I have seen a video of - I can't seem to find it - someone using a sort of keyboard, only smaller. She would use fewer key presses to type in English than on a standard keyboard, because she was typing in one grapheme at a time, or something like that.

Do the Chinese really think of Mandarin as containing discrete characters? Or do they consider the signs as compositions of each other? I haven't tried writing Chinese or something like that with some input device. Have you?