How does ulysses display characteristics of an epic hero in his encounter with the cyclops?

Odysseus' encounter with and escape from the Cyclops, Polyphemus, in Book 9 is considered to be his most significant achievement because he not only saves himself but also a number of his men through his cunning and intelligence--with one exception. Initially, he tells Polyphemus that his name is Nobody or Noman because he needs to remain anonymous in order not to evoke any retribution from any of the gods, like Poseidon, who are already trying to destroy the man known as Odysseus. When he finally tricks Polyphemus into letting him and his men, disguised as sheep, escape from Polyphemus's cave, Odysseus cannot keep from telling Polyphemus who has actually defeated him:

'Cyclops, if any one asks you who it was that put your eye out and spoiled your beauty, say it was the valiant warrior Ulysses, son of Laertes, who lives in Ithaca.' (Book IX)

This disclosure has been roundly criticized by readers and critics as an example of Odysseus' pride, and it is surely an instance in which Odysseus' pride overcomes common sense. As several critics have pointed out, however, disclosing his real name is an act of heroism and defiance--Odysseus, as one of the leading warrior-kings in the Trojan War, could not let his triumph over Polyphemus be a mystery. Fame and honor are an essential part of a warrior-king's being, and Odysseus' defeat of such a formidable opponent as Polyphemus had to become part of Odysseus' recorded achievements even if the disclosure of his name put him and his men at risk.

However, Odysseus demonstrates his heroic nature throughout the Odyssey in both significant and insignificant episodes, and personifies the virtues of a Bronze Age warrior king, with the addition of intelligence and endurance, attributes that allow him to survive long enough to retake his kingdom.

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