I’ve long had this theory that creative thinking is merely logical thinking, after taking a step back from the problem at hand, and looking at it at a space on level above, or a meta space, or perhaps adding an extra dimension into consideration.
For dance, taking a step back would mean instead of executing the sequence of moves, looking at what rules those moves are made out of, and then altering those rules. what you do is a product of how you move – so change how you move.
For music, a piece can start to feel flat and lifeless if you’re just playing interesting patterns in a scale. Perhaps you find one interesting pattern; then another interesting pattern. And then eventually you exhaust the variety of new note patterns, stuck playing by the rules of note patterns. A step back, what are the patterns made of? For one, they are a system – and as a system, they blend together differently: staccato, legato, accent, rhythm. For two, they are made of sound – which has texture, resonance, attack, amplitude.
What about problem solving? You’re playing within a certain framework of rules, a formal system. But that framework itself is defined in a formal way; the rules are somehow described – through meta-rules, which adhere to the same logical principles as rules themselves. If you are able to break out of the box and use the language of the meta-rules – you, applying logical thinking, make a creative leap, as observed by someone stuck playing by just the rules of the problem.