Kids build great things.
sahillavingia.com
sahillavingia.com
Montessori kids have been rewarded over the years for giving out-of-the-box answers and that's probably what their mind jumps to first. Their ignorance isn't what gives them the creative answers - the years of being taught to look for something different is.
If you want to start getting better answers out of your employees/coworkers/own mind figure out how to reward them for random ideas instead of pounding them down.
The second case is one where the common wisdom is wrong or the conditions that made it right are no longer true. This is where courage is more important than creativity, other people have also come up with similar ideas but either thought it was impossible or didn't push it far enough. Entrepreneurial examples abound but this happens in science, too, e.g. see Poisson's Dot (Poisson predicted it but thought it was impossible, so was discovered by someone else), the discovery of Neptune, etc. This sort of ignorance/naivete/gonzo attitude generally fuels startups. Of course, when the common wisdom is correct, then the startup fails, so there's some evidence bias here, too.
Now, the second one is more interesting. Let me tell you a story I read some time ago:
The hunters for a certain village were much better than their neighbors in bunting bison. This was due to the fact that their shaman each year gave them a map drawn on a piece of hide that predicted where the bison would be, and it would generally be right. One year, a hunter sneaked into the shaman's tent to see how he created these accurate maps. He say that that the shaman just treated the hide and did nothing else. When he asked him about it, the shaman said: "When I treat the hide, lines appear on the hide, guided by the Gods, that predict where the bison will be". These random lines were the secret of the hunters' success.
That sort of random search of the idea space is hard to do but can work wonders when it works.
-- Clarke's first law.
http://en.wikipedia.org/wiki/Clarkes_three_lawsIt's worth trying to do the impossible, right?