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Notes -
To be fair, (decimal) zero was an important mathematical concept invented in IndiaTo be fair, from what I could parse from the comments on that reddit link, it seems possible that they are using some scoring system where the mean is zero, e.g. you can score negative, so minimum score of zero would imply "at least average".
Given only this information, I don't think we can conclude how much India is putting their hand on the scales here.
It could be that this entrance exam is taken by people with a wide variety of degrees which do not enable them to complete a math PhD, that the standard deviation of the scores is 20, and the interview process is basically just approving them.
It could also be that the people sitting the Entrance exam all hold a Master's degree in math, that the standard deviation is 200 and that the interview process is weeding out a lot of people.
I am slightly against attributing too much of the difference between castes to HBD based on priors. My baseline for the HBD hypothesis are the Ashkenazi. The idea is that if you were a Jew in medieval Eastern Europe, intelligence lead to reproductive success -- if you were smart enough to become a Rabbi, you would probably increase the frequency of your genes in the population. By contrast, a very smart Christian probably became a priest, a profession associated (at least in the RCC) with below-average long term reproductive success.
By contrast, I do not believe that European aristocracy was likewise selected for intelligence. A cunning baron who schemed his way into becoming a count probably did less for the frequency of his genes than one who just fucked his servants, though I admit that this changes a bit if one only considers the gene pool of nobility.
Like the Ashkenazi and European Nobility (to some degree), and unlike most of the rest of society in medieval Europe, the caste system of India was strongly endogamous. This is a very double-edged sword, on the one hand, it prevents the selection effects from diluting, but on the other hand, it removes the possibility of getting advantageous genes from selected outsiders.
For HBD in the caste system, there would have to be different selection mechanisms in place in different castes. For the priesthood caste, it seems vaguely plausible that it at least selected against crass stupidity. For the warrior caste, my prior would be that the selection pressure was similar to European nobility, more brawns than brains. For traders, such an effect seems most plausible -- cunning might make the difference between just making ends meet and leaving a fortune to your descendants which will increase their reproductive success. For farmers, I don't exactly see anything which will select for them being stupid. If anything, a very smart European farmer might try his luck in a city (and thus cease to be a farmer, depriving that subpopulation of his genes) while a very smart Indian farmer was stuck being a farmer due to the caste system.
The argument for IQ differences between castes in India as I understand it is that Brahmins and Brahmins alone were selected for higher verbal intelligence because they were expected to memorize, recite, and discuss long and complex religious texts, and that those who were better at this were rewarded socially, financially, and by implication reproductively. If this were true, one would expect a bimodal distribution, with the 10% of the Indian population that are Brahmins having higher intelligence and the remaining 90% of all other castes clustering together (however, since each Brahmin jati was itself reproductively isolated from the others, this would introduce additional variation based on how strong the selection was in each case). I don't know enough about ancient Indian culture to know if this is a reasonable assumption, but it is analogous to arguments about Jews being selected for skill at making Talmudic arguments or interpreting the Torah.
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