The laws of logic do not prescribe the way our minds think; they prescribe the way our minds ought to think. - Arthur Eddington

Our model of Nature should not be like a building... for the populace to admire... until the edifice comes tumbling down. It should be like an engine with movable parts. ...[A]ny one lever ...is to be adjusted from time to time as the latest observations indicate. The aim of the theorist is to know the train of wheels which the lever sets in motion—that binding of the parts which is the soul of the engine.

I hope it will not shock experimental physicists too much if I say that we do not accept their observations unless they are confirmed by theory.

[Experimental Physicist] Phys. I cannot imagine myself perceiving non-Euclidean space!
Math. Look at the reflection of the room in a polished doorknob, and imagine yourself one of the actors in what you see going on there.