As for 'idiot savants' and mathematical recall. Maths is a unique subject, the procedures becme, if well learnt almost a part of the autonomic system itself. Like walking, talking and the processes of logical thought. These things are not available to a person who has never trained in them or been exposed to them previously. Do you note how in society some think logically while others, of no lesser capacities do not? (i would say this is a sociological fact, it is a fact of faculty development and culture as opposed to a lck of it.)
Given, stimulus and motivation drive higher faculties, e.g. running, heavier processes in math etc.
As for 'lightening speed' mathematics, beyond the thought behind the act of leaving the chair to go to answer the door or retrieve the bottle of beer from the fridge, or reading the pages of a book; beyond the initiative of the wont and/or desire to do so, how many are aware of the deeper processes which actually drive the muscles? It is very rarely I walk while thinking 'left, right, left, right', and I never ask the neuro receptors and motor neurons in my brian to control the miriads of muscles involved in the process of walking.
Biological mechanics are a marvel of the subconcious! And the sub conscious is so complex I have no hope of understanding it! I'll stick to building bridges )
