Thinking about the different arrangement of information is a process of simplification, not complication.
Organisation of information creates new understanding.
Because, the new organisation activates a distinct set of neurons in your brain, and different neural networks produce new answers to the question.
Viewing a game board from a new orientation activates a distinct set of neurons in your brain, and different neural networks produce new answers to the question.
Similarly, in everyday life, the brain provides different answers depending on how the incoming input is organised by language