You always see a subset of reality at any given moment. This has important implications.

The lens that contains the question and the lens that contains the answer are usually far apart. The rules of inference will help you stitch these lenses together to form a coherent film. Still, a leap of faith and some time is required before you accept the argument as valid.

A single mathematical object lives in multiple platonic worlds. You will always be seeing only one of those worlds. (Note, you can create lenses that connect two worlds but it will be a connecting tissue and not the worlds themselves). You might use a geometric lens once for a problem that is almost entirely solved through an algebraic lens. The objects don’t belong to any one lens.

Such is our platonic world. Being comfortable in such a world is imperative for abstract thinking.