My anecdote: a close friend's brother was working as a laborer on a pipeline dig. One day work halted for a couple of hours, during which the construction supervisor and engineer were huddled over some plans.
My friend's brother saunters past, looks over, and says "there's your problem," placing a finger on the plan. Then he walks on.
He had seen a triangle with angles not adding up to 180 degrees. He was right - that's where the problem was.