While the following story comes from a field of research other than economics, I found the human and epistemological drama completely engrossing and worth a listen.  I'll try not to be too much of a spoiler and just lay out the basics: 

On this past week's edition of the popular radio show/podcast "This American Life," the show's theme in two acts came under the banner of "So Crazy It Might Just Work."  The first act was set up like this: 

One day a successful cancer researcher named Jonathan Brody gave a talk at his alma mater, about how people in his field need to think outside the box if they're going to find a cure.  Afterward Jonathan's old music teacher Anthony Holland shared an idea that was way out of the box - killing cancer cells with sound waves.  Gabriel Rhodes tells what happened next.  Gabriel is also working on a documentary film version of this story, called The Cure. 

The unlikely pair ended up working together on a study to test Anthony's theory of destroying cancer cells with electromagnetic waves using randomized controlled lab tests; the ensuing collaboration is full of incredibly high hopes (curing cancer) but fraught with differences over the importance of controls, replication, clashing academic norms (think music composition vs. cancer research).  I'll leave it at that and let you enjoy.