For Whitman, the reinvention or invention of self is to transform how one sees the notion of self.  Whitman does not see the self as isolated from a larger contingent.  He does not see the individual as divorced from a social fabric.  The poem is one in which Whitman embraces this notion of self as one that is inseparable from conditions that transform identities, move past time, and makes the individual identify with truly cosmic forces:

It avails not, time nor place—distance avails not,/ I am with you, you men and women of a generation, or ever so many generations hence.

This notion of self is one of invention and reinvention.  The self is linked with the "Crowds of men and women attired in the usual costumes" or with the "smallest sights and hearings—on the walk in the street, and the passage over the river;" or with the ferry's " look on the river and sky."  For Whitman, the notion of the self's identity is one that is connected with so much of which the ferry's experience is a part.  There is an immediate identification of the self with elements larger than oneself, a convergence and divergence in these elements that force the individual to see themselves as a part of a larger experience broadening connection to people and experiences.  It is this notion of self in which Whitman sees reinvention for both himself and others who embrace such a varied notion of identity and being in the world.