Divided Attention

In his book A Cure for Gravity, musician Joe Jackson writes about the ability that good pianists develop to play different music with their left and right hands:

To keep both hands going, without either playing bum notes all over the place or losing the steady rhythmic feel, demands a kind of split consciousness, each hand independent but still under a centered, Zen-like control.
Is this relevant to drawing? One needs to pay attention to both the paper and the subject, but the paper diverts attention from the subject. What can psychology tell us about the optimum way to divide attention between the two, and how to learn to do so?

An analogue to the kind of study I'd like to see is described in "Hands Together" Wayback. This is a posting by neuroanatomist and piano teacher Tara Gaertner in her blog Training the Musical Brain: a neuroscience perspective on teaching and learning music..., in which she discusses whether it's better to teach piano pieces hands-separately or hands-together. Amongst the factors she considers are the effect of dividing attention on learning, the need for a hand to learn not to mirror the movements of the opposite hand, and the kinds of practicing behaviours that learners used. I have the impression that musicians think about such questions from the neurological point of view much more than artists do.