Where does innovation come from?

I just finished reading a book called Art and Physics (yes I am that nerdy) the premise of which is that major developments in modern art have anticipated breakthroughs in physics. It is a bit of a far-fetched idea, but the author (a surgeon) makes a good case. Ultimately it comes down to integration of right brain thinking (spatial, artistic, intuitive) with left brain thinking (logical, mathematical). Albert Einstein recognized that his breakthroughs arrived through the door on the right side of the brain when he said "Invention is not the product of logical thought, even though the product is tied to a logical structure."
I finished the book on a flight back from a meeting with the people at Lifecell, the company that makes a graft material called Alloderm (and a new one called Strattice.) I started using Alloderm about 10 years ago for certain problems that are associated with breast implants, such as rippling and malposition. It turned out to be very successful and so I published the techniques. A lot of very smart people started working with the idea, and now it is becoming a standard technique with breast reconstruction. It turns out that Alloderm is regenerative tissue, meaning that it actually replaces missing tissue. The field of regenerative medicine is in its infancy but the potential is extremely exciting.
The original idea was not a logical one, but one that arrived by seeing the problem globally. It was a right brain thing.