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I don't think they would be negatively correlated, I just think there are enough unknowns that the possibility is far from negligible. My priors are that the "no free lunch" theorem applies to intelligence, so if I had to guess I would expect some degree of tradeoff, particularly at the upper ends of performance (whether in intelligence or athleticism). Hence why we never see people elite in both running and swimming events despite both being strongly, positively correlated with "general athleticism".
There is no reason to believe the "no free lunch" theorem holds and plenty of reasons to believe it doesn't. There are lots of genes with purely deleterious effects (those which are fatal to embroys, for instance. Or cystic fibrosis).
Even if the tails come apart -- e.g. you cannot simultaneously MAXIMIZE running and swimming ability -- does not mean that there's no genetic free lunch. Starting from a genotype that wasn't near human capacity in either, you could increase both.
If I were to refine my thoughts, I would say I believe not in an absolute, universal no free lunch, but rather a weaker, "not much free lunch beyond a particular threshold". As you put it, where the tails might tend to come apart.
My concern lies there, at least to the extent that human progress depends on the abilities of the individuals at those tails.
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Wouldn't trade-offs being everywhere in evolutionary biology count? I'm not an expert, but as I understand it, if intelligence were a 'free lunch' wouldn't we expect to see far less variation in intelligence in humans? Natural selection having already optimised it?
The most significant drawback for IQ is 'doesn't want to have children' and longer reproduction cycles. Also, a fraction of variation in intelligence is non-linear (heterozygosity) which simple selection cannot maximize and this is why agriculture uses f1 seeds, albeit aiming other traits.
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There's lots of traits that haven't reached fixation, but this doesn't mean there's no free lunch. Evolution is slow and the environment changes much more quickly; we are not at equilibrium. The "no free lunch" theorem is equivalent to "all organisms are equally fit", which is clearly false.
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Natural selection was still in the process of optimizing our genes when they hit the point where their phenotypes could invent and spread much faster-optimizing memes and then (in an instant, geologically) start wondering whether faster optimization was possible for genes too. Even brain size growth, perhaps the cruelest obvious tradeoff, doesn't show any obvious signs of having leveled off.
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