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When poets refer to other great works, people, and events, it’s usually not accidental. Put on your super-sleuth hat and figure out why.
Literary and Philosophical References:
The Muse (20): The Muses were the ancient Greek goddesses of science and art. More importantly for this poem, they were believed to inspire the creation of poetry. Bringing up the Muses (or, in this case, just the Muse) in a poem, either to give them credit or to ask them for help, is an ancient tradition. Terence is partly hooking into that tradition and partly making fun of it, since he suggests that the beer that brewers make is "livelier" (20) than the poems that the muse inspires.
John Milton (21-22): The mighty John Milton is one of the most famous English poets who has ever lived. In this poem, the speaker makes and allusion to Milton's greatest work, the epic poem Paradise Lost. In the opening section of that poem, Milton promises "justifie the wayes of God to men." Terence takes that famous moment and tweaks it, saying basically that anyone who wanted to understand God's ways would be better off drinking beer than reading Paradise Lost. It's a gutsy move for a poet, but it fits in well with the poem's back-slapping barroom atmosphere.
King Mithridates (59-76): Mithridates VI Eupator was an ancient king, who ruled a land called Pontus (where Turkey and Armenia are today). He was famous for fighting several wars with the Romans, and finally being defeated by the great Roman general Pompey. In this poem, though, he shows up for a different reason: his resistance to poison. Our primary speaker Terence uses him as an example of the value of building up your resistance to hardship, whether you use poison or poetry.