What does the assumption Whitman begins "Song of Myself" with allow him to do? How is this assumption important throughout the rest of the poem?
Since Whitman believes all people are inherently the same in nature ("every atom belonging to me as good belongs to you"), stating that we shall assume the same things is a logical conclusion. How does this assumption play out throughout the rest of "Song of Myself"? Why is it important that this be explained in the first lines?
If you read the rest of the many sections of Whitman's lengthy and groundbreaking "Song of Myself," you will notice that one of its major themes is that of celebrating his unity with all of mankind. In numerous sections, Whitman describes all types of people going about their work, going about their days, living their lives, and he celebrates each one of them. He even gets in there with them and does their work, in order to feel more at one with them, and to experience life in the way that we do. Throughout the course of his poem, he goes sailing with sailors, clamming with fishermen, hunting with Native Americans, helps a runaway slave to escape, smokes peace pipes with Native Americans, traps with trappers, and spends time amongst all sorts and types of people. And each time that he does, he writes about how he feels unity with them; he feels at one with them. Every assertion he makes about other people in his poem hinges on the foundational statement that he opens the series with:
"what I assume you shall assume/For every atom belonging to me as good belongs to you."
Whitman's exuberance and enthusiasm for all of life, for all of his beliefs, and for all other people is stated in such a straightforward and unapologetic way; this voice of confidence speaks of his assurance that because we are all the same, we too must think like him. He doesn't apologize, he doesn't hesitate, he doesn't hum and haw and worry about offending anyone in his poem. He states things as he feels it, confidently assuming that we will understand, since we are the same. His confidence, his enthusiam and exhuberance all reflect the assumption that we are all of one mind, agreed on all subjects, and feeling what he is feeling. Only because he assumes this can he speak so openly, freely, and without guile or subversion.
I hope that those thoughts help a bit; good luck!