> we really know very little about what magical things make it happen in those rare and enchanted brains.
This type of thinking does not help. There is no magic, there is no enchantment, there is only vision - the ability to see, to imagine, what others fail to imagine. Then it is an issue of communication, to tune others so they can imagine the new entity too. I believe this is a communications issue, and those individuals with intellectual gifts have an inner voice that communicates in non-complex basic ideas the gifted see transparently inside complexity.
Case in point: when first learning about normalized numbers, a friend smarter than I in the same class remarked "Oh! they are talking about my 'minis'!" - my friend had figured out, realized the value of normalized numbers when learning basic multiplication in elementary, assumed the concept was obvious and incorporated it everywhere he used multiplication - to the ire of his elementary and high school math teachers. I lost track of him, but I last was aware of him being a cross disciplinary professor at Carnegie Mellon University.
This type of thinking does not help. There is no magic, there is no enchantment, there is only vision - the ability to see, to imagine, what others fail to imagine. Then it is an issue of communication, to tune others so they can imagine the new entity too. I believe this is a communications issue, and those individuals with intellectual gifts have an inner voice that communicates in non-complex basic ideas the gifted see transparently inside complexity.
Case in point: when first learning about normalized numbers, a friend smarter than I in the same class remarked "Oh! they are talking about my 'minis'!" - my friend had figured out, realized the value of normalized numbers when learning basic multiplication in elementary, assumed the concept was obvious and incorporated it everywhere he used multiplication - to the ire of his elementary and high school math teachers. I lost track of him, but I last was aware of him being a cross disciplinary professor at Carnegie Mellon University.