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NancyLebovitz comments on Rationality Quotes August 2013 - Less Wrong
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I chose Ramanujan as my example because mathematics is extremely meritocratic, as proven by how he went from poor/middle-class Indian on the verge of starving to England on the strength of his correspondence & papers. If there really were countless such people, we would see many many examples of starving farmers banging out some impressive proofs and achieving levels of fame somewhat comparable to Einstein; hence the reference class of peasant-Einsteins must be very small since we see so few people using sheer brainpower to become famous like Ramanujan.
(Or we could simply point out that with average IQs in the 70s and 80s, average mathematician IQs closer to 140s - or 4 standard deviations away, even in a population of billions we still would only expect a small handful of Ramanujans - consistent with the evidence. Gould, of course, being a Marxist who denies any intelligence, would not agree.)
It is worth pointing out that Ramanujan, while poor, was still a Brahmin.
And not just that, but he had more education than the poorest Indians, and probably more than the second poorest. And got his hands on a math textbook, which was probably pretty low probability.
My bet is that there aren't a lot of geniuses doing stoop labor, especially in traditional peasant situations, but there are some who would have been geniuses if they'd had enough food when young and some education.
Even the poorest Indians (or Chinese, for that matter) will sacrifice to put their children through school. Ramanujan's initial education does not seem to have been too extraordinary, before his gifts became manifest (he scored first in exams, and that was how he was able to go to a well-regarded high school; pg25).
Actually, we know how he got his initial textbooks, which was in a way which emphasizes his poverty; pg26-27:
So just as well he was being lent and awarded all his books, because certainly at age 11 as a poor Indian it's hard to see how he could afford expensive rare math or English books...
A rather tautological comment: yes, if we removed all the factors preventing people from being X, then presumably more people would be X...
Is the distribution for mathematicians in general stochastic with respect to IQ and a wealthy upbringing / proximity to cultural centres that reward such learning? That might give you signs of whether wealth / culture is a third correlate.
Otherwise, one way or the other, I'm not sure one person shifts the prob any appreciable distance.
It really depends on what 'prob' you're talking about. For example, the mean of some variable can be shifted an arbitrary amount by a single person if they are arbitrarily large, which is why "robust statistics" shuns the mean in favor of things like the median, and of course a single counter-example disproves a universal claim. When you are talking about lists of geniuses where the relevant group of geniuses might be 10 or 20 people, 1 person may be fairly meaningful because the group is so small.