How we cite our quotes:
For always roaming with a hungry heart
Much have I seen and known – cities of men
And manners, climates, councils, governments (12-14)
It's strange that Ulysses describes himself like a predatory animal, especially when we recall that he criticizes his subjects for being like animals (5). To "roam with a hungry heart" implies that he is attempting to satisfy a bodily desire; in the poem such desires or necessities are often likened to a kind of death, as in the line "as though to breathe were life" (24).
Yet all experience is an arch wherethrough
Gleams that untravelled world whose margin fades
Forever and forever when I move (19-21).
"Untravelled world" suggests a land to be explored or conquered; in one reading, that world is death, and Ulysses wants to leave it unconquered, so he keeps moving, prolonging his eventual visit there. In another reading, the "untravelled world" represents all the places he hasn't yet visited; all those places and death are conflated in a way that makes us wonder about the consequences of Ulysses' exploratory urge.
Life piled on life
Were all too little (24-25).
Ulysses' desire is insatiable, and he says that several lifetimes wouldn't be enough for all the things he wants to do and places he wants to go. The well-known sentiment expressed here, however, gives way to a larger critique about the order of the universe. Indeed, Ulysses implies that the boundaries nature has set – the terms of a lifetime, even of many lifetimes – are much too narrow for man's desire. It is almost as if man's desire is out of place in this world, too big for it.