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Vaniver 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.
Being a Brahmin does not put rice on the table. Again, he was on the brink of starving, he says; this screens off any group considerations - we know he was very poor.
It screens off any wealth considerations, with the exception of his education (which is midlly relevant). It has a big impact on the question of average IQ and ancestry, though. Brahmin average IQ is probably north of 100,* and so a first-rank mathematician coming from a Brahmin family of any wealth level is not as surprising as a first-rank mathematician coming from a Dalit family.
So we still need to explain the absence (as far as I know) of first rate Dalit mathematicians. Gould argues that they're there, and we're missing them; the hereditarian argues that they're not there. One way to distinguish between the two is to evaluate the counterfactual statement "if they were there, they wouldn't be missed," and while Ramanujan is evidence for that statement it's weakened because of the potential impact of caste prejudice / barriers.
(It seems like the example of China might be better; it seems that young clever people have had the opportunity to escape sweatshops and cotton fields and enter the imperial service / university system for quite some time. Again, though, this is confounded by Han IQ being probably slightly north of 100, and so may not generalize beyond Northeast Asia and Europe.)
*Unfortunately, there is very little solid research on Indian IQ by caste.
You'd need to examine the IQ of the poorer Brahmins, though, before you could say it's not surprising; otherwise if the poor Brahmins have the same IQs as equally poor Dalits, then it ought to be equally surprising.
But Ramanujan is evidence against the Great Filters of nationality and poverty, which ought to be much bigger filters against possible Einsteins than caste.
Yes, but I'm not very familiar with the background of major Chinese figures (eg. I just looked him up now and while I had assumed Confucius was a minor aristocrat, apparently he was actually the son of an army officer and "is said to have worked as a shepherd, cowherd, clerk, and a book-keeper."); plus, you'd want to look at the post-Tang major Chinese figures, but that will exclude most major Chinese figures period like all the major philosophers - looking up the Chinese philosophy table in Murray's Human Accomplishment, like the first 10 are all pre-examination (and Murray comments of one of them, " it was Zhu Xi who was responsible for making Mencius as well known as he is today, by including Mencius’s work as part of “The Four Books” that became the central texts for both primary education and the civil service examinations").
He's literally as much evidence against those filters as he is evidence against hypothetical very low prevalence of poor innate geniuses.
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.