Or, you had a certain innate intelligence to begin with, and are only now practicing with it.

At this point it's impossible to know one way or the other. Genetic intelligence versus developed intelligence is something that the top scientists of several fields are still investigating.

I don't think that we can really investigate "genetic intelligence" until we have a definition of intelligence which makes -any sense at all-, which we don't.

I find a lot of the opinions of neuroscientists I've talked to/read articles from to be really dogmatic in their interpretation of intelligence (probably because they aren't regularly faced with Very Hard Problems in the sense that mathematicians/computer scientists are - their conception of intelligence is often a little more superficial - but anyway, I'm massively generalizing).

My entire point is that I don't think it's useful to think about intelligence as a "thing." I think of the brain as a computational structure. At birth, it has certain properties. It changes in certain ways. It can get better or worse at certain tasks. Because Official People have to say Official Things they always treat their own statements about Intelligence as if they're objective and well-informed which, let me tell you, they are not.

Just because people disagree on exactly what constitutes intelligence doesn't exempt the brain from the same general limitations that we see elsewhere in physiology.

Take fast-twitch muscle tissue for one example. Different people have a genetic predisposition towards developing more or less fast-twitch muscle fibers, which gives them the potential to be faster runners or have faster reflexes. Now, that's not to say that someone without that predisposition can't train hard and also be fast; likewise, if someone with that predisposition doesn't make use of it on a regular basis, then they're not likely to be any quicker than anyone else in reasonably good physical condition.

However, assuming the same training regimen, the person with the beneficial genetics will always have an advantage.

There's no reason to think that intelligence -- regardless of definition -- doesn't work the same way. Yes, someone of average intelligence can work very hard and produce the same results as someone who's more intelligent and less motivated. But, you're comparing someone who's operating at their peak potential against someone who isn't.

I think cperciva's original point was merely that due to the nature of the field of mathematics, there's a huge barrier to entry where that genetic advantage becomes necessary. I disagree with that point only a little bit; if I worked really hard at it, I might be able to produce a small handful of exceptions against the very large body of evidence in cperciva's favor.

"There's no reason to think that intelligence -- regardless of definition -- doesn't work the same way."

I agree if what you mean is that there's no reason to believe that there is no fixed, genetically-determined components to intelligence. I disagree if you are making any sorts of claims about what these components are (as I said, I don't even think we can make gross claims like people are born with "good memories").

I also agree with the point that cultures look for certain intellectual traits in young children. I cannot say whether these particular traits are determined genetically because it is highly possible that we learn a great deal (and abstractly) even from the first day of our lives.

The thing is that (as another poster pointed out) there IS a salient statistic (g - for general intelligence) which we can be "better" or "worse" at - but its value in a field like math which requires highly specialized mental strategies is questionable.

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I think that you should look at the example of the polgar sisters - they were raised to be grandmasters in chess and 2/3 of them did (the other one become an international master). I think this puts a bullet in at least one interpretation of your theory.

I now think you're allowing your own prejudices on this subject cloud what you're reading, and what you're saying in response. I think I was fairly clear in my position that genetics plays an important role in intelligence, specifically because we have no indication that the brain is exempt from the same physiological rules that the rest of the human body obeys.

| I think that you should look at the example of the polgar sisters...

I specifically covered edge cases in mentioning the impact of training on innate ability.