Many important breakthroughs in science and innovation have resulted from:
Focusing on a subject in a logical, analytical way for some time, thinking through possible solutions.
Daydreaming or distracting the mind, but holding the same problem lightly 'at the back of the mind'.
The answer has often emerged on dreams or daydreams when the innovator was not trying so hard to find the answer. However, the daydream on its own did not achieve anything.