 Exploring is on a higher-sophistication level than piloting; and piloting is on a higher sophistication level than following a pilot’s lead. If Le Penseur is trying to find the proof of a new theorem then he is working on a higher accomplishment-level than he is in trying to teach his student his proof when he has got it; just as trying to teach it is on a higher-sophistication level than that on which his students are working in trying to master it.