Eureka Effect

The book of David Perkins "The Art and Logic of Breakthrough Thinking" of 2000 investigates whether there is a science behind finding new ideas. It is a fascinating topic and the book does a great job convincing the reader that there is some systematics. Here are two figures from the book which remind of the gradient method one uses to find maxima and minima. The solution is the maximum. One tries to find a potential which allows one to climb up. Of course at the beginning, when one has a challenging problem, there is no such potential and one has to meander around. The second picture illustrates that in real break through situations there are barriers which prevent that a solution can be found immediately.