muse (v.)
"to reflect, to be absorbed in thought," mid-14c., from Old French muser (12c.) "to ponder, dream, wonder; loiter, waste time," literally "to stand with one's nose in the air" (or, possibly, "to sniff about" like a dog who has lost the scent), from muse "muzzle," from Gallo-Roman *musa "snout," of unknown origin. Probably influenced in sense by muse (n.). Related: Mused; musing.
muse (n.)
late 14c., protectors of the arts, from Old French Muse and directly from Latin Musa, from Greek Mousa, "the Muse," also "music, song," from PIE root *men- "to think, remember" (see mind (n.)). Meaning "inspiring goddess of a particular poet" is from late 14c. The traditional names and specialties of the nine Muses, daughters of Zeus and Mnemosyne, are: Calliope (epic poetry), Clio (history), Erato (love poetry, lyric art), Euterpe (music, especially flute), Melpomene (tragedy), Polymnia (hymns), Terpsichore (dance), Thalia (comedy), Urania (astronomy).