muse (v.) Look up muse at Dictionary.com
"to be absorbed in thought," mid-14c., from O.Fr. muser (12c.) "to ponder, loiter, waste time," lit. "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-Romance *musa "snout," of unknown origin. Probably influenced in sense by Muse.
muse Look up muse at Dictionary.com
late 14c., protectors of the arts, from L. Musa, from Gk. Mousa, lit. "muse, music, song," from PIE root *mon-/*men-/*mn- "to think, remember" (see mind (n.)). The names of the nine Muses, daughters of Zeus and Mnemosyne (q.v.), and their specialties are traditionally: Calliope (epic poetry), Clio (history), Erato (love poetry, lyric art), Euterpe (music, especially flute), Melpomene (tragedy), Polymnia (hymns), Terpsichore (dance), Thalia (comedy), Urania (astronomy).