Hard Head

Some students completed a task that was given to them in little time and the Japanese teacher commented on how fast they were. The students replied 「のう が やわらかい」 with pride and said in reference to the teacher, 「のう が かたい」. So we can use 'hard' and 'soft' to refer to the sharpness of someone's mind. Now that I think about the English, what does 'sharpness' have to do with anything?