Acting teacher Sanford Meisner once said that the most basic goal for any actor was "living truthfully under imaginary circumstances". From what I've been able to glean about his method, it involves something similar to the way Zeami approached acting, where the pinnacle of one's work was in a kind of self-transcendence.
Meisner taught actors to strip out intellectual reactions about their performances, so that their performances — and especially their improvisations — come more from allowing their impulses to manifest clearly. Not randomly, but in a disciplined way. He thought of it in much the same way a musician would practice scales: from the outside, rather dull; but if you're the practitioner, and you are listening into the reptition, fascinating. John Cage comes to mind again: if something is boring, do it long enough and you'll find it's not boring at all but very interesting.
Given how unlike writing all this is, I strongly suspect writers might fare better the more they train themselves in the creative approaches employed by other art forms. The point is not to become a polymath, but simply to understand what's involved — to see how the other half lives, so to speak. But most crucially, they learn about what unique manner of work is demanded from you in each art form:
The visual arts. Some of the most rapturous time I've ever spent in my life was at some ungodly hour of the night at a convention — A-KON? AnimeFest? it's hard to remember — watching an artist working on a commission that needed to be in and done as of the next morning. It hammered home just how laborous and meticulous drawing is — how that one line that looks like it was just thrown across the paper in two seconds took minutes on end to plot out and seem spontaneous. Trying to teach myself to draw, and failing miserably at doing so, educated me firsthand in the degree of patience required to get any suitable results at all.
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Music. One of the memes making the rounds in the neurology-is-everything circuit is "Learn to play a musical instrument, even if you're terrible at it." The mere act of trying to learn has multiple payoffs, not least of which a profounder appreciation for what has to be done to make music exist at all. (Sorry, programming a sequencer is not playing music. Turntablism, on the other hand ... )
Programming. Actually learning how to use a computer, instead of just manipulate it like a vending machine, is an art form unto itself. Not everyone gets very far with it — I've gotten further than most, as this site can attest — but to even try to do it gives you a window into a kind of artistic discipline that's only just emerged and evolving rapidly.
Acting. See above.
The most profound lesson that comes of all this, I think is something Stanislavsky once said, and which I come back to often: Love the art in yourself, not yourself in the art.