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I mean this politely because I'm glad you're taking the time to understand, but you didn't quite grasp what he was saying.
Let me try to rephrase.
Each individual's IQ (really their g, which IQ measures decently for most purposes) is partly genetic and partly environmental. [EDIT: As I get to below, it's probably best here to understand 'environmental' as meaning 'random'.]
Say we want to define "genius" as starting at IQs of 140. Someone might naturally be at that level regardless of losing out on the potential environmental bonus. Someone else might genetically be somewhat below that level but still attain it because they got lucky on the environmental component. Either way they are 'geniuses' -- but one is substantially more likely to pass that trait on to their descendants, because they're that smart with or without the environmental portion.
With me so far?
Okay, so, imagine two populations. On average, one of them is smarter than the other. This one will produce more geniuses. The less-intelligent population may also produce geniuses, but these are more likely to be individuals who lucked out on the environmental factors. Put another way, some of them are genetically prone to genius, while others got lucky.
If you take the child of two geniuses from the first population, it's possible that those geniuses were also simply both lucky. But it's less likely than in the case of a child of two geniuses from the second population.
Does that make sense?
Now,
No, because there are substantial genetic differences between ancestral groups. The 'mean' in 'regression to the mean' is the mean of that child's ancestral group, and the more specific (say, only looking at the last few generations of ancestors) the more accurate. If an ancestral group has an average IQ of 110, the fact that people somewhere else have an average IQ of 85 doesn't somehow affect their children.
Also, I'm pretty sure that 'environmental' doesn't mean what you think it means here, but it's hard to say more without pressing you for details and either way it's too much to go into right now. I'll say that 'environment' includes all sorts of things like individual experiences and happenstance. Putting kids in the same house, school, and workplace doesn't result in identical kids. In fact at this level it would probably be more helpful for you to understand 'environmental' as meaning 'random' than anything to do with 'setting'.
That said, there are plenty of indications that even things we chalk up to as 'environmental' have their roots in heredity. Suppose someone gets in a fight in the wrong kind of bar and suffers some long-term psychological damage from what happens next. That's environmental, right? Could happen to anyone. But actually, even the tendency to be in such a situation is rooted in heritable personality traits.
No, it's not. Parents carry all sorts of traits which may not be expressed in their generation (their individual phenotype) but still express in their children.
As I understand the question, the answer is 'no' but I'll admit that I'm having a hard time understanding where you're coming from with the Obama thing.
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