An interesting and vivid analogy on the role of imagination in coming up with new ideas and approaches, from the blog of Michael Michalko:
Suppose you are watching a mime impersonating a man taking his dog out for a walk. The mime’s arm is outstretched as though holding the dog’s leash. As the mime’s arm is jerked back and forth, you “see” the dog straining at the leash to sniff this or that. The dog and the leash become the most real part of the scene, even though there is no dog or leash.
In the same way, when you make connections between your subject and something that is totally unrelated, your imagination fills in the gaps to create new ideas. It is this willingness to use your imagination to fill in the gaps that produces the unpredictable idea.
This is why Einstein claimed that imagination is more important than knowledge.