On the one hand, we have evidence that even subtle and intricate intellectual operations which ordinarily require strenuous concentration can equally be carried out preconsciously and without coming into consciousness. Instances of this are quite incon- testable; they may occur, for instance, during sleep, as is shown when some one finds, immedi- ately after waking, that he knows the solution of a difficult mathematical or other problem with which he had been wrestling in vain the day before.'