Lucretius's didactic poetry addresses a single person but cajoles his readers to heed his lesson, as he learned from Epicurus
Lucretius's poetry is didactic, that is, poetry that aims overtly to teach something. So the poet is not just a poet, he is a teacher, and the reader is his pupil. As Alison Sharrock has pointed out in a work on another didactic poem, Ovid's Art of Love, didactic poems have a slightly different relationship with their readership, because they make clear that, when reading the poem, we have a job to do: "didactic poetry makes explicit the activity of its readers by purporting to teach – someone".
That "someone" in the De Rerum Natura has a name: he is called Memmius and is usually identified with a wealthy Roman aristocrat and occasional holder of political office, C. Memmius, tribune of the people in 66BC. Epicureanism, with its suggestion that the pursuit of political power is pointless torment and that wealth is nothing compared to tranquillity, might seem an odd topic to address to such a figure; but there is no point preaching to the converted, and Lucretius's choice of Memmius to talk thus seems an apt one.
Lucretius addresses Memmius by name; even when there is no direct address to him, Lucretius writes the de Rerum Natura as a conversation, using the second person singular throughout: "you might think …", "you must be careful …", "if you believe this, then …". From the way he talks to his reader, we can be clear that he expects certain things from him, both positive and negative.
For example, as readers of the poem, we might be unhappy to discover that he thinks we are on occasion like silly children, scared of the dark, and so needing the light of Epicureanism, or afraid of taking our medicine, and so needing the bitter difficulties of philosophy to be sweetened by a coating of Lucretius's poetry. We might be annoyed to discover that, like a dinner party guest who doesn't know when to call a taxi, if we don't agree with Lucretius he will simply hound us with argument after argument, as he promises to in his first book, claiming his only concern is he'll get old and die before he's finished badgering us into agreement.
Then again, we might be flattered when he spends a lengthy passage refuting a whole host of philosophical rivals, as that implies we won't simply roll over and accept his theory without his having dealt with the others that we have heard of, or encouraged when he assures us that we are wise enough to follow the tracks he has set us without the need for the multiple arguments he goes on to threaten us with.
Of course, Lucretius simultaneously builds up a picture of himself as a diligent teacher, stuffed to the gills with examples and proofs, knowledgeable about rival philosophical systems and sympathetic to what we need to understand the truth of the universe. But Lucretius is merely a pupil himself, having learned from the master of compassionate and human learning, Epicurus.
That Epicurus is the master is abundantly clear from the De Rerum Natura. Three of its six books begin with eulogies of the man whose discoveries are such that he ought to be regarded as a god, according to the start of book five, and is, in book six, the single greatest thing that Athens ever produced. Lucretius, in contrast, claims he is scarcely up to the task: a swallow compared to a swan. He writes not to compete with Epicurus – that would be like a race between a bandy-legged kid and a thoroughbred racehorse – but out of love and respect for a man who, in his first book, is pictured as the first mortal bold enough to look heaven in the face: unafraid of thunderbolts or dire rumbling from the sky, he burst open the gates of the world and rescued mankind from its pervious condition, lying on the floor groveling and cowering in the face of unfounded superstitious practice.
This glorious and glorifying picture might seem to sit a little uncomfortably with Epicurus's philosophy. He encouraged his followers to live unknown, not seeking after glory or political power; yet it seems that a form of "hero cult" of Epicurus operated, with reflections on his courage in the face of his own painful death and celebrations of his birthday. But Lucretius is not encouraging us to worship Epicurus so much as use him as an example and inspiration for the good life. His praise of Epicurus fits his genre, too. Didactic poetry was regarded as a division of epic, and Epicurus offers Lucretius the ultimate epic hero: the man who marched beyond the ramparts of the world, as Lucretius puts it in book one, and freed humanity when it lay in chains by taking on the mysteries of the universe, and winning.