I recently had a epihany will reading a blog posting by Miko Matsumura of the website formerly known as the SOA center. Innovations is a by product of Power distribution, which more recently popularized in Chris Anderson's book the Long Tail. I propose that break thru innovation can follow the power curve distribution. Consider the following.
Power law graph
Thomas Edison supposedly had 1,600 experiments fail before he invented the light bulb, but a friend asked him why he was wasting so much time on the project when he wasn't accomplishing anything, Edison replied, "Of course I'm accomplishing something. I've learned 1,600 ways it doesn't work!"
Edison's "failures" if graphed would look like the yellow long tail of the above graph with the successes in the green area eventually leading to the invention of the light bulb. Another less visionary way of looking at Edison's innovation is the "80-20 Rule" which stated simply is that approximately 80% Edison's experiment failed (ways it didn't work) and 20% meet with some degree of success before his ultimate success. No one knows for sure what the actually distribution of Edison's experiment were, but this my theory of how innovations occur over time. More examples to follow this post.