I don’t really think there is any such thing as genius. The concept is so nebulous that you’d really have to define it in more detail, and as soon as you do, you effectively establish a skill set - which by it’s very nature begins to diminish the concept.
Suppose you say that genius is the ability to solve problems. Okay. Which problems? Linguistic? Mathematical? Visual-spatial? Pattern-matching?
If you can determine it as one of the above, in the end it’s pretty likely you could train the vast majority of people to substantially improve one or more of these skills.
Yes I agree that some people appear to be more adept at picking up certain material than others. But is there an element of chance, human interpretation or fallibility in these findings? You’d have to establish a keen link between brain structure and function (and use the results to somehow establish how this translates into “brilliance” in some individuals), and none of the studies I’ve seen so far (including those involving g) really show some people to be “superhumanly” gifted with universal “intelligence” (or something of the like).
I read an article in Scientific American a few years ago that described development in certain parts of the brain in some individuals resulting in “exaggerated effects” with respect to certain skills (i.e. right-hemisphere “visual spatial brilliance”), but you can hardly call it “genius”.
After all, with a certain amount of prolonged training, neurones in the brain respond to these specific skill sets. Think of these London Cab drivers. I don’t know about you, but I wouldn’t call them “genius”.
But a ha! You say, those guys had to learn this trait. It didn’t come naturally. Fine. But just remember, we have no way of knowing exactly what sensory experiences have shaped thier (re: Geniuses) brains. They may have unwittingly been exposed to certain stimuli that we just don’t know about (e.g. excessive TV accounting for high Vis-Spa skills).
On the other hand, I do think there may be something about genius in the personality. Maybe it’s something a little metaphysical, like whoever performed the first slam dunk. It just has that human aesthetic appeal about it that really isn’t defined by numbers or performance. It’s just a quality we humans have learned to appreciate, like Nikki Cox’s pert yet supple ass cheeks.