Quod Erat Demonstrandum This is how it works. After a long indwelling, shape awareness comes— kenning what must be the shape of the solution, if any exists. Once that shape is felt, reason, a sculptor's chisel, frees the shape from stone. Thus the solution, though seeming artificial, is not made but found. No mere invention, no child of human reason, QED came first.
I thought you might find this interesting. Give my regards to Kelly, et al.
http://cindybruchman.wordpress.com/2013/06/13/martians-star-trek-and-eccentric-pianists-in-films/