I think the common wisdom of what's possible is only broken by breaking one of the links in the chain of reasoning that makes people think it's impossible, and all those links form common wisdom in general.
Usually, when you think something is impossible that turns out not to be, it's because one of your assumptions was incorrect. But looking for the bad assumption is usually like looking for the bad stone in a pyramid - each assumption is in turn held up by other assumptions, and so on. And it's made more complicated by cross-relationships which can add an exponential aspect to the problem.
Usually, the bad assumption looks obvious in retrospect, but it's seldom that way before the insight.
