gwern comments on The Need for Universal Experience Classes - Less Wrong
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This is fictional evidence--are there real examples of otherwise unintelligent people being able to perform intricate calculations in specific domains? Most of the people I know who play the lottery don't think about the probabilities involved, which is probably why they're playing the lottery in the first place.
As a college student, I second shend's statement that high schoolers are lazy. It's one thing to engage students who are interested in their studies and enjoy thinking, but engaging the average high school student is much harder.
I do not know if this is strong enough evidence for you, but I offer the following text dump for consideration; from "The Predictive Value of IQ":
Also somewhat relevant http://xa.yimg.com/kq/groups/190222/1077302733/name/Kwon is a brain imaging study of Korean Go players; the expert professional Go players averaged IQ of 93, the control group 101.
From the Go paper:
So, they got (? or chose the profession because they were?) good at a number of specific tasks that are components of IQ, but they aren't good at IQ measuring tasks overall.
This Go paper is one of the things I point to as evidence that while strategy games may benefit you cognitively early on, there are diminishing returns and they probably set in well before expert skill levels.