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[Athene] drifted in like a breath of wind to where the girl slept, and came and stood above her head and spoke a word to her, likening herself to the daughter of Dymas, famed for seafaring, a girl of the same age, in whom her fancy delighted. (6.20-23)
One good reason for the gods to disguise themselves is that suddenly appearing in the middle of a human's bedroom could really freak that human out. Sure, Athene's probably not bad. But if Zeus appears in your bedroom? That is seriously bad news. Especially if you're a young, nubile woman. (And, let's face it: if Zeus is appearing in your bedroom, you're almost certainly a young, nubile woman.)
(Athene:) ‘But come now, let me make you so that no mortal can recognize you. For I will wither the handsome flesh that is on your flexible limbs, and ruin the brown hair on your head, and about you put on such a clout of cloth any man will loathe when he sees you wearing it; I will dim those eyes, that have been so handsome, so you will be unprepossessing to all the suitors and your wife and child, those whom you left behind in your palace.’ (13.396-403)
Odysseus’s disguise as a beggar is much like Athene’s former disguise as a mortal; by dressing below their stations, these two are able to test the integrity of those they deceive.
Eurylochos considers starvation the worst death of all and prefers to commit a crime against heaven than suffer so.
(Athene:) ‘[I will] tell you all the troubles you are destined to suffer in your well-wrought house; but you must, of necessity, endure all, and tell no one out of all the men and the women that you have come back from your wanderings, but you must endure much grief in silence, standing and facing men in their violence.’ (13.306-310)