Named after the Roman god Janus, Janusian Thinking involves holding two opposing ideas or images in your mind at the same time. Dr. Albert Rothenberg discovered this way of thinking in the early 1970s after concluding that most major scientific breakthroughs and artistic masterpieces occur through the process of formulating antithetical ideas and then trying to resolve them.
One of the most well-known discoveries that came out of the Janusian Thinking method was Physicist Niels Bohr’s complementarity in quantum theory (light can be either a wave of a particle). The creativity was creating seemingly impossible opposites and then finding the commonality between them. Another example provided by Rothenberg was related to Einstein’s Theory of Relativity where he considered both a person to both be falling (as off a building) and for no gravity to exist. An obvious contradiction since gravity causes the person to fall.
For example, imagine being forced to be both successful and a failure simultaneously. You might think of ways to continue to fail, yet still bring yourself success. Consider William Hung, the contestant on American Idol, who sang terribly, but achieved success by being so, so bad. I think he made an album? Here is a good article that describes the process in more detail.