where the source and outcomes of social capital are combined in a tautological sense. For the sake of not lengthening this answer, I'll not write more on the confusion of conceptualization of social capital, but you can definitely ask me if you need more information. I'll always maintain that the concept of social capital needs to be applied with far more limitation, caution and flexibility than recent research has warranted.In accordance with the idea of liberalism and meritocracy and neo-classical economics, human capital theory suggests that socio-economic position of a person is dependent on the human capital possessed by that person (education, skills, talents, experience, language fluency).In a meritocratic society, success in the labour market in thus dependent on human capital, conditional on equality of opportunity based on similar qualifications. The theory assumes that employers make rational hiring and promotion decisions based on credentials and ability. Thus human capital theory assumes that people’s position in society is a product of their functional importance in society, and ignores issues of class and power.While human capital theory can predict the returns of education in terms of income and occupation, the human capital theory cannot predict why some groups get better jobs than others, irrespective of education and other credentials. According to Lowe (1999), ‘Members of recent immigrant groups often end up working in low-status jobs, such as taxi-drivers or airport security guards, even though they may be highly educated and experienced.’ (Lowe, 1999:115)A person with high human capital would have adequate chances of success. However, this being an ideal situation, and the world being far from ideal conditions, the effect of human capital has been found to vary by ethnicity/race as well as immigrant status. These differences are oftentimes suggested to be resulting from discrimination and/or structural inequality or social capital. In agreement with Coleman, (1988), Potter (2000) suggests that ‘a human-capital rich person may lack the social connections which would constitute a deficit of social capital” (Potter, 2000: 42).To put it in a nutshell, the human capital one acquires is dependent on the social resources one is born into, and the social networks in which one finds oneself (Lin, 1999). The interplay between these two forms of capital is crucial with regards to economic performance.Economic Performance is largely dependent on the mechanisms of the operation of human capital as well as social capital. However, even though human capital could be said to be an important predictor of social mobility, attainment of human capital, (especially as conceptualized through behavioural and language skills) and its influence on career returns is often dependent on the acquiring of social capital.References:Akbari, Ather H. (1999).“Immigrant ‘Quality’ in Canada: More direct Evidence of Human Capital Content, 1956-1994”, International Migration Review, 38: 156-175.Becker, Gary S. (1994). “Investment in Human capital: A Theoretical Analysis” in R. Febrero and P.S. Schwartz (eds.), The Essence of Becker, Stanford, Hoover Institution Press, pp. 36-90.Beaujot, Roderic P. (1999) “Immigration and Demographic Structures” in S. S. Halli and Driedger (eds.) Immigrant Canada: Demographic, Economic, and Social Challenges”, Toronto, University of Toronto Press, pp. 93-115.Coleman, James, S. (1988). “Social Capital in the creation of Human Capital”. American Journal of Sociology, 94: S95-S121.Cheung, Pauline Hope; Rosalind Edwards; Harry Goulbourne; John Solomos. (2007). “Immigration, Social Cohesion and Social Capital: A Critical Review”. Critical Social Policy, 27, 24-49.Davenport, Thomas O.(1999) “Human Capital: What is it and Why People Invest in It”, San Francisco, Jossey- Bass Publishers. Driedger, Leo.Geschwender, James A. and Neil Guppy. (1994). “Ethnicity, Educational Attainment, and Earned Income Among Canadian-born Men and Women”. Canadian Ethnic Studies, 27(1): 67-83.Grant, Hugh M. and Ronald R Oertel. (1994) “Diminishing Returns to Immigration? Interpreting the Economic Experience of Canadian Immigrants”, Canadian Ethnic Studies, 30(3): 56-76.Jensen, Leif (1995)“Employment Hardship and Rural Minorities: Theory, Research, and Policy”. Blacks in Rural America, Stewart, James B., & Allen-Smith, Joyce E. [Eds], New Brunswick, NJ: Transaction Publishers, pp 119-138.Lin, Nan. (1999). “Social networks and status attainment”.Annual Review of Sociology, 25, 467-487.Lowe, Graham S. (1999) “Youth, Transitions, and the New World of Work in V.W. Marshall, W.R. Heinz, H Kruger, and A Verma (eds.), Restructuring Work and the Life Courses, Toronto, University of Toronto Press, pp. 29-44.Potter, Stephanie. 2000. The Social Resources to Immigrants: Effects on the Integration of Independent and Family Class Immigrants to Toronto, Canada from South Asia. University of Toronto.Sakamoto, Arthur (1988). “Labour Market Structure, Human Capital and earnings in Metropolitan Areas”, Social Forces, 67(1): 86-107.Wanner, Richard. A (1998). “Prejudice, Profit, or Productivity: Explaining Returns to Human Capital Among Male Immigrants to Canada, Canadian Ethnic Studies, 30(3) 24-55.