With future perfect (F2) you jump to a point in the future, turn round and say some action is finished then. Actually a complicated thing and cumbersome and in most cases you can express the same idea much simpler without using F2. This tense existed in Latin and it was imitated by writers.
In current English usage, muse can refer in general to a person who inspires an artist, writer, or musician.
Muse(noun) to think closely; to study in silence; to meditate. Muse(noun) to be absent in mind; to be so occupied in study or contemplation as not to observe passing scenes or things present; to be in a brown study.