Norma chose not to argue, but went back to her rooms to continue her efforts alone. It seemed to her that the more esoteric orders of mathematics did indeed have personalities, that certain theorems and integrals required finesse and considerations that simple arithmetic never demanded. Pacing, she wandered around to the back of the crystal slate, where she peered at the reverse of her equations. The backward symbols looked like nonsense, yet she forced herself to stare at the question from a different perspective. Earlier, the solvers had finished the previous set of tedious calculations, and while she had checked their work, the result still perplexed her. Knowing in her heart what the answer must be, she disregarded the slaves' result and returned to the front of the erasable crystal, where she scribbled so furiously that silvery numbers and symbols soon flowed across the hanging plate. Afterward she went front side to back, trying to discover an exit from her quandary.