Ulysses is like that guy you once knew who was totally happy taking whatever he could fit in his backpack and setting off for Europe, or Africa, or any other sprawling land mass. On one of those trips he got lost, was presumed dead, but later made it back home; now he's on his way out the door again because he's not done looking for new places. Ulysses knows he might die, but the search, the process of exploring, satisfies him in ways that nothing else can.
Ulysses wants to seek a "newer world," by which he means a world that isn't as ancient as his own; he wants to find a less primitive place where people are less animalistic than they are on Ithaca.
Ulysses is an explorer but also a colonizer; he doesn't only want to see new places, he wants to take what he can from them.