Is it farther or further?
"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-Romance *musa "snout," of unknown origin. Probably influenced in sense by muse (n.). Related: Mused; musing.
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).
Nine goddesses of classical mythology who presided over learning and the arts. They were especially associated with poetry. Ancient Greek or Roman writers would often begin their poems by asking for the aid of the Muses in their composition.
Note: Writers and artists to this day speak of their “muse,” meaning their source of inspiration.